A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

NASA Astrophysics Data System (ADS)

Taneja, Ankur; Higdon, Jonathan

2018-01-01

A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Attenuation of seismic waves in rocks saturated with multiphase fluids: theory and experiments

NASA Astrophysics Data System (ADS)

Tisato, N.; Quintal, B.; Chapman, S.; Podladchikov, Y.; Burg, J. P.

2016-12-01

Albeit seismic tomography could provide a detailed image of subsurface fluid distribution, the interpretation of the tomographic signals is often controversial and fails in providing a conclusive map of the subsurface saturation. However, tomographic information is important because the upward migration of multiphase fluids through the crust of the Earth can cause hazardous events such as eruptions, explosions, soil-pollution and earthquakes. In addition, multiphase fluids, such as hydrocarbons, represent important resources for economy. Seismic tomography can be improved considering complex elastic moduli and the attenuation of seismic waves (1/Q) that quantifies the energy lost by propagating elastic waves. In particular, a significant portion of the energy carried by the propagating wave is dissipated in saturated media by the wave-induced-fluid-flow (WIFF) and the wave-induced-gas-exsolution-dissolution (WIGED) mechanism. The latter describes how a propagating wave modifies the thermodynamic equilibrium between different fluid phases causing exsolution and dissolution of gas bubbles in the liquid, which in turn causes a significant frequency-dependent 1/Q and moduli dispersion. The WIGED theory was initially postulated for bubbly magmas but was only recently demonstrated and extended to bubbly water. We report the theory and laboratory experiments that have been performed to confirm the WIGED theory. In particular, we present i) attenuation measurements performed by means of the Broad Band Attenuation Vessel on porous media saturated with water and different gases, and ii) numerical experiments validating the laboratory observations. Then, we extend the theory to fluids and pressure-temperature conditions which are typical of phreatomagmatic and hydrocarbon domains and we compare the propagation of seismic waves in bubble-free and bubble-bearing subsurface domains. This work etends the knowledge of attenuation in rocks saturated with multiphase fluid and emphasizes that the WIGED mechanism is very important to image subsurface gas plumes.

Methods for compressible multiphase flows and their applications

NASA Astrophysics Data System (ADS)

Kim, H.; Choe, Y.; Kim, H.; Min, D.; Kim, C.

2018-06-01

This paper presents an efficient and robust numerical framework to deal with multiphase real-fluid flows and their broad spectrum of engineering applications. A homogeneous mixture model incorporated with a real-fluid equation of state and a phase change model is considered to calculate complex multiphase problems. As robust and accurate numerical methods to handle multiphase shocks and phase interfaces over a wide range of flow speeds, the AUSMPW+_N and RoeM_N schemes with a system preconditioning method are presented. These methods are assessed by extensive validation problems with various types of equation of state and phase change models. Representative realistic multiphase phenomena, including the flow inside a thermal vapor compressor, pressurization in a cryogenic tank, and unsteady cavitating flow around a wedge, are then investigated as application problems. With appropriate physical modeling followed by robust and accurate numerical treatments, compressible multiphase flow physics such as phase changes, shock discontinuities, and their interactions are well captured, confirming the suitability of the proposed numerical framework to wide engineering applications.

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources

NASA Astrophysics Data System (ADS)

Crochet, M. W.; Gonthier, K. A.

2013-12-01

Systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures. These equations often contain sources, referred to as nozzling terms, that cannot be posed in divergence form, and have proven to be particularly challenging in the development of finite-volume methods. Upwind schemes have recently shown promise in properly resolving the steady wave solution of the associated multiphase Riemann problem. However, these methods require a full characteristic decomposition of the system eigenstructure, which may be either unavailable or computationally expensive. Central schemes, such as the Kurganov-Tadmor (KT) family of methods, require minimal characteristic information, which makes them easily applicable to systems with an arbitrary number of phases. However, the proper implementation of nozzling terms in these schemes has been mathematically ambiguous. The primary objectives of this work are twofold: first, an extension of the KT family of schemes is proposed that formally accounts for the nonconservative nozzling sources. This modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense. Second, this modified method is applied to multiple, but equivalent, forms of the multiphase equations to perform a numerical study by solving several one-dimensional test problems. Both ideal and Mie-Grüneisen equations of state are used, with the results compared to an analytical solution. This study demonstrates that the magnitudes of the resulting numerical errors are sensitive to the form of the equations considered, and suggests an optimal form to minimize these errors. Finally, a separate modification of the wave propagation speeds used in the KT family is also suggested that can reduce the extent of numerical diffusion in multiphase flows.

Modeling: The Right Tool for the Job.

ERIC Educational Resources Information Center

Gavanasen, Varut; Hussain, S. Tariq

1993-01-01

Reviews the different types of models that can be used in groundwater modeling. Discusses the flow and contaminant transport models in the saturated zone, flow and contaminant transport in variably saturated flow regime, vapor transport, biotransformation models, multiphase models, optimization algorithms, and potentials pitfalls of using these…

TOUGHREACT: a new code of the TOUGH Family for Non-Isothermal multiphase reactive geochemical transport in variably saturated geologic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Tianfu; Sonnenthal, Eric; Spycher, Nicolas

Coupled modeling of subsurface multiphase fluid and heat flow, solute transport and chemical reactions can be used for the assessment of acid mine drainage remediation, waste disposal sites, hydrothermal convection, contaminant transport, and groundwater quality. We have developed a comprehensive numerical simulator, TOUGHREACT, which considers non-isothermal multi-component chemical transport in both liquid and gas phases. A wide range of subsurface thermo-physical-chemical processes is considered under various thermohydrological and geochemical conditions of pressure, temperature, water saturation, and ionic strength. The code can be applied to one-, two- or three-dimensional porous and fractured media with physical and chemical heterogeneity.

Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases

NASA Astrophysics Data System (ADS)

Pezzè, Luca; Ciampini, Mario A.; Spagnolo, Nicolò; Humphreys, Peter C.; Datta, Animesh; Walmsley, Ian A.; Barbieri, Marco; Sciarrino, Fabio; Smerzi, Augusto

2017-09-01

A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this Letter, we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the ultimate theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.

MODEL FOR HYSTERETIC CONSTITUTIVE RELATIONS GOVERNING MULTIPHASE FLOW. 1. SATURATION-PRESSURE RELATIONS

EPA Science Inventory

In these companion papers, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two- or three-phase (e.g., air-water or air-oil-water) porous media systems subject to arbitr...

A New Multiphase Equation of State for Composition B

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coe, Joshua Damon; Margevicius, Madeline Alma

2016-07-25

We describe the construction of a complete equation of state for the high explosive Composition B in its unreacted (inert) form, as well as chemical equilibrium calculations of its detonation products. The multiphase reactant EOS is of SESAME type, and was calibrated to ambient thermal and mechanical data, the shock initiation experiments of Dattelbaum, et al., and the melt line of trinitrotoluene (TNT).

Measurement and evaluation of the relationships between capillary pressure, relative permeability, and saturation for surrogate fluids for laboratory study of geological carbon sequestration

NASA Astrophysics Data System (ADS)

Mori, H.; Trevisan, L.; Sakaki, T.; Cihan, A.; Smits, K. M.; Illangasekare, T. H.

2013-12-01

Multiphase flow models can be used to improve our understanding of the complex behavior of supercritical CO2 (scCO2) in deep saline aquifers to make predictions for the stable storage strategies. These models rely on constitutive relationships such as capillary pressure (Pc) - saturation (Sw) and relative permeability (kr) - saturation (Sw) as input parameters. However, for practical application of these models, such relationships for scCO2 and brine system are not readily available for geological formations. This is due to the complicated and expensive traditional methods often used to obtain these relationships in the laboratory through high pressure and/or high-temperature controls. A method that has the potential to overcome the difficulty in conducting such experiments is to replicate scCO2 and brine with surrogate fluids that capture the density and viscosity effects to obtain the constitutive relationships under ambient conditions. This study presents an investigation conducted to evaluate this method. An assessment of the method allows us to evaluate the prediction accuracy of multiphase models using the constitutive relationships developed from this approach. With this as a goal, the study reports multiple laboratory column experiments conducted to measure these relationships. The obtained relationships were then used in the multiphase flow simulator TOUGH2 T2VOC to explore capillary trapping mechanisms of scCO2. A comparison of the model simulation to experimental observation was used to assess the accuracy of the measured constitutive relationships. Experimental data confirmed, as expected, that the scaling method cannot be used to obtain the residual and irreducible saturations. The results also showed that the van Genuchten - Mualem model was not able to match the independently measured kr data obtained from column experiments. Simulated results of fluid saturations were compared with saturation measurements obtained using x-ray attenuations. This comparison demonstrated that the experimentally derived constitutive relationships matched the experimental data more accurately than the simulation using constitutive relationships derived from scaling methods and van Genuchten - Mualem model. However, simulated imbibition fronts did not match well, suggesting the need for further study. In general, the study demonstrated the feasibility of using surrogate fluids to obtain both Pc - Sw and kr - Sw relationships to be used in multiphase models of scCO2 migration and entrapment.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evans, R.D.

The results of a research effort to develop a multiphase naturally fractured, lenticular reservoir simulator is presented. The simulator possesses the capability of investigating the effects of non-Darcy flow, Klinkenberg effect, and transient multiphase wellbore storage for wells with finite and infinite conductivity fractures. The simulator has been utilized to simulate actual pressure transient data for gas wells associated with the United States Department of Energy, Western Gas Sands Project, MWX Experiments. The results of these simulations are contained in the report as well as simulation results for hypothetical wells which are producing under multiphase flow conditions. In addition tomore » the reservoir simulation development, and theoretical and field case studies the results of an experimental program to investigate multiphase non-Darcy flow coefficients (inertial resistance coefficients or beta factors as they are sometimes called) are also presented. The experimental data was obtained for non-Darcy flow in porous and fractured media. The results clearly indicate the dependence of the non-Darcy flow coefficient upon liquid saturation. Where appropriate comparisons are made against data available in the open literature. In addition, theoretical development of a correlation to predict non-Darcy flow coefficients as a function of effective gas permeability, liquid saturations, and porosity is presentd. The results presented in this report will provide scientists and engineers tools to investigate well performance data and production trends for wells completed in lenticular, naturally fractured formations producing under non-Darcy, multiphase conditions. 65 refs., 57 figs., 15 tabs.« less

Pore scale study of multiphase multicomponent reactive transport during CO 2 dissolution trapping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Li; Wang, Mengyi; Kang, Qinjun

Solubility trapping is crucial for permanent CO 2 sequestration in deep saline aquifers. For the first time, a pore-scale numerical method is developed to investigate coupled scCO 2-water two-phase flow, multicomponent (CO 2(aq), H +, HCO 3 –, CO 3 2 – and OH –) mass transport, heterogeneous interfacial dissolution reaction, and homogeneous dissociation reactions. Pore-scale details of evolutions of multiphase distributions and concentration fields are presented and discussed. Time evolutions of several variables including averaged CO 2(aq) concentration, scCO 2 saturation, and pH value are analyzed. Specific interfacial length, an important variable which cannot be determined but is requiredmore » by continuum models, is investigated in detail. Mass transport coefficient or efficient dissolution rate is also evaluated. The pore-scale results show strong non-equilibrium characteristics during solubility trapping due to non-uniform distributions of multiphase as well as slow mass transport process. Complicated coupling mechanisms between multiphase flow, mass transport and chemical reactions are also revealed. Lastly, effects of wettability are also studied. The pore-scale studies provide deep understanding of non-linear non-equilibrium multiple physicochemical processes during CO 2 solubility trapping processes, and also allow to quantitatively predict some important empirical relationships, such as saturation-interfacial surface area, for continuum models.« less

Pore scale study of multiphase multicomponent reactive transport during CO 2 dissolution trapping

DOE PAGES

Chen, Li; Wang, Mengyi; Kang, Qinjun; ...

2018-04-26

Solubility trapping is crucial for permanent CO 2 sequestration in deep saline aquifers. For the first time, a pore-scale numerical method is developed to investigate coupled scCO 2-water two-phase flow, multicomponent (CO 2(aq), H +, HCO 3 –, CO 3 2 – and OH –) mass transport, heterogeneous interfacial dissolution reaction, and homogeneous dissociation reactions. Pore-scale details of evolutions of multiphase distributions and concentration fields are presented and discussed. Time evolutions of several variables including averaged CO 2(aq) concentration, scCO 2 saturation, and pH value are analyzed. Specific interfacial length, an important variable which cannot be determined but is requiredmore » by continuum models, is investigated in detail. Mass transport coefficient or efficient dissolution rate is also evaluated. The pore-scale results show strong non-equilibrium characteristics during solubility trapping due to non-uniform distributions of multiphase as well as slow mass transport process. Complicated coupling mechanisms between multiphase flow, mass transport and chemical reactions are also revealed. Lastly, effects of wettability are also studied. The pore-scale studies provide deep understanding of non-linear non-equilibrium multiple physicochemical processes during CO 2 solubility trapping processes, and also allow to quantitatively predict some important empirical relationships, such as saturation-interfacial surface area, for continuum models.« less

Pore scale study of multiphase multicomponent reactive transport during CO2 dissolution trapping

NASA Astrophysics Data System (ADS)

Chen, Li; Wang, Mengyi; Kang, Qinjun; Tao, Wenquan

2018-06-01

Solubility trapping is crucial for permanent CO2 sequestration in deep saline aquifers. For the first time, a pore-scale numerical method is developed to investigate coupled scCO2-water two-phase flow, multicomponent (CO2(aq), H+, HCO3-, CO32- and OH-) mass transport, heterogeneous interfacial dissolution reaction, and homogeneous dissociation reactions. Pore-scale details of evolutions of multiphase distributions and concentration fields are presented and discussed. Time evolutions of several variables including averaged CO2(aq) concentration, scCO2 saturation, and pH value are analyzed. Specific interfacial length, an important variable which cannot be determined but is required by continuum models, is investigated in detail. Mass transport coefficient or efficient dissolution rate is also evaluated. The pore-scale results show strong non-equilibrium characteristics during solubility trapping due to non-uniform distributions of multiphase as well as slow mass transport process. Complicated coupling mechanisms between multiphase flow, mass transport and chemical reactions are also revealed. Finally, effects of wettability are also studied. The pore-scale studies provide deep understanding of non-linear non-equilibrium multiple physicochemical processes during CO2 solubility trapping processes, and also allow to quantitatively predict some important empirical relationships, such as saturation-interfacial surface area, for continuum models.

Experimental multi-phase CO2-brine-rock interactions at elevated temperature and pressure: Implications for CO2 sequestration in deep-saline aquifers

USGS Publications Warehouse

Rosenbauer, R.J.; Koksalan, T.

2004-01-01

Long-term CO2 saturated brine-rock experiments were conducted to evaluate the effects of multiphase H2O-CO2 fluids on mineral equilibria and the potential for CO2 sequestration mineral phases within deep-saline aquifers. Experimental results were consistent with theoretical thermodynamic calculations when CO2-saturated brines were reacted with limestone rocks. The CO2-saturated brine-limestone reactions were characterized by compositional and mineralogical-changes in the aquifer fluid and formation rocks that were dependent on initial brine composition as were the changes in formation porosity, especially dissolved sulfate. The solubility of CO2 was enhanced in brines in the presence of both limestone and sandstone rocks relative to brines alone. Reactions between CO2 saturated brines and arkosic sandstones were characterized by desiccation of the brine and changes in the chemical composition of the brine suggesting fixation of CO2 in mineral phases. These reactions occured on a measurable but kinetically slow time scale at 120??C.

A genuinely discontinuous approach for multiphase EHD problems

NASA Astrophysics Data System (ADS)

Natarajan, Mahesh; Desjardins, Olivier

2017-11-01

Electrohydrodynamics (EHD) involves solving the Poisson equation for the electric field potential. For multiphase flows, although the electric field potential is a continuous quantity, due to the discontinuity in the electric permittivity between the phases, additional jump conditions at the interface, for the normal and tangential components of the electric field need to be satisfied. All approaches till date either ignore the jump conditions, or involve simplifying assumptions, and hence yield unconvincing results even for simple test problems. In the present work, we develop a genuinely discontinuous approach for the Poisson equation for multiphase flows using a Finite Volume Unsplit Volume of Fluid method. The governing equation and the jump conditions without assumptions are used to develop the method, and its efficiency is demonstrated by comparison of the numerical results with canonical test problems having exact solutions. Postdoctoral Associate, Department of Mechanical and Aerospace Engineering.

Laboratory-scale experiments and numerical modeling of cosolvent flushing of multi-component NAPLs in saturated porous media

NASA Astrophysics Data System (ADS)

Agaoglu, Berken; Scheytt, Traugott; Copty, Nadim K.

2012-10-01

This study examines the mechanistic processes governing multiphase flow of a water-cosolvent-NAPL system in saturated porous media. Laboratory batch and column flushing experiments were conducted to determine the equilibrium properties of pure NAPL and synthetically prepared NAPL mixtures as well as NAPL recovery mechanisms for different water-ethanol contents. The effect of contact time was investigated by considering different steady and intermittent flow velocities. A modified version of multiphase flow simulator (UTCHEM) was used to compare the multiphase model simulations with the column experiment results. The effect of employing different grid geometries (1D, 2D, 3D), heterogeneity and different initial NAPL saturation configurations was also examined in the model. It is shown that the change in velocity affects the mass transfer rate between phases as well as the ultimate NAPL recovery percentage. The experiments with low flow rate flushing of pure NAPL and the 3D UTCHEM simulations gave similar effluent concentrations and NAPL cumulative recoveries. Model simulations over-estimated NAPL recovery for high specific discharges and rate-limited mass transfer, suggesting a constant mass transfer coefficient for the entire flushing experiment may not be valid. When multi-component NAPLs are present, the dissolution rate of individual organic compounds (namely, toluene and benzene) into the ethanol-water flushing solution is found not to correlate with their equilibrium solubility values.

Multiphase porous media modelling: A novel approach to predicting food processing performance.

PubMed

Khan, Md Imran H; Joardder, M U H; Kumar, Chandan; Karim, M A

2018-03-04

The development of a physics-based model of food processing is essential to improve the quality of processed food and optimize energy consumption. Food materials, particularly plant-based food materials, are complex in nature as they are porous and have hygroscopic properties. A multiphase porous media model for simultaneous heat and mass transfer can provide a realistic understanding of transport processes and thus can help to optimize energy consumption and improve food quality. Although the development of a multiphase porous media model for food processing is a challenging task because of its complexity, many researchers have attempted it. The primary aim of this paper is to present a comprehensive review of the multiphase models available in the literature for different methods of food processing, such as drying, frying, cooking, baking, heating, and roasting. A critical review of the parameters that should be considered for multiphase modelling is presented which includes input parameters, material properties, simulation techniques and the hypotheses. A discussion on the general trends in outcomes, such as moisture saturation, temperature profile, pressure variation, and evaporation patterns, is also presented. The paper concludes by considering key issues in the existing multiphase models and future directions for development of multiphase models.

Upscaling Multiphase Fluid Flow in Naturally Fractured Reservoirs

NASA Astrophysics Data System (ADS)

Matthai, S.; Maghami-Nick, H.; Belayneh, M.; Geiger, S.

2009-04-01

Hydrocarbon recovery from fractured porous reservoirs is difficult to predict as it depends on the focusing of the flow and the local balance of viscous, gravitational, and capillary forces. Hecto-metre scale sub-volumes of fractured oil reservoirs contain thousands of fractures with highly variable flow properties, dimensions and orientations. This complexity precludes direct geometric incorporation into field scale multiphase flow models. Macroscopic laws of their integral effects on multiphase flow are required. These can be investigated by DFM (discrete fracture and matrix) numerical simulations based on discrete fracture models representing fractured reservoir analogues. Here we present DFM results indicating that hecto-metre-scale relative permeability, the time to water breakthrough, and the subsequent water cut primarily depend on the fracture-to-rock matrix flux ratio, qf/qm, quantifying the proportion of the cross-sectional flux that occurs through the fractures. Relative permeability during imbibition runs is best approximated by a rate-dependent new model taking into account capillary fracture-matrix transfer. The up-scaled fractional flow function fo(sw) derived from this new kri formulation is convex with a near-infinity slope at the residual water saturation. This implies that the hector-metre scale spatially averaged Buckley-Leverett equation for fractured porous media does not contain a shock, but a long leading edge in the averaged profile of the invading phase. This dispersive behaviour marks the progressively widening saturation front and an early water breakthrough observed in the discrete fracture reservoir analogues. Since fracture porosity φf is usually only a fraction of a percent, a cross-over from krw < kro to krw/kro ≈ qf/qm occurs after the first few percent of recovery, and because qf/qm ranges between 10-1,000, sweep efficiency ignoring the positive influence of counter-current imbibition is extremely low. The accuracy of reservoir performance predictions by the proposed fo(sw) up-scaling methodology depends on how well φf , qf/qm and a new parameter termed fraction of fracture matrix interface area in contact with the invading fluid, XA,if(si) can be constrained under in situ conditions.

Multiphase Equations of State for Polymer Materials at High Dynamic Pressures

NASA Astrophysics Data System (ADS)

Khishchenko, Konstantin V.

2015-06-01

Equations of state for materials over a wide range of pressures and temperatures are necessary for numerical simulations of shock-wave processes in condensed matter. Accuracy of calculation results is determined mainly by adequacy of equation of state of a medium. In this work, a new multiphase equation-of-state model is proposed with taking into account the polymorphic phase transformations, melting and evaporation. Thermodynamic calculations are carried out for 2 polymer materials (polymethylmethacrylate and polytetrafluoroethylene) in a broad region of the phase diagram. Obtained results are presented in comparison with available data of experiments at high dynamic pressures in shock and release waves. This work is supported by RSF, Grant 14-50-00124.

FINITE-ELEMENT ANALYSIS OF MULTIPHASE IMMISCIBLE FLOW THROUGH SOILS

EPA Science Inventory

A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equation...

Pore scale Assessment of Heat and Mass transfer in Porous Medium Using Phase Field Method with Application to Soil Borehole Thermal Storage (SBTES) Systems

NASA Astrophysics Data System (ADS)

Moradi, A.

2015-12-01

To properly model soil thermal performance in unsaturated porous media, for applications such as SBTES systems, knowledge of both soil hydraulic and thermal properties and how they change in space and time is needed. Knowledge obtained from pore scale to macroscopic scale studies can help us to better understand these systems and contribute to the state of knowledge which can then be translated to engineering applications in the field (i.e. implementation of SBTES systems at the field scale). One important thermal property that varies with soil water content, effective thermal conductivity, is oftentimes included in numerical models through the use of empirical relationships and simplified mathematical formulations developed based on experimental data obtained at either small laboratory or field scales. These models assume that there is local thermodynamic equilibrium between the air and water phases for a representative elementary volume. However, this assumption may not always be valid at the pore scale, thus questioning the validity of current modeling approaches. The purpose of this work is to evaluate the validity of the local thermodynamic equilibrium assumption as related to the effective thermal conductivity at pore scale. A numerical model based on the coupled Cahn-Hilliard and heat transfer equation was developed to solve for liquid flow and heat transfer through variably saturated porous media. In this model, the evolution of phases and the interfaces between phases are related to a functional form of the total free energy of the system. A unique solution for the system is obtained by solving the Navier-Stokes equation through free energy minimization. Preliminary results demonstrate that there is a correlation between soil temperature / degree of saturation and equivalent thermal conductivity / heat flux. Results also confirm the correlation between pressure differential magnitude and equilibrium time for multiphase flow to reach steady state conditions. Based on these results, the equivalent time for steady-state heat transfer is much larger than the equivalent time for steady-state multiphase flow for a given pressure differential. Moreover, the wetting phase flow and consequently heat transfer appear to be sensitive to contact angle and porosity of the domain.

Simulation of Liquid Droplet in Air and on a Solid Surface

NASA Astrophysics Data System (ADS)

Launglucknavalai, Kevin

Although multiphase gas and liquid phenomena occurs widely in engineering problems, many aspects of multiphase interaction like within droplet dynamics are still not quantified. This study aims to qualify the Lattice Boltzmann (LBM) Interparticle Potential multiphase computational method in order to build a foundation for future multiphase research. This study consists of two overall sections. The first section in Chapter 2 focuses on understanding the LBM method and Interparticle Potential model. It outlines the LBM method and how it relates to macroscopic fluid dynamics. The standard form of LBM is obtained. The perturbation solution obtaining the Navier-Stokes equations from the LBM equation is presented. Finally, the Interparticle Potential model is incorporated into the numerical LBM method. The second section in Chapter 3 presents the verification and validation cases to confirm the behavior of the single-phase and multiphase LBM models. Experimental and analytical results are used briefly to compare with numerical results when possible using Poiseuille channel flow and flow over a cylinder. While presenting the numerical results, practical considerations like converting LBM scale variables to physical scale variables are considered. Multiphase results are verified using Laplaces law and artificial behaviors of the model are explored. In this study, a better understanding of the LBM method and Interparticle Potential model is gained. This allows the numerical method to be used for comparison with experimental results in the future and provides a better understanding of multiphase physics overall.

Consistent multiphase-field theory for interface driven multidomain dynamics

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.; Pusztai, Tamás; Gránásy, László

2015-11-01

We present a multiphase-field theory for describing pattern formation in multidomain and/or multicomponent systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a way of constructing the free energy surface and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism, reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations, enables the use of arbitrary pairwise equilibrium interfacial properties, penalizes multiple junctions increasingly with the number of phases, ensures non-negative entropy production and the convergence of the dynamic solutions to the equilibrium solutions, and avoids the appearance of spurious phases on binary interfaces. The approach is tested for multicomponent phase separation and grain coarsening.

Hemochromatosis detection in a health screening program at an Alabama forest products mill.

PubMed

Barton, James C; Cheatwood, Susan M; Key, Timothy J; Acton, Ronald T

2002-08-01

We analyzed hemochromatosis detection in a 11.5-year multiphasic health screening program at a forest products mill. There were 2199 participants: 2032 Whites (1506 men, 526 women) and 167 African Americans (124 men, 43 women); 85.0% of employees were screened. Iron and transferrin saturation were measured in a serum biochemistry profile on specimens obtained after overnight fasting; ferritin was measured in participants with elevated iron concentrations or transferrin saturation > 48%. Participants with elevated ferritin levels underwent further evaluation. Eight White men were diagnosed to have hemochromatosis (frequency 0.0039 in Whites, 0.0053 in White men). The estimated cost per case detected was $8826. Family members of two participants with hemochromatosis were also diagnosed to have hemochromatosis or iron overload. We conclude that detecting hemochromatosis in a workplace multiphasic health screening program is efficacious and economical.

Characterization of heterogeneity in the Heletz sandstone from core to pore scale and quantification of its impact on multi-phase flow

DOE PAGES

Hingerl, Ferdinand F.; Yang, Feifei; Pini, Ronny; ...

2016-02-02

In this paper we present the results of an extensive multiscale characterization of the flow properties and structural and capillary heterogeneities of the Heletz sandstone. We performed petrographic, porosity and capillary pressure measurements on several subsamples. We quantified mm-scale heterogeneity in saturation distributions in a rock core during multi-phase flow using conventional X-ray CT scanning. Core-flooding experiments were conducted under reservoirs conditions (9 MPa, 50 °C) to obtain primary drainage and secondary imbibition relative permeabilities and residual trapping was analyzed and quantified. We provide parameters for relative permeability, capillary pressure and trapping models for further modeling studies. A synchrotron-based microtomographymore » study complements our cm- to mm-scale investigation by providing links between the micromorphology and mm-scale saturation heterogeneities.« less

Laboratory Scale Experiments and Numerical Modeling of Cosolvent flushing of NAPL Mixtures in Saturated Porous Media

NASA Astrophysics Data System (ADS)

Agaoglu, B.; Scheytt, T. J.; Copty, N. K.

2011-12-01

This study examines the mechanistic processes governing multiphase flow of a water-cosolvent-NAPL system in saturated porous media. Laboratory batch and column flushing experiments were conducted to determine the equilibrium properties of pure NAPL and synthetically prepared NAPL mixtures as well as NAPL recovery mechanisms for different water-ethanol contents. The effect of contact time was investigated by considering different steady and intermittent flow velocities. A modified version of multiphase flow simulator (UTCHEM) was used to compare the multiphase model simulations with the column experiment results. The effect of employing different grid geometries (1D, 2D, 3D), heterogeneity and different initial NAPL saturation configurations were also examined in the model. It is shown that the change in velocity affects the mass transfer rate between phases as well as the ultimate NAPL recovery percentage. The experiments with slow flow rate flushing of pure NAPL and the 3D UTCHEM simulations gave similar effluent concentrations and NAPL cumulative recoveries. The results were less consistent for fast non-equilibrium flow conditions. The dissolution process from the NAPL mixture into the water-ethanol flushing solutions was found to be more complex than dissolution expressions incorporated in the numerical model. The dissolution rate of individual organic compounds (namely Toluene and Benzene) from a mixture NAPL into the ethanol-water flushing solution is found not to correlate with their equilibrium solubility values.The implications of this controlled experimental and modeling study on field cosolvent remediation applications are discussed.

Laboratory-scale experiments and numerical modeling of cosolvent flushing of multi-component NAPLs in saturated porous media.

PubMed

Agaoglu, Berken; Scheytt, Traugott; Copty, Nadim K

2012-10-01

This study examines the mechanistic processes governing multiphase flow of a water-cosolvent-NAPL system in saturated porous media. Laboratory batch and column flushing experiments were conducted to determine the equilibrium properties of pure NAPL and synthetically prepared NAPL mixtures as well as NAPL recovery mechanisms for different water-ethanol contents. The effect of contact time was investigated by considering different steady and intermittent flow velocities. A modified version of multiphase flow simulator (UTCHEM) was used to compare the multiphase model simulations with the column experiment results. The effect of employing different grid geometries (1D, 2D, 3D), heterogeneity and different initial NAPL saturation configurations was also examined in the model. It is shown that the change in velocity affects the mass transfer rate between phases as well as the ultimate NAPL recovery percentage. The experiments with low flow rate flushing of pure NAPL and the 3D UTCHEM simulations gave similar effluent concentrations and NAPL cumulative recoveries. Model simulations over-estimated NAPL recovery for high specific discharges and rate-limited mass transfer, suggesting a constant mass transfer coefficient for the entire flushing experiment may not be valid. When multi-component NAPLs are present, the dissolution rate of individual organic compounds (namely, toluene and benzene) into the ethanol-water flushing solution is found not to correlate with their equilibrium solubility values. Copyright © 2012 Elsevier B.V. All rights reserved.

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Germanium multiphase equation of state

DOE PAGES

Crockett, Scott D.; Lorenzi-Venneri, Giulia De; Kress, Joel D.; ...

2014-05-07

A new SESAME multiphase germanium equation of state (EOS) has been developed using the best available experimental data and density functional theory (DFT) calculations. The equilibrium EOS includes the Ge I (diamond), the Ge II (β-Sn) and the liquid phases. The foundation of the EOS is based on density functional theory calculations which are used to determine the cold curve and the Debye temperature. Results are compared to Hugoniot data through the solid-solid and solid-liquid transitions. We propose some experiments to better understand the dynamics of this element

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Pore scale modelling of electrical and hydraulic properties of a semi-consolidated sandstone under unsaturated conditions

NASA Astrophysics Data System (ADS)

Cassiani, G.; dalla, E.; Brovelli, A.; Pitea, D.; Binley, A. M.

2003-04-01

The development of reliable constitutive laws to translate geophysical properties into hydrological ones is the fundamental step for successful applications of hydrogeophysical techniques. Many such laws have been proposed and applied, particularly with regard to two types of relationships: (a) between moisture content and dielectric properties, and (b) between electrical resistivity, rock structure and water saturation. The classical Archie's law belongs to this latter category. Archie's relationship has been widely used, starting from borehole logs applications, to translate geoelectrical measurements into estimates of saturation. However, in spite of its popularity, it remains an empirical relationship, the parameters of which must be calibrated case by case, e.g. on laboratory data. Pore-scale models have been recently recognized and used as powerful tools to investigate the constitutive relations of multiphase soils from a pore-scale point of view, because they bridge the microscopic and macroscopic scales. In this project, we develop and validate a three-dimensional pore-scale method to compute electrical properties of unsaturated and saturated porous media. First we simulate a random packing of spheres [1] that obeys the grain-size distribution and porosity of an experimental porous medium system; then we simulate primary drainage with a morphological approach [2]; finally, for each state of saturation during the drainage process, we solve the electrical conduction equation within the grain structure with a new numerical model and compute the apparent electrical resistivity of the porous medium. We apply the new method to a semi-consolidated Permo-Triassic Sandstone from the UK (Sherwood Sandstone) for which both pressure-saturation (Van Genuchten) and Archie's law parameters have been measured on laboratory samples. A comparison between simulated and measured relationships has been performed.

AM363 martensitic stainless steel: A multiphase equation of state

NASA Astrophysics Data System (ADS)

De Lorenzi-Venneri, Giulia; Crockett, Scott D.

2017-01-01

A multiphase equation of state for stainless steel AM363 has been developed within the Opensesame approach and has been entered as material 4295 in the LANL-SESAME Library. Three phases were constructed separately: the low pressure martensitic phase, the austenitic phase and the liquid. Room temperature data and the explicit introduction of a magnetic contribution to the free energy determined the martensitic phase, while shock Hugoniot data was used to determine the austenitic phase and the phase boundaries. More experimental data or First Principles calculations would be useful to better characterize the liquid.

Water Transport in the Micro Porous Layer and Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell

NASA Astrophysics Data System (ADS)

Qin, C.; Hassanizadeh, S. M.

2015-12-01

In this work, a recently developed dynamic pore-network model is presented [1]. The model explicitly solves for both water pressure and capillary pressure. A semi-implicit scheme is used in updating water saturation in each pore body, which considerably increases the numerical stability at low capillary number values. Furthermore, a multiple-time-step algorithm is introduced to reduce the computational effort. A number of case studies of water transport in the micro porous layer (MPL) and gas diffusion layer (GDL) are conducted. We illustrate the role of MPL in reducing water flooding in the GDL. Also, the dynamic water transport through the MPL-GDL interface is explored in detail. This information is essential to the reduced continua model (RCM), which was developed for multiphase flow through thin porous layers [2, 3]. C.Z. Qin, Water transport in the gas diffusion layer of a polymer electrolyte fuel cell: dynamic pore-network modeling, J Electrochimical. Soci., 162, F1036-F1046, 2015. C.Z. Qin and S.M. Hassanizadeh, Multiphase flow through multilayers of thin porous media: general balance equations and constitutive relationships for a solid-gas-liquid three-phase system, Int. J. Heat Mass Transfer, 70, 693-708, 2014. C.Z. Qin and S.M. Hassanizadeh, A new approach to modeling water flooding in a polymer electrolyte fuel cell, Int. J. Hydrogen Energy, 40, 3348-3358, 2015.

Prediction of Down-Gradient Impacts of DNAPL Source Depletion Using Tracer Techniques

NASA Astrophysics Data System (ADS)

Basu, N. B.; Fure, A. D.; Jawitz, J. W.

2006-12-01

Four simplified DNAPL source depletion models that have been discussed in the literature recently are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. One of the source depletion models, the equilibrium streamtube model, is shown to be relatively easily parameterized using non-reactive and reactive tracers. Non-reactive tracers are used to characterize the aquifer heterogeneity while reactive tracers are used to describe the mean DNAPL mass and its distribution. This information is then used in a Lagrangian framework to predict source remediation performance. In a Lagrangian approach the source zone is conceptualized as a collection of non-interacting streamtubes with hydrodynamic and DNAPL heterogeneity represented by the variation of the travel time and DNAPL saturation among the streamtubes. The travel time statistics are estimated from the non-reactive tracer data while the DNAPL distribution statistics are estimated from the reactive tracer data. The combined statistics are used to define an analytical solution for contaminant dissolution under natural gradient flow. The tracer prediction technique compared favorably with results from a multiphase flow and transport simulator UTCHEM in domains with different hydrodynamic heterogeneity (variance of the log conductivity field = 0.2, 1 and 3).

Multiphase flow of carbon dioxide and brine in dual porosity carbonates

NASA Astrophysics Data System (ADS)

Pentland, Christopher; Oedai, Sjaam; Ott, Holger

2014-05-01

The storage of carbon dioxide in subsurface formations presents a challenge in terms of multiphase flow characterisation. Project planning requires an understanding of multiphase flow characteristics such as the relationship between relative permeability and saturation. At present there are only a limited number of relative permeability relations for carbon dioxide-brine fluid systems, most of which are measured on sandstone rocks. In this study coreflood experiments are performed to investigate the relative permeability of carbon dioxide and brine in two dual porosity carbonate systems. Carbon dioxide is injected into the brine saturated rocks in a primary drainage process. The rock fluid system is pre-equilibrated to avoid chemical reactions and physical mass transfer between phases. The pressure drop across the samples, the amount of brine displaced and the saturation distribution within the rocks are measured. The experiments are repeated on the same rocks for the decane-brine fluid system. The experimental data is interpreted by simulating the experiments with a continuum scale Darcy solver. Selected functional representations of relative permeability are investigated, the parameters of which are chosen such that a least squares objective function is minimised (i.e. the difference between experimental observations and simulated response). The match between simulation and measurement is dependent upon the form of the functional representations. The best agreement is achieved with the Corey [Brooks and Corey, 1964] or modified Corey [Masalmeh et al., 2007] functions which best represent the relative permeability of brine at low brine saturations. The relative permeability of carbon dioxide is shown to be lower than the relative permeability of decane over the saturation ranges investigated. The relative permeability of the brine phase is comparable for the two fluid systems. These observations are consistent with the rocks being water-wet. During the experiment only a portion of the full saturation range is investigated, corresponding to carbon dioxide entering the macro pores of the dual porosity systems. Within this pore space the relative permeability behaviour is comparable to that measured in Berea sandstone. Brooks, R. H., and A. T. Corey (1964), Hydraulic properties of porous media, Hydrology Papers 3, Civil Engineering Dept., Colorado State Univ., Fort Collins, CO. Masalmeh, S., I. Abu-Shiekah, and X. Jing (2007), Improved Characterization and Modeling of Capillary Transition Zones in Carbonate Reservoirs, SPE Reserv. Eval. Eng., 10(2), doi:10.2118/109094-PA.

Impact of CO2 injection protocol on fluid-solid reactivity: high-pressure and temperature microfluidic experiments in limestone

NASA Astrophysics Data System (ADS)

Jimenez-Martinez, Joaquin; Porter, Mark; Carey, James; Guthrie, George; Viswanathan, Hari

2017-04-01

Geological sequestration of CO2 has been proposed in the last decades as a technology to reduce greenhouse gas emissions to the atmosphere and mitigate the global climate change. However, some questions such as the impact of the protocol of CO2 injection on the fluid-solid reactivity remain open. In our experiments, two different protocols of injection are compared at the same conditions (8.4 MPa and 45 C, and constant flow rate 0.06 ml/min): i) single phase injection, i.e., CO2-saturated brine; and ii) simultaneous injection of CO2-saturated brine and scCO2. For that purpose, we combine a unique high-pressure/temperature microfluidics experimental system, which allows reproducing geological reservoir conditions in geo-material substrates (i.e., limestone, Cisco Formation, Texas, US) and high resolution optical profilometry. Single and multiphase flow through etched fracture networks were optically recorded with a microscope, while processes of dissolution-precipitation in the etched channels were quantified by comparison of the initial and final topology of the limestone micromodels. Changes in hydraulic conductivity were quantified from pressure difference along the micromodel. The simultaneous injection of CO2-saturated brine and scCO2, reduced the brine-limestone contact area and also created a highly heterogeneous velocity field (i.e., low velocities regions or stagnation zones, and high velocity regions or preferential paths), reducing rock dissolution and enhancing calcite precipitation. The results illustrate the contrasting effects of single and multiphase flow on chemical reactivity and suggest that multiphase flow by isolating parts of the flow system can enhance CO2 mineralization.

A Comprehensive Strategy for the Assessment of Stability Conditions in Porous Media at Varying Levels of Water Saturation

NASA Astrophysics Data System (ADS)

Mihalache, Constance

Assessing the potential for instability in non-saturated geomaterials is of critical importance for the prevention of disastrous failures that occur through these materials, from natural hazards such as rainfall-induced flow slides, to underwater sediment collapse due to methane hydrate dissociation, to the failure of key infrastructure components. In particular, the gaseous and liquid phases present within the pores of a geomaterial play a vital role in its overall behavior, and consequently must be considered in stability analyses. In this work, analytical techniques are presented to evaluate material stability for the different saturation states that occur during a wetting process, where soils progress from unsaturated conditions in the funicular regime, to quasi-saturated conditions in the insular regime, to complete saturation. Each of these different saturation states involves different interactions between the pore fluids and the solid skeleton hosting them. For example, while unsaturated soil behavior is characterized by the capillary effects from the interface between the gaseous and liquid phases, the dominant effect of isolated bubbles within the quasi-saturated regime is to increase the compressibility of the interstitial fluid mixture. By considering the different characteristics of these saturation states, energy-based work input expressions are developed and then used to derive criteria for loss of controllability of the material response. These criteria are then used to assess the stability of geomaterials under various loading configurations. Then, to unite the funicular and insular saturation regimes, the same methodology is adapted to the derivation of comprehensive three-phase criteria for non-saturated soils. An alternative interpretation of such constitutive singularities is also derived, with reference to the ill-posedness of the mass balance equations that control the transient flow of the fluid constituents of a deformable multiphase porous medium. Lastly, the concepts considered throughout the study are applied to the solution of boundary-value problems, using a finite element approach. Overall, it is shown that depending on the considered saturation regime, different stability criteria need to be applied for the accurate interpretation of material behavior. These techniques provide a mechanistic interpretation for a range of processes, such as the nature of so-called "wetting-collapse" events, the variability of the instability line for flow failures acting through gassy sediments, and the onset of runaway failures at the transition between funicular and insular states.

Investigation of free vibration characteristics for skew multiphase magneto-electro-elastic plate

NASA Astrophysics Data System (ADS)

Kiran, M. C.; Kattimani, S.

2018-04-01

This article presents the investigation of skew multiphase magneto-electro-elastic (MMEE) plate to assess its free vibration characteristics. A finite element (FE) model is formulated considering the different couplings involved via coupled constitutive equations. The transformation matrices are derived to transform local degrees of freedom into the global degrees of freedom for the nodes lying on the skew edges. Effect of different volume fraction (Vf) on the free vibration behavior is explicitly studied. In addition, influence of width to thickness ratio, the aspect ratio, and the stacking arrangement on natural frequencies of skew multiphase MEE plate investigated. Particular attention has been paid to investigate the effect of skew angle on the non-dimensional Eigen frequencies of multiphase MEE plate with simply supported edges.

A statistical approach to the brittle fracture of a multi-phase solid

NASA Technical Reports Server (NTRS)

Liu, W. K.; Lua, Y. I.; Belytschko, T.

1991-01-01

A stochastic damage model is proposed to quantify the inherent statistical distribution of the fracture toughness of a brittle, multi-phase solid. The model, based on the macrocrack-microcrack interaction, incorporates uncertainties in locations and orientations of microcracks. Due to the high concentration of microcracks near the macro-tip, a higher order analysis based on traction boundary integral equations is formulated first for an arbitrary array of cracks. The effects of uncertainties in locations and orientations of microcracks at a macro-tip are analyzed quantitatively by using the boundary integral equations method in conjunction with the computer simulation of the random microcrack array. The short range interactions resulting from surrounding microcracks closet to the main crack tip are investigated. The effects of microcrack density parameter are also explored in the present study. The validity of the present model is demonstrated by comparing its statistical output with the Neville distribution function, which gives correct fits to sets of experimental data from multi-phase solids.

A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

NASA Astrophysics Data System (ADS)

Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

2018-01-01

In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed model has been found to perform better than the improved Z-S-C model in this aspect.

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

NASA Astrophysics Data System (ADS)

Henry de Frahan, Marc T.; Varadan, Sreenivas; Johnsen, Eric

2015-01-01

Although the Discontinuous Galerkin (DG) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, high-order accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. To represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie-Grüneisen family. Within the DG framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one- and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. The algorithm is implemented on parallel graphics processing units (GPU) to achieve high speedup.

Computational Flow Modeling of Hydrodynamics in Multiphase Trickle-Bed Reactors

NASA Astrophysics Data System (ADS)

Lopes, Rodrigo J. G.; Quinta-Ferreira, Rosa M.

2008-05-01

This study aims to incorporate most recent multiphase models in order to investigate the hydrodynamic behavior of a TBR in terms of pressure drop and liquid holdup. Taking into account transport phenomena such as mass and heat transfer, an Eulerian k-fluid model was developed resulting from the volume averaging of the continuity and momentum equations and solved for a 3D representation of the catalytic bed. Computational fluid dynamics (CFD) model predicts hydrodynamic parameters quite well if good closures for fluid/fluid and fluid/particle interactions are incorporated in the multiphase model. Moreover, catalytic performance is investigated with the catalytic wet oxidation of a phenolic pollutant.

Generating a Multiphase Equation of State with Swarm Intelligence

NASA Astrophysics Data System (ADS)

Cox, Geoffrey

2017-06-01

Hydrocode calculations require knowledge of the variation of pressure of a material with density and temperature, which is given by the equation of state. An accurate model needs to account for discontinuities in energy, density and properties of a material across a phase boundary. When generating a multiphase equation of state the modeller attempts to balance the agreement between the available data for compression, expansion and phase boundary location. However, this can prove difficult because minor adjustments in the equation of state for a single phase can have a large impact on the overall phase diagram. Recently, Cox and Christie described a method for combining statistical-mechanics-based condensed matter physics models with a stochastic analysis technique called particle swarm optimisation. The models produced show good agreement with experiment over a wide range of pressure-temperature space. This talk details the general implementation of this technique, shows example results, and describes the types of analysis that can be performed with this method.

A separate phase drag model and a surrogate approximation for simulation of the steam assisted gravity drainage (SAGD) process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padrino-Inciarte, Juan Carlos; Ma, Xia; VanderHeyden, W. Brian

General ensemble phase averaged equations for multiphase flows have been specialized for the simulation of the steam assisted gravity drainage (SAGD) process. In the average momentum equation, fluid-solid and fluid-fluid viscous interactions are represented by separate force terms. This equation has a form similar to that of Darcy’s law for multiphase flow but augmented by the fluid-fluid viscous forces. Models for these fluid-fluid interactions are suggested and implemented into the numerical code CartaBlanca. Numerical results indicate that the model captures the main features of the multiphase flow in the SAGD process, but the detailed features, such as plumes are missed.more » We find that viscous coupling among the fluid phases is important. Advection time scales for the different fluids differ by several orders of magnitude because of vast viscosity differences. Numerically resolving all of these time scales is time consuming. To address this problem, we introduce a steam surrogate approximation to increase the steam advection time scale, while keeping the mass and energy fluxes well approximated. This approximation leads to about a 40-fold speed-up in execution speed of the numerical calculations at the cost of a few percent error in the relevant quantities.« less

A separate phase drag model and a surrogate approximation for simulation of the steam assisted gravity drainage (SAGD) process

DOE PAGES

Padrino-Inciarte, Juan Carlos; Ma, Xia; VanderHeyden, W. Brian; ...

2016-01-01

General ensemble phase averaged equations for multiphase flows have been specialized for the simulation of the steam assisted gravity drainage (SAGD) process. In the average momentum equation, fluid-solid and fluid-fluid viscous interactions are represented by separate force terms. This equation has a form similar to that of Darcy’s law for multiphase flow but augmented by the fluid-fluid viscous forces. Models for these fluid-fluid interactions are suggested and implemented into the numerical code CartaBlanca. Numerical results indicate that the model captures the main features of the multiphase flow in the SAGD process, but the detailed features, such as plumes are missed.more » We find that viscous coupling among the fluid phases is important. Advection time scales for the different fluids differ by several orders of magnitude because of vast viscosity differences. Numerically resolving all of these time scales is time consuming. To address this problem, we introduce a steam surrogate approximation to increase the steam advection time scale, while keeping the mass and energy fluxes well approximated. This approximation leads to about a 40-fold speed-up in execution speed of the numerical calculations at the cost of a few percent error in the relevant quantities.« less

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Bertola, Marco; El, Gennady A.; Tovbis, Alexander

2016-10-01

Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

Computational methods for reactive transport modeling: An extended law of mass-action, xLMA, method for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg; Saar, Martin O.

2016-10-01

We present an extended law of mass-action (xLMA) method for multiphase equilibrium calculations and apply it in the context of reactive transport modeling. This extended LMA formulation differs from its conventional counterpart in that (i) it is directly derived from the Gibbs energy minimization (GEM) problem (i.e., the fundamental problem that describes the state of equilibrium of a chemical system under constant temperature and pressure); and (ii) it extends the conventional mass-action equations with Lagrange multipliers from the Gibbs energy minimization problem, which can be interpreted as stability indices of the chemical species. Accounting for these multipliers enables the method to determine all stable phases without presuming their types (e.g., aqueous, gaseous) or their presence in the equilibrium state. Therefore, the here proposed xLMA method inherits traits of Gibbs energy minimization algorithms that allow it to naturally detect the phases present in equilibrium, which can be single-component phases (e.g., pure solids or liquids) or non-ideal multi-component phases (e.g., aqueous, melts, gaseous, solid solutions, adsorption, or ion exchange). Moreover, our xLMA method requires no technique that tentatively adds or removes reactions based on phase stability indices (e.g., saturation indices for minerals), since the extended mass-action equations are valid even when their corresponding reactions involve unstable species. We successfully apply the proposed method to a reactive transport modeling problem in which we use PHREEQC and GEMS as alternative backends for the calculation of thermodynamic properties such as equilibrium constants of reactions, standard chemical potentials of species, and activity coefficients. Our tests show that our algorithm is efficient and robust for demanding applications, such as reactive transport modeling, where it converges within 1-3 iterations in most cases. The proposed xLMA method is implemented in Reaktoro, a unified open-source framework for modeling chemically reactive systems.

Shock Melting of Permafrost on Mars: Water Ice Multiphase Equation of State for Numerical Modeling and Its Testing

NASA Technical Reports Server (NTRS)

Ivanov, B. A.

2005-01-01

The presence of water/ice/brine in upper layers of Martian crust affects many processes of impact cratering. Modeling of these effects promises better understanding of Martian cratering records. We present here the new ANEOS-based multiphase equation of state for water/ice constructed for usage in hydrocodes and first numerical experiments on permafrost shock melting. Preliminary results show that due to multiple shock compression of ice inclusions in rocks the entropy jump in shocked ice is smaller than in pure ice for the same shock pressure. Hence previous estimates of ice melting during impact cratering on Mars should be re-evaluated. Additional information is included in the original extended abstract.

Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2016-11-01

Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.

Experience in using a numerical scheme with artificial viscosity at solving the Riemann problem for a multi-fluid model of multiphase flow

NASA Astrophysics Data System (ADS)

Bulovich, S. V.; Smirnov, E. M.

2018-05-01

The paper covers application of the artificial viscosity technique to numerical simulation of unsteady one-dimensional multiphase compressible flows on the base of the multi-fluid approach. The system of the governing equations is written under assumption of the pressure equilibrium between the "fluids" (phases). No interfacial exchange is taken into account. A model for evaluation of the artificial viscosity coefficient that (i) assumes identity of this coefficient for all interpenetrating phases and (ii) uses the multiphase-mixture Wood equation for evaluation of a scale speed of sound has been suggested. Performance of the artificial viscosity technique has been evaluated via numerical solution of a model problem of pressure discontinuity breakdown in a three-fluid medium. It has been shown that a relatively simple numerical scheme, explicit and first-order, combined with the suggested artificial viscosity model, predicts a physically correct behavior of the moving shock and expansion waves, and a subsequent refinement of the computational grid results in a monotonic approaching to an asymptotic time-dependent solution, without non-physical oscillations.

Numerical modeling of experimental observations on gas formation and multi-phase flow of carbon dioxide in subsurface formations

NASA Astrophysics Data System (ADS)

Pawar, R.; Dash, Z.; Sakaki, T.; Plampin, M. R.; Lassen, R. N.; Illangasekare, T. H.; Zyvoloski, G.

2011-12-01

One of the concerns related to geologic CO2 sequestration is potential leakage of CO2 and its subsequent migration to shallow groundwater resources leading to geochemical impacts. Developing approaches to monitor CO2 migration in shallow aquifer and mitigate leakage impacts will require improving our understanding of gas phase formation and multi-phase flow subsequent to CO2 leakage in shallow aquifers. We are utilizing an integrated approach combining laboratory experiments and numerical simulations to characterize the multi-phase flow of CO2 in shallow aquifers. The laboratory experiments involve a series of highly controlled experiments in which CO2 dissolved water is injected in homogeneous and heterogeneous soil columns and tanks. The experimental results are used to study the effects of soil properties, temperature, pressure gradients and heterogeneities on gas formation and migration. We utilize the Finite Element Heat and Mass (FEHM) simulator (Zyvoloski et al, 2010) to numerically model the experimental results. The numerical models capture the physics of CO2 exsolution, multi-phase fluid flow as well as sand heterogeneity. Experimental observations of pressure, temperature and gas saturations are used to develop and constrain conceptual models for CO2 gas-phase formation and multi-phase CO2 flow in porous media. This talk will provide details of development of conceptual models based on experimental observation, development of numerical models for laboratory experiments and modelling results.

Experimental multi-phase H2O-CO2 brine interactions at elevated temperature and pressure: Implications for CO2 sequestration in deep-saline aquifers

USGS Publications Warehouse

Rosenbauer, R.; Koksalan, T.

2004-01-01

The burning of fossil fuel and other anthropogenic activities have caused a continuous and dramatic 30% increase of atmospheric CO2 over the past 150 yr. CO2 sequestration is increasingly being viewed as a tool for managing these anthropogenic CO2 emissions to the atmosphere. CO2-saturated brine-rock experiments were carried out to evaluate the effects of multiphase H2O-CO2 fluids on mineral equilibria and the potential for CO2 sequestration in mineral phases within deep-saline aquifers. Experimental results were generally consistent with theoretical thermodynamic calculations. The solubility of CO2 was enhanced in brines in the presence of both limestone and sandstone relative to brines alone. Reactions between CO2 saturated brines and arkosic sandstones were characterized by desiccation of the brine and changes in the chemical composition of the brine suggesting fixation of CO2 in mineral phases. These reactions were occurring on a measurable but kinetically slow time scale at 120??C.

MUFITS Code for Modeling Geological Storage of Carbon Dioxide at Sub- and Supercritical Conditions

NASA Astrophysics Data System (ADS)

Afanasyev, A.

2012-12-01

Two-phase models are widely used for simulation of CO2 storage in saline aquifers. These models support gaseous phase mainly saturated with CO2 and liquid phase mainly saturated with H2O (e.g. TOUGH2 code). The models can be applied to analysis of CO2 storage only in relatively deeply-buried reservoirs where pressure exceeds CO2 critical pressure. At these supercritical reservoir conditions only one supercritical CO2-rich phase appears in aquifer due to CO2 injection. In shallow aquifers where reservoir pressure is less than the critical pressure CO2 can split in two different liquid-like and gas-like phases (e.g. Spycher et al., 2003). Thus a region of three-phase flow of water, liquid and gaseous CO2 can appear near the CO2 injection point. Today there is no widely used and generally accepted numerical model capable of the three-phase flows with two CO2-rich phases. In this work we propose a new hydrodynamic simulator MUFITS (Multiphase Filtration Transport Simulator) for multiphase compositional modeling of CO2-H2O mixture flows in porous media at conditions of interest for carbon sequestration. The simulator is effective both for supercritical flows in a wide range of pressure and temperature and for subcritical three-phase flows of water, liquid CO2 and gaseous CO2 in shallow reservoirs. The distinctive feature of the proposed code lies in the methodology for mixture properties determination. Transport equations and Darcy correlation are solved together with calculation of the entropy maximum that is reached in thermodynamic equilibrium and determines the mixture composition. To define and solve the problem only one function - mixture thermodynamic potential - is required. The potential is determined using a three-parametric generalization of Peng-Robinson equation of state fitted to experimental data (Todheide, Takenouchi, Altunin etc.). We apply MUFITS to simple 1D and 2D test problems of CO2 injection in shallow reservoirs subjected to phase changes between liquid and gaseous CO2. We consider CO2 injection into highly heterogeneous the 10th SPE reservoir. We provide analysis of physical phenomena that have control temperature distribution in the reservoir. The distribution is non-monotonic with regions of high and low temperature. The main phenomena responsible for considerable temperature decline around CO2 injection point is the liquid CO2 evaporation process. We also apply the code to real-scale 3D simulations of CO2 geological storage at supercritical conditions in Sleipner field and Johansen formation (Fig). The work is supported financially by the Russian Foundation for Basic Research (12-01-31117) and grant for leading scientific schools (NSh 1303.2012.1). CO2 phase saturation in Johansen formation after 50 years of injection and 1000 years of rest period

Measurement of Fracture Aperture Fields Using Ttransmitted Light: An Evaluation of Measurement Errors and their Influence on Simulations of Flow and Transport through a Single Fracture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Detwiler, Russell L.; Glass, Robert J.; Pringle, Scott E.

Understanding of single and multi-phase flow and transport in fractures can be greatly enhanced through experimentation in transparent systems (analogs or replicas) where light transmission techniques yield quantitative measurements of aperture, solute concentration, and phase saturation fields. Here we quanti@ aperture field measurement error and demonstrate the influence of this error on the results of flow and transport simulations (hypothesized experimental results) through saturated and partially saturated fractures. find that precision and accuracy can be balanced to greatly improve the technique and We present a measurement protocol to obtain a minimum error field. Simulation results show an increased sensitivity tomore » error as we move from flow to transport and from saturated to partially saturated conditions. Significant sensitivity under partially saturated conditions results in differences in channeling and multiple-peaked breakthrough curves. These results emphasize the critical importance of defining and minimizing error for studies of flow and transpoti in single fractures.« less

Multiphase flow modeling of a crude-oil spill site with a bimodal permeability distribution

USGS Publications Warehouse

Dillard, Leslie A.; Essaid, Hedeff I.; Herkelrath, William N.

1997-01-01

Fluid saturation, particle-size distribution, and porosity measurements were obtained from 269 core samples collected from six boreholes along a 90-m transect at a subregion of a crude-oil spill site, the north pool, near Bemidji, Minnesota. The oil saturation data, collected 11 years after the spill, showed an irregularly shaped oil body that appeared to be affected by sediment spatial variability. The particle-size distribution data were used to estimate the permeability (k) and retention curves for each sample. An additional 344 k estimates were obtained from samples previously collected at the north pool. The 613 k estimates were distributed bimodal lognormally with the two population distributions corresponding to the two predominant lithologies: a coarse glacial outwash deposit and fine-grained interbedded lenses. A two-step geostatistical approach was used to generate a conditioned realization of k representing the bimodal heterogeneity. A cross-sectional multiphase flow model was used to simulate the flow of oil and water in the presence of air along the north pool transect for an 11-year period. The inclusion of a representation of the bimodal aquifer heterogeneity was crucial for reproduction of general features of the observed oil body. If the bimodal heterogeneity was characterized, hysteresis did not have to be incorporated into the model because a hysteretic effect was produced by the sediment spatial variability. By revising the relative permeability functional relation, an improved reproduction of the observed oil saturation distribution was achieved. The inclusion of water table fluctuations in the model did not significantly affect the simulated oil saturation distribution.

FV-MHMM: A Discussion on Weighting Schemes.

NASA Astrophysics Data System (ADS)

Franc, J.; Gerald, D.; Jeannin, L.; Egermann, P.; Masson, R.

2016-12-01

Upscaling or homogenization techniques consist in finding block-equivalentor equivalent upscaled properties on a coarse grid from heterogeneousproperties defined on an underlying fine grid. However, this couldbecome costly and resource consuming. Harder et al., 2013, have developeda Multiscale Hybrid-Mixed Method (MHMM) of upscaling to treat Darcytype equations on heterogeneous fields formulated using a finite elementmethod. Recently, Franc et al. 2016, has extended this method of upscalingto finite volume formulation (FV-MHMM). Although convergence refiningLagrange multipliers space has been observed, numerical artefactscan occur while trapping numerically the flow in regions of low permeability. This work will present the development of the method along with theresults obtained from its classical formulation. Then, two weightingschemes and their benefits on the FV-MHMM method will be presented insome simple random permeability cases. Next example will involve alarger heterogeneous 2D permeability field extracted from the 10thSPE test case. Eventually, multiphase flow will be addressed asan extension of this single phase flow method. An elliptic pressureequation solved on the coarse grid via FV-MHMM will be sequentiallycoupled with a hyperbolic saturation equation on the fine grid. Theimproved accuracy thanks to the weighting scheme will be measuredcompared to a finite volume fine grid solution. References: Harder, C., Paredes, D. and Valentin, F., A family of multiscalehybrid-mixed finite element methods for the Darcy equation with roughcoefficients, Journal of Computational Physics, 2013. Franc J., Debenest G., Jeannin L., Egermann P. and Masson R., FV-MHMMfor reservoir modelling ECMOR XV-15th European Conference on the Mathematicsof Oil Recovery, 2015.

Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows.

PubMed

Liang, H; Shi, B C; Guo, Z L; Chai, Z H

2014-05-01

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

Identification of immiscible NAPL contaminant sources in aquifers by a modified two-level saturation based imperialist competitive algorithm.

PubMed

Ghafouri, H R; Mosharaf-Dehkordi, M; Afzalan, B

2017-07-01

A simulation-optimization model is proposed for identifying the characteristics of local immiscible NAPL contaminant sources inside aquifers. This model employs the UTCHEM 9.0 software as its simulator for solving the governing equations associated with the multi-phase flow in porous media. As the optimization model, a novel two-level saturation based Imperialist Competitive Algorithm (ICA) is proposed to estimate the parameters of contaminant sources. The first level consists of three parallel independent ICAs and plays as a pre-conditioner for the second level which is a single modified ICA. The ICA in the second level is modified by dividing each country into a number of provinces (smaller parts). Similar to countries in the classical ICA, these provinces are optimized by the assimilation, competition, and revolution steps in the ICA. To increase the diversity of populations, a new approach named knock the base method is proposed. The performance and accuracy of the simulation-optimization model is assessed by solving a set of two and three-dimensional problems considering the effects of different parameters such as the grid size, rock heterogeneity and designated monitoring networks. The obtained numerical results indicate that using this simulation-optimization model provides accurate results at a less number of iterations when compared with the model employing the classical one-level ICA. Copyright © 2017 Elsevier B.V. All rights reserved.

A New Multiphase Equation of State for SiO 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maerzke, Katie A.; Gammel, J. Tinka

SiO 2 is found as α-quartz at ambient conditions. Under shock compression, it transforms into a much higher density stishovite-like phase around 20 GPa, then into a liquid phase above 100 GPa. The SESAME library contains older equations of state for α-quartz, polycrystalline quartz, and fused quartz. These equations of state model the material as a single phase; i.e., there is no high pressure phase transition. Somewhat more recently (in 1992), Jon Boettger published equations of state for α-quartz, coesite, and stishovite, along with a phase transition model to mix them. However, we do not have a multiphase EOS thatmore » captures the phase transitions in this material. Others are working on a high-accuracy model for very high pressure SiO 2, since liquid quartz is used as an impedance matching standard above 100 GPa; however, we are focused on the 10-50 GPa range. This intermediate pressure range is most relevant for modeling the decomposition products of silicone polymers such as Sylgard 184 and SX358.« less

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

NASA Technical Reports Server (NTRS)

Chen, C. P.; Jiang, Y.; Kim, Y. M.; Shang, H. M.

1991-01-01

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

A Constitutive Equation Relating Composition and Microstructure to Properties in Ti-6Al-4V: As Derived Using a Novel Integrated Computational Approach

NASA Astrophysics Data System (ADS)

Ghamarian, Iman; Samimi, Peyman; Dixit, Vikas; Collins, Peter C.

2015-11-01

While it is useful to predict properties in metallic materials based upon the composition and microstructure, the complexity of real, multi-component, and multi-phase engineering alloys presents difficulties when attempting to determine constituent-based phenomenological equations. This paper applies an approach based upon the integration of three separate modeling approaches, specifically artificial neural networks, genetic algorithms, and Monte Carlo simulations to determine a mechanism-based equation for the yield strength of α+ β processed Ti-6Al-4V (all compositions in weight percent) which consists of a complex multi-phase microstructure with varying spatial and morphological distributions of the key microstructural features. Notably, this is an industrially important alloy yet an alloy for which such an equation does not exist in the published literature. The equation ultimately derived in this work not only can accurately describe the properties of the current dataset but also is consistent with the limited and dissociated information available in the literature regarding certain parameters such as intrinsic yield strength of pure hexagonal close-packed alpha titanium. In addition, this equation suggests new interesting opportunities for controlling yield strength by controlling the relative intrinsic strengths of the two phases through solid solution strengthening.

The prediction of the cavitation phenomena including population balance modeling

NASA Astrophysics Data System (ADS)

Bannari, Rachid; Hliwa, Ghizlane Zineb; Bannari, Abdelfettah; Belghiti, Mly Taib

2017-07-01

Cavitation is the principal reason behind the behavior's modification of the hydraulic turbines. However, the experimental observations can not be appropriate to all cases due to the limitations in the measurement techniques. The mathematical models which have been implemented, use the mixture multiphase frame. As well as, most of the published work is limited by considering a constant bubble size distribution. However, this assumption is not realist. The aim of this article is the implementation and the use of a non-homogeneous multiphase model which solve two phases transport equation. The evolution of bubble size is considered by the population balance equation. This study is based on the eulerian-eulerian model, associated to the cavitation model. All the inter-phase forces such as drag, lift and virtual mass are used.

Multiphase Equation of State and Strength Properties of Beryllium from AB INITIO and Quantum Molecular Dynamics Calculations.

NASA Astrophysics Data System (ADS)

Robert, G.; Sollier, A.; Legrand, Ph.

2007-12-01

In the framework of density functional theory, static properties and phonon spectra of beryllium have been calculated under high compression (for pressures up to 4 Mbar) for two solid phases: hexagonal compact (hcp) and body-centered cubic (bcc). The melting curve and some isotherms in the liquid phase have been calculated using quantum molecular dynamics. The coupling of these theoretical data to a quasi-harmonic approach (phonon moments) allows us to suggest a new theoretical phase diagram and to build a multiphase equation of state (EOS) valid in a large range of pressure and temperature. The resulting Hugoniot curves as well as the evolution of the longitudinal sound speed with both pressure and temperature are in good agreement with available experimental data.

Water saturation effects on P-wave anisotropy in synthetic sandstone with aligned fractures

NASA Astrophysics Data System (ADS)

Amalokwu, Kelvin; Chapman, Mark; Best, Angus I.; Minshull, Timothy A.; Li, Xiang-Yang

2015-08-01

The seismic properties of rocks are known to be sensitive to partial liquid or gas saturation, and to aligned fractures. P-wave anisotropy is widely used for fracture characterization and is known to be sensitive to the saturating fluid. However, studies combining the effect of multiphase saturation and aligned fractures are limited even though such conditions are common in the subsurface. An understanding of the effects of partial liquid or gas saturation on P-wave anisotropy could help improve seismic characterization of fractured, gas bearing reservoirs. Using octagonal-shaped synthetic sandstone samples, one containing aligned penny-shaped fractures and the other without fractures, we examined the influence of water saturation on P-wave anisotropy in fractured rocks. In the fractured rock, the saturation related stiffening effect at higher water saturation values is larger in the direction across the fractures than along the fractures. Consequently, the anisotropy parameter `ε' decreases as a result of this fluid stiffening effect. These effects are frequency dependent as a result of wave-induced fluid flow mechanisms. Our observations can be explained by combining a frequency-dependent fractured rock model and a frequency-dependent partial saturation model.

A compressible two-phase model for dispersed particle flows with application from dense to dilute regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGrath, Thomas P., E-mail: thomas.p.mcgrath@navy.mil; St Clair, Jeffrey G.; Department of Mechanical and Aerospace Engineering, University of Florida, 231 MAE-A, P.O. Box 116250, Gainesville, Florida 32611

2016-05-07

Multiphase flows are present in many important fields ranging from multiphase explosions to chemical processing. An important subset of multiphase flow applications involves dispersed materials, such as particles, droplets, and bubbles. This work presents an Eulerian–Eulerian model for multiphase flows containing dispersed particles surrounded by a continuous media such as air or water. Following a large body of multiphase literature, the driving force for particle acceleration is modeled as a direct function of both the continuous-phase pressure gradient and the gradient of intergranular stress existing within the particle phase. While the application of these two components of driving force ismore » well accepted in much of the literature, other models exist in which the particle-phase pressure gradient itself drives particle motion. The multiphase model treats all phases as compressible and is derived to ensure adherence to the 2nd Law of Thermodynamics. The governing equations are presented and discussed, and a characteristic analysis shows the model to be hyperbolic, with a degeneracy in the case that the intergranular stress, which is modeled as a configuration pressure, is zero. Finally, results from a two sample problems involving shock-induced particle dispersion are presented. The results agree well with experimental measurements, providing initial confidence in the proposed model.« less

A CSF-SPH method for simulating drainage and imbibition at pore-scale resolution while tracking interfacial areas

NASA Astrophysics Data System (ADS)

Sivanesapillai, Rakulan; Falkner, Nadine; Hartmaier, Alexander; Steeb, Holger

2016-09-01

We present a conservative smoothed particle hydrodynamics (SPH) model to study the flow of multiple, immiscible fluid phases in porous media using direct pore-scale simulations. Particular focus is put on continuously tracking the evolution of interfacial areas, which are considered to be important morphological quantities affecting multiphase transport in porous media. In addition to solving the Navier-Stokes equations, the model accounts for the effects of capillarity at interfaces and contact lines. This is done by means of incorporating the governing interfacial mass and momentum balances using the continuum surface force (CSF) method, thus rendering model calibration routines unnecessary and minimizing the set of constitutive and kinematic assumptions. We address the application of boundary conditions at rigid solid surfaces and study the predictive capability of the model as well as optimal choices for numerical parameters using an extensive model validation procedure. We demonstrate the applicability of the model to simulate multiphase flows involving partial wettability, dynamic effects, large density ratios (up to 1000), large viscosity ratios (up to 100), as well as fragmentation and coalescence of fluid phases. The model is used to study the evolution of fluid-fluid interfacial areas during saturation-controlled primary drainage and main imbibition of heterogeneous pore spaces at low capillary numbers. A variety of pore-scale effects, such as wetting phase entrapment and fragmentation due to snap-off, are observed. Specific fluid-fluid interfacial area is observed to monotonically increase during primary drainage and hysteretic effects are apparent during main imbibition.

A multiphase model for three-dimensional tumor growth

NASA Astrophysics Data System (ADS)

Sciumè, G.; Shelton, S.; Gray, W. G.; Miller, C. T.; Hussain, F.; Ferrari, M.; Decuzzi, P.; Schrefler, B. A.

2013-01-01

Several mathematical formulations have analyzed the time-dependent behavior of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the thermodynamically constrained averaging theory. A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TCs), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HCs); and an interstitial fluid for the transport of nutrients. The equations are solved by a finite element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTSs) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behavior: initially, the rapidly growing TCs tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable TCs whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case—mostly due to the relative adhesion of the TCs and HCs to the ECM, and the less favorable transport of nutrients. In particular, for HCs adhering less avidly to the ECM, the healthy tissue is progressively displaced as the malignant mass grows, whereas TC infiltration is predicted for the opposite condition. Interestingly, the infiltration potential of the tumor mass is mostly driven by the relative cell adhesion to the ECM. In the third case, a tumor cord model is analyzed where the malignant cells grow around microvessels in a three-dimensional geometry. It is shown that TCs tend to migrate among adjacent vessels seeking new oxygen and nutrients. This model can predict and optimize the efficacy of anticancer therapeutic strategies. It can be further developed to answer questions on tumor biophysics, related to the effects of ECM stiffness and cell adhesion on TC proliferation.

Orbital stability and energy estimate of ground states of saturable nonlinear Schrödinger equations with intensity functions in R2

NASA Astrophysics Data System (ADS)

Lin, Tai-Chia; Wang, Xiaoming; Wang, Zhi-Qiang

2017-10-01

Conventionally, the existence and orbital stability of ground states of nonlinear Schrödinger (NLS) equations with power-law nonlinearity (subcritical case) can be proved by an argument using strict subadditivity of the ground state energy and the concentration compactness method of Cazenave and Lions [4]. However, for saturable nonlinearity, such an argument is not applicable because strict subadditivity of the ground state energy fails in this case. Here we use a convexity argument to prove the existence and orbital stability of ground states of NLS equations with saturable nonlinearity and intensity functions in R2. Besides, we derive the energy estimate of ground states of saturable NLS equations with intensity functions using the eigenvalue estimate of saturable NLS equations without intensity function.

Shock Equation of State of Multi-Phase Epoxy-Based Composite (Al-MnO2-Epoxy)

DTIC Science & Technology

2010-10-01

single stage light gas gun , two...using three different loading techniques— single stage light gas gun , two stage light gas gun , and explosive loading—with multiple diagnostic...wave speed. B. Single stage gas gun loading experiments Four gas gun -driven equation of state experiments were conducted at NSWC-Indian Head using

A phase-field lattice Boltzmann model for simulating multiphase flows in porous media: Application and comparison to experiments of CO2 sequestration at pore scale

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Li, Yaofa; Bolster, Diogo; Christensen, Kenneth T.

2018-04-01

We implement a phase-field based lattice-Boltzmann (LB) method for numerical simulation of multiphase flows in heterogeneous porous media at pore scales with wettability effects. The present method can handle large density and viscosity ratios, pertinent to many practical problems. As a practical application, we study multiphase flow in a micromodel representative of CO2 invading a water-saturated porous medium at reservoir conditions, both numerically and experimentally. We focus on two flow cases with (i) a crossover from capillary fingering to viscous fingering at a relatively small capillary number, and (ii) viscous fingering at a relatively moderate capillary number. Qualitative and quantitative comparisons are made between numerical results and experimental data for temporal and spatial CO2 saturation profiles, and good agreement is found. In particular, a correlation analysis shows that any differences between simulations and results are comparable to intra-experimental differences from replicate experiments. A key conclusion of this work is that system behavior is highly sensitive to boundary conditions, particularly inlet and outlet ones. We finish with a discussion on small-scale flow features, such as the emergence of strong recirculation zones as well as flow in which the residual phase is trapped, including a close look at the detailed formation of a water cone. Overall, the proposed model yields useful information, such as the spatiotemporal evolution of the CO2 front and instantaneous velocity fields, which are valuable for understanding the mechanisms of CO2 infiltration at the pore scale.

Impact of eliminating fracture intersection nodes in multiphase compositional flow simulation

NASA Astrophysics Data System (ADS)

Walton, Kenneth M.; Unger, Andre J. A.; Ioannidis, Marios A.; Parker, Beth L.

2017-04-01

Algebraic elimination of nodes at discrete fracture intersections via the star-delta technique has proven to be a valuable tool for making multiphase numerical simulations more tractable and efficient. This study examines the assumptions of the star-delta technique and exposes its effects in a 3-D, multiphase context for advective and dispersive/diffusive fluxes. Key issues of relative permeability-saturation-capillary pressure (kr-S-Pc) and capillary barriers at fracture-fracture intersections are discussed. This study uses a multiphase compositional, finite difference numerical model in discrete fracture network (DFN) and discrete fracture-matrix (DFM) modes. It verifies that the numerical model replicates analytical solutions and performs adequately in convergence exercises (conservative and decaying tracer, one and two-phase flow, DFM and DFN domains). The study culminates in simulations of a two-phase laboratory experiment in which a fluid invades a simple fracture intersection. The experiment and simulations evoke different invading fluid flow paths by varying fracture apertures as oil invades water-filled fractures and as water invades air-filled fractures. Results indicate that the node elimination technique as implemented in numerical model correctly reproduces the long-term flow path of the invading fluid, but that short-term temporal effects of the capillary traps and barriers arising from the intersection node are lost.

Tracking interface and common curve dynamics for two-fluid flow in porous media

DOE PAGES

Mcclure, James E.; Miller, Cass T.; Gray, W. G.; ...

2016-04-29

Pore-scale studies of multiphase flow in porous medium systems can be used to understand transport mechanisms and quantitatively determine closure relations that better incorporate microscale physics into macroscale models. Multiphase flow simulators constructed using the lattice Boltzmann method provide a means to conduct such studies, including both the equilibrium and dynamic aspects. Moving, storing, and analyzing the large state space presents a computational challenge when highly-resolved models are applied. We present an approach to simulate multiphase flow processes in which in-situ analysis is applied to track multiphase flow dynamics at high temporal resolution. We compute a comprehensive set of measuresmore » of the phase distributions and the system dynamics, which can be used to aid fundamental understanding and inform closure relations for macroscale models. The measures computed include microscale point representations and macroscale averages of fluid saturations, the pressure and velocity of the fluid phases, interfacial areas, interfacial curvatures, interface and common curve velocities, interfacial orientation tensors, phase velocities and the contact angle between the fluid-fluid interface and the solid surface. Test cases are studied to validate the approach and illustrate how measures of system state can be obtained and used to inform macroscopic theory.« less

Direct Numerical Simulations of Dynamic Drainage and Imbibition to Investigate Capillary Pressure-Saturation-Interfacial Area Relation

NASA Astrophysics Data System (ADS)

Konangi, S.; Palakurthi, N. K.; Karadimitriou, N.; Comer, K.; Ghia, U.

2017-12-01

We present results of pore-scale direct numerical simulations (DNS) of drainage and imbibition in a quasi-two-dimensional (40µm thickness) porous medium with a randomly distributed packing of cylindrical obstructions. The Navier-Stokes (NS) equations are solved in the pore space on an Eulerian mesh using the open-source finite-volume computational fluid dynamics (CFD) code, OpenFOAM. The Volume-of-Fluid (VOF) method is employed to track the evolution of the fluid-fluid interface; a static contact angle is used to account for wall adhesion. From the DNS data, we focus on the macroscopic capillary pressure-saturation (Pc-Sw) relation, which is known to be hysteretic, i.e., this relation is flow process (such as drainage, imbibition and scanning curves) and history dependent. In order to overcome the problem of hysteresis, extended theories of multiphase flow hypothesized that the inclusion of specific interfacial area as a state variable will result in a unique relation between capillary pressure, saturation and interfacial area (Pc-Sw-awn). We study the role of specific interfacial area on hysteresis in the macroscopic Pc-Sw relation under non-equilibrium (dynamic) conditions. Under dynamic conditions, capillary pressure depends on the rate of change of the wetting phase saturation, and the dynamic Pc-Sw relation includes the changes caused by viscous effects. Simulations of drainage and imbibition are performed for two capillary numbers by controlling the flow rate of the non-wetting (polydimenthlysiloxane oil) and wetting (water) fluids. From these simulations, the Pc-Sw curves will be estimated; the Pc-S-awn surface will be constructed to determine whether the data points from drainage and imbibition processes fall on a unique surface under transient conditions. Different macroscopic capillary pressure definitions based on phase-averaged pressures and interfacial area will be evaluated. Understanding macroscopic capillary pressure definitions and the uniqueness of the Pc-S- awn relation is step towards complete description of two-phase flow at the Darcy scale.

Fourier Collocation Approach With Mesh Refinement Method for Simulating Transit-Time Ultrasonic Flowmeters Under Multiphase Flow Conditions.

PubMed

Simurda, Matej; Duggen, Lars; Basse, Nils T; Lassen, Benny

2018-02-01

A numerical model for transit-time ultrasonic flowmeters operating under multiphase flow conditions previously presented by us is extended by mesh refinement and grid point redistribution. The method solves modified first-order stress-velocity equations of elastodynamics with additional terms to account for the effect of the background flow. Spatial derivatives are calculated by a Fourier collocation scheme allowing the use of the fast Fourier transform, while the time integration is realized by the explicit third-order Runge-Kutta finite-difference scheme. The method is compared against analytical solutions and experimental measurements to verify the benefit of using mapped grids. Additionally, a study of clamp-on and in-line ultrasonic flowmeters operating under multiphase flow conditions is carried out.

EXPERIMENTAL INVESTIGATION OF RELATIVE PERMEABILITY UPSCALING FROM THE MICRO-SCALE TO THE MACRO-SCALE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laura J. Pyrak-Nolte; Ping Yu; JiangTao Cheng

2002-12-01

The principal challenge of upscaling techniques for multi-phase fluid dynamics in porous media is to determine which properties on the micro-scale can be used to predict macroscopic flow and spatial distribution of phases at core- and field-scales. The most notable outcome of recent theories is the identification of interfacial areas per volume for multiple phases as a fundamental parameter that determines much of the multi-phase properties of the porous medium. A formal program of experimental research was begun to directly test upscaling theories in fluid flow through porous media by comparing measurements of relative permeability and capillary-saturation with measurements ofmore » interfacial area per volume. During this reporting period, we have shown experimentally that the coherence detection can be performed in a borescope. The measurement of interfacial area per volume (IAV), capillary pressure and saturation in two dimensional micro-models structures has shown the existence of a unique relationship among these hydraulic parameters for different pore geometry. The measurement of interfacial area per volume on a three-dimensional natural sample, i.e., sandstone, is essentially completed for imbibition conditions.« less

CO 2 Leakage Into Shallow Aquifers: Modeling CO 2 Gas Evolution and Accumulation at Interfaces of Heterogeneity

DOE PAGES

Porter, Mark L.; Plampin, Michael; Pawar, Rajesh; ...

2014-12-31

The physicochemical processes associated with CO 2 leakage into shallow aquifer systems are complex and span multiple spatial and time scales. Continuum-scale numerical models that faithfully represent the underlying pore-scale physics are required to predict the long-term behavior and aid in risk analysis regarding regulatory and management decisions. This study focuses on benchmarking the numerical simulator, FEHM, with intermediate-scale column experiments of CO 2 gas evolution in homogeneous and heterogeneous sand configurations. Inverse modeling was conducted to calibrate model parameters and determine model sensitivity to the observed steady-state saturation profiles. It is shown that FEHM is a powerful tool thatmore » is capable of capturing the experimentally observed out ow rates and saturation profiles. Moreover, FEHM captures the transition from single- to multi-phase flow and CO 2 gas accumulation at interfaces separating sands. We also derive a simple expression, based on Darcy's law, for the pressure at which CO 2 free phase gas is observed and show that it reliably predicts the location at which single-phase flow transitions to multi-phase flow.« less

Some Boussinesq Equations with Saturation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christou, M. A.

2010-11-25

We investigate numerically some Boussinesq type equations with square or cubic and saturated nonlinearity. We examine the propagation, interaction and overtake interaction of soliton solutions. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the square or cubic nonlinearity without saturation. We calculate numerically the phase shift experienced by the solitons upon collision and conclude the impact of saturation.

The effect of a microscale fracture on dynamic capillary pressure of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Tang, Mingming; Lu, Shuangfang; Zhan, Hongbin; Wenqjie, Guo; Ma, Huifang

2018-03-01

Dynamic capillary pressure (DCP) effects, which is vital for predicting multiphase flow behavior in porous media, refers to the injection rate dependence capillary pressure observed during non-equilibrium displacement experiments. However, a clear picture of the effects of microscale fractures on DCP remains elusive. This study quantified the effects of microscale fractures on DCP and simulated pore-scale force and saturation change in fractured porous media using the multiphase lattice Boltzmann method (LBM). Eighteen simulation cases were carried out to calculate DCP as a function of wetting phase saturation. The effects of viscosity ratio and fracture orientation, aperture and length on DCP and DCP coefficient τ were investigated, where τ refers to the ratio of the difference of DCP and static capillary pressure (SCP) over the rate of wetting-phase saturation change versus time. Significant differences in τ values were observed between unfractured and fractured porous media. The τ values of fractured porous media were 1.1  × 104 Pa ms to 5.68 × 105 Pa ms, which were one or two orders of magnitude lower than those of unfractured porous media with a value of 4 × 106 Pa. ms. A horizontal fracture had greater effects on DCP and τ than a vertical fracture, given the same fracture aperture and length. This study suggested that a microscale fracture might result in large magnitude changes in DCP for two-phase flow.

Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.

The use of numerical programs in research and academic institutions

NASA Astrophysics Data System (ADS)

Scupi, A. A.

2016-08-01

This paper is conceived on the idea that numerical programs using computer models of physical processes can be used both for scientific research and academic teaching to study different phenomena. Computational Fluid Dynamics (CFD) is used today on a large scale in research and academic institutions. CFD development is not limited to computer simulations of fluid flow phenomena. Analytical solutions for most fluid dynamics problems are already available for ideal or simplified situations for different situations. CFD is based on the Navier- Stokes (N-S) equations characterizing the flow of a single phase of any liquid. For multiphase flows the integrated N-S equations are complemented with equations of the Volume of Fluid Model (VOF) and with energy equations. Different turbulent models were used in the paper, each one of them with practical engineering applications: the flow around aerodynamic surfaces used as unconventional propulsion system, multiphase flows in a settling chamber and pneumatic transport systems, heat transfer in a heat exchanger etc. Some of them numerical results were validated by experimental results. Numerical programs are also used in academic institutions where certain aspects of various phenomena are presented to students (Bachelor, Master and PhD) for a better understanding of the phenomenon itself.

Liquid spreading under partial wetting conditions

NASA Astrophysics Data System (ADS)

Chen, M.; Pahlavan, A. A.; Cueto-Felgueroso, L.; McKinley, G. H.; Juanes, R.

2013-12-01

Traditional mathematical descriptions of multiphase flow in porous media rely on a multiphase extension of Darcy's law, and lead to nonlinear second-order (advection-diffusion) partial differential equations for fluid saturations. Here, we study horizontal redistribution of immiscible fluids. The traditional Darcy-flow model predicts that the spreading of a finite amount of liquid in a horizontal porous medium never stops; a prediction that is not substantiated by observation. To help guide the development of new models of multiphase flow in porous media [1], we draw an analogy with the flow of thin films. The flow of thin films over flat surfaces has been the subject of much theoretical, experimental and computational research [2]. Under the lubrication approximation, the classical mathematical model for these flows takes the form of a nonlinear fourth-order PDE, where the fourth-order term models the effect of surface tension [3]. This classical model, however, effectively assumes that the film is perfectly wetting to the substrate and, therefore, does not capture the partial wetting regime. Partial wetting is responsible for stopping the spread of a liquid puddle. Here, we present experiments of (large-volume) liquid spreading over a flat horizontal substrate in the partial wetting regime, and characterize the four spreading regimes that we observe. We extend our previous theoretical work of two-phase flow in a capillary tube [4], and develop a macroscopic phase-field modeling of thin-film flows with partial wetting. Our model naturally accounts for the dynamic contact angle at the contact line, and therefore permits modeling thin-film flows without invoking a precursor film, leading to compactly-supported solutions that reproduce the spreading dynamics and the static equilibrium configuration observed in the experiments. We anticipate that this modeling approach will provide a natural mathematical framework to describe spreading and redistribution of immiscible fluids in porous media. [1] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 101, 244504 (2008). [2] D. Bonn et al., Rev. Mod. Phys. 81, 739-805 (2009). [3] H. E. Huppert, Nature 300, 427-429 (1982). [4] L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 108, 144502 (2012).

Dynamic fluid connectivity during steady-state multiphase flow in a sandstone.

PubMed

Reynolds, Catriona A; Menke, Hannah; Andrew, Matthew; Blunt, Martin J; Krevor, Samuel

2017-08-01

The current conceptual picture of steady-state multiphase Darcy flow in porous media is that the fluid phases organize into separate flow pathways with stable interfaces. Here we demonstrate a previously unobserved type of steady-state flow behavior, which we term "dynamic connectivity," using fast pore-scale X-ray imaging. We image the flow of N 2 and brine through a permeable sandstone at subsurface reservoir conditions, and low capillary numbers, and at constant fluid saturation. At any instant, the network of pores filled with the nonwetting phase is not necessarily connected. Flow occurs along pathways that periodically reconnect, like cars controlled by traffic lights. This behavior is consistent with an energy balance, where some of the energy of the injected fluids is sporadically converted to create new interfaces.

A Model to Couple Flow, Thermal and Reactive Chemical Transport, and Geo-mechanics in Variably Saturated Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.

2015-12-01

This paper presents the development of a THMC (thermal-hydrology-mechanics-chemistry) process model in variably saturated media. The governing equations for variably saturated flow and reactive chemical transport are obtained based on the mass conservation principle of species transport supplemented with Darcy's law, constraint of species concentration, equation of states, and constitutive law of K-S-P (Conductivity-Degree of Saturation-Capillary Pressure). The thermal transport equation is obtained based on the conservation of energy. The geo-mechanic displacement is obtained based on the assumption of equilibrium. Conventionally, these equations have been implicitly coupled via the calculations of secondary variables based on primary variables. The mechanisms of coupling have not been obvious. In this paper, governing equations are explicitly coupled for all primary variables. The coupling is accomplished via the storage coefficients, transporting velocities, and conduction-dispersion-diffusion coefficient tensor; one set each for every primary variable. With this new system of equations, the coupling mechanisms become clear. Physical interpretations of every term in the coupled equations will be discussed. Examples will be employed to demonstrate the intuition and superiority of these explicit coupling approaches. Keywords: Variably Saturated Flow, Thermal Transport, Geo-mechanics, Reactive Transport.

Compressible instability of rapidly expanding spherical material interfaces

NASA Astrophysics Data System (ADS)

Mankbadi, Mina Reda

The focus herein is on the instability of a material interface formed during an abrupt release of concentrated energy as in detonative combustion, explosive dispersals, and inertial-confinement fusion. These applications are modeled as a spherical shock-tube in which high-pressure gas initially contained in a small spherical shell is suddenly released. A forward-moving shock and an inward-moving secondary shock are formed, and between them a material interface develops that separates high-density fluid from the low-density one. The wrinkling of this interface controls mixing and energy release. The interface's stability is studied with and without the inclusion of metalized particulates. A numerical scheme is developed to discretize the full nonlinear equations of the base flow, and the 3D linearized perturbed flow equations. Linearization is followed by spherical harmonic decomposition of the disturbances, thereby reducing the 3D computational domain to one-dimensional radial domain. The 3D physical nature of the disturbances is maintained throughout the procedure. An extended Roe-Pike scheme coupled with a WENO scheme is developed to capture the discontinuities and accurately predict the disturbances. In Chapter 2, the contact interface's stability is analyzed in the inviscid single-phase. The disturbances grow exponentially and the growth rate is insensitive to the radial initial-disturbance profile. For wave numbers less than 100, the results are in accordance with previous theories but clarify that compressibility reduces the growth rate. Unlike the classical RTI, the growth rate reaches saturation at high wavenumbers. The parametric studies show that for specific ratios of initial pressure and temperature, the instability can be eliminated altogether. Chapter 3 discusses the full effects of viscosity and thermal diffusivity. Although Prandtl number effects are minimal, viscous effects dampen the high-wave numbers. For a given Reynolds number there is a peak wave number at which the disturbances are most amplified. In Chapter 4, the multiphase case with metalized particles is investigated. The quasi steady gas-particle interaction forces and heat transfer decelerate the contact interface and reduce its Atwood number, which results in reducing the growth of the interfacial instabilities. A parametric study of the multiphase instability is presented to assist in controlling the instability.

Volatile dynamics in crystal-rich magma bodies, perspectives from laboratory experiments and theory

NASA Astrophysics Data System (ADS)

Faroughi, S.; Parmigiani, A.; Huber, C.

2013-12-01

The amount of volatiles and the dynamics of bubbles play a significant role on the transition between different volcanic eruption behaviors. The transport of exsolved volatiles through zoned magma chambers is complex and remains poorly constrained. Here we focus on the different transport of volatiles under two end member regimes: crystal-poor systems (bubbles form a suspension) versus crystal-rich reservoirs (multiphase porous media flow). We present a combination of multiphase flow laboratory experiments (using silicon oil and water) and a theoretical argument based on Stokes flow streamfunctions to contrast the differences between the transport of exsolved volatiles in both regimes. The first set of experiments involves the buoyant migration of water droplets in silicon oil in the absence of glass beads. We measure the non-linear hydrodynamic interaction between bubbles and its effect on slowing down the average flux of water droplets as the water volume fraction increases. Our experimental results are compared to a theoretical argument in which a streamfunction formulation is used to estimate the effect of a suspension on bubble migration. We find a good agreement between the new theory and our experimental results. The second set of experiments focuses on the transport of water (non-wetting fluid) in porous media saturated with viscous silicon oils. Contrary to suspension dynamics, in multiphase porous media, an increase in the saturation of non-wetting fluid leads to a non-linear increase in its volumetric flux. The steady-state migration of non-wetting fluid is controlled by the formation of viscous fingering instability that greatly enhances transport. We propose that the regime of energy dissipation during the migration of bubbles in heterogeneous magma reservoirs can change, leading to bubble accumulation in crystal-poor regions as fingering becomes unstable and volatiles form a disperse bubble suspension.

Equations and simulations for multiphase compressible gas-dust flows

NASA Astrophysics Data System (ADS)

Oran, Elaine; Houim, Ryan

2014-11-01

Dust-gas multiphase flows are important in physical scenarios such as dust explosions in coal mines, asteroid impact disturbing lunar regolith, and soft aircraft landings dispersing desert or beach sand. In these cases, the gas flow regime can range from highly subsonic and nearly incompressible to supersonic and shock-laden flow, the grain packing can range from fully packed to completely dispersed, and both the gas and the dust can range from chemically inert to highly exothermic. To cover the necessary parameter range in a single model, we solve coupled sets of Navier-Stokes equations describing the background gas and the dust. As an example, a reactive-dust explosion that results in a type of shock-flame complex is described and discussed. Sponsored by the University of Maryland through Minta Martin Endowment Funds in the Department of Aerospace Engineering, and through the Glenn L. Martin Institute Chaired Professorship at the A. James Clark School of Engineering.

Predictive uncertainty analysis of plume distribution for geological carbon sequestration using sparse-grid Bayesian method

NASA Astrophysics Data System (ADS)

Shi, X.; Zhang, G.

2013-12-01

Because of the extensive computational burden, parametric uncertainty analyses are rarely conducted for geological carbon sequestration (GCS) process based multi-phase models. The difficulty of predictive uncertainty analysis for the CO2 plume migration in realistic GCS models is not only due to the spatial distribution of the caprock and reservoir (i.e. heterogeneous model parameters), but also because the GCS optimization estimation problem has multiple local minima due to the complex nonlinear multi-phase (gas and aqueous), and multi-component (water, CO2, salt) transport equations. The geological model built by Doughty and Pruess (2004) for the Frio pilot site (Texas) was selected and assumed to represent the 'true' system, which was composed of seven different facies (geological units) distributed among 10 layers. We chose to calibrate the permeabilities of these facies. Pressure and gas saturation values from this true model were then extracted and used as observations for subsequent model calibration. Random noise was added to the observations to approximate realistic field conditions. Each simulation of the model lasts about 2 hours. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid stochastic collocation method. This surrogate response surface global optimization algorithm is firstly used to calibrate the model parameters, then prediction uncertainty of the CO2 plume position is quantified due to the propagation from parametric uncertainty in the numerical experiments, which is also compared to the actual plume from the 'true' model. Results prove that the approach is computationally efficient for multi-modal optimization and prediction uncertainty quantification for computationally expensive simulation models. Both our inverse methodology and findings can be broadly applicable to GCS in heterogeneous storage formations.

Methane Leakage From Hydrocarbon Wellbores into Overlying Groundwater: Numerical Investigation of the Multiphase Flow Processes Governing Migration

NASA Astrophysics Data System (ADS)

Rice, Amy K.; McCray, John E.; Singha, Kamini

2018-04-01

Methane leakage due to compromised hydrocarbon well integrity can lead to impaired groundwater quality. Here we use a three-dimensional, multiphase (vapor and aqueous), multicomponent (methane, water, salt), numerical model (TOUGH2 EOS7C) to investigate hydrogeological conditions that could result in groundwater contamination from natural gas wellbore leakage that migrates upward toward a freshwater aquifer. The conceptual model used for the simulations assumes methane leakage at 20-30 m below groundwater. We perform 180 simulations for a sensitivity analysis, examining (1) multiphase flow parameters related to storage, capillarity, and relative permeability, including porosity (ϕ), initial fluid-phase saturation (SL), and van Genuchten n and α, (2) geostatistical variations in intrinsic permeability (ki), and (3) methane source-zone pressure. Simulated mean ki values are 10-18 and 10-13 m2 with variances of 1 and 5 m4. Simulated source-zone pressures range from just over ambient hydrostatic pressure at the depth of leakage (100 kPa) to the maximum pressure that steel casings are commonly rated to withstand (20,340 kPa). ki, initial SL, ϕ, and van Genuchten's n and α were the most important parameters in determining the volume of methane reaching groundwater during a given time period. Multiphase parameterization of formations underlying freshwater aquifers and overlying hydrocarbon production zones is fundamental to assessing aquifer vulnerability to methane leakage.

Fluid-particle characteristics in fully-developed cluster-induced turbulence

NASA Astrophysics Data System (ADS)

Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney

2014-11-01

In this study, we present a theoretical framework for collisional fluid-particle turbulence. To identify the key mechanisms responsible for energy exchange between the two phases, an Eulerian-Lagrangian strategy is used to simulate fully-developed cluster-inudced turbulence (CIT) under a range of Reynolds numbers, where fluctuations in particle concentration generate and sustain the carrier-phase turbulence. Using a novel filtering approach, a length-scale separation between the correlated particle velocity and uncorrelated granular temperature (GT) is achieved. This separation allows us to extract the instantaneous Eulerian volume fraction, velocity and GT fields from the Lagrangian data. Direct comparisons can thus be made with the relevant terms that appear in the multiphase turbulence model. It is shown that the granular pressure is highly anisotropic, and thus additional transport equations (as opposed to a single equation for GT) are necessary in formulating a predictive multiphase turbulence model. In addition to reporting the relevant contributions to the Reynolds stresses of each phase, two-point statistics, integral length/timescales, averages conditioned on the local volume fraction, and PDFs of the key multiphase statistics are presented and discussed. The research reported in this paper is partially supported by the HPC equipment purchased through U.S. National Science Foundation MRI Grant Number CNS 1229081 and CRI Grant Number 1205413.

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow

NASA Astrophysics Data System (ADS)

Huang, Rongzong; Wu, Huiying; Adams, Nikolaus A.

2018-05-01

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3 ) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

Verification of capillary pressure functions and relative permeability equations for gas production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jang, Jaewon

The understanding of multiphase fluid flow in porous media is of great importance in many fields such as enhanced oil recovery, hydrology, CO 2 sequestration, contaminants cleanup and natural gas production from hydrate bearing sediments. However, there are many unanswered questions about the key parameters that characterize gas and water flows in porous media. The characteristics of multiphase fluid flow in porous media such as water retention curve, relative permeability, preferential fluid flow patterns and fluid-particle interaction should be taken into consideration for a fundamental understanding of the behavior of pore scale systems.

The impact of capillary backpressure on spontaneous counter-current imbibition in porous media

NASA Astrophysics Data System (ADS)

Foley, Amir Y.; Nooruddin, Hasan A.; Blunt, Martin J.

2017-09-01

We investigate the impact of capillary backpressure on spontaneous counter-current imbibition. For such displacements in strongly water-wet systems, the non-wetting phase is forced out through the inlet boundary as the wetting phase imbibes into the rock, creating a finite capillary backpressure. Under the assumption that capillary backpressure depends on the water saturation applied at the inlet boundary of the porous medium, its impact is determined using the continuum modelling approach by varying the imposed inlet saturation in the analytical solution. We present analytical solutions for the one-dimensional incompressible horizontal displacement of a non-wetting phase by a wetting phase in a porous medium. There exists an inlet saturation value above which any change in capillary backpressure has a negligible impact on the solutions. Above this threshold value, imbibition rates and front positions are largely invariant. A method for identifying this inlet saturation is proposed using an analytical procedure and we explore how varying multiphase flow properties affects the analytical solutions and this threshold saturation. We show the value of this analytical approach through the analysis of previously published experimental data.

Numerical modelling of multiphase liquid-vapor-gas flows with interfaces and cavitation

NASA Astrophysics Data System (ADS)

Pelanti, Marica

2017-11-01

We are interested in the simulation of multiphase flows where the dynamical appearance of vapor cavities and evaporation fronts in a liquid is coupled to the dynamics of a third non-condensable gaseous phase. We describe these flows by a single-velocity three-phase compressible flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. The flow equations are solved by a mixture-energy-consistent finite volume wave propagation scheme, combined with simple and robust procedures for the treatment of the stiff relaxation terms. An analytical study of the characteristic wave speeds of the hierarchy of relaxed models associated to the parent model system is also presented. We show several numerical experiments, including two-dimensional simulations of underwater explosive phenomena where highly pressurized gases trigger cavitation processes close to a rigid surface or to a free surface. This work was supported by the French Government Grant DGA N. 2012.60.0011.00.470.75.01, and partially by the Norwegian Grant RCN N. 234126/E30.

EXPERIMENTAL INVESTIGATION OF RELATIVE PERMEABILITY UPSCALING FROM THE MICRO-SCALE TO THE MACRO-SCALE

DOE Office of Scientific and Technical Information (OSTI.GOV)

JiangTao Cheng; Ping Yu; William Headley

2001-12-01

The principal challenge of upscaling techniques for multi-phase fluid dynamics in porous media is to determine which properties on the micro-scale can be used to predict macroscopic flow and spatial distribution of phases at core- and field-scales. The most notable outcome of recent theories is the identification of interfacial areas per volume for multiple phases as a fundamental parameter that determines much of the multi-phase properties of the porous medium. A formal program of experimental research was begun to directly test upscaling theories in fluid flow through porous media by comparing measurements of relative permeability and capillary-saturation with measurements ofmore » interfacial area per volume. During this reporting period, we have shown experimentally and theoretically that the optical coherence imaging system is optimized for sandstone. The measurement of interfacial area per volume (IAV), capillary pressure and saturation in two dimensional micro-models structures that are statistically similar to real porous media has shown the existence of a unique relationship among these hydraulic parameters. The measurement of interfacial area per volume on a three-dimensional natural sample, i.e., sandstone, has the same length-scale as the values of IAV determined for the two-dimensional micro-models.« less

Simulating anomalous transport and multiphase segregation in porous media with the Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Matin, Rastin; Hernandez, Anier; Misztal, Marek; Mathiesen, Joachim

2015-04-01

Many hydrodynamic phenomena ranging from flows at micron scale in porous media, large Reynolds numbers flows, non-Newtonian and multiphase flows have been simulated on computers using the lattice Boltzmann (LB) method. By solving the Lattice Boltzmann Equation on unstructured meshes in three dimensions, we have developed methods to efficiently model the fluid flow in real rock samples. We use this model to study the spatio-temporal statistics of the velocity field inside three-dimensional real geometries and investigate its relation to the, in general, anomalous transport of passive tracers for a wide range of Peclet and Reynolds numbers. We extend this model by free-energy based method, which allows us to simulate binary systems with large-density ratios in a thermodynamically consistent way and track the interface explicitly. In this presentation we will present our recent results on both anomalous transport and multiphase segregation.

A Modified Benedict-Webb-Rubin Equation of State for the Thermodynamic Properties of R152a (1,1-difluoroethane)

NASA Astrophysics Data System (ADS)

Outcalt, Stephanie L.; McLinden, Mark O.

1996-03-01

A modified Benedict-Webb-Rubin (MBWR) equation of state has been developed for R152a (1,1-difluoroethane). The correlation is based on a selection of available experimental thermodynamic property data. Single-phase pressure-volume-temperature (PVT), heat capacity, and sound speed data, as well as second virial coefficient, vapor pressure, and saturated liquid and saturated vapor density data, were used with multi-property linear least-squares fitting to determine the 32 adjustable coefficients of the MBWR equation. Ancillary equations representing the vapor pressure, saturated liquid and saturated vapor densities, and the ideal gas heat capacity were determined. Coefficients for the equation of state and the ancillary equations are given. Experimental data used in this work covered temperatures from 162 K to 453 K and pressures to 35 MPa. The MBWR equation established in this work may be used to predict thermodynamic properties of R152a from the triple-point temperature of 154.56 K to 500 K and for pressures up to 60 MPa except in the immediate vicinity of the critical point.

Thermal instability in gravitationally stratified plasmas: implications for multiphase structure in clusters and galaxy haloes

NASA Astrophysics Data System (ADS)

McCourt, Michael; Sharma, Prateek; Quataert, Eliot; Parrish, Ian J.

2012-02-01

We study the interplay among cooling, heating, conduction and magnetic fields in gravitationally stratified plasmas using simplified, plane-parallel numerical simulations. Since the physical heating mechanism remains uncertain in massive haloes such as groups or clusters, we adopt a simple, phenomenological prescription which enforces global thermal equilibrium and prevents a cooling flow. The plasma remains susceptible to local thermal instability, however, and cooling drives an inward flow of material. For physically plausible heating mechanisms in clusters, the thermal stability of the plasma is independent of its convective stability. We find that the ratio of the cooling time-scale to the dynamical time-scale tcool/tff controls the non-linear evolution and saturation of the thermal instability: when tcool/tff≲ 1, the plasma develops extended multiphase structure, whereas when tcool/tff≳ 1 it does not. (In a companion paper, we show that the criterion for thermal instability in a more realistic, spherical potential is somewhat less stringent, tcool/tff≲ 10.) When thermal conduction is anisotropic with respect to the magnetic field, the criterion for multiphase gas is essentially independent of the thermal conductivity of the plasma. Our criterion for local thermal instability to produce multiphase structure is an extension of the cold versus hot accretion modes in galaxy formation that applies at all radii in hot haloes, not just to the virial shock. We show that this criterion is consistent with data on multiphase gas in galaxy groups and clusters; in addition, when tcool/tff≳ 1, the net cooling rate to low temperatures and the mass flux to small radii are suppressed enough relative to models without heating to be qualitatively consistent with star formation rates and X-ray line emission in groups and clusters.

Electrokinetic coupling in unsaturated porous media.

PubMed

Revil, A; Linde, N; Cerepi, A; Jougnot, D; Matthäi, S; Finsterle, S

2007-09-01

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions.

Laboratory and numerical decompression experiments: an insight into the nucleation and growth of bubbles

NASA Astrophysics Data System (ADS)

Spina, L.; Colucci, S.; De'Michieli Vitturi, M.; Scheu, B.; Dingwell, D. B.

2014-12-01

Numerical modeling, joined with experimental investigations, is fundamental for studying the dynamics of magmatic fluid into the conduit, where direct observations are unattainable. Furthermore, laboratory experiments can provide invaluable data to vunalidate complex multiphase codes. With the aim on unveil the essence of nucleation process, as well as the behavior of the multiphase magmatic fluid, we performed slow decompression experiments in a shock tube system. We choose silicon oil as analogue for the magmatic melt, and saturated it with Argon at 10 MPa for 72h. The slow decompression to atmospheric conditions was monitored through a high speed camera and pressure sensors, located into the experimental conduit. The experimental conditions of the decompression process have then been reproduced numerically with a compressible multiphase solver based on OpenFOAM. Numerical simulations have been performed by the OpenFOAM compressibleInterFoam solver for 2 compressible, non-isothermal immiscible fluids, using a VOF (volume of fluid) phase-fraction based interface capturing approach. The data extracted from 2D images obtained from laboratory analyses were compared to the outcome of numerical investigation, showing the capability of the model to capture the main processes studied.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kauweloa, K; Gutierrez, A; Bergamo, A

Purpose: There is growing interest about biological effective dose (BED) and its application in treatment plan evaluation due to its stronger correlation with treatment outcome. An approximate biological effective dose (BEDA) equation was introduced to simplify BED calculations by treatment planning systems in multi-phase treatments. The purpose of this work is to reveal its mathematical properties relative to the true, multi-phase BED (BEDT) equation. Methods: The BEDT equation was derived and used to reveal the mathematical properties of BEDA. MATLAB (MathWorks, Natick, MA) was used to simulate and analyze common and extreme clinical multi-phase cases. In those cases, percent errormore » (Perror) and Bland-Altman analysis were used to study the significance of the inaccuracies of BEDA for different combinations of total doses, numbers of fractions, doses per fractions and α over β values. All the calculations were performed on a voxel-basis in order to study how dose distributions would affect the accuracy of BEDA. Results: When the voxel dose-per-fractions (DPF) delivered by both phases are equal, BEDA and BEDT are equal. In heterogeneous dose distributions, which significantly vary between the phases, there are fewer occurrences of equal DPFs and hence the imprecision of BEDA is greater. It was shown that as the α over β ratio increased the accuracy of BEDA would improve. Examining twenty-four cases, it was shown that the range of DPF ratios for a 3 Perror varied from 0.32 to 7.50Gy, whereas for Perror of 1 the range varied from 0.50 to 2.96Gy. Conclusion: The DPF between the different phases should be equal in order to render BEDA accurate. OARs typically receive heterogeneous dose distributions hence the probability of equal DPFs is low. Consequently, the BEDA equation should only be used for targets or OARs that receive uniform or very similar dose distributions by the different treatment phases.« less

A novel consistent and well-balanced algorithm for simulations of multiphase flows on unstructured grids

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2017-12-01

We discuss the development and assessment of a robust numerical algorithm for simulating multiphase flows with complex interfaces and high density ratios on arbitrary polygonal meshes. The algorithm combines the volume-of-fluid method with an incremental projection approach for incompressible multiphase flows in a novel hybrid staggered/non-staggered framework. The key principles that characterise the algorithm are the consistent treatment of discrete mass and momentum transport and the similar discretisation of force terms appearing in the momentum equation. The former is achieved by invoking identical schemes for convective transport of volume fraction and momentum in the respective discrete equations while the latter is realised by representing the gravity and surface tension terms as gradients of suitable scalars which are then discretised in identical fashion resulting in a balanced formulation. The hybrid staggered/non-staggered framework employed herein solves for the scalar normal momentum at the cell faces, while the volume fraction is computed at the cell centroids. This is shown to naturally lead to similar terms for pressure and its correction in the momentum and pressure correction equations respectively, which are again treated discretely in a similar manner. We show that spurious currents that corrupt the solution may arise both from an unbalanced formulation where forces (gravity and surface tension) are discretised in dissimilar manner and from an inconsistent approach where different schemes are used to convect the mass and momentum, with the latter prominent in flows which are convection-dominant with high density ratios. Interestingly, the inconsistent approach is shown to perform as well as the consistent approach even for high density ratio flows in some cases while it exhibits anomalous behaviour for other scenarios, even at low density ratios. Using a plethora of test problems of increasing complexity, we conclusively demonstrate that the consistent transport and balanced force treatment results in a numerically stable solution procedure and physically consistent results. The algorithm proposed in this study qualifies as a robust approach to simulate multiphase flows with high density ratios on unstructured meshes and may be realised in existing flow solvers with relative ease.

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

Comprehensive Approaches to Multiphase Flows in Geophysics - Application to nonisothermal, nonhomogenous, unsteady, large-scale, turbulent dusty clouds I. Hydrodynamic and Thermodynamic RANS and LES Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

S. Dartevelle

2005-09-05

The objective of this manuscript is to fully derive a geophysical multiphase model able to ''accommodate'' different multiphase turbulence approaches; viz., the Reynolds Averaged Navier-Stokes (RANS), the Large Eddy Simulation (LES), or hybrid RANSLES. This manuscript is the first part of a larger geophysical multiphase project--lead by LANL--that aims to develop comprehensive modeling tools for large-scale, atmospheric, transient-buoyancy dusty jets and plume (e.g., plinian clouds, nuclear ''mushrooms'', ''supercell'' forest fire plumes) and for boundary-dominated geophysical multiphase gravity currents (e.g., dusty surges, diluted pyroclastic flows, dusty gravity currents in street canyons). LES is a partially deterministic approach constructed on either amore » spatial- or a temporal-separation between the large and small scales of the flow, whereas RANS is an entirely probabilistic approach constructed on a statistical separation between an ensemble-averaged mean and higher-order statistical moments (the so-called ''fluctuating parts''). Within this specific multiphase context, both turbulence approaches are built up upon the same phasic binary-valued ''function of presence''. This function of presence formally describes the occurrence--or not--of any phase at a given position and time and, therefore, allows to derive the same basic multiphase Navier-Stokes model for either the RANS or the LES frameworks. The only differences between these turbulence frameworks are the closures for the various ''turbulence'' terms involving the unknown variables from the fluctuating (RANS) or from the subgrid (LES) parts. Even though the hydrodynamic and thermodynamic models for RANS and LES have the same set of Partial Differential Equations, the physical interpretations of these PDEs cannot be the same, i.e., RANS models an averaged field, while LES simulates a filtered field. In this manuscript, we also demonstrate that this multiphase model fully fulfills the second law of thermodynamics and fulfills the necessary requirements for a well-posed initial-value problem. In the next manuscripts, we will further develop specific closures for multiphase RANS, LES, and hybrid-LES.« less

Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast.

PubMed

Shao, J Y; Shu, C; Huang, H B; Chew, Y T

2014-03-01

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

Numerical modelling of multiphase multicomponent reactive transport in the Earth's interior

NASA Astrophysics Data System (ADS)

Oliveira, Beñat; Afonso, Juan Carlos; Zlotnik, Sergio; Diez, Pedro

2018-01-01

We present a conceptual and numerical approach to model processes in the Earth's interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multicomponent in the sense that the compositions of the system and its constituent phases are expressed by a full set of fundamental chemical components (e.g. SiO2, Al2O3, MgO, etc.) rather than proxies. These chemical components evolve, react with and partition into different phases according to an internally consistent thermodynamic model. We combine concepts from Ensemble Averaging and Classical Irreversible Thermodynamics to obtain sets of macroscopic balance equations that describe the evolution of systems governed by multiphase multicomponent reactive transport (MPMCRT). Equilibrium mineral assemblages, their compositions and physical properties, and closure relations for the balance equations are obtained via a `dynamic' Gibbs free-energy minimization procedure (i.e. minimizations are performed on-the-fly as needed by the simulation). Surface tension and surface energy contributions to the dynamics and energetics of the system are taken into account. We show how complex rheologies, that is, visco-elasto-plastic, and/or different interfacial models can be incorporated into our MPMCRT ensemble-averaged formulation. The resulting model provides a reliable platform to study the dynamics and nonlinear feedbacks of MPMCRT systems of different nature and scales, as well as to make realistic comparisons with both geophysical and geochemical data sets. Several numerical examples are presented to illustrate the benefits and limitations of the model.

High-Fidelity Micromechanics Model Developed for the Response of Multiphase Materials

NASA Technical Reports Server (NTRS)

Aboudi, Jacob; Pindera, Marek-Jerzy; Arnold, Steven M.

2002-01-01

A new high-fidelity micromechanics model has been developed under funding from the NASA Glenn Research Center for predicting the response of multiphase materials with arbitrary periodic microstructures. The model's analytical framework is based on the homogenization technique, but the method of solution for the local displacement and stress fields borrows concepts previously employed in constructing the higher order theory for functionally graded materials. The resulting closed-form macroscopic and microscopic constitutive equations, valid for both uniaxial and multiaxial loading of periodic materials with elastic and inelastic constitutive phases, can be incorporated into a structural analysis computer code. Consequently, this model now provides an alternative, accurate method.

The application of single particle hydrodynamics in continuum models of multiphase flow

NASA Technical Reports Server (NTRS)

Decker, Rand

1988-01-01

A review of the application of single particle hydrodynamics in models for the exchange of interphase momentum in continuum models of multiphase flow is presented. Considered are the equations of motion for a laminar, mechanical two phase flow. Inherent to this theory is a model for the interphase exchange of momentum due to drag between the dispersed particulate and continuous fluid phases. In addition, applications of two phase flow theory to de-mixing flows require the modeling of interphase momentum exchange due to lift forces. The applications of single particle analysis in deriving models for drag and lift are examined.

A volume-filtered formulation to capture particle-shock interactions in multiphase compressible flows

NASA Astrophysics Data System (ADS)

Shallcross, Gregory; Capecelatro, Jesse

2017-11-01

Compressible particle-laden flows are common in engineering systems. Applications include but are not limited to water injection in high-speed jet flows for noise suppression, rocket-plume surface interactions during planetary landing, and explosions during coal mining operations. Numerically, it is challenging to capture these interactions due to the wide range of length and time scales. Additionally, there are many forms of the multiphase compressible flow equations with volume fraction effects, some of which are conflicting in nature. The purpose of this presentation is to develop the capability to accurately capture particle-shock interactions in systems with a large number of particles from dense to dilute regimes. A thorough derivation of the volume filtered equations is presented. The volume filtered equations are then implemented in a high-order, energy-stable Eulerian-Lagrangian framework. We show this framework is capable of decoupling the fluid mesh from the particle size, enabling arbitrary particle size distributions in the presence of shocks. The proposed method is then assessed against particle-laden shock tube data. Quantities of interest include fluid-phase pressure profiles and particle spreading rates. The effect of collisions in 2D and 3D are also evaluated.

A simple mass-conserved level set method for simulation of multiphase flows

NASA Astrophysics Data System (ADS)

Yuan, H.-Z.; Shu, C.; Wang, Y.; Shu, S.

2018-04-01

In this paper, a modified level set method is proposed for simulation of multiphase flows with large density ratio and high Reynolds number. The present method simply introduces a source or sink term into the level set equation to compensate the mass loss or offset the mass increase. The source or sink term is derived analytically by applying the mass conservation principle with the level set equation and the continuity equation of flow field. Since only a source term is introduced, the application of the present method is as simple as the original level set method, but it can guarantee the overall mass conservation. To validate the present method, the vortex flow problem is first considered. The simulation results are compared with those from the original level set method, which demonstrates that the modified level set method has the capability of accurately capturing the interface and keeping the mass conservation. Then, the proposed method is further validated by simulating the Laplace law, the merging of two bubbles, a bubble rising with high density ratio, and Rayleigh-Taylor instability with high Reynolds number. Numerical results show that the mass is a well-conserved by the present method.

Tar Production from Biomass Pyrolysis in a Fluidized Bed Reactor: A Novel Turbulent Multiphase Flow Formulation

NASA Technical Reports Server (NTRS)

Bellan, J.; Lathouwers, D.

2000-01-01

A novel multiphase flow model is presented for describing the pyrolysis of biomass in a 'bubbling' fluidized bed reactor. The mixture of biomass and sand in a gaseous flow is conceptualized as a particulate phase composed of two classes interacting with the carrier gaseous flow. The solid biomass is composed of three initial species: cellulose, hemicellulose and lignin. From each of these initial species, two new solid species originate during pyrolysis: an 'active' species and a char, thus totaling seven solid-biomass species. The gas phase is composed of the original carrier gas (steam), tar and gas; the last two species originate from the volumetric pyrolysis reaction. The conservation equations are derived from the Boltzmann equations through ensemble averaging. Stresses in the gaseous phase are the sum of the Newtonian and Reynolds (turbulent) contributions. The particulate phase stresses are the sum of collisional and Reynolds contributions. Heat transfer between phases, and heat transfer between classes in the particulate phase is modeled, the last resulting from collisions between sand and biomass. Closure of the equations must be performed by modeling the Reynolds stresses for both phases. The results of a simplified version (first step) of the model are presented.

Efficient Reservoir Simulation with Cubic Plus Association and Cross-Association Equation of State for Multicomponent Three-Phase Compressible Flow with Applications in CO2 Storage and Methane Leakage

NASA Astrophysics Data System (ADS)

Moortgat, J.

2017-12-01

We present novel simulation tools to model multiphase multicomponent flow and transport in porous media for mixtures that contain non-polar hydrocarbons, self-associating polar water, and cross-associating molecules like methane, ethane, unsaturated hydrocarbons, CO2 and H2S. Such mixtures often occur when CO2 is injected and stored in saline aquifers, or when methane is leaking into groundwater. To accurately predict the species transfer between aqueous, gaseous and oleic phases, and the subsequent change in phase properties, the self- and cross-associating behavior of molecules needs to be taken into account, particularly at the typical temperatures and pressures in deep formations. The Cubic-Plus-Association equation-of-state (EOS) has been demonstrated to be highly accurate for such problems but its excessive computational cost has prevented widespread use in reservoir simulators. We discuss the thermodynamical framework and develop sophisticated numerical algorithms that allow reservoir simulations with efficiencies comparable to a simple cubic EOS. This approach improves our predictive powers for highly nonlinear fluid behavior related to geological carbon sequestration, such as density driven flow and natural convection (solubility trapping), evaporation of water into the CO2-rich gas phase, and competitive dissolution-evaporation when CO2 is injected in, e.g., methane saturated aquifers. Several examples demonstrate the accuracy and robustness of this EOS framework for complex applications.

Non-stationary filtration mode during chemical reactions with the gas phase

NASA Astrophysics Data System (ADS)

Zavialov, Ivan; Konyukhov, Andrey; Negodyaev, Sergey

2015-04-01

An experimental and numerical study of filtration accompanied by chemical reactions between displacing fluid and solid skeleton is considered. Glass balls (400-500 μm in diameter) were placed in 1 cm gap between two glass sheets and were used as model porous medium. The baking soda was added to the glass balls. The 70% solution of acetic acid was used as the displacer. The modeling porous medium was saturated with a mineral oil, and then 70% solution of colored acetic acid was pumped through the medium. The glass balls and a mineral oil have a similar refractive index, so the model porous medium was optically transparent. During the filtration, the gas phase was generated by the chemical reactions between the baking soda and acetic acid, and time-dependent displacement of the chemical reaction front was observed. The front of the chemical reaction was associated with the most intensive gas separation. The front moved, stopped, and then moved again to the area where it had been already. We called this process a secondary oxidation wave. To describe this effect, we added to the balance equations a term associated with the formation and disappearance of phases due to chemical reactions. The equations were supplemented by Darcy's law for multiphase filtration. Nonstationarity front propagation of the chemical reaction in the numerical experiment was observed at Damköhler numbers greater than 100. The mathematical modelling was agreed well with the experimental results.

A New Numerical Scheme for Cosmic-Ray Transport

NASA Astrophysics Data System (ADS)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

Effect of CH4 on the CO2 breakthrough pressure and permeability of partially saturated low-permeability sandstone in the Ordos Basin, China

NASA Astrophysics Data System (ADS)

Zhao, Yan; Yu, Qingchun

2018-01-01

The behavior of CO2 that coexists with CH4 and the effect of CH4 on the CO2 stream need to be deeply analyzed and studied, especially in the presence of water. Our previous studies investigated the breakthrough pressure and permeability of pure CO2 in five partially saturated low-permeability sandstone core samples from the Ordos Basin, and we concluded that rocks with a small pore size and low permeability show considerable sealing capacity even under unsaturated conditions. In this paper, we selected three of these samples for CO2-CH4 gas-mixture breakthrough experiments under various degrees of water saturation. The breakthrough experiments were performed by increasing the gas pressure step by step until breakthrough occurred. Then, the effluent gas mixture was collected for chromatographic partitioning analysis. The results indicate that CH4 significantly affects the breakthrough pressure and permeability of CO2. The presence of CH4 in the gas mixture increases the interfacial tension and, thus, the breakthrough pressure. Therefore, the injected gas mixture that contains the highest (lowest) mole fraction of CH4 results in the largest (smallest) breakthrough pressure. The permeability of the gas mixture is greater than that for pure CO2 because of CH4, and the effective permeability decreases with increased breakthrough pressure. Chromatographic partitioning of the effluent mixture gases indicates that CH4 breaks through ahead of CO2 as a result of its weaker solubility in water. Correlations are established between (1) the breakthrough pressure and water saturation, (2) the effective permeability and water saturation, (3) the breakthrough pressure and effective permeability, and (4) the mole fraction of CO2/CH4 in the effluent mixture gases and water saturation. These results deepen our understanding of the multi-phase flow behavior in the porous media under unsaturated conditions, which have implications for formulating emergency response plans for gas leakage into unsaturated zones. Finally, knowing the flow characteristic of gas mixture can guide CO2 storage, CO2-EOR and CO2-ECBM projects. Future studies should pay attention to the effects of saline water with different salt types and concentrations on the multi-phase flow behavior with applications to geological CO2 storage and energy storage using CH4.

An Efficient Implementation of the GMC Micromechanics Model for Multi-Phased Materials with Complex Microstructures

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Bednarcyk, Brett A.

1997-01-01

An efficient implementation of the generalized method of cells micromechanics model is presented that allows analysis of periodic unidirectional composites characterized by repeating unit cells containing thousands of subcells. The original formulation, given in terms of Hill's strain concentration matrices that relate average subcell strains to the macroscopic strains, is reformulated in terms of the interfacial subcell tractions as the basic unknowns. This is accomplished by expressing the displacement continuity equations in terms of the stresses and then imposing the traction continuity conditions directly. The result is a mixed formulation wherein the unknown interfacial subcell traction components are related to the macroscopic strain components. Because the stress field throughout the repeating unit cell is piece-wise uniform, the imposition of traction continuity conditions directly in the displacement continuity equations, expressed in terms of stresses, substantially reduces the number of unknown subcell traction (and stress) components, and thus the size of the system of equations that must be solved. Further reduction in the size of the system of continuity equations is obtained by separating the normal and shear traction equations in those instances where the individual subcells are, at most, orthotropic. The reformulated version facilitates detailed analysis of the impact of the fiber cross-section geometry and arrangement on the response of multi-phased unidirectional composites with and without evolving damage. Comparison of execution times obtained with the original and reformulated versions of the generalized method of cells demonstrates the new version's efficiency.

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

Grain transport mechanics in shallow flow

USDA-ARS?s Scientific Manuscript database

A physical model based on continuum multiphase flow is described to represent saltating transport of grains in shallow overland flows. The two-phase continuum flow of water and sediment considers coupled St.Venant type equations. The interactive cumulative effect of grains is incorporated by a dispe...

Grain transport mechanics in shallow overland flow

USDA-ARS?s Scientific Manuscript database

A physical model based on continuum multiphase flow is described to represent saltating transport of grains in shallow overland flow. The two phase continuum flow of water and sediment considers coupled St.Venant type equations. The interactive cumulative effect of grains is incorporated by a disper...

EXPERIMENTAL INVESTIGATION OF RELATIVE PERMEABILITY UPSCALING FROM THE MICRO-SCALE TO THE MACRO-SCALE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laura J. Pyrak-Nolte; Nicholas J. Giordano; David D. Nolte

2004-03-01

The principal challenge of upscaling techniques for multi-phase fluid dynamics in porous media is to determine which properties on the micro-scale can be used to predict macroscopic flow and spatial distribution of phases at core- and field-scales. The most notable outcome of recent theories is the identification of interfacial areas per volume for multiple phases as a fundamental parameter that determines much of the multi-phase properties of the porous medium. A formal program of experimental research was begun to directly test upscaling theories in fluid flow through porous media by comparing measurements of relative permeability and capillary-saturation with measurements ofmore » interfacial area per volume. This project on the experimental investigation of relative permeability upscaling has produced a unique combination of three quite different technical approaches to the upscaling problem of obtaining pore-related microscopic properties and using them to predict macroscopic behavior. Several important ''firsts'' have been achieved during the course of the project. (1) Optical coherence imaging, a laser-based ranging and imaging technique, has produced the first images of grain and pore structure up to 1 mm beneath the surface of the sandstone and in a laboratory borehole. (2) Woods metal injection has connected for the first time microscopic pore-scale geometric measurements with macroscopic saturation in real sandstone cores. (3) The micro-model technique has produced the first invertible relationship between saturation and capillary pressure--showing that interfacial area per volume (IAV) provides the linking parameter. IAV is a key element in upscaling theories, so this experimental finding may represent the most important result of this project, with wide ramifications for predictions of fluid behavior in porous media.« less

Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice

ERIC Educational Resources Information Center

Koutsoyiannis, Demetris

2012-01-01

While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this…

Computational Fluid Dynamics Modeling of Nickel Hydrogen Batteries

NASA Technical Reports Server (NTRS)

Cullion, R.; Gu, W. B.; Wang, C. Y.; Timmerman, P.

2000-01-01

An electrochemical Ni-H2 battery model has been expanded to include thermal effects. A thermal energy conservation equation was derived from first principles. An electrochemical and thermal coupled model was created by the addition of this equation to an existing multiphase, electrochemical model. Charging at various rates was investigated and the results validated against experimental data. Reaction currents, pressure changes, temperature profiles, and concentration variations within the cell are predicted numerically and compared with available data and theory.

Recent advances in quantitative analysis of fluid interfaces in multiphase fluid flow measured by synchrotron-based x-ray microtomography

NASA Astrophysics Data System (ADS)

Schlueter, S.; Sheppard, A.; Wildenschild, D.

2013-12-01

Imaging of fluid interfaces in three-dimensional porous media via x-ray microtomography is an efficient means to test thermodynamically derived predictions on the relationship between capillary pressure, fluid saturation and specific interfacial area (Pc-Sw-Anw) in partially saturated porous media. Various experimental studies exist to date that validate the uniqueness of the Pc-Sw-Anw relationship under static conditions and with current technological progress direct imaging of moving interfaces under dynamic conditions is also becoming available. Image acquisition and subsequent image processing currently involves many steps each prone to operator bias, like merging different scans of the same sample obtained at different beam energies into a single image or the generation of isosurfaces from the segmented multiphase image on which the interface properties are usually calculated. We demonstrate that with recent advancements in (i) image enhancement methods, (ii) multiphase segmentation methods and (iii) methods of structural analysis we can considerably decrease the time and cost of image acquisition and the uncertainty associated with the measurement of interfacial properties. In particular, we highlight three notorious problems in multiphase image processing and provide efficient solutions for each: (i) Due to noise, partial volume effects, and imbalanced volume fractions, automated histogram-based threshold detection methods frequently fail. However, these impairments can be mitigated with modern denoising methods, special treatment of gray value edges and adaptive histogram equilization, such that most of the standard methods for threshold detection (Otsu, fuzzy c-means, minimum error, maximum entropy) coincide at the same set of values. (ii) Partial volume effects due to blur may produce apparent water films around solid surfaces that alter the specific fluid-fluid interfacial area (Anw) considerably. In a synthetic test image some local segmentation methods like Bayesian Markov random field, converging active contours and watershed segmentation reduced the error in Anw associated with apparent water films from 21% to 6-11%. (iii) The generation of isosurfaces from the segmented data usually requires a lot of postprocessing in order to smooth the surface and check for consistency errors. This can be avoided by calculating specific interfacial areas directly on the segmented voxel image by means of Minkowski functionals which is highly efficient and less error prone.

Impacts of relative permeability on CO2 phase behavior, phase distribution, and trapping mechanisms

NASA Astrophysics Data System (ADS)

Moodie, N.; McPherson, B. J. O. L.; Pan, F.

2015-12-01

A critical aspect of geologic carbon storage, a carbon-emissions reduction method under extensive review and testing, is effective multiphase CO2 flow and transport simulation. Relative permeability is a flow parameter particularly critical for accurate forecasting of multiphase behavior of CO2 in the subsurface. The relative per­meability relationship assumed and especially the irreducible saturation of the gas phase greatly impacts predicted CO2 trapping mechanisms and long-term plume migration behavior. A primary goal of this study was to evaluate the impact of relative permeability on efficacy of regional-scale CO2 sequestration models. To accomplish this we built a 2-D vertical cross-section of the San Rafael Swell area of East-central Utah. This model simulated injection of CO2 into a brine aquifer for 30 years. The well was then shut-in and the CO2 plume behavior monitored for another 970 years. We evaluated five different relative permeability relationships to quantify their relative impacts on forecasted flow results of the model, with all other parameters maintained uniform and constant. Results of this analysis suggest that CO2 plume movement and behavior are significantly dependent on the specific relative permeability formulation assigned, including the assumed irreducible saturation values of CO2 and brine. More specifically, different relative permea­bility relationships translate to significant differences in CO2 plume behavior and corresponding trapping mechanisms.

A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids

NASA Astrophysics Data System (ADS)

Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar

2014-11-01

We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.

Turbulence kinetic energy equation for dilute suspensions

NASA Technical Reports Server (NTRS)

Abou-Arab, T. W.; Roco, M. C.

1989-01-01

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

A refinement of the combination equations for evaporation

USGS Publications Warehouse

Milly, P.C.D.

1991-01-01

Most combination equations for evaporation rely on a linear expansion of the saturation vapor-pressure curve around the air temperature. Because the temperature at the surface may differ from this temperature by several degrees, and because the saturation vapor-pressure curve is nonlinear, this approximation leads to a certain degree of error in those evaporation equations. It is possible, however, to introduce higher-order polynomial approximations for the saturation vapor-pressure curve and to derive a family of explicit equations for evaporation, having any desired degree of accuracy. Under the linear approximation, the new family of equations for evaporation reduces, in particular cases, to the combination equations of H. L. Penman (Natural evaporation from open water, bare soil and grass, Proc. R. Soc. London, Ser. A193, 120-145, 1948) and of subsequent workers. Comparison of the linear and quadratic approximations leads to a simple approximate expression for the error associated with the linear case. Equations based on the conventional linear approximation consistently underestimate evaporation, sometimes by a substantial amount. ?? 1991 Kluwer Academic Publishers.

SAGUARO: a finite-element computer program for partially saturated porous flow problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

Multi-Phase Equilibrium and Solubilities of Aromatic Compounds and Inorganic Compounds in Sub- and Supercritical Water: A Review.

PubMed

Liu, Qinli; Ding, Xin; Du, Bowen; Fang, Tao

2017-11-02

Supercritical water oxidation (SCWO), as a novel and efficient technology, has been applied to wastewater treatment processes. The use of phase equilibrium data to optimize process parameters can offer a theoretical guidance for designing SCWO processes and reducing the equipment and operating costs. In this work, high-pressure phase equilibrium data for aromatic compounds+water systems and inorganic compounds+water systems are given. Moreover, thermodynamic models, equations of state (EOS) and empirical and semi-empirical approaches are summarized and evaluated. This paper also lists the existing problems of multi-phase equilibria and solubility studies on aromatic compounds and inorganic compounds in sub- and supercritical water.

Exhaust plumes and their interaction with missile airframes - A new viewpoint

NASA Technical Reports Server (NTRS)

Dash, S. M.; Sinha, N.

1992-01-01

The present, novel treatment of missile airframe-exhaust plume interactions emphasizes their simulation via a formal solution of the Reynolds-averaged Navier-Stokes (RNS) equation and is accordingly able to address the simulation requirements of novel missiles with nonconventional/integrated propulsion systems. The method is made possible by implicit RNS codes with improved artificial dissipation models, generalized geometric capabilities, and improved two-equation turbulence models, as well as by such codes' recent incorporation of plume thermochemistry and multiphase flow effects.

A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate.

PubMed

Fellner, Klemens; Kovtunenko, Victor A

2016-01-01

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.

Pore-scale study of multiphase reactive transport in fibrous electrodes of vanadium redox flow batteries

DOE PAGES

Chen, Li; He, YaLing; Tao, Wen -Quan; ...

2017-07-21

The electrode of a vanadium redox flow battery generally is a carbon fibre-based porous medium, in which important physicochemical processes occur. In this work, pore-scale simulations are performed to study complex multiphase flow and reactive transport in the electrode by using the lattice Boltzmann method (LBM). Four hundred fibrous electrodes with different fibre diameters and porosities are reconstructed. Both the permeability and diffusivity of the reconstructed electrodes are predicted and compared with empirical relationships in the literature. Reactive surface area of the electrodes is also evaluated and it is found that existing empirical relationship overestimates the reactive surface under lowermore » porosities. Further, a pore-scale electrochemical reaction model is developed to study the effects of fibre diameter and porosity on electrolyte flow, V II/V III transport, and electrochemical reaction at the electrolyte-fibre surface. Finally, evolution of bubble cluster generated by the side reaction is studied by adopting a LB multiphase flow model. Effects of porosity, fibre diameter, gas saturation and solid surface wettability on average bubble diameter and reduction of reactive surface area due to coverage of bubbles on solid surface are investigated in detail. It is found that gas coverage ratio is always lower than that adopted in the continuum model in the literature. Furthermore, the current pore-scale studies successfully reveal the complex multiphase flow and reactive transport processes in the electrode, and the simulation results can be further upscaled to improve the accuracy of the current continuum-scale models.« less

The Dependence of Water Permeability in Quartz Sand on Gas Hydrate Saturation in the Pore Space

NASA Astrophysics Data System (ADS)

Kossel, E.; Deusner, C.; Bigalke, N.; Haeckel, M.

2018-02-01

Transport of fluids in gas hydrate bearing sediments is largely defined by the reduction of the permeability due to gas hydrate crystals in the pore space. Although the exact knowledge of the permeability behavior as a function of gas hydrate saturation is of crucial importance, state-of-the-art simulation codes for gas production scenarios use theoretically derived permeability equations that are hardly backed by experimental data. The reason for the insufficient validation of the model equations is the difficulty to create gas hydrate bearing sediments that have undergone formation mechanisms equivalent to the natural process and that have well-defined gas hydrate saturations. We formed methane hydrates in quartz sand from a methane-saturated aqueous solution and used magnetic resonance imaging to obtain time-resolved, three-dimensional maps of the gas hydrate saturation distribution. These maps were fed into 3-D finite element method simulations of the water flow. In our simulations, we tested the five most well-known permeability equations. All of the suitable permeability equations include the term (1-SH)n, where SH is the gas hydrate saturation and n is a parameter that needs to be constrained. The most basic equation describing the permeability behavior of water flow through gas hydrate bearing sand is k = k0 (1-SH)n. In our experiments, n was determined to be 11.4 (±0.3). Results from this study can be directly applied to bulk flow analysis under the assumption of homogeneous gas hydrate saturation and can be further used to derive effective permeability models for heterogeneous gas hydrate distributions at different scales.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crandall, Dustin M.; Moore, Johnathan E.; Tudek, John K.

Evaluation of the fate and transport of carbon dioxide (CO 2) in deep reservoirs is crucial to the development of long-term geologic carbon sequestration (GCS) technologies. In this report, various studies using computed tomography (CT) scanning are utilized in conjunction with traditional flow tests to observe the multi-scale phenomena associated with CO 2 injection in geologic media. Pore scale analyses were performed to determine the infiltration characteristics of CO 2 into a brine saturated reservoir rock. Multiphase floods were performed to evaluate the saturation of CO 2 into a brine-saturated reservoir rock and determine how structural changes within the lithologymore » affect such interactions. Additionally, CO 2 induced swelling of unconventional reservoir rock was evaluated with respect to reductions in fracture transmissivity due to matrix swelling. These studies are just a few examples of the benefits of multi-scale CT imaging in conjunction with traditional laboratory methodology to gain a better understanding of the interactions between CO 2 and the lithologies it interacts with during GCS.« less

Study on Two-Phase Flow in Heterogeneous Porous Media by Light Transmission Method

NASA Astrophysics Data System (ADS)

Qiao, W.

2015-12-01

The non-aqueous phase liquid (NAPL) released to the subsurface can form residual ganglia and globules occupying pores and also accumulate and form pools, in which multiphase system forms. Determining transient fluid saturations in a multiphase system is essential to understand the flow characteristics of systems and to perform effective remediation strategies. As a non-destructive and non-invasive laboratory technique utilized for the measurement of liquid saturation in porous media, light transmission is of the lowest cost and safe. Utilization of Coupled Charge Device camera in light transmission systems provides a nearly instantaneous high-density array of spatial measurements over a very large dynamic range. The migration of NAPL and air spariging technique applied to remove NAPL in aquifer systems are typically two-phase flow problem. Because of the natural aquifer normally being heterogeneous, two 2-D sandboxes (Length55cm×width1.3cm×hight45cm) are set up to study the migration of gas and DNAPL in heterogeneous porous media based on light transmission method and its application in two-phase flow. Model D for water/gas system developed by Niemet and Selker (2001) and Model NW-A for water/NAPL system developed by Zhang et al. (2014) are applied for the calculation of fluid saturation in the two experiments, respectively. The gas injection experiments show that the gas moves upward in the irregular channels, piling up beneath the low permeability lenses and starting lateral movement. Bypassing the lenses, the gas moves upward and forms continuous distribution in the top of the sandbox. The faster of gas injects, the wider of gas migration will be. The DNAPL infiltration experiment shows that TCE mainly moves downward as the influence of gravity, stopping vertical infiltration when reaching the low permeability lenses because of its failure to overcome the capillary pressure. Then, TCE accumulates on the surface and starts transverse movement. Bypassing the lenses, TCE migrates down again and eventually accumulates at the bottom of the sandbox. The two models of quantification of fluid saturations for water/gas system and water/NAPL system developed in homogenous porous media give comparatively fit results to the observations and can be used to quantify fluid saturations in heterogeneous porous media.

TOUGH2 User's Guide Version 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pruess, K.; Oldenburg, C.M.; Moridis, G.J.

1999-11-01

TOUGH2 is a numerical simulator for nonisothermal flows of multicomponent, multiphase fluids in one, two, and three-dimensional porous and fractured media. The chief applications for which TOUGH2 is designed are in geothermal reservoir engineering, nuclear waste disposal, environmental assessment and remediation, and unsaturated and saturated zone hydrology. TOUGH2 was first released to the public in 1991; the 1991 code was updated in 1994 when a set of preconditioned conjugate gradient solvers was added to allow a more efficient solution of large problems. The current Version 2.0 features several new fluid property modules and offers enhanced process modeling capabilities, such asmore » coupled reservoir-wellbore flow, precipitation and dissolution effects, and multiphase diffusion. Numerous improvements in previously released modules have been made and new user features have been added, such as enhanced linear equation solvers, and writing of graphics files. The T2VOC module for three-phase flows of water, air and a volatile organic chemical (VOC), and the T2DM module for hydrodynamic dispersion in 2-D flow systems have been integrated into the overall structure of the code and are included in the Version 2.0 package. Data inputs are upwardly compatible with the previous version. Coding changes were generally kept to a minimum, and were only made as needed to achieve the additional functionalities desired. TOUGH2 is written in standard FORTRAN77 and can be run on any platform, such as workstations, PCs, Macintosh, mainframe and supercomputers, for which appropriate FORTRAN compilers are available. This report is a self-contained guide to application of TOUGH2 to subsurface flow problems. It gives a technical description of the TOUGH2 code, including a discussion of the physical processes modeled, and the mathematical and numerical methods used. Illustrative sample problems are presented along with detailed instructions for preparing input data.« less

Simulation of Flow for an Immersed Sphere

DTIC Science & Technology

2016-12-01

Problem Set-Up .................................................................................................... 18 4.0 Results...CFD computer codes are now widely applied in the commercial world for aircraft design with little requirement for wind tunnel testing. A wide range of...as the burning of fuel in gas turbine combustors. Intricate multiphase physics equations couple the behavior of gas phase CFD algorithms with

Investigating Stage-Sequential Growth Mixture Models with Multiphase Longitudinal Data

ERIC Educational Resources Information Center

Kim, Su-Young; Kim, Jee-Seon

2012-01-01

This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand…

Transport of water and ions in partially water-saturated porous media. Part 1. Constitutive equations

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

I developed a model of cross-coupled flow in partially saturated porous media based on electrokinetic coupling including the effect of ion filtration (normal and reverse osmosis) and the multi-component nature of the pore water (wetting) phase. The model also handles diffusion and membrane polarization but is valid only for saturations above the irreducible water saturation. I start with the local Nernst-Planck and Stokes equations and I use a volume-averaging procedure to obtain the generalized Ohm, Fick, and Darcy equations with cross-coupling terms at the scale of a representative elementary volume of the porous rock. These coupling terms obey Onsager's reciprocity, which is a required condition, at the macroscale, to keep the total dissipation function of the system positive. Rather than writing the electrokinetic terms in terms of zeta potential (the double layer electrical potential on the slipping plane located in the pore water), I developed the model in terms of an effective charge density dragged by the flow of the pore water. This effective charge density is found to be strongly controlled by the permeability and the water saturation. I also developed an electrical conductivity equation including the effect of saturation on both bulk and surface conductivities, the surface conductivity being associated with electromigration in the electrical diffuse layer coating the grains. This surface conductivity depends on the CEC of the porous material.

Carbon-dioxide storage in the subsurface: towards an understanding of crack development in the cap-rock including phase transition processes

NASA Astrophysics Data System (ADS)

Häberle, K.; Ehlers, W.

2012-04-01

Supercritical CO2 can be injected into deep saline aquifers to reduce the amount of CO2 in the atmosphere and thus, lessen the impact on the global warming. Qualified reservoirs should be in a sufficient depth to guarantee the thermodynamical environment for the supercritical state of CO2. Furthermore, an impermeable cap-rock layer must confine the reservoir layer, in order to collect the CO2 in the desired region. In CO2 storage it is crucial to guarantee the safety of the storage site and to eliminate possibilities of leakage. Therefore, deformation processes of the rock matrix and the cap-rock layer, which might be induced by the high pressure injection of CO2, must be investigated. The increase in stress may also cause crack development in the cap-rock layer. These could either be new developing fractures or the break-up of already existing but cemented cracks or faults. If such cracks occur, CO2 could migrate to shallower regions where the temperature and pressure cannot support the supercritical condition of the CO2 anymore. Thus, it is important to describe the phase transition process between supercritical, liquid and gaseous CO2. This requires a proper understanding of the thermodynamical behaviour of CO2 within the reservoir. The Theory of Porous Media (TPM) provides a useful continuum-mechanical basis to describe real natural systems in a thermodynamically consistent way. Hence, the TPM is applied to model multiphasic flow of CO2 and water and include elasto-plastic solid deformations of the porous matrix. The Peng-Robinson equation is implemented as a cubic equation of state to describe the phase behaviour of CO2 in the liquid, gaseous and supercritical region. However, in the two-phase region the isotherms show a horizontal section and kinks at the boiling and vapour curve. This cannot be represented by a continuously differentiable function such as the Peng-Robinson equation. To circumvent this problem, the Antoine equation provides additional information by defining the saturation pressure for a given temperature. The injection of CO2 will increase the reservoir pressure which then will cause solid deformations. The extended Finite Element Method (XFEM) will be used to account for the discontinuities arising from crack development due to these solid deformations. The XFEM bears the advantage that the finite element mesh must not be adapted to the crack. Instead, to describe the discontinuity of the crack, the field quantities are locally enriched by defining additional degrees of freedom at the intersected finite elements. Herein, special attention has to be paid to the matrix-fracture interaction of the fluid phases. Numerical examples are performed to investigate the injection of CO2 into a saline aquifer. These are computed with the FEM program PANDAS, which allows solutions of strongly coupled multiphasic problems in deformable porous media.

multiUQ: An intrusive uncertainty quantification tool for gas-liquid multiphase flows

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2017-11-01

Uncertainty quantification (UQ) can improve our understanding of the sensitivity of gas-liquid multiphase flows to variability about inflow conditions and fluid properties, creating a valuable tool for engineers. While non-intrusive UQ methods (e.g., Monte Carlo) are simple and robust, the cost associated with these techniques can render them unrealistic. In contrast, intrusive UQ techniques modify the governing equations by replacing deterministic variables with stochastic variables, adding complexity, but making UQ cost effective. Our numerical framework, called multiUQ, introduces an intrusive UQ approach for gas-liquid flows, leveraging a polynomial chaos expansion of the stochastic variables: density, momentum, pressure, viscosity, and surface tension. The gas-liquid interface is captured using a conservative level set approach, including a modified reinitialization equation which is robust and quadrature free. A least-squares method is leveraged to compute the stochastic interface normal and curvature needed in the continuum surface force method for surface tension. The solver is tested by applying uncertainty to one or two variables and verifying results against the Monte Carlo approach. NSF Grant #1511325.

A composite numerical model for assessing subsurface transport of oily wastes and chemical constituents

NASA Astrophysics Data System (ADS)

Panday, S.; Wu, Y. S.; Huyakorn, P. S.; Wade, S. C.; Saleem, Z. A.

1997-02-01

Subsurface fate and transport models are utilized to predict concentrations of chemicals leaching from wastes into downgradient receptor wells. The contaminant concentrations in groundwater provide a measure of the risk to human health and the environment. The level of potential risk is currently used by the U.S. Environmental Protection Agency to determine whether management of the wastes should conform to hazardous waste management standards. It is important that the transport and fate of contaminants is simulated realistically. Most models in common use are inappropriate for simulating the migration of wastes containing significant fractions of nonaqueous-phase liquids (NAPLs). The migration of NAPL and its dissolved constituents may not be reliably predicted using conventional aqueous-phase transport simulations. To overcome this deficiency, an efficient and robust regulatory assessment model incorporating multiphase flow and transport in the unsaturated and saturated zones of the subsurface environment has been developed. The proposed composite model takes into account all of the major transport processes including infiltration and ambient flow of NAPL, entrapment of residual NAPL, adsorption, volatilization, degradation, dissolution of chemical constituents, and transport by advection and hydrodynamic dispersion. Conceptually, the subsurface is treated as a composite unsaturated zone-saturated zone system. The composite simulator consists of three major interconnected computational modules representing the following components of the migration pathway: (1) vertical multiphase flow and transport in the unsaturated zone; (2) areal movement of the free-product lens in the saturated zone with vertical equilibrium; and (3) three-dimensional aqueous-phase transport of dissolved chemicals in ambient groundwater. Such a composite model configuration promotes computational efficiency and robustness (desirable for regulatory assessment applications). Two examples are presented to demonstrate the model verification and a site application. Simulation results obtained using the composite modeling approach are compared with a rigorous numerical solution and field observations of crude oil saturations and plume concentrations of total dissolved organic carbon at a spill site in Minnesota, U.S.A. These comparisons demonstrate the ability of the present model to provide realistic depiction of field-scale situations.

Multiphase-field model of small strain elasto-plasticity according to the mechanical jump conditions

NASA Astrophysics Data System (ADS)

Herrmann, Christoph; Schoof, Ephraim; Schneider, Daniel; Schwab, Felix; Reiter, Andreas; Selzer, Michael; Nestler, Britta

2018-04-01

We introduce a small strain elasto-plastic multiphase-field model according to the mechanical jump conditions. A rate-independent J_2 -plasticity model with linear isotropic hardening and without kinematic hardening is applied exemplary. Generally, any physically nonlinear mechanical model is compatible with the subsequently presented procedure. In contrast to models with interpolated material parameters, the proposed model is able to apply different nonlinear mechanical constitutive equations for each phase separately. The Hadamard compatibility condition and the static force balance are employed as homogenization approaches to calculate the phase-inherent stresses and strains. Several verification cases are discussed. The applicability of the proposed model is demonstrated by simulations of the martensitic transformation and quantitative parameters.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jensen, Brian James

There is a scientific need to obtain new data to constrain and refine next generation multi-phase equation-of-state (EOS) for metals. Experiments are needed to locate phase boundaries, determine transition kinetic times, and to obtain EOS and Hugoniot data for relevant phases. The objectives of the current work was to examine the multiphase properties for cerium including the dynamic melt boundary and the low-pressure solid-solid phase transition through the critical point. These objectives were addressed by performing plate impact experiment that used multiple experimental configuration including front-surface impact experiments to directly measure transition kinetics, multislug experiments that used the overtake methodmore » to measure sound speeds at pressure, and preheat experiments to map out phase boundaries. Preliminary data and analysis obtained for cerium will be presented.« less

Three Dimensional Simulations of Multiphase Flows Using a Lattice Boltzmann Method Suitable for High Density Ratios - 12126

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gokaltun, Seckin; McDaniel, Dwayne; Roelant, David

2012-07-01

Multiphase flows involving gas and liquid phases can be observed in engineering operations at various Department of Energy sites, such as mixing of slurries using pulsed-air mixers and hydrogen gas generation in liquid waste tanks etc. The dynamics of the gas phase in the liquid domain play an important role in the mixing effectiveness of the pulsed-air mixers or in the level of gas pressure build-up in waste tanks. To understand such effects, computational fluid dynamics methods (CFD) can be utilized by developing a three-dimensional computerized multiphase flow model that can predict accurately the behavior of gas motion inside liquid-filledmore » tanks by solving the governing mathematical equations that represent the physics of the phenomena. In this paper, such a CFD method, lattice Boltzmann method (LBM), is presented that can model multiphase flows accurately and efficiently. LBM is favored over traditional Navier-Stokes based computational models since interfacial forces are handled more effectively in LBM. The LBM is easier to program, more efficient to solve on parallel computers, and has the ability to capture the interface between different fluid phases intrinsically. The LBM used in this paper can solve for the incompressible and viscous flow field in three dimensions, while at the same time, solve the Cahn-Hillard equation to track the position of the gas-liquid interface specifically when the density and viscosity ratios between the two fluids are high. This feature is of primary importance since the previous LBM models proposed for multiphase flows become unstable when the density ratio is larger than 10. The ability to provide stable and accurate simulations at large density ratios becomes important when the simulation case involves fluids such as air and water with a density ratio around 1000 that are common to many engineering problems. In order to demonstrate the capability of the 3D LBM method at high density ratios, a static bubble simulation is conducted to solve for the pressure difference between the inside and outside of a gas bubble in a liquid domain. Once the results show that the method is in agreement with the Laplace law, buoyant bubble simulations are conducted. The initial results obtained for bubble shape during the rising process was found to be in agreement with the theoretical expectations. (authors)« less

The effect of small- and core-scale heterogeneity on the multiphase flow properties of CO2 and water in sandstones

NASA Astrophysics Data System (ADS)

Pini, R.; Benson, S. M.

2012-12-01

Capillary pressure and relative permeability functions are characteristic curves that, when coupled to the continuum-scale equations of motion, allow for a description of multiphase displacement processes in porous media. Traditionally, these properties are measured in the laboratory and are implemented into reservoir simulations to predict the behavior at the field-scale. There is an increasing awareness that detailed investigations are required to understand the role of the inherent heterogeneity of the rock samples used in the experiments on the measured multiphase properties. In fact, although a significant amount of simulation work has explored the effect of heterogeneities on Pc-kr-S relationships, very few experimental studies report on displacements with well-characterized, naturally heterogeneous media. To extend the current data set and to support these numerical findings, more laboratory data are therefore required that have been obtained under a variety of conditions and on cores from different geological settings. A direct practical implication of these studies would be the definition of a minimum scale at which heterogeneities have to be resolved, so that mathematical models would adequately capture the observed displacement patterns. Moreover, the coupling of experiments and theory will serve as a firm starting point for testing scale-up methods. In this study, results from core-flooding experiments are presented that have been carried out at representative conditions on a variety of naturally heterogeneous core samples. Results are presented from a newly developed technique that allows measuring drainage capillary pressure curves during core-flooding experiments; data have been collected at different temperature (25 and 50C), at different pressures (2 and 9MPa) and with different fluid pairs (CO2/water, N2/water and CO2/brine), thus showing the applicability of the novel technique in a wide range of interfacial tension levels. Additionally, Pc-S relationships on mm-scale subsets of the rock core have been obtained by combination with saturation measurements from X-ray CT scanning; these are of high relevance as they directly and non-destructively quantify small-scale capillary heterogeneity in these systems. The spatial variation of the capillary pressure curve is then described by means of so-called scaling factors, which are derived from scaling-laws based on the concept of similar media (such as the Leverett J-Function), and which can be related to other relevant petrophysical properties of the rock, such as porosity, permeability and grain size distribution. The role of core-scale capillary heterogeneity is investigated based on observations from a CO2/water core-flooding experiment on a rock core that possesses a heterogeneous feature of relatively simple geometry. An integrated approach is applied where these experimental results are combined with independent measurements of capillary pressure, porosity and permeability. It is shown that 3D saturation profiles obtained by X-ray CT scanning during the core-flooding experiment are essential for defining heterogeneous features and that the latter significantly affect the character of the measured relative permeability curve.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

A Generalized Multi-Phase Framework for Modeling Cavitation in Cryogenic Fluids

NASA Technical Reports Server (NTRS)

Dorney, Dan (Technical Monitor); Hosangadi, Ashvin; Ahuja, Vineet

2003-01-01

A generalized multi-phase formulation for cavitation in fluids operating at temperatures elevated relative to their critical temperatures is presented. The thermal effects and the accompanying property variations due to phase change are modeled rigorously. Thermal equilibrium is assumed and fluid thermodynamic properties are specified along the saturation line using the NIST-12 databank. Fundamental changes in the physical characteristics of the cavity when thermal effects become pronounced are identified; the cavity becomes more porous, the interface less distinct, and has increased entrainment when temperature variations are present. Quantitative estimates of temperature and pressure depressions in both liquid nitrogen and liquid hydrogen were computed and compared with experimental data of Hord for hydrofoils. Excellent estimates of the leading edge temperature and pressure depression were obtained while the comparisons in the cavity closure region were reasonable. Liquid nitrogen cavities were consistently found to be in thermal equilibrium while liquid hydrogen cavities exhibited small, but distinct, non-equilibrium effects.

The Intrinsic Variability in the Water Vapor Saturation Ratio Due to Turbulence

NASA Astrophysics Data System (ADS)

Anderson, Jesse Charles

The water vapor concentration plays an important role for many atmospheric processes. The mean concentration is key to understand water vapor's effect on the climate as a greenhouse gas. The fluctuations about the mean are important to understand heat fluxes between Earth's surface and the boundary layer. These fluctuations are linked to turbulence that is present in the boundary layer. Turbulent conditions are simulated in Michigan Tech's multiphase, turbulent reaction chamber, the pi chamber. Measurements for temperature and water vapor concentration were recorded under forced Rayleigh- Benard convection at several turbulent intensities. These were used to calculate the saturation ratio, often referred to as the relative humidity. The fluctuations in the water vapor concentration were found to be the more important than the temperature for the variability of the saturation ratio. The fluctuations in the saturation ratio result in some cloud droplets experiencing a higher supersaturation than other cloud droplets, causing those "lucky" droplets to grow at a faster rate than other droplets. This difference in growth rates could contribute to a broadening of the size distribution of cloud droplets, resulting in the enhancement of collision-coalescence. These fluctuations become more pronounced with more intense turbulence.

Micro-positron emission tomography for measuring sub-core scale single and multiphase transport parameters in porous media

NASA Astrophysics Data System (ADS)

Zahasky, Christopher; Benson, Sally M.

2018-05-01

Accurate descriptions of heterogeneity in porous media are important for understanding and modeling single phase (e.g. contaminant transport, saltwater intrusion) and multiphase (e.g. geologic carbon storage, enhanced oil recovery) transport problems. Application of medical imaging to experimentally quantify these processes has led to significant progress in material characterization and understanding fluid transport behavior at laboratory scales. While widely utilized in cancer diagnosis and management, cardiology, and neurology, positron emission tomography (PET) has had relatively limited applications in earth science. This study utilizes a small-bore micro-PET scanner to image and quantify the transport behavior of pulses of a conservative aqueous radiotracer injected during single and multiphase flow experiments in two heterogeneous Berea sandstone cores. The cores are discretized into axial-parallel streamtubes, and using the reconstructed micro-PET data, expressions are derived from spatial moment analysis for calculating sub-core tracer flux and pore water velocity. Using the flux and velocity measurements, it is possible to calculate porosity and saturation from volumetric flux balance, and calculate permeability and water relative permeability from Darcy's law. Second spatial moment analysis enables measurement of sub-core solute dispersion during both single phase and multiphase experiments. A numerical simulation model is developed to verify the assumptions of the streamtube dimension reduction technique. A variation of the reactor ratio is presented as a diagnostic metric to efficiently determine the validity of the streamtube approximation in core and column-scale experiments. This study introduces a new method to quantify sub-core permeability, relative permeability, and dispersion. These experimental and analytical methods provide a foundation for future work on experimental measurements of differences in transport behavior across scales.

GASOLINE: Smoothed Particle Hydrodynamics (SPH) code

NASA Astrophysics Data System (ADS)

N-Body Shop

2017-10-01

Gasoline solves the equations of gravity and hydrodynamics in astrophysical problems, including simulations of planets, stars, and galaxies. It uses an SPH method that features correct mixing behavior in multiphase fluids and minimal artificial viscosity. This method is identical to the SPH method used in the ChaNGa code (ascl:1105.005), allowing users to extend results to problems requiring >100,000 cores. Gasoline uses a fast, memory-efficient O(N log N) KD-Tree to solve Poisson's Equation for gravity and avoids artificial viscosity in non-shocking compressive flows.

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution. [rocket nozzle and orbital plume flow fields

NASA Technical Reports Server (NTRS)

Smith, S. D.

1984-01-01

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The proposed diffuse interface immersed boundary method is shown to be discretely mass-preserving while being temporally second-order accurate and exhibits nominal second-order accuracy in space. We examine the efficacy of the proposed approach through extensive numerical experiments involving one or more fluids and solids, that include two-particle sedimentation in homogeneous and stratified environment. The results from the numerical simulations show that the proposed methodology results in reduced spurious force oscillations in case of moving bodies while accurately resolving complex flow phenomena in multiphase flows with moving solids. These studies demonstrate that the proposed diffuse interface immersed boundary method, which could be related to a class of penalisation approaches, is a robust and promising alternative to computationally expensive conformal moving mesh algorithms as well as the class of sharp interface immersed boundary methods for multibody problems in multi-phase flows.

AOI 1— COMPUTATIONAL ENERGY SCIENCES:MULTIPHASE FLOW RESEARCH High-fidelity multi-phase radiation module for modern coal combustion systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Modest, Michael

The effects of radiation in particle-laden flows were the object of the present research. The presence of particles increases optical thickness substantially, making the use of the “optically thin” approximation in most cases a very poor assumption. However, since radiation fluxes peak at intermediate optical thicknesses, overall radiative effects may not necessarily be stronger than in gas combustion. Also, the spectral behavior of particle radiation properties is much more benign, making spectral models simpler (and making the assumption of a gray radiator halfway acceptable, at least for fluidized beds when gas radiation is not large). On the other hand, particlesmore » scatter radiation, making the radiative transfer equation (RTE) much more di fficult to solve. The research carried out in this project encompassed three general areas: (i) assessment of relevant radiation properties of particle clouds encountered in fluidized bed and pulverized coal combustors, (ii) development of proper spectral models for gas–particulate mixtures for various types of two-phase combustion flows, and (iii) development of a Radiative Transfer Equation (RTE) solution module for such applications. The resulting models were validated against artificial cases since open literature experimental data were not available. The final models are in modular form tailored toward maximum portability, and were incorporated into two research codes: (i) the open-source CFD code OpenFOAM, which we have extensively used in our previous work, and (ii) the open-source multi-phase flow code MFIX, which is maintained by NETL.« less

Numerical investigation of complex flooding schemes for surfactant polymer based enhanced oil recovery

NASA Astrophysics Data System (ADS)

Dutta, Sourav; Daripa, Prabir

2015-11-01

Surfactant-polymer flooding is a widely used method of chemical enhanced oil recovery (EOR) in which an array of complex fluids containing suitable and varying amounts of surfactant or polymer or both mixed with water is injected into the reservoir. This is an example of multiphase, multicomponent and multiphysics porous media flow which is characterized by the spontaneous formation of complex viscous fingering patterns and is modeled by a system of strongly coupled nonlinear partial differential equations with appropriate initial and boundary conditions. Here we propose and discuss a modern, hybrid method based on a combination of a discontinuous, multiscale finite element formulation and the method of characteristics to accurately solve the system. Several types of flooding schemes and rheological properties of the injected fluids are used to numerically study the effectiveness of various injection policies in minimizing the viscous fingering and maximizing oil recovery. Numerical simulations are also performed to investigate the effect of various other physical and model parameters such as heterogeneity, relative permeability and residual saturation on the quantities of interest like cumulative oil recovery, sweep efficiency, fingering intensity to name a few. Supported by the grant NPRP 08-777-1-141 from the Qatar National Research Fund (a member of The Qatar Foundation).

Translating landfill methane generation parameters among first-order decay models.

PubMed

Krause, Max J; Chickering, Giles W; Townsend, Timothy G

2016-11-01

Landfill gas (LFG) generation is predicted by a first-order decay (FOD) equation that incorporates two parameters: a methane generation potential (L 0 ) and a methane generation rate (k). Because non-hazardous waste landfills may accept many types of waste streams, multiphase models have been developed in an attempt to more accurately predict methane generation from heterogeneous waste streams. The ability of a single-phase FOD model to predict methane generation using weighted-average methane generation parameters and tonnages translated from multiphase models was assessed in two exercises. In the first exercise, waste composition from four Danish landfills represented by low-biodegradable waste streams was modeled in the Afvalzorg Multiphase Model and methane generation was compared to the single-phase Intergovernmental Panel on Climate Change (IPCC) Waste Model and LandGEM. In the second exercise, waste composition represented by IPCC waste components was modeled in the multiphase IPCC and compared to single-phase LandGEM and Australia's Solid Waste Calculator (SWC). In both cases, weight-averaging of methane generation parameters from waste composition data in single-phase models was effective in predicting cumulative methane generation from -7% to +6% of the multiphase models. The results underscore the understanding that multiphase models will not necessarily improve LFG generation prediction because the uncertainty of the method rests largely within the input parameters. A unique method of calculating the methane generation rate constant by mass of anaerobically degradable carbon was presented (k c ) and compared to existing methods, providing a better fit in 3 of 8 scenarios. Generally, single phase models with weighted-average inputs can accurately predict methane generation from multiple waste streams with varied characteristics; weighted averages should therefore be used instead of regional default values when comparing models. Translating multiphase first-order decay model input parameters by weighted average shows that single-phase models can predict cumulative methane generation within the level of uncertainty of many of the input parameters as defined by the Intergovernmental Panel on Climate Change (IPCC), which indicates that decreasing the uncertainty of the input parameters will make the model more accurate rather than adding multiple phases or input parameters.

Coupled flow and deformations in granular systems beyond the pendular regime

NASA Astrophysics Data System (ADS)

Yuan, Chao; Chareyre, Bruno; Darve, Felix

2017-06-01

A pore-scale numerical model is proposed for simulating the quasi-static primary drainage and the hydro-mechanical couplings in multiphase granular systems. The solid skeleton is idealized to a dense random packing of polydisperse spheres by DEM. The fluids (nonwetting and wetting phases) space is decomposed to a network of tetrahedral pores based on the Regular Triangulation method. The local drainage rules and invasion logic are defined. The fluid forces acting on solid grains are formulated. The model can simulate the hydraulic evolution from a fully saturated state to a low level of saturation but beyond the pendular regime. The features of wetting phase entrapments and capillary fingering can also be reproduced. Finally, a primary drainage test is performed on a 40,000 spheres of sample. The water retention curve is obtained. The solid skeleton first shrinks then swells.

Saturation Length of Erodible Sediment Beds Subject to Shear Flow

NASA Astrophysics Data System (ADS)

Casler, D. M.; Kahn, B. P.; Furbish, D. J.; Schmeeckle, M. W.

2016-12-01

We examine the initial growth and wavelength selection of sand ripples based on probabilistic formulations of the flux and the Exner equation. Current formulations of this problem as a linear stability analysis appeal to the idea of a saturation length-the lag between the bed stress and the flux-as a key stabilizing influence leading to selection of a finite wavelength. We present two contrasting formulations. The first is based on the Fokker-Planck approximation of the divergence form of the Exner equation, and thus involves particle diffusion associated with variations in particle activity, in addition to the conventionally assumed advective term. The role of a saturation length associated with the particle activity is similar to previous analyses. However, particle diffusion provides an attenuating influence on the growth of small wavelengths, independent of a saturation length, and is thus a sufficient, if not necessary, condition contributing to selection of a finite wavelength. The second formulation is based on the entrainment form of the Exner equation. As a precise, probabilistic formulation of conservation, this form of the Exner equation does not distinguish between advection and diffusion, and, because it directly accounts for all particle motions via a convolution of the distribution of particle hop distances, it pays no attention to the idea of a saturation length. The formulation and resulting description of initial ripple growth and wavelength selection thus inherently subsume the effects embodied in the ideas of advection, diffusion, and a saturation length as used in other formulations. Moreover, the formulation does not distinguish between bed load and suspended load, and is thus broader in application. The analysis reveals that the length scales defined by the distribution of hop distances are more fundamental than the saturation length in determining the initial growth or decay of bedforms. Formulations involving the saturation length coincide with the special case of an exponential distribution of hop distance, where the saturation length is equal to the mean hop distance.

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

NASA Technical Reports Server (NTRS)

Aboudi, Jacob; Pindera, Marek-Jerzy; Arnold, Steven M.

2002-01-01

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

The Biot coefficient for a low permeability heterogeneous limestone

NASA Astrophysics Data System (ADS)

Selvadurai, A. P. S.

2018-04-01

This paper presents the experimental and theoretical developments used to estimate the Biot coefficient for the heterogeneous Cobourg Limestone, which is characterized by its very low permeability. The coefficient forms an important component of the Biot poroelastic model that is used to examine coupled hydro-mechanical and thermo-hydro-mechanical processes in the fluid-saturated Cobourg Limestone. The constraints imposed by both the heterogeneous fabric and its extremely low intact permeability [K \\in (10^{-23},10^{-20}) m2 ] require the development of alternative approaches to estimate the Biot coefficient. Large specimen bench-scale triaxial tests (150 mm diameter and 300 mm long) that account for the scale of the heterogeneous fabric are complemented by results for the volume fraction-based mineralogical composition derived from XRD measurements. The compressibility of the solid phase is based on theoretical developments proposed in the mechanics of multi-phasic elastic materials. An appeal to the theory of multi-phasic elastic solids is the only feasible approach for examining the compressibility of the solid phase. The presence of a number of mineral species necessitates the use of the theories of Voigt, Reuss and Hill along with the theories proposed by Hashin and Shtrikman for developing bounds for the compressibility of the multi-phasic geologic material composing the skeletal fabric. The analytical estimates for the Biot coefficient for the Cobourg Limestone are compared with results for similar low permeability rocks reported in the literature.

Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment.

PubMed

Xenakis, A M; Lind, S J; Stansby, P K; Rogers, B D

2017-03-01

Tsunamis caused by landslides may result in significant destruction of the surroundings with both societal and industrial impact. The 1958 Lituya Bay landslide and tsunami is a recent and well-documented terrestrial landslide generating a tsunami with a run-up of 524 m. Although recent computational techniques have shown good performance in the estimation of the run-up height, they fail to capture all the physical processes, in particular, the landslide-entry profile and interaction with the water. Smoothed particle hydrodynamics (SPH) is a versatile numerical technique for describing free-surface and multi-phase flows, particularly those that exhibit highly nonlinear deformation in landslide-generated tsunamis. In the current work, the novel multi-phase incompressible SPH method with shifting is applied to the Lituya Bay tsunami and landslide and is the first methodology able to reproduce realistically both the run-up and landslide-entry as documented in a benchmark experiment. The method is the first paper to develop a realistic implementation of the physics that in addition to the non-Newtonian rheology of the landslide includes turbulence in the water phase and soil saturation. Sensitivity to the experimental initial conditions is also considered. This work demonstrates the ability of the proposed method in modelling challenging environmental multi-phase, non-Newtonian and turbulent flows.

Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment

PubMed Central

Lind, S. J.; Stansby, P. K.; Rogers, B. D.

2017-01-01

Tsunamis caused by landslides may result in significant destruction of the surroundings with both societal and industrial impact. The 1958 Lituya Bay landslide and tsunami is a recent and well-documented terrestrial landslide generating a tsunami with a run-up of 524 m. Although recent computational techniques have shown good performance in the estimation of the run-up height, they fail to capture all the physical processes, in particular, the landslide-entry profile and interaction with the water. Smoothed particle hydrodynamics (SPH) is a versatile numerical technique for describing free-surface and multi-phase flows, particularly those that exhibit highly nonlinear deformation in landslide-generated tsunamis. In the current work, the novel multi-phase incompressible SPH method with shifting is applied to the Lituya Bay tsunami and landslide and is the first methodology able to reproduce realistically both the run-up and landslide-entry as documented in a benchmark experiment. The method is the first paper to develop a realistic implementation of the physics that in addition to the non-Newtonian rheology of the landslide includes turbulence in the water phase and soil saturation. Sensitivity to the experimental initial conditions is also considered. This work demonstrates the ability of the proposed method in modelling challenging environmental multi-phase, non-Newtonian and turbulent flows. PMID:28413334

Theoretical analysis of multiphase flow during oil-well drilling by a conservative model

NASA Astrophysics Data System (ADS)

Nicolas-Lopez, Ruben

2005-11-01

In order to decrease cost and improve drilling operations is necessary a better understood of the flow mechanisms. Therefore, it was carried out a multiphase conservative model that includes three mass equations and a momentum equation. Also, the measured geothermal gradient is utilized by state equations for estimating physical properties of the phases flowing. The mathematical model is solved by numerical conservative schemes. It is used to analyze the interaction among solid-liquid-gas phases. The circulating system consists as follow, the circulating fluid is pumped downward into the drilling pipe until the bottom of the open hole then it flows through the drill bit, and at this point formation cuttings are incorporated to the circulating fluid and carried upward to the surface. The mixture returns up to the surface by an annular flow area. The real operational conditions are fed to conservative model and the results are matched up to field measurements in several oil wells. Mainly, flow rates, drilling rate, well and tool geometries are data to estimate the profiles of pressure, mixture density, equivalent circulating density, gas fraction and solid carrying capacity. Even though the problem is very complex, the model describes, properly, the hydrodynamics of drilling techniques applied at oil fields. *Authors want to thank to Instituto Mexicano del Petroleo and Petroleos Mexicanos for supporting this research.

Brine flow in heated geologic salt.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuhlman, Kristopher L.; Malama, Bwalya

This report is a summary of the physical processes, primary governing equations, solution approaches, and historic testing related to brine migration in geologic salt. Although most information presented in this report is not new, we synthesize a large amount of material scattered across dozens of laboratory reports, journal papers, conference proceedings, and textbooks. We present a mathematical description of the governing brine flow mechanisms in geologic salt. We outline the general coupled thermal, multi-phase hydrologic, and mechanical processes. We derive these processes governing equations, which can be used to predict brine flow. These equations are valid under a wide varietymore » of conditions applicable to radioactive waste disposal in rooms and boreholes excavated into geologic salt.« less

Multiphase aluminum equations of state via density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sjostrom, Travis; Crockett, Scott; Rudin, Sven

2016-10-03

We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. Our results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We also provide extensive comparison with experiment, and based on this we also provide amore » slightly modified equation of state for the aluminum 6061 alloy.« less

Application of a new multiphase multicomponent volcanic conduit model with magma degassing and crystallization to Stromboli volcano.

NASA Astrophysics Data System (ADS)

La Spina, Giuseppe; Burton, Mike; de'Michieli Vitturi, Mattia

2014-05-01

Volcanoes exhibit a wide range of eruption styles, from relatively slow effusive eruptions, generating lava flows and lava domes, to explosive eruptions, in which very large volumes of fragmented magma and volcanic gas are ejected high into the atmosphere. During an eruption, much information regarding the magma ascent dynamics can be gathered: melt and exsolved gas composition, crystal content, mass flow rate and ballistic velocities, to name just a few. Due to the lack of direct observations of the conduit itself, mathematical models for magma ascent provide invaluable tools for a better comprehension of the system. The complexity of the multiphase multicomponent gas-magma-solid system is reflected in the corresponding mathematical model; a set of non-linear hyperbolic partial differential and constitutive equations, which describe the physical system, has to be formulated and solved. The standard approach to derive governing equations for two-phase flow is based on averaging procedures, which leads to a system of governing equations in the form of mass, momentum and energy balance laws for each phase coupled with algebraic and differential source terms which represent phase interactions. For this work, we used the model presented by de' Michieli Vitturi et al. (EGU General Assembly Conference Abstracts, 2013), where a different approach based on the theory of thermodynamically compatible systems has been adopted to write the governing multiphase equations for two-phase compressible flow (with two velocities and two pressures) in the form of a conservative hyperbolic system of partial differential equations, coupled with non-differential source terms. Here, in order to better describe the multicomponent nature of the system, we extended the model adding several transport equations to the system for different crystal components and different gas species, and implementing appropriate equations of state. The constitutive equations of the model are chosen to reproduce both effusive and explosive eruptive activities at Stromboli volcano. Three different crystal components (olivine, pyroxene and feldspar) and two different gas species (water and carbon dioxide) are taken into account. The equilibrium profiles of crystallization as function of pressure, temperature and water content are modeled using the numerical codes AlphaMELTS and DAKOTA. The equilibrium of dissolved gas content, instead, is obtained using a non-linear fitting of data computed using VolatileCALC. With these data, we simulate numerically the lava effusion that occurred at Stromboli between 27 February and 2 April 2007, and find good agreement with the observed data (vesicularity, exsolved gas composition, crystal content and mass flow rate) at the vent. We find that the model is highly sensitive to input magma temperature, going from effusive to explosive eruption with temperature changes by just 20 °C. We thoroughly investigated through a sensitivity analysis the control of the temperature of magma chamber and of the radius of the conduit on the mass flow rate, obtaining also a set of admissible temperatures and conduit radii that produce results in agreement with the real observations.

Combination of microscopic model and VoF-multiphase approach for numerical simulation of nodular cast iron solidification

NASA Astrophysics Data System (ADS)

Subasic, E.; Huang, C.; Jakumeit, J.; Hediger, F.

2015-06-01

The ongoing increase in the size and capacity of state-of-the-art wind power plants is highlighting the need to reduce the weight of critical components, such as hubs, main shaft bearing housings, gear box housings and support bases. These components are manufactured as nodular iron castings (spheroid graphite iron, or SGI). A weight reduction of up to 20% is achievable by optimizing the geometry to minimize volume, thus enabling significant downsizing of wind power plants. One method for enhancing quality control in the production of thick-walled SGI castings, and thus reducing tolerances and, consequently, enabling castings of smaller volume is via a casting simulation of mould filling and solidification based on a combination of microscopic model and VoF-multiphase approach. Coupled fluid flow with heat transport and phase transformation kinetics during solidification is described by partial differential equations and solved using the finite volume method. The flow of multiple phases is described using a volume of fluid approach. Mass conservation equations are solved separately for both liquid and solid phases. At the micro-level, the diffusion-controlled growth model for grey iron eutectic grains by Wetterfall et al. is combined with a growth model for white iron eutectic grains. The micro-solidification model is coupled with macro-transport equations via source terms in the energy and continuity equations. As a first step the methodology was applied to a simple geometry to investigate the impact of mould-filling on the grey-to-white transition prediction in nodular cast iron.

Finite Element analyses of soil bioengineered slopes

NASA Astrophysics Data System (ADS)

Tamagnini, Roberto; Switala, Barbara Maria; Sudan Acharya, Madhu; Wu, Wei; Graf, Frank; Auer, Michael; te Kamp, Lothar

2014-05-01

Soil Bioengineering methods are not only effective from an economical point of view, but they are also interesting as fully ecological solutions. The presented project is aimed to define a numerical model which includes the impact of vegetation on slope stability, considering both mechanical and hydrological effects. In this project, a constitutive model has been developed that accounts for the multi-phase nature of the soil, namely the partly saturated condition and it also includes the effects of a biological component. The constitutive equation is implemented in the Finite Element (FE) software Comes-Geo with an implicit integration scheme that accounts for the collapse of the soils structure due to wetting. The mathematical formulation of the constitutive equations is introduced by means of thermodynamics and it simulates the growth of the biological system during the time. The numerical code is then applied in the analysis of an ideal rainfall induced landslide. The slope is analyzed for vegetated and non-vegetated conditions. The final results allow to quantitatively assessing the impact of vegetation on slope stability. This allows drawing conclusions and choosing whenever it is worthful to use soil bioengineering methods in slope stabilization instead of traditional approaches. The application of the FE methods show some advantages with respect to the commonly used limit equilibrium analyses, because it can account for the real coupled strain-diffusion nature of the problem. The mechanical strength of roots is in fact influenced by the stress evolution into the slope. Moreover, FE method does not need a pre-definition of any failure surface. FE method can also be used in monitoring the progressive failure of the soil bio-engineered system as it calculates the amount of displacements and strains of the model slope. The preliminary study results show that the formulated equations can be useful for analysis and evaluation of different soil bio-engineering methods of slope stabilization.

Large-Scale Multiphase Flow Modeling of Hydrocarbon Migration and Fluid Sequestration in Faulted Cenozoic Sedimentary Basins, Southern California

NASA Astrophysics Data System (ADS)

Jung, B.; Garven, G.; Boles, J. R.

2011-12-01

Major fault systems play a first-order role in controlling fluid migration in the Earth's crust, and also in the genesis/preservation of hydrocarbon reservoirs in young sedimentary basins undergoing deformation, and therefore understanding the geohydrology of faults is essential for the successful exploration of energy resources. For actively deforming systems like the Santa Barbara Basin and Los Angeles Basin, we have found it useful to develop computational geohydrologic models to study the various coupled and nonlinear processes affecting multiphase fluid migration, including relative permeability, anisotropy, heterogeneity, capillarity, pore pressure, and phase saturation that affect hydrocarbon mobility within fault systems and to search the possible hydrogeologic conditions that enable the natural sequestration of prolific hydrocarbon reservoirs in these young basins. Subsurface geology, reservoir data (fluid pressure-temperature-chemistry), structural reconstructions, and seismic profiles provide important constraints for model geometry and parameter testing, and provide critical insight on how large-scale faults and aquifer networks influence the distribution and the hydrodynamics of liquid and gas-phase hydrocarbon migration. For example, pore pressure changes at a methane seepage site on the seafloor have been carefully analyzed to estimate large-scale fault permeability, which helps to constrain basin-scale natural gas migration models for the Santa Barbara Basin. We have developed our own 2-D multiphase finite element/finite IMPES numerical model, and successfully modeled hydrocarbon gas/liquid movement for intensely faulted and heterogeneous basin profiles of the Los Angeles Basin. Our simulations suggest that hydrocarbon reservoirs that are today aligned with the Newport-Inglewood Fault Zone were formed by massive hydrocarbon flows from deeply buried source beds in the central synclinal region during post-Miocene time. Fault permeability, capillarity forces between the fault and juxtaposition of aquifers/aquitards, source oil saturation, and rate of generation control the efficiency of a petroleum trap and carbon sequestration. This research is focused on natural processes in real geologic systems, but our results will also contribute to an understanding of the subsurface behavior of injected anthropogenic greenhouse gases, especially when targeted storage sites may be influenced by regional faults, which are ubiquitous in the Earth's crust.

The Intrinsic Variability in the Water Vapor Saturation Ratio due to Turbulence

NASA Astrophysics Data System (ADS)

Anderson, J. C.; Cantrell, W. H.; Chandrakar, K. K.; Kostinski, A. B.; Niedermeier, D.; Shaw, R. A.

2017-12-01

In the atmosphere, the concentration of water vapor plays an important role in Earth's weather and climate. The mean concentration of water vapor is key to its efficiency as a greenhouse gas; the fluctuations about the mean are important for heat fluxes near the surface of earth. In boundary layer clouds, fluctuations in the water vapor concentration are linked to turbulence. Conditions representative of boundary layer clouds are simulated in Michigan Tech's multiphase, turbulent reaction chamber, the ∏ chamber, where the boundary conditions are controlled and repeatable. Measurements for temperature and water vapor concentration were recorded under forced Rayleigh-Bénard convection. As expected, the distributions for temperature and water vapor concentration broaden as the turbulence becomes more vigorous. From these two measurements the saturation ratio can be calculated. The fluctuations in the water vapor concentration are more important to the variability in the saturation ratio than fluctuations in temperature. In a cloud, these fluctuations in the saturation ratio can result in some cloud droplets experiencing much higher supersaturations. Those "lucky" droplets grow by condensation at a faster rate than other cloud droplets. The difference in the droplet growth rate could contribute to a broadened droplet distribution, which leads to the onset of collision-coalescence. With more intense turbulence these effect will become more pronounced as the fluctuations about the mean saturation ratio become more pronounced.

Toward multiscale modelings of grain-fluid systems

NASA Astrophysics Data System (ADS)

Chareyre, Bruno; Yuan, Chao; Montella, Eduard P.; Salager, Simon

2017-06-01

Computationally efficient methods have been developed for simulating partially saturated granular materials in the pendular regime. In contrast, one hardly avoid expensive direct resolutions of 2-phase fluid dynamics problem for mixed pendular-funicular situations or even saturated regimes. Following previous developments for single-phase flow, a pore-network approach of the coupling problems is described. The geometry and movements of phases and interfaces are described on the basis of a tetrahedrization of the pore space, introducing elementary objects such as bridge, meniscus, pore body and pore throat, together with local rules of evolution. As firmly established local rules are still missing on some aspects (entry capillary pressure and pore-scale pressure-saturation relations, forces on the grains, or kinetics of transfers in mixed situations) a multi-scale numerical framework is introduced, enhancing the pore-network approach with the help of direct simulations. Small subsets of a granular system are extracted, in which multiphase scenario are solved using the Lattice-Boltzman method (LBM). In turns, a global problem is assembled and solved at the network scale, as illustrated by a simulated primary drainage.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

PubMed

Vorobev, Anatoliy

2010-11-01

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

A New Unsteady Model for Dense Cloud Cavitation in Cryogenic Fluids

NASA Technical Reports Server (NTRS)

Hosangadi, Ashvin; Ahuja, Vineet

2005-01-01

Contents include the following: Background on thermal effects in cavitation. Physical properties of hydrogen. Multi-phase cavitation with thermal effect. Solution procedure. Cavitation model overview. Cavitation source terms. New cavitation model. Source term for bubble growth. One equation les model. Unsteady ogive simulations: liquid nitrogen. Unsteady incompressible flow in a pipe. Time averaged cavity length for NACA15 flowfield.

Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid-vapor for multi-phase flows

NASA Astrophysics Data System (ADS)

Nemati, Maedeh; Shateri Najaf Abady, Ali Reza; Toghraie, Davood; Karimipour, Arash

2018-01-01

The incorporation of different equations of state into single-component multiphase lattice Boltzmann model is considered in this paper. The original pseudopotential model is first detailed, and several cubic equations of state, the Redlich-Kwong, Redlich-Kwong-Soave, and Peng-Robinson are then incorporated into the lattice Boltzmann model. A comparison of the numerical simulation achievements on the basis of density ratios and spurious currents is used for presentation of the details of phase separation in these non-ideal single-component systems. The paper demonstrates that the scheme for the inter-particle interaction force term as well as the force term incorporation method matters to achieve more accurate and stable results. The velocity shifting method is demonstrated as the force term incorporation method, among many, with accuracy and stability results. Kupershtokh scheme also makes it possible to achieve large density ratio (up to 104) and to reproduce the coexistence curve with high accuracy. Significant reduction of the spurious currents at vapor-liquid interface is another observation. High-density ratio and spurious current reduction resulted from the Redlich-Kwong-Soave and Peng-Robinson EOSs, in higher accordance with the Maxwell construction results.

A simulation of rainfall infiltration based on two-phase flow

NASA Astrophysics Data System (ADS)

Wang, Jun; Xi, Niannian; Liu, Gang; Hao, Shuang

2016-04-01

Rainfall infiltration in slope usually is one of major reasons cause landslide, which involves multiphase flow coupling with soil, water and gas. In order to study the mechanism of landslide caused by rainfall infiltration, a simulation of rainfall infiltration of DaPing slope, which locates in the Three Gorges Region of China, is presented based on the numerical solution of governing equations of two-phase flow in this paper. The results of this research suggest that there are two sections can be divided in the surface of slope, one is inflow area and the other is overflow area, according to where it is infiltration and discharge. The general inflow area is on the upside of slope, while the overflow area is on the underside. The middle section of slope is on a fluctuant position between inflow and overflow area, which is dramatically affected by the water content inside of slope. Moreover, the average rate of infiltration is more stable in both inflow and overflow area, whose numerical value is depend on the geometry and transmission characteristics of slope. And the factors of rainfall characteristics, surface flow and temperature have little effect on them. Furthermore, in the inflow area, when rainfall intensity is higher than infiltration the rain on the surface of slope will run off, otherwise water and gas will completely infiltrate through soil. The situation is different in the overflow area whose overland flow condition is depended on whether it is saturated or not inside of slope. When it is saturated in the slope, there is no infiltration in the overflow area. But when it is unsaturated, the infiltration intensity will equal to rainfall intensity. In a summary, the difference from inflow and overflow area is the evidence that the landslide may likely to happen on the slope of overflow area when it comes to a rainfall. It is disadvantageous for slope stability when transmitting the pressure of saturated water weight at the top of slope through the pore gas to groundwater, the groundwater pressure will increased sharply.

Dynamic properties of interfaces in soft matter: Experiments and theory

NASA Astrophysics Data System (ADS)

Sagis, Leonard M. C.

2011-10-01

The dynamic properties of interfaces often play a crucial role in the macroscopic dynamics of multiphase soft condensed matter systems. These properties affect the dynamics of emulsions, of dispersions of vesicles, of biological fluids, of coatings, of free surface flows, of immiscible polymer blends, and of many other complex systems. The study of interfacial dynamic properties, surface rheology, is therefore a relevant discipline for many branches of physics, chemistry, engineering, and life sciences. In the past three to four decades a vast amount of literature has been produced dealing with the rheological properties of interfaces stabilized by low molecular weight surfactants, proteins, (bio)polymers, lipids, colloidal particles, and various mixtures of these surface active components. In this paper recent experiments are reviewed in the field of surface rheology, with particular emphasis on the models used to analyze surface rheological data. Most of the models currently used are straightforward generalizations of models developed for the analysis of rheological data of bulk phases. In general the limits on the validity of these generalizations are not discussed. Not much use is being made of recent advances in nonequilibrium thermodynamic formalisms for multiphase systems, to construct admissible models for the stress-deformation behavior of interfaces. These formalisms are ideally suited to construct thermodynamically admissible constitutive equations for rheological behavior that include the often relevant couplings to other fluxes in the interface (heat and mass), and couplings to the transfer of mass from the bulk phase to the interface. In this review recent advances in the application of classical irreversible thermodynamics, extended irreversible thermodynamics, rational thermodynamics, extended rational thermodynamics, and the general equation for the nonequilibrium reversible-irreversible coupling formalism to multiphase systems are also discussed, and shown how these formalisms can be used to generate a wide range of thermodynamically admissible constitutive models for the surface stress tensor. Some of the generalizations currently in use are shown to have only limited validity. The aim of this review is to stimulate new developments in the fields of experimental surface rheology and constitutive modeling of multiphase systems using nonequilibrium thermodynamic formalisms and to promote a closer integration of these disciplines.

Pseudorapidity Asymmetry and Centrality Dependence of Charged Hadron Spectra in d+Au collisions at sqrt(sNN) = 200 GeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, J.; Aggarwal, M.M.; Ahammed, Z.

2005-01-12

The pseudorapidity asymmetry and centrality dependence of charged hadron spectra in d+Au collisions at {radical}s{sub NN} = 200 GeV are presented. The charged particle density at mid-rapidity, its pseudorapidity asymmetry and centrality dependence are reasonably reproduced by a Multi-Phase Transport model, by HIJING, and by the latest calculations in a saturation model. Ratios of transverse momentum spectra between backward and forward pseudorapidity are above unity for p{sub T} below 5 GeV/c. The ratio of central to peripheral spectra in d+Au collisions shows enhancement at 2 < p{sub T} < 6 GeV/c, with a larger effect at backward rapidity than forwardmore » rapidity. Our measurements are in qualitative agreement with gluon saturation and in contrast to calculations based on incoherent multiple partonic scatterings.« less

Gas occurrence property in shales of Tuha basin northwest china

NASA Astrophysics Data System (ADS)

Chen, Jinlong; Huang, Zhilong

2017-04-01

Pore of rock under formation condition must be fulfilled by gas, oil, or water, so the volume of water and gas is equation to porous volume in shale gas. The occurrences states of gas are free gas, solution gas, and absorbed gas. Field analysis is used to obtain total gas content by improved lost gas recover method. Free gas content acquired by pore proportion of gas, which use measured pore volume minus water and oil saturation, convert gas content of standard condition by state equation. Water saturation obtain from core water content, oil saturation obtain from extract carbohydrate. Solution gas need gas solubility in oil and water to calculate solution gas content in standard condition. Absorbed gas, introduce Absorbed Gas Saturation ɛ, which acquire from isothermal adsorption volume vs field analysis gas content in many basins of published paper, need isothermal adsorption and Absorbed Gas Saturation to obtain absorbed gas content. All of the data build connect with logging value by regression equation. The gas content is 0.92-1.53 m3/t from field analysis, evaluate gas content is 1.33 m3/t average, free gas proportion is about 47%, absorbed gas counter for 49%, and solution gas is average 4%.

Experimental and theoretical investigation of LNAPL movement in stratified media during soil remediation.

PubMed

Lashanizadegan, A; Ayatollahi, Sh; Kazemi, H

2007-07-01

The saturation distribution and clean up efficiency of light non-aqueous phase liquid (LNAPL) in the strata beneath the earth has been the subject of many studies. Better understanding of LNAPL infiltration into layered soil is important for the effective design of remediation strategies. The objective of this study was to simulate LNAPL movement in homogenous and stratified porous media using gravity assisted inert gas injection (GAIGI) process as a cleaning technique. We used homogeneous and layered sandpacked transparent models that allows for visual observation of LNAPL movement in order to study LNAPL redistribution in a layered porous medium. Pore volume, porosity, absolute permeability, connate water saturation, and oil saturation of the models were determined experimentally. Seasonal water table movement and contaminated zone were established and then, under GAIGI process, clean up efficiency was determined. The downward displacement of LNAPL by gas drive resulted in very high LNAPL clean up efficiency. Using the contaminant production history in the homogeneous model, the LNAPL relative permeability was calculated and the results were extended to layered media. The numerical multi-phase flow model in porous media was validated with regard to the experimental results. This model is able to adequately reproduce the experimental LNAPL saturation profile and clean up efficiency.

Aspects of wellbore heat transfer during two-phase flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hasan, A.R.; Kabir, C.S.

1994-08-01

Wellbore fluid temperature is governed by the rate of heat loss from the wellbore to the surrounding formation, which in turn is a function of depth and production/injection time. The authors present an approach to estimate wellbore fluid temperature during steady-state two-phase flow. The method incorporates a new solution of the thermal diffusivity equation and the effect of both conductive and convective heat transport for the wellbore/formation system. For the multiphase flow in the wellbore, the Hasan-Kabir model has been adapted, although other mechanistic models may be used. A field example is used to illustrate the fluid temperature calculation proceduremore » and shows the importance of accounting for convection in the tubing/casing annulus. A sensitivity study shows that significant differences exist between the predicted wellhead temperature and the formation surface temperature and that the fluid temperature gradient is nonlinear. This study further shows that increased free gas lowers the wellhead temperature as a result of the Joule-Thompson effect. In such cases, the expression for fluid temperature developed earlier for single-phase flow should not be applied when multiphase flow is encountered. An appropriate expression is presented in this work for wellbores producing multiphase fluids.« less

A Step Towards CO2-Neutral Aviation

NASA Technical Reports Server (NTRS)

Brankovic, Andreja; Ryder, Robert C.; Hendricks, Robert C.; Huber, Marcia L.

2008-01-01

An approximation method for evaluation of the caloric equations used in combustion chemistry simulations is described. The method is applied to generate the equations of specific heat, static enthalpy, and Gibb's free energy for fuel mixtures of interest to gas turbine engine manufacturers. Liquid-phase fuel properties are also derived. The fuels investigated include JP-8, synthetic fuel, and two blends of JP-8 and synthetic fuel. The complete set of fuel property equations for both phases are implemented into a computational fluid dynamics (CFD) flow solver database, and multiphase, reacting flow simulations of a well-tested liquid-fueled combustor are performed. The simulations are a first step in understanding combustion system performance and operational issues when using alternate fuels, at practical engine operating conditions.

Solid-solution aqueous-solution equilibria: thermodynamic theory and representation

USGS Publications Warehouse

Glynn, P.D.; Reardon, E.J.

1990-01-01

Thorstenson and Plummer's (1977) "stoichiometric saturation' model is reviewed, and a general relation between stoichiometric saturation Kss constants and excess free energies of mixing is derived for a binary solid-solution B1-xCxA: GE = RT[ln Kss - xln(xKCA) - (l-x)ln((l-x)KBA)]. This equation allows a suitable excess free energy function, such as Guggenheim's (1937) sub-regular function, to be fitted from experimentally determined Kss constants. Solid-phase free energies and component activity-coefficients can then be determined from one or two fitted parameters and from the endmember solubility products KBA and KCA. A general form of Lippmann's (1977,1980) "solutus equation is derived from an examination of Lippmann's (1977,1980) "total solubility product' model. Lippmann's ??II or "total solubility product' variable is used to represent graphically not only thermodynamic equilibrium states and primary saturation states but also stoichiometric saturation and pure phase saturation states. -from Authors

Numerical Simulation of Shock/Detonation-Deformable-Particle Interaction with Constrained Interface Reinitialization

NASA Astrophysics Data System (ADS)

Zhang, Ju; Jackson, Thomas; Balachandar, Sivaramakrishnan

2015-06-01

We will develop a computational model built upon our verified and validated in-house SDT code to provide improved description of the multiphase blast wave dynamics where solid particles are considered deformable and can even undergo phase transitions. Our SDT computational framework includes a reactive compressible flow solver with sophisticated material interface tracking capability and realistic equation of state (EOS) such as Mie-Gruneisen EOS for multiphase flow modeling. The behavior of diffuse interface models by Shukla et al. (2010) and Tiwari et al. (2013) at different shock impedance ratio will be first examined and characterized. The recent constrained interface reinitialization by Shukla (2014) will then be developed to examine if conservation property can be improved. This work was supported in part by the U.S. Department of Energy and by the Defense Threat Reduction Agency.

Linear Power-Flow Models in Multiphase Distribution Networks: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernstein, Andrey; Dall'Anese, Emiliano

This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- frommore » advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Li; He, YaLing; Tao, Wen -Quan

The electrode of a vanadium redox flow battery generally is a carbon fibre-based porous medium, in which important physicochemical processes occur. In this work, pore-scale simulations are performed to study complex multiphase flow and reactive transport in the electrode by using the lattice Boltzmann method (LBM). Four hundred fibrous electrodes with different fibre diameters and porosities are reconstructed. Both the permeability and diffusivity of the reconstructed electrodes are predicted and compared with empirical relationships in the literature. Reactive surface area of the electrodes is also evaluated and it is found that existing empirical relationship overestimates the reactive surface under lowermore » porosities. Further, a pore-scale electrochemical reaction model is developed to study the effects of fibre diameter and porosity on electrolyte flow, V II/V III transport, and electrochemical reaction at the electrolyte-fibre surface. Finally, evolution of bubble cluster generated by the side reaction is studied by adopting a LB multiphase flow model. Effects of porosity, fibre diameter, gas saturation and solid surface wettability on average bubble diameter and reduction of reactive surface area due to coverage of bubbles on solid surface are investigated in detail. It is found that gas coverage ratio is always lower than that adopted in the continuum model in the literature. Furthermore, the current pore-scale studies successfully reveal the complex multiphase flow and reactive transport processes in the electrode, and the simulation results can be further upscaled to improve the accuracy of the current continuum-scale models.« less

Sound Speed and Attenuation in Multiphase Media

DTIC Science & Technology

2007-09-30

Number: N00014-04-1-0164 LONG-TERM GOALS One research goal developed from conducted shallow water (SW) acoustic transmission experiments in...code 1 only 14. ABSTRACT One research goal developed from conducted shallow water (SW) acoustic transmission experiments in sandy-silty areas [1...propagation code, such as Kraken [11], or with a poroelastic -parabolic-equation code, Ram, [ 12,13 ] with a depth dependent profiles and frequency

An Explicit Algorithm for the Simulation of Fluid Flow through Porous Media

NASA Astrophysics Data System (ADS)

Trapeznikova, Marina; Churbanova, Natalia; Lyupa, Anastasiya

2018-02-01

The work deals with the development of an original mathematical model of porous medium flow constructed by analogy with the quasigasdynamic system of equations and allowing implementation via explicit numerical methods. The model is generalized to the case of multiphase multicomponent fluid and takes into account possible heat sources. The proposed approach is verified by a number of test predictions.

Geothermal reservoir simulation

NASA Technical Reports Server (NTRS)

Mercer, J. W., Jr.; Faust, C.; Pinder, G. F.

1974-01-01

The prediction of long-term geothermal reservoir performance and the environmental impact of exploiting this resource are two important problems associated with the utilization of geothermal energy for power production. Our research effort addresses these problems through numerical simulation. Computer codes based on the solution of partial-differential equations using finite-element techniques are being prepared to simulate multiphase energy transport, energy transport in fractured porous reservoirs, well bore phenomena, and subsidence.

Contribution to modeling the viscosity Arrhenius-type equation for saturated pure fluids

NASA Astrophysics Data System (ADS)

Tian, Jianxiang; Zhang, Laibin

2016-09-01

Recently, Haj-Kacem et al. proposed an equation modeling the relationship between the two parameters of viscosity Arrhenius-type equations [Fluid Phase Equilibria 383, 11 (2014)]. The authors found that the two parameters are dependent upon each other in an exponential function form. In this paper, we reconsidered their ideas and calculated the two parameter values for 49 saturated pure fluids by using the experimental data in the NIST WebBook. Our conclusion is different with the ones of Haj-Kacem et al. We found that (the linearity shown by) the Arrhenius equation stands strongly only in low temperature range and that the two parameters of the Arrhenius equation are independent upon each other in the whole temperature range from the triple point to the critical point.

Empirical equations to predict the sulfur content of mafic magmas at sulfide saturation and applications to magmatic sulfide deposits

NASA Astrophysics Data System (ADS)

Li, Chusi; Ripley, Edward M.

2005-03-01

Empirical equations to predict the sulfur content of a mafic magma at the time of sulfide saturation have been developed based on several sets of published experimental data. The S content at sulfide saturation (SCSS) can be expressed as: ln X_{text S} = 1.229 - 0.74(10^4/T) - 0.021(P) - 0.311 ln X_{{text{FeO}}} - 6.166X_{{text{SiO}}_{text{2}}} - 9.153X_{{text{Na}}_{text{2}} {text{O + K}}_{text{2}} {text{O}}} - 1.914X_{{text{MgO}}} + 6.594X_{{text{FeO}}} where T is in degrees Kelvin, X is mole fraction and P is in kbar. The squared multiple correlation coefficient ( r 2) for the equation is 0.88. Application of the equation to data from sulfide-saturated mid-ocean ridge basalts (MORB) samples show that the SCSS is closely predicted for primitive MORBs, but that accuracy decreases for lower T (<1,130°C) and more evolved MORB samples. This suggests that because the calibrations are based on anhydrous experimental runs done at temperatures of 1,200°C and above, it is not possible to extrapolate them to significantly lower temperatures and hydrous conditions. Because the SCSS of a primitive MORB magma increases with decreasing P, sulfide saturation in MORB appears to be a function of the degree of en route assimilation of S from country rocks as well as the degree of fractional crystallization in shallow staging chambers. Application of the equation to the high- T impact melt sheet that produced the Sudbury Igneous Complex and associated Ni-Cu sulfide ores indicates that sulfide-saturation was reached at 1,500°C, well above the start of orthopyroxene crystallization at 1,190°C. This would permit ample time for the gravitational settling and collection of immiscible sulfide liquid that produced the high-grade ore bodies. The development of a platinum group element (PGE)-enriched layer in the Sonju Lake Intrusion of the Duluth Complex is thought to be due to the attainment of sulfide saturation in the magma after a period of fractional crystallization. Using the composition of the parent magma of the Sonju Lake Intrusion the presented equation indicates that sulfide saturation would have been reached at 60% crystallization, when iron oxide was a liquidus mineral; the prediction is in agreement with field evidence which indicates that PGE-enrichment occurs in the oxide-rich gabbro zone. Contamination and mixing processes that may be related to the attainment of sulfide saturation in mafic magmas can also be evaluated. Mixing of a siliceous melt and a liquid of olivine tholeiite composition, similar to that thought to be a reasonable parental composition for many Duluth Complex intrusions, can induce sulfide saturation at mixing ratios in excess of 0.1. If the contaminant contains low quantities of sulfur the mixing ratio required to promote saturation is reduced. Mixing of mafic magmas at various stages of fractionation is evaluated using magma compositions that are thought to be appropriate for the generation of the Merensky Reef in the Bushveld Complex. Magma mixing is shown to be an effective process for the attainment of sulfide saturation, depending strongly on the sulfur concentrations of the end-member magmas.

Formulation, Implementation and Validation of a Two-Fluid model in a Fuel Cell CFD Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Kunal; Cole, J. Vernon; Kumar, Sanjiv

2008-12-01

Water management is one of the main challenges in PEM Fuel Cells. While water is essential for membrane electrical conductivity, excess liquid water leads to flooding of catalyst layers. Despite the fact that accurate prediction of two-phase transport is key for optimal water management, understanding of the two-phase transport in fuel cells is relatively poor. Wang et. al. have studied the two-phase transport in the channel and diffusion layer separately using a multiphase mixture model. The model fails to accurately predict saturation values for high humidity inlet streams. Nguyen et. al. developed a two-dimensional, two-phase, isothermal, isobaric, steady state modelmore » of the catalyst and gas diffusion layers. The model neglects any liquid in the channel. Djilali et. al. developed a three-dimensional two-phase multicomponent model. The model is an improvement over previous models, but neglects drag between the liquid and the gas phases in the channel. In this work, we present a comprehensive two-fluid model relevant to fuel cells. Models for two-phase transport through Channel, Gas Diffusion Layer (GDL) and Channel-GDL interface, are discussed. In the channel, the gas and liquid pressures are assumed to be same. The surface tension effects in the channel are incorporated using the continuum surface force (CSF) model. The force at the surface is expressed as a volumetric body force and added as a source to the momentum equation. In the GDL, the gas and liquid are assumed to be at different pressures. The difference in the pressures (capillary pressure) is calculated using an empirical correlations. At the Channel-GDL interface, the wall adhesion affects need to be taken into account. SIMPLE-type methods recast the continuity equation into a pressure-correction equation, the solution of which then provides corrections for velocities and pressures. However, in the two-fluid model, the presence of two phasic continuity equations gives more freedom and more complications. A general approach would be to form a mixture continuity equation by linearly combining the phasic continuity equations using appropriate weighting factors. Analogous to mixture equation for pressure correction, a difference equation is used for the volume/phase fraction by taking the difference between the phasic continuity equations. The relative advantages of the above mentioned algorithmic variants for computing pressure correction and volume fractions are discussed and quantitatively assessed. Preliminary model validation is done for each component of the fuel cell. The two-phase transport in the channel is validated using empirical correlations. Transport in the GDL is validated against results obtained from LBM and VOF simulation techniques. The Channel-GDL interface transport will be validated against experiment and empirical correlation of droplet detachment at the interface.« less

Wave propagation through elastic porous media containing two immiscible fluids

NASA Astrophysics Data System (ADS)

Lo, Wei-Cheng; Sposito, Garrison; Majer, Ernest

2005-02-01

Acoustic wave phenomena in porous media containing multiphase fluids have received considerable attention in recent years because of an increasing scientific awareness of poroelastic behavior in groundwater aquifers. To improve quantitative understanding of these phenomena, a general set of coupled partial differential equations was derived to describe dilatational wave propagation through an elastic porous medium permeated by two immiscible fluids. These equations, from which previous models of dilatational wave propagation can be recovered as special cases, incorporate both inertial coupling and viscous drag in an Eulerian frame of reference. Two important poroelasticity concepts, the linearized increment of fluid content and the closure relation for porosity change, originally defined for an elastic porous medium containing a single fluid, also are generalized for a two-fluid system. To examine the impact of relative fluid saturation and wave excitation frequency (50, 100, 150, and 200 Hz) on free dilatational wave behavior in unconsolidated porous media, numerical simulations of the three possible modes of wave motion were conducted for Columbia fine sandy loam containing either an air-water or oil-water mixture. The results showed that the propagating (P1) mode, which results from in-phase motions of the solid framework and the two pore fluids, moves with a speed equal to the square root of the ratio of an effective bulk modulus to an effective density of the fluid-containing porous medium, regardless of fluid saturation and for both fluid mixtures. The nature of the pore fluids exerts a significant influence on the attenuation of the P1 wave. In the air-water system, attenuation was controlled by material density differences and the relative mobilities of the pore fluids, whereas in the oil-water system an effective kinematic shear viscosity of the pore fluids was the controlling parameter. On the other hand, the speed and attenuation of the two diffusive modes (P2, resulting from out-of-phase motions of the solid framework and the fluids, and P3, the result of capillary pressure fluctuations) were closely associated with an effective dynamic shear viscosity of the pore fluids. The P2 and P3 waves also had the same constant value of the quality factor, and by comparison of our results with previous research on these two dilatational wave modes in sandstones, both were found to be sensitive to the state of consolidation of the porous medium.

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

NASA Astrophysics Data System (ADS)

Abin, A.; Kalurachchi, J. J.; Kemblowski, M. W.; Chang, C.-M.

1996-08-01

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.

Reactive multiphase flow at the pore-scale: the melting of a crystalline framework during the injection of buoyant hot volatiles

NASA Astrophysics Data System (ADS)

Andrea, P.; Huber, C.; Bachmann, O.; Chopard, B.

2010-12-01

Multiphase reactive flows occur naturally in various environments in the shallow subsurface, e.g. CO2 injections in saturated reservoirs, exsolved methane flux in shallow sediments and H20-CO2 volatiles in magmatic systems. Because of their multiphase nature together with the nonlinear feedbacks between reactions (dissolution/melting or precipitation) and the flow field at the pore-scale, the study of these dynamical processes remains a great challenge. In this study we focus on the injection of buoyant hot volatiles exsolved from a magmatic intrusion underplating a crystal-rich magma (porous medium). We use some simple theoretical models and a pore-scale multiphase reactive lattice Boltzmann model to investigate how the heat carried by the volatile phase affects the evolution of the porous medium spatially and temporally. We find that when the reaction rate is relatively slow and when the injection rate of volatiles is large (high injection Capillary number), the dissolution of the porous medium can be described by a local Peclet number (ratio of advective to diffusive flux of heat/reactant in the main gas channel). When the injection rate of volatile is reduced, or when the reaction rate is large, the dynamics transition to more complex regimes, where subvertical gas channels are no longer stable and can break into disconnected gas slugs. For the case of the injection of hot volatiles in crystal-rich magmatic systems, we find that the excess enthalpy advected by buoyant volatiles penetrates the porous medium over distances ~r Pe, where r is the average radius of the volatile channel (~pore size). The transport of heat by buoyant gases through a crystal mush is therefore in most cases limited to distances < meters. Our results also suggest that buoyant volatiles can carry chemical species (Li,F, Cl) far into a mush as their corresponding local Peclet number is several orders of magnitude greater than that for heat, owing to their low diffusion coefficients.

Viscosity and surface tension effects during multiphase flow in propped fractures

NASA Astrophysics Data System (ADS)

Dzikowski, Michał; Dąbrowski, Marcin

2017-04-01

Geological sequestration of CO2 was proposed as an important mechanism to reduce its emission into atmosphere. CO2 exhibits a higher affinity to organic matter than methane molecules and, potentially, it could be pumped and stored in shale reservoirs while enhancing late stage shale gas production. A successful analysis of CO2 sequestration in low matrix permeability rocks such as shales requires a thorough understanding of multiphase flow in stimulated rock fractures, which provide most significant pathways for fluids in such systems. Multiphase fracture flows are also of great relevance to brine, oil and gas migration in petroleum systems, water and stream circulation in geothermal reservoirs, and chemical transport of non-aqueous phase liquids in shallow hydrogeological systems, particularly in partially saturated zones. There are various physical models that describe phenomena taking place during multiphase flow through porous media. One of key aspects that need to be considered are pore-scale effects related to capillarity. Unfortunately, detailed models that describe motion and evolution of phase or component boundary require direct numerical simulations and spatial resolutions that are hard to reach when considering industrial relevant systems. Main aim of the presented work was the development of reduced 2.5D models based on Brinkman approximation of thin domain flow that would be able to capture local scale phenomena without expensive 3D simulations. Presented approach was designed specifically to tackle incompressible and immiscible systems and is based on Continuous Surface Force approach presented by Brackbill et al., implemented using Lattice Boltzmann Method. Presented approach where firstly validated against standard test cases with known classical solution and known experimental data. In the second part, we present and discuss two component, immiscible permeability data for rough and propped fracture obtained with our code for a rage of proppants fraction, apertures and flow conditions.

Outcomes of a service teaching module on ODEs for physics students

NASA Astrophysics Data System (ADS)

Hyland, Diarmaid; van Kampen, Paul; Nolan, Brien C.

2018-07-01

This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore, necessary that students develop conceptual understanding of differential equations in addition to procedural skills. We have investigated the difficulties encountered by third-year students at Dublin City University in an introductory differential equations module. We developed a survey to identify these difficulties and administered it to students who had recently completed the module. We found that students' mathematical ability in relation to procedural competence is an issue in their study of differential equations, but not as severe an issue as their conceptual understanding. Mathematical competence alone is insufficient if we expect our students to be able to recognize the need for differential equations in a physical context and to be able to set up, solve and interpret the solutions of such equations. We discuss the implications of these results for the next stages of the research project.

A Step Towards CO2-Neutral Aviation

NASA Technical Reports Server (NTRS)

Brankovic, Andreja; Ryder, Robert C.; Hendricks, Robert C.; Huber, Marcia L.

2007-01-01

An approximation method for evaluation of the caloric equations used in combustion chemistry simulations is described. The method is applied to generate the equations of specific heat, static enthalpy, and Gibb's free energy for fuel mixtures of interest to gas turbine engine manufacturers. Liquid-phase fuel properties are also derived. The fuels include JP-8, synthetic fuel, and two fuel blends consisting of a mixture of JP-8 and synthetic fuel. The complete set of fuel property equations for both phases are implemented into a computational fluid dynamics (CFD) flow solver database, and multi-phase, reacting flow simulations of a well-tested liquid-fueled combustor are performed. The simulations are a first step in understanding combustion system performance and operational issues when using alternate fuels, at practical engine operating conditions.

Modeling of Thermal Performance of Multiphase Nuclear Fuel Cell Under Variable Gravity Conditions

NASA Technical Reports Server (NTRS)

Ding, Z.; Anghaie, S.

1996-01-01

A unique numerical method has been developed to model the dynamic processes of bulk evaporation and condensation processes, associated with internal heat generation and natural convection under different gravity levels. The internal energy formulation, for the bulk liquid-vapor phase change problems in an encapsulated container, was employed. The equations, governing the conservation of mass, momentum and energy for both phases involved in phase change, were solved. The thermal performance of a multiphase uranium tetra-fluoride fuel element under zero gravity, micro-gravity and normal gravity conditions has been investigated. The modeling yielded results including the evolution of the bulk liquid-vapor phase change process, the evolution of the liquid-vapor interface, the formation and development of the liquid film covering the side wall surface, the temperature distribution and the convection flow field in the fuel element. The strong dependence of the thermal performance of such multiphase nuclear fuel cell on the gravity condition has been revealed. Under all three gravity conditions, 0-g, 10(exp -3)-g, and 1-g, the liquid film is formed and covers the entire side wall. The liquid film covering the side wall is more isothermalized at the wall surface, which can prevent the side wall from being over-heated. As the gravity increases, the liquid film is thinner, the temperature gradient is larger across the liquid film and smaller across the vapor phase. This investigation provides valuable information about the thermal performance of multi-phase nuclear fuel element for the potential space and ground applications.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE PAGES

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-02-06

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Numerical Modeling of Buried Mine Explosions

DTIC Science & Technology

2001-03-01

Lawrence Livermore Laboratory Report, UCRL -50108, Rev. 1, June 1977. 12. Dobratz, B. M., and P. C. Crawford. “LLNL Explosives Handbook.” Lawrence...Livermore National Laboratory Report, UCRL -52997, January 1985. 13. Kerley, G. I. “Multiphase Equation of State for Iron.” Sandia National Laboratories...BOX 202797 AUSTIN TX 78720-2797 1 DARPA B KASPAR 3701 N FAIRFAX DR ARLINGTON VA 22203-1714 1 US MILITARY ACADEMY MATH SCI

Multicomponent, Multiphase Thermodynamics of Swelling Porous Media With Electroquasistatics. 1. Macroscale Field Equations

DTIC Science & Technology

2001-08-08

entropy inequality with independent variables consistent with several natural systems and apply the resulting constitutive theory near equi- librium...1973. [3] L. S. Bennethum and J. H. Cushman. Multiscale , hybrid mixture theory for swelling systems - I: Balance laws. International Journal of...Engineering Science, 34(2):125–145, 1996. [4] L. S. Bennethum and J. H. Cushman. Multiscale , hybrid mixture theory for swelling systems - II: Constitutive

A Conformal, Fully-Conservative Approach for Predicting Blast Effects on Ground Vehicles

DTIC Science & Technology

2014-04-01

time integration  Approximate Riemann Fluxes (HLLE, HLLC) ◦ Robust mixture model for multi-material flows  Multiple Equations of State ◦ Perfect Gas...Loci/CHEM: Chemically reacting compressible flow solver . ◦ Currently in production use by NASA for the simulation of rocket motors, plumes, and...vehicles  Loci/DROPLET: Eulerian and Lagrangian multiphase solvers  Loci/STREAM: pressure-based solver ◦ Developed by Streamline Numerics and

Unified multiphase modeling for evolving, acoustically coupled systems consisting of acoustic, elastic, poroelastic media and septa

NASA Astrophysics Data System (ADS)

Lee, Joong Seok; Kang, Yeon June; Kim, Yoon Young

2012-12-01

This paper presents a new modeling technique that can represent acoustically coupled systems in a unified manner. The proposed unified multiphase (UMP) modeling technique uses Biot's equations that are originally derived for poroelastic media to represent not only poroelastic media but also non-poroelastic ones ranging from acoustic and elastic media to septa. To recover the original vibro-acoustic behaviors of non-poroelastic media, material parameters of a base poroelastic medium are adjusted depending on the target media. The real virtue of this UMP technique is that interface coupling conditions between any media can be automatically satisfied, so no medium-dependent interface condition needs to be imposed explicitly. Thereby, the proposed technique can effectively model any acoustically coupled system having locally varying medium phases and evolving interfaces. A typical situation can occur in an iterative design process. Because the proposed UMP modeling technique needs theoretical justifications for further development, this work is mainly focused on how the technique recovers the governing equations of non-poroelastic media and expresses their interface conditions. We also address how to describe various boundary conditions of the media in the technique. Some numerical studies are carried out to demonstrate the validity of the proposed modeling technique.

Simulating single-phase and two-phase non-Newtonian fluid flow of a digital rock scanned at high resolution

NASA Astrophysics Data System (ADS)

Tembely, Moussa; Alsumaiti, Ali M.; Jouini, Mohamed S.; Rahimov, Khurshed; Dolatabadi, Ali

2017-11-01

Most of the digital rock physics (DRP) simulations focus on Newtonian fluids and overlook the detailed description of rock-fluid interaction. A better understanding of multiphase non-Newtonian fluid flow at pore-scale is crucial for optimizing enhanced oil recovery (EOR). The Darcy scale properties of reservoir rocks such as the capillary pressure curves and the relative permeability are controlled by the pore-scale behavior of the multiphase flow. In the present work, a volume of fluid (VOF) method coupled with an adaptive meshing technique is used to perform the pore-scale simulation on a 3D X-ray micro-tomography (CT) images of rock samples. The numerical model is based on the resolution of the Navier-Stokes equations along with a phase fraction equation incorporating the dynamics contact model. The simulations of a single phase flow for the absolute permeability showed a good agreement with the literature benchmark. Subsequently, the code is used to simulate a two-phase flow consisting of a polymer solution, displaying a shear-thinning power law viscosity. The simulations enable to access the impact of the consistency factor (K), the behavior index (n), along with the two contact angles (advancing and receding) on the relative permeability.

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

DOE PAGES

Bernstein, Andrey; Wang, Cong; Dall'Anese, Emiliano; ...

2018-01-01

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for themore » non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.« less

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernstein, Andrey; Wang, Cong; Dall'Anese, Emiliano

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for themore » non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.« less

Pairwise Interaction Extended Point-Particle (PIEP) model for multiphase jets and sedimenting particles

NASA Astrophysics Data System (ADS)

Liu, Kai; Balachandar, S.

2017-11-01

We perform a series of Euler-Lagrange direct numerical simulations (DNS) for multiphase jets and sedimenting particles. The forces the flow exerts on the particles in these two-way coupled simulations are computed using the Basset-Bousinesq-Oseen (BBO) equations. These forces do not explicitly account for particle-particle interactions, even though such pairwise interactions induced by the perturbations from neighboring particles may be important especially when the particle volume fraction is high. Such effects have been largely unaddressed in the literature. Here, we implement the Pairwise Interaction Extended Point-Particle (PIEP) model to simulate the effect of neighboring particle pairs. A simple collision model is also applied to avoid unphysical overlapping of solid spherical particles. The simulation results indicate that the PIEP model provides a more elaborative and complicated movement of the dispersed phase (droplets and particles). Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) project N00014-16-1-2617.

Numerical simulation for the air entrainment of aerated flow with an improved multiphase SPH model

NASA Astrophysics Data System (ADS)

Wan, Hang; Li, Ran; Pu, Xunchi; Zhang, Hongwei; Feng, Jingjie

2017-11-01

Aerated flow is a complex hydraulic phenomenon that exists widely in the field of environmental hydraulics. It is generally characterised by large deformation and violent fragmentation of the free surface. Compared to Euler methods (volume of fluid (VOF) method or rigid-lid hypothesis method), the existing single-phase Smooth Particle Hydrodynamics (SPH) method has performed well for solving particle motion. A lack of research on interphase interaction and air concentration, however, has affected the application of SPH model. In our study, an improved multiphase SPH model is presented to simulate aeration flows. A drag force was included in the momentum equation to ensure accuracy of the air particle slip velocity. Furthermore, a calculation method for air concentration is developed to analyse the air entrainment characteristics. Two studies were used to simulate the hydraulic and air entrainment characteristics. And, compared with the experimental results, the simulation results agree with the experimental results well.

Evaluation of infiltration models in contaminated landscape.

PubMed

Sadegh Zadeh, Kouroush; Shirmohammadi, Adel; Montas, Hubert J; Felton, Gary

2007-06-01

The infiltration models of Kostiakov, Green-Ampt, and Philip (two and three terms equations) were used, calibrated, and evaluated to simulate in-situ infiltration in nine different soil types. The Osborne-Moré modified version of the Levenberg-Marquardt optimization algorithm was coupled with the experimental data obtained by the double ring infiltrometers and the infiltration equations, to estimate the model parameters. Comparison of the model outputs with the experimental data indicates that the models can successfully describe cumulative infiltration in different soil types. However, since Kostiakov's equation fails to accurately simulate the infiltration rate as time approaches infinity, Philip's two-term equation, in some cases, produces negative values for the saturated hydraulic conductivity of soils, and the Green-Ampt model uses piston flow assumptions, we suggest using Philip's three-term equation to simulate infiltration and to estimate the saturated hydraulic conductivity of soils.

Microstructural characterization of hydrogen induced cracking in TRIP-assisted steel by EBSD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laureys, A., E-mail: Aurelie.Laureys@UGent.be; Depover, T.; Petrov, R.

2016-02-15

The present work evaluates hydrogen induced cracking by performing an elaborate EBSD (Electron BackScatter Diffraction) study in a steel with transformation induced plasticity (TRIP-assisted steel). This type of steel exhibits a multiphase microstructure which undergoes a deformation induced phase transformation. Additionally, each microstructural constituent displays a different behavior in the presence of hydrogen. The aim of this study is to obtain a better understanding on the mechanisms governing hydrogen induced crack initiation and propagation in the hydrogen saturated multiphase structure. Tensile tests on notched samples combined with in-situ electrochemical hydrogen charging were conducted. The tests were interrupted at stresses justmore » after reaching the tensile strength, i.e. before macroscopic failure of the material. This allowed to study hydrogen induced crack initiation and propagation by SEM (Scanning Electron Microscopy) and EBSD. A correlation was found between the presence of martensite, which is known to be very susceptible to hydrogen embrittlement, and the initiation of hydrogen induced cracks. Initiation seems to occur mostly by martensite decohesion. High strain regions surrounding the hydrogen induced crack tips indicate that further crack propagation may have occurred by the HELP (hydrogen-enhanced localized plasticity) mechanism. Small hydrogen induced cracks located nearby the notch are typically S-shaped and crack propagation was dominantly transgranularly. The second stage of crack propagation consists of stepwise cracking by coalescence of small hydrogen induced cracks. - Highlights: • Hydrogen induced cracking in TRIP-assisted steel is evaluated by EBSD. • Tensile tests were conducted on notched hydrogen saturated samples. • Crack initiation occurs by a H-Enhanced Interface DEcohesion (HEIDE) mechanism. • Crack propagation involves growth and coalescence of small cracks. • Propagation is governed by the characteristics of phases on the crack path.« less

Saturated liquid density of 1,1-difluoroethane(R 152a) and thermodynamic properties along the vapor-liquid coexistence curve

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sato, H.; Okada, M.; Uematsu, M.

1987-01-01

Saturated liquid densities of 1,1-difluoroethane (CH/sub 3/CHF/sub 2/) are measured at temperatures from 223 K to 363 K with the estimated uncertainty of +-0.2% by a magnetic densimetry. The experimental results are compared with the available experimental data and some correlations and equations of state. A simple correlation for the saturated liquid density is developed as a function of temperature. This correlation covers the temperature range up to the critical point which reproduces the present experimental results with the percent means deviation of 0.11%. Adding the available experimental data with respect to the vapor pressure, critical parameters, saturated vapor density,more » and the second virial coefficient to the present saturated liquid density data, the parameters of the Redlich-Kwong-Soave equation of state are determined and the thermodynamic properties along the vapor-liquid coexistence curve are derived.« less

Rugged Energy Landscapes in Multiphase Porous Media Flow: A Discrete-Domain Description

NASA Astrophysics Data System (ADS)

Cueto-Felgueroso, L.; Juanes, R.

2015-12-01

Immiscible displacements in porous media involve a complex sequence of pore-scale events, from the smooth, reversible displacement of interfaces to abrupt interfacial reconfigurations and rapid pore invasion cascades. Discontinuous changes in pressure or saturation have been referred to as Haines jumps, and they emerge as a key mechanism to understand the origin of hysteresis in porous media flow. Hysteresis persists at the many-pore scale: when multiple cycles of drainage and imbibition of a porous sample are conducted, a dense hysteresis diagram emerges. The interpretation of hysteresis as a consequence of irreversible transitions and multistability is at the heart of early hysteresis models, and in recent experiments, and points to an inherently non-equilibrium behavior. For a given volume fraction of fluids occupying the pore space, many stable configurations are possible, due to the tortuous network of nonuniform pores and throats that compose the porous medium, and to complex wetting and capillary transitions. Multistability indicates that porous media systems exhibit rugged energy landscapes, where the system may remain pinned at local energy minima for long times. We address the question of developing a zero-dimensional model that inherits the path-dependence and `'bursty'' behavior of immiscible displacements, and propose a discrete-domain model that captures the role of metastability and local equilibria in the origin of hysteresis. We describe the porous medium and fluid system as a discrete set of weakly connected, multistable compartments, charaterized by a unique free energy function. This description does not depend explicitly on past saturations, turning points, or drainage/imbibition labels. The system behaves hysteretically, and we rationalize its behavior as sweeping a complex metastability diagram, with dissipation arising from discrete switches among metastable branches. The hysteretic behavior of the pressure-saturation curve is controlled by the topography of the energy landscape, through the number of metastable regions of the compartments and characteristic height of the energy barriers separating the different basins. Our model opens the door to fully explore the interplay between hysteresis and fluctuations in multiphase displacements in porous media.

Collector modulation in high-voltage bipolar transistor in the saturation mode: Analytical approach

NASA Astrophysics Data System (ADS)

Dmitriev, A. P.; Gert, A. V.; Levinshtein, M. E.; Yuferev, V. S.

2018-04-01

A simple analytical model is developed, capable of replacing the numerical solution of a system of nonlinear partial differential equations by solving a simple algebraic equation when analyzing the collector resistance modulation of a bipolar transistor in the saturation mode. In this approach, the leakage of the base current into the emitter and the recombination of non-equilibrium carriers in the base are taken into account. The data obtained are in good agreement with the results of numerical calculations and make it possible to describe both the motion of the front of the minority carriers and the steady state distribution of minority carriers across the collector in the saturation mode.

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

NASA Astrophysics Data System (ADS)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

Lattice Boltzmann study of slip flow over structured surface with transverse slots

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Kai; Wang, Lei; Hou, Guoxiang; Leng, Wenjun

2018-04-01

Slip flow over structured superhydrophobic surface with transverse slots is investigated by the lattice Boltzmann method. The Shan-Chen multiphase model is employed to simulate the flow over gas bubbles in the slots. The Carnahan-Starling equation of state is applied to obtain large density ratio. The interface thickness of the multiphase model is discussed. We find that the Cahn number Cn should be smaller than 0.02 when the temperature T = 0.5T c to restrict the influence of interface thickness on slip length. Influences of slot fraction on slip length is then studied, and the result is compared with single LB simulation of which the interface is treated as free-slip boundary. The slip length obtained by the multiphase model is a little smaller. After that, the shape of the liquid-gas interface is considered, and simulations with different initial protrusion angles and capillary numbers are performed. Effective slip length as a function of initial protrusion angle is obtained. The result is in qualitative agreement with a previous study and main features are reproduced. Furthermore, the influence of Capillary number Ca is studied. Larger Ca causes larger interface deformation and smaller slip length. But when the interface is concaving into the slot, this influence is less obvious.

Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity

NASA Astrophysics Data System (ADS)

Hamon, F. P.; Mallison, B.; Tchelepi, H.

2016-12-01

In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem to compute the numerical flux. Heterogeneous numerical tests demonstrate that this extended IHU scheme is non-oscillatory and convergent upon refinement. They also illustrate the superior accuracy and nonlinear convergence rate of the IHU scheme compared with the standard phase-based upstream weighting approach.

Effect of wettability on two-phase quasi-static displacement: Validation of two pore scale modeling approaches

NASA Astrophysics Data System (ADS)

Verma, Rahul; Icardi, Matteo; Prodanović, Maša

2018-05-01

Understanding of pore-scale physics for multiphase flow in porous media is essential for accurate description of various flow phenomena. In particular, capillarity and wettability strongly influence capillary pressure-saturation and relative permeability relationships. Wettability is quantified by the contact angle of the fluid-fluid interface at the pore walls. In this work we focus on the non-trivial interface equilibria in presence of non-neutral wetting and complex geometries. We quantify the accuracy of a volume-of-fluid (VOF) formulation, implemented in a popular open-source computational fluid dynamics code, compared with a new formulation of a level set (LS) method, specifically developed for quasi-static capillarity-dominated displacement. The methods are tested in rhomboidal packings of spheres for a range of contact angles and for different rhomboidal configurations and the accuracy is evaluated against the semi-analytical solutions obtained by Mason and Morrow (1994). While the VOF method is implemented in a general purpose code that solves the full Navier-Stokes (NS) dynamics in a finite volume formulation, with additional terms to model surface tension, the LS method is optimized for the quasi-static case and, therefore, less computationally expensive. To overcome the shortcomings of the finite volume NS-VOF system for low capillary number flows, and its computational cost, we introduce an overdamped dynamics and a local time stepping to speed up the convergence to the steady state, for every given imposed pressure gradient (and therefore saturation condition). Despite these modifications, the methods fundamentally differ in the way they capture the interface, as well as in the number of equations solved and in the way the mean curvature (or equivalently capillary pressure) is computed. This study is intended to provide a rigorous validation study and gives important indications on the errors committed by these methods in solving more complex geometry and dynamics, where usually many sources of errors are interplaying.

Guide to the Revised Ground-Water Flow and Heat Transport Simulator: HYDROTHERM - Version 3

USGS Publications Warehouse

Kipp, Kenneth L.; Hsieh, Paul A.; Charlton, Scott R.

2008-01-01

The HYDROTHERM computer program simulates multi-phase ground-water flow and associated thermal energy transport in three dimensions. It can handle high fluid pressures, up to 1 ? 109 pascals (104 atmospheres), and high temperatures, up to 1,200 degrees Celsius. This report documents the release of Version 3, which includes various additions, modifications, and corrections that have been made to the original simulator. Primary changes to the simulator include: (1) the ability to simulate unconfined ground-water flow, (2) a precipitation-recharge boundary condition, (3) a seepage-surface boundary condition at the land surface, (4) the removal of the limitation that a specified-pressure boundary also have a specified temperature, (5) a new iterative solver for the linear equations based on a generalized minimum-residual method, (6) the ability to use time- or depth-dependent functions for permeability, (7) the conversion of the program code to Fortran 90 to employ dynamic allocation of arrays, and (8) the incorporation of a graphical user interface (GUI) for input and output. The graphical user interface has been developed for defining a simulation, running the HYDROTHERM simulator interactively, and displaying the results. The combination of the graphical user interface and the HYDROTHERM simulator forms the HYDROTHERM INTERACTIVE (HTI) program. HTI can be used for two-dimensional simulations only. New features in Version 3 of the HYDROTHERM simulator have been verified using four test problems. Three problems come from the published literature and one problem was simulated by another partially saturated flow and thermal transport simulator. The test problems include: transient partially saturated vertical infiltration, transient one-dimensional horizontal infiltration, two-dimensional steady-state drainage with a seepage surface, and two-dimensional drainage with coupled heat transport. An example application to a hypothetical stratovolcano system with unconfined ground-water flow is presented in detail. It illustrates the use of HTI with the combination precipitation-recharge and seepage-surface boundary condition, and functions as a tutorial example problem for the new user.

A new interpretation of the Keller-Segel model based on multiphase modelling.

PubMed

Byrne, Helen M; Owen, Markus R

2004-12-01

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.

Coupled hydromechanical and electromagnetic disturbances in unsaturated porous materials

NASA Astrophysics Data System (ADS)

Revil, A.; Mahardika, H.

2013-02-01

A theory of cross-coupled flow equations in unsaturated soils is necessary to predict (1) electroosmotic flow with application to electroremediation and agriculture, (2) the electroseismic and the seismoelectric effects to develop new geophysical methods to characterize the vadose zone, and (3) the streaming current, which can be used to investigate remotely ground water flow in unsaturated conditions in the capillary water regime. To develop such a theory, the cross-coupled generalized Darcy and Ohm constitutive equations of transport are extended to unsaturated conditions. This model accounts for inertial effects and for the polarization of porous materials. Rather than using the zeta potential, like in conventional theories for the saturated case, the key parameter used here is the quasi-static volumetric charge density of the pore space, which can be directly computed from the quasi-static permeability. The apparent permeability entering Darcy's law is also frequency dependent with a critical relaxation time that is, in turn, dependent on saturation. A decrease of saturation increases the associated relaxation frequency. The final form of the equations couples the Maxwell equations and a simplified form of two-fluid phases Biot theory accounting for water saturation. A generalized expression of the Richard equation is derived, accounting for the effect of the vibration of the skeleton during the passage of seismic waves and the electrical field. A new expression is obtained for the effective stress tensor. The model is tested against experimental data regarding the saturation and frequency dependence of the streaming potential coupling coefficient. The model is also adapted for two-phase flow conditions and a numerical application is shown for water flooding of a nonaqueous phase liquid (NAPL, oil) contaminated aquifer. Seismoelectric conversions are mostly taking place at the NAPL (oil)/water encroachment front and can be therefore used to remotely track the position of this front. This is not the case for other geophysical methods.

Coupled hydromechanical and electromagnetic disturbances in unsaturated porous materials

PubMed Central

Revil, A; Mahardika, H

2013-01-01

A theory of cross-coupled flow equations in unsaturated soils is necessary to predict (1) electroosmotic flow with application to electroremediation and agriculture, (2) the electroseismic and the seismoelectric effects to develop new geophysical methods to characterize the vadose zone, and (3) the streaming current, which can be used to investigate remotely ground water flow in unsaturated conditions in the capillary water regime. To develop such a theory, the cross-coupled generalized Darcy and Ohm constitutive equations of transport are extended to unsaturated conditions. This model accounts for inertial effects and for the polarization of porous materials. Rather than using the zeta potential, like in conventional theories for the saturated case, the key parameter used here is the quasi-static volumetric charge density of the pore space, which can be directly computed from the quasi-static permeability. The apparent permeability entering Darcy's law is also frequency dependent with a critical relaxation time that is, in turn, dependent on saturation. A decrease of saturation increases the associated relaxation frequency. The final form of the equations couples the Maxwell equations and a simplified form of two-fluid phases Biot theory accounting for water saturation. A generalized expression of the Richard equation is derived, accounting for the effect of the vibration of the skeleton during the passage of seismic waves and the electrical field. A new expression is obtained for the effective stress tensor. The model is tested against experimental data regarding the saturation and frequency dependence of the streaming potential coupling coefficient. The model is also adapted for two-phase flow conditions and a numerical application is shown for water flooding of a nonaqueous phase liquid (NAPL, oil) contaminated aquifer. Seismoelectric conversions are mostly taking place at the NAPL (oil)/water encroachment front and can be therefore used to remotely track the position of this front. This is not the case for other geophysical methods. PMID:23741078

Accurate solution of the Poisson equation with discontinuities

NASA Astrophysics Data System (ADS)

Nave, Jean-Christophe; Marques, Alexandre; Rosales, Rodolfo

2017-11-01

Solving the Poisson equation in the presence of discontinuities is of great importance in many applications of science and engineering. In many cases, the discontinuities are caused by interfaces between different media, such as in multiphase flows. These interfaces are themselves solutions to differential equations, and can assume complex configurations. For this reason, it is convenient to embed the interface into a regular triangulation or Cartesian grid and solve the Poisson equation in this regular domain. We present an extension of the Correction Function Method (CFM), which was developed to solve the Poisson equation in the context of embedded interfaces. The distinctive feature of the CFM is that it uses partial differential equations to construct smooth extensions of the solution in the vicinity of interfaces. A consequence of this approach is that it can achieve high order of accuracy while maintaining compact discretizations. The extension we present removes the restrictions of the original CFM, and yields a method that can solve the Poisson equation when discontinuities are present in the solution, the coefficients of the equation (material properties), and the source term. We show results computed to fourth order of accuracy in two and three dimensions. This work was partially funded by DARPA, NSF, and NSERC.

Pore network modeling to explore the effects of compression on multiphase transport in polymer electrolyte membrane fuel cell gas diffusion layers

NASA Astrophysics Data System (ADS)

Fazeli, Mohammadreza; Hinebaugh, James; Fishman, Zachary; Tötzke, Christian; Lehnert, Werner; Manke, Ingo; Bazylak, Aimy

2016-12-01

Understanding how compression affects the distribution of liquid water and gaseous oxygen in the polymer electrolyte membrane fuel cell gas diffusion layer (GDL) is vital for informing the design of improved porous materials for effective water management strategies. Pore networks extracted from synchrotron-based micro-computed tomography images of compressed GDLs were employed to simulate liquid water transport in GDL materials over a range of compression pressures. The oxygen transport resistance was predicted for each sample under dry and partially saturated conditions. A favorable GDL compression value for a preferred liquid water distribution and oxygen diffusion was found for Toray TGP-H-090 (10%), yet an optimum compression value was not recognized for SGL Sigracet 25BC. SGL Sigracet 25BC exhibited lower transport resistance values compared to Toray TGP-H-090, and this is attributed to the additional diffusion pathways provided by the microporous layer (MPL), an effect that is particularly significant under partially saturated conditions.

Numerical modeling of interface displacement in heterogeneously wetting porous media

NASA Astrophysics Data System (ADS)

Hiller, T.; Brinkmann, M.; Herminghaus, S.

2013-12-01

We use the mesoscopic particle method stochastic rotation dynamics (SRD) to simulate immiscible multi-phase flow on the pore and sub-pore scale in three dimensions. As an extension to the standard SRD method, we present an approach on implementing complex wettability on heterogeneous surfaces. We use 3D SRD to simulate immiscible two-phase flow through a model porous medium (disordered packing of spherical beads) where the substrate exhibits different spatial wetting patterns. The simulations are designed to resemble experimental measurements of capillary pressure saturation. We show that the correlation length of the wetting patterns influences the temporal evolution of the interface and thus percolation, residual saturation and work dissipated during the fluid displacement. Our numerical results are in qualitatively good agreement with the experimental data. Besides of modeling flow in porous media, our SRD implementation allows us to address various questions of interfacial dynamics, e.g. the formation of capillary bridges between spherical beads or droplets in microfluidic applications to name only a few.

Reflection of acoustic wave from the elastic seabed with an overlying gassy poroelastic layer

NASA Astrophysics Data System (ADS)

Chen, Weiyun; Wang, Zhihua; Zhao, Kai; Chen, Guoxing; Li, Xiaojun

2015-10-01

Based on the multiphase poroelasticity theory, the reflection characteristics of an obliquely incident acoustic wave upon a plane interface between overlying water and a gassy marine sediment layer with underlying elastic solid seabed are investigated. The sandwiched gassy layer is modelled as a porous material with finite thickness, which is saturated by two compressible and viscous fluids (liquid and gas). The closed-form expression for the amplitude ratio of the reflected wave, called reflection coefficient, is derived theoretically according to the boundary conditions at the upper and lower interfaces in our proposed model. Using numerical calculation, the influences of layer thickness, incident angle, wave frequency and liquid saturation of sandwiched porous layer on the reflection coefficient are analysed, respectively. It is revealed that the reflection coefficient is closely associated with incident angle and sandwiched layer thickness. Moreover, in different frequency ranges, the dependence of the wave reflection characteristics on moisture (or gas) variations in the intermediate marine sediment layer is distinguishing.

Computational Flow Analysis of Ultra High Pressure Firefighting Technology with Application to Long Range Nozzle Design

DTIC Science & Technology

2010-03-01

release; distribution unlimited. Ref AFRL/RXQ Public Affairs Case # 10-100. Document contains color images . Although aqueous fire fighting agent...in conjunction with the standard Eulerian multiphase flow model. The two- equation k- model was selected due to its wide industrial application in...energy (k) and its dissipation rate (). Because of their heuristic development, RANS models have applicable limitations and in general must be

Plasma Heating and Ultrafast Semiconductor Laser Modulation Through a Terahertz Heating Field

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Ning, C. Z.

2000-01-01

Electron-hole plasma heating and ultrafast modulation in a semiconductor laser under a terahertz electrical field are investigated using a set of hydrodynamic equations derived from the semiconductor Bloch equations. The self-consistent treatment of lasing and heating processes leads to the prediction of a strong saturation and degradation of modulation depth even at moderate terahertz field intensity. This saturation places a severe limit to bandwidth achievable with such scheme in ultrafast modulation. Strategies for increasing modulation depth are discussed.

Experimental and numerical investigations on freeze-drying of porous media with prebuilt porosity

NASA Astrophysics Data System (ADS)

Wang, Wei; Yang, Jing; Hu, Dapeng; Pan, Yanqiu; Wang, Shihao; Chen, Guohua

2018-05-01

Freeze-drying of initially porous frozen material was investigated aimed at improving the process economics by reducing drying time and raising productivity. Experimental results showed that freeze-drying can be significantly enhanced by the frozen material with prebuilt porosity, and about 31% of drying time can be saved compared with the conventionally solid frozen material under the tested operating conditions. A multiphase transport model was formulated based on the local mass non-equilibrium assumption. Numerical results showed excellent agreements between measured and predicted drying curves. Analyses of saturation and temperature profiles displayed that volumetric sublimation-desorption can occur for the initially porous frozen material.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

An improved method for estimating capillary pressure from 3D microtomography images and its application to the study of disconnected nonwetting phase

NASA Astrophysics Data System (ADS)

Li, Tianyi; Schlüter, Steffen; Dragila, Maria Ines; Wildenschild, Dorthe

2018-04-01

We present an improved method for estimating interfacial curvatures from x-ray computed microtomography (CMT) data that significantly advances the potential for this tool to unravel the mechanisms and phenomena associated with multi-phase fluid motion in porous media. CMT data, used to analyze the spatial distribution and capillary pressure-saturation (Pc-S) relationships of liquid phases, requires accurate estimates of interfacial curvature. Our improved method for curvature estimation combines selective interface modification and distance weighting approaches. It was verified against synthetic (analytical computer-generated) and real image data sets, demonstrating a vast improvement over previous methods. Using this new tool on a previously published data set (multiphase flow) yielded important new insights regarding the pressure state of the disconnected nonwetting phase during drainage and imbibition. The trapped and disconnected non-wetting phase delimits its own hysteretic Pc-S curve that inhabits the space within the main hysteretic Pc-S loop of the connected wetting phase. Data suggests that the pressure of the disconnected, non-wetting phase is strongly modified by the pore geometry rather than solely by the bulk liquid phase that surrounds it.

Large eddy simulation of cavitating flows

NASA Astrophysics Data System (ADS)

Gnanaskandan, Aswin; Mahesh, Krishnan

2014-11-01

Large eddy simulation on unstructured grids is used to study hydrodynamic cavitation. The multiphase medium is represented using a homogeneous equilibrium model that assumes thermal equilibrium between the liquid and the vapor phase. Surface tension effects are ignored and the governing equations are the compressible Navier Stokes equations for the liquid/vapor mixture along with a transport equation for the vapor mass fraction. A characteristic-based filtering scheme is developed to handle shocks and material discontinuities in non-ideal gases and mixtures. A TVD filter is applied as a corrector step in a predictor-corrector approach with the predictor scheme being non-dissipative and symmetric. The method is validated for canonical one dimensional flows and leading edge cavitation over a hydrofoil, and applied to study sheet to cloud cavitation over a wedge. This work is supported by the Office of Naval Research.

Core Flooding Experiments Combined with X-rays and Micro-PET Imaging as a Tool to Calculate Fluid Saturations in a Fracture

NASA Astrophysics Data System (ADS)

Gran, M.; Zahasky, C.; Garing, C.; Pollyea, R. M.; Benson, S. M.

2017-12-01

One way to reduce CO2 emissions is to capture CO2 generated in power plants and other industrial sources to inject it into a geological formation. Sedimentary basins are the ones traditionally used to store CO2 but the emission sources are not always close to these type of basins. In this case, basalt rocks present a good storage alternative due their extent and also their potential for mineral trapping. Flow through basaltic rocks is governed by the permeable paths provided by rock fractures. Hence, knowing the behavior of the multiphase flow in these fractures becomes crucial. With the aim to describe how aperture and liquid-gas interface changes in the fracture affect relative permeability and what are the implications of permeability stress dependency, a series of core experiments were conducted. To calculate fracture apertures and fluid saturations, core flooding experiments combined with medical X-Ray CT scanner and micro-PET imaging (Micro Positron Emission Tomography) were performed. Capillary pressure and relative permeability drainage curves were simultaneously measured in a fractured basalt core under typical storage reservoir pressures and temperatures. The X-Ray scanner allows fracture apertures to be measured quite accurately even for fractures as small as 30 µ, but obtaining fluid saturations is not straightforward. The micro-PET imaging provides dynamic measurements of tracer distributions which can be used to calculate saturation. Here new experimental data is presented and the challenges associated with measuring fluid saturations using both X-Rays and micro-PET are discussed.

Comparison of two-dimensional and three-dimensional simulations of dense nonaqueous phase liquids (DNAPLs): Migration and entrapment in a nonuniform permeability field

NASA Astrophysics Data System (ADS)

Christ, John A.; Lemke, Lawrence D.; Abriola, Linda M.

2005-01-01

The influence of reduced dimensionality (two-dimensional (2-D) versus 3-D) on predictions of dense nonaqueous phase liquid (DNAPL) infiltration and entrapment in statistically homogeneous, nonuniform permeability fields was investigated using the University of Texas Chemical Compositional Simulator (UTCHEM), a 3-D numerical multiphase simulator. Hysteretic capillary pressure-saturation and relative permeability relationships implemented in UTCHEM were benchmarked against those of another lab-tested simulator, the Michigan-Vertical and Lateral Organic Redistribution (M-VALOR). Simulation of a tetrachloroethene spill in 16 field-scale aquifer realizations generated DNAPL saturation distributions with approximately equivalent distribution metrics in two and three dimensions, with 2-D simulations generally resulting in slightly higher maximum saturations and increased vertical spreading. Variability in 2-D and 3-D distribution metrics across the set of realizations was shown to be correlated at a significance level of 95-99%. Neither spill volume nor release rate appeared to affect these conclusions. Variability in the permeability field did affect spreading metrics by increasing the horizontal spreading in 3-D more than in 2-D in more heterogeneous media simulations. The assumption of isotropic horizontal spatial statistics resulted, on average, in symmetric 3-D saturation distribution metrics in the horizontal directions. The practical implication of this study is that for statistically homogeneous, nonuniform aquifers, 2-D simulations of saturation distributions are good approximations to those obtained in 3-D. However, additional work will be needed to explore the influence of dimensionality on simulated DNAPL dissolution.

MultiLaue: A Technique to Extract d-spacings from Laue XRD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gainsforth, Zack; Marcus, Matthew A.; Tamura, Nobumichi

We present that broad spectrum X-ray Diffraction (XRD) is named Laue after Max von Laue, and is the original XRD technique. Today, monochromatic XRD is more common because Bragg's equation allows determination of d-spacings where Laue does not. Laue still remains in use for single crystal systems because it can be used to make very accurate unit cell determinations as well as for strain and orientation mapping. Lastly, a Laue technique which could provide unambiguous determination of lattice spacings, a la Bragg's equation would be a huge leap forward, especially for multiphase samples such as meteorites, interplanetary dust particles andmore » some geological specimens.« less

MultiLaue: A Technique to Extract d-spacings from Laue XRD

DOE PAGES

Gainsforth, Zack; Marcus, Matthew A.; Tamura, Nobumichi; ...

2016-07-25

We present that broad spectrum X-ray Diffraction (XRD) is named Laue after Max von Laue, and is the original XRD technique. Today, monochromatic XRD is more common because Bragg's equation allows determination of d-spacings where Laue does not. Laue still remains in use for single crystal systems because it can be used to make very accurate unit cell determinations as well as for strain and orientation mapping. Lastly, a Laue technique which could provide unambiguous determination of lattice spacings, a la Bragg's equation would be a huge leap forward, especially for multiphase samples such as meteorites, interplanetary dust particles andmore » some geological specimens.« less

Direct numerical simulation of a combusting droplet with convection

NASA Technical Reports Server (NTRS)

Liang, Pak-Yan

1992-01-01

The evaporation and combustion of a single droplet under forced and natural convection was studied numerically from first principles using a numerical scheme that solves the time-dependent multiphase and multispecies Navier-Stokes equations and tracks the sharp gas-liquid interface cutting across an arbitrary Eulerian grid. The flow fields both inside and outside of the droplet are resolved in a unified fashion. Additional governing equations model the interphase mass, energy, and momentum exchange. Test cases involving iso-octane, n-hexane, and n-propanol droplets show reasonable comparison rate, and flame stand-off distance. The partially validated code is, thus, readied to be applied to more demanding droplet combustion situations where substantial drop deformation render classical models inadequate.

Opening-mode cracking in asphalt pavements : crack initiation and saturation.

DOT National Transportation Integrated Search

2009-12-01

This paper investigates the crack initiation and saturation for opening-mode cracking. Using elastic governing equations : and a weak form stress boundary condition, we derive an explicit solution of elastic fields in the surface course and : obtain ...

A hybrid formulation for the numerical simulation of condensed phase explosives

NASA Astrophysics Data System (ADS)

Michael, L.; Nikiforakis, N.

2016-07-01

In this article we present a new formulation and an associated numerical algorithm, for the simulation of combustion and transition to detonation of condensed-phase commercial- and military-grade explosives, which are confined by (or in general interacting with one or more) compliant inert materials. Examples include confined rate-stick problems and interaction of shock waves with gas cavities or solid particles in explosives. This formulation is based on an augmented Euler approach to account for the mixture of the explosive and its products, and a multi-phase diffuse interface approach to solve for the immiscible interaction between the mixture and the inert materials, so it is in essence a hybrid (augmented Euler and multi-phase) model. As such, it has many of the desirable features of the two approaches and, critically for our applications of interest, it provides the accurate recovery of temperature fields across all components. Moreover, it conveys a lot more physical information than augmented Euler, without the complexity of full multi-phase Baer-Nunziato-type models or the lack of robustness of augmented Euler models in the presence of more than two components. The model can sustain large density differences across material interfaces without the presence of spurious oscillations in velocity and pressure, and it can accommodate realistic equations of state and arbitrary (pressure- or temperature-based) reaction-rate laws. Under certain conditions, we show that the formulation reduces to well-known augmented Euler or multi-phase models, which have been extensively validated and used in practice. The full hybrid model and its reduced forms are validated against problems with exact (or independently-verified numerical) solutions and evaluated for robustness for rate-stick and shock-induced cavity collapse case-studies.

An immersed boundary method for fluid-structure interaction with compressible multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Li; Currao, Gaetano M. D.; Han, Feng; Neely, Andrew J.; Young, John; Tian, Fang-Bao

2017-10-01

This paper presents a two-dimensional immersed boundary method for fluid-structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid-structure interaction coupling. In the flow solver, the compressible multiphase Navier-Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge-Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.

An improved model of fission gas atom transport in irradiated uranium dioxide

NASA Astrophysics Data System (ADS)

Shea, J. H.

2018-04-01

The hitherto standard approach to predicting fission gas release has been a pure diffusion gas atom transport model based upon Fick's law. An additional mechanism has subsequently been identified from experimental data at high burnup and has been summarised in an empirical model that is considered to embody a so-called fuel matrix 'saturation' phenomenon whereby the fuel matrix has become saturated with fission gas so that the continued addition of extra fission gas atoms results in their expulsion from the fuel matrix into the fuel rod plenum. The present paper proposes a different approach by constructing an enhanced fission gas transport law consisting of two components: 1) Fick's law and 2) a so-called drift term. The new transport law can be shown to be effectively identical in its predictions to the 'saturation' approach and is more readily physically justifiable. The method introduces a generalisation of the standard diffusion equation which is dubbed the Drift Diffusion Equation. According to the magnitude of a dimensionless Péclet number, P, the new equation can vary from pure diffusion to pure drift, which latter represents a collective motion of the fission gas atoms through the fuel matrix at a translational velocity. Comparison is made between the saturation and enhanced transport approaches. Because of its dependence on P, the Drift Diffusion Equation is shown to be more effective at managing the transition from one type of limiting transport phenomenon to the other. Thus it can adapt appropriately according to the reactor operation.

Ultrafast Saturation of Electronic-Resonance-Enhanced Coherent Anti-Stokes Raman Scattering and Comparison for Pulse Durations in the Nanosecond to Femtosecond Regime

DTIC Science & Technology

2016-02-05

electronic-resonance-enhanced CARS (ERE- CARS ) configuration is calculated. We demonstrate that while underdamping condition is a suffi- cient condition for...saturation of ERE- CARS with the long-pulse excitations, a transient-gain must be achieved to saturate ERE- CARS signal for ultrafast probe regime. We...ultrafast ERE- CARS . From a simplified analytical solution and a detailed numerical calculation based on density-matrix equations, the saturation threshold

Scale-dependent coupling of hysteretic capillary pressure, trapping, and fluid mobilities

NASA Astrophysics Data System (ADS)

Doster, F.; Celia, M. A.; Nordbotten, J. M.

2012-12-01

Many applications of multiphase flow in porous media, including CO2-storage and enhanced oil recovery, require mathematical models that span a large range of length scales. In the context of numerical simulations, practical grid sizes are often on the order of tens of meters, thereby de facto defining a coarse model scale. Under particular conditions, it is possible to approximate the sub-grid-scale distribution of the fluid saturation within a grid cell; that reconstructed saturation can then be used to compute effective properties at the coarse scale. If both the density difference between the fluids and the vertical extend of the grid cell are large, and buoyant segregation within the cell on a sufficiently shorte time scale, then the phase pressure distributions are essentially hydrostatic and the saturation profile can be reconstructed from the inferred capillary pressures. However, the saturation reconstruction may not be unique because the parameters and parameter functions of classical formulations of two-phase flow in porous media - the relative permeability functions, the capillary pressure -saturation relationship, and the residual saturations - show path dependence, i.e. their values depend not only on the state variables but also on their drainage and imbibition histories. In this study we focus on capillary pressure hysteresis and trapping and show that the contribution of hysteresis to effective quantities is dependent on the vertical length scale. By studying the transition from the two extreme cases - the homogeneous saturation distribution for small vertical extents and the completely segregated distribution for large extents - we identify how hysteretic capillary pressure at the local scale induces hysteresis in all coarse-scale quantities for medium vertical extents and finally vanishes for large vertical extents. Our results allow for more accurate vertically integrated modeling while improving our understanding of the coupling of capillary pressure and relative permeabilities over larger length scales.

Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows

NASA Astrophysics Data System (ADS)

Li, Qing; Luo, K. H.

2014-05-01

The pseudopotential lattice Boltzmann (LB) model is a popular model in the LB community for simulating multiphase flows. Recently, several thermal LB models, which are based on the pseudopotential LB model and constructed within the framework of the double-distribution-function LB method, were proposed to simulate thermal multiphase flows [G. Házi and A. Márkus, Phys. Rev. E 77, 026305 (2008), 10.1103/PhysRevE.77.026305; L. Biferale, P. Perlekar, M. Sbragaglia, and F. Toschi, Phys. Rev. Lett. 108, 104502 (2012), 10.1103/PhysRevLett.108.104502; S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012), 10.1016/j.ijheatmasstransfer.2012.04.037; M. R. Kamali et al., Phys. Rev. E 88, 033302 (2013), 10.1103/PhysRevE.88.033302]. The objective of the present paper is to show that the effect of the forcing term on the temperature equation must be eliminated in the pseudopotential LB modeling of thermal flows. First, the effect of the forcing term on the temperature equation is shown via the Chapman-Enskog analysis. For comparison, alternative treatments that are free from the forcing-term effect are provided. Subsequently, numerical investigations are performed for two benchmark tests. The numerical results clearly show that the existence of the forcing-term effect will lead to significant numerical errors in the pseudopotential LB modeling of thermal flows.

Revisiting the Phase Curves of WASP-43b: Confronting Re-analyzed Spitzer Data with Cloudy Atmospheres

NASA Astrophysics Data System (ADS)

Mendonça, João M.; Malik, Matej; Demory, Brice-Olivier; Heng, Kevin

2018-04-01

Recently acquired Hubble and Spitzer phase curves of the short-period hot Jupiter WASP-43b make it an ideal target for confronting theory with data. On the observational front, we re-analyze the 3.6 and 4.5 μm Spitzer phase curves and demonstrate that our improved analysis better removes residual red noise due to intra-pixel sensitivity, which leads to greater fluxes emanating from the nightside of WASP-43b, thus reducing the tension between theory and data. On the theoretical front, we construct cloud-free and cloudy atmospheres of WASP-43b using our Global Circulation Model (GCM), THOR, which solves the non-hydrostatic Euler equations (compared to GCMs that typically solve the hydrostatic primitive equations). The cloud-free atmosphere produces a reasonable fit to the dayside emission spectrum. The multi-phase emission spectra constrain the cloud deck to be confined to the nightside and have a finite cloud-top pressure. The multi-wavelength phase curves are naturally consistent with our cloudy atmospheres, except for the 4.5 μm phase curve, which requires the presence of enhanced carbon dioxide in the atmosphere of WASP-43b. Multi-phase emission spectra at higher spectral resolution, as may be obtained using the James Webb Space Telescope, and a reflected-light phase curve at visible wavelengths would further constrain the properties of clouds in WASP-43b.

A New and General Formulation of the Parametric HFGMC Micromechanical Method for Three-Dimensional Multi-Phase Composites

NASA Technical Reports Server (NTRS)

Haj-Ali, Rami; Aboudi, Jacob

2012-01-01

The recent two-dimensional (2-D) parametric formulation of the high fidelity generalized method of cells (HFGMC) reported by the authors is generalized for the micromechanical analysis of three-dimensional (3-D) multiphase composites with periodic microstructure. Arbitrary hexahedral subcell geometry is developed to discretize a triply periodic repeating unit-cell (RUC). Linear parametric-geometric mapping is employed to transform the arbitrary hexahedral subcell shapes from the physical space to an auxiliary orthogonal shape, where a complete quadratic displacement expansion is performed. Previously in the 2-D case, additional three equations are needed in the form of average moments of equilibrium as a result of the inclusion of the bilinear terms. However, the present 3-D parametric HFGMC formulation eliminates the need for such additional equations. This is achieved by expressing the coefficients of the full quadratic polynomial expansion of the subcell in terms of the side or face average-displacement vectors. The 2-D parametric and orthogonal HFGMC are special cases of the present 3-D formulation. The continuity of displacements and tractions, as well as the equilibrium equations, are imposed in the average (integral) sense as in the original HFGMC formulation. Each of the six sides (faces) of a subcell has an independent average displacement micro-variable vector which forms an energy-conjugate pair with the transformed average-traction vector. This allows generating symmetric stiffness matrices along with internal resisting vectors for the subcells which enhances the computational efficiency. The established new parametric 3-D HFGMC equations are formulated and solution implementations are addressed. Several applications for triply periodic 3-D composites are presented to demonstrate the general capability and varsity of the present parametric HFGMC method for refined micromechanical analysis by generating the spatial distributions of local stress fields. These applications include triply periodic composites with inclusions in the form of a cavity, spherical inclusion, ellipsoidal inclusion, discontinuous aligned short fiber. A 3-D repeating unit-cell for foam material composite is simulated.

Diffuse-Interface Modelling of Flow in Porous Media

NASA Astrophysics Data System (ADS)

Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim

2016-11-01

Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.

The Effect of Wettability Heterogeneity on Relative Permeability of Two-Phase Flow in Porous Media: A Lattice Boltzmann Study

DOE PAGES

Zhao, Jianlin; Kang, Qinjun; Yao, Jun; ...

2018-02-27

Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. In this study, to investigate the effect of wettability heterogeneity on relative permeability of two-phase flow in porous media, a multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate oil/water two-phase flow in porous media with different oil-wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil-wet solid fraction under a constant water saturation. However, as themore » water saturation decreases to an intermediate value (about 0.4–0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water-wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability-related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two-phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. Lastly, the relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.« less

The Effect of Wettability Heterogeneity on Relative Permeability of Two-Phase Flow in Porous Media: A Lattice Boltzmann Study

NASA Astrophysics Data System (ADS)

Zhao, Jianlin; Kang, Qinjun; Yao, Jun; Viswanathan, Hari; Pawar, Rajesh; Zhang, Lei; Sun, Hai

2018-02-01

Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. To investigate the effect of wettability heterogeneity on relative permeability of two-phase flow in porous media, a multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate oil/water two-phase flow in porous media with different oil-wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil-wet solid fraction under a constant water saturation. However, as the water saturation decreases to an intermediate value (about 0.4-0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water-wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability-related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two-phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. The relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.

The Effect of Wettability Heterogeneity on Relative Permeability of Two-Phase Flow in Porous Media: A Lattice Boltzmann Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Jianlin; Kang, Qinjun; Yao, Jun

Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. In this study, to investigate the effect of wettability heterogeneity on relative permeability of two-phase flow in porous media, a multi-relaxation-time color-gradient lattice Boltzmann model is adopted to simulate oil/water two-phase flow in porous media with different oil-wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil-wet solid fraction under a constant water saturation. However, as themore » water saturation decreases to an intermediate value (about 0.4–0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water-wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability-related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two-phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. Lastly, the relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper.« less

Theory of wave propagation in partially saturated double-porosity rocks: a triple-layer patchy model

NASA Astrophysics Data System (ADS)

Sun, Weitao; Ba, Jing; Carcione, José M.

2016-04-01

Wave-induced local fluid flow is known as a key mechanism to explain the intrinsic wave dissipation in fluid-saturated rocks. Understanding the relationship between the acoustic properties of rocks and fluid patch distributions is important to interpret the observed seismic wave phenomena. A triple-layer patchy (TLP) model is proposed to describe the P-wave dissipation process in a double-porosity media saturated with two immiscible fluids. The double-porosity rock consists of a solid matrix with unique host porosity and inclusions which contain the second type of pores. Two immiscible fluids are considered in concentric spherical patches, where the inner pocket and the outer sphere are saturated with different fluids. The kinetic and dissipation energy functions of local fluid flow (LFF) in the inner pocket are formulated through oscillations in spherical coordinates. The wave propagation equations of the TLP model are based on Biot's theory and the corresponding Lagrangian equations. The P-wave dispersion and attenuation caused by the Biot friction mechanism and the local fluid flow (related to the pore structure and the fluid distribution) are obtained by a plane-wave analysis from the Christoffel equations. Numerical examples and laboratory measurements indicate that P-wave dispersion and attenuation are significantly influenced by the spatial distributions of both, the solid heterogeneity and the fluid saturation distribution. The TLP model is in reasonably good agreement with White's and Johnson's models. However, differences in phase velocity suggest that the heterogeneities associated with double-porosity and dual-fluid distribution should be taken into account when describing the P-wave dispersion and attenuation in partially saturated rocks.

Relating oxygen partial pressure, saturation and content: the haemoglobin-oxygen dissociation curve.

PubMed

Collins, Julie-Ann; Rudenski, Aram; Gibson, John; Howard, Luke; O'Driscoll, Ronan

2015-09-01

The delivery of oxygen by arterial blood to the tissues of the body has a number of critical determinants including blood oxygen concentration (content), saturation (S O2 ) and partial pressure, haemoglobin concentration and cardiac output, including its distribution. The haemoglobin-oxygen dissociation curve, a graphical representation of the relationship between oxygen satur-ation and oxygen partial pressure helps us to understand some of the principles underpinning this process. Historically this curve was derived from very limited data based on blood samples from small numbers of healthy subjects which were manipulated in vitro and ultimately determined by equations such as those described by Severinghaus in 1979. In a study of 3524 clinical specimens, we found that this equation estimated the S O2 in blood from patients with normal pH and S O2 >70% with remarkable accuracy and, to our knowledge, this is the first large-scale validation of this equation using clinical samples. Oxygen saturation by pulse oximetry (S pO2 ) is nowadays the standard clinical method for assessing arterial oxygen saturation, providing a convenient, pain-free means of continuously assessing oxygenation, provided the interpreting clinician is aware of important limitations. The use of pulse oximetry reduces the need for arterial blood gas analysis (S aO2 ) as many patients who are not at risk of hypercapnic respiratory failure or metabolic acidosis and have acceptable S pO2 do not necessarily require blood gas analysis. While arterial sampling remains the gold-standard method of assessing ventilation and oxygenation, in those patients in whom blood gas analysis is indicated, arterialised capillary samples also have a valuable role in patient care. The clinical role of venous blood gases however remains less well defined.

Experimental and numerical study on frost heave of saturated rock under uniform freezing conditions

NASA Astrophysics Data System (ADS)

Lv, Zhitao; Xia, Caichu; Li, Qiang

2018-04-01

A series of freezing experiments are conducted on saturated sandstone and mortar specimens to investigate the frost heave of saturated rock under uniform freezing conditions. The experimental results show that the frost heave of saturated rock is isotropic under uniform freezing conditions. During the freezing process, three stages are observed in the curves of variation of total frost heaving strain versus time: the thermal contraction stage, the frost heaving stage and the steady stage. Moreover, the amount of final stable frost heave first increases and then decreases with decrease in freezing temperature, and the maximum final stable frost heave occurs at different freezing temperature in saturated sandstone and mortar. Furthermore, a coupled thermal-mechanical (TM) model of frost heave of saturated rock is proposed in which a constraint coefficient \\zeta is used to consider the susceptibility of the internal rock grain structure to the expansion of pore ice. Then, numerical simulations are implemented with COMSOL to solve the governing equations of the TM model. Comparisons of the numerical results with the experimental results are performed to demonstrate the reliability of the model. The influences of elastic modulus and porosity on frost heave are also investigated, and the results show that the total frost heaving strain decreases non-linearly with increasing elastic modulus, and the decrease is significant when the elastic modulus is less than 3000 MPa, or approximately five times the elastic modulus of ice. In addition, the total frost heaving strain increases linearly with increasing porosity. Finally, an empirical equation between total frost heaving strain and freezing temperature is proposed and the equation well describes the variation of total frost heaving strain with freezing temperature.

Persistent Homology to describe Solid and Fluid Structures during Multiphase Flow

NASA Astrophysics Data System (ADS)

Herring, A. L.; Robins, V.; Liu, Z.; Armstrong, R. T.; Sheppard, A.

2017-12-01

The question of how to accurately and effectively characterize essential fluid and solid distributions and structures is a long-standing topic within the field of porous media and fluid transport. For multiphase flow applications, considerable research effort has been made to describe fluid distributions under a range of conditions; including quantification of saturation levels, fluid-fluid pressure differences and interfacial areas, and fluid connectivity. Recent research has effectively used topological metrics to describe pore space and fluid connectivity, with researchers demonstrating links between pore-scale nonwetting phase topology to fluid mobilization and displacement mechanisms, relative permeability, fluid flow regimes, and thermodynamic models of multiphase flow. While topology is clearly a powerful tool to describe fluid distribution, topological metrics by definition provide information only on the connectivity of a phase, not its geometry (shape or size). Physical flow characteristics, e.g. the permeability of a fluid phase within a porous medium, are dependent on the connectivity of the pore space or fluid phase as well as the size of connections. Persistent homology is a technique which provides a direct link between topology and geometry via measurement of topological features and their persistence from the signed Euclidean distance transform of a segmented digital image (Figure 1). We apply persistent homology analysis to measure the occurrence and size of pore-scale topological features in a variety of sandstones, for both the dry state and the nonwetting phase fluid during two-phase fluid flow (drainage and imbibition) experiments, visualized with 3D X-ray microtomography. The results provide key insights into the dominant topological features and length scales of a media which control relevant field-scale engineering properties such as fluid trapping, absolute permeability, and relative permeability.

A unified analysis of solidification in Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Lu, Ming-Fang

2012-04-01

The simulation of multiphase solidification process can be handled by combining the VOF (Volume of Fluid) transport equation, in which the continuum mechanics model is used to simulate the melt/solid interface and the conservation of mass, momentum, and energy. Because the melt phase, the solid phase, and the melt/solid interface are controlled by a single control equation; if the enthalpy model based on porosity concept represents the processing of the phase transformation range, it is possible to solve the problem of phase transformation in the same way as solving the single-phase problem. Once the energy field of enthalpy for each step in time is resolved, the position of the interface can be precisely calculated with the use of VOF equation. This type of novel VOF method can be applied to find out the conditions of vertical Bridgman crystal growing located on the earth or under microgravity.

A unified analysis of solidification in Bridgman crystal growth

NASA Astrophysics Data System (ADS)

Lu, Ming-Fang

2011-11-01

The simulation of multiphase solidification process can be handled by combining the VOF (Volume of Fluid) transport equation, in which the continuum mechanics model is used to simulate the melt/solid interface and the conservation of mass, momentum, and energy. Because the melt phase, the solid phase, and the melt/solid interface are controlled by a single control equation; if the enthalpy model based on porosity concept represents the processing of the phase transformation range, it is possible to solve the problem of phase transformation in the same way as solving the single-phase problem. Once the energy field of enthalpy for each step in time is resolved, the position of the interface can be precisely calculated with the use of VOF equation. This type of novel VOF method can be applied to find out the conditions of vertical Bridgman crystal growing located on the earth or under microgravity.

On a Multiphase Multicomponent Model of Biofilm Growth

NASA Astrophysics Data System (ADS)

Friedman, Avner; Hu, Bei; Xue, Chuan

2014-01-01

Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within the biofilm region Ω( t), and the solvent in the surrounding region D( t). The interface between the two regions, Γ( t), is a free boundary. In this paper, we consider a mathematical model that consists of a Stokes equation for the EPS with bacteria attached to it, a Stokes equation for the solvent in Ω( t) and another for the solvent in D( t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly within Ω( t) and across the free surface Γ( t). We prove the existence and uniqueness of a solution, with a smooth surface Γ( t), for a small time interval.

Quantum molecular dynamics simulation of shock-wave experiments in aluminum

NASA Astrophysics Data System (ADS)

Minakov, D. V.; Levashov, P. R.; Khishchenko, K. V.; Fortov, V. E.

2014-06-01

We present quantum molecular dynamics calculations of principal, porous, and double shock Hugoniots, release isentropes, and sound velocity behind the shock front for aluminum. A comprehensive analysis of available shock-wave data is performed; the agreement and discrepancies of simulation results with measurements are discussed. Special attention is paid to the melting region of aluminum along the principal Hugoniot; the boundaries of the melting zone are estimated using the self-diffusion coefficient. Also, we make a comparison with a high-quality multiphase equation of state for aluminum. Independent semiempirical and first-principle models are very close to each other in caloric variables (pressure, density, particle velocity, etc.) but the equation of state gives higher temperature on the principal Hugoniot and release isentropes than ab initio calculations. Thus, the quantum molecular dynamics method can be used for calibration of semiempirical equations of state in case of lack of experimental data.

Quantum molecular dynamics simulation of shock-wave experiments in aluminum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minakov, D. V.; Khishchenko, K. V.; Fortov, V. E.

2014-06-14

We present quantum molecular dynamics calculations of principal, porous, and double shock Hugoniots, release isentropes, and sound velocity behind the shock front for aluminum. A comprehensive analysis of available shock-wave data is performed; the agreement and discrepancies of simulation results with measurements are discussed. Special attention is paid to the melting region of aluminum along the principal Hugoniot; the boundaries of the melting zone are estimated using the self-diffusion coefficient. Also, we make a comparison with a high-quality multiphase equation of state for aluminum. Independent semiempirical and first-principle models are very close to each other in caloric variables (pressure, density,more » particle velocity, etc.) but the equation of state gives higher temperature on the principal Hugoniot and release isentropes than ab initio calculations. Thus, the quantum molecular dynamics method can be used for calibration of semiempirical equations of state in case of lack of experimental data.« less

A multiphase equation of state of three solid phases, liquid, and gas for titanium

NASA Astrophysics Data System (ADS)

Pecker, S.; Eliezer, S.; Fisher, D.; Henis, Z.; Zinamon, Z.

2005-08-01

A multiple-phase equation of state of the α phase, β phase, ω phase, liquid, and gas for titanium is presented. This equation of state is thermodynamically consistent, based on a three-term semiempirical model for the Helmholtz free energy. The parameters of the free energy are first evaluated from the experimental data and solid-state theoretical calculations. Then, the values of the parameters are adjusted using a numerical minimization scheme based on the simplex algorithm, to values that best reproduce measured phase diagrams and other experimental data. The predicted phase diagram shows a compression-induced β-ω transition, up to a β-ω-liquid triple point at ˜45GPa and ˜2200K. For pressures above this triple point, the melting occurs from the ω phase. Moreover, no β-ω transition is predicted along the Hugoniot curve starting at STP conditions.

Lagrangian particle method for compressible fluid dynamics

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang

2018-06-01

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

Numerical modeling of the early interaction of a planar shock with a dense particle field

NASA Astrophysics Data System (ADS)

Regele, Jonathan; Blanquart, Guillaume

2011-11-01

Dense compressible multiphase flows are of interest for multiphase turbomachinary and energetic material detonations. Still, there is little understanding of the detailed interaction mechanisms between shock waves and dense (particle volume fraction αd > 0 . 001) particle fields. A recent experimental study [Wagner et al, AIAA Aero. Sci., Orlando, 2011-188] has focused on the impingement of a planar shock wave on a dense particle curtain. In the present work, numerical solutions of the Euler equations in one and two dimensions are performed for a planar shock wave impinging on a fixed particle curtain and are compared to the experimental data for early times. Comparison of the one- and two-dimensional results demonstrate that the one-dimensional description captures the large scale flow behavior, but is inadequate to capture all the details observed in the experiments. The two-dimensional solutions are shown to reproduce the experimentally observed flow structures and provide insight into how these details originate.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

Free-product plume distribution and recovery modeling prediction in a diesel-contaminated volcanic aquifer

NASA Astrophysics Data System (ADS)

Hernández-Espriú, Antonio; Martínez-Santos, Pedro; Sánchez-León, Emilio; Marín, Luis E.

Light non-aqueous phase liquids (LNAPL) represent one of the most serious problems in aquifers contaminated with petroleum hydrocarbons liquids. To design an appropriate remediation strategy it is essential to understand the behavior of the plume. The aim of this paper is threefold: (1) to characterize the fluid distribution of an LNAPL plume detected in a volcanic low-conductivity aquifer (∼0.4 m/day from slug tests interpretation), (2) to simulate the recovery processes of the free-product contamination and (3) to evaluate the primary recovery efficiency of the following alternatives: skimming, dual-phase extraction, Bioslurping and multi-phase extraction wells. The API/Charbeneau analytical model was used to investigate the recovery feasibility based on the geological properties and hydrogeological conditions with a multi-phase (water, air, LNAPL) transport approach in the vadose zone. The modeling performed in this research, in terms of LNAPL distribution in the subsurface, show that oil saturation is 7% in the air-oil interface, with a maximum value of 70% in the capillary fringe. Equilibrium between water and LNAPL phases is reached at a depth of 1.80 m from the air-oil interface. On the other hand, the LNAPL recovery model results suggest a remarkable enhancement of the free-product recovery when simultaneous extra-phase extraction was simulated from wells, in addition to the LNAPL lens. Recovery efficiencies were 27%, 65%, 66% and 67% for skimming, dual-phase extraction, Bioslurping and multi-phase extraction, respectively. During a 3-year simulation, skimmer wells and multi-phase extraction showed the lowest and highest LNAPL recovery rates, with expected values from 207 to 163 and 2305 to 707 l-LNAPL/day, respectively. At a field level we are proposing a well distribution arrangement that alternates pairs of dual-phase well-Bioslurping well. This not only improves the recovery of the free-product plume, but also pumps the dissolve plume and enhances in situ biodegradation in the vadose zone. Thus, aquifer and soil remediation can be achieved at a shorter time. Rough calculations suggest that LNAPL can be recovered at an approximate cost of 6-10/l.

Advanced computational multi-fluid dynamics: a new model for understanding electrokinetic phenomena in porous media

NASA Astrophysics Data System (ADS)

Gulamali, M. Y.; Saunders, J. H.; Jackson, M. D.; Pain, C. C.

2009-04-01

We present results from a new computational multi-fluid dynamics code, designed to model the transport of heat, mass and chemical species during flow of single or multiple immiscible fluid phases through porous media, including gravitational effects and compressibility. The model also captures the electrical phenomena which may arise through electrokinetic, electrochemical and electrothermal coupling. Building on the advanced computational technology of the Imperial College Ocean Model, this new development leads the way towards a complex multiphase code using arbitrary unstructured and adaptive meshes, and domains decomposed to run in parallel over a cluster of workstations or a dedicated parallel computer. These facilities will allow efficient and accurate modelling of multiphase flows which capture large- and small-scale transport phenomena, while preserving the important geology and/or surface topology to make the results physically meaningful and realistic. Applications include modelling of contaminant transport in aquifers, multiphase flow during hydrocarbon production, migration of carbon dioxide during sequestration, and evaluation of the design and safety of nuclear reactors. Simulations of the streaming potential resulting from multiphase flow in laboratory- and field-scale models demonstrate that streaming potential signals originate at fluid fronts, and at geologic boundaries where fluid saturation changes. This suggests that downhole measurements of streaming potential may be used to inform production strategies in oil and gas reservoirs. As water encroaches on an oil production well, the streaming-potential signal associated with the water front encompasses the well even when the front is up to 100 m away, so the potential measured at the well starts to change significantly relative to a distant reference electrode. Variations in the geometry of the encroaching water front could be characterized using an array of electrodes positioned along the well, but a good understanding of the local reservoir geology will be required to identify signals caused by the front. The streaming potential measured at a well will be maximized in low-permeability reservoirs produced at a high rate, and in thick reservoirs with low shale content.

DENSITY-DEPENDENT FLOW IN ONE-DIMENSIONAL VARIABLY-SATURATED MEDIA

EPA Science Inventory

A one-dimensional finite element is developed to simulate density-dependent flow of saltwater in variably saturated media. The flow and solute equations were solved in a coupled mode (iterative), in a partially coupled mode (non-iterative), and in a completely decoupled mode. P...

Towards an avatar for deciphering the modes of three-phase interactions in lava lakes

NASA Astrophysics Data System (ADS)

Suckale, J.; Qin, Z.; Culha, C.; Lev, E.

2016-12-01

An avatar is the virtual representation of a character, system or idea. Here, we present progress towards building a numerical avatar for lava lakes that allows us to constrain the modes of multiphase interactions between crystals, gas, and magmatic fluid in the interior of lava lakes. We focus on lava lakes, because they expose the free surface of magma to direct observations. They hence offer a unique window into different regimes of the three-phase flow dynamics of crystals, gases, and melts in magmatic convection more generally. The multiphase interactions between crystals, gases and melt give rise to nonlinear and unstable behavior in magmatic systems and are hence key for understanding the behavior of the bulk magma, but are notoriously difficult to capture in numerical models. Our avatar approach solves the full set of governing equations entailing the momentum, mass, and energy balance for each of the three phases at the scale of individual crystals or bubble interfaces. It hence obviates the need for simplifying assumptions regarding the individual behavior of the three phases or their mutual coupling to achieve a minimally preconditioned virtual representation of a lava lake. To identify the multi-phase regime at depth, we compute the observational signatures of different multiphase regimes, both in terms of surface velocity and temperature distribution, and compare the computed synthetic data to observational surface data for lava lakes. We focus specifically on the lava lake dynamics at Mount Erebus, Antarctica, and Kīlauea, Hawai'i. These two lava lakes are particularly well observed, which presents a compelling opportunity for closely linking modeling and observations. The also exhibit notably different circulation patterns. We hypothesize that Erebus and Kīlauea highlight different mechanisms through which multiphase interactions alter magmatic convection and eruptive behavior in basaltic systems. We suggest that volumetric flow effects like bubble dynamics and spatially heterogeneous crystal retention may dominate the behavior at Erebus and that surface effects resulting primarily from the formation of a cool skin on top of the lake govern the dynamics observed at Kīlauea.

Method of determining interwell oil field fluid saturation distribution

DOEpatents

Donaldson, Erle C.; Sutterfield, F. Dexter

1981-01-01

A method of determining the oil and brine saturation distribution in an oil field by taking electrical current and potential measurements among a plurality of open-hole wells geometrically distributed throughout the oil field. Poisson's equation is utilized to develop fluid saturation distributions from the electrical current and potential measurement. Both signal generating equipment and chemical means are used to develop current flow among the several open-hole wells.

Archie's Saturation Exponent for Natural Gas Hydrate in Coarse-Grained Reservoirs

NASA Astrophysics Data System (ADS)

Cook, Ann E.; Waite, William F.

2018-03-01

Accurately quantifying the amount of naturally occurring gas hydrate in marine and permafrost environments is important for assessing its resource potential and understanding the role of gas hydrate in the global carbon cycle. Electrical resistivity well logs are often used to calculate gas hydrate saturations, Sh, using Archie's equation. Archie's equation, in turn, relies on an empirical saturation parameter, n. Though n = 1.9 has been measured for ice-bearing sands and is widely used within the hydrate community, it is highly questionable if this n value is appropriate for hydrate-bearing sands. In this work, we calibrate n for hydrate-bearing sands from the Canadian permafrost gas hydrate research well, Mallik 5L-38, by establishing an independent downhole Sh profile based on compressional-wave velocity log data. Using the independently determined Sh profile and colocated electrical resistivity and bulk density logs, Archie's saturation equation is solved for n, and uncertainty is tracked throughout the iterative process. In addition to the Mallik 5L-38 well, we also apply this method to two marine, coarse-grained reservoirs from the northern Gulf of Mexico Gas Hydrate Joint Industry Project: Walker Ridge 313-H and Green Canyon 955-H. All locations yield similar results, each suggesting n ≈ 2.5 ± 0.5. Thus, for the coarse-grained hydrate bearing (Sh > 0.4) of greatest interest as potential energy resources, we suggest that n = 2.5 ± 0.5 should be applied in Archie's equation for either marine or permafrost gas hydrate settings if independent estimates of n are not available.

Complex Equilibrium Calculations of Nonideal Multiphase Systems (CEC- NMS) and Applications to Liquid Metal Fuel Combustion

DTIC Science & Technology

1989-03-15

3. F 2(g) -Li(L) 4. SF 6(g)-Li(L ) - vii - Several different modeling techniques are used to accurately estimate the activity coefficients of the...electrolytes with molecular species. The gas phase of the electrolytic solution is modeled using a pressure-explicit second order virial equation. The pure...calculated using the van Laar model . - viii - ACKNOWLEDGMENT This research was sponsored by the Office of Naval Research, Contract No. N00014-85--k

Advancements in dynamic kill calculations for blowout wells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kouba, G.E.; MacDougall, G.R.; Schumacher, B.W.

1993-09-01

This paper addresses the development, interpretation, and use of dynamic kill equations. To this end, three simple calculation techniques are developed for determining the minimum dynamic kill rate. Two techniques contain only single-phase calculations and are independent of reservoir inflow performance. Despite these limitations, these two methods are useful for bracketing the minimum flow rates necessary to kill a blowing well. For the third technique, a simplified mechanistic multiphase-flow model is used to determine a most-probable minimum kill rate.

Multi-Scale Homogenization for 3D Multiphase Composites: Development of Robust Software Tools for Material/Structural Characterization Across Length Scales

DTIC Science & Technology

2013-11-01

person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number...position‐dependent  [ ]. Thanks  to  this  relation, eqs.  (1)  can be reduced to a single ( vectorial ) equation for the displacement  :     ⋅ 0. (3

Application of a constant hole volume Sanchez-Lacombe equation of state to mixtures relevant to polymeric foaming.

PubMed

von Konigslow, Kier; Park, Chul B; Thompson, Russell B

2018-06-06

A variant of the Sanchez-Lacombe equation of state is applied to several polymers, blowing agents, and saturated mixtures of interest to the polymer foaming industry. These are low-density polyethylene-carbon dioxide and polylactide-carbon dioxide saturated mixtures as well as polystyrene-carbon dioxide-dimethyl ether and polystyrene-carbon dioxide-nitrogen ternary saturated mixtures. Good agreement is achieved between theoretically predicted and experimentally determined solubilities, both for binary and ternary mixtures. Acceptable agreement with swelling ratios is found with no free parameters. Up-to-date pure component Sanchez-Lacombe characteristic parameters are provided for carbon dioxide, dimethyl ether, low-density polyethylene, nitrogen, polylactide, linear and branched polypropylene, and polystyrene. Pure fluid low-density polyethylene and nitrogen parameters exhibit more moderate success while still providing acceptable quantitative estimations. Mixture estimations are found to have more moderate success where pure components are not as well represented. The Sanchez-Lacombe equation of state is found to correctly predict the anomalous reversal of solubility temperature dependence for low critical point fluids through the observation of this behaviour in polystyrene nitrogen mixtures.

Modelling mass transfer during venting/soil vapour extraction: Non-aqueous phase liquid/gas mass transfer coefficient estimation

NASA Astrophysics Data System (ADS)

Esrael, D.; Kacem, M.; Benadda, B.

2017-07-01

We investigate how the simulation of the venting/soil vapour extraction (SVE) process is affected by the mass transfer coefficient, using a model comprising five partial differential equations describing gas flow and mass conservation of phases and including an expression accounting for soil saturation conditions. In doing so, we test five previously reported quations for estimating the non-aqueous phase liquid (NAPL)/gas initial mass transfer coefficient and evaluate an expression that uses a reference NAPL saturation. Four venting/SVE experiments utilizing a sand column are performed with dry and non-saturated sand at low and high flow rates, and the obtained experimental results are subsequently simulated, revealing that hydrodynamic dispersion cannot be neglected in the estimation of the mass transfer coefficient, particularly in the case of low velocities. Among the tested models, only the analytical solution of a convection-dispersion equation and the equation proposed herein are suitable for correctly modelling the experimental results, with the developed model representing the best choice for correctly simulating the experimental results and the tailing part of the extracted gas concentration curve.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

The viscosity of the refrigerant 1,1-difluoroethane along the saturation line

NASA Astrophysics Data System (ADS)

van der Gulik, P. S.

1993-07-01

The viscosity coefficient of the refrigerant R152a (1,1-difluoroethane) has been measured along the saturation line both in the saturated liquid and in the saturated vapor. The data have been obtained every 10 K from 243 up to 393 K by means of a vibrating-wire viscometer using the free damped oscillation method. The density along the saturation line was calculated from the equation of state given by Tamatsu et al. with application of the saturated vapor-pressure correlation given by Higashi et al. An interesting result is that in the neighborhood of the critical point, the kinematic viscosity of the saturated liquid seems to coincide with that of the saturated vapor. The results for the saturated liquid are in satisfying agreement with those of Kumagai and Takahashi and of Phillips and Murphy. A comparison of the saturatedvaport data with the unsaturated-vapor data of Takahashi et al. shows some discrepancies.

Connection equation and shaly-sand correction for electrical resistivity

USGS Publications Warehouse

Lee, Myung W.

2011-01-01

Estimating the amount of conductive and nonconductive constituents in the pore space of sediments by using electrical resistivity logs generally loses accuracy where clays are present in the reservoir. Many different methods and clay models have been proposed to account for the conductivity of clay (termed the shaly-sand correction). In this study, the connectivity equation (CE), which is a new approach to model non-Archie rocks, is used to correct for the clay effect and is compared with results using the Waxman and Smits method. The CE presented here requires no parameters other than an adjustable constant, which can be derived from the resistivity of water-saturated sediments. The new approach was applied to estimate water saturation of laboratory data and to estimate gas hydrate saturations at the Mount Elbert well on the Alaska North Slope. Although not as accurate as the Waxman and Smits method to estimate water saturations for the laboratory measurements, gas hydrate saturations estimated at the Mount Elbert well using the proposed CE are comparable to estimates from the Waxman and Smits method. Considering its simplicity, it has high potential to be used to account for the clay effect on electrical resistivity measurement in other systems.

From dry to saturated thermal conductivity: mixing-model correction charts and new conversion equations for sedimentary rocks

NASA Astrophysics Data System (ADS)

Fuchs, Sven; Schütz, Felina; Förster, Andrea; Förster, Hans-Jürgen

2013-04-01

The thermal conductivity (TC) of a rock is, in collaboration with the temperature gradient, the basic parameter to determine the heat flow from the Earth interior. Moreover, it forms the input into models targeted on temperature prognoses for geothermal reservoirs at those depths not yet reached by boreholes. Thus, rock TC is paramount in geothermal exploration and site selection. Most commonly, TC of a rock is determined in the laboratory on samples that are either dry or water-saturated. Because sample saturation is time-consuming, it is desirable, especially if large numbers of samples need to be assessed, to develop an approach that quickly and reliably converts dry-measured bulk TC into the respective saturated value without applying the saturation procedure. Different petrophysical models can be deployed to calculate the matrix TC of a rock from the bulk TC and vice versa, if the effective porosity is known (e.g., from well logging data) and the TC of the saturation fluid (e.g., gas, oil, water) is considered. We have studied for a large suite of different sedimentary rocks the performance of two-component (rock matrix, porosity) models that are widely used in geothermics (arithmetic mean, geometric mean, harmonic mean, Hashin and Shtrikman mean, and effective medium theory mean). The data set consisted of 1147 TC data from three different sedimentary basins (North German Basin, Molasse Basin, Mesozoic platform sediments of the northern Sinai Microplate in Israel). Four lithotypes (sandstone, mudstone, limestone, dolomite) were studied exhibiting bulk TC in the range between 1.0 and 6.5 W/(mK). The quality of fit between measured (laboratory) and calculated bulk TC values was studied separately for the influence of lithotype, saturation fluid (water and isooctane), and rock anisotropy (parallel and perpendicular to bedding). The geometric mean model displays the best correspondence between calculated and measured bulk TC, however, the relation is not satisfying. To improve the fit of the models, correction equations are calculated based on the statistical data. In addition, the application of correction equations allows a significant improvement of the accuracy of bulk TC data calculated. However, the "corrected" geometric mean constitutes the only model universally applicable to different types of sedimentary rocks and, thus, is recommended for the calculation of bulk TC. Finally, the statistical analysis also resulted in lithotype-specific conversion equations, which permit a calculation of the water-saturated bulk TC from dry-measured TC and porosity (e.g., well-log-derived porosity). This approach has the advantage that the saturated bulk TC could be calculated readily without application of any mixing model. The expected errors with this approach are in the range between 5 and 10 % (Fuchs et al., 2013).

The temperature dependence of ponded infiltration under isothermal conditions

USGS Publications Warehouse

Constantz, J.; Murphy, F.

1991-01-01

A simple temperature-sensitive modification to the Green and Ampt infiltration equation is described; this assumes that the temperature dependence of the hydraulic conductivity is reciprocally equal to the temperature dependence of the viscosity of liquid water, and that both the transmission zone saturation and the wetting front matric potential gradient are independent of temperature. This modified Green and Ampt equation is compared with ponded, isothermal infiltration experiments run on repacked columns of Olympic Sand and Aiken Loam at 5, 25, and 60??C. Experimental results showed increases in infiltration rates of at least 300% between 5 and 60??C for both soil materials, with subsequent increases in cumulative infiltration of even greater magnitudes for the loam. There is good agreement between measured and predicted initial infiltration rates at 25??C for both soil materials, yet at 60??C, the predicted results overestimate initial infiltration rates for the sand and underestimate initial rates for the loam. Measurements of the wetting depth vs. cumulative infiltration indicate that the transmission zone saturation increased with increasing temperature for both soil materials. In spite of this increased saturation with temperature, the final infiltration rates at both 25 and 60??C were predicted accurately using the modified Green and Ampt equation. This suggests that increased saturation occurred primarily in dead-end pore spaces, so that transmission zone hydraulic conductivities were unaffected by these temperature-induced changes in saturation. In conclusion, except for initial infiltration rates at 60??C, the measured influence of temperature on infiltration rates was fully accounted for by the temperature dependence of the viscosity of liquid water. ?? 1991.

Using passive capillary lysimeter water flux measurements to improve flow predictions in variably saturated soils.

USDA-ARS?s Scientific Manuscript database

Passive capillary lysimeters (PCLs) are uniquely suited for measuring water fluxes in variably-saturated soils. The objective of this work was to compare PCL flux measurements with simulated fluxes obtained with a calibrated unsaturated flow model. The Richards equation-based model was calibrated us...

Torsional vibration of a pipe pile in transversely isotropic saturated soil

NASA Astrophysics Data System (ADS)

Zheng, Changjie; Hua, Jianmin; Ding, Xuanming

2016-09-01

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot's poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Adapting HYDRUS-1D to simulate overland flow and reactive transport during sheet flow deviations

USDA-ARS?s Scientific Manuscript database

The HYDRUS-1D code is a popular numerical model for solving the Richards equation for variably-saturated water flow and solute transport in porous media. This code was adapted to solve rather than the Richards equation for subsurface flow the diffusion wave equation for overland flow at the soil sur...

Pore pressure diffusion and the hydrologic response of nearly saturated, thin landslide deposits of rainfall

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haneberg, W.C.

1991-11-01

Previous workers have correlated slope failures during rainstorms with rainfall intensity, rainfall duration, and seasonal antecedent rainfall. This note shows how such relationships can be interpreted using a periodic steady-state solution to the well-known linear pressure diffusion equation. Normalization of the governing equation yields a characteristic response time that is a function of soil thickness, saturated hydraulic conductivity, and pre-storm effective porosity, and which is analogous to the travel time of a piston wetting front. The effects of storm frequency and magnitude are also successfully quantified using dimensionless attenuation factors and lag times.

Equations for the determination of humidity from dewpoint and psychrometric data

NASA Technical Reports Server (NTRS)

Parish, O. O.; Putnam, T. W.

1977-01-01

A general expression based on the Claperon-Clausius differential equation that relates saturation vapor pressure, absolute temperature, and the latent heat of transformation was derived that expresses saturation vapor pressure as a function of absolute temperature. This expression was then used to derive general expressions for vapor pressure, absolute humidity, and relative humidity as functions of either dewpoint and ambient temperature or psychrometric parameters. Constants for all general expressions were then evaluated to give specific expressions in both the international system of units and U.S. customary units for temperatures above and below freezing.

Viscoelasticity of multiphase fluids: future directions

NASA Astrophysics Data System (ADS)

Tisato, Nicola; Spikes, Kyle; Javadpour, Farzam

2016-04-01

Recently, it has been demonstrated that rocks saturated with bubbly fluids attenuate seismic waves as the propagating elastic wave causes a thermodynamic disequilibrium between the liquid and the gas phases. The new attenuation mechanism, which is called wave-induced-gas-exsolution-dissolution (WIGED) and previously, was only postulated, opens up new perspectives for exploration geophysics as it could potentially improve the imaging of the subsurface. In particular, accounting for WIGED during seismic inversion could allow to better decipher seismic waves to disclose information about saturating phases. This will improve, for instance, the mapping of subsurface gas-plumes that might form during anthropogenic activities or natural phenomena such as those prior to volcanic eruptions. In the present contribution we will report the theory and the numerical method utilized to calculate the seismic-wave-attenuation related to WIGED and we will underline the assumptions and the limitations related to the theory. Then, we will present the experimental and the numerical strategy that we will employ to improve WIGED theory in order to incorporate additional effects, such as the role of interfacial tensions, or to extend it to fluid-fluid interaction

Effects of Faults on Petroleum Fluid Dynamics, Borderland Basins of Southern California

NASA Astrophysics Data System (ADS)

Jung, B.; Garven, G.; Boles, J. R.

2012-12-01

Multiphase flow modeling provides a useful quantitative tool for understanding crustal processes such as petroleum migration in geological systems, and also for characterizing subsurface environmental issues such as carbon sequestration in sedimentary basins. However, accurate modeling of multi-fluid behavior is often difficult because of the various coupled and nonlinear physics affecting multiphase fluid saturation and migration, including effects of capillarity and relative permeability, anisotropy and heterogeneity of the medium, and the effects of pore pressure, composition, and temperature on fluid properties. Regional fault structures also play a strong role in controlling fluid pathlines and mobility, so considering hydrogeologic effects of these structures is critical for testing exploration concepts, and for predicting the fate of injected fluids. To address these issues on spatially large and long temporal scales, we have developed a 2-D multiphase fluid flow model, coupled to heat flow, using a hybrid finite element and finite volume method. We have had good success in applying the multiphase flow model to fundamental issues of long-distance petroleum migration and accumulation in the Los Angeles basin, which is intensely faulted and disturbed by transpressional tectonic stresses, and host to the world's richest oil accumulation. To constrain the model, known subsurface geology and fault structures were rendered using geophysical logs from industry exploration boreholes and published seismic profiles. Plausible multiphase model parameters were estimated, either from known fault permeability measurements in similar strata in the Santa Barbara basin, and from known formation properties obtained from numerous oil fields in the Los Angeles basin. Our simulations show that a combination of continuous hydrocarbon generation and primary migration from upper Miocene source rocks in the central LA basin synclinal region, coupled with a subsiding basin fluid dynamics, favored the massive accumulation and alignment of hydrocarbon pools along the Newport-Inglewood fault zone (NIFZ). According to our multiphase flow calculations, the maximum formation water velocities within fault zones likely ranged between 1 ~ 2 m/yr during the middle Miocene to Pliocene (13 to 2.6 Ma). The estimated time for long-distance (~ 25 km) petroleum migration from source beds in the central basin to oil fields along the NIFZ is approximately 150,000 ~ 250,000 years, depending on the effective permeability assigned to the faults and adjacent interbedded sandstone and siltstone "petroleum aquifers". With an average long-distance flow rate (~ 0.6 m/yr) and fault permeability of 100 millidarcys (10-13 m2), the total petroleum oil of Inglewood oil field of 450 million barrels (~ 1.6 × 105 m3) would have accumulated rather quickly, likely over 25,000 years or less. The results also suggest that besides the thermal and structural history of the basin, the fault permeability, capillary pressure, and the configuration of aquifer and aquitard layers played an important role in controlling petroleum migration rates, patterns of flow, and the overall fluid mechanics of petroleum accumulation.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit time discretization to yield a fully implicit method. In the HU scheme, the phase flux is divided into two parts based on the driving force. The viscous-driven and buoyancy-driven phase fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total-velocity. The buoyancy-driven flux across an interface is always counter-current and is upwinded such that the heavier fluid goes downward and the lighter fluid goes upward. We analyze the properties of the Implicit Hybrid Upwinding (IHU) scheme. It is shown that IHU is locally conservative and produces monotone, physically-consistent numerical solutions. The IHU solutions show numerical diffusion levels that are slightly higher than those for standard FIM (i.e., implicit PPU). The primary advantage of the IHU scheme is that the numerical overall-flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions. This is in contrast to the standard phase-potential upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the boundary between co-current and counter-current flows.

Dark solitons in mode-locked lasers.

PubMed

Ablowitz, Mark J; Horikis, Theodoros P; Nixon, Sean D; Frantzeskakis, Dimitri J

2011-03-15

Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model that incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve (mode-lock) into dark solitons under appropriate requirements also met in experimental observations. The resulting pulses are essentially dark solitons of the unperturbed nonlinear Schrödinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.

Coupled Thermo-Hydro-Mechanical Numerical Framework for Simulating Unconventional Formations

NASA Astrophysics Data System (ADS)

Garipov, T. T.; White, J. A.; Lapene, A.; Tchelepi, H.

2016-12-01

Unconventional deposits are found in all world oil provinces. Modeling these systems is challenging, however, due to complex thermo-hydro-mechanical processes that govern their behavior. As a motivating example, we consider in situ thermal processing of oil shale deposits. When oil shale is heated to sufficient temperatures, kerogen can be converted to oil and gas products over a relatively short timespan. This phase change dramatically impact both the mechanical and hydrologic properties of the rock, leading to strongly coupled THMC interactions. Here, we present a numerical framework for simulating tightly-coupled chemistry, geomechanics, and multiphase flow within a reservoir simulator (the AD-GPRS General Purpose Research Simulator). We model changes in constitutive behavior of the rock using a thermoplasticity model that accounts for microstructural evolution. The multi-component, multiphase flow and transport processes of both mass and heat are modeled at the macroscopic (e.g., Darcy) scale. The phase compositions and properties are described by a cubic equation of state; Arrhenius-type chemical reactions are used to represent kerogen conversion. The system of partial differential equations is discretized using a combination of finite-volumes and finite-elements, respectively, for the flow and mechanics problems. Fully implicit and sequentially implicit method are used to solve resulting nonlinear problem. The proposed framework is verified against available analytical and numerical benchmark cases. We demonstrate the efficiency, performance, and capabilities of the proposed simulation framework by analyzing near well deformation in an oil shale formation.

A compositional multiphase model for groundwater contamination by petroleum products: 1. Theoretical considerations

USGS Publications Warehouse

Corapcioglu, M. Yavuz; Baehr, Arthur L.

1987-01-01

A mathematical model is developed to describe the fate of hydrocarbon constituents of petroleum products introduced to soils as an immiscible liquid from sources such as leaking underground storage tanks and ruptured pipelines. The problem is one of multiphase transport (oil (immiscible), air, and water phases) of a reactive contaminant with constituents such as benzene, toluene, and xylene found in refined petroleum products like gasoline. In the unsaturated zone, transport of each constituent can occur as a solute in the water phase, vapor in the air phase, and as an unaltered constituent in the oil phase. Additionally, the model allows for adsorption. Molecular transformations, microbially mediated or abiotic, are incorporated as sink terms in the conservation of mass equations. An equilibrium approximation, applicable to any immiscible organic contaminant is applied to partition constituent mass between the air, oil, water, and adsorbed phases for points in the region where the oil phase exists. Outside the oil plume the equilibrium approximation takes on a simpler form to partition constituent mass between the air, water, and adsorbed phases only. Microbial degradation of petroleum products is first discussed in a general model, then the conservation of mass equation for oxygen is incorporated into the analysis which takes advantage of the key role played by oxygen in the metabolism of hydrocarbon utilizing microbes in soil environments. Approximations to two subproblems, oil plume establishment in the unsaturated zone, and solute and vapor transport subsequent to immiscible plume establishment are then developed from the general model.

Archie’s saturation exponent for natural gas hydrate in coarse-grained reservoirs

USGS Publications Warehouse

Cook, Ann E.; Waite, William F.

2018-01-01

Accurately quantifying the amount of naturally occurring gas hydrate in marine and permafrost environments is important for assessing its resource potential and understanding the role of gas hydrate in the global carbon cycle. Electrical resistivity well logs are often used to calculate gas hydrate saturations, Sh, using Archie's equation. Archie's equation, in turn, relies on an empirical saturation parameter, n. Though n = 1.9 has been measured for ice‐bearing sands and is widely used within the hydrate community, it is highly questionable if this n value is appropriate for hydrate‐bearing sands. In this work, we calibrate n for hydrate‐bearing sands from the Canadian permafrost gas hydrate research well, Mallik 5L‐38, by establishing an independent downhole Sh profile based on compressional‐wave velocity log data. Using the independently determined Sh profile and colocated electrical resistivity and bulk density logs, Archie's saturation equation is solved for n, and uncertainty is tracked throughout the iterative process. In addition to the Mallik 5L‐38 well, we also apply this method to two marine, coarse‐grained reservoirs from the northern Gulf of Mexico Gas Hydrate Joint Industry Project: Walker Ridge 313‐H and Green Canyon 955‐H. All locations yield similar results, each suggesting n ≈ 2.5 ± 0.5. Thus, for the coarse‐grained hydrate bearing (Sh > 0.4) of greatest interest as potential energy resources, we suggest that n = 2.5 ± 0.5 should be applied in Archie's equation for either marine or permafrost gas hydrate settings if independent estimates of n are not available.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

Application of numerical grid generation for improved CFD analysis of multiphase screw machines

NASA Astrophysics Data System (ADS)

Rane, S.; Kovačević, A.

2017-08-01

Algebraic grid generation is widely used for discretization of the working domain of twin screw machines. Algebraic grid generation is fast and has good control over the placement of grid nodes. However, the desired qualities of grid which should be able to handle multiphase flows such as oil injection, may be difficult to achieve at times. In order to obtain fast solution of multiphase screw machines, it is important to further improve the quality and robustness of the computational grid. In this paper, a deforming grid of a twin screw machine is generated using algebraic transfinite interpolation to produce initial mesh upon which an elliptic partial differential equations (PDE) of the Poisson’s form is solved numerically to produce smooth final computational mesh. The quality of numerical cells and their distribution obtained by the differential method is greatly improved. In addition, a similar procedure was introduced to fully smoothen the transition of the partitioning rack curve between the rotors thus improving continuous movement of grid nodes and in turn improve robustness and speed of the Computational Fluid Dynamic (CFD) solver. Analysis of an oil injected twin screw compressor is presented to compare the improvements in grid quality factors in the regions of importance such as interlobe space, radial tip and the core of the rotor. The proposed method that combines algebraic and differential grid generation offer significant improvement in grid quality and robustness of numerical solution.

Multiphase flow calculation software

DOEpatents

Fincke, James R.

2003-04-15

Multiphase flow calculation software and computer-readable media carrying computer executable instructions for calculating liquid and gas phase mass flow rates of high void fraction multiphase flows. The multiphase flow calculation software employs various given, or experimentally determined, parameters in conjunction with a plurality of pressure differentials of a multiphase flow, preferably supplied by a differential pressure flowmeter or the like, to determine liquid and gas phase mass flow rates of the high void fraction multiphase flows. Embodiments of the multiphase flow calculation software are suitable for use in a variety of applications, including real-time management and control of an object system.

Evaluation of liquid aerosol transport through porous media

NASA Astrophysics Data System (ADS)

Hall, R.; Murdoch, L.; Falta, R.; Looney, B.; Riha, B.

2016-07-01

Application of remediation methods in contaminated vadose zones has been hindered by an inability to effectively distribute liquid- or solid-phase amendments. Injection as aerosols in a carrier gas could be a viable method for achieving useful distributions of amendments in unsaturated materials. The objectives of this work were to characterize radial transport of aerosols in unsaturated porous media, and to develop capabilities for predicting results of aerosol injection scenarios at the field-scale. Transport processes were investigated by conducting lab-scale injection experiments with radial flow geometry, and predictive capabilities were obtained by developing and validating a numerical model for simulating coupled aerosol transport, deposition, and multi-phase flow in porous media. Soybean oil was transported more than 2 m through sand by injecting it as micron-scale aerosol droplets. Oil saturation in the sand increased with time to a maximum of 0.25, and decreased with radial distance in the experiments. The numerical analysis predicted the distribution of oil saturation with only minor calibration. The results indicated that evolution of oil saturation was controlled by aerosol deposition and subsequent flow of the liquid oil, and simulation requires including these two coupled processes. The calibrated model was used to evaluate field applications. The results suggest that amendments can be delivered to the vadose zone as aerosols, and that gas injection rate and aerosol particle size will be important controls on the process.

Multiphase flow experiments, mathematical modeling and numerical simulation of the water - gas - solute movement

NASA Astrophysics Data System (ADS)

Li, Y.; Ma, X.; Su, N.

2013-12-01

The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.

The picosecond structure of ultra-fast rogue waves

NASA Astrophysics Data System (ADS)

Klein, Avi; Shahal, Shir; Masri, Gilad; Duadi, Hamootal; Sulimani, Kfir; Lib, Ohad; Steinberg, Hadar; Kolpakov, Stanislav A.; Fridman, Moti

2018-02-01

We investigated ultrafast rogue waves in fiber lasers and found three different patterns of rogue waves: single- peaks, twin-peaks, and triple-peaks. The statistics of the different patterns as a function of the pump power of the laser reveals that the probability for all rogue waves patterns increase close to the laser threshold. We developed a numerical model which prove that the ultrafast rogue waves patterns result from both the polarization mode dispersion in the fiber and the non-instantaneous nature of the saturable absorber. This discovery reveals that there are three different types of rogue waves in fiber lasers: slow, fast, and ultrafast, which relate to three different time-scales and are governed by three different sets of equations: the laser rate equations, the nonlinear Schrodinger equation, and the saturable absorber equations, accordingly. This discovery is highly important for analyzing rogue waves and other extreme events in fiber lasers and can lead to realizing types of rogue waves which were not possible so far such as triangular rogue waves.

Modeling and simulation of surfactant-polymer flooding using a new hybrid method

NASA Astrophysics Data System (ADS)

Daripa, Prabir; Dutta, Sourav

2017-04-01

Chemical enhanced oil recovery by surfactant-polymer (SP) flooding has been studied in two space dimensions. A new global pressure for incompressible, immiscible, multicomponent two-phase porous media flow has been derived in the context of SP flooding. This has been used to formulate a system of flow equations that incorporates the effect of capillary pressure and also the effect of polymer and surfactant on viscosity, interfacial tension and relative permeabilities of the two phases. The coupled system of equations for pressure, water saturation, polymer concentration and surfactant concentration has been solved using a new hybrid method in which the elliptic global pressure equation is solved using a discontinuous finite element method and the transport equations for water saturation and concentrations of the components are solved by a Modified Method Of Characteristics (MMOC) in the multicomponent setting. Numerical simulations have been performed to validate the method, both qualitatively and quantitatively, and to evaluate the relative performance of the various flooding schemes for several different heterogeneous reservoirs.

Adaptation, saturation, and physiological masking in single auditory-nerve fibers.

PubMed

Smith, R L

1979-01-01

Results are reviewed concerning some effects, at a units's characteristic frequency, of a short-term conditioning stimulus on the responses to perstimulatory and poststimulatory test tones. A phenomenological equation is developed from the poststimulatory results and shown to be consistent with the perstimulatory results. According to the results and equation, the response to a test tone equals the unconditioned or unadapted response minus the decrement produced by adaptation to the conditioning tone. Furthermore, the decrement is proportional to the driven response to the conditioning tone and does not depend on sound intensity per se. The equation has a simple interpretation in terms of two processes in cascade--a static saturating nonlinearity followed by additive adaptation. Results are presented to show that this functional model is sufficient to account for the "physiological masking" produced by wide-band backgrounds. According to this interpretation, a sufficiently intense background produces saturation. Consequently, a superimposed test tone cause no change in response. In addition, when the onset of the background precedes the onset of the test tone, the total firing rate is reduced by adaptation. Evidence is reviewed concerning the possible correspondence between the variables in the model and intracellular events in the auditory periphery.

Phase relations in the system NaCl-KCl-H2O: V. Thermodynamic-PTX analysis of solid-liquid equilibria at high temperatures and pressures

USGS Publications Warehouse

Sterner, S.M.; Chou, I.-Ming; Downs, R.T.; Pitzer, Kenneth S.

1992-01-01

The Gibbs energies of mixing for NaCl-KCl binary solids and liquids and solid-saturated NaCl-KCl-H2O ternary liquids were modeled using asymmetric Margules treatments. The coefficients of the expressions were calibrated using an extensive array of binary solvus and solidus data, and both binary and ternary liquidus data. Over the PTX range considered, the system exhibits complete liquid miscibility among all three components and extensive solid solution along the anhydrous binary. Solid-liquid and solid-solid phase equilibria were calculated by using the resulting equations and invoking the equality of chemical potentials of NaCl and KCl between appropriate phases at equilibrium. The equations reproduce the ternary liquidus and predict activity coefficients for NaCl and KCl components in the aqueous liquid under solid-saturation conditions between 673 and 1200 K from vapor saturation up to 5 kbar. In the NaCl-KCl anhydrous binary system, the equations describe phase equilibria and predict activity coefficients of the salt components for all stable compositions of solid and liquid phases between room temperature and 1200 K and from 1 bar to 5 kbar. ?? 1992.

Thermodynamic Properties of Dimethyl Carbonatea)

NASA Astrophysics Data System (ADS)

Zhou, Yong; Wu, Jiangtao; Lemmon, Eric W.

2011-12-01

A thermodynamic property formulation for dimethyl carbonate has been developed with the use of available experimental thermodynamic property data. The equation of state was developed with multiproperty fitting methods involving pressure-density-temperature (pρT), heat capacity, vapor pressure, and saturated-liquid density data. The equation of state conforms to the Maxwell criterion for two-phase liquid-vapor equilibrium states, and is valid for temperatures from the triple-point temperature (277.06 ± 0.63) K to 600 K, for pressures up to 60 MPa, and for densities up to 12.12 mol dm-3. The extrapolation behavior of the equation of state at low and high temperatures and pressures is reasonable. The uncertainties (k = 2, indicating a 95% confidence level) of the equation of state in density are 0.05% for saturated-liquid states below 350 K, rising to 0.1% in the single phase between 278 K and 400 K at pressures up to 60 MPa. Due to the lack of reliable data outside this region, the estimated uncertainties increase to 0.5% to 1% in the vapor and critical regions. The uncertainties in vapor pressure are 0.6% from 310 K to 400 K, and increase to 1% at higher temperatures and to 2% at lower temperatures due to a lack of experimental data. The uncertainty in isobaric heat capacity and speed of sound in the liquid phase at saturation or atmospheric pressure is 0.5% from 280 K to 335 K. The uncertainties are higher for all properties in the critical region. Detailed comparisons between experimental and calculated data, and an analysis of the equation, have been performed.

A novel approach to model hydraulic and electrical conductivity in fractal porous media

NASA Astrophysics Data System (ADS)

Ghanbarian, B.; Daigle, H.; Sahimi, M.

2014-12-01

Accurate prediction of conductivity in partially-saturated porous media has broad applications in various phenomena in porous media, and has been studied intensively since the 1940s by petroleum, chemical and civil engineers, and hydrologists. Many of the models developed in the past are based on the bundle of capillary tubes. In addition, pore network models have also been developed for simulating multiphase fluid flow in porous media and computing the conductivity in unsaturated porous media. In this study, we propose a novel approach using concepts from the effective-medium approximation (EMA) and percolation theory to model hydraulic and electrical conductivity in fractal porous media whose pore-size distributions exhibit power-law scaling. In our approach, the EMA, originally developed for predicting electrical conductivity of composite materials, is used to predict the effective conductivity, from complete saturation to some intermediate water content that represents a crossover point. Below the crossover water content, but still above a critical saturation (percolation threshold), a universal scaling predicted by percolation theory, a power law that expresses the dependence of the conductivity on the water content (less a critical water saturation) with an exponent of 2, is invoked to describe the effective conductivity. In order to evaluate the accuracy of the approach, experimental data were used from the literature. The predicted hydraulic conductivities for most cases are in excellent agreement with the data. In a few cases the theory underestimates the hydraulic conductivities, which correspond to porous media with very broad pore-size distribution in which the largest pore radius is more than 7 orders of magnitude greater than the smallest one. The approach is also used to predict the saturation dependence of the electrical conductivity for experiments in which capillary pressure data are available. The results indicate that the universal scaling of the electrical conductivity is valid from the percolation threshold all the way up to the complete saturation point. Our results confirm those reported previously by Ewing and Hunt (2006) who argued that the electrical conductivity should follow universal scaling over the entire range of saturation.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

NASA Astrophysics Data System (ADS)

Neill, Duff

2017-01-01

We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a closed form expression, and find it to be jet geometry independent, up to the number of legs of the dipole in the active jet. Enabling the asymptotic expansion is the correct perturbative seed, where we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.

Research on the Log Interpretation Method of Tuffaceous Sandstone Reservoirs of X Depression in Hailar-Tamtsag Basin

NASA Astrophysics Data System (ADS)

Liu, S.; Pan, B.

2015-12-01

The logging evaluation of tuffaceous sandstone reservoirs is always a difficult problem. Experiments show that the tuff and shale have different logging responses. Since the tuff content exerts an influence on the computation of shale content and the parameters of the reservoir, and the accuracy of saturation evaluation is reduced. Therefore, the effect of tuff on the calculation of saturation cannot be ignored. This study takes the tuffaceous sandstone reservoirs in the X depression of Hailar-Tamtsag basin as an example to analyze. And the electric conduction model of tuffaceous sandstone reservoirs is established. The method which combines bacterial foraging algorithm and particle swarm optimization algorithm is used to calculate the content of reservoir components in well logging for the first time, and the calculated content of tuff and shale corresponds to the results analysis of thin sections. The experiment on cation exchange capacity (CEC) proves that tuff has conductivity, and the conversion relationship between CEC and resistivity proposed by Toshinobu Iton has been improved. According to the rock electric experiment under simulated reservoir conditions, the rock-electro parameters (a, b, m and n) are determined. The improved relationship between CEC and resistivity and the rock-electro parameters are used in the calculation of saturation. Formula (1) shows the saturation equation of the tuffaceous reservoirs:According to the comparative analysis between irreducible water saturation and the calculated saturation, we find that the saturation equation used CEC data and rock-electro parameters has a better application effect at oil layer than Archie's formulas.

Incorporating interfacial phenomena in solidification models

NASA Technical Reports Server (NTRS)

Beckermann, Christoph; Wang, Chao Yang

1994-01-01

A general methodology is available for the incorporation of microscopic interfacial phenomena in macroscopic solidification models that include diffusion and convection. The method is derived from a formal averaging procedure and a multiphase approach, and relies on the presence of interfacial integrals in the macroscopic transport equations. In a wider engineering context, these techniques are not new, but their application in the analysis and modeling of solidification processes has largely been overlooked. This article describes the techniques and demonstrates their utility in two examples in which microscopic interfacial phenomena are of great importance.

Non-equilibrium radiation from viscous chemically reacting two-phase exhaust plumes

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Mikatarian, R. R.; Ring, L. R.; Anderson, P. G.

1976-01-01

A knowledge of the structure of the rocket exhaust plumes is necessary to solve problems involving plume signatures, base heating, plume/surface interactions, etc. An algorithm is presented which treats the viscous flow of multiphase chemically reacting fluids in a two-dimensional or axisymmetric supersonic flow field. The gas-particle flow solution is fully coupled with the chemical kinetics calculated using an implicit scheme to calculate chemical production rates. Viscous effects include chemical species diffusion with the viscosity coefficient calculated using a two-equation turbulent kinetic energy model.

Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred

2014-09-01

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013), 10.1103/PhysRevE.88.013304] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method.

PubMed

Safari, Hesameddin; Rahimian, Mohammad Hassan; Krafczyk, Manfred

2014-09-01

In the present article, we extend and generalize our previous article [H. Safari, M. H. Rahimian, and M. Krafczyk, Phys. Rev. E 88, 013304 (2013)] to include the gradient of the vapor concentration at the liquid-vapor interface as the driving force for vaporization allowing the evaporation from the phase interface to work for arbitrary temperatures. The lattice Boltzmann phase-field multiphase modeling approach with a suitable source term, accounting for the effect of the phase change on the velocity field, is used to solve the two-phase flow field. The modified convective Cahn-Hilliard equation is employed to reconstruct the dynamics of the interface topology. The coupling between the vapor concentration and temperature field at the interface is modeled by the well-known Clausius-Clapeyron correlation. Numerous validation tests including one-dimensional and two-dimensional cases are carried out to demonstrate the consistency of the presented model. Results show that the model is able to predict the flow features around and inside an evaporating droplet quantitatively in quiescent as well as convective environments.

Lagrangian particle method for compressible fluid dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less

A multiphase ion-transport analysis of the electrostatic disjoining pressure: implications for binary droplet coalescence

NASA Astrophysics Data System (ADS)

Mason, Lachlan; Gebauer, Felix; Bart, Hans-Jörg; Stevens, Geoffrey; Harvie, Dalton

2016-11-01

Understanding the physics of emulsion coalescence is critical for the robust simulation of industrial solvent extraction processes, in which loaded organic and raffinate phases are separated via the coalescence of dispersed droplets. At the droplet scale, predictive collision-outcome models require an accurate description of the repulsive surface forces arising from electrical-double-layer interactions. The conventional disjoining-pressure treatment of double-layer forces, however, relies on assumptions which do not hold generally for deformable droplet collisions: namely, low interfacial curvature and negligible advection of ion species. This study investigates the validity bounds of the disjoining pressure approximation for low-inertia droplet interactions. A multiphase ion-transport model, based on a coupling of droplet-scale Nernst-Planck and Navier-Stokes equations, predicts ion-concentration fields that are consistent with the equilibrium Boltzmann distribution; indicating that the disjoining-pressure approach is valid for both static and dynamic interactions in low-Reynolds-number settings. The present findings support the development of coalescence kernels for application in macro-scale population balance modelling.

A novel partitioning method for block-structured adaptive meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Lin, E-mail: lin.fu@tum.de; Litvinov, Sergej, E-mail: sergej.litvinov@aer.mw.tum.de; Hu, Xiangyu Y., E-mail: xiangyu.hu@tum.de

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtainmore » the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.« less

A novel partitioning method for block-structured adaptive meshes

NASA Astrophysics Data System (ADS)

Fu, Lin; Litvinov, Sergej; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-07-01

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

Lagrangian particle method for compressible fluid dynamics

DOE PAGES

Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang

2018-02-09

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less

Modeling Subgrid Scale Droplet Deposition in Multiphase-CFD

NASA Astrophysics Data System (ADS)

Agostinelli, Giulia; Baglietto, Emilio

2017-11-01

The development of first-principle-based constitutive equations for the Eulerian-Eulerian CFD modeling of annular flow is a major priority to extend the applicability of multiphase CFD (M-CFD) across all two-phase flow regimes. Two key mechanisms need to be incorporated in the M-CFD framework, the entrainment of droplets from the liquid film, and their deposition. Here we focus first on the aspect of deposition leveraging a separate effects approach. Current two-field methods in M-CFD do not include appropriate local closures to describe the deposition of droplets in annular flow conditions. As many integral correlations for deposition have been proposed for lumped parameters methods applications, few attempts exist in literature to extend their applicability to CFD simulations. The integral nature of the approach limits its applicability to fully developed flow conditions, without geometrical or flow variations, therefore negating the scope of CFD application. A new approach is proposed here that leverages local quantities to predict the subgrid-scale deposition rate. The methodology is first tested into a three-field approach CFD model.

Single- and two-phase flow in microfluidic porous media analogs based on Voronoi tessellation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Mengjie; Xiao, Feng; Johnson-Paben, Rebecca

2012-01-01

The objective of this study was to create a microfluidic model of complex porous media for studying single and multiphase flows. Most experimental porous media models consist of periodic geometries that lend themselves to comparison with well-developed theoretical predictions. However, most real porous media such as geological formations and biological tissues contain a degree of randomness and complexity that is not adequately represented in periodic geometries. To design an experimental tool to study these complex geometries, we created microfluidic models of random homogeneous and heterogeneous networks based on Voronoi tessellations. These networks consisted of approximately 600 grains separated by amore » highly connected network of channels with an overall porosity of 0.11 0.20. We found that introducing heterogeneities in the form of large cavities within the network changed the permeability in a way that cannot be predicted by the classical porosity-permeability relationship known as the Kozeny equation. The values of permeability found in experiments were in excellent agreement with those calculated from three-dimensional lattice Boltzmann simulations. In two-phase flow experiments of oil displacement with water we found that the surface energy of channel walls determined the pattern of water invasion, while the network topology determined the residual oil saturation. These results suggest that complex network topologies lead to fluid flow behavior that is difficult to predict based solely on porosity. The microfluidic models developed in this study using a novel geometry generation algorithm based on Voronoi tessellation are a new experimental tool for studying fluid and solute transport problems within complex porous media.« less

Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar

NASA Technical Reports Server (NTRS)

Jacobsen, Richard T.; Stewart, Richard B.

1973-01-01

Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity velocity of sound, the isotherm derivative, and the isochor derivative. The thermodynamic property tables are based on an equation of state, P=P (p,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-p-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-p-T data and, simultaneously, to isochoric heat capacity data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.

Application of the Modified Compaction Material Model to the Analysis of Landmine Detonation in Soil with Various Degrees of Water Saturation

DTIC Science & Technology

2007-01-01

Equation of State R2 – Constant in JWL Equation of State σ – Yield Stress T – Temperature...v – Specific volume w – Constant in JWL Equation of State x – Spatial coordinate y – Spatial coordinate Y – Yield stress Subscripts Comp – Value at...Constant in JWL Equation of State α – Porosity B – Compaction Modulus B1 – Strain Hardening Constant B2 – Constant in JWL Equation of State

NETL Crosscutting Research Video Series: Multiphase Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tingwen; Vaidheeswaran, Avinash

For over 30 years, NETL’s work in multiphase flow science has served as one of the cornerstones of the lab’s research portfolio. Multiphase flow refers to the simultaneous flow of gases, liquids and/or solid materials. The goal of the multiphase flow science team is to provide computational modeling tools to help offset the risk and cost of multiphase reactor development.

Stress and Dilatancy Relation of Methane Hydrate Bearing Sand with Various Fines Content

NASA Astrophysics Data System (ADS)

Hyodo, M.

2016-12-01

This study presents an experimental and numerical study on the shear behaviour of methane hydrate bearing sand with variable confining pressures and methane hydrate saturations. A representative grading curve of Nankai Trough is selected as the grain size distribution of host sand to artificially produce the methane hydrate bearing sand. A shear strength estimation equation for methane hydrate bearing sand from test results is established. A simple constitutive model has been proposed to predict the stress-strain response of methane hydrate bearing sand based on a few well-known relationships. Experimental results indicate that the inclination of stress-dilatancy curve becomes steeper with a rise in methane hydrate saturation. A revised stress-dilatancy equation has been integrated with this simple model to consider the variance in the inclination of stress-dilatancy curve. The mean stress Pcr at critical state when the peak stress ratio reduces to the residual stress ratio increases with the level of methane hydrate saturation. The dilatancy parameter a tends to increase with the methane hydrate saturation. The shear deformability parameter A exhibits a decreasing tendency with the rise in methane hydrate saturation at each confining pressure. This model is capable of reasonably predicting the strength and stiffness enhancement and the dilation behaviour as methane hydrate saturation increases. The volumetric variation from contraction to expansion of MH bearing sand at a lower confining pressure and only pure volumetric contraction a higher confining pressure can be represented by this simple model.

High-resolution simulations of multi-phase flow in magmatic-hydrothermal systems with realistic fluid properties

NASA Astrophysics Data System (ADS)

Geiger, S.; Driesner, T.; Matthai, S.; Heinrich, C.

2002-12-01

Realistic modelling of multi-phase fluid flow, energy and component transport in magmatic-hydrothermal systems is very challenging because hydrological properties of fluids and rocks vary over many orders of magnitude and the geometric complexities of such systems. Furthermore, density dependent component transport and transient permeability variations due to P-T changes and fluid-rock interactions introduce additional difficulties. As a result, the governing equations for the hydrodynamics, energy and component transport, and thermodynamics in magmatic hydrothermal systems are highly non-linear and strongly coupled. Essential requirements of a numerical formulation for such a system are: (1) a treatment of the hydrodynamics that can accurately resolve complex geological structures and represent the highly variable fluid velocities herein, (2) a realistic thermodynamic representation of the fluid properties including the wide P-T-X range of liquid+vapour coexistence for the highly saline fluids, and (3) an accurate handling of the highly contrasting transport properties of the two fluids. We are combining higher order finite-element (FE) methods with total variation diminishing finite volume (TVDFV) methods to model the hydrodynamics and energy and component transport of magmatic hydrothermal systems. Combined FE and TVDFV methods are mass and shock preserving, yield great geometric flexibility in 2D and 3D [2]. Furthermore, efficient matrix solvers can be employed to model fluid flow in geologically realistic structures [5]. The governing equations are linearized by operator-splitting and solved sequentially using a Picard iteration scheme. We chose the system water-NaCl as a realistic proxy for natural fluids occurring in magmatic-hydrothermal systems. An in-depth evaluation of the available experimental and theoretical data led to a consistent and accurate set of formulations for the PVTXH relations that are valid from 0 to 800 C, 0 to 500 MPa, and 0 to 1 XNaCl. Dynamic viscosities are currently approximated by the approach of Palliser and McKibbin [4]. The numerical solutions of the governing equations and the equation of state are embedded in our object-oriented C++ code CSP3D4.0 [6]. Comparisons of the numerical solutions carried out with CSP for solute transport with analytical solutions and classical test cases for density dependent flow (i.e., Elder problem [1]) show very good agreement. The numerical solutions carried out with CSP and the established United States Geological Survey code HYDROTHERM [3] for multi-phase flow and energy transport also yield a very good agreement. Fluid inclusion data can be used to constrain the PTX properties of the hydrothermal fluids in numerical solutions. [1] Journal of Fluid Mechanics 27, 609-623 [2] ANU Mathematical Research Report, MRR01-023 [3] USGS Water Investigations Report 94-4045 [4] Transport in Porous Media 33, 155-171 [5] AAPG Bulletin 80, 1763-1779 [6] CSP User's Guide, Dept. of Earth Sciences ETH Zurich

Multiphysics Modelling of Sodium Sulfur Battery

NASA Astrophysics Data System (ADS)

Mason, Jerry Hunter

Due to global climate change and the desire to decrease greenhouse gas emissions, large scale energy storage has become a critical issue. Renewable energy sources such as wind and solar will not be a viable energy source unless the storage problem is solved. One of the practical and cost effective solutions for this problem is sodium sulfur batteries. These batteries are comprised of liquid electrode materials suspended in porous media and operate at relatively high temperatures (>300°C). The sodium anode and the sulfur/sodium-polysulfide cathode are separated by a solid electrolyte made of beta-alumina or NASICON material. Due to the use of porous materials in the electrodes, capillary pressure and the combination of capillary action and gravity become important. Capillary pressure has a strong dependence on the wetting phase (liquid electrode material) saturation; therefore sharp concentration gradients can occur between the inert gas and the electrode liquid, especially within the cathode. These concentration gradients can have direct impacts on the electrodynamics of the battery as they may produce areas of high electrical potential variation, which can decrease efficiency and even cause failures. Then, thermal management also becomes vital since the electrochemistry and material properties are sensitive to temperature gradients. To investigate these phenomena in detail and to attempt to improve upon battery design a multi-dimensional, multi-phase code has been developed and validated in this study. Then a porous media flow model is implemented. Transport equations for charge, mass and heat are solved in a time marching fashion using finite volume method. Material properties are calculated and updated as a function of time. The porous media model is coupled with the continuity equation and a separate diffusion equation for the liquid sodium in the melt. The total mass transport model is coupled with charge transport via Faraday's law. Results show that overpotential is significantly higher in the porous region of the cathode as was predicted by models in the literature. Overpotential is also high on the electrolyte surface and wall. Alternative electrode configurations with high resistive layers recommended by previous researchers also produce areas of high potential gradient. New electrode designs including conductivity gradients and porous media property variations are simulated and compared to previous designs and then recommendations are made for optimum cell operating conditions.

Coupled multiphase flow and geomechanics analysis of the 2011 Lorca earthquake

NASA Astrophysics Data System (ADS)

Jha, B.; Hager, B. H.; Juanes, R.; Bechor, N.

2013-12-01

We present a new approach for modeling coupled multiphase flow and geomechanics of faulted reservoirs. We couple a flow simulator with a mechanics simulator using the unconditionally stable fixed-stress sequential solution scheme [Kim et al, 2011]. We model faults as surfaces of discontinuity using interface elements [Aagaard et al, 2008]. This allows us to model stick-slip behavior on the fault surface for dynamically evolving fault strength. We employ a rigorous formulation of nonlinear multiphase geomechanics [Coussy, 1995], which is based on the increment in mass of fluid phases instead of the traditional, and less accurate, scheme based on the change in porosity. Our nonlinear formulation is capable of handling strong capillarity and large changes in saturation in the reservoir. To account for the effect of surface stresses along fluid-fluid interfaces, we use the equivalent pore pressure in the definition of the multiphase effective stress [Coussy et al, 1998; Kim et al, 2013]. We use our simulation tool to study the 2011 Lorca earthquake [Gonzalez et al, 2012], which has received much attention because of its potential anthropogenic triggering (long-term groundwater withdrawal leading to slip along the regional Alhama de Murcia fault). Our coupled fluid flow and geomechanics approach to model fault slip allowed us to take a fresh look at this seismic event, which to date has only been analyzed using simple elastic dislocation models and point source solutions. Using a three-dimensional model of the Lorca region, we simulate the groundwater withdrawal and subsequent unloading of the basin over the period of interest (1960-2010). We find that groundwater withdrawal leads to unloading of the crust and changes in the stress across the impermeable fault plane. Our analysis suggests that the combination of these two factors played a critical role in inducing the fault slip that ultimately led to the Lorca earthquake. Aagaard, B. T., M. G. Knepley, and C. A. Williams (2013), Journal of Geophysical Research, Solid Earth, 118, 3059-3079 Coussy, O. (1995), Mechanics of Porous Continua, John Wiley and Sons, England. Coussy, O., R. Eymard, and T. Lassabatere (1998), J. Eng. Mech., 124(6), 658-557. Kim, J., H. A. Tchelepi, and R. Juanes (2011), Comput. Methods Appl. Mech. Eng., 200, 1591-1606. Gonzalez, P. J., K. F. Tiampo, M. Palano, F. Cannavo, and J. Fernandez (2012), Nature Geoscience.

Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

NASA Astrophysics Data System (ADS)

Bhadauria, B. S.; Singh, M. K.; Singh, A.; Singh, B. K.; Kiran, P.

2016-12-01

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

NETL Crosscutting Research Video Series: Multiphase Flow (Short Version)

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

For over 30 years, NETL’s work in multiphase flow science has served as one of the cornerstones of the lab’s research portfolio. Multiphase flow refers to the simultaneous flow of gases, liquids and/or solid materials. The goal of the multiphase flow science team is to provide computational modeling tools to help offset the risk and cost of multiphase reactor development.

A correlated Walks' theory for DNA denaturation

NASA Astrophysics Data System (ADS)

Mejdani, R.

1994-08-01

We have shown that by using a correlated Walks' theory for the lattice gas model on a one-dimensional lattice, we can study, beside the saturation curves obtained before for the enzyme kinetics, also the DNA denaturation process. In the limit of no interactions between sites the equation for melting curves of DNA reduces to the random model equation. Thus our leads naturally to this classical equation in the limiting case.

The thermodynamic properties of oxygen and nitrogen. Part 2: Thermodynamic properties of oxygen from 100 R to 600 R with pressure to 5000 psia

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

An equation of state is presented for liquid and gaseous oxygen for temperatures from 100 R to 600 R and pressures to 5000 psia. The pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Representative comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation of state. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data, and simultaneously to isochoric heat capacity data, and to data which define the phase equilibrium for the saturated liquid and saturated vapor. The equation of state is estimated to be accurate for the liquid to within 0.1 percent in density, to within 0.2 percent for the vapor below the critical temperature and for states above the critical temperatures to 250 K, and within 0.1 percent for supercritical states at temperatures from 250 K to 300 K. The vapor pressure equation is accurate to within + or - 0.01 K between the triple point and the critical point.

Analysis of Flame Deflector Spray Nozzles in Rocket Engine Test Stands

NASA Technical Reports Server (NTRS)

Sachdev, Jai S.; Ahuja, Vineet; Hosangadi, Ashvin; Allgood, Daniel C.

2010-01-01

The development of a unified tightly coupled multi-phase computational framework is described for the analysis and design of cooling spray nozzle configurations on the flame deflector in rocket engine test stands. An Eulerian formulation is used to model the disperse phase and is coupled to the gas-phase equations through momentum and heat transfer as well as phase change. The phase change formulation is modeled according to a modified form of the Hertz-Knudsen equation. Various simple test cases are presented to verify the validity of the numerical framework. The ability of the methodology to accurately predict the temperature load on the flame deflector is demonstrated though application to an actual sub-scale test facility. The CFD simulation was able to reproduce the result of the test-firing, showing that the spray nozzle configuration provided insufficient amount of cooling.

Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

2016-06-01

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Lattice Boltzmann model for three-phase viscoelastic fluid flow

NASA Astrophysics Data System (ADS)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

Transport Phenomena During Equiaxed Solidification of Alloys

NASA Technical Reports Server (NTRS)

Beckermann, C.; deGroh, H. C., III

1997-01-01

Recent progress in modeling of transport phenomena during dendritic alloy solidification is reviewed. Starting from the basic theorems of volume averaging, a general multiphase modeling framework is outlined. This framework allows for the incorporation of a variety of microscale phenomena in the macroscopic transport equations. For the case of diffusion dominated solidification, a simplified set of model equations is examined in detail and validated through comparisons with numerous experimental data for both columnar and equiaxed dendritic growth. This provides a critical assessment of the various model assumptions. Models that include melt flow and solid phase transport are also discussed, although their validation is still at an early stage. Several numerical results are presented that illustrate some of the profound effects of convective transport on the final compositional and structural characteristics of a solidified part. Important issues that deserve continuing attention are identified.

Second order upwind Lagrangian particle method for Euler equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Phase Behavior of Salt-Free Polyelectrolyte Gel-Surfactant Systems.

PubMed

Andersson, Martin; Hansson, Per

2017-06-22

Ionic surfactants tend to collapse the outer parts of polyelectrolyte gels, forming shells that can be used to encapsulate other species including protein and peptide drugs. In this paper, the aqueous phase behavior of covalently cross-linked polyacrylate networks containing sodium ions and dodecyltrimethylammonium ions as counterions is investigated by means of swelling isotherms, dye staining, small-angle X-ray scattering, and confocal Raman spectroscopy. The equilibrium state is approached by letting the networks absorb pure water. With an increasing fraction of surfactant ions, the state of the water-saturated gels is found to change from being swollen and monophasic, via multiphasic states, to collapsed and monophasic. The multiphasic gels have a swollen, micelle-lean core surrounded by a collapsed, micelle-rich shell, or a collapsed phase forming a spheroidal inner shell separating two micelle-lean parts. It is shown that the transition between monophasic and core-shell states can be induced by variation of the osmotic pressure and variation of the charge of the micelles by forming mixed micelles with the nonionic surfactant octaethyleneglycol monododecylether. The experimental data are compared with theoretical predictions of a model derived earlier. In the calculations, the collapsed shell is assumed to be homogeneous, an approximation introduced here and shown to be excellent for a wide range of compositions. The theoretical results highlight the electrostatic and hydrophobic driving forces behind phase separation.

An Interpolation Method for Obtaining Thermodynamic Properties Near Saturated Liquid and Saturated Vapor Lines

NASA Technical Reports Server (NTRS)

Nguyen, Huy H.; Martin, Michael A.

2003-01-01

The availability and proper utilization of fluid properties is of fundamental importance in the process of mathematical modeling of propulsion systems. Real fluid properties provide the bridge between the realm of pure analytiis and empirical reality. The two most common approaches used to formulate thermodynamic properties of pure substances are fundamental (or characteristic) equations of state (Helmholtz and Gibbs functions) and a piecemeal approach that is described, for example, in Adebiyi and Russell (1992). This paper neither presents a different method to formulate thermodynamic properties of pure substances nor validates the aforementioned approaches. Rather its purpose is to present a method to be used to facilitate the accurate interpretation of fluid thermodynamic property data generated by existing property packages. There are two parts to this paper. The first part of the paper shows how efficient and usable property tables were generated, with the minimum number of data points, using an aerospace industry standard property package (based on fundamental equations of state approach). The second part describes an innovative interpolation technique that has been developed to properly obtain thermodynamic properties near the saturated liquid and saturated vapor lines.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kopeliovich, B. Z.; Potashnikova, I. K.; Schmidt, Ivan

A bootstrap equation for self-quenched gluon shadowing leads to a reduced magnitude of broadening for partons propagating through a nucleus. Saturation of small-x gluons in a nucleus, which has the form of transverse momentum broadening of projectile gluons in pA collisions in the nuclear rest frame, leads to a modification of the parton distribution functions in the beam compared with pp collisions. In nucleus-nucleus collisions all participating nucleons acquire enhanced gluon density at small x, which boosts further the saturation scale. Solution of the reciprocity equations for central collisions of two heavy nuclei demonstrate a significant, up to several times,more » enhancement of Q{sub sA}{sup 2}, in AA compared with pA collisions.« less

Influence of the nuclear matter equation of state on the r-mode instability using the finite-range simple effective interaction

NASA Astrophysics Data System (ADS)

Pattnaik, S. P.; Routray, T. R.; Viñas, X.; Basu, D. N.; Centelles, M.; Madhuri, K.; Behera, B.

2018-05-01

The characteristic physical properties of rotating neutron stars under the r-mode oscillation are evaluated using the finite-range simple effective interaction. Emphasis is given on examining the influence of the stiffness of both the symmetric and asymmetric parts of the nuclear equation of state on these properties. The amplitude of the r-mode at saturation is calculated using the data of particular neutron stars from the considerations of ‘spin equilibrium’ and ‘thermal equilibrium’. The upper limit of the r-mode saturation amplitude is found to lie in the range 10‑8–10‑6, in agreement with the predictions of earlier work.

The Onset of Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer with Non-Equilibrium Model

PubMed Central

Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong

2013-01-01

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically. PMID:24312193

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

PubMed

Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong

2013-01-01

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

Evaluation of residual oil saturation after waterflood in a carbonate reservoir

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verma, M.K.; Boucherit, M.; Bouvier, L.

Four different approaches, including special core analysis (SCAL), log-inject-log, thermal-decay-time (TDT) logs, and material balance, were used to narrow the range of residual oil saturation (ROS) after waterflood, S[sub orw], in a carbonate reservoir in Qatar to between 23% and 27%. An equation was developed that relates S[sub orw] with connate-water saturation, S[sub wi], and porosity. This paper presents the results of S[sub orw] determinations with four different techniques: core waterflood followed by centrifuging, log-inject-log, TDT logging, and material balance.

Three-dimensional analytic model of the magnetic field for the Chalk River Superconducting Cyclotron

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davies, W.G.; Lee-Whiting, G.E.; Douglas, S.R.

1994-07-01

A three-dimensional analytic model of the magnetic field for the TASCC cyclotron that satisfies Maxwell`s equations exactly has been constructed for use with the new differential-algebra orbit-dynamics code. The model includes: (1) the superconducting coils; (2) the saturated iron poles; (3) the partially saturated yoke; (4) the saturated-iron trim rods. Lines of dipole density along the edges of the hills account for the non-uniformities and edge effects and along with three yoke constants constitute the only free parameters.

Smoothed particle hydrodynamics method for evaporating multiphase flows.

PubMed

Yang, Xiufeng; Kong, Song-Charng

2017-09-01

The smoothed particle hydrodynamics (SPH) method has been increasingly used for simulating fluid flows; however, its ability to simulate evaporating flow requires significant improvements. This paper proposes an SPH method for evaporating multiphase flows. The present SPH method can simulate the heat and mass transfers across the liquid-gas interfaces. The conservation equations of mass, momentum, and energy were reformulated based on SPH, then were used to govern the fluid flow and heat transfer in both the liquid and gas phases. The continuity equation of the vapor species was employed to simulate the vapor mass fraction in the gas phase. The vapor mass fraction at the interface was predicted by the Clausius-Clapeyron correlation. An evaporation rate was derived to predict the mass transfer from the liquid phase to the gas phase at the interface. Because of the mass transfer across the liquid-gas interface, the mass of an SPH particle was allowed to change. Alternative particle splitting and merging techniques were developed to avoid large mass difference between SPH particles of the same phase. The proposed method was tested by simulating three problems, including the Stefan problem, evaporation of a static drop, and evaporation of a drop impacting a hot surface. For the Stefan problem, the SPH results of the evaporation rate at the interface agreed well with the analytical solution. For drop evaporation, the SPH result was compared with the result predicted by a level-set method from the literature. In the case of drop impact on a hot surface, the evolution of the shape of the drop, temperature, and vapor mass fraction were predicted.

Water Displacement in Oil-Wet Tight Reservoirs by Dynamic Network Simulation

NASA Astrophysics Data System (ADS)

Wang, Y.; Li, M.; Chen, M.

2017-12-01

Pore network simulation is an effective tool for studying the multiphase flow in porous media. Based on the topological information and pore-throat size distribution obtained from the analysis of Scanning Electron Microscope (SEM) and constant-rate mercury injection (CRMI) for tight cores (composed by micro-nano scale throats and micro scale pores), a simple cubic (SC) pore-throat network was built with equilateral triangular cross-section throats and cubic bodies. Rules for oil and water movement and redistribution were devised in accordance with the physics process at pore-throat scale. Water flooding from oil-saturated under irreducible water were simulated by considering the changing displacement rate and viscosity ratio at the slightly oil-wet condition (the static contact angle ranges between π/2 to 2π/3). Different from the double pressure field algorithm, a single pressure field which solved by using successive over relaxation method was used with the flow of irreducible water in corners was ignored while its swilling was take into consideration. Dynamic of displacement fronts, relative permeability curves and residual oil saturation were obtained. It showed that there were obviously snap-off at low capillary number (Nc<10-5) and fingering at high capillary number (Nc<10-4) even at a favorable viscosity ratio (M=1). The magnitude of viscosity ratio effect on relative permeability depended largely on the capillary number, which the effect wasn't noticeable for a high capillary number. For residual oil saturation Sor, it showed that Sor decreased with the increase of capillary number at different viscosity ratio. Changing of residual oil saturation from simulation was in good agreement with the experimental results in a certain range, which indicated that this network model could be used to character the water flooding in tight reservoirs.

Simplified contaminant source depletion models as analogs of multiphase simulators

NASA Astrophysics Data System (ADS)

Basu, Nandita B.; Fure, Adrian D.; Jawitz, James W.

2008-04-01

Four simplified dense non-aqueous phase liquid (DNAPL) source depletion models recently introduced in the literature are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. The spill and subsequent dissolution of DNAPLs was simulated in domains having different hydrologic characteristics (variance of the log conductivity field = 0.2, 1 and 3) using the multiphase flow and transport simulator UTCHEM. The dissolution profiles were fitted using four analytical models: the equilibrium streamtube model (ESM), the advection dispersion model (ADM), the power law model (PLM) and the Damkohler number model (DaM). All four models, though very different in their conceptualization, include two basic parameters that describe the mean DNAPL mass and the joint variability in the velocity and DNAPL distributions. The variability parameter was observed to be strongly correlated with the variance of the log conductivity field in the ESM and ADM but weakly correlated in the PLM and DaM. The DaM also includes a third parameter that describes the effect of rate-limited dissolution, but here this parameter was held constant as the numerical simulations were found to be insensitive to local-scale mass transfer. All four models were able to emulate the characteristics of the dissolution profiles generated from the complex numerical simulator, but the one-parameter PLM fits were the poorest, especially for the low heterogeneity case.

Simplified contaminant source depletion models as analogs of multiphase simulators.

PubMed

Basu, Nandita B; Fure, Adrian D; Jawitz, James W

2008-04-28

Four simplified dense non-aqueous phase liquid (DNAPL) source depletion models recently introduced in the literature are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. The spill and subsequent dissolution of DNAPLs was simulated in domains having different hydrologic characteristics (variance of the log conductivity field=0.2, 1 and 3) using the multiphase flow and transport simulator UTCHEM. The dissolution profiles were fitted using four analytical models: the equilibrium streamtube model (ESM), the advection dispersion model (ADM), the power law model (PLM) and the Damkohler number model (DaM). All four models, though very different in their conceptualization, include two basic parameters that describe the mean DNAPL mass and the joint variability in the velocity and DNAPL distributions. The variability parameter was observed to be strongly correlated with the variance of the log conductivity field in the ESM and ADM but weakly correlated in the PLM and DaM. The DaM also includes a third parameter that describes the effect of rate-limited dissolution, but here this parameter was held constant as the numerical simulations were found to be insensitive to local-scale mass transfer. All four models were able to emulate the characteristics of the dissolution profiles generated from the complex numerical simulator, but the one-parameter PLM fits were the poorest, especially for the low heterogeneity case.

Pulse oximetry in the pulmonary tissue for the non-invasive measurement of mixed venous oxygen saturation.

PubMed

Nitzan, Meir; Nitzan, Itamar

2013-08-01

The oxygen saturation of the systemic arterial blood is associated with the adequacy of respiration, and can be measured non-invasively by pulse oximetry in the systemic tissue. The oxygen saturation of the blood in the pulmonary artery, the mixed venous blood, reflects the balance between oxygen supply to the systemic tissues and their oxygen demand. The mixed venous oxygen saturation has also clinical significance because it is used in Fick equation for the quantitative measurement of cardiac output. At present the measurement of the mixed venous oxygen saturation is invasive and requires insertion of a Swan-Ganz catheter into the pulmonary artery. We suggest a noninvasive method for the measurement of the mixed venous oxygen saturation in infants, pulmonary pulse oximetry. The method is similar to the systemic pulse oximetry, which is based on the different light absorption curves of oxygenated and deoxygenated hemoglobin and on the analysis of photoplethysmographic curves in two wavelengths. The proposed pulmonary pulse oximeter includes light-sources of two wavelengths in the infrared, which illuminate the pulmonary tissue through the thoracic wall. Part of the light which is scattered back from the pulmonary tissue and passes through the thoracic wall is detected, and for each wavelength a pulmonary photoplethysmographic curve is obtained. The pulmonary photoplethysmographic curves reflect blood volume increase during systole in the pulmonary arteries in the lung tissue, which contain mixed venous blood. The ratio R of the amplitude-to-baseline ratio for the two wavelengths is related to the mixed venous oxygen saturation through equations derived for the systemic pulse oximetry. The method requires the use of extinction coefficients values for oxygenated and deoxygenated hemoglobin, which can be found in the literature. Copyright © 2013 Elsevier Ltd. All rights reserved.

Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

NASA Astrophysics Data System (ADS)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neill, Duff

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometrymore » independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

The asymptotic form of non-global logarithms, black disc saturation, and gluonic deserts

DOE PAGES

Neill, Duff

2017-01-25

Here, we develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. Furthermore, this equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We also compute the decay width analytically, giving a closed form expression, and find it to be jet geometrymore » independent, up to the number of legs of the dipole in the active jet. By enabling the asymptotic expansion we find that the perturbative seed is correct; we perturb around an anzats encoding formally no real emissions, an intuition motivated by the buffer region found in jet dynamics. This must be supplemented with the correct application of the BFKL approximation to the BMS equation in collinear limits. Comparing to the asymptotics of the conformally related evolution equation encountered in small-x physics, the Balitisky-Kovchegov (BK) equation, we find that the asymptotic form of the non-global logarithms directly maps to the black-disc unitarity limit of the BK equation, despite the contrasting physical pictures. Indeed, we recover the equations of saturation physics in the final state dynamics of QCD.« less

40 CFR 1065.645 - Amount of water in an ideal gas.

Code of Federal Regulations, 2014 CFR

2014-07-01

... vapor pressure of water in paragraph (a) of this section or another appropriate equation and, depending... converting the last term in each equation. (a) Vapor pressure of water. Calculate the vapor pressure of water... use a different relationship of the vapor pressure of water to a given saturation temperature...

Numerical modelling of hydrologically-driven slope instability by means of porous media mechanics

NASA Astrophysics Data System (ADS)

Kakogiannou, Evanthia; Sanavia, Lorenzo; Lora, Marco; Schrefler, Bernhard

2015-04-01

Heavy rainfall can trigger slope failure which generally involves shallow soil deposit of different grading and origin usually in a state of partial saturation. In this case of slope instability, the behaviour of the soil slope is closely related not only to the distribution of pore-water pressure but also to the stress state during rainfall infiltration involving both mechanical and hydrological processes. In order to understand better these physical key processes, in this research work, the modelling of rainfall induced slope failure is considered as a coupled variably saturated hydro-mechanical problem. Therefore, the geometrically linear finite element code Comes-Geo for non-isothermal elasto-plastic multiphase solid porous materials is used, as developed by B.A. Schrefler and his co-workers. In this context, a detailed numerical analysis of an experimental slope stability test due to rainfall infiltration is presented. The main goals of this work are to understand the triggering mechanisms during the progressive failure, the effect of using different constitutive models of the mechanical soil behavior on the numerical results and the use of the second order work criterion on the detection of slope instability.

Documentation of computer program VS2D to solve the equations of fluid flow in variably saturated porous media

USGS Publications Warehouse

Lappala, E.G.; Healy, R.W.; Weeks, E.P.

1987-01-01

This report documents FORTRAN computer code for solving problems involving variably saturated single-phase flow in porous media. The flow equation is written with total hydraulic potential as the dependent variable, which allows straightforward treatment of both saturated and unsaturated conditions. The spatial derivatives in the flow equation are approximated by central differences, and time derivatives are approximated either by a fully implicit backward or by a centered-difference scheme. Nonlinear conductance and storage terms may be linearized using either an explicit method or an implicit Newton-Raphson method. Relative hydraulic conductivity is evaluated at cell boundaries by using either full upstream weighting, the arithmetic mean, or the geometric mean of values from adjacent cells. Nonlinear boundary conditions treated by the code include infiltration, evaporation, and seepage faces. Extraction by plant roots that is caused by atmospheric demand is included as a nonlinear sink term. These nonlinear boundary and sink terms are linearized implicitly. The code has been verified for several one-dimensional linear problems for which analytical solutions exist and against two nonlinear problems that have been simulated with other numerical models. A complete listing of data-entry requirements and data entry and results for three example problems are provided. (USGS)

Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.

Effect of soil property uncertainties on permafrost thaw projections: a calibration-constrained analysis: Modeling Archive

DOE Data Explorer

J.C. Rowland; D.R. Harp; C.J. Wilson; A.L. Atchley; V.E. Romanovsky; E.T. Coon; S.L. Painter

2016-02-02

This Modeling Archive is in support of an NGEE Arctic publication available at doi:10.5194/tc-10-341-2016. This dataset contains an ensemble of thermal-hydro soil parameters including porosity, thermal conductivity, thermal conductivity shape parameters, and residual saturation of peat and mineral soil. The ensemble was generated using a Null-Space Monte Carlo analysis of parameter uncertainty based on a calibration to soil temperatures collected at the Barrow Environmental Observatory site by the NGEE team. The micro-topography of ice wedge polygons present at the site is included in the analysis using three 1D column models to represent polygon center, rim and trough features. The Arctic Terrestrial Simulator (ATS) was used in the calibration to model multiphase thermal and hydrological processes in the subsurface.

Verification and Validation (V&V) Methodologies for Multiphase Turbulent and Explosive Flows. V&V Case Studies of Computer Simulations from Los Alamos National Laboratory GMFIX codes

NASA Astrophysics Data System (ADS)

Dartevelle, S.

2006-12-01

Large-scale volcanic eruptions are inherently hazardous events, hence cannot be described by detailed and accurate in situ measurements; hence, volcanic explosive phenomenology is inadequately constrained in terms of initial and inflow conditions. Consequently, little to no real-time data exist to Verify and Validate computer codes developed to model these geophysical events as a whole. However, code Verification and Validation remains a necessary step, particularly when volcanologists use numerical data for mitigation of volcanic hazards as more often performed nowadays. The Verification and Validation (V&V) process formally assesses the level of 'credibility' of numerical results produced within a range of specific applications. The first step, Verification, is 'the process of determining that a model implementation accurately represents the conceptual description of the model', which requires either exact analytical solutions or highly accurate simplified experimental data. The second step, Validation, is 'the process of determining the degree to which a model is an accurate representation of the real world', which requires complex experimental data of the 'real world' physics. The Verification step is rather simple to formally achieve, while, in the 'real world' explosive volcanism context, the second step, Validation, is about impossible. Hence, instead of validating computer code against the whole large-scale unconstrained volcanic phenomenology, we rather suggest to focus on the key physics which control these volcanic clouds, viz., momentum-driven supersonic jets and multiphase turbulence. We propose to compare numerical results against a set of simple but well-constrained analog experiments, which uniquely and unambiguously represent these two key-phenomenology separately. Herewith, we use GMFIX (Geophysical Multiphase Flow with Interphase eXchange, v1.62), a set of multiphase- CFD FORTRAN codes, which have been recently redeveloped to meet the strict Quality Assurance, verification, and validation requirements from the Office of Civilian Radioactive Waste Management of the US Dept of Energy. GMFIX solves Navier-Stokes and energy partial differential equations for each phase with appropriate turbulence and interfacial coupling between phases. For momentum-driven single- to multi-phase underexpanded jets, the position of the first Mach disk is known empirically as a function of both the pressure ratio, K, and the particle mass fraction, Phi at the nozzle. Namely, the higher K, the further downstream the Mach disk and the higher Phi, the further upstream the first Mach disk. We show that GMFIX captures these two essential features. In addition, GMFIX displays all the properties found in these jets, such as expansion fans, incident and reflected shocks, and subsequent downstream mach discs, which make this code ideal for further investigations of equivalent volcanological phenomena. One of the other most challenging aspects of volcanic phenomenology is the multiphase nature of turbulence. We also validated GMFIX in comparing the velocity profiles and turbulence quantities against well constrained analog experiments. The velocity profiles agree with the analog ones as well as these of production of turbulent quantities. Overall, the Verification and the Validation experiments although inherently challenging suggest GMFIX captures the most essential dynamical properties of multiphase and supersonic flows and jets.

Determining water saturation in diatomite using wireline logs, Lost Hills field, California

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bilodeau, B.J.

1995-12-31

There is a long-held paradigm in the California oil industry that wireline log evaluation does not work in Monterey Formation lithologies. This study demonstrates that it is possible to calculate accurate oil saturation from wireline log data in the diatomite reservoir at Lost Hills field, California. The ability to calculate simple but accurate oil saturation is important because it allows field management teams to map pay, plan development and waterflood programs, and make estimates of reserves more accurate than those based on core information alone. Core data from eight wells were correlated with modern resistivity and porosity logs, incorporating moremore » than 2000 ft of reservoir section. Porosity was determined from bulk density and water saturation was determined using the Archie equation. Crossplots of corrected core oil saturation versus Archie oil saturation (1-S{sub w}) confirm the accuracy of the algorithm. Improvements in the accuracy and precision of the calculated oil saturation will require more detailed reservoir characterization to take into account lithologic variation.« less

Phase-Shifted Based Numerical Method for Modeling Frequency-Dependent Effects on Seismic Reflections

NASA Astrophysics Data System (ADS)

Chen, Xuehua; Qi, Yingkai; He, Xilei; He, Zhenhua; Chen, Hui

2016-08-01

The significant velocity dispersion and attenuation has often been observed when seismic waves propagate in fluid-saturated porous rocks. Both the magnitude and variation features of the velocity dispersion and attenuation are frequency-dependent and related closely to the physical properties of the fluid-saturated porous rocks. To explore the effects of frequency-dependent dispersion and attenuation on the seismic responses, in this work, we present a numerical method for seismic data modeling based on the diffusive and viscous wave equation (DVWE), which introduces the poroelastic theory and takes into account diffusive and viscous attenuation in diffusive-viscous-theory. We derive a phase-shift wave extrapolation algorithm in frequencywavenumber domain for implementing the DVWE-based simulation method that can handle the simultaneous lateral variations in velocity, diffusive coefficient and viscosity. Then, we design a distributary channels model in which a hydrocarbon-saturated sand reservoir is embedded in one of the channels. Next, we calculated the synthetic seismic data to analytically and comparatively illustrate the seismic frequency-dependent behaviors related to the hydrocarbon-saturated reservoir, by employing DVWE-based and conventional acoustic wave equation (AWE) based method, respectively. The results of the synthetic seismic data delineate the intrinsic energy loss, phase delay, lower instantaneous dominant frequency and narrower bandwidth due to the frequency-dependent dispersion and attenuation when seismic wave travels through the hydrocarbon-saturated reservoir. The numerical modeling method is expected to contribute to improve the understanding of the features and mechanism of the seismic frequency-dependent effects resulted from the hydrocarbon-saturated porous rocks.

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

Rigorous derivation of porous-media phase-field equations

NASA Astrophysics Data System (ADS)

Schmuck, Markus; Kalliadasis, Serafim

2017-11-01

The evolution of interfaces in Complex heterogeneous Multiphase Systems (CheMSs) plays a fundamental role in a wide range of scientific fields such as thermodynamic modelling of phase transitions, materials science, or as a computational tool for interfacial flow studies or material design. Here, we focus on phase-field equations in CheMSs such as porous media. To the best of our knowledge, we present the first rigorous derivation of error estimates for fourth order, upscaled, and nonlinear evolution equations. For CheMs with heterogeneity ɛ, we obtain the convergence rate ɛ 1 / 4 , which governs the error between the solution of the new upscaled formulation and the solution of the microscopic phase-field problem. This error behaviour has recently been validated computationally in. Due to the wide range of application of phase-field equations, we expect this upscaled formulation to allow for new modelling, analytic, and computational perspectives for interfacial transport and phase transformations in CheMSs. This work was supported by EPSRC, UK, through Grant Nos. EP/H034587/1, EP/L027186/1, EP/L025159/1, EP/L020564/1, EP/K008595/1, and EP/P011713/1 and from ERC via Advanced Grant No. 247031.

Modelling and calculation of flotation process in one-dimensional formulation

NASA Astrophysics Data System (ADS)

Amanbaev, Tulegen; Tilleuov, Gamidulla; Tulegenova, Bibigul

2016-08-01

In the framework of the assumptions of the mechanics of the multiphase media is constructed a mathematical model of the flotation process in the dispersed mixture of liquid, solid and gas phases, taking into account the degree of mineralization of the surface of the bubbles. Application of the constructed model is demonstrated on the example of one-dimensional stationary flotation and it is shown that the equations describing the process of ascent of the bubbles are singularly perturbed ("rigid"). The effect of size and concentration of bubbles and the volumetric content of dispersed particles on the flotation process are analyzed.

EDITORIAL: Measurement techniques for multiphase flows Measurement techniques for multiphase flows

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Murai, Yuichi

2009-11-01

Research on multiphase flows is very important for industrial applications, including power stations, vehicles, engines, food processing and so on. Multiphase flows originally have nonlinear features because of multiphase systems. The interaction between the phases plays a very interesting role in the flows. The nonlinear interaction causes the multiphase flows to be very complicated. Therefore techniques for measuring multiphase flows are very useful in helping to understand the nonlinear phenomena. The state-of-the-art measurement techniques were presented and discussed at the sixth International Symposium on Measurement Techniques for Multiphase Flows (ISMTMF2008) held in Okinawa, Japan, on 15-17 December 2008. This special feature of Measurement Science and Technology includes selected papers from ISMTMF2008. Okinawa has a long history as the Ryukyus Kingdom. China, Japan and many western Pacific countries have had cultural and economic exchanges through Okinawa for over 1000 years. Much technical and scientific information was exchanged at the symposium in Okinawa. The proceedings of ISMTMF2008 apart from these special featured papers were published in Journal of Physics: Conference Series vol. 147 (2009). We would like to express special thanks to all the contributors to the symposium and this special feature. This special feature will be a milestone in measurement techniques for multiphase flows.

Thermal buoyancy on magneto hydrodynamic flow over a vertical saturated porous surface with viscous dissipation

NASA Astrophysics Data System (ADS)

Nirmala, P. H.; Saila Kumari, A.; Raju, C. S. K.

2018-04-01

In the present article, we studied the magnetohydro dynamic flow induced heat transfer from vertical surface embedded in a saturated porous medium in the presence of viscous dissipation. Appropriate similarity transformations are used to transmute the non-linear governing partial differential equations to non-linear ODE. To solve these ordinary differential equations (ODE) we used the well-known integral method of Von Karman type. A comparison has been done and originates to be in suitable agreement with the previous published results. The tabulated and graphical results are given to consider the physical nature of the problem. From this results we found that the magnetic field parameter depreciate the velocity profiles and improves the heat transfer rate of the flow.

Helicity Evolution at Small x

NASA Astrophysics Data System (ADS)

Sievert, Michael; Kovchegov, Yuri; Pitonyak, Daniel

2017-01-01

We construct small- x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of ln2(1 / x) in the polarization-dependent evolution along with the powers of ln(1 / x) in the unpolarized evolution which includes saturation effects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-Nc and large-Nc &Nf limits. After solving the large-Nc equations numerically we obtain the following small- x asymptotics for the flavor-singlet g1 structure function along with quarks hPDFs and helicity TMDs (in absence of saturation effects): g1S(x ,Q2) ΔqS(x ,Q2) g1L S(x ,kT2) (1/x) > αh (1/x) 2.31√{αsNc/2 π. We also give an estimate of how much of the proton's spin may be at small x and what impact this has on the so-called ``spin crisis.'' Work supported by the U.S. DOE, Office of Science, Office of Nuclear Physics under Award Number DE-SC0004286 (YK), the RIKEN BNL Research Center, and TMD Collaboration (DP), and DOE Contract No. DE-SC0012704 (MS).

A poroelastic medium saturated by a two-phase capillary fluid

NASA Astrophysics Data System (ADS)

Shelukhin, V. V.

2014-09-01

By Landau's approach developed for description of superfluidity of 2He, we derive a mathematical model for a poroelastic medium saturated with a two-phase capillary fluid. The model describes a three-velocity continuum with conservation laws which obey the basic principles of thermodynamics and which are consistent with the Galilean transformations. In contrast to Biot' linear theory, the equations derived allow for finite deformations. As the acoustic analysis reveals, there is one more longitudinal wave in comparison with the poroelastic medium saturated with a one-phase fluid. We prove that such a result is due to surface tension.

Bistability By Self-Reflection In A Saturable Absorber

NASA Astrophysics Data System (ADS)

Roso-Franco, Luis

1987-01-01

Propagation of laser light through a saturable absorber is theoretically studied. Computed steady state solutions of the Maxwell equations describing the unidimensional propagation of a plane monochromatic wave without introducing the slowly-varying envelope approximation are presented showing how saturation effects can influence the absorption of the field. At a certain range of refractive index and extintion coefficients, computed solutions display a very susprising behaviour, and a self-reflected wave appears inside the absorber. This can be useful for a new kind of biestable device, similar to a standard bistable cavity but with the back mirror self-induced by the light.

Fictitious domain method for fully resolved reacting gas-solid flow simulation

NASA Astrophysics Data System (ADS)

Zhang, Longhui; Liu, Kai; You, Changfu

2015-10-01

Fully resolved simulation (FRS) for gas-solid multiphase flow considers solid objects as finite sized regions in flow fields and their behaviours are predicted by solving equations in both fluid and solid regions directly. Fixed mesh numerical methods, such as fictitious domain method, are preferred in solving FRS problems and have been widely researched. However, for reacting gas-solid flows no suitable fictitious domain numerical method has been developed. This work presents a new fictitious domain finite element method for FRS of reacting particulate flows. Low Mach number reacting flow governing equations are solved sequentially on a regular background mesh. Particles are immersed in the mesh and driven by their surface forces and torques integrated on immersed interfaces. Additional treatments on energy and surface reactions are developed. Several numerical test cases validated the method and a burning carbon particles array falling simulation proved the capability for solving moving reacting particle cluster problems.

Modeling of the processes of natural and waste water purification in the reactor-clarifier

NASA Astrophysics Data System (ADS)

Primak, O. D.; Skolubovich, Yu. L.; Fedorova, N. N.; Voitov, E. L.

2018-03-01

The results of the filtration process simulation in a reactor-clarifier installation using a suspended loading layer are presented. Calculations were carried out in ANSYS Fluent on the basis of the Navier-Stokes equations supplemented by the equations of the Eulerian model of multiphase taking into account granularity of the particle phase. The unsteady picture of the formation of a fluidized («boiling») layer of particles is obtained. The results of parametric calculations allowing to estimate the effect of the flow velocity, the loading layer thickness, the thickness of sand and other parameters on the fluidized bed structure are presented. The liquid flow rate at which the loading grains are not washed out is determined. The diameter of particles and the height of the loading layer, at which the filter material is suspended and thus normal operation of the plant is ensured, are defined.

Pairwise Force Smoothed Particle Hydrodynamics model for multiphase flow: Surface tension and contact line dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tartakovsky, Alexandre M.; Panchenko, Alexander

2016-01-01

We present a novel formulation of the Pairwise Force Smoothed Particle Hydrodynamics Model (PF-SPH) and use it to simulate two- and three-phase flows in bounded domains. In the PF-SPH model, the Navier-Stokes equations are discretized with the Smoothed Particle Hydrodynamics (SPH) method and the Young-Laplace boundary condition at the fluid-fluid interface and the Young boundary condition at the fluid-fluid-solid interface are replaced with pairwise forces added into the Navier-Stokes equations. We derive a relationship between the parameters in the pairwise forces and the surface tension and static contact angle. Next, we demonstrate the accuracy of the model under static andmore » dynamic conditions. Finally, to demonstrate the capabilities and robustness of the model we use it to simulate flow of three fluids in a porous material.« less

The thermodynamic properties of oxygen and nitrogen. Part 1: Thermodynamic properties of nitrogen from 115 R to 3500 R with pressures to 150000 psia

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

An equation of state is presented for liquid and gaseous nitrogen for temperatures from 115 R to 3500 R and pressures to 150,000 psia. All of the pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been identified and applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation in representing the data. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data and, simultaneously, to constant volume data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and saturated vapor. The methods of weighting the various data for simultaneous fitting are presented and discussed. The equation of state is estimated to be accurate to within 0.5 percent in the liquid region, to within 0.1 percent for supercritical isotherms up to 15,000 psia, and to within 0.3 percent from 15,000 to 150,000 psia.

Nanoparticle Additives for Multiphase Systems: Synthesis, Formulation and Characterization

DTIC Science & Technology

2012-01-01

ADDITIVES FOR MULTIPHASE SYSTEMS: SYNTHESIS , FORMULATION AND CHARACTERIZATION Vinod Kanniah University of Kentucky, vinodkanniah@gmail.com This Doctoral...UKnowledge@lsv.uky.edu. Recommended Citation Kanniah, Vinod, "NANOPARTICLE ADDITIVES FOR MULTIPHASE SYSTEMS: SYNTHESIS , FORMULATION AND CHARACTERIZATION...00-00-2012 to 00-00-2012 4. TITLE AND SUBTITLE Nanoparticle Additives for Multiphase Systems: Synthesis , Formulation and Characterization 5a

Melt Segregation and Tidal Heating at Io

NASA Astrophysics Data System (ADS)

Rajendar, A.; Dufek, J.; Roberts, J. H.; Paty, C. S.

2011-12-01

Recent evidence of melt beneath Io's surface (Khurana et al., 2010) and repeated observation of volcanic activity and features consistent with volcanic activity at the surface (e.g. Veeder et al, 1994; Rathbun et al., 2004; Lopes-Gautier et al., 1999; Smith et al., 1979) has raised further questions about the structure of the Galilean moon and the processes that shape it. In this study we examine the thermal state, melt fraction, and multiphase dynamics of melt segregation within Io's interior. Using a coupled multiphase dynamics and tidal heating model we explore the location, spatial extent, and temporal residence times of melt in Io's subsurface, as well as response to orbital parameters. In a thermally evolving body subject to tidal forcing, in which melt production and migration takes place, feedback can occur with respect to the physical and thermal properties. We explore this feedback to produce a thermal model of Io, taking into account the rate of tidal heating and fluid motion within the interior. First, a layered model of the internal structure is assumed. The equations of motion for forced oscillations in a layered spherical body are then solved using the propagator matrix method (Sabadini and Vermeesen, 2004) to obtain the displacements and strains due to tidal motion (Roberts and Nimmo, 2008). From this, the radial distribution of tidal heat generation within Io is calculated. This radial heating profile is then used as input for a multi-phase fluid model in order to obtain an estimate of the radial temperature distribution and thus the material properties and melt fractions. In the multiphase model individual phases (melt and solid residue) separately conserve mass, momentum and enthalpy (Dufek and Bachmann, 2010) allowing us to explore melt segregation phenomena. Enthalpy closure is provided by the MELTS (Ghiorso and Sack, 1995) thermodynamics algorithm, which is called at each point in space. This accounts for the partitioning between latent and sensible heat, and updates the physical properties of the melt and solid phase such as density and heat capacity. With this approach we explore the sensitivity of melt generation and the time between melt production and eruption (the residence time) to mantle chemistry and the layered structure of the moon.

Estimation of hepatic extracellular volume fraction using multiphasic liver computed tomography for hepatic fibrosis grading.

PubMed

Yoon, Jeong Hee; Lee, Jeong Min; Klotz, Ernst; Jeon, Ju Hyun; Lee, Kyung-Bun; Han, Joon Koo; Choi, Byung Ihn

2015-04-01

The purpose of this study was to determine whether hepatic extracellular volume fractions (fECVs) measured using multiphasic liver computed tomography (CT) can be used to quantify the severity of hepatic fibrosis (HF). This retrospective study was approved by our institutional review board, and the requirement for informed consent was waived. A total of 141 patients (male-female ratio, 109:32; mean [SD] age, 59.4 [11.4] years) histologically diagnosed with HF (F0-F1 = 33 and F2-F4 = 108) underwent multiphasic liver CT. Absolute enhancements (in Hounsfield unit) of the liver parenchyma (Eliver) and aorta (Eaorta) 3 minutes after contrast administration were measured on subtraction images of precontrast and equilibrium phase scans using nonrigid registration software. The fECV was calculated using the following equation: fECV (%) = Eliver/Eaorta × (100 - Hematocrit [%]). Correlation between fECV and HF stage was evaluated using the Spearman correlation coefficient. The fECVs were compared between F0-F1 and ≥F2 as well as between child A and child B or C. Diagnostic performance of fECV in predicting significant HF (≥F2) was assessed using receiver operating curve analysis. The fECVs showed a significant correlation with pathologic HF staging (r = 0.493, P < 0.001). The F2-F4 showed significantly higher fECVs than did F0 to F1 (33.6% [4.7%] vs 27.7% [4.4%]; P < 0.001). The fECVs were significantly higher in the patients with child B or C than those with child A (35.2% [7.0%] vs 31.3% [4.2%]; P < 0.001). The fECV values higher than 28.76% provided 87.5% sensitivity and 71.0% specificity in detecting significant HF (area under the curve, 0.832; P < 0.0001). Because fECV was shown to increase along with HF progression, the estimation of fECV using routine multiphasic liver CT may have the potential to detect significant HF.

A multiphase model for tissue construct growth in a perfusion bioreactor.

PubMed

O'Dea, R D; Waters, S L; Byrne, H M

2010-06-01

The growth of a cell population within a rigid porous scaffold in a perfusion bioreactor is studied, using a three-phase continuum model of the type presented by Lemon et al. (2006, Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol., 52, 571-594) to represent the cell population (and attendant extracellular matrix), culture medium and porous scaffold. The bioreactor system is modelled as a 2D channel containing the cell-seeded rigid porous scaffold (tissue construct) which is perfused with culture medium. The study concentrates on (i) the cell-cell and cell-scaffold interactions and (ii) the impact of mechanotransduction mechanisms on construct composition. A numerical and analytical analysis of the model equations is presented and, depending upon the relative importance of cell aggregation and repulsion, markedly different cell movement is revealed. Additionally, mechanotransduction effects due to cell density, pressure and shear stress-mediated tissue growth are shown to generate qualitative differences in the composition of the resulting construct. The results of our simulations indicate that this model formulation (in conjunction with appropriate experimental data) has the potential to provide a means of identifying the dominant regulatory stimuli in a cell population.

Computational methods for reactive transport modeling: A Gibbs energy minimization approach for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg

2016-02-01

We present a numerical method for multiphase chemical equilibrium calculations based on a Gibbs energy minimization approach. The method can accurately and efficiently determine the stable phase assemblage at equilibrium independently of the type of phases and species that constitute the chemical system. We have successfully applied our chemical equilibrium algorithm in reactive transport simulations to demonstrate its effective use in computationally intensive applications. We used FEniCS to solve the governing partial differential equations of mass transport in porous media using finite element methods in unstructured meshes. Our equilibrium calculations were benchmarked with GEMS3K, the numerical kernel of the geochemical package GEMS. This allowed us to compare our results with a well-established Gibbs energy minimization algorithm, as well as their performance on every mesh node, at every time step of the transport simulation. The benchmark shows that our novel chemical equilibrium algorithm is accurate, robust, and efficient for reactive transport applications, and it is an improvement over the Gibbs energy minimization algorithm used in GEMS3K. The proposed chemical equilibrium method has been implemented in Reaktoro, a unified framework for modeling chemically reactive systems, which is now used as an alternative numerical kernel of GEMS.

Droplet evaporation and combustion in a liquid-gas multiphase system

NASA Astrophysics Data System (ADS)

Muradoglu, Metin; Irfan, Muhammad

2017-11-01

Droplet evaporation and combustion in a liquid-gas multiphase system are studied computationally using a front-tracking method. One field formulation is used to solve the flow, energy and species equations with suitable jump conditions. Both phases are assumed to be incompressible; however, the divergence-free velocity field condition is modified to account for the phase change at the interface. Both temperature and species gradient driven phase change processes are simulated. Extensive validation studies are performed using the benchmark cases: The Stefan and the sucking interface problems, d2 law and wet bulb temperature comparison with the psychrometric chart values. The phase change solver is then extended to incorporate the burning process following the evaporation as a first step towards the development of a computational framework for spray combustion. We used detailed chemistry, variable transport properties and ideal gas behaviour for a n-heptane droplet combustion; the chemical kinetics being handled by the CHEMKIN. An operator-splitting approach is used to advance temperature and species mass fraction in time. The numerical results of the droplet burning rate, flame temperature and flame standoff ratio show good agreement with the experimental and previous numeric.

Recent advances in high-order WENO finite volume methods for compressible multiphase flows

NASA Astrophysics Data System (ADS)

Dumbser, Michael

2013-10-01

We present two new families of better than second order accurate Godunov-type finite volume methods for the solution of nonlinear hyperbolic partial differential equations with nonconservative products. One family is based on a high order Arbitrary-Lagrangian-Eulerian (ALE) formulation on moving meshes, which allows to resolve the material contact wave in a very sharp way when the mesh is moved at the speed of the material interface. The other family of methods is based on a high order Adaptive Mesh Refinement (AMR) strategy, where the mesh can be strongly refined in the vicinity of the material interface. Both classes of schemes have several building blocks in common, in particular: a high order WENO reconstruction operator to obtain high order of accuracy in space; the use of an element-local space-time Galerkin predictor step which evolves the reconstruction polynomials in time and that allows to reach high order of accuracy in time in one single step; the use of a path-conservative approach to treat the nonconservative terms of the PDE. We show applications of both methods to the Baer-Nunziato model for compressible multiphase flows.

Dynamic coupling of subsurface and seepage flows solved within a regularized partition formulation

NASA Astrophysics Data System (ADS)

Marçais, J.; de Dreuzy, J.-R.; Erhel, J.

2017-11-01

Hillslope response to precipitations is characterized by sharp transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Locally, the transition between these two regimes is triggered by soil saturation. Here we develop an integrative approach to simultaneously solve the subsurface flow, locate the potential fully saturated areas and deduce the generated saturation excess overland flow. This approach combines the different dynamics and transitions in a single partition formulation using discontinuous functions. We propose to regularize the system of partial differential equations and to use classic spatial and temporal discretization schemes. We illustrate our methodology on the 1D hillslope storage Boussinesq equations (Troch et al., 2003). We first validate the numerical scheme on previous numerical experiments without saturation excess overland flow. Then we apply our model to a test case with dynamic transitions from purely subsurface flow dynamics to simultaneous surface and subsurface flows. Our results show that discretization respects mass balance both locally and globally, converges when the mesh or time step are refined. Moreover the regularization parameter can be taken small enough to ensure accuracy without suffering of numerical artefacts. Applied to some hundreds of realistic hillslope cases taken from Western side of France (Brittany), the developed method appears to be robust and efficient.

Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid

NASA Astrophysics Data System (ADS)

Song, Yongjia; Hu, Hengshan; Rudnicki, John W.

2017-04-01

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

Numerical modelling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Wright, J. C.; Forest, C. B.; O'Connell, R.; Truitt, J. L.

2000-10-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a newly developed 3-D pseudo-spectral simulation of the MHD equations; results of the simulations will be compared to the experimental results obtained from the experiment. The code, Dynamo, is in Fortran90 and allows for full evolution of the magnetic and velocity fields. The induction equation governing B and the Navier-Stokes equation governing V are solved. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James (M.L. Dudley and R.W. James, Time-dependant kinematic dynamos with stationary flows, Proc. R. Soc. Lond. A 425, p. 407 (1989)). Initial results on magnetic field saturation, generated by the simultaneous evolution of magnetic and velocity fields be presented using a variety of mechanical forcing terms.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

NASA Astrophysics Data System (ADS)

Gjennestad, Magnus Aa.; Gruber, Andrea; Lervåg, Karl Yngve; Johansen, Øyvind; Ervik, Åsmund; Hammer, Morten; Munkejord, Svend Tollak

2017-11-01

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose thermodynamic properties are calculated using the Span-Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge-Kutta method. We demonstrate close to fifth-order convergence for advection-diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.

A numerical solution of the problem of crown forest fire initiation and spread

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. The study takes in to account the mutual interaction of the forest fires and three-dimensional atmosphere flows. The research is done by means of mathematical modeling of physical processes. It is based on numerical solution of Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. It is assumed that the forest during a forest fire can be modeled as a two-temperature multiphase non-deformable porous reactive medium. A discrete analog for the system of equations was obtained by means of the control volume method. The developed model of forest fire initiation and spreading would make it possible to obtain a detailed picture of the variation in the velocity, temperature and chemical species concentration fields with time. Mathematical model and the result of the calculation give an opportunity to evaluate critical conditions of the forest fire initiation and spread which allows applying the given model for of means for preventing fires.

On a nonlinear model for tumour growth with drug application

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2015-05-01

We investigate the dynamics of a nonlinear system modelling tumour growth with drug application. The tumour is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumour is given by Brinkman's equation. The domain occupied by the tumour in this setting is a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behaviour, diffusion and viscosity in the weak formulation. Both the solutions and the domain are rather general, no symmetry assumption is required and the result holds for large initial data. This article is part of a research programme whose aim is the investigation of the effect of drug application in tumour growth.

Gas production and migration in landfills and geological materials.

PubMed

Nastev, M; Therrien, R; Lefebvre, R; Gélinas, P

2001-11-01

Landfill gas, originating from the anaerobic biodegradation of the organic content of waste, consists mainly of methane and carbon dioxide, with traces of volatile organic compounds. Pressure, concentration and temperature gradients that develop within the landfill result in gas emissions to the atmosphere and in lateral migration through the surrounding soils. Environmental and safety issues associated with the landfill gas require control of off-site gas migration. The numerical model TOUGH2-LGM (Transport of Unsaturated Groundwater and Heat-Landfill Gas Migration) has been developed to simulate landfill gas production and migration processes within and beyond landfill boundaries. The model is derived from the general non-isothermal multiphase flow simulator TOUGH2, to which a new equation of state module is added. It simulates the migration of five components in partially saturated media: four fluid components (water, atmospheric air, methane and carbon dioxide) and one energy component (heat). The four fluid components are present in both the gas and liquid phases. The model incorporates gas-liquid partitioning of all fluid components by means of dissolution and volatilization. In addition to advection in the gas and liquid phase, multi-component diffusion is simulated in the gas phase. The landfill gas production rate is proportional to the organic substrate and is modeled as an exponentially decreasing function of time. The model is applied to the Montreal's CESM landfill site, which is located in a former limestone rock quarry. Existing data were used to characterize hydraulic properties of the waste and the limestone. Gas recovery data at the site were used to define the gas production model. Simulations in one and two dimensions are presented to investigate gas production and migration in the landfill, and in the surrounding limestone. The effects of a gas recovery well and landfill cover on gas migration are also discussed.

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.

Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics

NASA Astrophysics Data System (ADS)

Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.

2016-03-01

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian-Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocity fluctuations into spatially correlated and uncorrelated components, used to define the components of the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, "Numerical study of collisional particle dynamics in cluster-induced turbulence," J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocity fluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics.

Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Capecelatro, Jesse, E-mail: jcaps@illinois.edu; Desjardins, Olivier; Fox, Rodney O.

Simulations of strongly coupled (i.e., high-mass-loading) fluid-particle flows in vertical channels are performed with the purpose of understanding the fundamental physics of wall-bounded multiphase turbulence. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions are presented, and the unclosed terms that are retained in the context of fully developed channel flow are evaluated in an Eulerian–Lagrangian (EL) framework for the first time. A key distinction between the RA formulation presented in the current work and previous derivations of multiphase turbulence models is the partitioning of the particle velocity fluctuations into spatially correlated and uncorrelated components, used to define the components ofmore » the particle-phase turbulent kinetic energy (TKE) and granular temperature, respectively. The adaptive spatial filtering technique developed in our previous work for homogeneous flows [J. Capecelatro, O. Desjardins, and R. O. Fox, “Numerical study of collisional particle dynamics in cluster-induced turbulence,” J. Fluid Mech. 747, R2 (2014)] is shown to accurately partition the particle velocity fluctuations at all distances from the wall. Strong segregation in the components of granular energy is observed, with the largest values of particle-phase TKE associated with clusters falling near the channel wall, while maximum granular temperature is observed at the center of the channel. The anisotropy of the Reynolds stresses both near the wall and far away is found to be a crucial component for understanding the distribution of the particle-phase volume fraction. In Part II of this paper, results from the EL simulations are used to validate a multiphase Reynolds-stress turbulence model that correctly predicts the wall-normal distribution of the two-phase turbulence statistics.« less

Non-Markovian Effects in Turbulent Diffusion in Magnetized Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zagorodny, Anatoly; Weiland, Jan

2009-10-08

The derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is presented. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.

Petrophysics of low-permeability medina sandstone, northwestern Pennsylvania, Appalachian Basin

USGS Publications Warehouse

Castle, J.W.; Byrnes, A.P.

1998-01-01

Petrophysical core testing combined with geophysical log analysis of low-permeability, Lower Silurian sandstones of the Appalachian basin provides guidelines and equations for predicting gas producibility. Permeability values are predictable from the borehole logs by applying empirically derived equations based on correlation between in-situ porosity and in-situ effective gas permeability. An Archie-form equation provides reasonable accuracy of log-derived water saturations because of saturated brine salinities and low clay content in the sands. Although measured porosity and permeability average less than 6% and 0.1 mD, infrequent values as high as 18% and 1,048 mD occur. Values of effective gas permeability at irreducible water saturation (Swi) range from 60% to 99% of routine values for the highest permeability rocks to several orders of magnitude less for the lowest permeability rocks. Sandstones having porosity greater than 6% and effective gas permeability greater than 0.01 mD exhibit Swi less than 20%. With decreasing porosity, Swi sharply increases to values near 40% at 3 porosity%. Analysis of cumulative storage and flow capacity indicates zones with porosity greater than 6% generally contain over 90% of flow capacity and hold a major portion of storage capacity. For rocks with Swi < 20%, gas relative permeabilities exceed 45%. Gas relative permeability and hydrocarbon volume decrease rapidly with increasing Swi as porosity drops below 6%. At Swi above 40%, gas relative permeabilities are less than approximately 10%.

Nonlinear asymmetric tearing mode evolution in cylindrical geometry

DOE PAGES

Teng, Qian; Ferraro, N.; Gates, David A.; ...

2016-10-27

The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ' ql(w), Δ'A(w). In this work, we present a simple method to calculate the quasilinear stability index Δ'ql rigorously, for poloidal mode number m ≥ 2. Δ' ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ' 0, w, wlnw, and w2.more » Δ' A is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δ' ql and Δ' A is consistent with the more accurate expression calculated perturbatively. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. Lastly, it is also confirmed by the simulation that the Δ' A has to be considered in calculating island saturation.« less

[Stimulation parameters for automatic examination of color vision].

PubMed

Sommerhalder, J; Pelizzone, M; Roth, A

1997-05-01

We have developed a polyvalent computer controlled instrument, which uses the "two equation method" (Rayleigh and Moreland equations) to measure human colour vision. This "colorimeter" (or anomaloscope) was used to determine the influence of some important stimulation parameters. The influence of stimulus exposure time, observation field size, absolute stimulus luminance, saturation and luminance mismatches between mixture and reference stimuli were measured on our computer controlled colorimeter. All subjects were normal observers. 1) An exposure time of 2s was found to be optimal for clinical work. 2) The Moreland equation on a 7 degrees observation field yields results in which population variability is comparable to a Rayleigh equation on a 2 degrees field. 3) A retinal illuminance between 40 and 1000 trolands can be used for automated Moreland matches. 4) The saturation of the reference field for the Moreland match can be preset to a fixed value. 5) It is important to vary automatically the radiance of the reference field to provide an approximate luminance match as the ratio of primaries in the mixture field is changed. These measurements allows us to determine optimal conditions for automated colour vision examinations and to make recommendations for an international standard.

Liquefaction of Saturated Soil and the Diffusion Equation

NASA Astrophysics Data System (ADS)

Sawicki, Andrzej; Sławińska, Justyna

2015-06-01

The paper deals with the diffusion equation for pore water pressures with the source term, which is widely promoted in the marine engineering literature. It is shown that such an equation cannot be derived in a consistent way from the mass balance and the Darcy law. The shortcomings of the artificial source term are pointed out, including inconsistencies with experimental data. It is concluded that liquefaction and the preceding process of pore pressure generation and the weakening of the soil skeleton should be described by constitutive equations within the well-known framework of applied mechanics. Relevant references are provided

Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure.

PubMed

Ravazzoli, C L; Santos, J E; Carcione, J M

2003-04-01

We investigate the acoustic and mechanical properties of a reservoir sandstone saturated by two immiscible hydrocarbon fluids, under different saturations and pressure conditions. The modeling of static and dynamic deformation processes in porous rocks saturated by immiscible fluids depends on many parameters such as, for instance, porosity, permeability, pore fluid, fluid saturation, fluid pressures, capillary pressure, and effective stress. We use a formulation based on an extension of Biot's theory, which allows us to compute the coefficients of the stress-strain relations and the equations of motion in terms of the properties of the single phases at the in situ conditions. The dry-rock moduli are obtained from laboratory measurements for variable confining pressures. We obtain the bulk compressibilities, the effective pressure, and the ultrasonic phase velocities and quality factors for different saturations and pore-fluid pressures ranging from normal to abnormally high values. The objective is to relate the seismic and ultrasonic velocity and attenuation to the microstructural properties and pressure conditions of the reservoir. The problem has an application in the field of seismic exploration for predicting pore-fluid pressures and saturation regimes.

Polar Kerr Effect from Time-Reversal Symmetry Breaking in the Heavy-Fermion Superconductor PrOs4Sb12

NASA Astrophysics Data System (ADS)

Levenson-Falk, E. M.; Schemm, E. R.; Aoki, Y.; Maple, M. B.; Kapitulnik, A.

2018-05-01

We present polar Kerr effect measurements of the filled skutterudite superconductor PrOs4 Sb12 . Simultaneous ac susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle θK develops below the superconducting transition, saturating at ˜300 nrad at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured θK(T ) to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the B phase at TC 2. We discuss the possible explanations for this result and its impact on the understanding of multiphase and inhomogeneous superconductivity in PrOs4 Sb12 .

Nucleation and growth of tin whiskers

NASA Astrophysics Data System (ADS)

Cheng, Jing; Vianco, Paul T.; Zhang, Bei; Li, James C. M.

2011-06-01

Pure tin film of one micron thick was evaporated onto a silicon substrate with chromium and nickel underlayers. The tinned silicon disk was bent by applying a dead load at the center and supported below around the edge to apply biaxial compressive stresses to the tin layer. After 180 C vacuum annealing for 1,2,4,6, and 8 weeks, tin whiskers/hillocks grew. A quantitative method revealed that the overall growth rate decreased with time with a tendency for saturation. A review of the literature showed in general, tin whisker growth has a nucleation period, a growth period and a period of saturation, very similar to recrystallization or phase transformation. In fact we found our data fit Avrami equation very well. This equation shows that the nucleation period was the first week.

Oscillatory multiphase flow strategy for chemistry and biology.

PubMed

Abolhasani, Milad; Jensen, Klavs F

2016-07-19

Continuous multiphase flow strategies are commonly employed for high-throughput parameter screening of physical, chemical, and biological processes as well as continuous preparation of a wide range of fine chemicals and micro/nano particles with processing times up to 10 min. The inter-dependency of mixing and residence times, and their direct correlation with reactor length have limited the adaptation of multiphase flow strategies for studies of processes with relatively long processing times (0.5-24 h). In this frontier article, we describe an oscillatory multiphase flow strategy to decouple mixing and residence times and enable investigation of longer timescale experiments than typically feasible with conventional continuous multiphase flow approaches. We review current oscillatory multiphase flow technologies, provide an overview of the advancements of this relatively new strategy in chemistry and biology, and close with a perspective on future opportunities.

Demonstrating the saturation of stimulated Brillouin scattering by ion acoustic decay using fully kinetic simulations

DOE PAGES

Chapman, T.; Winjum, B. J.; Brunner, S.; ...

2015-09-01

The saturation of stimulated Brillouin scattering (SBS) by the decay to turbulence of the ion acoustic wave (IAW) that participates in the three-wave SBS interaction is demonstrated using a quasi-noiseless one-dimensional numerical solution to the Vlasov-Maxwell system of equations. This simulation technique permits careful examination of the decay process and its role in the complex evolution of SBS. Here, the IAW decay process is shown to be an effective SBS saturation mechanism. In our example, the instantaneous plasma reflectivity saturates at ~30% and drops to ~0% as a direct consequence of IAW decay. A contrasting example where the reflectivity ismore » controlled by dephasing due to the nonlinear frequency of the IAW is also discussed.« less

The unsaturated flow in porous media with dynamic capillary pressure

NASA Astrophysics Data System (ADS)

Milišić, Josipa-Pina

2018-05-01

In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on the saturation. Following the approach given in [13] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed-derivative term by combining the information from the capillary pressure with the obtained a priori estimates on the saturation.

Modulational-instability-induced supercontinuum generation with saturable nonlinear response

NASA Astrophysics Data System (ADS)

Raja, R. Vasantha Jayakantha; Porsezian, K.; Nithyanandan, K.

2010-07-01

We theoretically investigate the supercontinuum generation (SCG) on the basis of modulational instability (MI) in liquid-core photonic crystal fibers (LCPCF) with CS2-filled central core. The effect of saturable nonlinearity of LCPCF on SCG in the femtosecond regime is studied using an appropriately modified nonlinear Schrödinger equation. We also compare the MI induced spectral broadening with SCG obtained by soliton fission. To analyze the quality of the pulse broadening, we study the coherence of the SC pulse numerically. It is evident from the numerical simulation that the response of the saturable nonlinearity suppresses the broadening of the pulse. We also observe that the MI induced SCG in the presence of saturable nonlinearity degrades the coherence of the SCG pulse when compared to unsaturated medium.

Modulational-instability-induced supercontinuum generation with saturable nonlinear response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raja, R. Vasantha Jayakantha; Porsezian, K.; Nithyanandan, K.

2010-07-15

We theoretically investigate the supercontinuum generation (SCG) on the basis of modulational instability (MI) in liquid-core photonic crystal fibers (LCPCF) with CS{sub 2}-filled central core. The effect of saturable nonlinearity of LCPCF on SCG in the femtosecond regime is studied using an appropriately modified nonlinear Schroedinger equation. We also compare the MI induced spectral broadening with SCG obtained by soliton fission. To analyze the quality of the pulse broadening, we study the coherence of the SC pulse numerically. It is evident from the numerical simulation that the response of the saturable nonlinearity suppresses the broadening of the pulse. We alsomore » observe that the MI induced SCG in the presence of saturable nonlinearity degrades the coherence of the SCG pulse when compared to unsaturated medium.« less

The effect of saturated steam vapor temperature on heat consumption in the process of color modification of acacia wood

NASA Astrophysics Data System (ADS)

Dzurenda, Ladislav

2017-09-01

This paper presents the heat consumption on the process of colour modification of acacia timber with measures 30 x 55 x 500 mm in pressure autoclaves AZ 240 using saturated water steam with temperatures from t = 110 to 140 °C following the regimes of colour homogenisation of I., II. and III. degree. The dependance of the heat consumption normative QTFS on the temparature of saturated water steam in the process of colour homogenisation of acacia timber following these regimes describes the equation: QTFS = 1.1122.t -13.903 kWh.m-3.

Period locking due to delayed feedback in a laser with saturable absorber.

PubMed

Carr, T W

2003-08-01

We consider laser with saturable absorber operating in the pulsating regime that is subject to delayed feedback. Alone, both the saturable absorber and delayed feedback cause the clockwise output to become unstable to periodic output via Hopf bifurcations. The delay feedback causes the laser pulse period to lock to an integer fraction of the feedback time. We derive a map from the original model to describe the periodic pulsations of the laser. Equations for the period of the laser predict the occurrence of the different locking states as well as the value of the pump when there is a switch between the locked states.

A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S."bala"

2016-11-01

The explosive dispersal of particles is an example of a complex multiphase and multi-species fluid flow problem. This problem has many engineering applications including particle-laden explosives. In these flows, the detonation products of the explosive cannot be treated as a perfect gas so a real gas equation of state is used to close the governing equations (unlike air, which uses the ideal gas equation for closure). As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both of the state equations must be satisfied. One of the more accurate, yet computationally expensive, methods to deal with this is a scheme that iterates between the two equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work strives to create a multi-fidelity surrogate model of this process. We then study the performance of the model with respect to the iterative method by performing both gas-only and particle laden flow simulations using an Eulerian-Lagrangian approach with a finite volume code. Specifically, the model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel modeling approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Temperature-dependent poroelastic and viscoelastic effects on microscale-modelling of seismic reflections in heavy oil reservoirs

NASA Astrophysics Data System (ADS)

Ciz, Radim; Saenger, Erik H.; Gurevich, Boris; Shapiro, Serge A.

2009-03-01

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rocks.

Capillary pressure-saturation relations in quartz and carbonate sands: Limitations for correlating capillary and wettability influences on air, oil, and supercritical CO2 trapping

NASA Astrophysics Data System (ADS)

Wang, Shibo; Tokunaga, Tetsu K.; Wan, Jiamin; Dong, Wenming; Kim, Yongman

2016-08-01

Capillary pressure (Pc)-saturation (Sw) relations are essential for predicting equilibrium and flow of immiscible fluid pairs in soils and deeper geologic formations. In systems that are difficult to measure, behavior is often estimated based on capillary scaling of easily measured Pc-Sw relations (e.g., air-water, and oil-water), yet the reliability of such approximations needs to be examined. In this study, 17 sets of brine drainage and imbibition curves were measured with air-brine, decane-brine, and supercritical (sc) CO2-brine in homogeneous quartz and carbonate sands, using porous plate systems under ambient (0.1 MPa, 23°C) and reservoir (12.0 MPa, 45°C) conditions. Comparisons between these measurements showed significant differences in residual nonwetting phase saturation, Snw,r. Through applying capillary scaling, changes in interfacial properties were indicated, particularly wettability. With respect to the residual trapping of the nonwetting phases, Snwr, CO2 > Snwr, decane > Snwr, air. Decane-brine and scCO2-brine Pc-Sw curves deviated significantly from predictions assuming hydrophilic interactions. Moreover, neither the scaled capillary behavior nor Snw,r for scCO2-brine were well represented by decane-brine, apparently because of differences in wettability and viscosities, indicating limitations for using decane (and other organic liquids) as a surrogate fluid in studies intended to apply to geological carbon sequestration. Thus, challenges remain in applying scaling for predicting capillary trapping and multiphase displacement processes across such diverse fields as vadose zone hydrology, enhanced oil recovery, and geologic carbon sequestration.

Capillary pressure - saturation relations in quartz and carbonate sands: Limitations for correlating capillary and wettability influences on air, oil, and supercritical CO2 trapping

NASA Astrophysics Data System (ADS)

Tokunaga, T. K.; Wang, S.; Wan, J.; Dong, W.; Kim, Y.

2016-12-01

Capillary pressure (Pc) - saturation (Sw) relations are essential for predicting equilibrium and flow of immiscible fluid pairs in soils and deeper geologic formations. In systems that are difficult to measure, behavior is often estimated based on capillary scaling of easily measured Pc-Sw relations (e.g., air-water, and oil-water), yet the reliability of such approximations needs to be examined. In this study, seventeen sets of brine drainage and imbibition curves were measured with air-brine, decane-brine, and supercritical (sc) CO2-brine in homogeneous quartz and carbonate sands, using porous plate systems under ambient (0.1 MPa, 23 °C) and reservoir (12.0 MPa, 45 °C) conditions. Comparisons between these measurements showed significant differences in residual nonwetting phase saturation, Snw,r. Through applying capillary scaling, changes in interfacial properties were indicated, particularly wettability. With respect to the residual trapping of the nonwetting phases, Snwr, CO2 > Snwr, decane > Snwr, air. Decane-brine and scCO2-brine Pc-Sw curves deviated significantly from predictions assuming hydrophilic interactions. Moreover, neither the scaled capillary behavior nor Snw,r for scCO2-brine were well represented by decane-brine, apparently because of differences in wettability and viscosities, indicating limitations for using decane (and other organic liquids) as a surrogate fluid in studies intended to apply to geological carbon sequestration. Thus, challenges remain in applying scaling for predicting capillary trapping and multiphase displacement processes across such diverse fields as vadose zone hydrology, enhanced oil recovery, and geologic carbon sequestration.

A New Critical State Model for Geomechanical Behavior of Methane Hydrate-Bearing Sands

NASA Astrophysics Data System (ADS)

Lin, J. S.; Xing, P.; Rutqvist, J.; Seol, Y.; Choi, J. H.

2014-12-01

Methane hydrate bearing sands behave like sands once the hydrate has dissociated, but could exhibit a substantial increase in the shear strength, stiffness and dilatancy as the degree of hydrate saturation increases. A new critical state model was developed that incorporates the spatially mobilized plane (SMP) concept, which has been proven effective in modeling mechanical behavior of sands. While this new model was built on the basic constructs of the critical state model, important enhancements were introduced. The model adopted the t-stress concept, which defined the normal and shear stress on the SMP, in describing the plastic behavior of the soil. In this connection the versatile Matsuoka-Nakai yield criterion was also employed, which defined the general three dimensional yield behavior. The resulting constitutive law was associated in the t-stress space, but became non-associated in the conventional p-q stress space as it should be for sands. The model also introduced a generalized degree of hydrate saturation concept that was modified from the pioneering work of the Cambridge group. The model gives stress change when the sands are subjected to straining, and/or to hydrate saturation changes. The performance of the model has been found satisfactory using data from laboratory triaxial tests on reconstituted samples and core samples taken from Nankai Trough, Japan. The model has been implemented into FLAC3D. A coupling example with the multiphase flow code, TOUGH+, is presented which simulates the mechanical behavior of a sample when the surrounding temperature has been raised, and the hydrate undergoes state change and no longer resides in the stability zone.

Erratum to: Blood HbO2 and HbCO2 dissociation curves at varied O2, CO2, pH, 2,3-DPG and temperature levels.

PubMed

Dash, Ranjan K; Bassingthwaighte, James B

2010-04-01

New mathematical model equations for O(2) and CO(2) saturations of hemoglobin (S(HbO)(2) and S(HbCO)(2) are developed here from the equilibrium binding of O(2) and CO(2) with hemoglobin inside RBCs. They are in the form of an invertible Hill-type equation with the apparent Hill coefficients KHbO(2) and KHbCO(2) in the expressions for SHbO(2) and SHbCO(2) dependent on the levels of O(2) and CO(2) partial pressures (P(O)(2) and P(CO)(2)), pH, 2,3-DPG concentration, and temperature in blood. The invertibility of these new equations allows PO(2) and PCO(2) to be computed efficiently from S(HbO)(2) and S(HbCO)(2) and vice versa. The oxyhemoglobin (HbO(2)) and carbamino-hemoglobin (HbCO(2)) dissociation curves computed from these equations are in good agreement with the published experimental and theoretical curves in the literature. The model solutions describe that, at standard physiological conditions, the hemoglobin is about 97.2% saturated by O(2) and the amino group of hemoglobin is about 13.1% saturated by CO(2). The O(2) and CO(2) content in whole blood are also calculated here from the gas solubilities, hematocrits, and the new formulas for S(HbO)(2) and S(HbCO)(2). Because of the mathematical simplicity and invertibility, these new formulas can be conveniently used in the modeling of simultaneous transport and exchange of O(2) and CO(2) in the alveoli-blood and blood-tissue exchange systems.

An alternative explicit model expression equivalent to the integrated michaelis-menten equation and its application to nonlinear saturation pharmacokinetics.

PubMed

Goličnik, Marko

2011-06-01

Many pharmacodynamic processes can be described by the nonlinear saturation kinetics that are most frequently based on the hyperbolic Michaelis-Menten equation. Thus, various time-dependent solutions for drugs obeying such kinetics can be expressed in terms of the Lambert W(x)-omega function. However, unfortunately, computer programs that can perform the calculations for W(x) are not widely available. To avoid this problem, the replacement of the integrated Michaelis-Menten equation with an empiric integrated 1--exp alternative model equation was proposed recently by Keller et al. (Ther Drug Monit. 2009;31:783-785), although, as shown here, it was not necessary. Simulated concentrations of model drugs obeying Michaelis-Menten elimination kinetics were generated by two approaches: 1) calculation of time-course data based on an approximation equation W2*(x) performed using Microsoft Excel; and 2) calculation of reference time-course data based on an exact W(x) function built in to the Wolfram Mathematica. I show here that the W2*(x) function approximates the actual W(x) accurately. W2*(x) is expressed in terms of elementary mathematical functions and, consequently, it can be easily implemented using any of the widely available software. Hence, with the example of a hypothetical drug, I demonstrate here that an equation based on this approximation is far better, because it is nearly equivalent to the original solution, whereas the same characteristics cannot be fully confirmed for the 1--exp model equation. The W2*(x) equation proposed here might have an important role as a useful shortcut in optional software to estimate kinetic parameters from experimental data for drugs, and it might represent an easy and universal analytical tool for simulating and designing dosing regimens.

New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor

NASA Technical Reports Server (NTRS)

Srivastava, R. C.; Coen, J. L.

1992-01-01

The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.

Acoustic Velocity Log Numerical Simulation and Saturation Estimation of Gas Hydrate Reservoir in Shenhu Area, South China Sea

PubMed Central

Xiao, Kun; Zou, Changchun; Xiang, Biao; Liu, Jieqiong

2013-01-01

Gas hydrate model and free gas model are established, and two-phase theory (TPT) for numerical simulation of elastic wave velocity is adopted to investigate the unconsolidated deep-water sedimentary strata in Shenhu area, South China Sea. The relationships between compression wave (P wave) velocity and gas hydrate saturation, free gas saturation, and sediment porosity at site SH2 are studied, respectively, and gas hydrate saturation of research area is estimated by gas hydrate model. In depth of 50 to 245 m below seafloor (mbsf), as sediment porosity decreases, P wave velocity increases gradually; as gas hydrate saturation increases, P wave velocity increases gradually; as free gas saturation increases, P wave velocity decreases. This rule is almost consistent with the previous research result. In depth of 195 to 220 mbsf, the actual measurement of P wave velocity increases significantly relative to the P wave velocity of saturated water modeling, and this layer is determined to be rich in gas hydrate. The average value of gas hydrate saturation estimated from the TPT model is 23.2%, and the maximum saturation is 31.5%, which is basically in accordance with simplified three-phase equation (STPE), effective medium theory (EMT), resistivity log (Rt), and chloride anomaly method. PMID:23935407

Numerical and Physical Modelling of Bubbly Flow Phenomena - Final Report to the Department of Energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrea Prosperetti

This report describes the main features of the results obtained in the course of this project. A new approach to the systematic development of closure relations for the averaged equations of disperse multiphase flow is outlined. The focus of the project is on spatially non-uniform systems and several aspects in which such systems differ from uniform ones are described. Then, the procedure used in deriving the closure relations is given and some explicit results shown. The report also contains a list of publications supported by this grant and a list of the persons involved in the work.

Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bertola, M.; Tovbis, A.

2017-09-01

Finite-gap (algebro-geometric) solutions to the focusing Nonlinear Schrödinger Equation (fNLS) i ψ_t + ψ_{xx} + 2|ψ|^2ψ=0, are quasi-periodic solutions that represent nonlinear multi-phase waves. In general, a finite-gap solution for (0-1) is defined by a collection of Schwarz symmetrical spectral bands and of real constants (initial phases), associated with the corresponding bands. In this paper we prove an interesting new formula for the maximal amplitude of a finite-gap solution to the focusing Nonlinear Schrödinger equation with given spectral bands: the amplitude does not exceed the sum of the imaginary parts of all the endpoints in the upper half plane. In the case of the straight vertical bands, that amounts to the half of the sum of the length of all the bands. The maximal amplitude will be attained for certain choices of the initial phases. This result is an important part of a criterion for the potential presence of the rogue waves in finite-gap solutions with a given set of spectral endpoints, obtained in Bertola et al. (Proc R Soc A, 2016. doi: 10.1098/rspa.2016.0340). A similar result was also obtained for the defocusing Nonlinear Schrödinger equation.

A three-dimensional meso-macroscopic model for Li-Ion intercalation batteries

DOE PAGES

Allu, S.; Kalnaus, S.; Simunovic, S.; ...

2016-06-09

Through this study, we present a three-dimensional computational formulation for electrode-electrolyte-electrode system of Li-Ion batteries. The physical consistency between electrical, thermal and chemical equations is enforced at each time increment by driving the residual of the resulting coupled system of nonlinear equations to zero. The formulation utilizes a rigorous volume averaging approach typical of multiphase formulations used in other fields and recently extended to modeling of supercapacitors [1]. Unlike existing battery modeling methods which use segregated solution of conservation equations and idealized geometries, our unified approach can model arbitrary battery and electrode configurations. The consistency of multi-physics solution also allowsmore » for consideration of a wide array of initial conditions and load cases. The formulation accounts for spatio-temporal variations of material and state properties such as electrode/void volume fractions and anisotropic conductivities. The governing differential equations are discretized using the finite element method and solved using a nonlinearly consistent approach that provides robust stability and convergence. The new formulation was validated for standard Li-ion cells and compared against experiments. Finally, its scope and ability to capture spatio-temporal variations of potential and lithium distribution is demonstrated on a prototypical three-dimensional electrode problem.« less

Two-phase flow visualization under reservoir conditions for highly heterogeneous conglomerate rock: A core-scale study for geologic carbon storage.

PubMed

Kim, Kue-Young; Oh, Junho; Han, Weon Shik; Park, Kwon Gyu; Shinn, Young Jae; Park, Eungyu

2018-03-20

Geologic storage of carbon dioxide (CO 2 ) is considered a viable strategy for significantly reducing anthropogenic CO 2 emissions into the atmosphere; however, understanding the flow mechanisms in various geological formations is essential for safe storage using this technique. This study presents, for the first time, a two-phase (CO 2 and brine) flow visualization under reservoir conditions (10 MPa, 50 °C) for a highly heterogeneous conglomerate core obtained from a real CO 2 storage site. Rock heterogeneity and the porosity variation characteristics were evaluated using X-ray computed tomography (CT). Multiphase flow tests with an in-situ imaging technology revealed three distinct CO 2 saturation distributions (from homogeneous to non-uniform) dependent on compositional complexity. Dense discontinuity networks within clasts provided well-connected pathways for CO 2 flow, potentially helping to reduce overpressure. Two flow tests, one under capillary-dominated conditions and the other in a transition regime between the capillary and viscous limits, indicated that greater injection rates (potential causes of reservoir overpressure) could be significantly reduced without substantially altering the total stored CO 2 mass. Finally, the capillary storage capacity of the reservoir was calculated. Capacity ranged between 0.5 and 4.5%, depending on the initial CO 2 saturation.

The thermodynamic properties of oxygen and nitrogen

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

The development of a single equation of state for oxygen and nitrogen based on the thermodynamic properties of the gases is described. The coefficients of the equation of state were determined by simultaneous least squares fits to values of isochoric heat capacity and saturation density values used to define the criteria for phase equilibrium. Tables of data for the conditions of both gases are included.

NLO evolution of color dipole

DOE PAGES

Balitsky, Ian; Chirilli, Giovanni A.

2008-09-01

The small-x deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities.

Macroscopic momentum and mechanical energy equations for incompressible single-phase flow in porous media.

PubMed

Paéz-García, Catherine Teresa; Valdés-Parada, Francisco J; Lasseux, Didier

2017-02-01

Modeling flow in porous media is usually focused on the governing equations for mass and momentum transport, which yield the velocity and pressure at the pore or Darcy scales. However, in many applications, it is important to determine the work (or power) needed to induce flow in porous media, and this can be achieved when the mechanical energy equation is taken into account. At the macroscopic scale, this equation may be postulated to be the result of the inner product of Darcy's law and the seepage velocity. However, near the porous medium boundaries, this postulate seems questionable due to the spatial variations of the effective properties (velocity, permeability, porosity, etc.). In this work we derive the macroscopic mechanical energy equation using the method of volume averaging for the simple case of incompressible single-phase flow in porous media. Our analysis shows that the result of averaging the pore-scale version of the mechanical energy equation at the Darcy scale is not, in general, the expected product of Darcy's law and the seepage velocity. As a matter of fact, this result is only applicable in the bulk region of the porous medium and, in the derivation of this result, the properties of the permeability tensor are determinant. Furthermore, near the porous medium boundaries, a more novel version of the mechanical energy equation is obtained, which incorporates additional terms that take into account the rapid variations of structural properties taking place in this particular portion of the system. This analysis can be applied to multiphase and compressible flows in porous media and in many other multiscale systems.

Visualizing and Quantifying Pore Scale Fluid Flow Processes With X-ray Microtomography

NASA Astrophysics Data System (ADS)

Wildenschild, D.; Hopmans, J. W.; Vaz, C. M.; Rivers, M. L.

2001-05-01

When using mathematical models based on Darcy's law it is often necessary to simplify geometry, physics or both and the capillary bundle-of-tubes approach neglects a fundamentally important characteristic of porous solids, namely interconnectedness of the pore space. New approaches to pore-scale modeling that arrange capillary tubes in two- or three-dimensional pore space have been and are still under development: Network models generally represent the pore space by spheres while the pore throats are usually represented by cylinders or conical shapes. Lattice Boltzmann approaches numerically solve the Navier-Stokes equations in a realistic microscopically disordered geometry, which offers the ability to study the microphysical basis of macroscopic flow without the need for a simplified geometry or physics. In addition to these developments in numerical modeling techniques, new theories have proposed that interfacial area should be considered as a primary variable in modeling of a multi-phase flow system. In the wake of this progress emerges an increasing need for new ways of evaluating pore-scale models, and for techniques that can resolve and quantify phase interfaces in porous media. The mechanisms operating at the pore-scale cannot be measured with traditional experimental techniques, however x-ray computerized microtomography (CMT) provides non-invasive observation of, for instance, changing fluid phase content and distribution on the pore scale. Interfacial areas have thus far been measured indirectly, but with the advances in high-resolution imaging using CMT it is possible to track interfacial area and curvature as a function of phase saturation or capillary pressure. We present results obtained at the synchrotron-based microtomography facility (GSECARS, sector 13) at the Advanced Photon Source at Argonne National Laboratory. Cylindrical sand samples of either 6 or 1.5 mm diameter were scanned at different stages of drainage and for varying boundary conditions. A significant difference in fluid saturation and phase distribution was observed for different drainage conditions, clearly showing preferential flow and a dependence on the applied flow rate. For the 1.5 mm sample individual pores and water/air interfaces could be resolved and quantified using image analysis techniques. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Basic Energy Sciences, Office of Science, under Contract No. W-31-109-Eng-38.

MBSSAS: A code for the computation of margules parameters and equilibrium relations in binary solid-solution aqueous-solution systems

USGS Publications Warehouse

Glynn, P.D.

1991-01-01

The computer code MBSSAS uses two-parameter Margules-type excess-free-energy of mixing equations to calculate thermodynamic equilibrium, pure-phase saturation, and stoichiometric saturation states in binary solid-solution aqueous-solution (SSAS) systems. Lippmann phase diagrams, Roozeboom diagrams, and distribution-coefficient diagrams can be constructed from the output data files, and also can be displayed by MBSSAS (on IBM-PC compatible computers). MBSSAS also will calculate accessory information, such as the location of miscibility gaps, spinodal gaps, critical-mixing points, alyotropic extrema, Henry's law solid-phase activity coefficients, and limiting distribution coefficients. Alternatively, MBSSAS can use such information (instead of the Margules, Guggenheim, or Thompson and Waldbaum excess-free-energy parameters) to calculate the appropriate excess-free-energy of mixing equation for any given SSAS system. ?? 1991.

Prediction of unsaturated flow and water backfill during infiltration in layered soils

NASA Astrophysics Data System (ADS)

Cui, Guotao; Zhu, Jianting

2018-02-01

We develop a new analytical infiltration model to determine water flow dynamics around layer interfaces during infiltration process in layered soils. The model mainly involves the analytical solutions to quadratic equations to determine the flux rates around the interfaces. Active water content profile behind the wetting front is developed based on the solution of steady state flow to dynamically update active parameters in sharp wetting front infiltration equations and to predict unsaturated flow in coarse layers before the front reaches an impeding fine layer. The effect of water backfill to saturate the coarse layers after the wetting front encounters the impeding fine layer is analytically expressed based on the active water content profiles. Comparison to the numerical solutions of the Richards equation shows that the new model can well capture water dynamics in relation to the arrangement of soil layers. The steady state active water content profile can be used to predict the saturation state of all layers when the wetting front first passes through these layers during the unsteady infiltration process. Water backfill effect may occur when the unsaturated wetting front encounters a fine layer underlying a coarse layer. Sensitivity analysis shows that saturated hydraulic conductivity is the parameter dictating the occurrence of unsaturated flow and water backfill and can be used to represent the coarseness of soil layers. Water backfill effect occurs in coarse layers between upper and lower fine layers when the lower layer is not significantly coarser than the upper layer.

Slow light in saturable absorbers: Progress in the resolution of a controversy

NASA Astrophysics Data System (ADS)

Macke, Bruno; Razdobreev, Igor; Ségard, Bernard

2017-06-01

There are two opposing models in the analysis of the slow transmission of light pulses through saturable absorbers. The canonical incoherent bleaching model simply explains the slow transmission by combined effects of saturation and of noninstantaneous response of the medium resulting in absorption of the front part of the incident pulse larger than that of its rear. The second model, referred to as the coherent-population-oscillations (CPO) model, considers light beams whose intensity is slightly pulse modulated and attributes the time delay of the transmitted pulse to a reduction of the group velocity. We point out some inconsistencies in the CPO model and show that the two models lie in reality on the same hypotheses, the equations derived in the duly rectified CPO model being local expressions of the integral equations obtained in the incoherent bleaching model. When intense pulses without background are used, the CPO model, based on linearized equations, breaks down. The incoherent bleaching model then predicts that the transmitted light should vanish when the intensity of the incident light is strictly zero. This point is confirmed by the experiments that we have performed on ruby with square-wave incident pulses and we show that the whole shape of the observed pulses agrees with that derived analytically by means of the incoherent bleaching model. We also determine in this model the corresponding evolution of the fluorescence light, which seems to have been evidenced in other experiments.

Theory of the milieu dependent isomerisation dynamics of reducing sugars applied to d-erythrose.

PubMed

Kaufmann, Martin; Mügge, Clemens; Kroh, Lothar W

2015-12-11

Quantitative (1)H selective saturation transfer NMR spectroscopy ((1)H SST qNMR) was used to fully describe the milieu dependent dynamics of the isomeric system of d-erythrose. Thermodynamic activation parameters are calculated for acidic as well as for basic catalysis combining McConnell's modified Bloch equations for the chemical exchange solved for the constraint of saturating the non-hydrated acyclic isomer, the Eyring equation and Hudson's equation for pH dependent catalysis. A detailed mathematical examination describing the milieu dependent dynamics of sugar isomerisation is provided. Thermodynamic data show evidence that photo-catalysed sugar isomerisation as well as degradation has to be considered. Approximations describing the pH and temperature dependence of thermodynamic activation parameters are derived that indicate the possibility of photo-affecting equilibrium constants. Moreover, the results show that isomerisation dynamics are closely related to degradation kinetics and that sugars' reactivities are altered by the concentration of acyclic carbonyl isomer and the sum of its ring closing rate constants. Additionally, it is concluded that sugar solutions show a limited self-stabilising behaviour. Copyright © 2015 Elsevier Ltd. All rights reserved.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Gassmann Theory Applies to Nanoporous Media

NASA Astrophysics Data System (ADS)

Gor, Gennady Y.; Gurevich, Boris

2018-01-01

Recent progress in extraction of unconventional hydrocarbon resources has ignited the interest in the studies of nanoporous media. Since many thermodynamic and mechanical properties of nanoscale solids and fluids differ from the analogous bulk materials, it is not obvious whether wave propagation in nanoporous media can be described using the same framework as in macroporous media. Here we test the validity of Gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, Vycor glass, saturated with two different fluids, argon, and n-hexane. Predictions of the Gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements and the bulk moduli of the solid and fluid constituents. The solid bulk modulus can be estimated from adsorption-induced deformation or from elastic effective medium theory. The fluid modulus can be calculated according to the Tait-Murnaghan equation at the solvation pressure in the pore. Substitution of these parameters into the Gassmann equation provides predictions consistent with measured data. Our findings set up a theoretical framework for investigation of fluid-saturated nanoporous media using ultrasonic elastic wave propagation.

Internal structure of multiphase zinc-blende wurtzite gallium nitride nanowires.

PubMed

Jacobs, B W; Ayres, V M; Crimp, M A; McElroy, K

2008-10-08

In this paper, the internal structure of novel multiphase gallium nitride nanowires in which multiple zinc-blende and wurtzite crystalline domains grow simultaneously along the entire length of the nanowire is investigated. Orientation relationships within the multiphase nanowires are identified using high-resolution transmission electron microscopy of nanowire cross-sections fabricated with a focused ion beam system. A coherent interface between the zinc-blende and wurtzite phases is identified. A mechanism for catalyst-free vapor-solid multiphase nanowire nucleation and growth is proposed.

Vapor-Saturated Melting of Fertile Peridotite Revisited: A new Experimental Approach and Re-evaluation of the Hydrous Peridotite Solidus

NASA Astrophysics Data System (ADS)

Grove, T. L.

2001-12-01

The vapor-saturated melting relations of peridotite have been determined for a fertile mantle composition of Hart and Zindler (1986, Chem Geol 57: 247) over the pressure range of 1.2 to 2.4 GPa. For example, at 1.2 GPa melt is present at a temperature of 980° C and at 2.4 GPa melt is present at 920° C. These temperatures should be viewed as maximum values for the vapor-saturated solidus (although see below) because the initial melting temperature of multi-phase, multicomponent systems can often be difficult to detect. At 2.4 GPa the melt composition is highly silica-undersaturated and very aluminous ( ~ 21 wt. % Al2O3). Wet mantle melts are thought to be high in silica, but this is not the case for these hydrous melts. At 1.2 GPa, melt fractions are too small to allow reliable analysis. The experiments have been carried out in a piston cylinder apparatus using Au capsules. The starting material is an oxide mixture containing 14.5 wt. % H2O added as brucite. Free water present in the experiment after quenching indicates subsolidus conditions. The absence of fluid in experiments above the vapor-saturated solidus shows that all of the free H2O is dissolved in the melt. The high H2O content of the starting material moves the bulk composition close to the vapor-saturated melt composition, therefore increasing the amount of melt produced close to the solidus and making detection of low melt fraction possible. Studies of the hydrous peridotite solidus carried out between 1970 and 1975 by Mysen and Boettcher, Kushiro and others, Green and Millhollen and others at 2.0 GPa ranged from < 800 to ~ 1000° C, a variation of over 200 degrees. In a subduction zone environment a fluid-rich component released from the slab ascends into hotter overlying mantle and melting initiates at the vapor-saturated solidus. Melting would begin at a depth of ~ 75 km in the mantle wedge, for a realistic thermal structure. Melting would continue as these initial H2O-rich buoyant melts ascend into hotter, shallower mantle and re-equilibrate with their surroundings. The initiation of melting deep in the mantle wedge has implications for both chemical and mechanical processes in the subduction zone environment.

Damping Effect of an Unsaturated-Saturated System on Tempospatial Variations of Pressure Head and Specific Flux

NASA Astrophysics Data System (ADS)

Yang, C.; Zhang, Y. K.; Liang, X.

2014-12-01

Damping effect of an unsaturated-saturated system on tempospatialvariations of pressurehead and specificflux was investigated. The variance and covariance of both pressure head and specific flux in such a system due to a white noise infiltration were obtained by solving the moment equations of water flow in the system and verified with Monte Carlo simulations. It was found that both the pressure head and specific flux in this case are temporally non-stationary. The variance is zero at early time due to a deterministic initial condition used, then increases with time, and approaches anasymptotic limit at late time.Both pressure head and specific flux arealso non-stationary in space since the variance decreases from source to sink. The unsaturated-saturated systembehavesasa noise filterand it damps both the pressure head and specific flux, i.e., reduces their variations and enhances their correlation. The effect is stronger in upper unsaturated zone than in lower unsaturated zone and saturated zone. As a noise filter, the unsaturated-saturated system is mainly a low pass filter, filtering out the high frequency components in the time series of hydrological variables. The damping effect is much stronger in the saturated zone than in the saturated zone.

Multiphasic modelling of bone-cement injection into vertebral cancellous bone.

PubMed

Bleiler, Christian; Wagner, Arndt; Stadelmann, Vincent A; Windolf, Markus; Köstler, Harald; Boger, Andreas; Gueorguiev-Rüegg, Boyko; Ehlers, Wolfgang; Röhrle, Oliver

2015-01-01

Percutaneous vertebroplasty represents a current procedure to effectively reinforce osteoporotic bone via the injection of bone cement. This contribution considers a continuum-mechanically based modelling approach and simulation techniques to predict the cement distributions within a vertebra during injection. To do so, experimental investigations, imaging data and image processing techniques are combined and exploited to extract necessary data from high-resolution μCT image data. The multiphasic model is based on the Theory of Porous Media, providing the theoretical basis to describe within one set of coupled equations the interaction of an elastically deformable solid skeleton, of liquid bone cement and the displacement of liquid bone marrow. The simulation results are validated against an experiment, in which bone cement was injected into a human vertebra under realistic conditions. The major advantage of this comprehensive modelling approach is the fact that one can not only predict the complex cement flow within an entire vertebra but is also capable of taking into account solid deformations in a fully coupled manner. The presented work is the first step towards the ultimate and future goal of extending this framework to a clinical tool allowing for pre-operative cement distribution predictions by means of numerical simulations. Copyright © 2015 John Wiley & Sons, Ltd.

Device-scale CFD modeling of gas-liquid multiphase flow and amine absorption for CO 2 capture: Original Research Article: Device-scale CFD modeling of gas-liquid multiphase flow and amine absorption for CO 2 capture

DOE PAGES

Pan, Wenxiao; Galvin, Janine; Huang, Wei Ling; ...

2018-03-25

In this paper we aim to develop a validated device-scale CFD model that can predict quantitatively both hydrodynamics and CO 2 capture efficiency for an amine-based solvent absorber column with random Pall ring packing. A Eulerian porous-media approach and a two-fluid model were employed, in which the momentum and mass transfer equations were closed by literature-based empirical closure models. We proposed a hierarchical approach for calibrating the parameters in the closure models to make them accurate for the packed column. Specifically, a parameter for momentum transfer in the closure was first calibrated based on data from a single experiment. Withmore » this calibrated parameter, a parameter in the closure for mass transfer was next calibrated under a single operating condition. Last, the closure of the wetting area was calibrated for each gas velocity at three different liquid flow rates. For each calibration, cross validations were pursued using the experimental data under operating conditions different from those used for calibrations. This hierarchical approach can be generally applied to develop validated device-scale CFD models for different absorption columns.« less

A multiphase three-dimensional multi-relaxation time (MRT) lattice Boltzmann model with surface tension adjustment

NASA Astrophysics Data System (ADS)

Ammar, Sami; Pernaudat, Guillaume; Trépanier, Jean-Yves

2017-08-01

The interdependence of surface tension and density ratio is a weakness of pseudo-potential based lattice Boltzmann models (LB). In this paper, we propose a 3D multi-relaxation time (MRT) model for multiphase flows at large density ratios. The proposed model is capable of adjusting the surface tension independently of the density ratio. We also present the 3D macroscopic equations recovered by the proposed forcing scheme. A high order of isotropy for the interaction force is used to reduce the amplitude of spurious currents. The proposed 3D-MRT model is validated by verifying Laplace's law and by analyzing its thermodynamic consistency and the oscillation period of a deformed droplet. The model is then applied to the simulation of the impact of a droplet on a dry surface. Impact dynamics are determined and the maximum spread factor calculated for different Reynolds and Weber numbers. The numerical results are in agreement with data published in the literature. The influence of surface wettability on the spread factor is also investigated. Finally, our 3D-MRT model is applied to the simulation of the impact of a droplet on a wet surface. The propagation of transverse waves is observed on the liquid surface.

Cavitating Propeller Performance in Inclined Shaft Conditions with OpenFOAM: PPTC 2015 Test Case

NASA Astrophysics Data System (ADS)

Gaggero, Stefano; Villa, Diego

2018-05-01

In this paper, we present our analysis of the non-cavitating and cavitating unsteady performances of the Potsdam Propeller Test Case (PPTC) in oblique flow. For our calculations, we used the Reynolds-averaged Navier-Stokes equation (RANSE) solver from the open-source OpenFOAM libraries. We selected the homogeneous mixture approach to solve for multiphase flow with phase change, using the volume of fluid (VoF) approach to solve the multiphase flow and modeling the mass transfer between vapor and water with the Schnerr-Sauer model. Comparing the model results with the experimental measurements collected during the Second Workshop on Cavitation and Propeller Performance - SMP'15 enabled our assessment of the reliability of the open-source calculations. Comparisons with the numerical data collected during the workshop enabled further analysis of the reliability of different flow solvers from which we produced an overview of recommended guidelines (mesh arrangements and solver setups) for accurate numerical prediction even in off-design conditions. Lastly, we propose a number of calculations using the boundary element method developed at the University of Genoa for assessing the reliability of this dated but still widely adopted approach for design and optimization in the preliminary stages of very demanding test cases.

Constitutive equations for multiphase TRIP steels at high rates of strain

NASA Astrophysics Data System (ADS)

van Slycken, J.; Verleysen, P.; Degrieck, J.; Bouquerel, J.

2006-08-01

Multiphase TRansformation Induced Plasticity (TRIP) steels show an excellent combination of high strength and high strain values, making them ideally suited for use in vehicle body structures. A complex synergy of three different phases (ferrite, bainite and austenite) on the one hand, and the meta-stable character of the austenite on the other hand, give the material indeed a high energy absorption potential. The knowledge and understanding of the dynamic behaviour of these sheet steels is essential to investigate the impact-dynamic characteristics of the structures. Therefore split Hopkinson tensile tests are performed in a strain rate range of 500 to 2000 s-1. Three TRIP steel grades with a different Al and Si content were studied. The experimental results show that these steels preserve their excellent shock-absorbing properties in dynamic conditions. The typical high strain rate loading conditions and the complex behaviour of TRIP steels offer a unique investigation opportunity. This behaviour can be described with phenomenological material models that can be used for numerical simulations of car crashes. The Johnson-Cook model, a frequently used model in finite element codes, is well-suited to describe the dynamic behaviour of the investigated TRIP steels. This model is compared to the Rusinek-Klepaczko model.

Associations between DSM-5 section III personality traits and the Minnesota Multiphasic Personality Inventory 2-Restructured Form (MMPI-2-RF) scales in a psychiatric patient sample.

PubMed

Anderson, Jaime L; Sellbom, Martin; Ayearst, Lindsay; Quilty, Lena C; Chmielewski, Michael; Bagby, R Michael

2015-09-01

Our aim in the current study was to evaluate the convergence between Diagnostic and Statistical Manual of Mental Disorders, fifth edition (DSM-5) Section III dimensional personality traits, as operationalized via the Personality Inventory for DSM-5 (PID-5), and Minnesota Multiphasic Personality Inventory 2-Restructured Form (MMPI-2-RF) scale scores in a psychiatric patient sample. We used a sample of 346 (171 men, 175 women) patients who were recruited through a university-affiliated psychiatric facility in Toronto, Canada. We estimated zero-order correlations between the PID-5 and MMPI-2-RF substantive scale scores, as well as a series of exploratory structural equation modeling (ESEM) analyses to examine how these scales converged in multivariate latent space. Results generally showed empirical convergence between the scales of these two measures that were thematically meaningful and in accordance with conceptual expectations. Correlation analyses showed significant associations between conceptually expected scales, and the highest associations tended to be between scales that were theoretically related. ESEM analyses generated evidence for distinct internalizing, externalizing, and psychoticism factors across all analyses. These findings indicate convergence between these two measures and help further elucidate the associations between dysfunctional personality traits and general psychopathology. (c) 2015 APA, all rights reserved.

Optimization of Simplex Atomizer Inlet Port Configuration through Computational Fluid Dynamics and Experimental Study for Aero-Gas Turbine Applications

NASA Astrophysics Data System (ADS)

Marudhappan, Raja; Chandrasekhar, Udayagiri; Hemachandra Reddy, Koni

2017-10-01

The design of plain orifice simplex atomizer for use in the annular combustion system of 1100 kW turbo shaft engine is optimized. The discrete flow field of jet fuel inside the swirl chamber of the atomizer and up to 1.0 mm downstream of the atomizer exit are simulated using commercial Computational Fluid Dynamics (CFD) software. The Euler-Euler multiphase model is used to solve two sets of momentum equations for liquid and gaseous phases and the volume fraction of each phase is tracked throughout the computational domain. The atomizer design is optimized after performing several 2D axis symmetric analyses with swirl and the optimized inlet port design parameters are used for 3D simulation. The Volume Of Fluid (VOF) multiphase model is used in the simulation. The orifice exit diameter is 0.6 mm. The atomizer is fabricated with the optimized geometric parameters. The performance of the atomizer is tested in the laboratory. The experimental observations are compared with the results obtained from 2D and 3D CFD simulations. The simulated velocity components, pressure field, streamlines and air core dynamics along the atomizer axis are compared to previous research works and found satisfactory. The work has led to a novel approach in the design of pressure swirl atomizer.

Device-scale CFD modeling of gas-liquid multiphase flow and amine absorption for CO 2 capture: Original Research Article: Device-scale CFD modeling of gas-liquid multiphase flow and amine absorption for CO 2 capture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Wenxiao; Galvin, Janine; Huang, Wei Ling

In this paper we aim to develop a validated device-scale CFD model that can predict quantitatively both hydrodynamics and CO 2 capture efficiency for an amine-based solvent absorber column with random Pall ring packing. A Eulerian porous-media approach and a two-fluid model were employed, in which the momentum and mass transfer equations were closed by literature-based empirical closure models. We proposed a hierarchical approach for calibrating the parameters in the closure models to make them accurate for the packed column. Specifically, a parameter for momentum transfer in the closure was first calibrated based on data from a single experiment. Withmore » this calibrated parameter, a parameter in the closure for mass transfer was next calibrated under a single operating condition. Last, the closure of the wetting area was calibrated for each gas velocity at three different liquid flow rates. For each calibration, cross validations were pursued using the experimental data under operating conditions different from those used for calibrations. This hierarchical approach can be generally applied to develop validated device-scale CFD models for different absorption columns.« less

Dark soliton fiber lasers.

PubMed

Tang, Dingyuan; Guo, Jun; Song, Yufeng; Zhang, Han; Zhao, Luming; Shen, Deyuan

2014-08-11

Dark soliton formation and soliton dynamics in all-normal dispersion cavity fiber ring lasers without an anti-saturable absorber in cavity is studied both theoretically and numerically. It is shown that under suitable conditions the dark solitons formed could be described by the nonlinear Schrödinger equation. The dark soliton formation in an all-normal-dispersion cavity erbium-doped fiber ring laser without an anti-saturable absorber in cavity is first experimentally demonstrated. Individual dark solitons are experimentally identified. Excellent agreement between theory and experiment is observed.

Polar Kerr Effect from Time-Reversal Symmetry Breaking in the Heavy-Fermion Superconductor PrOs 4 Sb 12

DOE PAGES

Levenson-Falk, Eli M.; Schemm, E. R.; Aoki, Y.; ...

2018-05-04

Here, we present polar Kerr effect measurements of the filled skutterudite superconductor PrOs 4Sb 12. Simultaneous ac susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle θ K develops below the superconducting transition, saturating at ~300 nrad at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured θ K(T) to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the B phase at Tmore » C2. We discuss the possible explanations for this result and its impact on the understanding of multiphase and inhomogeneous superconductivity in PrOs 4Sb 12.« less

Polar Kerr Effect from Time-Reversal Symmetry Breaking in the Heavy-Fermion Superconductor PrOs 4 Sb 12

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levenson-Falk, Eli M.; Schemm, E. R.; Aoki, Y.

Here, we present polar Kerr effect measurements of the filled skutterudite superconductor PrOs 4Sb 12. Simultaneous ac susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle θ K develops below the superconducting transition, saturating at ~300 nrad at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured θ K(T) to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the B phase at Tmore » C2. We discuss the possible explanations for this result and its impact on the understanding of multiphase and inhomogeneous superconductivity in PrOs 4Sb 12.« less

Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods

NASA Technical Reports Server (NTRS)

Chau, Jessica Furrer; Or, Dani; Sukop, Michael C.; Steinberg, S. L. (Principal Investigator)

2005-01-01

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.

Flow rate impacts on capillary pressure and interface curvature of connected and disconnected fluid phases during multiphase flow in sandstone

NASA Astrophysics Data System (ADS)

Herring, Anna L.; Middleton, Jill; Walsh, Rick; Kingston, Andrew; Sheppard, Adrian

2017-09-01

We investigate capillary pressure-saturation (PC-S) relationships for drainage-imbibition experiments conducted with air (nonwetting phase) and brine (wetting phase) in Bentheimer sandstone cores. Three different flow rate conditions, ranging over three orders of magnitude, are investigated. X-ray micro-computed tomographic imaging is used to characterize the distribution and amount of fluids and their interfacial characteristics. Capillary pressure is measured via (1) bulk-phase pressure transducer measurements, and (2) image-based curvature measurements, calculated using a novel 3D curvature algorithm. We distinguish between connected (percolating) and disconnected air clusters: curvatures measured on the connected phase interfaces are used to validate the curvature algorithm and provide an indication of the equilibrium condition of the data; curvature and volume distributions of disconnected clusters provide insight to the snap-off processes occurring during drainage and imbibition under different flow rate conditions.

Liquid Water Saturation and Oxygen Transport Resistance in Polymer Electrolyte Membrane Fuel Cell Gas Diffusion Layers

NASA Astrophysics Data System (ADS)

Muirhead, Daniel

In this thesis, the relative humidity (RH) of the cathode reactant gas was investigated as a factor which influences gas diffusion layer (GDL) liquid water accumulation and mass transport-related efficiency losses over a range of operating current densities in a polymer electrolyte membrane (PEM) fuel cell. Limiting current measurements were used to characterize fuel cell oxygen transport resistance while simultaneous measurements of liquid water accumulation were conducted using synchrotron X-ray radiography. GDL porosity distributions were characterized with micro-computed tomography (microCT). The work presented here can be used by researchers to develop improved numerical models to predict GDL liquid water accumulation and to inform the design of next-generation GDL materials to mitigate mass transport-related efficiency losses. This work also contributes an extensive set of concurrent performance and liquid water visualization data to the PEM fuel cell field that can be used for validating multiphase transport models.

Technical Report on NETL's Non Newtonian Multiphase Slurry Workshop: A path forward to understanding non-Newtonian multiphase slurry flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guenther, Chris; Garg, Rahul

2013-08-19

The Department of Energy’s (DOE) National Energy Technology Laboratory (NETL) sponsored a workshop on non-Newtonian multiphase slurry at NETL’s Morgantown campus August 19 and 20, 2013. The objective of this special two-day meeting of 20-30 invited experts from industry, National Labs and academia was to identify and address technical issues associated with handling non-Newtonian multiphase slurries across various facilities managed by DOE. Particular emphasis during this workshop was placed on applications managed by the Office of Environmental Management (EM). The workshop was preceded by two webinars wherein personnel from ORP and NETL provided background information on the Hanford WTP projectmore » and discussed the critical design challenges facing this project. In non-Newtonian fluids, viscosity is not constant and exhibits a complex dependence on applied shear stress or deformation. Many applications under EM’s tank farm mission involve non-Newtonian slurries that are multiphase in nature; tank farm storage and handling, slurry transport, and mixing all involve multiphase flow dynamics, which require an improved understanding of the mechanisms responsible for rheological changes in non-Newtonian multiphase slurries (NNMS). To discuss the issues in predicting the behavior of NNMS, the workshop focused on two topic areas: (1) State-of-the-art in non-Newtonian Multiphase Slurry Flow, and (2) Scaling up with Confidence and Ensuring Safe and Reliable Long-Term Operation.« less

[Effect of humic acids on migration and transformation of NH4(+) -N in saturated aquifer].

PubMed

Meng, Qing-Jun; Zhang, Yan; Feng, Qi-Yan; Zhang, Shuang-Sheng

2011-11-01

Isothermal adsorption experiment was used to study the adsorbing process of NH4(+) -N in quartz sands under the conditions with and without humic acid; the Langmuir and Freundlich equations were used to fit the absorption result and the maximum adsorption capacity of NH4(+) -N by quarts sands was calculated. Through the soil column experiments, the concentration of NH4(+) -N, NO3(-) -N and NO2(-) -N in effluent water in the tested soil column was investigated, and the effect of humic acid on migration and transformation of NH4(+) -N in saturated aquifer was analyzed, and Pseudo-second-order Kinetics Equation and Two-step Adsorption Kinetics Rate Equation were applied to fit the kinetic processes. The results showed that both Langmuir and Freundlich models can well describe the isothermal adsorption process of NH4(+) -N on the surface of quartz sands, which means that NH4(+) -N adsorbed by the quartz sand was mainly in the form of monolayer adsorption. The humic acid could increase the adsorption capacity of NH4(+) -N on quartz sand, and the saturated adsorption capacity was 0.354 mg x g(-1) under the condition with humic acid and 0.205 mg x g(-1) with the absence of humic acid. The experiment indicated that humic acid increased the adsorption capacity of NH4(+) -N on the surface of quartz sand by increasing adsorption space in the initial stage. After saturation, humic acid influenced the migration and transformation of NH4(+) -N to NO3(-) -N and NO2(-) -N probably through providing carbon source and energy for microorganisms such as nitrifying bacteria and then resulting in lower NH4(+) -N concentration in effluent water. Both Pseudo-second-order Kinetics Equation and Two-step Adsorption Kinetics Rate Equations can well describe the process of NH4(+) -N adsorption kinetics on quartz sand (R2 = 0.997 7 and R2 = 0.998 1 with humic acid; R2 = 0.992 3 and R2 = 0.994 4 without humic acid), indicating that this process was chemical adsorption. By comparing the adsorption rate coefficient of Two-step Adsorption Kinetics Rate Equation k3 (0.247 and 0.143, respectively) and k4 (0.006 27 and 0.001 7) between the treatments with and without humic acid, it can be referred that NH4(+) -N was non-orientated adsorption on active points of the quartz sand at the initial stage, and the humic acid could increase the equilibrium adsorption quantity(q(e)) of NH4(+) -N on quartz sands.

Modeling interfacial area transport in multi-fluid systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yarbro, Stephen Lee

1996-11-01

Many typical chemical engineering operations are multi-fluid systems. They are carried out in distillation columns (vapor/liquid), liquid-liquid contactors (liquid/liquid) and other similar devices. An important parameter is interfacial area concentration, which determines the rate of interfluid heat, mass and momentum transfer and ultimately, the overall performance of the equipment. In many cases, the models for determining interfacial area concentration are empirical and can only describe the cases for which there is experimental data. In an effort to understand multiphase reactors and the mixing process better, a multi-fluid model has been developed as part of a research effort to calculate interfacialmore » area transport in several different types of in-line static mixers. For this work, the ensemble-averaged property conservation equations have been derived for each fluid and for the mixture. These equations were then combined to derive a transport equation for the interfacial area concentration. The final, one-dimensional model was compared to interfacial area concentration data from two sizes of Kenics in-line mixer, two sizes of concurrent jet and a Tee mixer. In all cases, the calculated and experimental data compared well with the highest scatter being with the Tee mixer comparison.« less

A New Model for Simulating Gas Metal Arc Welding based on Phase Field Model

NASA Astrophysics Data System (ADS)

Jiang, Yongyue; Li, Li; Zhao, Zhijiang

2017-11-01

Lots of physical process, such as metal melting, multiphase fluids flow, heat and mass transfer and thermocapillary effect (Marangoni) and so on, will occur in gas metal arc welding (GMAW) which should be considered as a mixture system. In this paper, based on the previous work, we propose a new model to simulate GMAW including Navier-Stokes equation, the phase field model and energy equation. Unlike most previous work, we take the thermocapillary effect into the phase field model considering mixture energy which is different of volume of fluid method (VOF) widely used in GMAW before. We also consider gravity, electromagnetic force, surface tension, buoyancy effect and arc pressure in momentum equation. The spray transfer especially the projected transfer in GMAW is computed as numerical examples with a continuous finite element method and a modified midpoint scheme. Pulse current is set as welding current as the numerical example to show the numerical simulation of metal transfer which fits the theory of GMAW well. From the result compared with the data of high-speed photography and VOF model, the accuracy and stability of the model and scheme are easily validated and also the new model has the higher precieion.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steiner, Andrew W.; Lattimer, James M.; Brown, Edward F.

We investigate constraints on neutron star structure arising from the assumptions that neutron stars have crusts, that recent calculations of pure neutron matter limit the equation of state of neutron star matter near the nuclear saturation density, that the high-density equation of state is limited by causality and the largest high-accuracy neutron star mass measurement, and that general relativity is the correct theory of gravity. We explore the role of prior assumptions by considering two classes of equation of state models. In a first, the intermediate- and high-density behavior of the equation of state is parameterized by piecewise polytropes. Inmore » the second class, the high-density behavior of the equation of state is parameterized by piecewise continuous line segments. The smallest density at which high-density matter appears is varied in order to allow for strong phase transitions above the nuclear saturation density. We critically examine correlations among the pressure of matter, radii, maximum masses, the binding energy, the moment of inertia, and the tidal deformability, paying special attention to the sensitivity of these correlations to prior assumptions about the equation of state. It is possible to constrain the radii of 1.4 solar mass neutron stars to be larger than 10 km, even without consideration of additional astrophysical observations, for example, those from photospheric radius expansion bursts or quiescent low-mass X-ray binaries. We are able to improve the accuracy of known correlations between the moment of inertia and compactness as well as the binding energy and compactness. Furthermore, we also demonstrate the existence of a correlation between the neutron star binding energy and the moment of inertia.« less

Experimental and numerical investigation of DNAPL infiltration and spreading in a 2-D sandbox by means of light transmission method

NASA Astrophysics Data System (ADS)

Zheng, F.; Shi, X.; Wu, J.; Gao, Y. W.

2013-12-01

Chlorinated solvents such as trichloroethene (TCE) and tetrachloroethene (PCE) are widespread groundwater contaminants often referred to as dense non-aqueous phase liquids (DNAPLs). Accuracy description of the spreading behavior and configuration for subsurface DNAPL migration is important, especially favourable for design effective remediation strategies. In this study, a 2-D experiment was conducted to investigate the infiltration behavior and spatial distribution of PCE in saturated porous media. Accusand 20/30 mesh sand (Unimin, Le Sueur, MN) was used as the background medium with two 70/80 and 60/70 mesh lenses embedded to simulate heterogeneous conditions. Dyed PCE of 100 ml was released into the flow cell at a constant rate of 2ml/min using a Harvard Apparatus syringe pump with a 50 ml glass syringe for two times, and 5 ml/min water was continuously injected through the inlet at the left side of the sandbox, while kept the same effluent rate at right side to create hydrodynamic condition. A light transmission (LT) system was used to record the migration of PCE and determine the saturation distribution of PCE in the sandbox experiment with a thermoelectrically air-cooled charged-coupled device (CCD) camera. All images were processed using MATLAB to calculate thickness-averaged PCE saturation for each pixel. Mass balance was checked through comparing injected known mounts of PCE with that calculated from LT analysis. Results showed that LT method is effective to delineate PCE migration pathways and quantify the saturation distribution. The relative errors of total PCE volumes calculated by LT analysis at different times were within 15% of the injected PCE volumes. The simulation are conducted using the multiphase modeling software T2VOC, which calibrated by the LT analysis results of three recorded time steps to fit with the complete spatial-temporal distribution of the PCE saturation. Model verification was then performed using the other eight recorded time steps. Simulated results showed that the model could successfully reproduce the migration pathways and distribution configuration observed from the laboratory experiment and LT analysis, excepted for a smaller pool height on the lenses, and a lower saturation values in PCE accumulation area due to local heterogeneities. Due to the influence of water flow, the PCE distribution was asymmetrical, and the PCE distribution area, pool height as well as PCE saturation in the accumulation region at right side was much greater. Acknowledge: This work is financially supported by the National Nature Science Foundation of China grants No. 41030746 and 41172206.

A Senior Project-Based Multiphase Motor Drive System Development

ERIC Educational Resources Information Center

Abdel-Khalik, Ayman S.; Massoud, Ahmed M.; Ahmed, Shehab

2016-01-01

Adjustable-speed drives based on multiphase motors are of significant interest for safety-critical applications that necessitate wide fault-tolerant capabilities and high system reliability. Although multiphase machines are based on the same conceptual theory as three-phase machines, most undergraduate electrical machines and electric drives…

Direct Numerical Simulation of Liquid Transport Through Fibrous Porous Media

NASA Astrophysics Data System (ADS)

Palakurthi, Nikhil Kumar

Fluid flow through fibrous media occurs in many industrial processes, including, but not limited, to fuel cell technology, drug delivery patches, sanitary products, textile reinforcement, filtration, heat exchangers, and performance fabrics. Understanding the physical processes involved in fluid flow through fibrous media is essential for their characterization as well as for the optimization and development of new products. Macroscopic porous-media equations require constitutive relations, which account for the physical processes occurring at the micro-scale, to predict liquid transport at the macro-scale. In this study, micro-scale simulations were conducted using conventional computational fluid dynamics (CFD) technique (finite-volume method) to determine the macroscopic constitutive relations. The first part of this thesis deals with the single-phase flow in fibrous media, following which multi-phase flow through fibrous media was studied. Darcy permeability is an important parameter that characterizes creeping flow through a fibrous porous medium. It has a complex dependence on the medium's properties such as fibers' in-plane and through-plane orientation, diameter, aspect ratio, curvature, and porosity. A suite of 3D virtual fibrous structures with a wide range of geometric properties were constructed, and the permeability values of the structures were calculated by solving the 3D incompressible Navier-Stokes equations. The through-plane permeability was found to be a function of only the fiber diameter, the fibers' through-plane orientation, and the porosity of the medium. The numerical results were used to extend a permeability-porosity relation, developed in literature for 3D isotropic fibrous media, to a wide range of fibers' through-plane orientations. In applications where rate of capillary penetration is important, characterization of porous media usually involves determination of either the effective pore radius from capillary penetration experiments or a representative pore radius (R50) from pore-size distribution data. The relationship between effective and representative pore radii was studied by performing direct simulations of capillary penetration of a wetting liquid using a finite-volume-based volume-of-fluid (VOF) method. The simulated unidirectional liquid penetration through fibrous media followed Lucas-Washburn kinetics (L ˜ t1/2), except during the initial stages, which are dominated by inertial forces. Even though fluid properties and contact angle were kept constant in the simulations, the effective pore radii were found to be quite different from the representative radii. It can be concluded that the differences between effective and representative pore radii did not arise from contact angle variations. The unsaturated flow through fibrous media at the macro-scale is typically described using Richard's equation which requires constitutive relations: capillary pressure and permeability as a function of liquid saturation. In the present study, the quasi-static capillary pressure-saturation (P c-S) relationship for the primary drainage in a 3D isotropic fibrous medium was determined by performing micro-scale simulations using a VOF method. The Pc-S relationship obtained from the VOF method was compared with the results from the full-morphology (FM) method. Good agreement was observed between the results from the VOF and FM methods, thus suggesting that the FM method, a computationally less intensive method as compared to VOF method, may be sufficient for estimating the Pc-S relationship for primary drainage.

TOUGH3 v1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

PAU, GEORGE; JUNG, YOOJIN; FINSTERLE, STEFAN

2016-09-14

TOUGH3 V1.0 capabilities to simulate multi-dimensional, multi-phase, multi-component, non-isothermal flow and transport in fractured porous media, with applications geosciences and reservoir engineering and other application areas. TOUGH3 V1.0 supports a number of different combinations of fluids and components (updated equation-of-state (EOS) modules from previous versions of TOUGH, including EOS1, EOS2, EOS3, EOS4, EOS5, EOS7, EOS7R, EOS7C, EOS7CA, EOS8, EOS9, EWASG, TMVOC, ECO2N, and ECO2M). This upgrade includes (a) expanded list of updated equation-of-state (EOS) modules, (b) new hysteresis models, (c) new implementation of parallel and solver functionalities, (d) new linear solver options based on PETSc libraries, (e) new automatic buildmore » system that automatically downloads and builds third-party libraries and TOUGH3, (f) new printout in CSV format, (g) dynamic memory allocation, (h) various user features, and (i) bug fixes.« less

Large eddy simulation modeling of particle-laden flows in complex terrain

NASA Astrophysics Data System (ADS)

Salesky, S.; Giometto, M. G.; Chamecki, M.; Lehning, M.; Parlange, M. B.

2017-12-01

The transport, deposition, and erosion of heavy particles over complex terrain in the atmospheric boundary layer is an important process for hydrology, air quality forecasting, biology, and geomorphology. However, in situ observations can be challenging in complex terrain due to spatial heterogeneity. Furthermore, there is a need to develop numerical tools that can accurately represent the physics of these multiphase flows over complex surfaces. We present a new numerical approach to accurately model the transport and deposition of heavy particles in complex terrain using large eddy simulation (LES). Particle transport is represented through solution of the advection-diffusion equation including terms that represent gravitational settling and inertia. The particle conservation equation is discretized in a cut-cell finite volume framework in order to accurately enforce mass conservation. Simulation results will be validated with experimental data, and numerical considerations required to enforce boundary conditions at the surface will be discussed. Applications will be presented in the context of snow deposition and transport, as well as urban dispersion.

Multi-dimensional computer simulation of MHD combustor hydrodynamics

NASA Astrophysics Data System (ADS)

Berry, G. F.; Chang, S. L.; Lottes, S. A.; Rimkus, W. A.

1991-04-01

Argonne National Laboratory is investigating the nonreacting jet gas mixing patterns in an MHD second stage combustor by using a 2-D multiphase hydrodynamics computer program and a 3-D single phase hydrodynamics computer program. The computer simulations are intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may lead to improvement of the downstream MHD channel performance. A 2-D steady state computer model, based on mass and momentum conservation laws for multiple gas species, is used to simulate the hydrodynamics of the combustor in which a jet of oxidizer is injected into an unconfined cross stream gas flow. A 3-D code is used to examine the effects of the side walls and the distributed jet flows on the non-reacting jet gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

Revisiting kinetic boundary conditions at the surface of fuel droplet hydrocarbons: An atomistic computational fluid dynamics simulation

PubMed Central

Nasiri, Rasoul

2016-01-01

The role of boundary conditions at the interface for both Boltzmann equation and the set of Navier-Stokes equations have been suggested to be important for studying of multiphase flows such as evaporation/condensation process which doesn’t always obey the equilibrium conditions. Here we present aspects of transition-state theory (TST) alongside with kinetic gas theory (KGT) relevant to the study of quasi-equilibrium interfacial phenomena and the equilibrium gas phase processes, respectively. A two-state mathematical model for long-chain hydrocarbons which have multi-structural specifications is introduced to clarify how kinetics and thermodynamics affect evaporation/condensation process at the surface of fuel droplet, liquid and gas phases and then show how experimental observations for a number of n-alkane may be reproduced using a hybrid framework TST and KGT with physically reasonable parameters controlling the interface, gas and liquid phases. The importance of internal activation dynamics at the surface of n-alkane droplets is established during the evaporation/condensation process. PMID:27215897

A new high-performance 3D multiphase flow code to simulate volcanic blasts and pyroclastic density currents: example from the Boxing Day event, Montserrat

NASA Astrophysics Data System (ADS)

Ongaro, T. E.; Clarke, A.; Neri, A.; Voight, B.; Widiwijayanti, C.

2005-12-01

For the first time the dynamics of directed blasts from explosive lava-dome decompression have been investigated by means of transient, multiphase flow simulations in 2D and 3D. Multiphase flow models developed for the analysis of pyroclastic dispersal from explosive eruptions have been so far limited to 2D axisymmetric or Cartesian formulations which cannot properly account for important 3D features of the volcanic system such as complex morphology and fluid turbulence. Here we use a new parallel multiphase flow code, named PDAC (Pyroclastic Dispersal Analysis Code) (Esposti Ongaro et al., 2005), able to simulate the transient and 3D thermofluid-dynamics of pyroclastic dispersal produced by collapsing columns and volcanic blasts. The code solves the equations of the multiparticle flow model of Neri et al. (2003) on 3D domains extending up to several kilometres in 3D and includes a new description of the boundary conditions over topography which is automatically acquired from a DEM. The initial conditions are represented by a compact volume of gas and pyroclasts, with clasts of different sizes and densities, at high temperature and pressure. Different dome porosities and pressurization models were tested in 2D to assess the sensitivity of the results to the distribution of initial gas pressure, and to the total mass and energy stored in the dome, prior to 3D modeling. The simulations have used topographies appropriate for the 1997 Boxing Day directed blast on Montserrat, which eradicated the village of St. Patricks. Some simulations tested the runout of pyroclastic density currents over the ocean surface, corresponding to observations of over-water surges to several km distances at both locations. The PDAC code was used to perform 3D simulations of the explosive event on the actual volcano topography. The results highlight the strong topographic control on the propagation of the dense pyroclastic flows, the triggering of thermal instabilities, and the elutriation of finest particles, and demonstrated the formation of dense pyroclastic flows by drainage of clasts sedimented from dilute flows. Fundamental and accurate hazard information can be obtained from the simulations, and the 3D displays are readily comprehended by officials and the public, making them very effective tools for risk mitigation.

Simulating Water Flow in Variably Saturated Soils - Exploring the Advantage of Three-dimensional Models

NASA Astrophysics Data System (ADS)

Hopp, L.; Ivanov, V. Y.

2010-12-01

There is still a debate in rainfall-runoff modeling over the advantage of using three-dimensional models based on partial differential equations describing variably saturated flow vs. models with simpler infiltration and flow routing algorithms. Fully explicit 3D models are computationally demanding but allow the representation of spatially complex domains, heterogeneous soils, conditions of ponded infiltration, and solute transport, among others. Models with simpler infiltration and flow routing algorithms provide faster run times and are likely to be more versatile in the treatment of extreme conditions such as soil drying but suffer from underlying assumptions and ad-hoc parameterizations. In this numerical study, we explore the question of whether these two model strategies are competing approaches or if they complement each other. As a 3D physics-based model we use HYDRUS-3D, a finite element model that numerically solves the Richards equation for variably-saturated water flow. As an example of a simpler model, we use tRIBS+VEGGIE that solves the 1D Richards equation for vertical flow and applies Dupuit-Forchheimer approximation for saturated lateral exchange and gravity-driven flow for unsaturated lateral exchange. The flow can be routed using either the D-8 (steepest descent) or D-infinity flow routing algorithms. We study lateral subsurface stormflow and moisture dynamics at the hillslope-scale, using a zero-order basin topography, as a function of storm size, antecedent moisture conditions and slope angle. The domain and soil characteristics are representative of a forested hillslope with conductive soils in a humid environment, where the major runoff generating process is lateral subsurface stormflow. We compare spatially integrated lateral subsurface flow at the downslope boundary as well as spatial patterns of soil moisture. We illustrate situations where both model approaches perform equally well and identify conditions under which the application of a fully-explicit 3D model may be required for a realistic description of the hydrologic response.

Limitations of predicting in vivo biostability of multiphase polyurethane elastomers using temperature-accelerated degradation testing.

PubMed

Padsalgikar, Ajay; Cosgriff-Hernandez, Elizabeth; Gallagher, Genevieve; Touchet, Tyler; Iacob, Ciprian; Mellin, Lisa; Norlin-Weissenrieder, Anna; Runt, James

2015-01-01

Polyurethane biostability has been the subject of intense research since the failure of polyether polyurethane pacemaker leads in the 1980s. Accelerated in vitro testing has been used to isolate degradation mechanisms and predict clinical performance of biomaterials. However, validation that in vitro methods reproduce in vivo degradation is critical to the selection of appropriate tests. High temperature has been proposed as a method to accelerate degradation. However, correlation of such data to in vivo performance is poor for polyurethanes due to the impact of temperature on microstructure. In this study, we characterize the lack of correlation between hydrolytic degradation predicted using a high temperature aging model of a polydimethylsiloxane-based polyurethane and its in vivo performance. Most notably, the predicted molecular weight and tensile property changes from the accelerated aging study did not correlate with clinical explants subjected to human biological stresses in real time through 5 years. Further, DMTA, ATR-FTIR, and SAXS experiments on samples aged for 2 weeks in PBS indicated greater phase separation in samples aged at 85°C compared to those aged at 37°C and unaged controls. These results confirm that microstructural changes occur at high temperatures that do not occur at in vivo temperatures. In addition, water absorption studies demonstrated that water saturation levels increased significantly with temperature. This study highlights that the multiphase morphology of polyurethane precludes the use of temperature accelerated biodegradation for the prediction of clinical performance and provides critical information in designing appropriate in vitro tests for this class of materials. © 2014 Wiley Periodicals, Inc.

Helicity evolution at small-x

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2016-01-13

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of α s ln 2(1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation efects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c & N f limits. As a cross-check,more » in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.« less

A fundamental equation of state for 1,1-difluoroethane (HFC-152a)

NASA Astrophysics Data System (ADS)

Tillner-Roth, R.

1995-01-01

A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable ( p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.

Optimization of CW Fiber Lasers With Strong Nonlinear Cavity Dynamics

NASA Astrophysics Data System (ADS)

Shtyrina, O. V.; Efremov, S. A.; Yarutkina, I. A.; Skidin, A. S.; Fedoruk, M. P.

2018-04-01

In present work the equation for the saturated gain is derived from one-level gain equations describing the energy evolution inside the laser cavity. It is shown how to derive the parameters of the mathematical model from the experimental results. The numerically-estimated energy and spectrum of the signal are in good agreement with the experiment. Also, the optimization of the output energy is performed for a given set of model parameters.

Heuristic approach to capillary pressures averaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coca, B.P.

1980-10-01

Several methods are available to average capillary pressure curves. Among these are the J-curve and regression equations of the wetting-fluid saturation in porosity and permeability (capillary pressure held constant). While the regression equation seem completely empiric, the J-curve method seems to be theoretically sound due to its expression based on a relation between the average capillary radius and the permeability-porosity ratio. An analysis is given of each of these methods.

An Interpolation Method for Obtaining Thermodynamic Properties Near Saturated Liquid and Saturated Vapor Lines

NASA Technical Reports Server (NTRS)

Nguyen, Huy H.; Martin, Michael A.

2004-01-01

The two most common approaches used to formulate thermodynamic properties of pure substances are fundamental (or characteristic) equations of state (Helmholtz and Gibbs functions) and a piecemeal approach that is described in Adebiyi and Russell (1992). This paper neither presents a different method to formulate thermodynamic properties of pure substances nor validates the aforementioned approaches. Rather its purpose is to present a method to generate property tables from existing property packages and a method to facilitate the accurate interpretation of fluid thermodynamic property data from those tables. There are two parts to this paper. The first part of the paper shows how efficient and usable property tables were generated, with the minimum number of data points, using an aerospace industry standard property package. The second part describes an innovative interpolation technique that has been developed to properly obtain thermodynamic properties near the saturated liquid and saturated vapor lines.

Chaos and wave propagation regimes

NASA Astrophysics Data System (ADS)

Colosi, John

2003-04-01

Ray chaos theory and parabolic equation numerical modeling were two thrusts of Fred Tappert's research that were perpetually in tension. Fred was interested in the problem of identifying wave propagation regimes, most notably the strong focusing caustic regime and its evolution into the saturation regime. On the one hand, chaos theory held the seed of the complexity Fred believed existed in ocean acoustic wavefields; on the other hand ocean acoustic ray chaos theory (which Fred helped to pioneer) was a disdainful approximation to the full wave treatments offered by parabolic equation calculations. Fred was convinced that the saturation limit could not be obtained using ray theory and therefore he examined a new field of inquiry: a blend of chaotic ray insight and full wave dynamics called wave chaos. This talk will discuss some of Fred's insights on this topic and how they relate to observations from basin scale acoustic transmissions.

Transport of water and ions in partially water-saturated porous media. Part 2. Filtration effects

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

A new set of constitutive equations describing the transport of the ions and water through charged porous media and considering the effect of ion filtration is applied to the problem of reverse osmosis and diffusion of a salt. Starting with the constitutive equations derived in Paper 1, I first determine specific formula for the osmotic coefficient and effective diffusion coefficient of a binary symmetric 1:1 salt (such as KCl or NaCl) as a function of a dimensionless number Θ corresponding to the ratio between the cation exchange capacity (CEC) and the salinity. The modeling is first carried with the Donnan model used to describe the concentrations of the charge carriers in the pore water phase. Then a new model is developed in the thin double layer approximation to determine these concentrations. These models provide explicit relationships between the concentration of the ionic species in the pore space and those in a neutral reservoir in local equilibrium with the pore space and the CEC. The case of reverse osmosis and diffusion coefficient are analyzed in details for the case of saturated and partially saturated porous materials. Comparisons are done with experimental data from the literature obtained on bentonite. The model predicts correctly the influence of salinity (including membrane behavior at high salinities), porosity, cation type (K+ versus Na+), and water saturation on the osmotic coefficient. It also correctly predicts the dependence of the diffusion coefficient of the salt with the salinity.

Development of a Long-Column Method to Test Constitutive Relations for LNAPL Movement in Two-Phase Systems

NASA Astrophysics Data System (ADS)

Oostrom, M.; Zhong, L.; Wietsma, T.; Covert, M.

2007-12-01

Multifluid relative permeability - saturation - capillary pressure (k-S-P) empirical constitutive models are components of numerical simulators that are used to predict fluid distributions following a nonaqueous phase liquid (NAPL) contamination event or during remediation. The S-P parameter values for these empirical models are either obtained from the literature or determined experimentally by fitting the models to measured data. Most of the experimental emphasis so far has been on testing the S-P component of the k-S-P constitutive relations. Due to the difficulties in obtaining quality relative permeability laboratory data for multiphase systems, testing of the k-S models that are used in multifluid flow simulators has been virtually non-existent. A new tool, the Multiple Location Saturation Pressure Apparatus (MLSPA), located in PNNL's EMSL Subsurface Flow and Transport Laboratory, has been developed to obtain data sets that can be used to test both S-P and k-S relationships for two-phase NAPL-water systems. The MLSPA is a long column (~1 m) equipped with several hydrophilic and hydrophobic pressure transducers. Fluid saturations are determined along the length of a column using a dual-energy gamma radiation system. Although the MLSPA is limited to porous media with a relatively small entry pressure and fairly homogeneous pore-size distributions, it offers the distinct advantage of obtaining S-P data at multiple locations. Besides for static determinations of S-P relations, the MLSPA offers the benefit that it can be used for more dynamic experiments where fluid pressures are changed more rapidly. The data sets produced by the dynamic experiments can be used in relative permeability models. Results of several experiments with crude-oil brine systems will be presented.

Ground Water in the Southern Lihue Basin, Kauai, Hawaii

USGS Publications Warehouse

Izuka, Scot K.; Gingerich, Stephen B.

1998-01-01

A multi-phased study of ground-water resources, including well drilling, aquifer tests, analysis of ground-water discharge, and numerical ground-water modeling, indicates that the rocks of the southern Lihue Basin, Kauai, have permeabilities that are much lower than in most other areas of ground-water development in the Hawaiian islands. The regional hydraulic conductivity of the Koloa Volcanics, which dominates fresh ground-water flow in the basin, is about 0.275 foot per day. The Waimea Canyon Basalt which surrounds the basin and underlies the Koloa Volcanics within the basin is intruded by dikes that reduce the bulk hydraulic conductivity of the rocks to about 1.11 feet per day. The low permeabilities result in steeper head gradients compared with other areas in the Hawaiian islands, and a higher proportion of ground-water discharging to streams than to the ocean. Water levels rise from near sea level at the coast to several hundreds of feet above sea level at the center of the basin a few miles inland. The high inland water levels are part of a completely saturated ground-water system. Because of the low regional hydraulic conductivity and high influx of water from recharge in the southern Lihue Basin, the rocks become saturated nearly to the surface and a variably saturated/unsaturated (perched) condition is not likely to exist. Streams incising the upper part of the aquifer drain ground water and keep the water levels just below the surface in most places. Streams thus play an important role in shaping the water table in the southern Lihue Basin. At least 62 percent of the ground water discharging from the aquifer in the southern Lihue Basin seeps to streams; the remainder seeps directly to the ocean or is withdrawn by wells.

A Combined Micro-CT Imaging/Microfluidic Approach for Understating Methane Recovery in Coal Seam Gas Reservoirs

NASA Astrophysics Data System (ADS)

Mostaghimi, P.; Armstrong, R. T.; Gerami, A.; Lamei Ramandi, H.; Ebrahimi Warkiani, M.

2015-12-01

Coal seam methane is a form of natural gas stored in coal beds and is one of the most important unconventional resources of energy. The flow and transport in coal beds occur in a well-developed system of natural fractures that are also known as cleats. We use micro-Computed Tomography (CT) imaging at both dry and wet conditions to resolve the cleats below the resolution of the image. Scanning Electron Microscopy (SEM) is used for calibration of micro-CT data. Using soft lithography technique, the cleat system is duplicated on a silicon mould. We fabricate a microfluidic chip using Polydimethylsiloxane (PDMS) to study both imbibition and drainage in generated coal structures for understating gas and water transport in coal seam reservoirs. First, we use simple patterns observed on coal images to analyse the effects of wettability, cleat size and distribution on flow behaviour. Then, we study transport in a coal by injecting both distilled water and decane with a rate of 1 microliter/ min into the fabricated cleat structure (Figure 1), initially saturated with air. We repeat the experiment for different contact angles by plasma treating the microfluidic chip, and results show significant effects of wettability on the displacement efficiency. The breakthrough time in the imbibition setup is significantly longer than in the drainage. Using rapid video capturing, and high resolution microscopy, we measure the saturation of displacing fluid with respect to time. By measuring gas and liquid recovery in the outlet at different saturation, we predict relative permeability of coal. This work has important applications for optimising gas recovery and our results can serve as a benchmark in the verification of multiphase numerical models used in coal seam gas industry.

Computational Design for Multifunctional Microstructural Composites

NASA Astrophysics Data System (ADS)

Chen, Yuhang; Zhou, Shiwei; Li, Qing

As an important class of natural and engineered materials, periodic microstructural composites have drawn substantial attention from the material research community for their excellent flexibility in tailoring various desirable physical behaviors. To develop periodic cellular composites for multifunctional applications, this paper presents a unified design framework for combining stiffness and a range of physical properties governed by quasi-harmonic partial differential equations. A multiphase microstructural configuration is sought within a periodic base-cell design domain using topology optimization. To deal with conflicting properties, e.g. conductivity/permeability versus bulk modulus, the optimum is sought in a Pareto sense. Illustrative examples demonstrate the capability of the presented procedure for the design of multiphysical composites and tissue scaffolds.

A model and numerical method for compressible flows with capillary effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmidmayer, Kevin, E-mail: kevin.schmidmayer@univ-amu.fr; Petitpas, Fabien, E-mail: fabien.petitpas@univ-amu.fr; Daniel, Eric, E-mail: eric.daniel@univ-amu.fr

2017-04-01

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results onmore » droplet breakup induced by a shock wave.« less

Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

PubMed

Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping

2011-02-01

We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity. ©2011 American Physical Society

Ideal solar cell equation in the presence of photon recycling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lan, Dongchen, E-mail: d.lan@unsw.edu.au; Green, Martin A., E-mail: m.green@unsw.edu.au

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

Hydrate Formation in Gas-Rich Marine Sediments: A Grain-Scale Model

NASA Astrophysics Data System (ADS)

Holtzman, R.; Juanes, R.

2009-12-01

We present a grain-scale model of marine sediment, which couples solid- and multiphase fluid-mechanics together with hydrate kinetics. The model is applied to investigate the spatial distribution of the different methane phases - gas and hydrate - within the hydrate stability zone. Sediment samples are generated from three-dimensional packs of spherical grains, mapping the void space into a pore network by tessellation. Gas invasion into the water-saturated sample is simulated by invasion-percolation, coupled with a discrete element method that resolves the grain mechanics. The coupled model accounts for forces exerted by the fluids, including cohesion associated with gas-brine surface tension. Hydrate growth is represented by a hydrate film along the gas-brine interface, which increases sediment cohesion by cementing the grain contacts. Our model of hydrate growth includes the possible rupture of the hydrate layer, which leads to the creation of new gas-water interface. In previous work, we have shown that fine-grained sediments (FGS) exhibit greater tendency to fracture, whereas capillary invasion is the preferred mode of methane gas transport in coarse-grained sediments (CGS). The gas invasion pattern has profound consequences on the hydrate distribution: a larger area-to-volume ratio of the gas cluster leads to a larger drop in gas pressure inside the growing hydrate shell, causing it to rupture. Repeated cycles of imbibition and hydrate growth accompanied by trapping of gas allow us to determine the distribution of hydrate and gas within the sediment as a function of time. Our pore-scale model suggests that, even when film rupture takes place, the conversion of gas to hydrate is slow. This explains two common field observations: the coexistence of gas and hydrate within the hydrate stability zone in CGS, and the high methane fluxes through fracture conduits in FGS. These results demonstrate the importance of accounting for the strong coupling among multiphase flow, sediment mechanics, and hydrate formation. Our model explains the remarkable differences in hydrate distribution and saturation between fine- and coarse-grained sediments, and promotes the quantitative understanding of the role of methane hydrate in seafloor stability and the global carbon cycle, including the size of the hydrate energy resource, and estimates of methane fluxes into the ocean and the atmosphere.

FOREWORD: International Symposium of Cavitation and Multiphase Flow (ISCM 2014)

NASA Astrophysics Data System (ADS)

Wu, Yulin

2015-01-01

The International Symposium on Cavitation and Multiphase Flow (ISCM 2014) was held in Beijing, China during 18th-21st October, 2014, which was jointly organized by Tsinghua University, Beijing, China and Jiangsu University, Zhenjiang, China. The co-organizer was the State Key Laboratory of Hydroscience and Engineering, Beijing, China. Cavitation and multiphase flow is one of paramount topics of fluid mechanics with many engineering applications covering a broad range of topics, e.g. hydraulic machinery, biomedical engineering, chemical and process industry. In order to improve the performances of engineering facilities (e.g. hydraulic turbines) and to accelerate the development of techniques for medical treatment of serious diseases (e.g. tumors), it is essential to improve our understanding of cavitation and Multiphase Flow. For example, the present development towards the advanced hydrodynamic systems (e.g. space engine, propeller, hydraulic machinery system) often requires that the systems run under cavitating conditions and the risk of cavitation erosion needs to be controlled. The purpose of the ISCM 2014 was to discuss the state-of-the-art cavitation and multiphase flow research and their up-to-date applications, and to foster discussion and exchange of knowledge, and to provide an opportunity for the researchers, engineers and graduate students to report their latest outputs in these fields. Furthermore, the participants were also encouraged to present their work in progress with short lead time and discuss the encountered problems. ISCM 2014 covers all aspects of cavitation and Multiphase Flow, e.g. both fundamental and applied research with a focus on physical insights, numerical modelling and applications in engineering. Some specific topics are: Cavitating and Multiphase Flow in hydroturbines, pumps, propellers etc. Numerical simulation techniques Cavitation and multiphase flow erosion and anti-erosion techniques Measurement techniques for cavitation and multiphase flow detection Fluid-structure interaction induced by cavitation and multiphase flow Multi-scale modelling of cavitating flows and Multiphase Flow Cavitation nuclei: theory and experiments Supercavitation and its applications Synergetic effects of cavitation and silt-laden erosion Shock waves and microjets generated by cavitation Nonlinear oscillations of gas and vapour bubbles Fundamentals of physics of acoustic cavitation Sonochemistry and sonoluminescence Biomedical applications of cavitation effects Ultrasonic cavitation for molten metal treatment Cavitation for enhanced heat transfer The ISCM 2014 brought together 95 scientists, researchers and graduate students from 11 countries, affiliated with universities, technology centers and industrial firms to debate topics related to advanced technologies for cavitation and Multiphase Flow, which would enhance the sustainable development of cavitation and Multiphase Flow in interdisciplinary sciences and technology. The technical committee selected 54 technical papers on the following topics: (i) Hydrodynamic Cavitation, (ii) Super Cavitation, (iii) Pump Cavitation, (iv) Acoustic Cavitation, (v) Interdisciplinary Research of Cavitation and Multi-Phase Flows, and 13 invited plenary and invited forum lectures, which were presented at the symposium, to be included in the proceedings. All the papers of ISCM 2014, which are published in this Volume of IOP Conference Series: Materials Science and Engineering, had been peer reviewed through processes administered by the editors of the ISCM 2014, those are Yulin WU, Shouqi YUAN, Zhengwei WANG, Shuhong LIU, Xingqi LUO, Fujun WANG and Guoyu WANG. The papers published in this Volume include 54 technical papers and 3 full length texts of the invited lectures. We sincerely hope that the International Symposium on Cavitation and Multiphase Flow is a significant step forward in the world wide efforts to address the present challenges in the modern science and technology. Professor Yulin WU Chairman of the Local Organizing Committee International Symposium on Cavitation and Multiphase Flow (ISCM 2014) October, 2014

3D seismic modeling in geothermal reservoirs with a distribution of steam patch sizes, permeabilities and saturations, including ductility of the rock frame

NASA Astrophysics Data System (ADS)

Carcione, José M.; Poletto, Flavio; Farina, Biancamaria; Bellezza, Cinzia

2018-06-01

Seismic propagation in the upper part of the crust, where geothermal reservoirs are located, shows generally strong velocity dispersion and attenuation due to varying permeability and saturation conditions and is affected by the brittleness and/or ductility of the rocks, including zones of partial melting. From the elastic-plastic aspect, the seismic properties (seismic velocity, quality factor and density) depend on effective pressure and temperature. We describe the related effects with a Burgers mechanical element for the shear modulus of the dry-rock frame. The Arrhenius equation combined to the octahedral stress criterion define the Burgers viscosity responsible of the brittle-ductile behaviour. The effects of permeability, partial saturation, varying porosity and mineral composition on the seismic properties is described by a generalization of the White mesoscopic-loss model to the case of a distribution of heterogeneities of those properties. White model involves the wave-induced fluid flow attenuation mechanism, by which seismic waves propagating through small-scale heterogeneities, induce pressure gradients between regions of dissimilar properties, where part of the energy of the fast P-wave is converted to slow P (Biot)-wave. We consider a range of variations of the radius and size of the patches and thin layers whose probability density function is defined by different distributions. The White models used here are that of spherical patches (for partial saturation) and thin layers (for permeability heterogeneities). The complex bulk modulus of the composite medium is obtained with the Voigt-Reuss-Hill average. Effective pressure effects are taken into account by using exponential functions. We then solve the 3D equation of motion in the space-time domain, by approximating the White complex bulk modulus with that of a set of Zener elements connected in series. The Burgers and generalized Zener models allows us to solve the equations with a direct grid method by the introduction of memory variables. The algorithm uses the Fourier pseudospectral method to compute the spatial derivatives. It is tested against an analytical solution obtained with the correspondence principle. We consider two main cases, namely the same rock frame (uniform porosity and permeability) saturated with water and a distribution of steam patches, and water-saturated background medium with thin layers of dissimilar permeability. Our model indicates how seismic properties change with the geothermal reservoir temperature and pressure, showing that both seismic velocity and attenuation can be used as a diagnostic tool to estimate the in situ conditions.

A Multi-Fidelity Surrogate Model for the Equation of State for Mixtures of Real Gases

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Koneru, Rahul; Balachandar, S.; Rollin, Bertrand

2017-11-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the products of detonated explosives must be treated as real gases while the ideal gas equation of state is used for the ambient air. As the products expand outward, they mix with the air and create a region where both state equations must be satisfied. One of the most accurate, yet expensive, methods to handle this problem is an algorithm that iterates between both state equations until both pressure and thermal equilibrium are achieved inside of each computational cell. This work creates a multi-fidelity surrogate model to replace this process. This is achieved by using a Kriging model to produce a curve fit which interpolates selected data from the iterative algorithm. The surrogate is optimized for computing speed and model accuracy by varying the number of sampling points chosen to construct the model. The performance of the surrogate with respect to the iterative method is tested in simulations using a finite volume code. The model's computational speed and accuracy are analyzed to show the benefits of this novel approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Analysis of a Multi-Fidelity Surrogate for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S.

2017-06-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the detonation products of the explosive must be treated as real gas while the ideal gas equation of state is used for the surrounding air. As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both state equations must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between both equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work aims to use a multi-fidelity surrogate model to replace this process. A Kriging model is used to produce a curve fit which interpolates selected data from the iterative algorithm using Bayesian statistics. We study the model performance with respect to the iterative method in simulations using a finite volume code. The model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel approach. Also, optimizing the combination of model accuracy and computational speed through the choice of sampling points is explained. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program as a Cooperative Agreement under the Predictive Science Academic Alliance Program under Contract No. DE-NA0002378.

H-division quarterly report, October--December 1977. [Lawrence Livermore Laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1978-02-10

The Theoretical EOS Group develops theoretical techniques for describing material properties under extreme conditions and constructs equation-of-state (EOS) tables for specific applications. Work this quarter concentrated on a Li equation of state, equation of state for equilibrium plasma, improved ion corrections to the Thomas--Fermi--Kirzhnitz theory, and theoretical estimates of high-pressure melting in metals. The Experimental Physics Group investigates properties of materials at extreme conditions of pressure and temperature, and develops new experimental techniques. Effort this quarter concerned the following: parabolic projectile distortion in the two-state light-gas gun, construction of a ballistic range for long-rod penetrators, thermodynamics and sound velocities inmore » liquid metals, isobaric expansion measurements in Pt, and calculation of the velocity--mass profile of a jet produced by a shaped charge. Code development was concentrated on the PELE code, a multimaterial, multiphase, explicit finite-difference Eulerian code for pool suppression dynamics of a hypothetical loss-of-coolant accident in a nuclear reactor. Activities of the Fluid Dynamics Group were directed toward development of a code to compute the equations of state and transport properties of liquid metals (e.g. Li) and partially ionized dense plasmas, jet stability in the Li reactor system, and the study and problem application of fluid dynamic turbulence theory. 19 figures, 5 tables. (RWR)« less

Dissipative Dynamics with Exotic Beams

NASA Astrophysics Data System (ADS)

di Toro, M.; Colonna, M.; Greco, V.; Ferini, G.; Rizzo, C.; Rizzo, J.; Baran, V.; Wolter, H. H.; Zielinska-Pfabe, M.

2008-04-01

Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation and at high nucleon momenta. In this report we present a selection of reaction observables particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS) At low and Fermi energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. Predictions are shown for fusion, deep-inelastic and fragmentation collisions induced by neutron rich projectiles. At all energies the isospin transport data are supplying valuable information on value and slope of the symmetry term below saturation. The importance of studying violent collisions with radioactive beams in this energy range is finally stressed.

Unsaturated hydraulic properties of Sphagnum moss and peat reveal trimodal pore-size distributions

NASA Astrophysics Data System (ADS)

Weber, Tobias K. D.; Iden, Sascha C.; Durner, Wolfgang

2017-01-01

In ombrotrophic peatlands, the moisture content of the vadose zone (acrotelm) controls oxygen diffusion rates, redox state, and the turnover of organic matter. Whether peatlands act as sinks or sources of atmospheric carbon thus relies on variably saturated flow processes. The Richards equation is the standard model for water flow in soils, but it is not clear whether it can be applied to simulate water flow in live Sphagnum moss. Transient laboratory evaporation experiments were conducted to observe evaporative water fluxes in the acrotelm, containing living Sphagnum moss, and a deeper layer containing decomposed moss peat. The experimental data were evaluated by inverse modeling using the Richards equation as process model for variably-saturated flow. It was tested whether water fluxes and time series of measured pressure heads during evaporation could be simulated. The results showed that the measurements could be matched very well providing the hydraulic properties are represented by a suitable model. For this, a trimodal parametrization of the underlying pore-size distribution was necessary which reflects three distinct pore systems of the Sphagnum constituted by inter-, intra-, and inner-plant water. While the traditional van Genuchten-Mualem model led to great discrepancies, the physically more comprehensive Peters-Durner-Iden model which accounts for capillary and noncapillary flow, led to a more consistent description of the observations. We conclude that the Richards equation is a valid process description for variably saturated moisture fluxes over a wide pressure range in peatlands supporting the conceptualization of the live moss as part of the vadose zone.

Correcting reaction rates measured by saturation-transfer magnetic resonance spectroscopy

NASA Astrophysics Data System (ADS)

Gabr, Refaat E.; Weiss, Robert G.; Bottomley, Paul A.

2008-04-01

Off-resonance or spillover irradiation and incomplete saturation can introduce significant errors in the estimates of chemical rate constants measured by saturation-transfer magnetic resonance spectroscopy (MRS). Existing methods of correction are effective only over a limited parameter range. Here, a general approach of numerically solving the Bloch-McConnell equations to calculate exchange rates, relaxation times and concentrations for the saturation-transfer experiment is investigated, but found to require more measurements and higher signal-to-noise ratios than in vivo studies can practically afford. As an alternative, correction formulae for the reaction rate are provided which account for the expected parameter ranges and limited measurements available in vivo. The correction term is a quadratic function of experimental measurements. In computer simulations, the new formulae showed negligible bias and reduced the maximum error in the rate constants by about 3-fold compared to traditional formulae, and the error scatter by about 4-fold, over a wide range of parameters for conventional saturation transfer employing progressive saturation, and for the four-angle saturation-transfer method applied to the creatine kinase (CK) reaction in the human heart at 1.5 T. In normal in vivo spectra affected by spillover, the correction increases the mean calculated forward CK reaction rate by 6-16% over traditional and prior correction formulae.