The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model

Biot-flow and squirt-flow are the two most important fluid flow mechanisms in porous media containing fluids. Based on the BISQ （Biot-Squirt） model where the two mechanisms are treated simultaneously, the elastic wave-field simulation in the porous medium is limited to two-dimensions and two-components （2D2C） or two-dimensions and three-components （2D3C）. There is no previous report on wave simulation in three- dimensions and three-components. Only through three dimensional numerical simulations can we have an overall understanding of wave field coupling relations and the spatial distribution characteristics between the solid and fluid phases in the dual-phase anisotropic medium. In this paper, based on the BISQ equation, we present elastic wave propagation in a three dimensional dual-phase anisotropic medium simulated by the staggered-grid high-order finite-difference method. We analyze the resulting wave fields and show that the results are an improvement.

Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media

To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling.

AVO forwarding modeling in two-phase media: multiconstrained matrix mineral modulus inversion

AVO forward modeling is based on two-phase medium theory and is considered an effective method for describing reservoir rocks and fluids. However, the method depends on the input matrix mineral bulk modulus and the rationality of the two-phase medium model. We used the matrix mineral bulk modulus inversion method and multiple constraints to obtain a two-phase medium model with physical meaning. The proposed method guarantees the reliability of the obtained AVO characteristicsin two-phase media. By the comparative analysis of different lithology of the core sample, the advantages and accuracy of the inversion method can be illustrated. Also, the inversion method can be applied in LH area, and the AVO characteristics can be obtained when the porosity, fluid saturation, and other important lithology parameters are changed. In particular, the reflection coefficient amplitude difference between the fast P wave and S wave as a function of porosity at the same incidence angle, and the difference in the incidence angle threshold can be used to decipher porosity.

Pore-Scale Investigation of Coupled Two-Phase and Reactive Transport in the Cathode Electrode of Proton Exchange Membrane Fuel Cells

A three-dimensional multicomponent multiphase lattice Boltzmann model(LBM)is established to model the coupled two-phase and reactive transport phenomena in the cathode electrode of proton exchange membrane fuel cells.The gas diff usion layer(GDL)and microporous layer(MPL)are stochastically reconstructed with the inside dynamic distribution of oxygen and liquid water resolved,and the catalyst layer is simplifi ed as a superthin layer to address the electrochemical reaction,which provides a clear description of the fl ooding eff ect on mass transport and performance.Diff erent kinds of electrodes are reconstructed to determine the optimum porosity and structure design of the GDL and MPL by comparing the transport resistance and per-formance under the fl ooding condition.The simulation results show that gradient porosity GDL helps to increase the reactive area and average concentration under fl ooding.The presence of the MPL ensures the oxygen transport space and reaction area because liquid water cannot transport through micropores.Moreover,the MPL helps in the uniform distribution of oxygen for an effi cient in-plane transport capacity.Crack and perforation structures can accelerate the water transport in the assembly.The systematic perforation design yields the best performance under fl ooding by separating the transport of liquid water and oxygen.

A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM-Θ model is also better than the k-ε-kp-Θ model and the k-ε-kp-εp-Θ model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.

Coupled Model of Two-phase Debris Flow,Sediment Transport and Morphological Evolution

The volume fraction of the solid and liquid phase of debris flows, which evolves simultaneously across terrains, largely determines the dynamic property of debris flows. The entrainment process significantly influences the amplitude of the volume fraction. In this paper, we present a depth-averaged two-phase debris-flow model describing the simultaneous evolution of the phase velocity and depth, the solid and fluid volume fractions and the bed morphological evolution. The model employs the Mohr–Coulomb plasticity for the solid stress, and the fluid stress is modeled as a Newtonian viscous stress. The interfacial momentum transfer includes viscous drag and buoyancy. A new extended entrainment rate formula that satisfies the boundary momentum jump condition （Iverson and Ouyang, 2015） is presented. In this formula, the basal traction stress is a function of the solid volume fraction and can take advantage of both the Coulomb and velocity-dependent friction models. A finite volume method using Roe’s Riemann approximation is suggested to solve the equations. Three computational cases are conducted and compared with experiments or previous results. The results show that the current computational model and framework are robust and suitable for capturing the characteristics of debris flows.

REVIEW ON MATHEMATICAL ANALYSIS OF SOME TWO-PHASE FLOW MODELS

The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.

Comparison of a Full Second-Order Moment Model and an Algebraic Stress Two-Phase Turbulence Model for Simulating Bubble-Liquid Flows in a Bubble Column

A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM

In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations.

Transient pressure analysis of polymer flooding fractured wells with oil-water two-phase flow

The oil-water two-phase flow pressure-transient analysis model for polymer flooding fractured well is established by considering the comprehensive effects of polymer shear thinning,shear thickening,convection,diffusion,adsorption retention,inaccessible pore volume and effective permeability reduction.The finite volume difference and Newton iteration methods are applied to solve the model,and the effects of fracture conductivity coefficient,injected polymer mass concentration,initial polymer mass concentration and water saturation on the well-test type curves of polymer flooding fractured wells are discussed.The results show that with the increase of fracture conductivity coefficient,the pressure conduction becomes faster and the pressure drop becomes smaller,so the pressure curve of transitional flow goes downward,the duration of bilinear flow becomes shorter,and the linear flow appears earlier and lasts longer.As the injected polymer mass concentration increases,the effective water phase viscosity increases,and the pressure loss increases,so the pressure and pressure derivative curves go upward,and the bilinear flow segment becomes shorter.As the initial polymer mass concentration increases,the effective water phase viscosity increases,so the pressure curve after the wellbore storage segment moves upward as a whole.As the water saturation increases,the relative permeability of water increases,the relative permeability of oil decreases,the total oil-water two-phase mobility becomes larger,and the pressure loss is reduced,so the pressure curve after the wellbore storage segment moves downward as a whole.The reliability and practicability of this new model are verified by the comparison of the results from simplified model and commercial well test software,and the actual well test data.

Two-phase nonlocal integral models with a bi-Helmholtz averaging kernel for nanorods

In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform technique.The unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform process.In the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary edges.The effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.

Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.

THE STUDY ON THREE-DIMENSIONAL MATHEMATICAL MODEL OF RIVER BED EROSION FOR WATER-SEDIMENT TWO-PHASE FLOW

Based on the tensor analysis of water-sediment two-phase how, the basic model equations for clear water flow and sediment-laden flow are deduced in the general curve coordinates for natural water variable-density turbulent how. Furthermore, corresponding boundary conditions are also presented in connection with the composition and movement of non-uniform bed material. The theoretical results are applied to the calculation of the float open caisson in the construction period and good results are obtained.

LARGE TIME BEHAVIOR OF GLOBAL STRONG SOLUTIONS TO A TWO-PHASE MODEL WITH A MAGNETIC FIELD

In this paper,the Cauchy problem for a two-phase model with a magnetic field in three dimensions is considered.Based on a new linearized system with respect to(c−c_(∞),P−P_(∞),u,H)for constants c_(∞)≥0 and P_(∞)>0,the existence theory of global strong solution is established when the initial data is close to its equilibrium in three dimensions for the small H^(2) initial data.We improve the existence results obtained by Wen and Zhu in[40]where an additional assumption that the initial perturbations are bounded in L^(1)-norm was needed.The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence.As a by-product,the time decay estimates of the solution and its derivatives in the L^(2)-norm are obtained.

CFD studies of scraper built in SPA clarifying tank based on mixture solid-liquid two-phase flow model

In the industrial process of producing the strong phosphoric acid(SPA),clarification of the solution is essential to the ultimate product.However,the large viscosity of sediment and the induced interface interaction result in difficulties when the SPA is clarified.CFD numerical methodology was applied to simulate internal flow field and performance of the low speed scraper based on Mixture solidliquid two-phase flow model.Sediment deposition was generated by loading solid particles at the bottom of clarifying vessel.The moving mesh and RNG k-εmodel were used to simulate the rotational turbulent flow in clarifying tank.Variables studied,amongst others,were the scraper rotation speed and the mounting height,which could affect the solid suspension height.Features of flow field and solid volume fraction distribution in computational domain were presented and analyzed.The numerical reports of the scraper torque and velocities of inlet and outlet filed were obtained.It seems the torque value of rotatio-nal axis and particle suspending height augment with an increasing rotating speed.Meanwhile,a high revolving speed is good for the deposition discharge.The particle fraction distribution in meridional surface and horizontal surface at fixed rotation speed were analyzed to determine the corresponding optimal installation height.The simulating results reflect the flow field is marginally stirred by the scraper and proper working parameters are obtained,in which case the comprehensive properties of the scraper and the clarifying tank are superior.

Measurement of Mass Transfer Coefficients and Their Modelling of Continuous Counter-Current Aqueous Two-Phase System in a Packed Extraction Column

Overall dispersed side volumetric mass transfer coefficients for protein and amino acids were measured in continuous countercurrent PEG4000/KHP aqueous two-phase systems in a 57mm I.D. packed extraction column. A model for overall dispersed side volumetric mass transfer coefficients was derived by describing the motion of the drops based upon Navier-Stokes equation combined with the relationship between mass transfer coefficients and the drop velocity. The model provides good predictions and can be successfully used in aqueous two-phase extraction. The average relative deviation between calculated values and experimental data ranges from 8% to 14%.

A Numerical Sirnulation of Gas-Particle Two-Phase Flow in a Suspension Bed Using DifFusion Flux Model

A mathematical modei of two-dimensional turbulent gas-particle twophase flow based on the modified diffusion flux modei (DFM) and a numerical simulation method to analyze the gas-particle flow structures are developed. The modified diffusion flux modei, in which the acceleration due to various forces is taken into account for the calculation of the diffusion velocity of particles, is applicable to the analysis of multi-dimensional gas-particle two-phase turbulent flow. In order to verify its accuracy and efficiency, the numerical simulation by DFM is compared with experimental studies and the prediction by k-ε-kp two-fluid modei, which shows a reasonable agreement. It is confirmed that the modified diffusion flux modei is suitable for simulating the multi-dimensional gas-particle two-phase flow.

Heat transfer model of two-phase flow across tube bundle in submerged combustion vaporizer

In order to optimize the design of the submerged combustion vaporizer(SCV), an experimental apparatus was set up to investigate the heat transfer character outside the tube bundle in SCV. Several experiments were conducted using water and CO_2 as the heat transfer media in the tubes, respectively. The results indicated that hot air flux, the initial liquid level height and the tube pitch ratio had great influence on the heat transfer coefficient outside the tube bundle(ho). Finally, the air flux associated factor β and height associated factor γ were introduced to propose a new hocorrelation. After verified by experiments using cold water, high pressure CO_2 and liquid N_2 as heat transfer media, respectively, it was found that the biggest deviation between the predicted and the experimental values was less than 25%.

A K-εTWO-EQUATION TURBULENCE MODEL FOR THE SOLID-LIQUID TWO-PHASE FLOWS

A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.