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Journal articles on the topic 'Immiscible two-Phase flow'

Author: Grafiati

Published: 30 November 2024

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1

Deng, Yongbo, Zhenyu Liu, and Yihui Wu. "Topology Optimization of Capillary, Two-Phase Flow Problems." Communications in Computational Physics 22, no. 5 (October 31, 2017): 1413–38. http://dx.doi.org/10.4208/cicp.oa-2017-0003.

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AbstractThis paper presents topology optimization of capillary, the typical two-phase flow with immiscible fluids, where the level set method and diffuse-interface model are combined to implement the proposed method. The two-phase flow is described by the diffuse-interface model with essential no slip condition imposed on the wall, where the singularity at the contact line is regularized by the molecular diffusion at the interface between two immiscible fluids. The level set method is utilized to express the fluid and solid phases in the flows and the wall energy at the implicit fluid-solid interface. Based on the variational procedure for the total free energy of two-phase flow, the Cahn-Hilliard equations for the diffuse-interface model are modified for the two-phase flow with implicit boundary expressed by the level set method. Then the topology optimization problem for the two-phase flow is constructed for the cost functional with general formulation. The sensitivity analysis is implemented by using the continuous adjoint method. The level set function is evolved by solving the Hamilton-Jacobian equation, and numerical test is carried out for capillary to demonstrate the robustness of the proposed topology optimization method. It is straightforward to extend this proposed method into the other two-phase flows with two immiscible fluids.

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2

Sun, Wen Tao, and Huai Yu Zhang. "Finite element method for two-phase immiscible flow." Numerical Methods for Partial Differential Equations 15, no. 4 (July 1999): 407–16. http://dx.doi.org/10.1002/(sici)1098-2426(199907)15:4<407::aid-num1>3.0.co;2-w.

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3

Mitrović, Darko, and Andrej Novak. "Two-Phase Nonturbulent Flow with Applications." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/439704.

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We model dynamics of two almost immiscible fluids of different densities using the Stokes equations with the Dirac distribution representing the sink or source point. The equations are solved by regularizing the Dirac distribution and then using an iterative procedure based on the finite element method. Results have potential applications in water pollution problems and we present two relevant situations. In the first one, we simulate extraction of a light liquid trapped at the bottom of a pond/lake and, after being disturbed, it rises toward the surface. In the second case, we simulate heavy liquid leaking from a source and slowly dropping on an uneven bottom.

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4

Shao, Sihong, and Tiezheng Qian. "A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces." Communications in Computational Physics 11, no. 3 (March 2012): 831–62. http://dx.doi.org/10.4208/cicp.071210.040511a.

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AbstractWe develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the On-sager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.

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5

Langlo, Peder, and Magne S. Espedal. "Macrodispersion for two-phase, immiscible flow in porous media." Advances in Water Resources 17, no. 5 (January 1994): 297–316. http://dx.doi.org/10.1016/0309-1708(94)90033-7.

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6

Chen, Zhangxin. "Numerical Analysis for Two-phase Flow in Porous Media." Computational Methods in Applied Mathematics 3, no. 1 (2003): 59–75. http://dx.doi.org/10.2478/cmam-2003-0006.

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Abstract In this paper we derive error estimates for finite element approximations for partial differential systems which describe two-phase immiscible flows in porous media. These approximations are based on mixed finite element methods for pressure and velocity and characteristic finite element methods for saturation. Both incompressible and compressible flows are considered. Error estimates of optimal order are obtained.

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7

YEH, LI-MING. "ON TWO-PHASE FLOW IN FRACTURED MEDIA." Mathematical Models and Methods in Applied Sciences 12, no. 08 (August 2002): 1075–107. http://dx.doi.org/10.1142/s0218202502002045.

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A model describing two-phase, incompressible, immiscible flow in fractured media is discussed. A fractured medium is regarded as a porous medium consisting of two superimposed continua, a continuous fracture system and a discontinuous system of medium-sized matrix blocks. Transport of fluids through the medium is primarily within the fracture system. No flow is allowed between blocks, and only matrix-fracture flow is possible. Matrix block system plays the role of a global source distributed over the entire medium. Two-phase flow in a fractured medium is strongly related to phase mobilities and capillary pressures. In this work, four relations for these functions are presented, and the existence of weak solutions under each relation will also be shown.

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8

Xu, Peng, Ming-Zhou Yu, Shu-Xia Qiu, and Bo-Ming Yu. "Monte Carlo simulation of a two-phase flow in an unsaturated porous media." Thermal Science 16, no. 5 (2012): 1382–85. http://dx.doi.org/10.2298/tsci1205382x.

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Relative permeability is a significant transport property which describes the simultaneous flow of immiscible fluids in porous media. A pore-scale physical model is developed for the two-phase immiscible flow in an unsaturated porous media according to the statistically fractal scaling laws of natural porous media, and a predictive calculation of two-phase relative permeability is presented by Monte Carlo simulation. The tortuosity is introduced to characterize the highly irregular and convoluted property of capillary pathways for fluid flow through a porous medium. The computed relative permeabilities are compared with empirical formulas and experimental measurements to validate the current model. The effect of fractal dimensions and saturation on the relative permeabilities is also discussed

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9

HOWISON, SAM D. "A note on the two-phase Hele-Shaw problem." Journal of Fluid Mechanics 409 (April 25, 2000): 243–49. http://dx.doi.org/10.1017/s0022112099007740.

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We discuss some techniques for finding explicit solutions to immiscible two-phase flow in a Hele-Shaw cell, exploiting properties of the Schwartz function of the interface between the fluids. We also discuss the question of the well-posedness of this problem.

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10

Kačur, Jozef, Benny Malengier, and Pavol Kišon. "Numerical Modeling of Two Phase Flow under Centrifugation." Defect and Diffusion Forum 326-328 (April 2012): 221–26. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.221.

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Numerical modeling of two-phase flow under centrifugation is presented in 1D.A new method is analysed to determine capillary-pressure curves. This method is based onmodeling the interface between the zone containing only wetting liquid and the zone containingwetting and non wetting liquids. This interface appears when into a fully saturated sample withwetting liquid we inject a non-wetting liquid. By means of this interface an efficient and correctnumerical approximation is created based upon the solution of ODE and DAE systems. Bothliquids are assumed to be immiscible and incompressible. This method is a good candidate tobe used in solution of inverse problem. Some numerical experiments are presented.

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11

Dongxiao, Zhang, and Hamdi Tchelepi. "Stochastic Analysis of Immiscible Two-Phase Flow in Heterogeneous Media." SPE Journal 4, no. 04 (December 1, 1999): 380–88. http://dx.doi.org/10.2118/59250-pa.

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12

Valdes-Parada, Francisco J., and G. Espinosa-Paredes. "Darcy's Law for Immiscible Two-Phase Flow: A Theoretical Development." Journal of Porous Media 8, no. 6 (2005): 557–67. http://dx.doi.org/10.1615/jpormedia.v8.i6.20.

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13

Riaz, Amir, and Hamdi A. Tchelepi. "Numerical simulation of immiscible two-phase flow in porous media." Physics of Fluids 18, no. 1 (January 2006): 014104. http://dx.doi.org/10.1063/1.2166388.

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14

TSUMAYA, Akira, and Hirotada OHASHI. "Immiscible Lattice Gases for Two-Phase Flow with Different Densities." Transactions of the Japan Society of Mechanical Engineers Series B 67, no. 659 (2001): 1687–93. http://dx.doi.org/10.1299/kikaib.67.1687.

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15

Saad, Mazen. "Slightly compressible and immiscible two-phase flow in porous media." Nonlinear Analysis: Real World Applications 15 (January 2014): 12–26. http://dx.doi.org/10.1016/j.nonrwa.2013.04.008.

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16

Sinha, Santanu, and Alex Hansen. "Effective rheology of immiscible two-phase flow in porous media." EPL (Europhysics Letters) 99, no. 4 (August 1, 2012): 44004. http://dx.doi.org/10.1209/0295-5075/99/44004.

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17

Espedal, Magne S., and Richard E. Ewing. "Characteristic petrov-galerkin subdomain methods for two-phase immiscible flow." Computer Methods in Applied Mechanics and Engineering 64, no. 1-3 (October 1987): 113–35. http://dx.doi.org/10.1016/0045-7825(87)90036-3.

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18

Fadimba, Koffi B. "Pressure/Saturation System for Immiscible Two-Phase Flow: Uniqueness Revisited." Applied Mathematics 02, no. 05 (2011): 541–50. http://dx.doi.org/10.4236/am.2011.25071.

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19

Roman, Sophie, Cyprien Soulaine, Moataz Abu AlSaud, Anthony Kovscek, and Hamdi Tchelepi. "Particle velocimetry analysis of immiscible two-phase flow in micromodels." Advances in Water Resources 95 (September 2016): 199–211. http://dx.doi.org/10.1016/j.advwatres.2015.08.015.

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20

Kim, Junseok. "A diffuse-interface model for axisymmetric immiscible two-phase flow." Applied Mathematics and Computation 160, no. 2 (January 2005): 589–606. http://dx.doi.org/10.1016/j.amc.2003.11.020.

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21

Sun, Wentao. "VARIABLE GRID FINITE DIFFERENCE METHOD FOR TWO-DIMENSIONAL TWO-PHASE IMMISCIBLE FLOW." Acta Mathematica Scientia 18, no. 4 (October 1998): 379–86. http://dx.doi.org/10.1016/s0252-9602(17)30591-x.

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22

Kozubková, Milada, Jana Jablonská, Marian Bojko, František Pochylý, and Simona Fialová. "Multiphase Flow in the Gap Between Two Rotating Cylinders." MATEC Web of Conferences 328 (2020): 02017. http://dx.doi.org/10.1051/matecconf/202032802017.

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The research of liquids composed of two (or more) mutually immiscible components is a new emerging area. These liquids represent new materials, which can be utilized as lubricants, liquid seals or as fluid media in biomechanical devices. The investigation of the problem of immiscible liquids started some years ago and soon it was evident that it will have a great application potential. Recently, there has been an effort to use ferromagnetic or magnetorheological fluids in the construction of dumpers or journal bearings. Their advantage is a significant change in dynamic viscosity depending on magnetic induction. In combination with immiscible liquids, qualitatively new liquids can be developed for future technologies. In our case, immiscible fluids increase the dynamic properties of the journal hydrodynamic bearing. The article focuses on the stability of single-phase and subsequently multiphase flow of liquids in the gap between two concentric cylinders, one of which rotates. The aim of the analysis was to study the effect of viscosity and density on the stability/instability of the flow, which is manifested by Taylor vortices. Methods of experimental and mathematical analysis were used for the analysis in order to verify mathematical models of laminar and turbulent flow of immiscible liquids.

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23

Herard, Jean-Marc, and Guillaume Jomée. "Pressure relaxation in some multiphase flow models." ESAIM: Proceedings and Surveys 72 (2023): 19–40. http://dx.doi.org/10.1051/proc/202372019.

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We consider in this paper multiphase flow models involving two, three or four fields, in total mechanical and thermodynamical disequilibrium. Thus several pressure fields arise, and we precisely focus here on the pressure relaxation process, while restricting to four distinct multiphase flow models. The first two models only involve immiscible compressible components, while the last two hybrid models involve both miscible and immiscible components. It is shown that some -weak- restrictions may occur on pressure gaps, which are unlikely to appear in practice. Evenmore, three-phase flow models may involve a non-monotone behaviour in the return to pressure equilibrium.

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24

KOCH, JAN, ANDREAS RÄTZ, and BEN SCHWEIZER. "Two-phase flow equations with a dynamic capillary pressure." European Journal of Applied Mathematics 24, no. 1 (September 21, 2012): 49–75. http://dx.doi.org/10.1017/s0956792512000307.

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We investigate the motion of two immiscible fluids in a porous medium described by a two-phase flow system. In the capillary pressure relation, we include static and dynamic hysteresis. The model is well established in the context of the Richards equation, which is obtained by assuming a constant pressure for one of the two phases. We derive an existence result for this hysteresis two-phase model for non-degenerate permeability and capillary pressure curves. A discretization scheme is introduced and numerical results for fingering experiments are obtained. The main analytical tool is a compactness result for two variables that are coupled by a hysteresis relation.

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25

Whitaker, Stephen. "Flow in porous media II: The governing equations for immiscible, two-phase flow." Transport in Porous Media 1, no. 2 (1986): 105–25. http://dx.doi.org/10.1007/bf00714688.

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26

Biancofiore, Luca, François Gallaire, Patrice Laure, and Elie Hachem. "Direct numerical simulations of two-phase immiscible wakes." Fluid Dynamics Research 46, no. 4 (April 11, 2014): 041409. http://dx.doi.org/10.1088/0169-5983/46/4/041409.

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27

Bussac, Jean. "Study of relaxation processes in a two-phase flow model." ESAIM: Proceedings and Surveys 72 (2023): 2–18. http://dx.doi.org/10.1051/proc/202372002.

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This work concerns the analysis of the relaxation processes toward thermodynamical equilibrium arising in a compressible immiscible two-phase flow. Classically the relaxation processes are taken into account through dynamical systems which are coupled to the dynamics of the flow. The present paper compares two types of source terms which are commonly used: a BGK-like system and a mixture entropy gradient type. For both systems, main properties are investigated (agreement with second principle of thermodynamics, existence of solutions, maximum principle,...) and numerical experiments illustrate their asymptotic behaviour.

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28

Guan, Qiangshun, Yit Fatt Yap, Hongying Li, and Zhizhao Che. "Modeling of Nanofluid-Fluid Two-Phase Flow and Heat Transfer." International Journal of Computational Methods 15, no. 08 (October 31, 2018): 1850072. http://dx.doi.org/10.1142/s021987621850072x.

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This paper presents a model for two-phase nanofluid-fluid flow and heat transfer. The nonuniform nanoparticles are transported using Buongiorno model by convection, Brownian diffusion and thermophoresis. This is the first attempt to employ Buongiorno model for two-phase nanofluid-fluid flow. The moving interface between the nanofluid and the immiscible fluid is captured using the level-set method. The model is first verified and then demonstrated for coupled flow and heat transfer in (1) a water–alumina nanofluid-filled cavity with a rising silicone oil drop and (2) stratified flow of water–alumina nanofluid, pure water and silicone oil in a channel.

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29

Allen, F. R., and D. A. Puckett. "Theoretical and Experimental Studies of Rate-Dependent Two-Phase Immiscible Flow." SPE Production Engineering 1, no. 01 (January 1, 1986): 62–74. http://dx.doi.org/10.2118/10972-pa.

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30

Amaziane, B., L. Pankratov, and A. Piatnitski. "Homogenization of immiscible compressible two–phase flow in random porous media." Journal of Differential Equations 305 (December 2021): 206–23. http://dx.doi.org/10.1016/j.jde.2021.10.012.

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31

Suekane, Tetsuya, and Taiyo Kitani. "C121 Natural convection of immiscible two-phase flow in porous media." Proceedings of the Thermal Engineering Conference 2013 (2013): 73–74. http://dx.doi.org/10.1299/jsmeted.2013.73.

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32

Izumi, Reona, and Tetsuya Suekane. "Behavior of fingering of immiscible two phase flow in porous media." Proceedings of the Thermal Engineering Conference 2016 (2016): I132. http://dx.doi.org/10.1299/jsmeted.2016.i132.

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33

Gunstensen, Andrew K., and Daniel H. Rothman. "Lattice-Boltzmann studies of immiscible two-phase flow through porous media." Journal of Geophysical Research: Solid Earth 98, B4 (April 10, 1993): 6431–41. http://dx.doi.org/10.1029/92jb02660.

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34

Amaziane, B., M. Jurak, L. Pankratov, and A. Piatnitski. "Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media." Nonlinear Analysis: Real World Applications 43 (October 2018): 192–212. http://dx.doi.org/10.1016/j.nonrwa.2018.02.012.

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35

Hochmuth, David P., and Daniel K. Sunada. "Ground-Water Model of Two-Phase Immiscible Flow in Coarse Material." Ground Water 23, no. 5 (September 1985): 617–26. http://dx.doi.org/10.1111/j.1745-6584.1985.tb01510.x.

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36

Jurak, Mladen, Alexandre Koldoba, Andrey Konyukhov, and Leonid Pankratov. "Nonisothermal immiscible compressible thermodynamically consistent two-phase flow in porous media." Comptes Rendus Mécanique 347, no. 12 (December 2019): 920–29. http://dx.doi.org/10.1016/j.crme.2019.11.015.

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37

Hérard, J. M., and H. Mathis. "A three-phase flow model with two miscible phases." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 4 (July 2019): 1373–89. http://dx.doi.org/10.1051/m2an/2019028.

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The paper concerns the modelling of a compressible mixture of a liquid, its vapor and a gas. The gas and the vapor are miscible while the liquid is immiscible with the gaseous phases. This assumption leads to non symmetric constraints on the void fractions. We derive a three-phase three-pressure model endowed with an entropic structure. We show that interfacial pressures are uniquely defined and propose entropy-consistent closure laws for the source terms. Naturally one exhibits that the mechanical relaxation complies with Dalton’s law on the phasic pressures. Then the hyperbolicity and the eigenstructure of the homogeneous model are investigated and we prove that it admits a symmetric form leading to a local existence result. We also derive a barotropic variant which possesses similar properties.

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38

YEH, LI-MING. "HOMOGENIZATION OF TWO-PHASE FLOW IN FRACTURED MEDIA." Mathematical Models and Methods in Applied Sciences 16, no. 10 (October 2006): 1627–51. http://dx.doi.org/10.1142/s0218202506001650.

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In a fractured medium, there is an interconnected system of fracture planes dividing the porous rock into a collection of matrix blocks. The fracture planes, while very thin, form paths of high permeability. Most of the fluids reside in matrix blocks, where they move very slow. Let ε denote the size ratio of the matrix blocks to the whole medium and let the width of the fracture planes and the porous block diameter be in the same order. If permeability ratio of matrix blocks to fracture planes is of order ε2, microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as ε goes to 0. If the ratio is smaller than order ε2, the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order ε2, then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.

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39

Zhang, Xu Bin, Dan Chen, Yan Wang, and Wang Feng Cai. "Liquid-Liquid Two-Phase Flow Patterns and Mass Transfer Characteristics in a Circular Microchannel." Advanced Materials Research 482-484 (February 2012): 89–94. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.89.

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In this paper, flow patterns and mass transfer characteristics of two immiscible fluids in a T-junction circular microchannel were investigated. Four flow patterns, i.e. slug flow, irregular flow, parallel flow and annular flow, were captured by a CCD method, which were resulted from the competition among interfacial tension, viscous force and inertia force. Besides, the overall volumetric mass transfer coefficients ka for the four flow patterns was determined experimentally. The values of ka are in the range of 0.006~0.545s−1 and mainly dependent on the superficial velocity and the flow pattern regime.

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40

Guérillot, Dominique, Mostafa Kadiri, and Saber Trabelsi. "Buckley–Leverett Theory for Two-Phase Immiscible Fluids Flow Model with Explicit Phase-Coupling Terms." Water 12, no. 11 (October 29, 2020): 3041. http://dx.doi.org/10.3390/w12113041.

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The theory of two-phase immiscible flow in porous media is based on the extension of single phase models through the concept of relative permeabilities. It mimics Darcy’s law for a fixed average saturation through the introduction of saturation-based permeabilities to model the momentum exchange between the phases. In this paper, we present a model of two-phase flow, based on the extension of Darcy’s law including the effect of capillary pressure, but considering in addition the coupling between the phases modeled through flow cross-terms. In this work, we extend the Buckley–Leverett theory to the subsequent model, and provide numerical experiments shading the light on the effect of the coupling cross-terms in comparison to the classical Darcy’s approach.

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41

Sorbie, K. S., A. Y. Al Ghafri, A. Skauge, and E. J. Mackay. "On the Modelling of Immiscible Viscous Fingering in Two-Phase Flow in Porous Media." Transport in Porous Media 135, no. 2 (September 29, 2020): 331–59. http://dx.doi.org/10.1007/s11242-020-01479-w.

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Abstract Viscous fingering in porous media is an instability which occurs when a low-viscosity injected fluid displaces a much more viscous resident fluid, under miscible or immiscible conditions. Immiscible viscous fingering is more complex and has been found to be difficult to simulate numerically and is the main focus of this paper. Many researchers have identified the source of the problem of simulating realistic immiscible fingering as being in the numerics of the process, and a large number of studies have appeared applying high-order numerical schemes to the problem with some limited success. We believe that this view is incorrect and that the solution to the problem of modelling immiscible viscous fingering lies in the physics and related mathematical formulation of the problem. At the heart of our approach is what we describe as the resolution of the “M-paradox”, where M is the mobility ratio, as explained below. In this paper, we present a new 4-stage approach to the modelling of realistic two-phase immiscible viscous fingering by (1) formulating the problem based on the experimentally observed fractional flows in the fingers, which we denote as $$ f_{\rm w}^{*} $$ f w ∗ , and which is the chosen simulation input; (2) from the infinite choice of relative permeability (RP) functions, $$ k_{\rm rw}^{*} $$ k rw ∗ and $$ k_{\rm ro}^{*} $$ k ro ∗ , which yield the same $$ f_{\rm w}^{*} $$ f w ∗ , we choose the set which maximises the total mobility function, $$ \lambda_{\text{T}}^{{}} $$ λ T (where $$ \lambda_{\text{T}}^{{}} = \lambda_{\text{o}}^{{}} + \lambda_{\text{w}}^{{}} $$ λ T = λ o + λ w ), i.e. minimises the pressure drop across the fingering system; (3) the permeability structure of the heterogeneous domain (the porous medium) is then chosen based on a random correlated field (RCF) in this case; and finally, (4) using a sufficiently fine numerical grid, but with simple transport numerics. Using our approach, realistic immiscible fingering can be simulated using elementary numerical methods (e.g. single-point upstreaming) for the solution of the two-phase fluid transport equations. The method is illustrated by simulating the type of immiscible viscous fingering observed in many experiments in 2D slabs of rock where water displaces very viscous oil where the oil/water viscosity ratio is $$ (\mu_{\text{o}} /\mu_{\text{w}} ) = 1600 $$ ( μ o / μ w ) = 1600 . Simulations are presented for two example cases, for different levels of water saturation in the main viscous finger (i.e. for 2 different underlying $$ f_{\rm w}^{*} $$ f w ∗ functions) produce very realistic fingering patterns which are qualitatively similar to observations in several respects, as discussed. Additional simulations of tertiary polymer flooding are also presented for which good experimental data are available for displacements in 2D rock slabs (Skauge et al., in: Presented at SPE Improved Oil Recovery Symposium, 14–18 April, Tulsa, Oklahoma, USA, SPE-154292-MS, 2012. 10.2118/154292-MS, EAGE 17th European Symposium on Improved Oil Recovery, St. Petersburg, Russia, 2013; Vik et al., in: Presented at SPE Europec featured at 80th EAGE Conference and Exhibition, Copenhagen, Denmark, SPE-190866-MS, 2018. 10.2118/190866-MS). The finger patterns for the polymer displacements and the magnitude and timing of the oil displacement response show excellent qualitative agreement with experiment, and indeed, they fully explain the observations in terms of an enhanced viscous crossflow mechanism (Sorbie and Skauge, in: Proceedings of the EAGE 20th Symposium on IOR, Pau, France, 2019). As a sensitivity, we also present some example results where the adjusted fractional flow ($$ f_{\rm w}^{*} $$ f w ∗ ) can give a chosen frontal shock saturation, $$ S_{\rm wf}^{*} $$ S wf ∗ , but at different frontal mobility ratios, $$ M(S_{\rm wf}^{*} ) $$ M ( S wf ∗ ) . Finally, two tests on the robustness of the method are presented on the effect of both rescaling the permeability field and on grid coarsening. It is demonstrated that our approach is very robust to both permeability field rescaling, i.e. where the (kmax/kmin) ratio in the RCF goes from 100 to 3, and also under numerical grid coarsening.

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42

Yan, Guanxi, Zi Li, Thierry Bore, Sergio Andres Galindo Torres, Alexander Scheuermann, and Ling Li. "Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation." Energies 14, no. 13 (July 5, 2021): 4044. http://dx.doi.org/10.3390/en14134044.

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The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

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Gong, Wenbo, and Jinhui Liu. "Effect of Wettability Heterogeneity on Water-Gas Two-Phase Displacement Behavior in a Complex Pore Structure by Phase-Field Model." Energies 15, no. 20 (October 17, 2022): 7658. http://dx.doi.org/10.3390/en15207658.

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Understanding the immiscible displacement mechanism in porous media is vital to enhancing the hydrocarbon resources in the oil and gas reservoir. Improving resource recovery requires quantitatively characterizing the effect of wettability heterogeneity on the immiscible displacement behaviors at the pore scale, which can be used to predict the displacement distribution of multiphase fluids and evaluate the optimal wettability strategy in porous media. The heterogeneity of fluid wettability in a natural rock makes it extremely hard to directly observe the fluid displacement behaviors in the reservoir rocks and quantify the sensitivity of preferential displacement path and displacement efficiency to wettability distribution. In this study, the phase-field model coupling wettability heterogeneity was established. The gas-water two-phase displacement process was simulated under various wettability distributions and injecting flux rates in a complex pore structure. The effect of wettability heterogeneity on immiscible displacement behavior was analyzed. The results indicated that wettability heterogeneity significantly affects the fluid displacement path and invasion patterns, while the injecting flux rate negatively influences the capillary–viscous crossover flow regime. The continuous wetting patches enhanced the preferential flow and hindered displacement, whereas the dalmatian wetting patches promoted a higher displacement efficiency. The results of the fractal dimensions and specific surface area also quantitatively show the effects of wettability distribution and heterogeneity on the complexity of the two-phase fluid distribution. The research provides the theoretical foundation and analysis approach for designing an optimal wettability strategy for injecting fluid into unconventional oil and gas reservoirs.

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44

Jurak, M., L. Pankratov, and A. Vrbaški. "Discretization schemes for the two simplified global double porosity models of immiscible incompressible two-phase flow." Journal of Physics: Conference Series 2701, no. 1 (February 1, 2024): 012077. http://dx.doi.org/10.1088/1742-6596/2701/1/012077.

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Abstract We present the discretization schemes for the two simplified homogenized models of immiscible incompressible two-phase flow in double porosity media with thin fractures. The two models were derived previously by the authors by different linearizations of the nonlinear local problem called the imbibition equation which appears in the homogenized model after passage to the limit as ε → 0. The models are fully homogenized with the matrix-fracture source terms expressed as a convolution.

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Amaziane, B., M. Jurak, L. Pankratov, and A. Piatnitski. "Homogenization of nonisothermal immiscible incompressible two-phase flow in double porosity media." Nonlinear Analysis: Real World Applications 61 (October 2021): 103323. http://dx.doi.org/10.1016/j.nonrwa.2021.103323.

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Joshaghani, M. S., B. Riviere, and M. Sekachev. "Maximum-principle-satisfying discontinuous Galerkin methods for incompressible two-phase immiscible flow." Computer Methods in Applied Mechanics and Engineering 391 (March 2022): 114550. http://dx.doi.org/10.1016/j.cma.2021.114550.

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Jeptanui, Flomena, Jacob Bitok, and Titus Rotich. "Two Phase Immiscible Fluids Flow Through A Porous Media: Finite Volume Approach." International Journal of Scientific and Research Publications (IJSRP) 11, no. 12 (December 24, 2021): 460–69. http://dx.doi.org/10.29322/ijsrp.11.12.2021.p12067.

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Michel, Anthony. "A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media." SIAM Journal on Numerical Analysis 41, no. 4 (January 2003): 1301–17. http://dx.doi.org/10.1137/s0036142900382739.

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Yardley, B. W. D., and S. H. Bottrell. "Immiscible fluids in metamorphism: Implications of two-phase flow for reaction history." Geology 16, no. 3 (1988): 199. http://dx.doi.org/10.1130/0091-7613(1988)016<0199:ifimio>2.3.co;2.

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Henning, Patrick, Mario Ohlberger, and Ben Schweizer. "Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media." Computational Geosciences 19, no. 1 (November 14, 2014): 99–114. http://dx.doi.org/10.1007/s10596-014-9455-6.

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