Pore-scale investigation of viscous coupling effects for two-phase flow in porous media

Abstract

Recent studies have revealed that viscous coupling effects in immiscible two-phase flow, caused by momentum transfer between the two fluid phases, can be important in porous medium systems. In this work, we use a three-dimensional parallel processing version of a two-fluid-phase lattice Boltzmann (LB) model to investigate this phenomenon. A multiple-relaxation-time (MRT) approximation of the LB equations is used in the simulator, which leads to a viscosity-independent velocity field. We validate our model by verifying the velocity profile for two-phase flow through a channel with a square cross section. We then simulate co-current flow through a sphere-pack porous medium and obtain correlations of the relative permeabilities as a function of capillary number, wettability, and the fluid viscosities. The results are qualitatively consistent with experimental observations. In addition, we calculate the generalized permeability coefficients and show that the coupling coefficients are significant and the matrix is nonsymmetric. We also find a strong correlation between the relative permeability and interfacial area between fluids, indicating that both the common extension of Darcy's Law and the generalized formulation accounting for viscous coupling effects do not provide adequate insight into two-phase flow processes in porous media. This work lends additional support for the hypothesis that interfacial area is a key variable for multiphase flow in porous medium systems.

Multiphase lattice Boltzmann simulations for porous media applications

“…The inter-particle potential model has also been used to determine relative permeabilities [199,200,204,207]. Effects of capillary number, wettability, and viscosity ratio, as well as the porous structures on the relative permeability were investigated in detail.…”

“…[37,43,97,98,[197][198][199][200][201][202][203][204][205][206][207], because of its simplicity and easy implementation. Pan et al [197] used the MCMP inter-particle potential model to simulate two-phase flow in a porous medium comprised of a synthetic packing with a relatively uniform distribution of spheres.…”

Simulation of liquid water breakthrough in a nanotomography reconstruction of a carbon paper gas‐diffusion layer

“…In this paper, the MRT approach is applied to the S-C model. In the MRT S-C model, each fluid component is modelled by the following equation [23]:…”

Transient Modeling of CPL Based on Mesoscaled Analysis by Lattice Boltzmann Method

“…It is proved that the lattice BGK method is consistent with the Navier-Stokes equation for fluid flow through ChapmanEnskog expansion (Benzi et al, 1992). As a flexible and effective numerical method, it finds increasing applications in simulating complex flow, heat, and mass transfer problems (Chen and Doolen, 1998;Xuan et al, 2007;Li et al, 2005;Orazio et al, 2003). An important advantage of the lattice Boltzmann method is that it can simulate the interfacial force between the two different phases conveniently and catch the interface of the two different phases clearly.…”