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[1] We simulate two-fluid-phase flow at the pore scale using a lattice Boltzmann (LB) approach. Using a parallel processing version of the Shan-Chen model that we developed, we simulate a set of ideal two-fluid systems and a model two-fluid-phase porous medium system comprised of a synthetic packing with a relatively uniform distribution of spheres. We use the set of ideal two-phase systems to validate the approach and provide parameter information, which we then use to simulate a sphere-pack system. The spherepack system is designed to mimic laboratory experiments conducted to evaluate the hysteretic capillary pressure saturation relation for a system consisting of water, tetrachloroethylene, and a glass bead porous medium. Good agreement is achieved between the measured hysteretic capillary pressure saturation relations and the LB simulations when comparing entry pressure, displacement slopes, irreducible saturation, and residual entrapment. Our results further show that while qualitatively similar results are obtained when comparing systems consisting of 1200 spheres and 150 spheres, there is a significant difference between these two levels, suggesting a lower bound on the size of a representative elementary volume.

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.

We use two pore-scale approaches, lattice-Boltzmann (LB) and pore-network modeling, to simulate single-phase flow in simulated sphere packings that vary in porosity and sphere-size distribution. For both modeling approaches, we determine the size of the representative elementary volume with respect to the permeability. Permeabilities obtained by LB modeling agree well with Rumpf and Gupte's experiments in sphere packings for small Reynolds numbers. The LB simulations agree well with the empirical Ergun equation for intermediate but not for small Reynolds numbers. We suggest a modified form of Ergun's equation to describe both low and intermediate Reynolds number flows. The pore-network simulations agree well with predictions from the effective-medium approximation but underestimate the permeability due to the simplified representation of the porous media. Based on LB simulations in packings with log-normal sphere-size distributions, we suggest a permeability relation with respect to the porosity, as well as the mean and standard deviation of the sphere diameter.

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