Numerical Study of Side Boundary Effects in Pore-Scale Digital Rock Flow Simulations

This work presents a numerical study of side boundary effects in pore-scale digital rock flow simulations, where the side boundaries are often treated as no-slip walls. While the capillary end effects from inlet and outlet boundaries are well known, the influence of side boundaries has not been systematically studied, especially for two-phase flow. We employ a well-established three-dimensional color-gradient lattice Boltzmann model to simulate immiscible two-phase flow on both real and synthetic rock samples. Our results reveal significant artifacts in small samples caused by side boundaries, leading to non-representative saturation profiles, even though absolute permeability remains consistent with larger samples. In drainage, non-wetting phase saturation is substantially lower near the side boundaries due to increased trapping of the wetting phase, while in imbibition, the wetting phase preferentially flows along the walls, forming steep V-shaped saturation profiles near the side boundaries. Increasing sample size can reduce boundary influence, but this is often impractical for certain samples, owing to, for instance, high computational demands. Enforcing periodic boundary conditions directly on the side boundaries only marginally improves saturation near the boundaries for the drainage cases, as poor pore connectivity across quasi-periodic boundaries remains a limitation, especially in low-porosity media, while the approach causes unphysically high wetting phase saturation near the side boundaries during imbibition. An alternative approach is to generate synthetic rock samples that are inherently periodic in the transverse directions, enabling more representative two-phase flow simulations. By comparing simulations with no-slip and periodic boundary conditions on a low porosity synthetic rock sample, the side boundary effects can cause more than 10% differences in steady-state saturation. Thus, synthetically generated periodic digital rock samples offer a promising solution for pore-scale studies of low-porosity media.