Accurate quantification of average capillary pressure is important for understanding the fluid flow and retention of a partially saturated porous medium. In the multicomponent pseudopotential Shan–Chen lattice Boltzmann method, the diffuse interfaces and spurious velocities make the capillary pressure sensitive to how the bulk of a fluid phase is defined and sampled. In this work we compare the classical volume-averaged measure of capillary pressure with local measures weighted by interface length, obtained either from interface curvature via the Young–Laplace law or from local sampling across the interface. First, a procedure is discussed to identify the critical pore width, which is established as the key geometric feature that must be resolved for accurate capillary pressure calculation, since doing so captures most fluid–fluid interfaces that control the volume-averaged capillary pressure. Then, the capillary pressure estimates are evaluated using a grid convergence study as well as verification of the Young–Laplace relation at the local scale. In ordered porous media, the volume-averaged capillary pressure agrees closely with the length-weighted average of local capillary pressures. In heterogeneous porous media, however, it differs because local capillary pressures are distributed heterogeneously and clusters contribute unequally to phase volume and interface length. Using the color-gradient formulation as a benchmark, we show that the Shan–Chen formulation yields accurate capillary pressure predictions when bulk regions are identified carefully. • Improves capillary pressure ( P c ) accuracy in heterogeneous porous media. • Identifies critical pore width required for accurate P c . • Preserves physical surface tension across resolution for grid-invariant P c in LBM. • Compares volume-based and interface-based P c measures in heterogeneous porous media. • Benchmarks P c from two lattice Boltzmann formulations against analytical estimates.
Joseph et al. (Fri,) studied this question.