A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media, this problem has been seldom investigated using direct numerical simulation(DNS). Only a few studies have sought to numerically solve Navier—Stokes equations with level-set(LS) or volume-of-fluid(VoF) methods, each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume(CV) domain.The Shan—Chen multiphase multicomponent lattice Boltzmann method(SC-LBM) has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations.Therefore, this study applied it to explore two-phase displacement in a single representative elementary volume(REV) of two-dimensional(2D) porous media. As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media, this work seeks to identify dynamic nonequilibrium effects on capillary pressure—saturation relationship(Pc—S) for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions. The simulation outcomes show that Pc, S and specific interfacial area(anw) had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions. With finer adjustments to the increase in pressure over more steps, dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasisteady-state inflow/outflow conditions. Furthermore, triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical Pc—S. The results showed overshoot and undershoot of Pcto S in loops of the nonequilibrium hysteresis.In addition, the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers(Re and Ca). The analysis of REV-scale flow regimes showed higher Re(1 < Re < 10) for more significant dynamic nonequilibrium effects. This indicates that inertia is critical for transient twophase flow in porous media under dynamic nonequilibrium conditions.