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(P_(c)—S)for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions.The simulation outcomes show that P_(c),S and specific interfacial area(a_(nw))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 P_(c)to 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.