Memory effect on gas percolation in saturated porous media

This work investigates the path of gas locally injected and rising through a water-saturated porous medium. Gas migration through the pores network is modeled using a Gaussian distribution of capillary overpressure superimposed on a linear pressure gradient induced by gravity. Previous studies have shown that the superposition of individual gas pathways significantly affects the overall invasion morphology, impacting various practical applications. The originality of the present simulation lies in incorporating the effect of prior pathways on subsequent ones, thereby accounting for the system's memory. The final invasion zone morphology, shaped by multiple gas pathways, is quantified as a function of the memory effect, ranging from a diffusivelike invasion to a meandering progression when the influence of prior paths is substantial. Notably, we find that the probability of revisiting previously occupied sites, which quantifies the tendency of gas to follow an established path, follows a logistic function.