Spontaneous imbibition dynamics in two-dimensional porous media: A generalized interacting multi-capillary model

The capillary bundle model, wherein the flow dynamics of a porous medium is predicted from that independent cylindrical tubes/capillaries whose radii are distributed according to medium's pore size distribution, has been used extensively. However, as it lacks an interaction between channels, this model fails at predicting complex configuration, including those involving two-phase flow. We propose here predict spontaneous imbibition in quasi-two-dimensional media based on planar interacting capillaries. dynamics, and particular, breakthrough time, global wetting fluid saturation breakthrough, which carries leading meniscus governed by distribution capillaries' their spatial arrangement. For system consisting 20 capillaries, time can be 39% smaller than classic, non-interacting, identical depending arrangement stochastic approach use capillaries for quantitative predictions. Comparing bundles with same diameter sizes target medium, computing average behavior randomly chosen samples such different arrangements, we obtain predictions position bulk saturating front visible front, agree well measurements taken literature. This semi-analytical very quick run could useful provide fast one-dimensional porosity structure reasonably considered two-dimensional, e.g., paper, thin general, or layered aquifers.