Modeling water infiltration in unsaturated porous media by interacting lattice gas‐cellular automata

Abstract

A two‐dimensional lattice gas‐cellular automaton fluid model with long‐range interactions (Appert and Zaleski, 1990) is used to simulate saturated and unsaturated water infiltration in porous media. Water and gas within the porous medium are simulated by applying the dense and the light phase, respectively, of the cellular automaton fluid. Various wetting properties can be modeled when adjusting the corresponding solid‐liquid interactions. The lattice gas rules include a gravity force step to allow buoyancy‐driven flow. The model handles with ease complex geometries of the solid, and an algorithm for generating random porous media is presented. The results of four types of simulation experiments are presented: (1) We verified Poiseuille's law for steady and saturated flow between two parallel plates. (2) We analyzed transient water infiltration between two parallel plates of varying degrees of saturation and various apertures. (3) Philip's infiltration equation was adequately simulated in an unsaturated porous medium. (4) Infiltration into an aggregated medium containing one vertical parallel crack was simulated. Further applications of this lattice gas method for studying unsaturated flow in porous media are discussed.