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Water permeation into a porous medium is a common but important phenomenon in many engineering fields such as hydraulic fracturing. The water permeation front moves with time and may significantly impact the field variable evolution near the water front. Many algorithms have been developed to calculate this water front motion, but few numerical algorithms have been available to calculate the water front motion in anisotropic fluid-solid couplings with high computational efficiency. In this study, a numerical model is proposed to investigate the front motion of water permeation into an anisotropic porous medium. This model fully couples the mechanical deformation, fluid flow, and water front motion. The water front motion is calculated based on a directional Darcy’s flow in the anisotropic porous medium, and a revised formula with a correction coefficient is developed for the estimation of permeation depth. After verification with three sets of experimental data, this model is used to numerically investigate the impacts of permeability, viscosity, permeability anisotropy, and mechanical anisotropy on water front motion. Numerical results show that the proposed model can well describe the anisotropic water permeation process with reasonable accuracy. The permeation depth increases with permeability, mobility, and mechanical anisotropy but decreases with viscosity and permeability anisotropy. The correction coefficient mainly depends on porosity evolution, flow pattern, mobility, permeability anisotropy, and mechanical anisotropy.

Numerical Simulations on the Front Motion of Water Permeation into Anisotropic Porous Media