A Non‐Local Richards Equation to Model Unsaturated Flow in Highly Heterogeneous Media under Nonequilibrium Pressure Conditions

This paper presents an upscaled model for unsaturated flow in highly heterogeneous media. Flow in the highly conductive domain is described with Richards' equation, while water exchange with poorly conductive blocks is captured by a non‐local sink term with a diffusive memory kernel. The model is tested with a numerical test case. We study the impact of mass transfer between high and low conductivity zones on flow in unsaturated media. A dual continuum approach that assumes capillary‐dominated flow in the slow continuum gives a system of coupled flow equations for the water saturations in the mobile and in the slow domain, whose coupling term is directly related to the evolution of the averaged water content in the slow domain. We show that linearization of the nonlinear diffusion equation that governs capillary flow in the slow continuum captures well the essential features of the time evolution of the averaged water content in the slow domain. This allows one to derive a non‐local Richards equation for the water content in the mobile domain that is characterized by a memory kernel that encodes the local mass transfer dynamics as well as the geometry of the slow zones. Comparison of the model predictions to the results of numerical simulations of infiltration in a vertically layered medium shows that the non‐local approach describes well nonequilibrium effects due to mass transfer between high and low conductivity zones.