Fundamental theorem for porous media in hydrostatic equilibrium

This study derives the theorem for the local volume average of a gradient (or divergence) for the fluid phase in hydrostatic equilibrium. Recently, Takatsu (2017) [21] has modified the conventional theorem for the local volume average of a gradient for the flow through porous media. We extend the modified theorem to the fluid phase in hydrostatic equilibrium, and show that the difference between the theorems for both cases is caused by the boundary condition at the surface of the fluid phase volume. The resulting gradient of an average pressure for hydrostatic equilibrium is consistent with Darcy's law with < u >((f)) = 0. Furthermore, we obtain the theorem for the local volume average of a gradient (or divergence) for the solid phase volume and that for the representative elementary volume. (C) 2019 Elsevier Ltd. All rights reserved.