Generalization of darcy’s law: Non-Darcian liquid flow in Low-Permeability media

Abstract

Darcy’s Law was discovered by Henry Darcy (1803-1858) based on experimental observations of steady-state water flow through sand columns. It states that water flux in saturated porous media is linearly proportional to hydraulic gradient. For low-permeability porous media, however, Darcy’s law is not adequate because of the strong fluid-solid interaction that results in non-linear flux-gradient relationships. This chapter presents a new phenomenological relationship between water flux and hydraulic gradient, or a generalized Darcy’s law. The traditional form of Darcy’s law and two other generalizations for low-permeability media, proposed by other researchers, are shown to be special cases of the generalization. The consistency between the generalization and experimental observations from different sources is demonstrated. The generalized Darcy’s law and its variations are used to attack several key technical issues facing the geoscience community, including the relative importance of diffusion in the excavation damaged zone for a shale repository of high-level nuclear waste, the accurate measurement of relative permeability for multiphase flow in a low-permeability porous medium, non-Darcian flow behavior during imbibition of fracturing fluids into a shale gas reservoir, and formation of the pressure seal in shale formations.