An analytical solution for transient radial flow through unsaturated fractured porous media

Abstract

This paper presents analytical solutions for one‐dimensional radial transient flow through a horizontal, unsaturated fractured rock formation. In these solutions, unsaturated flow through fractured media is described by a linearized Richards' equation, while fracture‐matrix interaction is handled using the dual‐continuum concept. Although linearizing Richards' equation requires a specially correlated relationship between relative permeability and capillary pressure functions for both fractures and matrix, these specially formed relative permeability and capillary pressure functions are still physically meaningful. These analytical solutions can thus be used to describe the transient behavior of unsaturated flow in fractured media under the described model conditions. They can also be useful in verifying numerical simulation results, which as demonstrated in this paper, are otherwise difficult to validate.