Modelling effective permeability of fracture networks in permeable rock formations by singular integral equations method

In this paper, theoretical and numerical formulations of plane steady-state fluid flow in a fractured porous rock are used to investigate its effective permeability. If the far field inflow is uniform, the theoretical solution shows that the pressure field in the matrix is a function of the discharge in the fracture network. A numerical resolution based on singular integral equations is employed to derive the general problem of many intersected fractures in order to obtain the pressure field in anisotropic matrix. This solution allows computing the flux in the fractures which is the key issue for upscalling the equivalent permeability. This paper presents in detail the method for deriving the equivalent permeability from this solution. This method is applied to two real cases: an Excavation Damage Zone (EDZ) around a deep underground gallery and a geological rock formation presenting several families of fractures. The results of the both cases show that the developed method provides an easy and efficient way to determine the equivalent permeability of the fractured porous rock medium. This equivalent permeability can be implemented in analytical and numerical tools for continuous media towards estimating the flow characteristics in the rock formation.