The shape factor that appears in dual-porosity models of single-phase flow in naturally fractured reservoirs is investigated. Previously derived analytical expressions for a few simple geometries (spheres, cubes, slabs, etc.) are first reviewed. A general numerical procedure is presented that allows the shape factor of an arbitrarily shaped block to be found using a fine-grid simulation of flow into a single matrix block with constant-pressure boundary conditions. From these various results, a scaling law is suggested that expresses the shape factor in terms of the block’s volume V, the block’s outer surface area S, and a diffusion length l. This expression is α = 5S/, where γ = V1/3 for a three-dimensional block, and γ = A1/2 for a two-dimensional prismatic block with cross-sectional area A. For all cases analyzed, this expression predicts the shape factor within an error of less than 10%. This seems to be the first accurate, general expression available for estimating the shape factors of irregularly shaped matrix blocks such as are formed by the intersection of realistic fracture networks.

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