Matrix-fracture transfer shape factors for dual-porosity simulators

Matrix-fracture transfer shape factors for dual-porosity simulation of naturally-fractured reservoirs were derived by combining analytical solutions of pressure diffusion for various flow geometries. The resulting equations describing the matrix-fracture flow were cast in a form similar to those proposed by Barenblatt et al. 11Barenblatt et al. (1960). arren and Root 22Warren and Root (1963). without making the pseudo-steady state assumption. Shape factors representing one, two and three parallel sets of fractures were obtained. A generalized matrix-fracture transfer function for a non-isotropic, rectangular matrix block was also derived. Fine-grid single-porosity and one-block dual-porosity models were used to verify the results. The results of fine-grid and one-block dual-porosity models were in good agreement. The shape factors derived in this paper are consistent with observations made in several publications on dual-porosity simulation studies.