Rigorous Derivation of the Kazemi-Gilman-Elsharkawy Generalized Dual Porosity Shape Factor

Kazemi et al.[7] suggested to use an empirical matrix/fracture transfer function, verified based on experimental data of Mattax and Kyte[9]. Kazemi et al. showed that for rectangles and cylinders the formula reduces to the well known forms of the shape factor. In the mean time many authors indicated the validity of the formula, but no theoretical proof was offered so far.<br>This paper derives the Kazemi-Gilman-Elsharkawy (KSE) shape factor using Control Volume Finite Difference discretization on the fracture-matrix dual continuum.<br>It will be shown that the KSE shape factor is valid for multiphase fow of compressible fluids irrespective of matrix block shape. Additionally an extension to tensorial matrix permeability is given.