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This paper investigates the implications of the various linearization schemes considered in the analytical solution of the transient-state nonlinear capillary diffusion equation for derivation of the matrix-fracture-transfer models for naturally fractured petroleum reservoirs. The analysis is carried out by considering a restricted and hindered matrix-fracture interface fluid transfer owing to the finite-skin present at reservoir matrix block surfaces separated with intersecting fractures. The skin is attributed due to the formation of a stationary fluid film or an actual skin because of formation damage by various processes, such as deposition of minerals and other debris, and adverse rock-fluid interactions. The approximation errors associated with the linearization of the nonlinear capillary diffusion model are quantified. It is demonstrated that such errors may be negligible when compared to the uncertainties involved in actual reservoir data. This nevertheless depends greatly on the reservoir rock and fluid properties, and choice of linearization and manipulation methods. |
