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The simulation of fractured reservoir is conventionally performed by using dual porosity formulation in which the type of transfer function may be critical. Over the past few years, various models with their strength and weakness have been developed to account for matrix-fracture interporosity flow. However, some of them are unable to simulate some mechanisms like gravity drainage. In this work, the most well-known transfer functions have been examined for simulation of the gravity drainage in a single block model and an improvement has been introduced to modify them. The validation of the developed approach have been done by using fine grid simulation  

An exact analytical solution for one-dimensional fluid flow through rock matrix block is presented. The nonlinearity induced from flow functions makes the governing equations describing this mechanism difficult to be analytically solved. In this paper, an analytical solution to the infiltration problems considering non-linear relative permeability functions is presented for finite depth, despite its profound and fundamental importance. Elimination of the nonlinear terms in the equation, as a complex and tedious task, is done by applying several successive mathematical manipulations including: Hopf-Cole transformation to obtain a diffusive type PDE; an exponential type transformation to get a...