A mathematical model is presented which forms the basis of a multiphase, three dimensional reservoir simulator for characterizing multiphase flow in naturally fractured, lenticular formations. The model is general in that it can treat the presence or absence of natural fractures and/or sand lenses in a statistical fashion based upon a known distribution for each. A double porosity medium is approximated by an equivalent single porosity medium for each cell block. Similarly an equivalent permeability for each cell block is approximated by calculating an effective principal permeability as a function of rock matrix and fracture permeabilities. In any given cell block the fractures can have any orientation. The model can be used to simulate the behavior of a double porosity medium composed of heterogeneous, anisotropic rock matrix, and a heterogeneous, anisotropic fracture system. In addition it possesses the capability of including sand lense lenticularity and hydraulically created fractures with finite or infinite conductivity. Simulation results are presented for an actual field case and for hypothetical wells producing under multiphase flow conditions.

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