A fully-implict mimetic finite difference method (MFD) for fractured carbonatereservoir simulation is presented. MFD, as a novel discritization, has been applied to many fields due to its local conservativeness and applicability of any shape of polygon. Here we extend it to fractured reservoirs. Our scheme is based on MFD method and discrete fracture model (DFM). This scheme supports general polyhedral meshes, which gives an advantage for reservoir simulation application. The principle of the MFD method and the corresponding numerical formula for discrete fracture model are described in details. In order to assure flux conservation, fully implicit method is employed. We test our method through some examples to show the accuracy and robustness.

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