This paper describes a new control volume based finite difference scheme for pertroleum reservoir simulation which can be used with unstructured grids. The numerical scheme to model fluid flow is shown to be easily used for Voronoi grids in 2D. It can also be used with certain grometrical limitations for 3D Voronoi grids. The scheme can be used without any significant limitations for triangle or tetrahedron based grids where control volumes are constructured around their vertices. It assumes uniform properties inside such control volumes. Full, anisotropic and asymmetric permeability tensor can be easily handled with the proposed method. TShe permeability tensor can vary from block to block. Thus it will be of great value in modeling fluid flow in reservoirs where principal directions of permeability varies between beds or within a bed. The paper also presents an analyisis of some of the published flexible gridding schemes which use a control volume type algebraic approximation and demonstrate the advantages of the method presented here. The technique for grid construction is also discussed. Test results presented here demonstrate the need for proper representation of reservoir geometry to predict the correct flow behavior. The gridding scheme described in this paper achieves that purpose.
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