Accurate representation of complex reservoir geology using non-orthogonal meshes, upscaling of high-resolution geostatistical reservoir models including cross-flow effects, and strongly heterogeneous anisotropic permeable media such as cross-bedded sands and thin-bedded turbidite channels all individually or in combination give rise to simulation models with full-tensor permeability fields. Such anisotropic multiphase flow problems can be solved accurately on arbitrary non-orthogonal structured and unstructured meshes using the mimetic finite volume method. The discretization operator of the mimetic finite volume method satisfies conservation laws, and theorems of vector and tensor calculus on non-orthogonal, non-smooth, structured and unstructured computational meshes. In this paper, we demonstrate the formulation of a threedimensional variant of the mimetic finite volume method for corner-point geometry hexahedral meshes. We also discuss the results and issues associated with the implementation of the mimetic finite volume discretization operator in a parallel, fully-implicit research reservoir simulator developed using a general compositional formulation. Simulation results are presented for a variety of cases involving flow through geologically complex systems.
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