A class of difference methods that rigorously treat distorted grids and full 3D tensor permeabilities is described. The approximations are based on conventional nodal Galerkin finite element methods. By varying the element shapes and integration quadrature a variety of control volume methods with various difference stencils are produced. Accuracy, consistency and flux continuity are assured by the strong theoretical basis of the Galerkin finite element method. Tests of an implementation based on 3D hexahedral elements are reported. A compositional simulation with a full 27-point method was found to require less that twice the computation time of conventional 7-point methods.

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