The permeability tensor in three-dimensional space is given by a symmetric and positive definite matrix. Advances in reservoir characterization and geostatistics facilitate the construction of fine scale reservoir images. Some degree of upscaling is almost always required to make the problem computationally amenable. The upscaled permeabilities calculated thus are, in general, full tensor quantities. Homogenization of discrete-fracture domains also leads to full-tensor permeabilities of the equivalent permeability field. A formal infrastructure to treat full-tensor permeability field has been developed in this paper along with an understanding of the impact of such a field.

A novel co-ordinate transformation scheme is proposed where the cross permeability terms are eliminated and an equivalent diagonal-tensor permeability field is generated. The multiphase flow equations are solved using the finite-element discretization. Galerkin finite element method is employed and the model equations are solved fully implicitly.

First, it is demonstrated that full-tensor representation is necessary to preserve the flow characteristics in the fine-grid domain in both the cases. It is then shown how the computational complexity of the full-tensor simulation could be reduced using the transformation scheme. The novel transformation scheme thus offers the computational simplicity of the diagonal-tensor representation, while preserving the rigor of the full-tensor approach. The effect of using the full-tensor field from homogenized fracture permeabilities is described.

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