Curvilinear Coordinate Systems for Reservoir Simulation

This paper presents a set of curvilinear coordinate transformations that lead to no mixed derivative terms in transformed flow equations. The transformations are created by examining the transformed flow equations and by showing that the mixed derivative terms are zero if the transformation satisfies a system of differential equations that depend on the geometry and rock property distribution within the reservoir. Numerical examples with a black-oil simulator are presented to show the increased accuracy resulting from the use of the curvilinear coordinate system and the importance of eliminating the mixed derivative terms.