Effect of cross derivatives in discretization schemes in structured non-orthogonal meshes for compositional reservoir simulation

Corner-point meshes have been implemented in several commercial reservoir simulators due to their flexibility to deal with several important features of the hydrocarbon bearing-reservoirs, such as irregular boundaries, geologic fractures, and faults. Although this type of mesh presents an important step in discretization of the domains for reservoirs, some parts of the approximate equation in discretized formulations are neglected in most commercial simulators. The neglected terms are related to the cross derivatives and, in general, are neglected to produce the same Jacobian stencil as when Cartesian grids are employed. This work presents an investigation of the effect of cross derivatives in discretization schemes using structured non-orthogonal boundary-fitted meshes in conjunction with a compositional reservoir simulator. The main goal is to investigate the difference between the numerical results with and without the cross derivatives that arise when the Cartesian equations are written for a transformed plane. We used an in-house compositional reservoir simulator to carry out this study. The component mass balance equations for a compositional, multiphase, multi-component fluid flow are solved using a fully implicit reservoir simulator in conjunction with the finite volume method. The results of several reservoir simulation case studies that were performed to carry out this study are presented in this paper.