A 3D hybrid element-based finite-volume method for heterogeneous and anisotropic compositional reservoir simulation.

Abstract

3D unstructured grids for heterogeneous and anisotropic compositional reservoir simulation in conjunction with an element-based finite-volume method (EbFVM) are presented. The approximate equations of the EbFVM adopted in this work are obtained from integration of the compositional material balance equations directly to each element type. Using this approach, the final approximation equations do not impose any limitation on the element shape. The methodology used in this work is suitable for modeling complex features of reservoirs such as irregular boundaries, fractures, faults, inclined and distorted wells. The mesh for 3D dimensional domains can be built of hexahedrons, tetrahedrons, pyramids and prisms, or a combination of these elements. According to the number of vertices, each element is divided into sub-elements and then mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex creating a cell vertex approach. It is expected that the approach employed in this work will have less grid orientation effect than the one using Cartesian meshes since more gridblocks are used in the approximated equations. The results for several compositional reservoir simulation case studies are presented to demonstrate the application of the method.