Comparison of structured and unstructured formulations for compositional reservoir simulation

Abstract

The main goal of the present work is to compare Corner Point and unstructured grids based on Element-based Finite Volume Method (EbFVM) applied to compositional multiphase/multi- component flow in petroleum reservoirs. Unlike the reservoir production, the numerical solution is dependent on the grid and numerical approach used to discretize the material balance equations. Commercial simulators, which use structured Corner Point grids, usually neglect the cross terms that arise from the transformation of equations from the physical to the computational plane. This approximation may lead to substantial errors in mass flux calculation due to the cross terms influence when highly non-orthogonal grids are used. Another important approach to discretize the reservoir is the use of unstructured grids in conjunction with the finite-volume method. This methodology is well known as EbFVM and it is a locally conservative method. For the aforementioned reasons, the EbFVM is expected to more flexibly handle complex geometries and provide greater accuracy. However, EbFVM is also computationally more expensive than Corner Point grids due the large stencil of the Jacobian matrix. In the present work, we are going to implement two types of grids in an in-house compositional simulator developed at the University of Texas at Austin known as UTCOMP. The Corner Point grids are going to be generated using a commercial simulator. Although the EbFVM 3D grids can be composed of hexahedrons, tetrahedrons, prisms, and pyramids only hexahedrons and tetrahedrons are going to be used to match the hexahedrons of the Corner Point grids. In order to use the corner point grid to create the grid for the EbFVM, the Corner Point must be preprocessed to be adapted to the EbFVM, eliminating the hanging nodes. The comparison of the results of the two grid types will be presented in terms of oil and gas production, saturation fields, and CPU time. The EbFVM presented itself as a viable alternative to the traditional Corner Point geometries. It is observed that the EbFVM is capable of achieving an approximate numerical solution compared to traditional Corner Point methods with a much coarser grid and lower computational cost.