Comparison of two volume balance fully implicit approaches in conjunction with unstructured grids for compositional reservoir simulation

In reservoir simulation, compositional modeling is one of the most commonly used approaches for enhanced oil recovery processes. The methods used to solve the equations arising from the modeling of fluid flow in the reservoirs involve the degree of implicitness and the selection of the primary and secondary equations; primary and secondary variables have a great impact on the computational time. In this work, we implement and compare two fully implicit methods based on volume balance approach. The two methods share the same set of primary variables: pressure and total number of moles of each component. The total number of moles of each component is solved with use its material balance equation, whereas the pressure is solved with use of a volume balance equation. The difference between the two methods is in the nature of the volume balance equation. Whereas for one of the formulations the volume balance equation is the volume constraint and hence the only terms that appear in the Jacobian matrix are those from the volume in which the volume balance is evaluated, the second formulation considers an expanded form of the volume constraint. The main advantage of this expanded equation is that the Jacobian matrix involves information from the volume in which the balance is performed and from all neighboring volumes. The element-based finite-volume method in conjunction with unstructured grids for 2D and 3D reservoirs is used to discretize the material and volume balance equations. For two dimensions, quadrilateral and triangular elements are considered, whereas for three dimensions, hexahedral, prismatic, tetrahedral, and pyramidal elements are considered. The implementations were performed with the UTCOMP simulator developed at the University of Texas at Austin. We compare the performance of the two above-mentioned fully implicit formulations with the implicit pressure explicit composition (IMPEC) formulation of the UTCOMP simulator. The results of several case studies are compared in terms of volumetric oil and gas rates and the total CPU time. The results show good agreement between the production rates and saturation fields for all formulations. Additionally, the performance of the fully implicit methods was superior to that of the IMPEC method as a larger number of grid blocks were used in the simulations.