Consistent Discretization Methods for Reservoir Simulation on Cut-Cell Grids

Abstract

Discretization methods have been developed to accompany a novel cut-cell gridding technique for reservoir simulation that preserves the orthogonality characteristic in the lateral direction. A major drawback of the cut-cell gridding method is that polyhedral cells emerge near faults that have relatively small volumes. Pragmatic but non-rigorous approximation methods have been developed in the past to merge these cells with their neighbors so that the grid representation fits the two-point flux approximation (TPFA) framework. In this work, we take a different approach and investigate the global and local applications of select consistent discretization methods in the vicinity of fault representations on cut-cell grids. We develop and test consistent discretization methods that are of low computational cost and do not require major intrusive changes to the solver structure of commercial reservoir simulators. Cell-centered methods such as multi-point flux approximation (MPFA), average multi-point flux approximation (AvgMPFA), and nonlinear two-point flux approximation (NTPFA) methods fit naturally into the framework of existing industrial-grade simulators. Therefore, we develop and test variants of the AvgMPFA and NTPFA methods that are specifically designed to operate on cut-cell grids. An implementation of the well-established but computationally expensive MPFA method is also made for cut-cell grids to serve as a reference to computations with AvgMPFA and NTPFA. All investigated methods are implemented within the framework of a full-physics 3D research simulator with a general compositional formulation, which encompasses black-oil models. We use a set of synthetic cut-cell grid models of varying complexity including conceptual models and a field-scale model. We compare the novel cut-cell adapted AvgMPFA and NTPFA simulation results in terms of accuracy and computational performance against the ones computed with reference MPFA and TPFA methods. We observe that AvgMPFA consistently yields more accurate and computationally efficient simulations than NTPFA on cut-cell grids. Moreover, AvgMPFA hybrids run faster than NTPFA hybrids when compared on the same problem for the same hybridization strategy. On the other hand, the computational performance of AvgMPFA degrades more rapidly compared to NTPFA with increasing "rings" of orthogonal blocks around cut-cells owing to its relatively wider stencil. Auspiciously, only one or two "rings" of orthogonal blocks around cut cells are sufficient with AvgMPFA to deliver high accuracy.