Triple mesh methods and their application to two-phase flow in porous media

Abstract

The computational cost of simulation on fine-scale reservoir models can be prohibitively expensive. While upscaling typically helps in reducing cost, it also results in a reduction in accuracy. Two-scale approaches such as dual mesh methods (DMM) have been developed over time in an attempt to reduce simulation cost while maintaining near fine-scale levels of accuracy and resolution. While these two-scale methods can be very effective in improving accuracy, they can be quite expensive as well. This paper presents two multimesh methods, namely, the Triple Mesh Method (TMM) and the Extended Triple Mesh Method (ETMM). Both methods involve introducing a third grid at an intermediate scale between the coarse and fine scales. These involve two levels of upscaling of the grid properties and two levels of downscaling the solutions to the flow equation. TMM involves two successive local downscaling steps of the flow solution from the coarsest to the finest mesh. ETMM on the other hand involves two successive extended local downscaling steps of the flow solution from the coarsest to the finest mesh. Each downscaling step in ETMM involves the application of ‘Directional Oversampling’ first introduced in the extended dual mesh method EDMM. These two methods along with DMM and EDMM methods were tested on different waterflooding problems and results compared with the coarse-scale and fine-scale solutions. The results show both ETMM and TMM to be effective in error reduction and also more cost effective than their respective dual mesh alternatives.