Extended Dual Mesh Method with applications in two-phase flow in heterogeneous porous media

Modern geological models typically contain too many cells that make running reservoir simulations at times impractical or prohibitively costly. While upscaling helps with this problem, upscaled models typically suffer loss in accuracy. Different multiscale and dual mesh methods have been developed in an attempt to achieve fine-scale accuracy at reduced computational cost. This paper presents a dual-grid simulation method called Extended Dual Mesh Method (EDMM). EDMM is aimed at reducing homogenization and numerical dispersion errors inherent in upscaled models. In EDMM, velocities are first solved on the coarse scale. Fine-scale velocity fields are then computed by solving extended (oversampled) local flow problems with Neumann boundary conditions similar to Dual Mesh Method (DMM). These extended local problems are constructed such that local and global conservation is guaranteed. To achieve this, we propose a new concept of called Directional Oversampling (DO). DO ensures flux continuity between oversampled partitions therefore guaranteeing that the obtained global finescale velocity field is conservative. The resulting fine flux field is then used to compute fine-scale saturation. Also proposed is a new approach for calculating the coarse block interface transmissibilities using fine-scaleblock mobilities thereby improving the coupling between the coarse-scale and fine-scale models. EDMM combines the simplicity of the DMM with the accuracy improvement of oversampling and is compatible with any upscaling technique. Examples were used to test the accuracy and robustness of EDMM and results were compared to the fine-scale, DMM and coarse-scale solutions. Results show that the method is a significant improvement on the DMM, much better than coarse grid results and comparable in quality to fine-scale solutions whilst maintaining speed comparable to DMM. Two error indicators, the water cut error and the breakthrough error, were employed in quantify accuracy of the different solution methods relative to the fine scale solution. The indicators show EDMM to be multiple times more accurate than DMM and in some examples orders of magnitudes more accurate. This work demonstrates EDMM to be accurate not only in predicting the water breakthrough at producer wells but also at predicting water-cut after breakthrough.