Improved upscaling of reservoir flow using combination of dual mesh method and vorticity-based gridding

A novel technique for upscaling of detailed geological reservoir descriptions is presented. The technique aims at reducing both numerical dispersion and homogenization error generated due to incorporating a coarse computational grid and assigning effective permeability to coarse-grid blocks, respectively. In particular, we consider implicit-pressure explicit-saturation scheme where homogenization error impacts the accuracy of the coarse-grid solution of the pressure equation. To reduce the homogenization error, we employ the new vorticity-based gridding that generates a non-uniform coarse grid with high resolution at high vorticity zones. In addition, to control numerical dispersion, we use dual mesh method (DMM) which uses different grids to solve pressure and saturation equations. The coarse grid generated from vorticity is used for computation of pressure, and the reference fine grid is used for updating saturation explicitly. The strongest point of the method is that dual mesh method has been incorporated onto non-uniform grid structure. This combination removes the need to solve the full fine grid for two-phase flow modeling, resulting in a less computationally demanding and more accurate upscaling technique. To evaluate the method, we run two-phase simulation using different 2D test cases. Our results indicate that the non-uniform DMM is more accurate than the uniform DMM due to using vorticity-based grids. The speedup achieved in the computation is significant depending on the complexity of model and degree of upscaling.