Vorticity-Based PEBI Grids for Improved Upscaling of Two Phase Flow

Abstract

Abstract Highly detailed geological models, which are primary inputs to reservoir simulator, necessitate the reduction of number of grid blocks to be used in the solution of flow equations. However preparing a coarse scale model that can mimic the fine scale behavior is a challenging task. Cartesian grid suffers from some shortcomings, as in adaptation with geological and geometrical features and the phenomenon of grid orientation effect that motivates the use of unstructured grid. Different methods have been used for this purpose, but no one is robust enough that justifies the need for more research. In this paper, we propose an unstructured grid generation scheme that utilizes the vorticity of fluid flow in porous media as the determining parameter for background grid generation. It entails the simulation of single-phase flow on the fine grid and obtaining the velocity field and subsequently vorticity map. Vorticity is then used to generate the background grid that plays an essential role in the generation of desired final coarse grid. At this stage user needs to determine the value of some parameters such as maximum and minimum spacing, vorticity cut-off and intensity degree. Advancing front method and Delaunay triangulation are then resorted to provide the triangular and Voronoi (PEBI) grid. The developed technique, which aims at capturing both flow and geologic details, produces grids with higher resolution at critical vorticity areas, such as around layer boundaries, and with lower resolution where vorticity is negligible, like in homogenous regions. This technique is applied to two channelized and heterogeneous models and the results are presented. Two-phase flow simulations are performed on the generated coarse grids and the results are compared with the ones of fine scale grid and uniformly generated coarse grids. The results show a greater accuracy compared to uniformly gridded models.