Optimization-based Upscaling for Two-Phase Flow Through Porous Media: Structured Grid Generation

The process of coarsening the detailed geological model of a reservoir to simulation models is known as upscaling. There are two fundamental steps in the procedure of upscaling, i.e., defining the coarse grid geometry and calculating the average properties for the generated coarse grid. In this paper, the focus will be on investigating the applicability of optimization in the context of coarse grid geometry definition. To do so, different objective function candidates will be defined, and their behavior in terms of predicting the two-phase flow accuracy of coarse grids will be analyzed to determine the proper objective function. A modified objective function employing the idea of analytical dual-mesh method will be defined to reduce the optimization process time. This objective function will be employed to generate the optimum Cartesian structured coarse grid geometry using global optimization techniques. The performance of the proposed grid generation technique will be investigated through various highly heterogeneous test cases under different boundary conditions, mobility ratios, upscaling levels, and permeability upscaling methods.