Unstructured-Coarse-Grid Generation Using Background-Grid Approach

Abstract

Summary Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized gridpoint density and a minimized number of gridblocks, especially for coarse-grid generation from a fine-grid geological model. In any coarse-grid generation, proper distribution of gridpoints, which form the basis of numerical gridblocks, is a challenging task. We show that this can be achieved effectively by a novel grid-generation approach based on a background grid that stores gridpoint spacing parameters. Spacing parameter (L) can be described by Poisson's equation (∇2L = G), where the local density of gridpoints is controlled by a variable source term (G); see Eq. 1. This source term can be based on different gridpoint density indicators, such as permeability variations, fluid velocity, or their combination (e.g., vorticity) where they can be extracted from the reference fine grid. Once a background grid is generated, advancing-front triangulation (AFT) and then Delaunay tessellation are invoked to form the final (coarse) gridblocks. The algorithm produces grids varying smoothly from high- to low-density gridpoints, thus minimizing use of grid-smoothing and -optimization techniques. This algorithm is quite flexible, allowing choice of the gridding indicator, hence providing the possibility of comparing the grids generated with different indicators and selecting the best. In this paper, the capabilities of approach in generation of unstructured coarse grids from fine geological models are illustrated using 2D highly heterogeneous test cases. Flexibility of algorithm to gridding indicator is demonstrated using vorticity, permeability variation, and velocity. Quality of the coarse grids is evaluated by comparing their two-phase-flow simulation results to those of fine grid and uniform coarse grid. Results demonstrate the robustness and attractiveness of the approach, as well as relative quality/performance of grids generated by using different indicators.