Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized grid point density and minimized number of gridblocks especially for coarse grid generation from a fine grid geological model.
In any coarse grid generation, proper distribution of grid points, which form basis of numerical gridblocks, is a challenging task. We show that this can be effectively achieved by generating a background grid that stores grid point spacing parameter.
Spacing (L) can be described by Poisson's equation () where the local density of grid points is controlled by a variable source term (G). This source term can be based on different grid point density indicators such as permeability variations, fluid velocity or their combination e.g. vorticity, where they can be extracted from reference fine grid. Once background grid is generated, advancing front triangulation and then Delaunay tessellation are invoked to form the final (coarse) gridblocks. This algorithm is quite flexible, allowing choice of the gridding indicator and thus 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 a highly heterogeneous test case. 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 approach, as well as relative quality/performance of grids generated by using different indicators.
Introduction
Practical handling of detailed geological models has long been a serious challenge for reservoir simulation and management. Efficient coarsening of the fine-scale model is a potential choice to alleviate the problem and has been addressed by several researchers. Original grids may be coarsened to generate structured or unstructured grids, each having pros and cons. As long as structured grid works well, it is preferable to unstructured one. However, when the physical domain is highly heterogeneous and geometrically complex, structured grids may fail to well capture the complex features, unless very fine grid is used. This contributes to the need for use of unstructured grid.
Unstructured grid generation (UGG) techniques generally entail three steps: grid point insertion, triangulation and construction of gridblocks. Insertion of grid points is completely arbitrary and is the main advantage of UGG. It is well understood that computational grid points have to be distributed in the physical domain in a way that these are denser where flow and rock properties are varying more or their magnitude are large. Thus areas such as near wells, high flow regions, fractures, faults etc are potential regions to be gridded finer. Several methods for the grid point insertion have been used in reservoir simulation. Local grid refinement (LGR) has been developed with this idea. Cartesian local grid refinement1,2 and hybrid local grid refinement3 are two well-known types of LGR. As these grids are based on a Cartesian grid, both have the difficulty in aligning the grid lines with complex features and boundaries. Modular gridding, proposed by Palagi and Aziz4, uniformly distribute the grid points in the domain, resulting in a coarse uniform Voronoi grid (base grid). Then several local grid systems suitable for specific geological and geometrical feature are constructed independently and placed in the appropriate location of that feature in the base grid. This procedure is able to generate flexible grids. However, it could only capture the notable features such as faults, large fractures, vertical and horizontal wells. It does not necessarily capture flow and rock heterogeneities.
