Sequentially Adapted Flow-Based PEBI Grids for Reservoir Simulation

Abstract

Summary A technique for the sequential generation of perpendicular-bisectional (PEBI) grids adapted to flow information is presented and applied. The procedure includes a fine-scale flow solution, the generation of an initial streamline-isopotential grid, grid optimization, and upscaling. The grid optimization is accomplished through application of a hybrid procedure with gradient and Laplacian smoothing steps, while the upscaling is based on a global-local procedure that makes use of the global solution used in the grid-determination step. The overall procedure is successfully applied to a complex channelized reservoir model involving changing well conditions. The gridding and upscaling procedures presented here may also be suitable for use with other types of structured or unstructured grid systems. Introduction Modern geological and geostatistical tools provide highly detailed descriptions of the spatial variation of reservoir properties, resulting in fine-grid models consisting of 107 to 108 gridblocks. As a consequence of this high level of detail, these models cannot be used directly in numerical reservoir simulators, but need to be coarsened significantly. Coarsening requires the averaging of rock parameters from the fine scale to the coarse scale. This process is referred to as upscaling. For simulation of flow in porous media, the upscaling of permeability is of particular interest. A large body of literature exists on this topic; for a comprehensive review of existing techniques, see Durlofsky (2005). To preserve as much of the geological information of the fine grid as possible, the grid coarsening should not be performed uniformly, but with more refinement in areas that are expected to have large impact on the flow, including structural features, such as faults. Although grid-generation techniques based on purely static, nonflow-based considerations have been shown to produce reasonable results(Garcia et al. 1992), the application of flow-based grids is often preferable. Flow-based grids require the solution of some type of fine-scale problem. They are then constructed by exploiting the information obtained from streamlines (and possibly isopotentials) either directly or indirectly. Depending on the type of grid used, points will be defined as cell vertices or nodes, resulting in either a corner-point geometry or point-distributed grid. Several gridding techniques for reservoir simulation have been introduced along these lines, as we now discuss.

Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance

“…Unstructured grids used in reservoir modelling, commonly employ Delaunay-voronoi (PEBI) grids for spatial discretization of domain [60]. Voronoi grids can be made to conform to geological features by special treatment such that their cells become aligned to these features.…”

“…Grids based on voronoi diagrams remain predominant in reservoir simulation [9,31,58,60,61,64,76]. Voronoibased grids are locally orthogonal and permit two-point flux approximation if the permeability field is isotropic, or if the grid is generated to be K-orthogonal [64].…”

Horizontal simulation grids as alternative to structure-based grids for thin oil-zone problems: a comparison study on a Troll segment

“…We concluded above that the most critical factor in thin oil-zone problems was the representation of the well path, so the preferred approach would be to utilize a grid which could honor both geology and well paths. Unstructured grids, noticeably Voronoi-or PEBI-grids (see, e.g., [10,12] and the references herein) allow for accurate modeling of both geology and well paths, and as such appear to be ideal for handling of the problem in question. As an example, Mundal, Keilegavlen, and Aavatsmark [11] studied near-well flow on generalized grids in two dimensions.…”

Unstructured Cut-Cell Grids for Modeling Complex Reservoirs

“…Unfortunately, the generation of the multiblock structure for complex reservoir geometries requires significant user expertise and has proved challenging to automate. More-general unstructured approaches such as Voronoi grids and perpendicular bisector grids (Heinemann et al 1991;Palagi and Aziz 1994;Hale 2001) have continued to receive much attention (Skoreyko et al 2003;Mlacnik et al 2006;Katzmayr and Ganzen 2009;Branets et al 2009;Evazi and Mahani 2010;Merland et al 2011). Moyen et al (2004) pointed out that the GeoChron framework can be used to map properties onto an unstructured polyhedral grid.…”