Modeling Reservoir Geometry With Irregular Grids

Summary This paper describes a practical method in which irregular or locally irregular grids are used in reservoir simulation with the advantages of flexible approximation of reservoir geometry and reduced grid-orientation effects. Finite-difference equations are derived from an integral formulation of the reservoir model equations equivalent to the commonly used differential equations. Integrating over gridblocks results in material-balance equations for each block. This leads to a finite-volume method that combines the advantages of finite-element methods (flexible grids) with those of finite-difference methods (intuitive interpretation of flow terms). Grid-orientation effects are investigated. For grids based on triangular elements, the more isotropic distribution of gridpoints diminishes the orientation effect significantly. Numerical examples show that the regions of interest in a reservoir can be simulated efficiently and that well flow can be represented accurately.