Application of a Local Grid Refinement Technique to Model Impermeable Barriers in Reservoir Simulation
Authors: Gourley E.N. , Ertekin T. 
Published: December 2007

Abstract
In this study, a static local grid refinement technique is incorporated into three numerical simulation models to test the technique's performance in modeling impermeable flow barriers. Several faulted systems are examined to test the effectiveness of the local grid refinement technique as compared to a coarse grid system, a fine grid system and a conventionally refined grid system. The local grid refinement method is applied to three numerical models: a single-phase slightly compressible flow simulator, a single-phase compressible flow simulator, and a three-phase black oil simulator. Compared to the fine grid system, the locally refined grid system offers a decrease in computational time with a significant improvement in accuracy over the coarse grid results.

Introduction
Reservoir simulation is a widely used tool in the oil industry. The results from a simulation study are used to help design the most economical means of producing the reservoir. In order to effectively simulate how a reservoir behaves, one needs to have a model that accurately and efficiently captures the physical processes in place.
The overall numerical accuracy of a simulation study is predominantly controlled by the size of the grid blocks. However, as the size of the grid blocks are reduced to increase the degree of accuracy, the more computational work is needed to obtain the solution. An efficient technique to overcome this dilemma is to only refine the coarse grid in regions where a fine grid is needed. These regions include the near wellbore domain, saturation fronts, and geological discontinuities such as impermeable barriers. Refinement in the near wellbore domain better approximates the radial flow geometry that occurs around the well. Refinement along saturation fronts minimizes numerical dispersion of the front. Refinement around the fault planes gives a more accurate representation of the flow geometry within the immediate vicinity of the geological discontinuity.
The first level of discretization of the spatial domain is usually coarse. If all the coarse blocks are subdivided into smaller blocks then a fine grid is generated. In conventional grid refinement only certain regions are subdivided into smaller blocks and the new grid lines are extended to the boundaries of the reservoir. In local grid refinement only certain regions are refined and the new grid lines are only introduced within the refined region. These grid systems are presented in Figure 1.
Earlier work in localized grids indicates that local grid refinement is an efficient technique for modeling complex geometries in reservoirs. Forsyth and Sammon utilized an adaptive-implicit technique along with completely flexible gridblock connections for local grid refinement and modeling of faults and pinchouts. The adaptive-implicit nature of the technique enables some regions of the reservoir to be solved with a fully-implicit model while other regions are solved using the implicit pressure and explicit saturation method.
The local grid refinement technique implemented in this study was earlier used by Biterge and Ertekin. The motivation for this technique was "to develop a simple, efficient, stable, general refinement procedure for multi-dimensional, non-linear, parabolic problems." This technique solves a coarse grid system first. The solution of the coarse grid then provides the boundary conditions for the locally refined sections. Both static and dynamic multi-level local grid refinement options were tested in single-phase and multi-phase reservoirs.
The static and dynamic local grid refinement techniques were used by Manik and Ertekin for the purpose of well coning studies. In their study, the local grid refinement was not only applied to the near wellbore domain, but also implemented along the oil-water interface. The dynamic local grid refinement option was utilized to capture more accurately the oil-water interface movement through the reservoir over time. Two reservoir geometries were studied. The first system was a simple rectangular reservoir representing a blanket sand connected to a strong bottom-water drive. The second system was an anticline reservoir-aquifer system. P. 49^