A Practical Method for Minimizing the Grid Orientation Effect in Reservoir Simulation
Authors: Wolcott D.S. , Kazemi H. , Dean R.H. 
Published: December 2007

Abstract
Reservoir flow simulators are used to predict the performance of oil and gas reservoirs. One of the most significant short comings of conventional reservoir simulators is they produce different results when the orientation of the computational grid is changed. Grid orientation can cause variations in predicted recovery of more than 22% for miscible floods with a mobility of 50. Therefore, in this situation, evaluating infill drilling or pattern realignment with a conventional simulator can be impractical. The objective is to provide a practical method for reducing grid orientation and numerical dispersion.
A technique is presented that utilizes a nine-point formulation of the pressure and saturation equations with a third order accurate total variation diminishing (TVD) scheme. This new technique outperforms previous techniques by reducing the grid orientation difference to less than one percent even when using coarse grids. In addition, the technique reduces numerical dispersion and produces sharper flood fronts. The practical contribution of this new work is that it can be coded in a simulator with minor coding additions. The method provides improved accuracy for simulating infill drilling, pattern realignment, horizontal well, immiscible or miscible flooding projects.

Introduction
Large scale reservoir flow simulators use finite-difference formulations, and are used to predict the performance of oil and gas reservoirs. They are useful for IOR projects/processes such as infill drilling, horizontal wells, immiscible flooding (e.g., waterflooding and miscible flooding (e.g., CO2 and hydrocarbon gas). Even after many years of use and development of new numerical techniques. there still remain a number of areas where reservoir simulators can be improved. One of the most significant shortcomings of conventional five-point finite-difference reservoir simulators is they produce a different result when the grid orientation is changed (diagonal versus parallel). This problem can be partially alleviated when nine-point finite-difference or finite-element methods are used.
The number of finite-difference grid blocks used in a simulation is important. Generally, the more grid blocks used, the more accurate the numerical solution and the more detailed the description of the reservoir fluid distribution. However, for practical simulations there is a limit to the number of grid blocks. In addition, using more grid blocks does not necessarily reduce the grid orientation error. Grid orientation occurs because numerical truncation error is asymmetric.
The objective of this work is to provide a practical method for minimizing grid orientation, improving numerical accuracy, and reducing numerical dispersion to prevent smearing of flood fronts and rate forecasts. This work documents the grid orientation error for miscible and immiscible systems using the most common as well as recently developed numerical methods. Understanding the magnitude of grid orientation error will provide the practicing engineer with a tool to gauge how much of the recovery change comes from, for example, re-orienting or adding wells.