Reduction Of Grid Orientation Effects In Reservoir Simulation

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper presents a method for reducing the effect of grid orientation on computed numerical results in finite difference reservoir simulation. The method involves modification to the interblock phase transmissibilities normally calculated and the use of a two-point weighting scheme in calculating mobilities. These are minor changes to an IMPES type simulator. Example problems of unit mobility ratio and high mobility ratio with both long and short transition zones are included. The results indicate that neither the transmissibility modification nor the two-point weighting scheme are sufficient by themselves to correct the error although the two-point. weighting of mobility has the greatest effect. Introduction Many reservoir simulation problems involve the study of displacement patterns of injected fluids. Results of such studies using finite difference models are affected by grid orientation errors in which fluid tends to flow in the direction of the grid axes rather than diagonal to them. This paper presents a method for reducing grid orientation effects, inherent in finite difference simulators, by modification of the interblock phase transmissibilities to account for diagonal flow. Incorporation of the modified transmissibility is a minor change to an IMPES type simulator and when used with two-point upstream mobility weighting gives excellent results. The grid orientation problem is illustrated by a quarter of a five spot overlain by two different finite difference grids. A diagonal grid has its coordinate axes parallel to the sides of the quadrant of the five spot, with the injection and production wells on diagonally opposite corners of the grid.