A New Grid Block System for Reducing Grid Orientation Effect

Abstract The grid orientation effect (GOE) is a long-standing problem plagueing reservoir simulators that employ finite difference schemes. A rotation of the computational grids yields a substantially different solution under certain circumstances. A Cartesian grid with one axis parallel to the line joining an injector and producer gives a solution significantly different from a grid that has the axes oriented at 45° to this line. This article presents a new grid system that can reduce the grid orientation effect. This system involves using a unique grid-block assignment where rectangular grid blocks are interspersed with octagonal grid blocks. The boundaries are populated with triangular grid blocks. The entire domain consists of a “structured” grid block system referred to as the hybrid grid block (HGB).

[1]  D. W. Peaceman Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability , 1983 .

[2]  J. L. Yanosik,et al.  A Nine-Point, Finite-Difference Reservoir Simulator for Realistic Prediction of Adverse Mobility Ratio Displacements , 1979 .

[3]  G. E. Robertson,et al.  Grid-Orientation Effects and the Use of Orthogonal Curvilinear Coordinates in Reservoir Simulation , 1978 .

[4]  Karsten Pruess,et al.  A Seven-Point Finite Difference Method for Improved Grid Orientation Performance in Pattern Steamfloods , 1983 .

[5]  Stephen C.M. Ko,et al.  A Weighted Nine-Point Finite-Difference Scheme For Eliminating The Grid Orientation Effect In Numerical Reservoir Simulation , 1979 .

[6]  A.C.F. Correa,et al.  High-Resolution Schemes for Conservation Laws: Applications to Reservoir Engineering , 1992 .

[7]  B. F. Towler,et al.  Reduction of Grid-Orientation Effects in Reservoir Simulation With Generalized Upstream Weighting , 1985 .

[8]  Y. M. Chen,et al.  Modeling reservoir geometry with irregular grids , 1991 .

[9]  M. R. Todd,et al.  Methods for Increased Accuracy in Numerical Reservoir Simulators , 1972 .

[10]  P. Vinsome,et al.  One approach to the grid orientation problem in reservoir simulation , 1981 .

[11]  Hossein Kazemi,et al.  Mixed five-point/nine-point finite-difference formulation of multiphase flow in petroleum reservoirs , 1992 .

[12]  Keith H. Coats A consistent method for calculating transmissibilities in nine-point difference equations , 1983 .

[13]  A. R. Merchant,et al.  Higher Order Flux Update Function Method for Reduction of Numerical Dispersion and Grid Orientation Effect in Reservoir Simulation , 1994 .

[14]  Hossein Kazemi,et al.  A Practical Method for Minimizing the Grid Orientation Effect in Reservoir Simulation , 1996 .

[15]  Stanley Osher,et al.  Minimization of Grid Orientation Effects Through Use of Higher Order Finite Difference Methods , 1993 .

[16]  P. C. Shah A Nine-Point Finite Difference Operator for Reduction of the Grid Orientation Effect , 1983 .