A higher-order finite-difference compositional simulator

Chang, Y.-b., Pope, G.A. and Sepehrnoori, K., 1990. A higher-order finite-difference compositional simulator. J. Pet. Sci. Eng., 5: 35-50. A third-order finite-difference method was applied to a new three-dimensional, four-phase, equation-of-slate, compositional simulator. The third-order scheme was tested for first-contact miscible flow, waterflooding, immiscible, and multiple-contact miscible condensing gas displacements. The authors show that this method agrees with a two-dimensional, analytical solution. The authors also show that the higher-order method has less grid orientation effect than either one-point or two-point upstream weighting methods. A grid refinement study shows that it also has less numerical dispersion. This method was easy to implement and requires only a small increase in storage. Computation time can be reduced since the reduction in numerical dispersion allows larger grid blocks to be used while maintaining an accurate solution. For example, for a one-dimensional multiple-contact miscible displacement the computational time was reduced by a factor of 34.5 compared to the same accuracy using one-point upstream weighting.