Representation of High Rate Gas Wells in Reservoir Simulation

Abstract

Abstract The paper presents an analysis of nonlinear Darcy flow of gas in reservoirs. The equations employed in the analysis are derived from an integration of the fundamental equations describing the flow of real gases in homogeneous porous media. The equations are derived in terms of squares of pressure for radial steady and pseudo steady flow systems. The analysis indicates that the squared-gradient nonlinearity present in the gas flow differential equation results in a pressure drop and rate relationship symptomatic of non-Darcy flow. The magnitude of the nonlinear contribution to pressure drop is similar to that computed on the basis of non-Darcy theory. This raises the possibility that observed nonlinearities may not be due to non-Darcy effects but merely a result of fluid property variations. The implication of the findings to the simulation of gas wells is also discussed. The results suggest that for a typical radial grid system with fine grids near the well, it may be unnecessary and incorrect to include additional terms to account for deviations from Darcy flow. In large and rectangular grids however, nonlinear terms are required for correct representation. These additional terms are shown to relate to grid size and shape, and are necessary not because Darcy's law is invalid but because the grids are of finite size.