Modeling of Real Gas Flow Behavior in Porous Media

Chien, Tony
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Due to the highly nonlinear variation of gas density and viscosity with respect to pressure, no analytical solution to the real gas diffusivity equation has ever been presented in the literature. Analytical solutions used in gas well testing and pressure analysis are based on idealized assumptions, such as small and/or constant gas compressibility and constant hydraulic diffusivity. These solutions, though widely used and easily applied, are not accurate. This research presents a detailed investigation in the behavior of real gas flow through porous media. Starting from the most fundamental flow equation a new real gas potential is implemented to transform the nonlinear flow equation into a quasi-linear diffusivity equation. The effects of pressure-dependent fluid and rock properties such as gas viscosity, compressibility, porosity and permeability are included. Advanced analytical derivations with respect to nonconstant hydraulic diffusivity are performed, and an analytical solution method is successfully developed. Multiple-rate and multiple-well systems as well as bounded reservoirs of any shape are rigorously implemented by using the principle of superposition and an unsteady-state bounding technique. Validation of the model is favorably achieved by comparison with finite-difference simulation and type curve matching. Reservoir pressures and flowing bottomhole pressures calculated by the analytical solution presented in this study are more accurate than by those methods published in the literature. The new solution method is also applicable to a broad range of pressure changes and different flow periods. This is a significant contribution to transient pressure analysis, long-term well performance tests and production forecasts in natural gas reservoirs. Moreover, since the pressure-dependent porosity and permeability are included in this study, the general solution may be applied to abnormally pressured reservoirs and tight gas sands for improved predictions of gas reserves and flow performance.