A Semi-Analytic (p/z) Rate-Time Relation for the Analysis and Prediction of Gas Well Performance

In this paper we present a rigorous theoretical development of solutions for boundary-dominated gas flow during reservoir depletion. These solutions were derived by directly coupling the stabilized flow equation with the gas material balance equation. Due to the highly nonlinear nature of the gas flow equation, pseudopressure and pseudotime functions have been used over the years for the analysis of production rate and cumulative production data. While the pseudopressure and pseudotime functions do provide a rigorous linearization of the gas flow equation, these transformations do not provide direct solutions. In addition, the pseudotime function requires the average reservoir pressure history, which in most cases is simply not available. Our approach uses functional models to represent the viscosity-compressibility product as a function of the reservoir pressure/z-factor (p/z) profile. These models provide approximate, but direct, solutions for modeling gas flow during the boundary-dominated flow period. For convenience, the solutions are presented in terms of dimensionless variables and expressed as type curve plots. Other products of this work are explicit relations for p/z and Gp(t). These solutions can be easily adapted for field applications such as the prediction of rate or cumulative production. We also provide verification of our new flow rate and pressure solutions using the results of numerical simulation and we demonstrate the application of these solutions using a field example.