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

Abstract This paper presents a rigorous theoretical development of long term boundary-dominated flow solutions which involve direct coupling of the stabilized flow equation with the gas material balance equation. Due to the highly non-linear 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 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 historywhich in most cases is simply not available. Our approach uses functional models to relate the viscosity-compressibility product with the reservoir pressure (p/z) profile. These models provide approximate, but direct, solutions for modelling 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 rate prediction. We also provide verification of our new flowrate and pressure solutions using numerical simulation results and we demonstrate the application of these solutions using a field example.

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