A Full-Stage Productivity Equation for Constant-Volume Gas Reservoirs and Its Application

Abstract

Gas well production involves various stages, including stable, variable, and declining production. However, existing production-capacity equations typically apply only to the stable production stage, limiting their effectiveness in evaluating gas well productivity across all stages. To address this, the material balance equation and Darcy’s equation were employed to account for changes in average formation pressure due to pressure drop funnels. The concept of a pressure-conversion skin factor was introduced, and its approximation was developed, leading to the establishment and solution of a full-stage productivity equation. Numerical simulations were then conducted to verify the accuracy and applicability of this equation. The findings are as follows: ① The full-stage productivity equation remains effective even when production rates and pressure are not constant, with the only potential source of inaccuracy being the approximative solution for the pressure conversion-skin factor. ② Numerical simulations demonstrated that the approximate solution closely matched the numerical simulation results for average formation pressure across various production stages and fundamental parameters, showing a consistent trend and high precision. The approximate and independent approximation solutions for absolute open-flow capacity were nearly identical, indicating the full-stage productivity equation’s applicability throughout the production of gas wells. ③ Application results revealed that the full-stage productivity equation offers superior accuracy compared to the modified isochronous well test. ④ The approximate solution generally provides slightly higher accuracy, and the independent approximate solution effectively eliminates the influence of gas leakage radius. Therefore, the use of the approximate solution is recommended to calculate the average formation pressure and the independent approximate solution to calculate the absolute open-flow capacity. The full-stage productivity equation developed in this study is not constrained by the production system, making it suitable for productivity evaluation across all stages of gas well production. This has significant implications for the effective development of gas fields.