Analytical Method for High-Speed Non-Darcy Seepage Equations Considering the Inertia-Turbulence Effect of Natural Gas

This paper describes a method and theory for predicting the productivity of natural gas wells and analyzing well test data. The method is based on mathematical and physical equations and the flow characteristics of natural gas in porous media. It establishes a nonlinear and unstable partial differential equation for seepage considering the turbulence effect, and introduces a dimensionless transformation function based on pressure, time, and location. By solving the analytical solution of this equation, the productivity of natural gas wells can be predicted, and well test data can be analyzed. The calculated results show that: (1) Simplified calculations using original formation pressure will result in significantly underestimated results, while simplification using average parameters is reasonable but still has errors; (2) Well test model calculations show that the bottomhole pressure decreases when considering the inertia-turbulence effect; (3) Calculation of gas well production using the bottomhole flowing pressure model shows a decrease when considering the inertia-turbulence effect.