The Prediction of Distribution of Temperature, Pressure, Density, and Velocity in High-Temperature-High-Pressure Gas Wells

In this article, we present a coupled system model of differential equations concerning pressure, temperature, density, and velocity in high-temperature-high-pressure wells, according to mass, momentum, and energy balances. We present an algorithm solution model, along with the fourth-order Runge-Kutta method. The basic data of well X (high-temperature-high-pressure gas well), 7,100 m deep, in China, is used for case history calculations and a sensitivity analysis is made for the model. Gas pressure, temperature, velocity, and density curve graphs along the depth of the well are plotted with different outputs, intuitively reflecting the gas flow law and the characteristics of heat transfer along a formation. The results can provide technical reliability in the process of designing well tests in high-temperature-high-pressure gas wells and a dynamic analysis of production.