Prediction of Temperature and Pressure Distribution in HTHP Injection Gas Wells with Thermal Effect of Wellbore

Abstract In this article, a coupled system model of differential equations was derived in radial form to predict the pressure, temperature of formation, and temperature of wellbore in high-temperature–high-pressure gas wells. In the model, the thermal effect of formation was simplified as heat conduction, both the steady heat transmission model in the gas wellbore and the unsteady heat conduction model in the formation were considered, and the pressure effect due to variations in temperature was considered according to the gas equation of state, which links the temperature with the pressure. The finite difference method was used to simulate the solutions of the coupled models. The basic data for X Well (high-temperature–high-pressure gas well, 7,100 m deep) in China were used for case history calculations and a sensitivity analysis was performed for the models. Graphs of the curves for gas pressure and temperature along the depth of the well were plotted with different gradients, injection volumes, and the characteristic of heat transfer in the formation. The results provide technical reliability in well test design in high-temperature–high-pressure gas wells and the dynamic analysis of production. Keywords: coupled systemdiffusivity equationfinite difference methodhigh-temperature–high-pressurepredictionthermal effect