In this paper, a coupled system model of partial differential
equations
(PDEs) concerning pressure, temperature, velocity, and holdup for
a gas–oil–water three-phase steady flow in high-temperature–high-pressure
(HTHP) wells is presented. A solution framework shared by the basic
models is built, making it convenient to perform to solve. An algorithm
solution model using the fourth-order Runge–Kutta method is
given. Basic data from “X Well” (HTHP well, 7110 m deep,
in Sichuan, PRC) is used as a case study for calculations and a sensitivity
analysis is performed on the model. Pressure, temperature, velocity,
and hold-up curve graphs, along with the depth of the well, are plotted
at different depths. A trend and sensitivity analysis are conducted
to test the parameter characteristics. In addition, a comparison between
the present model and other models is conducted to illustrate the
effectiveness of the model and the algorithm. The results provide
both technical reliability for well test design in HTHP gas wells
and provides a dynamic analysis of production.