Abstract
A coupled system model of partial differential equations concerning pressure, temperature, and velocity of gas–liquid–liquid three-phase transient flow in high-temperature, high-pressure (HTHP) wells is presented, according to mass, momentum, and energy balances as well as the stated equation of gas. A solution framework shared by the basic models is built, which makes it convenient to perform the solution process. The finite difference method was adopted to simulate the model. Based on the unified solution framework, the singular value decomposition (SVD) algorithm is employed to solve the large linear equations for the proposed model. The average value is adopted to solve the redundancy of model. The basic data for X Well (a 7,110-m-deep HTHP well in Sichuan, China) were used for case history calculations. Pressure, temperature, and velocity curve graphs along the depth of the well were plotted at different times, intuitively reflecting the flow law and the characteristics of heat transfer along a formation. The results can provide technical reliability in the process of designing well tests for HTHP gas wells and a dynamic analysis of production.
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