Transient temperature behavior and analysis of single-phase liquid-water geothermal reservoirs during drawdown and buildup tests: Part I. Theory, new analytical and approximate solutions

This work focuses on transient temperature responses of single-phase liquid-water geothermal reservoirs to constant-rate drawdown and buildup tests. New analytical and approximate solutions are presented for predicting drawdown and buildup sand-face transient temperature behaviors of a fully penetrating vertical well in an infinite-acting homogeneous reservoirs. The solutions account for the effects of Joule-Thomson (J-T) heating/cooling, transient adiabatic fluid expansion/compression, convection, and conduction. The solutions are compared and verified with the solutions from three different non-isothermal simulators that solve the mass and thermal energy balance equations rigorously and simultaneously. The impacts of various parameters such as wellbore storage, skin zone near the wellbore, thermal conductivity, and outer reservoir boundary conditions on the sand-face temperature responses are also investigated and discussed. Drawdown and buildup sand-face temperature data are shown to exhibit three infinite-acting radial flow (IARF) periods (represented by semi-log straight-line equations); early-time IARF reflecting the adiabatic expansion/compression effects in the skin zone if it exists, intermediate-time IARF reflecting the J-T effect in the skin zone, and late-time IARF reflecting the J-T effect in the non-skin zone. In an accompanying paper (Part II), we present an interpretation and analysis methodology based on the analytical solutions derived here for parameter estimation from temperature transient data jointly with pressure transient data.