Closed-loop U-shaped geothermal wells show great potential owing to their special well-depth structure, which can provide a good flow rate and heat extraction. However, no advanced process parameter optimization method is available for U-shaped geothermal wells. To effectively describe the heat transfer processes of U-shaped geothermal wells, an analytical solution that couples transient heat conduction in the surrounding soil (or rocks) with the quasisteady heat transfer process in boreholes was developed. This modelling approach depends on many common elements, such as the thermophysical properties of the working fluid and series of resistances for various elements in the wellbore. Subsequently, based on the exergy analysis method, the optimal operating flow rate was defined and a design method for the optimal flow rate was developed. Results indicate that to obtain the maximum exergy efficiency, different optimal flow rates for the U-shaped geothermal well are achieved at different stages of the heating period. This findings of this study expand the research ideas of the process parameter optimization of U-shaped geothermal wells and provide a theoretical basis for developing an optimal circulating-flow-rate design for U-shaped geothermal wells.

闭环U型地热井由于其特殊的井深结构，可以提供良好的流量和热量提取，显示出巨大的潜力。然而，U形地热井尚无先进的工艺参数优化方法。为了有效描述U形地热井的传热过程，开发了一种将周围土壤（或岩石）中的瞬态热传导与钻孔中的准稳态传热过程耦合的解析解。这种建模方法取决于许多常见元素，例如工作流体的热物理特性和井筒中各种元素的一系列阻力。随后，基于火用分析方法，定义了最佳运行流量，并开发了最佳流量的设计方法。结果表明，为了获得最大火用效率，U形地热井在加热期的不同阶段实现了不同的最佳流量。本研究成果拓展了U形地热井工艺参数优化的研究思路，为U形地热井循环流量优化设计提供了理论依据。