This article presents a solution to the geothermal problem of transient heat production from hot dry rocks using a horizontal well. Dimensionless forms of the governing equations are derived, including conduction in the rock, convection between the wellbore rock and the fluid, and advection and conduction in the fluid along the well. Ten model material and geometric parameters are reduced to three dimensionless parameters: $\alpha =4\frac{L}{D}\mathit{St}$ is the ratio of the rate of heat storage in the fluid to the rate the heat convection to the fluid from the rock, $\beta =\frac{1}{\mathit{Pe}}$ is the ratio of the rate of conductive versus advective heat transfer in the fluid, and $\gamma =2\frac{L}{D}\mathit{Bi}$ is the ratio of heat convection to the rock from the fluid to the rate of heat depletion in the rock. An axisymmetric finite element method (FEM) program is developed and yields the solution for the temperature of the rock mass and fluid over time. For physically meaningful inputs, analysis indicates that the effect of $\beta$ is negligible, that combinations of very large $\alpha$ and very low $\gamma$ (and vice versa) do not occur, and that all other things being equal, increasing $\alpha$ or decreasing $\gamma$ leads to higher fluid outlet temperatures. System response at different times and dimensionless temperature are captured in contour plots for values of $\alpha$ and $\gamma$ spanning practical injection rates, well geometries and fluid and rock properties. Power law response surface models are fitted using model outputs at discrete intervals and provide a means to accurately and rapidly compute the temperature-time histories of practical geothermal systems.

本文提出了使用水平井从干热岩中产生瞬时热量的地热问题的解决方案。推导出控制方程的无量纲形式，包括岩石中的传导、井筒岩石与流体之间的对流、以及流体中沿井的平流和传导。十个模型材料和几何参数减少为三个无量纲参数：$\alpha =4\frac{升}{D}\mathit{英石}$ 是流体中的蓄热率与岩石对流体的热对流率之比， $\beta =\frac{1}{\mathit{聚乙烯}}$ 是流体中传导与对流热传递的比率，和 $\gamma =2\frac{升}{D}\mathit{双}$是从流体到岩石的热对流与岩石中热量消耗率的比率。开发了轴对称有限元方法 (FEM) 程序，并生成了岩体和流体温度随时间变化的解。对于具有物理意义的输入，分析表明$\beta$ 可以忽略不计，非常大的组合 $\alpha$ 而且非常低 $\gamma$ （反之亦然）不会发生，并且所有其他事物都相同，增加 $\alpha$ 或减少 $\gamma$导致更高的流体出口温度。不同时间的系统响应和无量纲温度在等高线图中捕获$\alpha$ 和 $\gamma$涵盖实际注入率、井几何形状以及流体和岩石特性。幂律响应面模型使用离散间隔的模型输出进行拟合，并提供一种方法来准确快速地计算实际地热系统的温度-时间历程。