热储岩层单条裂隙换热概念模型的解及相关讨论

Semi-analytic Solutions to Thermal Exchange Conceptual Models for a Single Fracture in a Geothermal Reservoir and Related Discussions

在地热开采工程中,单条裂隙换热的概念模型分析是裂隙岩体换热研究中的基本问题。借鉴已有的平面二维域内单条裂隙和平行裂隙概念模型,针对地热井与周围岩体换热问题,推导了轴对称二维坐标下管状裂隙换热模型在Laplace域内的解析解。数值逆变换后得到的时域内温度解与有限元模拟给出的解吻合良好,从而验证了该解的正确性。围绕概念模型相关假定,讨论了忽略岩体纵向导热系数、忽略水岩界面两侧温差等假设的合理性。数值模拟结果表明,裂隙水换热问题可忽略水的导热性。当研究问题尺度在百米及以上时,水岩界面温差可以忽略。忽略岩石基质纵向导热性将无法考虑周围岩石的热补给,会造成计算开采温度10%以内的相对误差。所建议的分析方法和计算结果可为有关问题的设计分析提供参考。

In geothermal energy extraction engineering, thermal exchange in a conceptual model with a single fracture embedded is a classic issue. Based on the existing conceptual models and their analytical solutions in a two-dimensional domain, a new conceptual model characterizing thermal exchange between a borehole and ambient rock matrix is proposed. The analytical solu- tion in Laplace space is derived by using integral-transformation method. After implementing nu- merical inverse transformation, the semi-analytical solution is compared with the results of the numerical model, which proves the correctness of the semi-analytical solution. The rationalities of some hypotheses （such as local thermal equilibrium assumption, etc. ） are deeply investigated according to numerical simulations. The results indicate that the thermal conductivity of the fluid can be omitted under any circumstances. When the scope of the problem to be analyzed ranges from hundreds of meters to kilometers, the temperature difference between the fracture water and the fracture surface can be neglected. Nevertheless, the relative error of the thermal produc- tion can reach up to 10%when thermal conduction of the rock in longitudinal direction is omit- ted. All these results can be devoted to thermal production evaluation in geothermal energy ex-traction engineering.