Department of Environmental and Geosciences, Sam Houston State University, Huntsville, TX 77340, USA.
Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843, USA.
J Contam Hydrol. 2022 Feb;245:103950. doi: 10.1016/j.jconhyd.2021.103950. Epub 2021 Dec 31.
In this study, a fully coupled analytical model is developed for thermal energy transfer in a single fracture-rock matrix system where the coupling implies that the governing equations of thermal transfer in the fracture and rock matrix are supplemented with the continuity conditions of temperature and thermal flux at the interfaces of the fracture-rock matrix. The proposed model accounts for thermal convection, longitudinal thermal conduction and thermal dispersion in the fracture, and transverse thermal conduction in the rock matrix. The fully coupled two-dimensional model is established to investigate the thermal energy transfer processes, assess the spatiotemporal temperature distribution in the fracture and rock matrix system and investigate the role of the rock matrix. The solutions are verified with the existing studies and proven to be accurate and robust. The present study demonstrates that: 1) thermal dispersion in the fracture plays an important role in the temperature distribution in the fracture and rock matrix domains, and longitudinal thermal conduction in the fracture has minor effects on the temperature distribution in the system; 2) transverse thermal conduction in the rock matrix is a critical parameter that determines the spatiotemporal temperature distribution in both the fracture and the rock matrix domains. Ignoring thermal conduction in the rock matrix will lead to a significant overestimation of temperature in the short and long terms; 3) the sensitivity analysis implies that thermal energy transfer in the system is sensitive to the fluid velocity in the fracture, thermal dispersivity in the fracture and thermal conductivity in the rock matrix, and less sensitive to thermal conductivity in the fracture.
在这项研究中，开发了一个完全耦合的分析模型，用于研究单裂隙-岩石基质系统中的热能传递，其中的耦合意味着在裂隙和岩石基质的热传递控制方程中补充了温度和热通量在裂隙-岩石基质界面处的连续性条件。所提出的模型考虑了裂隙中的热对流、纵向热传导和热弥散，以及岩石基质中的横向热传导。建立了完全耦合的二维模型，以研究热能传递过程，评估裂隙和岩石基质系统中的时空温度分布，并研究岩石基质的作用。通过与现有研究的验证，证明了该模型的准确性和鲁棒性。本研究表明：1）裂隙中的热弥散在裂隙和岩石基质域中的温度分布中起着重要作用，而裂隙中的纵向热传导对系统中的温度分布影响较小；2）岩石基质中的横向热传导是决定裂隙和岩石基质域中时空温度分布的关键参数。忽略岩石基质中的热传导会导致在短期和长期内对温度的显著高估；3）敏感性分析表明，系统中的热能传递对裂隙中的流体速度、裂隙中的热弥散率和岩石基质中的热导率敏感，而对裂隙中的热导率不敏感。
