Various geoscientific processes in the shallow subsurface experience a temperature difference between the solid and the liquid or gaseous phase. Prominent examples include the injection of cold water into a hot host rock, the fast intrusion of supercritical CO2 from the mantle into shallower regions, or the rainwater infiltration into partially frozen soil. In such an absence of local thermal equilibrium between phases, heat transfer needs to be described explicitly by Newton's law of cooling and depends on the heat transfer coefficient and the specific heat transfer area between the involved phases. Despite various works, the quantification and the dissolution of dependencies of the heat transfer coefficient remain ambiguous. The study of heat transfer is separated between porous and fractured materials due to the different geometry, the applied flow rules, and common fields of applications. Identifying scenarios in which heat transfer effects in a local thermal non-equilibrium (LTNE) situation are relevant is already a challenging task but in past years more and more scenarios with persistent differences in phase temperatures were found. In this contribution, the mathematical governing equations for heat transfer between solid rock and moving fluid are given and various approaches of parameterization are discussed. This discussion of heat transfer includes various types of heat transfer mechanisms that can occur in the subsurface. Subsequently, the state of the art for heat transfer in porous and fractured media is presented with a special emphasis on resolving dependencies on geometry (grain size, fracture aperture) and flow velocity. Possible solution strategies addressing heat transfer in heterogeneous fractured porous media are presented, and possible applications with relevant LTNE effects are discussed with an outlook on future challenges in the field of geothermal energy exploitation and storage, shallow multi-phase infiltration scenarios, CO2 sequestration, and underground H2 storage.

中文翻译：

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多孔和裂隙岩石中的多相传热

浅层地下的各种地球科学过程会经历固相、液相或气相之间的温差。突出的例子包括将冷水注入热的主岩中，超临界二氧化碳从地幔快速侵入较浅的区域，或者雨水渗透到部分冻土中。在相之间缺乏局部热平衡的情况下，传热需要通过牛顿冷却定律明确描述，并且取决于传热系数和所涉及相之间的特定传热面积。尽管进行了各种工作，但传热系数依赖性的量化和消除仍然不明确。由于几何形状、应用的流动规则和常见应用领域的不同，多孔材料和断裂材料的传热研究是分开的。识别与局部热非平衡 (LTNE) 情况下的传热效应相关的场景已经是一项具有挑战性的任务，但在过去几年中，我们发现了越来越多具有持续相温差异的场景。在这篇文章中，给出了固体岩石和运动流体之间传热的数学控制方程，并讨论了各种参数化方法。对传热的讨论包括可能发生在地下的各种类型的传热机制。随后，介绍了多孔和裂缝介质中传热的最新技术，特别强调解决对几何形状（粒度、裂缝孔径）和流速的依赖性。提出了解决异质裂隙多孔介质传热问题的可能解决方案策略，并讨论了相关 LTNE 效应的可能应用，展望了地热能开发和储存、浅层多相渗透场景、二氧化碳封存和地下氢气储存。