Multi-phase heat transfer in porous and fractured rock

Abstract

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.