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A novel description of heat transfer between fluid and rough-walled fractures in porous rock

Applicant Dr. Thomas Heinze
Subject Area Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
Geotechnics, Hydraulic Engineering
Palaeontology
Geophysics
Physical Geography
Term from 2018 to 2023
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 418091647
 
Final Report Year 2024

Final Report Abstract

Heat transfer in fractured porous media is an essential process in the earth system. It is driving mechanism in natural phenomena like geysers, hydrothermal and volcanic systems, as well as in geo-hazards like rockfalls and earthquakes. Further, it is the base for several industrial applications like geothermal systems. Fluid flow in fractured porous media is quite well understood. A broad range of approaches exists including continuum mechanics, multiple domains and an explicit definition of fractures. However, with respect to heat transfer recent models have two major drawbacks: They often only consider thermal equilibrium between the solid and fluid phase and they lack a suitable representation of fractures in the heat transfer process. Both obstacles are strongly connected, as fractures with high flow velocities often cause local thermal non-equilibrium but there is no suitable description for heat transfer between rock matrix and fracture fluid. In this project, a novel model was developed to describe heat transfer in fractures across spatial and temporal scales. The essential parameter according to Newton's law of cooling is the heat transfer coefficient, which depends on other geometric, thermal and hydraulic parameters. However, the available parameters for determining the heat transfer coefficient differ between the individual scales. A cross-scale description must therefore rely on parameters that are available in all scales or can be scaled using dimensionless variables. As part of this project, over 300 laboratory experiments from the literature were reviewed, supplemented by our own experiments, which were carried out in cooperation, and analyzed in order to determine the heat transfer coefficient for these. The heat transfer coefficient is not a variable that can be determined directly from laboratory measurements. Instead, a theoretical model was developed to derive the heat transfer coefficient from the laboratory results. For the available data sets on the laboratory scale, hydraulic fracture opening width and flow velocity were identified as the most significant influencing variables. Although more than 35 roughness parameters for the fracture surfaces were recorded and tested, no systematic influence could be determined. The possible influence of surface roughness and flow-through surface is intrinsically contained in the experimental data in the fissure opening width, as these only become relevant for very small fissure opening widths. For scaling purposes, these two parameters were therefore used together with the fissure density in order to establish a scale-independent relationship between the dimensionless variables Nusselt, Prandtl and Reynolds number.

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