Heat transfer across scales: from single fractures to fracture networks

Temperature estimation in hydrothermal reservoirs is a critical point for the feasibility of geothermal projects and subsequent processes, such as chemical and biological activity as well as thermal stresses. As flowing fluid and surrounding host rock locally diverge in temperature until equilibrium occurs, heat transfer between phases needs to be described. However, this is a challenging task, especially in fractures, because the heat transfer coefficient depends on various parameters, such as flow velocity and aperture. Heat transfer characteristics in fracture networks, and their dependence on fracture network characteristics, have been rarely studied so far.

Starting from a newly developed analytical solution of heat transfer in single fractures, a consistent formulation for heat transfer in fractured reservoirs is presented. Using an intermediate step of bench-scale experiments, the sensitivity of the temperature field in the fracture network with respect to the heat transfer coefficient is investigated. Due to multiple flow paths within a reservoir, the heat transfer capabilities of individual fractures can become less relevant in well-connected reservoirs. On the other hand, single fractures with uncommon velocity or aperture values can cause local heterogeneities in the temperature field due to the velocity-dependent heat transfer.

Bridging the gap between well-defined networks with a limited number of fractures and large-scale fracture networks of arbitrary shape requires a change in the parameters used. On large scale, effective values such as fracture density and anisotropic permeability are more suitable and accessible than single fracture apertures. To incorporate such a change in parameterization, a new theoretical framework based on the assumption of fracture networks with a regular geometry is presented.

The presented work sheds new light on the heat transfer mechanisms in fractures and fracture networks and is the first attempt to derive a consistent mathematical framework for heat transfer in fractures across scales.