Quantitative Modeling of Thermo-Hydraulic Transport in Geothermal Fractures: A Diffuse Interface Perspective

Geothermal energy systems are gaining importance as stable, CO$_2$-neutral energy sources supporting both climate goals and energy security. Accurate simulation of coupled heat and fluid flow in fractured media is critical for optimizing their efficiency. Diffuse interface models, grounded in phase-field theory, offer a promising alternative to classical sharp interface formulations. By avoiding explicit interface tracking, they naturally accommodate topological changes and enable efficient coupling between physical fields, which is particularly advantageous for geothermal systems.

In this study, we model fluid flow and heat transfer using the incompressible Navier–Stokes equations for a Newtonian fluid, with temperature treated as a passive scalar to allow one-way coupling from fluid flow to heat transport. Within the diffuse interface framework, various approximations exist to enforce no-slip boundary conditions at the fluid–solid interface in a diffuse manner, e.g., by introducing a dissipative term in the momentum equations. Since the specific choice of approximation significantly influences the accuracy of the diffuse model, we additionally employ an interface-orientation-dependent formulation of the heat flux to improve the thermal solution.
... mehr

These improvements are implemented in the finite-difference in-house solver Pace3D and validated against analytical benchmarks, yielding errors typically below 1 % for the velocity and the temperature field. Furthermore, realistic fracture geometries are synthetically generated via spectral synthesis method[6] and assembled into flow channels. For these complicated geometries, we assess the convergence behavior of the phase-field model and compare it to a voxel-based sharp interface representation, demonstrating that phase-field models maintain acceptable accuracy even at low resolution. Finally, we investigate the influence of fracture geometry on heat transfer efficiency under varying thermal and flow conditions. The results highlight the sensitivity of convective transport to fracture morphology and boundary conditions, and lay the foundation for advanced phase-field models incorporating crystallization and dissolution processes in fractured geothermal systems.