Unraveling Anomalous Thermal Transport in Fracture–Matrix Systems: Interplay Between Advective Transport and Matrix Conduction

Heat transport in geological fractures is controlled by the heterogeneity of the fracture aperture arising from wall roughness. Spatial variations in aperture, here obtained from self-affine fracture walls, generate pronounced channelization, wall-contact regions, and quasi-stagnant zones where velocities drop sharply. This geometric structure controls transmissivity and governs the localization of velocities.

We investigate how these roughness-induced flow patterns shape thermal dynamics over time. At early times, fast channels inhibit heat uptake. As fluid particles increasingly explore low-velocity pockets, intermediate-time heat exchange accelerates, revealing the buffering role of quasi-stagnant regions. At late times, conduction into the surrounding rock matrix imposes a robust t ^-1/2 scaling of the fracture-to-matrix heat flux, consistent with semi-infinite diffusion.

To quantify these mechanisms, we employ a stochastic Time-Domain Random Walk (TDRW) framework in which fracture–matrix heat exchange is represented through a Lévy–Smirnov residence-time kernel, providing a physically based description of non-local conduction. We analyse the temporal evolution of thermal breakthrough-curve (BTC) moments, demonstrating how roughness-controlled residence-time distributions regulate heat-exchange efficiency.

By combining TDRW simulations with high-resolution aperture fields and finite-element benchmarks, we characterize the interplay between aperture heterogeneity, velocity localization, and matrix conduction. The results clarify the physical origin of the observed non-Fickian thermal response and provide guidance for interpreting temperature signals in geothermal systems and thermal tracer tests.