In the realm of energy and environmental research, understanding heat transfer in complex geological systems is crucial for various applications, from geothermal energy to subsurface thermal storage. A team of researchers from the University of California, Berkeley, and the Swiss Federal Institute of Technology in Lausanne has delved into this topic, exploring how the roughness of walls in fractured media affects the coupled flow and heat transport. Their work, published in the journal Physical Review Fluids, offers insights that could enhance the efficiency and design of energy systems that interact with the subsurface.
The researchers—Alessandro Lenci, Yves Méheust, Maria Klepikova, Vittorio Di Federico, and Daniel M. Tartakovsky—developed a sophisticated modeling framework to capture the intricate dynamics of heat transfer in fractured media. Their approach combines a time-domain random walk (TDRW) representation of advective and conductive transport within the fractures with a semi-analytical model of conductive heat exchange with the surrounding low-permeability matrix. This framework is designed to account for the complex interplay between flow localization induced by aperture heterogeneity and matrix conduction, which gives rise to anomalous thermal behavior.
One of the key innovations in their model is the use of a Lévy-Smirnov distribution to describe matrix trapping times, derived from first-passage theory. This distribution captures the heavy-tailed dynamics typical of fractured systems, where heat transfer can exhibit significant variability over time. The model also incorporates a nonlocal convolution integral based on Duhamel’s principle to compute heat flux at the fracture-matrix interface, accounting for thermal memory effects. This approach allows for a more accurate representation of the complex interactions between the fractures and the matrix.
To validate their model, the researchers compared its predictions against analytical benchmarks and finite-element simulations, ensuring its accuracy and reliability. They then conducted Monte Carlo simulations over stochastic aperture fields to quantify the influence of various factors, including fracture closure, correlation length, and Péclet number. Their results revealed a transition from superdiffusive to subdiffusive regimes, driven by the competition between advective transport along preferential paths, dispersion induced by aperture variability, and matrix-driven heat conduction.
In the long-time regime, the researchers observed a characteristic t^-1/2 decay in heat exchange, highlighting the long-term behavior of thermal transport in fractured media. At early times, limited thermal penetration into the matrix led to weaker interfacial fluxes, underscoring the role of matrix thermal inertia. This insight is particularly relevant for designing systems that require efficient heat exchange over different time scales.
The proposed framework offers a physically consistent and computationally efficient way to simulate thermal transport in complex fractured systems. This has significant implications for the energy sector, particularly in geothermal energy, subsurface thermal storage, and engineered heat exchange in low-permeability environments. By better understanding and modeling these processes, engineers and scientists can develop more effective and efficient energy systems that harness the Earth’s subsurface resources.
The research was published in Physical Review Fluids, a peer-reviewed journal that focuses on the fundamental physics of fluid dynamics. This publication ensures that the findings are rigorously reviewed and validated, providing a solid foundation for further research and practical applications in the energy industry.
This article is based on research available at arXiv.