Non‐Fourier thermal transport in fractured geological media

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Abstract
In a similar way to solute transport, heat transfer in porous media is governed by advection and dispersion processes, and “non‐Fourier” behavior, characterized by early breakthrough and long tailing, might also be expected to occur. While “non‐Fickian” solute transport has been studied extensively and an effective mathematical framework (the Continuous Time Random Walk (CTRW)) has been developed to describe it, there has been little experimental or numerical investigation of non‐Fourier thermal transfer in porous media. As a result of different transfer rates for heat and solute transport, it is unclear if non‐Fourier may occur or when it can be adequately modeled by an advection‐diffusion equation. We conducted high‐resolution finite element–finite volume numerical simulations of heat transfer in two geologically realistic fractured porous domains. We calculated thermal breakthrough curves at various locations in the domains and analyzed them with a CTRW model adapted for heat transfer. Our analysis shows that heat transport in the first, well‐connected fracture network is Fourier‐like, even though the thermal front is highly irregular. Consequently, it can be modeled by an advection‐diffusion equation using macroscopic dispersivities. By contrast, heat transport in the second, poorly connected fracture pattern is highly non‐Fourier. Hence, the classical advection‐diffusion equation is unable to capture the main features, but they can be modeled successfully by CTRW. The occurrence of non‐Fourier behavior has important implications for a range of processes including geothermal reservoir engineering, radioactive waste storage, and enhanced oil recovery.

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