Impact of Matrix Diffusion on Heat Transport Through Heterogeneous Fractured Aquifers

Heat transport in fractured aquifers is determined by the combined effects of flow velocity heterogeneity in the fracture system, and diffusive exchange between the fluid in the fractures and the rock matrix, which can be assumed as impervious. We analyze the impacts of this diffusive exchange on the response to heat transport, as opposite to the pure advective displacement, which governs solute transport. We focus on the post-peak behavior where we observe pre-asymptotic regimes with slopes that differ from the signature of matrix diffusion, which exhibits a decay rate of -3/2. This deviation is driven by the variability of both velocity field and fracture aperture field. We derive theoretical models that predict these pre-asymptotic tails under three extreme cases that can be related with specific network structures, that is, networks dominated by large or small fractures, networks with highly or poorly channelized flow. These theoretical predictions are compared with results from numerical simulations in different sets of three-dimensional discrete fracture networks. We determine that the combined observation of solute and heat transport responses allows classifying the network in terms of connectivity structure, and partially characterizing the fracture aperture variability in terms of upscaled parameters.