Local thermal non-equilibrium in heterogeneous porous media identified through 3D heat transport modelling

Modelling heat transport in porous aquifers is generally based on the assumption of an instantaneous local thermal equilibrium (LTE) between the solid and the fluid phase. Previous studies have revealed that this assumption can be violated, e.g. in the presence of fast or preferential flow causing delayed heat diffusion into the grain structure matrix, referred to as local thermal non-equilibrium (LTNE). However, conditions and scales at which LTNE effects should be taken into account in natural heterogeneous sediments are almost unexplored. We study the relation between macro-scale heterogeneity, thermal dispersion and LTNE through numerical simulations of heat transport in three-dimensional heterogeneous hydraulic conductivity fields. The advection-diffusion equation is solved using the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source, parallel finite element framework. The spatial and temporal evolution of the heat plume generated by a line source under steady-state flow conditions is examined. For understanding the propagation of heat plumes, the role of delayed diffusion caused by LTNE effects needs to be distinguished from hydro-mechanical dispersion. Therefore, we estimate the thermal dispersion and the effective thermal retardation for each time step using a stochastic approach. LTNE effects are present, when the effective thermal retardation deviates from the predicted, apparent thermal retardation. Simulations show good agreement between the effective and the apparent thermal retardation for homogeneous hydraulic conductivity. With increasing heterogeneity, characterized by a higher variance of the log-conductivity, the effective retardation becomes lower than the apparent retardation at early times. Furthermore, we estimate the effective thermal retardation for a homogeneous flow field with added thermal dispersion based on the dispersion coefficients resulting from the heterogeneous simulations. We find that there is a significant difference in the evolution of effective retardation between the homogeneous and the heterogeneous case both of the same thermal dispersion, which we associate to LTNE effects. Our modelling approach thus allows to quantify LTNE induced by field-scale heterogeneity.