Effective thermal retardation in aquifers of heterogeneous hydraulic conductivity

Abstract

Thermal retardation and dispersion are important processes affecting advective heat transport in sedimentary aquifers, yet little is known how they are influenced by heterogeneity of hydraulic conductivity. We investigate the effect of macro-scale heterogeneity on transient heat transport in a three-dimensional domain through direct numerical Monte-Carlo simulations. The model describes the evolution of a heat plume in a heterogeneous aquifer generated by a borehole heat exchanger. We characterize the transport by calculating the dispersion coefficient and effective thermal retardation factor as ensemble average of the heterogeneous realizations. In addition to different degrees of heterogeneity, we examine the influence of the thermal Péclet number on the effective thermal retardation factor. Simulations reveal that for homogeneous hydraulic conductivity, the effective thermal retardation factor equals the predicted, apparent thermal retardation factor. However, in heterogeneous cases, the effective thermal retardation factor is substantially lower than the apparent value at early times, with this effect becoming more pronounced as the Péclet number increases. We attribute the deviation of the effective thermal retardation factor from the apparent value to preferential flow through zones with higher hydraulic conductivity and delayed local heat diffusion into zones with lower hydraulic conductivity. Assuming that the effective thermal retardation factor differs from the apparent value in the presence of local thermal non-equilibrium (LTNE) effects, we call the observed effect “field-scale LTNE.” Finally, we derive a formula estimating effective thermal retardation as a function of log-conductivity variance and the Péclet number. Our results can improve heat tracer techniques in hydraulically heterogeneous environments.