New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers

Abstract

A fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (d_p) of porous media for determining when LTNE effects occur (denoted as g(d_p, q)) and when they become significant (denoted as f(d_p, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(d_p, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(d_p, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature-time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd-9-4305-2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm.