New criteria for assessing local thermal nonequilibrium conditions in porous aquifers and their impact on heat transport in porous media

A critical assumption in many investigations of heat transfer in porous media is local thermal equilibrium (LTE), which assumes an instant exchange of thermal energy between the solid and the fluid phases of a porous medium. Although significant progress has been made in quantifying the occurrence and consequences of local thermal nonequilibrium (LTNE), which entails temperature differences between the fluid and adjacent solid phases, there is currently no straightforward equation to ascertain the occurrence and significance of LTNE effects in heat transport through porous media. Here we develop a numerical model that integrates LTE and LTNE models and introduce two simple criteria based on Darcy fluxes and particle sizes of porous media to determine the occurrence and significance of LTNE effects. Simulation results show that, depending on the experimental conditions, using an LTE model can result in underestimating as well as overestimation of both effective thermal dispersion and Darcian fluxes. The reliability of the proposed criteria is validated through three typical datasets and corresponding numerical models: (1) a heat tracer test in a laboratory column with different Darcian fluxes (10–55 m/d) and a relatively large grain size (10–20 mm); (2) a field test in an alluvial aquifer with small particle sizes (0.75–1 mm) and high Darcian fluxes (60 m/d); and (3) a field test in streambed sediments having large particle sizes (greater than 15 mm) and low Darcian fluxes (less than 0.5 m/d). Simulation results highlight that the potential LTNE effects should be considered when using heat as a tracer to characterize heat transport in porous media in the presence of low Darcian fluxes and large particle sizes.