On the Limitations and Implications of Modeling Heat Transport in Porous Aquifers by Assuming Local Thermal Equilibrium

Heat transport in natural porous media, such as aquifers or streambeds, is generally modeled assuming local thermal equilibrium (LTE) between the fluid and solid phases. Yet, the mathematical and hydrogeological conditions and implications of this simplification have not been fully established for natural porous media. To quantify the occurrence and effects of local thermal disequilibrium during heat transport, we systematically compared thermal breakthrough curves from a LTE with those calculated using a local thermal nonequilibrium (LTNE) model, explicitly allowing for different temperatures in the fluid and solid phases. For the LTNE model, we developed a new correlation for the heat transfer coefficient representative of the conditions in natural porous aquifers using six published experimental results. By conducting an extensive parameter study (>50,000 simulations), we show that LTNE effects do not occur for grain sizes smaller than 7 mm or for groundwater flow velocities that are slower than 1.6 m day⁻¹. The limits of LTE are likely exceeded in gravel aquifers or in the vicinity of pumped bores. For such aquifers, the use of a LTE model can lead to an underestimation of the effective thermal dispersion by a factor of up to 30 or higher, while the advective thermal velocity remains unaffected for most conditions. Based on a regression analysis of the simulation results, we provide a criterion which can be used to determine if LTNE effects are expected for particular conditions.