Experimental evidence for local thermal non-equilibrium during heat transport in sand representative of natural conditions

Abstract

When modelling heat transport in hydrogeological systems, a standard assumption is local thermal equilibrium (LTE), which implies that the porous medium temperature at the interface between the solid and fluid instantaneously reaches equilibrium. Few studies have investigated the validity of the LTE assumption and its violation, also known as local thermal non-equilibrium (LTNE), as well as its impact on the accuracy of heat transport models. While the theoretical conditions under which LTNE occurs in natural groundwater flow have recently been revealed, these have not yet been experimentally verified. We examined the applicability of the LTE assumption by conducting systematic laboratory experiments using eight distinct flow velocities (Reynolds number, Re < 0.37) through sand (0.76 mm grain size), injecting both heat and solute as tracers and observing the response at multiple points downstream. Theoretical heat transport parameters were calculated from solute tracer experiments by applying a retardation factor, and the results were subsequently compared to the actual parameters estimated from heat tracing. Our experimental results confirm that the LTE assumption can be violated under natural groundwater flow conditions, and that LTNE impacts thermal dispersion coefficients more significantly than thermal front velocities. The largest differences between the predicted and estimated thermal transport parameters were 112% and 13% for the dispersion coefficients and velocities, respectively. Our results demonstrate that LTNE effects need to be considered in heat transport modelling especially when analyzing thermal dispersion coefficients.