Evaluation of Non-Fourier Heat Transfer on Temperature Evolution in an Aquifer Thermal Energy Storage System

The heat transport in fractured porous rocks is classically modeled employing the advection–dispersion equation (ADE). However, the nature of heat transfer in fractured reservoir rocks may not be represented by the effective medium properties when the ADE formulation is adopted. In this study, a modified mathematical model describing non-Fourier heat transport in an aquifer thermal energy storage (ATES) system is proposed employing the fractional calculus theory. This mathematical model incorporates the effect of heat losses to the surrounding impermeable rock formations. The Laplace transformation method is applied to derive the semi-analytical solutions describing the dimensionless temperature evolution in the confined aquifer, and the surrounding impermeable rocks (i.e., underlying and overlying rocks). Detailed parametric studies are performed to investigate the role of the introduced parameters, i.e., the fractional order of differentiation, generalized friction coefficient and aquifer pseudo-effective thermal conductivity on the propagation of heat within the ATES system. Computations performed on the derived solutions demonstrate that the temperature profiles in the confined aquifer and the surrounding rocks are influenced by the magnitude of the respective fractional exponents. In addition, observation of the temperature profiles within the thermally perturbed zones demonstrates that larger values of the fractional order of differentiation lead to efficient heat transfer within the ATES system. Furthermore, analysis of the results indicates that the impact of the aquifer pseudo-effective thermal conductivity on the temperature propagation in the ATES system is limited to the aquifer only. The derived solutions will find widespread application in designing and simulating the heat injection performance in an ATES system and assessing the influence of non-Fourier heat transport and geological parameters on temperature transients through porous media.