A consequence-oriented indicator for dominant heat transfer regime identification in HT‑ATES: The Buoyant Flow Heat Transfer Number

Reliable identification of the dominant heat-transfer regime is essential for evaluating the thermal performance of high-temperature aquifer thermal energy storage (HT-ATES). The Rayleigh number ( Ra ) is widely used for this purpose, but it primarily characterizes the tendency of buoyancy-driven transport relative to thermal diffusion rather than its realized thermal consequence over a finite operating period. This study proposes the Buoyant Flow Heat Transfer Number ( Nh ), a consequence-oriented dimensionless indicator derived from governing-equation-based scaling analysis. Nh characterizes the finite-time thermal effect of buoyancy-driven transport and incorporates buoyancy-driven mobility, injection duration, aquifer thermal-storage capacity, and the thermal-front transition scale. Based on 1944 numerical simulation cases, the critical threshold was determined from the development subset as Nh* = 1.2 and evaluated using an independent test subset. For aquifer thicknesses of 20, 40, and 60 m, Nh achieved identification accuracies of 98.51%, 96.80%, and 95.42%, respectively, all exceeding the corresponding Ra -based values of 93.28%, 94.40%, and 93.89%. Further diagnostic analysis of the complete dataset yielded only 64 misclassified cases for Nh , compared with 135 for Ra . These results demonstrate that Nh provides higher identification accuracy and greater stability than Ra . Further analysis indicates that this performance advantage arises from its consequence-oriented physical interpretation, which enables more consistent responses to variations in aquifer thickness, unit-thickness injection rate, and reservoir porosity. These results demonstrate that Nh is a reliable indicator for identifying the dominant heat transfer regime in HT-ATES and provides a consequence-oriented framework for buoyancy-influenced heat transport in porous media.