Analytical solution for estimating transient vertical groundwater flux from temperature-depth profiles
2022
Lin, Ying-Fan | Chang, Chia-Hao | Tsai, Jui-Pin
Many studies have developed analytical models for describing the subsurface heat transfer to estimate the infiltration rate, that is, the vertical groundwater flux (VGF). These studies assumed that the VGF was constant in time to acquire mathematical tractability. However, the assumption generally violates the natural system and cannot delineate the transient behavior of the VGF. Such an illogical assumption would contribute to unreliable estimation of the VGF from field-observed temperature-depth (TD) profiles. To accurately estimate VGF based on an analytical model, this study develops a new analytical heat-transfer model and a novel inverse approach to estimate the transient VGF. The analytical model is verified by a numerical model based on the finite-element method. We further perform the sensitivity analysis to the analytical model to examine the temperature response to changes in the thermal parameters. It reveals that thermal dispersion has a minor effect on temperature. The results of the numerical experiment show that the present approach can yield the correct transient VGF. Finally, the present approach is applied to estimate the transient VGF for a field case study. The results show that the predicted VGF and the measured VGF are almost consistent, revealing that our method is feasible for the estimation of VGF in the field.
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