Semi-analytical model of heat transport around a well with wellbore mixing effect under multi-step flow rate

Abstract

Modeling heat transport around a well is critical for evaluations of aquifer thermal energy storage (ATES). In this study, an innovative heat transport model considering the wellbore mixing effect under multi-step flow rate in an aquifer system is proposed, where thermal conduction, thermal dispersion, and convection occur in the aquifer. Wellbore mixing effect refers to the influence of mixing processes between the injected water and original water in the well on heat transport in aquifer, which was ignored in existing models. A semi-analytical solution derived from Laplace transform method and Green’s function method has been validated by the numerical modeling and field experimental studies. Results show that the wellbore mixing effect should not be ignored in analyzing heat transport around a well in the ATES system, and the new solution satisfactorily interprets the field data. The influence of the thermal dispersion on thermal transfer near the injection/extraction well is sensitive and should not be negligible. Morris global sensitivity analysis demonstrates that the output temperature is most sensitive to the variations of the parameters of wellbore water volume and extraction rate than the others. The influence of water volume decreases with time, and the most sensitive parameter becomes extraction rate in the late stage of the extraction phase. The newly developed model can shed some light on the thermal transfer processes in the ATES system and better interpret the experimental data of the single-well push–pull tests.