Abstract
Necessary intermittence after heat extraction for a deep borehole heat exchanger (DBHE) is beneficial for sustainable operation. This paper centers on the fast simulation for thermal recovery characteristics of DBHE under intermittent condition. First of all, in view of the existing temperature gradient and multi-layer heterogeneity of rock underground that could never be ignored for DBHE, we extend the classical finite line source model based on heat source theory and superposition principle to account for the vertical heat flux distribution varying along depth and heterogeneous thermal conductivities in the multi-layer rock zone. Moreover, a fast simulation approach for heat transfer analysis inside the borehole coupled with the extended finite line source model is put forward to depict the transient thermal response and dynamic thermal recovery of rock outside borehole. To the authors’ knowledge, no such algorithm for deep BHE has yet been suggested in the previous literature. This approach has proven to be reliable and efficient enough for DBHE simulation under the intermittent condition. Simulation results show that at least 65 days of intermittence for the model in study should be spared after the heating season to achieve sustainable heat extraction in the next cyclic operation. Compared to the detailed solution based on full discretization numerical schemes, the relative error for borehole bottom temperature was 0.79%. In addition, comparison of the simulation results for thermal performance during the heating season in a three-year cyclic operation with 205 days intermittence shows that both the outflow temperature and heat extraction rate in the subsequent cycle after intermittence are in good agreement with the full 3D numerical solution in the reference (with a relative error of 6.36% for the outflow temperature and 9.3% for the heat extraction rate). Regarding the calculation speed, around a 13 times acceleration can be achieved. Finally, it is also promising to be applicable for thermal recovery simulation after heat extraction of vertical closed loop borehole heat exchangers at arbitrary length from shallow to deep.
Highlights
As one of the primary choices to replace conventional energy sources, geothermal energy is becoming more and more attractive with local availability, low operational cost, and low CO2 emissions and has been rapidly developed for space heating and cooling over the recent decades [1]
We focus on studying the thermal recovery characteristics of deep borehole heat exchanger (DBHE) under intermittent condition, which contributes to the sustainable operation of it
Based on heat source theory and superposition principle, we extend the classical finite line source model to account for the vertical heat flux distribution varying along depth and heterogeneous thermal conductivities in the multi-layer rock zone
Summary
As one of the primary choices to replace conventional energy sources, geothermal energy is becoming more and more attractive with local availability, low operational cost, and low CO2 emissions and has been rapidly developed for space heating and cooling over the recent decades [1]. We focus on studying the thermal recovery characteristics of DBHE under intermittent condition, which contributes to the sustainable operation of it. A fast simulation approach employing the hybrid solutions for heat transfer analysis inside the borehole coupled with the extended finite line source model is put forward to depict the transient thermal response and dynamic thermal recovery of rock zone outside borehole. Borehole temperature evolution with time during the intermittent period as well as thermal performance of DBHE during heating season in a three-year cyclic operation with intermittence after heat extraction are compared carefully.
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