A Fast Simulation Approach to the Thermal Recovery Characteristics of Deep Borehole Heat Exchanger after Heat Extraction

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.

Study on the Influence of Borehole Heat Capacity on Deep Coaxial Borehole Heat Exchanger

“…As a kind of clean energy, geothermal energy is widely studied, and geothermal energy conversion is often realized through a ground-source heat pump system. Compared with the traditional shallow ground heat exchanger, the deep borehole heat exchanger can obtain more heat from soil; it has therefore been widely studied by researchers around the world [1]. Deep coaxial borehole heat exchanger (DCBHE) has the characteristics of good heat transfer performance and structural stability, and it is a common type of deep borehole heat exchanger for extracting medium-deep geothermal energy [2].…”

Heat Transfer Modeling on High-Temperature Charging and Discharging of Deep Borehole Heat Exchanger with Transient Strong Heat Flux

“…This drawback has blocked its application in the thermal analysis of deep boreholes. In efforts to relieve the shortcomings of analytical modeling, different numerical models for the heat transfer of DBHE have also been presented over the past years [6][7][8][9][10][11][29][30][31][32][33]. Compared with the analytical approach, numerical models feature strong adaptability and flexibility.…”

Numerical Analysis of Enhanced Conductive Deep Borehole Heat Exchangers

“…Closed-wellbore models are generally coupled with a reservoir model to account for the heat exchange and fluid flow in the surrounding porous or fractured rocks [6]. Fast simulations using a finite line source model have also been performed to investigate intermittent conditions in a DBHE [19]. Closed wells have been investigated with several geothermal gradients from 25 to 50 • C/km and between 2 to 6 km.…”