A dimension reduction algorithm for numerical simulation of multi-borehole heat exchangers. (December 2021) - Zhang, Fangfang; Fang, Liang; Jia, Linrui; Man, Yi; Cui, Ping; Zhang, Wenke; Fang, Zhaohong
Abstract: Aimed at applications in ground-coupled heat pump and thermal energy storage systems, this paper presents a heat transfer model of a deep borehole cluster, taking into account the geothermal gradient in the subsurface and the real connection conditions of the two regions inside and outside the borehole. The superposition principle is proven valid in a mathematical sense for such models in certain conditions, and the three-dimensional heat conduction problem for a multi-borehole heat exchanger may be decomposed into a number of two-dimensional single-borehole problems. Then, a new dimension reduction algorithm is proposed for simulation of heat transfer in the deep borehole cluster. Using this algorithm, comparisons with other commercial model and simulations on example cases show that computational efficiency can be improved by orders of magnitude compared with traditional three-dimensional software. Highlights: A new heat transfer model of a deep borehole cluster was developed. The geothermal gradient and connection conditions on boreholes were considered. The superposition principle was proven valid on the boundary of the borehole walls. A dimension reduction algorithm was proposed for a deep borehole cluster. The proposed model has a high computational efficiency.