Study on thermal radius and capacity of multiple deep borehole heat exchangers: Analytical solution, algorithm and application based on Response Factor Matrix method (RFM)

The deep borehole heat exchanger systems (DBHE) are offering potential low carbon heating for buildings. However, the study of DBHE is hindered by both modeling and system complexity. Although some analytical models of DBHE are presented in literature, the involved expression of complex integral calculation on the contrary slows down the computation speed and many calculations are redundant in algorithm. In this study, a Response Factor Matrix method (RFM) is proposed based on simple analytical expression and well-designed data structure for DBHE. The RFM can be prefabricated and then used in each time step updates of temperature field. A superposition algorithm is designed for fast computation of DBHE array. The proposed model and algorithms are verified by measurements from two independent engineering projects. Based on the new tool, both thermal radius and heating capacity of DBHE array are investigated in details. The step-ascending pattern of thermal radius is recognized. The correlation of borehole spacing and system heating capacity is identified. In the end, the computational efficiency of the new tool is justified and some outlooks are proposed for a further development and applications.