Effects of arrangement geometry and number of boreholes on thermal interaction coefficient of multi-borehole heat exchangers

In large-scale ground-source heat pump applications, a large number of borehole heat exchangers are used and performance losses become an important issue due to thermal interactions. Dependency of total performance losses on borehole spacing can analytically be expressed by using thermal interaction coefficient. For a given application field, interaction coefficient depends on number of boreholes (N), aspect ratio of borehole's arrangement geometry and operation time. In this study, functional dependencies of interaction coefficient on N and aspect ratio are investigated by considering different rectangular borehole arrangements. Dependencies of both thermal interaction coefficient and total heat transfer rate on aspect ratio are computationally examined. Also, the effects of number of boreholes and operation time on interaction coefficient are studied. The results showed that the values of both interaction coefficient and performance losses decrease with the decrease of aspect ratio of a borehole field. Aspect ratio dependency of total unit heat transfer rate becomes more evident in case of shorter borehole spacing. Furthermore, a strong dependency of interaction coefficient on N is observed when N is much smaller than a critical value, N-c, although an asymptotic behavior appears and dependency on N becomes negligible for N > N-c. Some empiric expressions are proposed for aspect ratio and N dependency of interaction coefficient as well as N-c. The results and the proposed expressions can be used to make an energy efficient and optimal design of a BHE field by maximizing the total performance while minimizing the field allocation and the thermal losses.