A contribution towards the determination of g-functions using the finite line source

Abstract

This paper examines the thermal response of bore fields using the concept of g-functions introduced by Eskilson. In the first part of the paper, the original concept of the g-functions is reviewed. Then, a new method is proposed to approximate the g-functions. The method accounts for the variation of heat extraction rates among boreholes due to thermal interaction among boreholes and for the buried depth to borehole height ratio (D/H) which was not included in Eskilson's original work. The new method is based on the analytical finite line source and the solution is not limited to regular borehole spacing. Borehole-to-borehole and group-to-borehole response factors are evaluated and then temporal superposition of heat extraction rates is applied in the Laplace domain. The heat extraction rates obtained with the proposed method showed good agreement with Eskilson's numerical model. The differences observed can be explained by the fact that two different boundary conditions are used at the borehole wall. However, for small simulation times, the differences are small and the response factors are almost identical for up to 10 and 6 years for 3 × 2 and 10 × 10 bore fields, respectively. For large bore fields, thermal interactions among boreholes become important and the differences observed between the proposed model and the g-function increase. For instance, the g-function of a 10 × 10 bore field obtained with the proposed method overestimates the g-function by 32% at steady-state. Finally, the effect of the buried depth (D) is examined using the proposed method. It is shown that the response factor of a 5 m borehole buried at depths of 1 and 3 m differ by 19%.