Effect of Borehole Material on Analytical Solutions of the Heat Transfer Model of Ground Heat Exchangers Considering Groundwater Flow

Abstract

Groundwater flow is one of the most important factors for the design of a ground heat exchanger (GHEX) since the thermal environment of the ground around the buried GHEX is significantly affected by heat convection due to the groundwater flow. Several preceding studies have been conducted to develop analytical solutions to the heat transfer model of GHEX with consideration of groundwater flow. One of these solutions is the combined heat transfer model of conduction and convection. However, the developed combined analytical models are inapplicable to all of the configurations of ordinary GHEXs because these solutions assume that the inner part of the borehole is thermally inert or consists of the same material as that of the surrounding ground. In this paper, the applicability of the combined solid cylindrical heat source model, which is the most suitable to energy piles until now, was evaluated by performing a series of numerical analyses. In the numerical analysis, the inner part of the borehole was modeled as two different materials (i.e., permeable ground formation and impermeable fill such as concrete) to evaluate applicability of the analytical solution along with different diameter-length (D/L) ratios of borehole. In a small value of the D/L ratio, the analytical solution to the combined heat transfer model is in good agreement with the result of numerical analysis. On the other hand, when increasing the D/L ratio, the analytical solution significantly overestimates the effect of groundwater flow on the heat transfer of GHEXs because the analytical solution disregards the existence of the impermeable region in the borehole. Consequently, such tendency is more critical in the GHEX with a large D/L ratio such as large-diameter energy piles.