Effects of Ground Heat Flux on Performance of Vertical Borehole Heat Exchangers

Abstract

There are various analytical and semi-analytical modelling techniques used for prediction of the impacts of borehole heat exchangers (BHEs) on the thermal conditions in the subsurface. They are attractive because they are easy to use, compact and computationally efficient. However, (semi-)analytical formulations also cut down the complexity of the conditions in the field by limited resolution of variations in space and time, and by often simplified specifications of boundary conditions. In this presentation, we focus on the definition of the land surface boundary condition in line source solutions. As BHEs are thin elongated forms that can be approximated by a linear shape function, the main attention is commonly given to radial heat transfer, but less so on the axial effects. Given the long operation time, however, the sharp physical boundary at the top may exert a substantial influence on the temperature evolution in the shallow ground and thus influence the performance of the ground source heat pump. We examine formulations with Dirichlet type boundaries included in the line source equation. Homogeneous as well as inhomogeneous implementations are feasible, which offer new flexibilities for simulation of nonuniform land surface impacts such as those associated with varying land use types. The presented approach also facilitates an account for the accelerated ground heat flux due to global warming and to urbanization which can be observed in so-called subsurface urban heat islands in many cities. As a consequence, it is revealed by the results for synthetic scenarios that the neglect of such effects may underestimate the regeneration capacity of BHEs operated in an unbalanced mode.