Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales

Ground (or geothermal) heat exchangers are attracting a great deal of attention as a way of using shallow geothermal energy. This paper provides not only a critical review but also a thorough introduction to the analysis of heat transfer by borehole and foundation pile ground heat exchangers, with an emphasis on different analytical models. The literature is reviewed in a time-scale framework because of the diversity of the time and space scales involved in the thermal processes of ground heat exchangers. We summarize, discuss, and evaluate major advances in this field, including heat-source models, short-time models, models for energy piles, in situ thermal-response tests, indoor sandbox experiments, and parameter estimation as an inverse problem. Of particular note is that the unit-step temperature response (i.e., G-function) of a ground heat exchanger with one U-shaped pipe is calculated; and six analytical models are compared: an infinite cylinder-source model, two infinite line-source models, two finite line-source models, and a composite-medium line-source model. This paper closes by identifying several unsolved problems that require solutions.