Analytical modelling approach of ground freezing and thawing around ground heat collectors

Abstract Ground heat collectors represent shallow geothermal devices that are buried in the upper metres of the ground with strong thermal coupling to ground surface. Therefore, during seasonal operation, heat extraction in winter can cause temporal freezing of the soil surrounding the collector. The transient latent heat transfer during freezing and thawing can be crucial for the performance of a collector, and it adds complexity to the model-based representation of the devices. Here, a novel analytical model is presented that accounts for these processes and simulates the evolution of thermal ground conditions during operation of different collector variants. It combines heat source-based solutions with thermal power balancing depending on a given collector geometry and temporal superposition for varying heat loads. By comparison with high-resolution numerical model results, the obtained fast analytical predictions represent the thermal regime around horizontal pipe installations and vertical planar trench collectors within seconds very well, achieving temperature deviations of less than 1.4 K and accuracies over 85.6% for predicting of the thickness of the frozen ground. This regime is inspected in particular with respect to collector wall temperature and the maximum horizontal extension of the frozen soil. The findings demonstrate the suitability of the new model framework to be used in the planning and design phase for optimal layout of collectors, as well for straightforward representation of complex freezing and thawing processes during operation.