Influence of spatially variable ground heat flux on closed-loop geothermal systems: Line source model with nonhomogeneous Cauchy-type top boundary conditions

Borehole heat exchangers (BHEs) utilize the shallow ground to extract geothermal energy. Mostly they are installed in urbanized areas, where the thermal regime is strongly influenced by pavements, buildings and other urban infrastructures. In order to account for the spatial and temporal variability in the above-ground urban temperatures, a new semi-analytical model with a Cauchy-type top boundary is introduced. With this model, it is possible to estimate the transient three-dimensional temperature field in the near-surface ground influenced by the interaction of BHEs, horizontal groundwater flow, land use type and associated surface air temperature (SAT). It is verified with a numerical model and sensitivity analyses are conducted to examine the relevance of the prevailing thermal regime. By adopting a dimensionless formulation, it is shown that the decoupling between temperature fields at the ground surface restraints heat fluxes and penetration depth of thermal signals above ground. A systematic comparison with traditional Dirichlet-type boundary conditions shows that a fixed temperature formulation generally overestimates the thermal effect of land surface signals on thermal plumes of BHEs. This is also addressed by investigating the ground energy balance during operation of the geothermal system.