Natural convection in groundwater-filled boreholes used as ground heat exchangers

In most of the world, borehole heat exchangers used with closed-loop ground source heat pump systems are backfilled with a low permeability grout to prevent water contamination. However, in Scandinavian countries, a different approach is taken - the borehole is sealed at the top and cased down to solid bedrock. The borehole then naturally fills with groundwater in the annular space between the U-tube and the borehole wall. Compared to grouted boreholes, the groundwater filling is advantageous in that it generally results in low borehole thermal resistance due to buoyancy-driven natural convection enhancing the heat transfer. Although this phenomena has been reported in several papers since the late 1980s, no calculation models have been available for use in either design tools or simulation programs. This paper presents experimental measurements from a single well-instrumented borehole under a range of heat transfer rates and annulus temperatures. Nusselt numbers for natural convection in the annulus are correlated against modified Rayleigh number. The results are verified by comparing to borehole thermal resistances predicted with the correlations to actual measurements from a range of boreholes in Sweden and Norway.