Analytical and Numerical Investigation on Depth and Pipe Configuration for Coaxial Borehole Heat Exchanger, A Preliminary Study

Existing research on the performance of shallow geothermal systems are prone to investigate the ground as a large thermal mass at a constant temperature despite possible temperature increase at depths otherwise commonly known as the geothermal gradient. Most of the existing analytical models that predict the heat exchange between a borehole heat exchanger with the soil does not allow for the geothermal gradients to be accounted for. The few models that actually does account for the geothermal gradients, on the other hand, does so by enforcing a pre-existing temperature gradient only. We are presenting a bottom up approach in this paper to solve the temperature distribution by accounting for both the convective heat transfer from the working fluid and the conductive heat transfer through both the pipe and the soil. Assuming the heat transfer is entirely axisymmetric, we approach the problem by solving the Navier-stokes equation and energy equation with a finite difference solver that calculates the temporal change of temperature with given diameter, depth of borehole and geothermal gradient. The heat transfer through the pipe and into the ground can therefore be further calculated. We were able to determine a CBHE configuration that allows maximized thermal output by assuming a synthetic heating/cooling load for year-round production of heat.