A Coupled FEM Model for Numerical Simulation of Rechargeable Shallow Geothermal BHE Systems

Abstract

This article shows the results of a FEM simulation approach of borehole heat exchanger (BHE) arrays. The direct implementation of a BHE within a 3D model is a challenging numerical problem caused by the geometry of the borehole with extreme depth-radius ratio. Since this ratio makes the exact calculation of the pipe flow practically impossible we assume a mean pipe flow velocity and calculate the heat transfer within the BHE with empirical approaches (Nusselt number). The simulations include the heat transfer issues in presence of groundwater flow which may lead to advective dominated heat transport in the subsurface. We use the FEM based software COMSOL Multiphysics to solve the coupled system of partial differential equations determining the problem. Our model has been validated by comparing the results with an existing geothermal BHE array of a triangular arrangement located on a test site at the Institute for Solar Energy Research near Hameln/Germany. This test site includes heat pump systems allowing the emulation of different charging and discharging regimes. Special focus lies on recharging options from solar energy in the summer season. Thermal parameters of the system were determined by thermal response tests (TRTs). Hydraulic parameters are estimated through series of pumping tests in the two wells located in the direct vicinity of the BHEs. These pumping tests are evaluated by Hydraulic Tomography which gives us detailed information about the spatial distribution of the relevant hydraulic parameters for groundwater flow. For the validation we compare field data of heat extraction/infiltration test runs of the BHEs with model output. The validated model is used to enhance the synergy effects of coupled geothermal and solar systems. It can also be applied for long time predictions of BHE systems and for the improvement and optimization of geothermal systems of various types.