Modeling insulated borehole heat exchangers

In the heating sector, borehole heat exchangers have become popular for supplying renewable energy. They tap into the subsurface to extract geothermal energy for heating purposes. For advanced applications, borehole heat exchangers require insulation in the upper part of the borehole either to meet legal requirements or to improve their performance. A priori numerical heat transport models of the subsurface are imperative for the systems' planning and design. Only fully discretized models can account for depth-dependent borehole properties like insulated sections, but the model setup is cumbersome and the simulations come at high computational cost. Hence, these models are often not suitable for the simulation of larger installations. This study presents an analytical solution for the simulation of the thermal interactions of partly insulated borehole heat exchangers. A benchmark with a fully discretized OpenGeoSys model confirms sufficient accuracy of the analytical solution. In an application example, the functionality of the tool is demonstrated by finding the ideal length of a borehole insulation using mathematical optimization and by quantifying the effect of the insulation on the borehole heat exchanger performance. The presented method allows for accommodation of future advancements in borehole heat exchangers in numerical simulations at comparatively low computational cost.