Numerical and finite element analysis of heat transfer in a closed loop geothermal system

Analysis of the thermal regime created by a geothermal borehole heat exchanger is performed using a closed form radial heat flow equation, a geothermal borehole heat exchanger design tool, and a finite-element model. Climatic, heat exchanger construction, and building load data are entered into the heat exchanger design tool to create a theoretical model along with thermal parameters from a number of geological formations. Output data from the design tool model are used in conjunction with the closed form radial heat flow equation to calculate the predicted temperature with respect to time and distance from the heat exchanger for the modeled ground formations. The output data from the design tool are also used to create a number of finite-element method models against which the predictions calculated using the closed form radial heat flow equation can be compared. A good correlation between the temperatures predicted by the finite-element models and the closed form equation calculations is observed. However, when used within its recommended limiting conditions, the closed form equation is shown to slightly underestimate the temperature of the ground when compared with the finite-element model predictions. The limiting conditions associated with the closed form equation are discussed in the context of the output from the finite-element method models.