GEOMETRY EFFECTS ON THE PERFORMANCE OF RESIDENTIAL VERTICAL GEOTHERMAL HEAT PUMPS

Although the promise of environmentally friendly, low-cost energy harvesting for heating and cooling of residential properties has been known for nearly 30 years, the adoption of the technology has been slow in the United States. These geothermal systems, known as ground-source heat pumps (GSHP), consist of a field of vertical boreholes in the ground with pipes carrying a heat transfer fluid into the earth to gain access to the stable year-round temperatures underground. However, a significant portion of the cost of these systems is in the installation of the pipes, with a return on investment on the order of a decade. The main cost in the installation is the depth of the boreholes, and a better way to estimate the required depth based on system usage is needed. We focus on this talk on systems with a concentric geometry, where coolant from the residence flows down the center tube, and returns in the annular region between the inner and outer tubes. Heat transfer between the coolant and the soil occurs along the outer tube. We take advantage of the small aspect ratio of the pipes in the modeling of the heat transfer in these systems, and in the case of an uniform annular spacing, spectral methods applied to our resulting model give a characteristic value that determines the length-scale over which thermal exchange takes place as a function of the fluid flow rate and the design parameters of the system. This length is optimized when the gap thickness of the annulus is minimized based on this model. This work is supported by a grant from the National Science Foundation, DMS-1004795.