Ground Heat Exchangers: Analytical and Numerical Modeling and Experimental Validation

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Chemical Engineering


Knowledge of the thermal response characteristics of the ground heat exchanger (GHX) in the early stage of a step heat input is essential for the design or simulation of ground source heat pump systems (GSHP). Recently this has assumed even a greater importance as the building cooling loads dominate in many regions due to the general warming trend and there is an urgent need for developing hybrid systems. In an operating GSHP system, the heat flux across the borehole boundary builds up gradually as the rise of the fluid temperature is dampened by the thermal mass of the aggregate fluid. Currently analytical models are based on the assumption of steady heat flux across the borehole boundary. Further, the thermal capacity of the fluid is also not considered. Consequently these models have limited usefulness for predicting the early stage behavior.

In this dissertation, the lack of adequate models has been specifically addressed using two distinctly different approaches. First an e-tube representation has been developed to represent the U-tube geometry. A classical analytical solution has been adapted to model the temperature response of the fluid directly. Since this solution is limited to only homogenous media, a method has been outlined to overcome the difficulties when the grout envelope is present. In an alternative approach, Laplace domain solutions have been obtained for the grouted boreholes. Both the average fluid temperature and borehole boundary temperature have been obtained using the Gaver- Stehfest numerical inversion algorithm from these solutions. Both sets of solutions compare very well with results from finite element modeling. Fluid and ground temperatures have been monitored for a large real GHX for over a year in an effort to further validate the solutions experimentally.

The effect of changing the tube spacing ratio of the U-tube geometry in different media on the fluid temperature has been studied in detail. It is observed that with the appropriate values of a dimensionless variable (Biot no.), results from both the analytical and the semi-analytical solutions agree closely with the results of the FE models of the U- tube geometry if the spacing ratio between the two legs is below a threshold value. Under identical fluid flow conditions, the threshold is higher in a medium with higher thermal conductivity. Direct measurement of the thermal conductivity was limited only to the top layer of a multi-strata subsurface ground. The ground temperature data was analyzed to derive the undisturbed ground temperature and extend the thermal conductivity measurements. The average water temperature data from the field observation did not match the modeled values, possibly due to several assumptions made in modeling the physical configuration from the real system data Availability of the numerical and analytical solutions open up new dimension for system simulation and design of hybrid systems These models also provide an opportunity to use the early time borehole temperature data from thermal response test rather than fluid temperatures, to obtain a quicker, more accurate evaluation of ground thermal properties.

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