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Theoretical Basis
The theory behind the vertical borehole module is based on the cylindrical source model and allows for quick but accurate length or temperature calculations based on limited data input.

The vertical bore length equations used in the Borehole Design module are based upon the solution for heat transfer from a cylinder buried in the earth. The method was developed and tested by Carslaw and Jaeger (Carslaw and Jaeger, 1947). The solution yields a temperature difference between the outer cylindrical surface and the undisturbed far field soil temperature. Ingersoll suggested using the equation and its solution for the sizing of ground heat exchangers in cases where the extraction or rejection occurs in periods of less than six hours (where the simple line source model fails) (Ingersoll, 1954). The borehole module’s equations include the suggestions of Kavanaugh and Deerman, who adjusted the methods of Ingersoll to account for U-tube arrangement and hourly heat variations (Kavanaugh and Deerman, 1991). It also employs the borehole resistance calculation techniques suggested by Remund and Paul to account for pipe placement, grout conductivity, and borehole size (Paul, 1997).

Additionally, the software calculates the amount of energy absorbed by or withdrawn from the ground using the load information collected from the individual zones and their relationship to the equipment selected.

The calculations find the conditions for long-term, steady state operation of borehole fields based on the desired heat pump inlet temperatures. In order to provide an optimum design and prevent system failure, the combination of parameters must allow for proper extraction or dissipation of energy from or to the earth at the location of interest.

The most complete description of the calculations and input data can be found in Chapter 3 of the book, Ground Source Heat Pumps - Design of Geothermal Systems for Commercial and Institutional Buildings, by S.P. Kavanaugh and K. Rafferty, 1997. In extensive tests, this model consistently proved to be the most accurate when compared with calibrated data from actual installations (Hughes and Shonder, 1998).