Analytical g-function for inclined boreholes in ground-source heat pump systems

In the design of ground-source heat pump systems, the calculation of the total length of the bore field is very important because it is responsible for the major part of the initial cost. Some technologies, like direct expansion systems and pile systems, often use inclined boreholes. Most design methods do not consider this effect and may overestimate the total length needed for a typical application. This paper gives a method for the calculation of time response factors in a form called g-function for inclined boreholes. The analytical model can be used in a parameterized optimization algorithm to design an optimum bore field. The method is a generalization of a method previously proposed for vertical boreholes. Comparison of the new g-function with tabulated values found in the literature is given, and an application for a typical design is presented as an example.