Modelling the ground volume for numerically generating single borehole heat exchanger response factors according to the cylindrical source approach

• Temperature response factors have been obtained for a single borehole heat exchanger (BHE) when modeled as a finite length cylindrical source (FCS).
• Different BHE wall boundary conditions have been analyzed: the classic constant heat flux and the imposed temperature at the heat source surface.
• A numerical model created in Comsol environment has been validated against analytical available solutions with great accuracy (average error below 1%).
• Obtained results are useful for spatial and temporal superposition schemes and g-function generation.
• A new correlation has been proposed to evaluate the steady state behavior of the single BHE at different boundary conditions.

Borehole heat exchangers (BHE) are the most common solution for ground coupled heat pumps (GCHP). The thermal interactions with ground and the GCHP performance are strictly related to a number of factors, including the ground properties, the BHE field geometry, the sequence and strength of heat loads required by the building. A typical assumption to solve this problem is assuming the ground volume as a purely conductive medium with constant properties: in such a way the transient Fourier equation can be solved either analytically or numerically with a reasonable computational effort provided that a simple BHE geometry is considered. According to this approach suitable temperature response factors can be calculated: they account for constant heat transfer rate conditions and they can be later applied to superposition techniques for simulating transient heat loads to/from the ground. In literature a number of reference geometries and related temperature response factors for BHE modelling are available. They include the infinite and finite line source and the infinite cylindrical source, at imposed heat transfer rate or even imposed temperature. The aim of this paper is to develop a reliable numerical model for generating temperature response factors for the single BHE according to different geometrical and boundary conditions. A detailed analysis is carried out to recast the Fourier equation and to efficiently solve it with suitable numerical parameters. The results are compared with literature analytical data and new insights are provided to the temperature response factor approach for simulating GCHP systems.