Energy and exergy analysis of a geothermal heat pump air conditioning system

• The energy and exergy analysis of a GSHP versus a ASHP system is considered.
• The model works on a time scale of a year, with a refinement of less than an hour.
• Flexibility and efficiency are combined by an analytical model and numerical inversion.
• For which order of λ and α the GSHP is not competitive respect to ASHP is determined.
• The economic feasibility of GSHP in mild climates lies on an annual operation.

This paper considers the energy analysis of a heat pump system coupled to the ground by means of vertical exchangers, to verify which thermodynamic boundary conditions, in terms of thermal conductivity and diffusivity of the ground and the grout, make it competitive in comparison with other technologies harnessing atmospheric air as the heat source. The comparison is based on the maximum theoretical efficiency available in correspondence to the temperature effectively assumed by the thermal energy reservoirs in contact with the evaporator and the condenser during the operating conditions. The comparison of the two sources/sinks of heat, i.e. the ground and atmospheric air, represents the comparison between the time trend of the exergy of the two reservoirs required by an ideal GSHP and ASHP respectively. A fully transient heat transfer model able to handle on a time scale of a year or more and with a refinement of less than an hour is considered, since short term variations have significant effects on the overall performance of GSHP. In this paper the borehole heat transfer problem in the Laplace domain is solved for any trend and duration of thermal loads, taking into account an existing analytical approximation model of the full solution proposed by Lamarche and Beauchamp. A numerical inversion using the Inverse Discrete Fourier Transform is then applied to obtain the time domain solution. The method combines the flexibility and accuracy of the analytical model with the superior efficiency of the computational time offered by the numerical inversion if compared with that of methods based on the convolution scheme.