Superposition of the single point source solution to generate temperature response factors for geothermal piles

Abstract

Geothermal piles are a very promising technique to exploit the low enthalpy resource for ground coupled heat pumps. In fact, they are heat exchangers integrated in the foundation structures of the buildings, with reduced need in term of ground surface availability and diminished drilling costs. Unfortunately, to evaluate the ground thermal response to their presence it is not possible to use classical analytical solutions due to their low aspect ratio and to the relevant effect of the heat capacity of the inner cylindrical volume. In addition, different shapes of the pipe arrangement are possible: helix around the foundation pile or a series of vertical pipes connected through U bends at top and bottom of the cylindrical volume. This study proposes a semi-analytical method to model ground heat exchangers with a great flexibility concerning their shape. The method, called Multiple Point Sources (MPS), applies the spatial superposition of the analytical solution for the Single Point Source. It has been validated by means of the comparison with literature analytical methods and FEM results for helix heat exchangers. Finally, it has been applied to find the temperature response factor for different shapes of heat exchanger in geothermal piles.

A global model for fast calculation of the thermal response factor of large-scale boreholes heat exchangers combining the FLS model, the 2D heat equation and a three-points method

“…Considering the radial distances between borehole 1 and the other boreholes, B occurs twice: from 1 to 2 and from 1 to 3; occurs once: from 1 to 5; 2B occurs twice: from 1 to 3 and from 1 to 7; occurs twice: from 1 to 6 and from 1to 8; occurs once: from 1 to 9. Combining the self-effect, the borehole wall temperature of borehole 1 under all boreholes' effects at timestep m is given by: (10) Similarly, other boreholes' temperatures can be derived from the number of times each radial distance occurs.…”

“…Fast and accurate calculation of these temperatures is essential for the long-term evaluation of the GCHP performance and the proper design of the system [6,7]. The temperature variation of a point in the ground can be represented in a dimensionless form by introducing a proper thermal response factor (also called temperature response factor in some references [8][9][10]), which gives the relation between the temperature variation and the overall heat extraction rate in the borehole field. The most utilised method to analyse a vertical GHE consisting of large-scale boreholes is firstly to use a heat transfer model of a single borehole to obtain the thermal response factor of one borehole, and secondly to apply Duhamel's superposition principle [11] to evaluate the temperature responses caused by all the boreholes in the field [12].…”

Experimental Hydration Temperature Increase in Borehole Heat Exchangers during Thermal Response Tests for Geothermal Heat Pump Design

“…Very recently, Morchio and Fossa [35] tackled the problem of TRT analysis with deep boreholes (up to 800 m), when the geothermal gradient effects can lead to temperature crossing in the bottom part of the heat exchanger. From the same research group, the TRT analysis in terms of proper temperature response factors is further extended to geothermal pipes [36]. Franco and Conti [37] present an updated and comprehensive review of the various TRT types and explore the perspective to combine TRT and routine geotechnical tests.…”