A methodology for the calculation of response functions for geothermal fields with arbitrarily oriented boreholes – Part 2

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This paper presents the design process of a 4x4 Laboratory Borehole Storage (LABS) model through analytical and numerical analyses. This LABS is intended to generate reference Thermal Response Functions (TRFs) as well as to be a validation tool for borehole heat transfer models. The objective of this design process is to determine suitable geometrical and physical parameters for the LABS. An analytical scaling analysis is first performed and important scaling constraints are derived. In particular, it is shown that the downscaling process leads to significantly higher values for Neumann and convective boundary conditions whereas the Fourier number is invariant. A numerical model is then used to verify the scaling laws, determine the size of the LABS, as well as to evaluate the influence of top surface convection and borehole radius on generated TRFs. An adequate shape for the LABS is found to be a quarter cylinder of radius and height 1.0 m, weighing around 1.2 tonnes. Natural convection on the top boundary proves to have a significant effect on the generated TRF with deviations of at least 15%. This convection effect is proposed as an explanation for the difference observed between experimental and analytical results in Cimmino and Bernier (2015). A numerical reproduction of their test leads to a relative difference of 1.1% at the last reported time. As small borehole radii are challenging to reproduce in a LABS, the effect of the borehole radius on TRFs is investigated. It is found that Eskilson's radius correction (1987) is not fully satisfactory and a new correction method must be undertaken.

Section: Verifications On the Real-scale Numerical Modelmentioning

confidence: 63%

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Design of a laboratory borehole storage model

Mazzotti¹,

Jiang²,

Monzó³

et al. 2018

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“…Such function varies according to many thermal properties and geometrical relations and is different for each GHE. In the last years, many authors have come up with new strategies to construct g-function under different assumptions (Cimmino and Bernier 2014;Lazzarotto and Björk 2016;Marcotte and Pasquier 2014;Cimmino, et al 2013;Dusseault, et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Near-instant g-function construction with artificial neural networks

Dusseault¹,

Pasquier²

2018

“…All these models assume that the heat injection rate per unit borehole length is uniform along the borehole, contrary to the original g-function definition proposed by Eskilson that assumes a uniform mean azimuthal borehole wall temperature along the borehole. As the resulting value of is not uniform along the borehole, its mean value is used instead to define the g-functions (Zeng et al 2002;Lamarche and Beauchamp 2007;Claesson and Javed 2011;Cimmino and Bernier 2014;Cimmino et al 2013) and its calculation can be reduced to a single integral (Lamarche and Beauchamp 2007;Claesson and Javed 2011) that is discretized using the midpoint rule with one (Cimmino et al 2013) or more segments (Cimmino and Bernier 2014;Lazzarotto and Björk 2016) or the trapezoidal rule with multiple segments along the boreholes (Lamarche 2017). Furthermore, a primitive function for the integral can be obtained for the steady-state and time-harmonic cases leading to simple analytical expressions.…”

Section: Introductionmentioning

confidence: 99%

Application of matched asymptotic expansion techniques to the analysis of geothermal heat exchangers

Hermanns¹,

Ibáñez²

2018

Most theoretical models for the thermal response of geothermal heat exchangers assume the mean azimuthal borehole wall temperature to be uniform along the boreholes. This simplifying assumption, closely related to the g-functions introduced by Eskilson in 1987, has dominated the research field for the past 30 years, allowing the analysis of large geothermal heat exchangers in reasonable amounts of time. The assumption, however, is not physically correct, which hinders the attainable accuracy. By using matched asymptotic expansion techniques, analytical models for the thermal response of geothermal heat exchangers are derived, which do not require the aforementioned simplification. The resulting expressions, applicable to geothermal heat exchangers with irregularly placed heterogeneous boreholes, show accuracy and flexibility levels comparable to SBM, but with a computational cost in line with the use of g-functions.