Design of the Geothermal Borefield: BHEDesigner8
Ground coupled heat pumps (GCHPs) are an energy efficient solution for building heating and cooling, capable of meeting a wide variety of energy requirements, from small residential units to large commercial buildings. . The most common solution for extracting / injecting heat transfer rate into the ground is represented by the closedcycle vertical heat exchangers in which a single or double U pipe is inserted into a hole made in the ground. The correct sizing of the vertical heat exchanger system (borehole heat exchangers, BHEs) requires accurate knowledge of the thermal properties of the ground and of the heat exchanger, the evaluation of the timevarying demands in heating and cooling of the building and the desired heat pump performance.
The purpose of sizing the BHE field is essentially the definition of the total length of the borehole heat exchangers and their best configuration (number of BHEs and their geometric arrangement).
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To describe and predict the heat exchange due to the thermal interaction between the BHE field and the surrounding ground, the hypotheses of pure heat conduction and uniform ground thermophysical properties are commonly adopted. Under these assumptions, different basic solutions of the ground thermal response to the presence of the probe field are available, called Temperature Response Factors (TRF) or commonly gfunctions. These basic solutions differ from each other depending on whether the single BHE is modeled as an infinite linear source (ILS), an infinite cylindrical source (ICS), a finite linear source (FLS) or a system of multiple finite linear sources described by suitable gfunctions.
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Various procedures for sizing the probe field have been proposed and are currently being implemented in commercial computing codes, including Earth Energy Designer (EED) and GLHEPRO.
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Kavanaugh and Rafferty (K&R) proposed a method, subsequently recommended by the American Society of Heating Refrigerating and AirConditioning Engineers (ASHRAE), which allows sizing the BHE system by considering three representative heat loads of the building, calculated from the knowledge of monthly (or hourly) loads. In particular, the ASHRAE (K&R) method is based on the hypothesis that the behavior of the probe field in real operating conditions can be represented by its response to three elementary heat loads, i.e. a multiyear load (at least 10 years), a monthly load and a multihour load (6 hours).
ASHRAE method for sizing the BHE field: the three elementary thermal loads Δτ y = 10 years; Δτ m = 1 month; Δτ h = 6 hours [7]
The three heat transfer rate types (multiannual, monthly and hourly in [W]) constitute a synthetic representation of the heat exchange to the ground over a time horizon of 10 years [7] , [1] . The three heat pulses take into account the most unfavorable operating condition (peak load, [8] ) for the heat extraction / injection to the ground during the “worst” month of the year.
Thermal loads representative of the timevarying heat exchange to the ground in building heating mode
The ASHRAE method is based on the elementary solution of an infinite cylindrical source (ICS), with a correction, known as the Temperature Penalty, capable of taking into account the effects due to the presence of multiple BHEs in the field. The strengths of this method are simplicity and solidity and its accuracy depends on the correct estimate of the Temperature Penalty parameter.
Many methods have been proposed in recent years (including the use of gfunctions in the superposition scheme provided by K&R) for the evaluation of the Temperature Penalty, often characterized by long and complex and even inaccurate procedures [16] . The model called Tp8, fast and accurate like no other method for sizing the geothermal probe field of this type, is widely described in scientific articles to which the reader is addressed for further information [1] , [16].
The validation of the Tp8 model has been demonstrated in a series of papers, including paper [18], also available online.
The advantages of the Tp8 method include the possibility of considering, during the sizing procedure, multiple geometries of the BHE field, minimizing the need to iterate over the number and length of BHEs as a function of the geometrical configuration of the probe field.
Required length H of the heat exchangers: comparison between EED code (H) and algorithm Tp8 (H8).
Geometries of the BHE fields. Rtype: rectangular and square configurations. NonR: slender rectangle configurations, inline, L, O and U (Source: Science and Technology for the Built Environment, DOI: 10.1080 / 23744731.2016.1208537)
BHEDesigner8: the online version of the ASHRAE Tp8 method
BHEDesigner8 is a tool that the "Solar and Geothermal Lab" research group active in the Dime Department of the University of Genoa has decided to develop and make available for free to researchers and designers from all over the world active in the field of geothermal heat pumps (here a video on RaiNews, in Italian).
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Any suggestion and help from the users of BHEDesigner8 will be appreciated and profitably implemented.
BHEDesigner8 is currently a tool available in the form of an Excel application transposed into a web environment via the SpreadsheetConverter interface. In the future, this web app may evolve into different programming languages. The algorithm requests the building heat loads (positive values in heating mode) on a monthly basis, the ground thermophysical properties and the expected performance of the heat pump in the tenth year of operation, as described by the carrier fluid (ground side) expected temperature which corresponds to the expected COP at the peak. The outputs of the calculation code are the total required length (BHE depth H times the overall number of boreholes) of the BHEs and the configuration of the BHE field associated with it. The algorithm and its parameters have been optimized by comparing the results related to 1200 borefield configurations as described by their "true" gfunctions. The validation has been performed for dimensionless BHE distances in the range 0.03<B/H<0.125. As in other known commercial codes for the sizing of the BHE field, the heat loads to the building are supplied as monthly values, together with the corresponding peak loads (see for example Cullin and Spitler paper about that) in heating and cooling. The thermal resistance of BHE (if its value is not already known) can be calculated through the webapp using Paul's semiempirical model, adopted by the Italian Standard UNI11466.
A complete description of the model is available in the articles by M.Fossa (20112022), by M.Fossa and D. Rolando (20152018), in a series of Master's Theses of the University of Genoa (20122021) and in Davide Rolando's PhD thesis (2015). Davide Rolando, formerly a PhD and Postdoc student at Unige, is currently working as a Researcher at the KTH in Stockholm at the Department of Energy Technology.
Thanks for the useful suggestions, discussions and collaborations go first of all to Prof. Michel Bernier (Polytech Montreal) and also to Prof. Antonella Priarone (Dime University of Genoa), to Dr José Acuña (KTH Stockholm), to Dr. Fabio Minchio (3f Engineering, Italy), to Dr. Danila Dalla Pietà (Fichtner Italy).
Francesco Berti, Imola, is acknoweldged for his fundamental guidance and bright contribution in realizing and conceiving the electronics and the control of the Dime TRT machine.
Further thanks for the development of BHEDesigner8 go to Eng. Stefano Morchio and Eng. Mattia Parenti, PhD students (2022) at the Dime Dept. of the University of Genoa.
References Ashrae Tp8
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M.Fossa, Correct Design of Vertical BHE Systems Through the Improvement of the Ashrae Method, Science and Technology for the Built Environment, 2017, DOI: 10.1080 / 23744731.2016.1208537.

ND Paul, The effect of grout conductivity on vertical heat exchanger design and performance, Master Thesis, South Dakota State University, 1996.

H. Zeng, N. Diao, Z. Fang, Heat transfer analysis of boreholes in vertical ground heat exchangers, Int. J. Heat Mass Transf., 2003.

Bernier, M. 2006. Closedloop groundcoupled heat pump systems., ASHRAE Journal 48 (9): 12–9.

D. Dalla Pietà, M. Fossa, A Tool for Borehole Heat Exchanger Design for GroundSource Heat Pump Applications, Climamed Conference 2007, pp. 527543, Genova, Italy, September 2007.

M.Fossa, O.Cauret, M. Bernier, Comparing the Thermal Performance of Ground Heat Exchangers of Various Lengths, Effstock Int. Conference, Stockholm, June 2009.

M. Fossa, the Temperature Penalty Approach to the Design of Borehole Heat Exchangers for Heat Pump Applications, Energy and Buildings, vol. 43; p. 14731479, 2011.

JR Cullin, JD Spitler, A computationally efficient hybrid time step methodology for simulation of ground heat exchangers, Geothermics, Volume 40, Issue 2, 2011, Pages 144156, ISSN 03756505, https://doi.org/10.1016/ j.geothermics.2011.01.001

M. Fossa, F. Minchio, The effect of borefield geometry and ground thermal load profile on hourly thermal response of geothermal heat pump systems, Energy, Volume 51, n.1, pp. 323329, 2013.

P.Monzo, J.Acuña, M.Fossa, B. Palm, Numerical generation of the temperature response factors for a Borehole Heat Exchangers field, Proceedings of the European Geothermal Congress 2013. p. 18, ISBN: 9782805202261, Pisa, 3/6/2013.

Ahmadfard, M., and M. Bernier. 2014. An alternative to ASHRAE's design length equation for sizing borehole heat exchangers. ASHRAE Annual Conference, Seattle, WA, June 28 – July 2, 1–8.

M.Fossa, D. Rolando, Improving the Ashrae Method for Vertical Geothermal Borefield Design, Energy and Buildings, vol. 93, pp. 315323, 2015.

ASHRAE. 2015. Chapter 34, ASHRAE HandbookHVAC Applications: Geothermal Energy. Atlanta: ASHRAE.

A.Priarone, M.Fossa, Modeling the Ground Volume for Numerically Generating Single Borehole Heat Exchanger Response Factors according to the Cylindrical Source Approach, Geothermics, 58, pp. 3238, 2015.

D. Rolando, J.Acuña and M. Fossa, A Web Application for Geothermal Borefield Design, Proceedings World Geothermal Congress 2015 Melbourne, Australia, 1925 April 2015.

M.Fossa, D. Rolando, Improved Ashrae method for BHE field design at 10 year horizon, Energy and Buildings, 116, 114–121, 2016.

A.Priarone, M.Fossa, Temperature Response Factors at Different Boundary Conditions for Modeling the Single Borehole Heat Exchanger, Applied Thermal Engineering, 2016.

M.Fossa, D. Rolando, A.Priarone, An Investigation on the Effects of Different Time Resolutions in the Design and Simulation of BHE Fields. Proc. IGSHPA Conference, Denver (CO) March 1416, 2017. https://shareok.org/handle/11244/49344.

S. Morchio, M. Fossa, On the ground thermal conductivity estimation with coaxial borehole heat exchangers according to different undisturbed ground temperature profiles, Applied Thermal Engineering, Volume 173, June 2020.

S. Morchio, M. Fossa, and R.A. Beier Study on the best heat transfer rate in thermal response test experiments with coaxial and Upipe borehole heat exchangers, Applied Thermal Engineering, 200, 117621, 2022.