A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application

Ali H. Tarrad

doi:doi:10.11648/j.ajese.20190304.12

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A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application

Ali H. Tarrad

Published in American Journal of Environmental Science and Engineering (Volume 3, Issue 4)

Received: 18 October 2019 Accepted: 6 November 2019 Published: 19 November 2019

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Abstract

The ground source coupled heat pump is considered as one of the most important technologies utilized in the field of sustainable energy. The borehole thermal resistance has a great impact on the total thermal resistance between the fluid that flows inside the buried U-tube and ground. This issue is related directly to the heat transfer efficiency of the ground part of the heat pump and the effective coefficient of performance of the heat pump system. The capability of the ground heat exchanger to dissipate or absorb energy to or from the ground determines the size and geometry configuration of these heat exchangers. The present research represents a model for the prediction of the borehole thermal resistance of a ground heat exchanger. The U-tube heat source or sink was replaced by a single equivalent concentric tube in the borehole possessing equal thermal resistance as that of the original U-tube heat exchanger. The model was applied for four different U-tube/borehole configurations, the test U-tubes were (9.52) mm, (12.7) mm, (15.88) mm, and (19.05) mm for a borehole to U-tube diameter ratios range of (3.94) to (7.88). The correlation showed a nonlinear dependency for the equivalent tube diameter and hence the thermal resistance of the filling on the U-tube diameter. It has also shown that for the same U-tube/borehole configuration, increasing of the U-tube legs spacing reduces the thermal resistance and approaching a minimum as the tube legs are located close to the borehole wall. Further, for the same borehole size, the thermal resistance exhibited a decrease as the U-tube size was increased and vice versa. At a borehole size of (75) mm, shank spacing to tube diameter ratio of (2), and a grout thermal conductivity of (0.78) W/m.K, the borehole total thermal resistance of the (9.52) mm U-tube size was higher than that of the (19.05) mm by (74)%. The model revealed that the grout thermal conductivity plays an important role in the thermal resistance assessment; the latter showed a decrease as the thermal conductivity increases to the highest test value of 1.9 W/m.K. The predicted thermal resistance was compared with other available correlations in the open literature and found to be consistent in the data trend and magnitudes with acceptable margin.

Published in	American Journal of Environmental Science and Engineering (Volume 3, Issue 4)
DOI	10.11648/j.ajese.20190304.12
Page(s)	75-83
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

DX Geothermal System, Borehole Thermal Design, Vertical U-tube, Thermal Resistance Correlation

References

[1]	S. Kavanaugh, “Simulation and experimental verification of vertical ground coupled heat pump systems”, PhD. Thesis, Oklahoma State University, USA, 1985.
[2]	H. Zeng, N. Diao, Z. Z. Fang Z., “Heat transfer analysis of boreholes in vertical ground heat exchangers”, International journal of Heat and Mass Transfer 46, 4467-4481, 2003.
[3]	N. Muttil, K. W. Chau, “Neural network and genetic programming for modeling coastal algal blooms. Int. J. Environ. Pollution, 28, 223-238, 2006.
[4]	L. R., Ingersoll, O. J. Zobel, A. C. Ingersoll, “Heat conduction with engineering and Geological application”, McGraw Hill: New York, 1948.
[5]	H. S. Carslaw, J. C. Jaeger, “Conduction of heat in solids”, 2nd ed.; Oxford University Press: London, 1959.
[6]	L. R. Ingersoll, O. J. Zobel, A. C. Ingersoll, “Heat conduction with engineering, Geological and other applications”, revised edition; University of Wisconsin Press: Madison, 1954.
[7]	L. Garbai, S. Méhes, “Heat capacity of vertical ground heat exchangers with single U-tube installation in the function of time”, Wseas Transactions on Heat and Mass Transfer, 3 (3), 177-186, July 2008.
[8]	S. Chen, J. Mao, X. Han, C. Li, L. Liu, “Numerical analysis of the factors influencing a vertical U-Tube ground heat exchanger”, Sustainability, 8, 1-12, 2016, doi: 10.3390/su8090882.
[9]	Z. Sagia, “Borehole resistance and heat conduction around vertical ground heat exchangers”, The Open Chemical Engineering Journal, 6, 32-40, 2012.
[10]	Ö. Kizilkan, I. Dincer, “Evaluation of thermal characteristics of a borehole thermal energy storage system”, Proceeding of the Sixth International Exergy, Energy and Environment Symposium (IEEES-6), 1-4 July 2013.
[11]	J. Claesson, A. Dunand, “Heat extraction from the ground by horizontal pipes- A mathematical Analysis”, Document D1, Swedish Council for Building Research, Stockholm, 1983.
[12]	V. C. Mei, V. D. Baxter, “Performance of a ground coupled heat pump with multiple dissimilar U-tube coils in series. ASHRAE Transactions, 92 (2A), 30-42, 1986.
[13]	R. D. Fischer, G. H. Stickford., “Technical and economic feasibility of horizontal, multiple shallow-well and deep-well ground coupling, ORNUSub/80-78001 3&06. Oak Ridge, Tenn.: Oak Ridge National Laboratory, 1983.
[14]	J. E. Bose, J. D. Parker, F. C. McQuiston, “Design/Data manual for closed-loop ground-coupled heat pump systems”, American Society of Heating, Refrigeration and Air Conditioning Engineers (ASHRAE): Atlanta, 1985.
[15]	Y. Gu, D. L. O’Neal, “Development of an Equivalent Diameter Expression for Vertical U-Tubes Used in Ground-Coupled Heat Pumps. ASHRAE Transactions, 104 (2), 1-9, 1998.
[16]	H. M. Sharqawy, E. M. Mokheimer, H. M. Badr, “Effective pipe-to-borehole thermal resistance for vertical ground heat exchangers”, Geothermics, 38, 271–277, 2009.
[17]	C. P. Remund, “Borehole thermal resistance: laboratory and field studies”, ASHRAE Trans., 105, 439-445, 1999.
[18]	J. P. Holman, “Heat Transfer”, 10th edition, McGraw-Hill, chapter 3, 83-86, 2010.
[19]	J. A. Shonder, J. V. Beck, “Determining effective soil formation thermal properties from field data using a parameter estimation technique”, ASHRAE Trans., 105, 458-466, 1999.

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Ali H. Tarrad. (2019). A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application. American Journal of Environmental Science and Engineering, 3(4), 75-83. https://doi.org/10.11648/j.ajese.20190304.12

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ACS Style

Ali H. Tarrad. A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application. Am. J. Environ. Sci. Eng. 2019, 3(4), 75-83. doi: 10.11648/j.ajese.20190304.12

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AMA Style

Ali H. Tarrad. A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application. Am J Environ Sci Eng. 2019;3(4):75-83. doi: 10.11648/j.ajese.20190304.12

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@article{10.11648/j.ajese.20190304.12,
  author = {Ali H. Tarrad},
  title = {A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application},
  journal = {American Journal of Environmental Science and Engineering},
  volume = {3},
  number = {4},
  pages = {75-83},
  doi = {10.11648/j.ajese.20190304.12},
  url = {https://doi.org/10.11648/j.ajese.20190304.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajese.20190304.12},
  abstract = {The ground source coupled heat pump is considered as one of the most important technologies utilized in the field of sustainable energy. The borehole thermal resistance has a great impact on the total thermal resistance between the fluid that flows inside the buried U-tube and ground. This issue is related directly to the heat transfer efficiency of the ground part of the heat pump and the effective coefficient of performance of the heat pump system. The capability of the ground heat exchanger to dissipate or absorb energy to or from the ground determines the size and geometry configuration of these heat exchangers. The present research represents a model for the prediction of the borehole thermal resistance of a ground heat exchanger. The U-tube heat source or sink was replaced by a single equivalent concentric tube in the borehole possessing equal thermal resistance as that of the original U-tube heat exchanger. The model was applied for four different U-tube/borehole configurations, the test U-tubes were (9.52) mm, (12.7) mm, (15.88) mm, and (19.05) mm for a borehole to U-tube diameter ratios range of (3.94) to (7.88). The correlation showed a nonlinear dependency for the equivalent tube diameter and hence the thermal resistance of the filling on the U-tube diameter. It has also shown that for the same U-tube/borehole configuration, increasing of the U-tube legs spacing reduces the thermal resistance and approaching a minimum as the tube legs are located close to the borehole wall. Further, for the same borehole size, the thermal resistance exhibited a decrease as the U-tube size was increased and vice versa. At a borehole size of (75) mm, shank spacing to tube diameter ratio of (2), and a grout thermal conductivity of (0.78) W/m.K, the borehole total thermal resistance of the (9.52) mm U-tube size was higher than that of the (19.05) mm by (74)%. The model revealed that the grout thermal conductivity plays an important role in the thermal resistance assessment; the latter showed a decrease as the thermal conductivity increases to the highest test value of 1.9 W/m.K. The predicted thermal resistance was compared with other available correlations in the open literature and found to be consistent in the data trend and magnitudes with acceptable margin.},
 year = {2019}
}

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TY  - JOUR
T1  - A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application
AU  - Ali H. Tarrad
Y1  - 2019/11/19
PY  - 2019
N1  - https://doi.org/10.11648/j.ajese.20190304.12
DO  - 10.11648/j.ajese.20190304.12
T2  - American Journal of Environmental Science and Engineering
JF  - American Journal of Environmental Science and Engineering
JO  - American Journal of Environmental Science and Engineering
SP  - 75
EP  - 83
PB  - Science Publishing Group
SN  - 2578-7993
UR  - https://doi.org/10.11648/j.ajese.20190304.12
AB  - The ground source coupled heat pump is considered as one of the most important technologies utilized in the field of sustainable energy. The borehole thermal resistance has a great impact on the total thermal resistance between the fluid that flows inside the buried U-tube and ground. This issue is related directly to the heat transfer efficiency of the ground part of the heat pump and the effective coefficient of performance of the heat pump system. The capability of the ground heat exchanger to dissipate or absorb energy to or from the ground determines the size and geometry configuration of these heat exchangers. The present research represents a model for the prediction of the borehole thermal resistance of a ground heat exchanger. The U-tube heat source or sink was replaced by a single equivalent concentric tube in the borehole possessing equal thermal resistance as that of the original U-tube heat exchanger. The model was applied for four different U-tube/borehole configurations, the test U-tubes were (9.52) mm, (12.7) mm, (15.88) mm, and (19.05) mm for a borehole to U-tube diameter ratios range of (3.94) to (7.88). The correlation showed a nonlinear dependency for the equivalent tube diameter and hence the thermal resistance of the filling on the U-tube diameter. It has also shown that for the same U-tube/borehole configuration, increasing of the U-tube legs spacing reduces the thermal resistance and approaching a minimum as the tube legs are located close to the borehole wall. Further, for the same borehole size, the thermal resistance exhibited a decrease as the U-tube size was increased and vice versa. At a borehole size of (75) mm, shank spacing to tube diameter ratio of (2), and a grout thermal conductivity of (0.78) W/m.K, the borehole total thermal resistance of the (9.52) mm U-tube size was higher than that of the (19.05) mm by (74)%. The model revealed that the grout thermal conductivity plays an important role in the thermal resistance assessment; the latter showed a decrease as the thermal conductivity increases to the highest test value of 1.9 W/m.K. The predicted thermal resistance was compared with other available correlations in the open literature and found to be consistent in the data trend and magnitudes with acceptable margin.
VL  - 3
IS  - 4
ER  -

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Author Information

Ali H. Tarrad

Université de Lorraine, CNRS, LEMTA, Nancy, France

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Plain Text BibTeX RIS

APA Style

Ali H. Tarrad. (2019). A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application. American Journal of Environmental Science and Engineering, 3(4), 75-83. https://doi.org/10.11648/j.ajese.20190304.12

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ACS Style

Ali H. Tarrad. A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application. Am. J. Environ. Sci. Eng. 2019, 3(4), 75-83. doi: 10.11648/j.ajese.20190304.12

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AMA Style

Ali H. Tarrad. A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application. Am J Environ Sci Eng. 2019;3(4):75-83. doi: 10.11648/j.ajese.20190304.12

Copy | Download

@article{10.11648/j.ajese.20190304.12,
  author = {Ali H. Tarrad},
  title = {A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application},
  journal = {American Journal of Environmental Science and Engineering},
  volume = {3},
  number = {4},
  pages = {75-83},
  doi = {10.11648/j.ajese.20190304.12},
  url = {https://doi.org/10.11648/j.ajese.20190304.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajese.20190304.12},
  abstract = {The ground source coupled heat pump is considered as one of the most important technologies utilized in the field of sustainable energy. The borehole thermal resistance has a great impact on the total thermal resistance between the fluid that flows inside the buried U-tube and ground. This issue is related directly to the heat transfer efficiency of the ground part of the heat pump and the effective coefficient of performance of the heat pump system. The capability of the ground heat exchanger to dissipate or absorb energy to or from the ground determines the size and geometry configuration of these heat exchangers. The present research represents a model for the prediction of the borehole thermal resistance of a ground heat exchanger. The U-tube heat source or sink was replaced by a single equivalent concentric tube in the borehole possessing equal thermal resistance as that of the original U-tube heat exchanger. The model was applied for four different U-tube/borehole configurations, the test U-tubes were (9.52) mm, (12.7) mm, (15.88) mm, and (19.05) mm for a borehole to U-tube diameter ratios range of (3.94) to (7.88). The correlation showed a nonlinear dependency for the equivalent tube diameter and hence the thermal resistance of the filling on the U-tube diameter. It has also shown that for the same U-tube/borehole configuration, increasing of the U-tube legs spacing reduces the thermal resistance and approaching a minimum as the tube legs are located close to the borehole wall. Further, for the same borehole size, the thermal resistance exhibited a decrease as the U-tube size was increased and vice versa. At a borehole size of (75) mm, shank spacing to tube diameter ratio of (2), and a grout thermal conductivity of (0.78) W/m.K, the borehole total thermal resistance of the (9.52) mm U-tube size was higher than that of the (19.05) mm by (74)%. The model revealed that the grout thermal conductivity plays an important role in the thermal resistance assessment; the latter showed a decrease as the thermal conductivity increases to the highest test value of 1.9 W/m.K. The predicted thermal resistance was compared with other available correlations in the open literature and found to be consistent in the data trend and magnitudes with acceptable margin.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application
AU  - Ali H. Tarrad
Y1  - 2019/11/19
PY  - 2019
N1  - https://doi.org/10.11648/j.ajese.20190304.12
DO  - 10.11648/j.ajese.20190304.12
T2  - American Journal of Environmental Science and Engineering
JF  - American Journal of Environmental Science and Engineering
JO  - American Journal of Environmental Science and Engineering
SP  - 75
EP  - 83
PB  - Science Publishing Group
SN  - 2578-7993
UR  - https://doi.org/10.11648/j.ajese.20190304.12
AB  - The ground source coupled heat pump is considered as one of the most important technologies utilized in the field of sustainable energy. The borehole thermal resistance has a great impact on the total thermal resistance between the fluid that flows inside the buried U-tube and ground. This issue is related directly to the heat transfer efficiency of the ground part of the heat pump and the effective coefficient of performance of the heat pump system. The capability of the ground heat exchanger to dissipate or absorb energy to or from the ground determines the size and geometry configuration of these heat exchangers. The present research represents a model for the prediction of the borehole thermal resistance of a ground heat exchanger. The U-tube heat source or sink was replaced by a single equivalent concentric tube in the borehole possessing equal thermal resistance as that of the original U-tube heat exchanger. The model was applied for four different U-tube/borehole configurations, the test U-tubes were (9.52) mm, (12.7) mm, (15.88) mm, and (19.05) mm for a borehole to U-tube diameter ratios range of (3.94) to (7.88). The correlation showed a nonlinear dependency for the equivalent tube diameter and hence the thermal resistance of the filling on the U-tube diameter. It has also shown that for the same U-tube/borehole configuration, increasing of the U-tube legs spacing reduces the thermal resistance and approaching a minimum as the tube legs are located close to the borehole wall. Further, for the same borehole size, the thermal resistance exhibited a decrease as the U-tube size was increased and vice versa. At a borehole size of (75) mm, shank spacing to tube diameter ratio of (2), and a grout thermal conductivity of (0.78) W/m.K, the borehole total thermal resistance of the (9.52) mm U-tube size was higher than that of the (19.05) mm by (74)%. The model revealed that the grout thermal conductivity plays an important role in the thermal resistance assessment; the latter showed a decrease as the thermal conductivity increases to the highest test value of 1.9 W/m.K. The predicted thermal resistance was compared with other available correlations in the open literature and found to be consistent in the data trend and magnitudes with acceptable margin.
VL  - 3
IS  - 4
ER  -

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