Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process

Mohammed Hirpho Tobe; Zerihun Kinfe Birhanu

doi:doi:10.11648/j.ajam.20200803.13

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Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process

Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu

Published in American Journal of Applied Mathematics (Volume 8, Issue 3)

Received: 26 March 2020 Accepted: 12 May 2020 Published: 27 May 2020

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Abstract

Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.

Published in	American Journal of Applied Mathematics (Volume 8, Issue 3)
DOI	10.11648/j.ajam.20200803.13
Page(s)	89-97
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), 2020. Published by Science Publishing Group

Keywords

Porous Media, Heat Transfer, Fluid Flow, Finite Element Method, Homogeneous Aquifer Thermal Energy Storage System

References

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APA Style

Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu. (2020). Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process. American Journal of Applied Mathematics, 8(3), 89-97. https://doi.org/10.11648/j.ajam.20200803.13

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ACS Style

Mohammed Hirpho Tobe; Zerihun Kinfe Birhanu. Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process. Am. J. Appl. Math. 2020, 8(3), 89-97. doi: 10.11648/j.ajam.20200803.13

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AMA Style

Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu. Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process. Am J Appl Math. 2020;8(3):89-97. doi: 10.11648/j.ajam.20200803.13

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@article{10.11648/j.ajam.20200803.13,
  author = {Mohammed Hirpho Tobe and Zerihun Kinfe Birhanu},
  title = {Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process},
  journal = {American Journal of Applied Mathematics},
  volume = {8},
  number = {3},
  pages = {89-97},
  doi = {10.11648/j.ajam.20200803.13},
  url = {https://doi.org/10.11648/j.ajam.20200803.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200803.13},
  abstract = {Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.},
 year = {2020}
}

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TY  - JOUR
T1  - Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process
AU  - Mohammed Hirpho Tobe
AU  - Zerihun Kinfe Birhanu
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200803.13
DO  - 10.11648/j.ajam.20200803.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 89
EP  - 97
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200803.13
AB  - Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.
VL  - 8
IS  - 3
ER  -

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Author Information

Mohammed Hirpho Tobe

Department of Mathematics, Ambo University, Ambo, Ethiopia
Zerihun Kinfe Birhanu

Department of Mathematics, Hawassa University, Hawassa, Ethiopia

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APA Style

Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu. (2020). Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process. American Journal of Applied Mathematics, 8(3), 89-97. https://doi.org/10.11648/j.ajam.20200803.13

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ACS Style

Mohammed Hirpho Tobe; Zerihun Kinfe Birhanu. Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process. Am. J. Appl. Math. 2020, 8(3), 89-97. doi: 10.11648/j.ajam.20200803.13

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AMA Style

Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu. Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process. Am J Appl Math. 2020;8(3):89-97. doi: 10.11648/j.ajam.20200803.13

Copy | Download

@article{10.11648/j.ajam.20200803.13,
  author = {Mohammed Hirpho Tobe and Zerihun Kinfe Birhanu},
  title = {Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process},
  journal = {American Journal of Applied Mathematics},
  volume = {8},
  number = {3},
  pages = {89-97},
  doi = {10.11648/j.ajam.20200803.13},
  url = {https://doi.org/10.11648/j.ajam.20200803.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200803.13},
  abstract = {Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process
AU  - Mohammed Hirpho Tobe
AU  - Zerihun Kinfe Birhanu
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200803.13
DO  - 10.11648/j.ajam.20200803.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 89
EP  - 97
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200803.13
AB  - Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.
VL  - 8
IS  - 3
ER  -

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