Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process
American Journal of Applied Mathematics
Volume 8, Issue 3, June 2020, Pages: 89-97
Received: Mar. 26, 2020; Accepted: May 12, 2020; Published: May 27, 2020
Views 217      Downloads 91
Authors
Mohammed Hirpho Tobe, Department of Mathematics, Ambo University, Ambo, Ethiopia
Zerihun Kinfe Birhanu, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
Article Tools
Follow on us
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.
Keywords
Porous Media, Heat Transfer, Fluid Flow, Finite Element Method, Homogeneous Aquifer Thermal Energy Storage System
To cite this article
Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu, Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process, American Journal of Applied Mathematics. Vol. 8, No. 3, 2020, pp. 89-97. doi: 10.11648/j.ajam.20200803.13
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
H. O. Paksoy, Z. Gürbüz, B. Turgut, D. Dikici, H. Evliya, Aquifer thermal storage (ATES) for air-conditioning of a supermarket in Turkey, Renew. Energy. 29 (2004) 1991–1996.
[2]
K. S. Lee, S. J. Jeong, Numerical modelling on the performance of aquifer thermal energy storage system under cyclic flow regime, Int. J. Green Energy. 5 (2008) 1–14.
[3]
O. Andersson, Aquifer thermal energy storage (ATES), in Therm. Energy Storage Sustain. Energy Consum., Springer, 2007: pp. 155–176.
[4]
A. Vandenbohede, Solute transport in heterogeneous aquifers parameter identification and its use in groundwater pollution and salt water intrusion problems, (2004).
[5]
T. Probert, G. Hellsröm, J. Glaesson, Thermohydraulic evaluation of two ATES projects in southern Sweden, in: Proc. Int. Symp. Aquifer Therm. Energy Storage, Tuscaloosa, AL, USA, 1994: pp. 73–81.
[6]
H. O. Paksoy, O. Andersson, S. Abaci, H. Evliya, B. Turgut, Heating and cooling of a hospital using solar energy coupled with seasonal thermal energy storage in an aquifer, Renew. Energy. 19 (2000) 117–122.
[7]
D. M. Allen, M. M. Ghomshei, T. L. Sadler-Brown, A. Dakin, D. Holtz, The current status of geothermal exploration and development in Canada, in: Proc. from World Geotherm. Congr., 2000: pp. 55–58.
[8]
S. Dharma, Modeling of aquifer thermal energy storage (ATES) using heat and solute transport in 3D (HST3D), Civ. Eng. Dimens. 11 (2009) 119–126.
[9]
R. T. Rabbimov, G. Y. Umarov, R. A. Zakhidov, Storage of solar energy in a sandy-gravel ground, Appl. Sol. Energy (USSR)(Engl. Transl.);(United States). 7 (1971).
[10]
C. F. Meyer, D. K. Todd, Conserving energy with heat storage wells, Environ. Sci. Technol. 7 (1973) 512–516.
[11]
J. P. Sauty, A. C. Gringarten, A. Menjoz, P. A. Landel, Sensible energy storage in aquifers: 1. A theoretical study, Water Resour. Res. 18 (1982) 245–252.
[12]
C.-S. Chen, D. L. Reddell, Temperature distribution around a well during thermal injection and a graphical technique for evaluating aquifer thermal properties, Water Resour. Res. 19 (1983) 351–363.
[13]
H. D. Voigt, F. Haefner, Heat transfer in aquifers with finite caprock thickness during a thermal injection process, Water Resour. Res. 23 (1987) 2286–2292.
[14]
J. P. Ziagos, D. D. Blackwell, A model for the transient temperature effects of horizontal fluid flow in geothermal systems, J. Volcanol. Geotherm. Res. 27 (1986) 371–397.
[15]
K.-Y. Li, S.-Y. Yang, H.-D. Yeh, An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system, Hydrol. Process. 24 (2010) 3676–3688.
[16]
S.-Y. Yang, H.-D. Yeh, Solution for flow rates across the wellbore in a two-zone confined aquifer, J. Hydraul. Eng. 128 (2002) 175–183.
[17]
G. S. Bödvarsson, C. F. Tsang, Injection and thermal breakthrough in fractured geothermal reservoirs, J. Geophys. Res. Solid Earth. 87 (1982) 1031–1048.
[18]
B. Zerihun, K. Nils-Otto, K. Harald, K. Anne, Analytical and Numerical Solutions of Radially Symmetric Aquifer Thermal Energy Storage Problems, n. d.
[19]
G. Evans, J. Blackledge, P. Yardley, Numerical methods for partial differential equations, Springer Science & Business Media, 2012.
[20]
Z. Li, Z. Qiao, T. Tang, Numerical Solutions of Partial Differential Equations–An Introduction to Finite Difference and Finite Element Methods, Cent. Res. Sci. Comput. Dep. Math. North Carolina. (2011).
[21]
W. Zulehner, Lecture Notes for the Course Numerical Methods for Partial Differential Equations, (2006).
[22]
D. N. Arnold, lecture notes on Numerical Analysis of Partial Differential Equations, (2005).
[23]
Birhanu, Z. K., Kitterød, N.-O., Krogstad, H., Kværnø, A.: Analytical and Numerical Solutions of Radially Symmetric Aquifer Thermal Energy Storage Problems. Hydrol. Earth Syst. Sci. Discuss. 1–19 (2017).
[24]
Ganguly, S., Mohan Kumar, M. S., Date, A., Akbarzadeh, A.: Numerical investigation of temperature distribution and thermal performance while charging-discharging thermal energy in aquifer. Appl. Therm. Eng. 115, 756–773 (2017).
[25]
Gao, L., Zhao, J., An, Q., Wang, J., Liu, X.: A review on system performance studies of aquifer thermal energy storage. Energy Procedia. 142, 3537–3545 (2017).
[26]
Ganguly, S., Kumar, M. S. M.: A numerical model for transient temperature distribution in an Aquifer Thermal Energy Storage system with multiple wells. Lowl. Technol. Int. 17, 179–188 (2015).
[27]
Ganguly, S., Tan, L., Date, A., Kumar, M.: Numerical Investigation of Temperature Distribution in a Confined Heterogeneous Geothermal Reservoir Due to Injection-production. Energy Procedia. 110, 143–148 (2017).
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186