Analytical solution of formation temperature distribution under dynamic heat load of borehole heat exchangers

LI Jiashu; DAI Chuanshan; LEI Haiyan; MA Fei

doi:10.16030/j.cnki.issn.1000-3665.202205040

Volume 50 Issue 2

Mar. 2023

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LI Jiashu, DAI Chuanshan, LEI Haiyan, et al. Analytical solution of formation temperature distribution under dynamic heat load of borehole heat exchangers[J]. Hydrogeology & Engineering Geology, 2023, 50(2): 198-206 doi: 10.16030/j.cnki.issn.1000-3665.202205040

Citation:

LI Jiashu, DAI Chuanshan, LEI Haiyan, et al. Analytical solution of formation temperature distribution under dynamic heat load of borehole heat exchangers[J]. Hydrogeology & Engineering Geology, 2023, 50(2): 198-206 doi: 10.16030/j.cnki.issn.1000-3665.202205040

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Analytical solution of formation temperature distribution under dynamic heat load of borehole heat exchangers

doi: 10.16030/j.cnki.issn.1000-3665.202205040

LI Jiashu^1
,,
DAI Chuanshan^{1, 2},
LEI Haiyan^{1, 2
,
,},
MA Fei^{1, 2}

1.
School of Mechanical Engineering, Tianjin University, Tianjin　300350, China
2.
Key Laboratory of Efficient Utilization of Low and Medium Grade Energy , Ministry of Education （Tianjin University）, Tianjin　300350, China

Received Date: 2022-05-16
Rev Recd Date: 2022-09-22

Available Online: 2023-02-27

Publish Date: 2023-03-15

Abstract

Abstract

The borehole heat exchanger (BHE) is a key component using shallow geothermal energy in ground source heat pump systems (GSHPS), and reasonable pipe spacing design has a great impact on the heat transfer performance and economy of the GSHPs. In most of real applications, the thermal disturbance radius of the maximum heat load per unit length (that is, the most unfavorable case) is often used as the design basis, and this makes it difficult to achieve the technical and economic optimization of the ground source heat pump system. This paper proposes a simple but more practical mathematical method to obtain the thermal disturbance radius of the borehole heat exchanger. The method first derives an analytical solution of the formation temperature distribution around the borehole under the boundary condition of periodic heat flow. On this basis, the actual dynamic building heating and cooling load is approximately expanded into a finite of sine and cosine periodic functions with the Fourier series. By superimposing the analytical solution corresponding to each periodic function obtained by Fourier series expansion of the original dynamic load, the variation of formation temperature distribution under the actual dynamic heating and cooling load conditions can be obtained.
- ground source heat pump system,
- borehole heat exchanger,
- analytical model,
- periodic dynamic heat loads,
- Fourier series expansion

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References(25)

References

[1]	LUND J W,TOTH A N. Direct utilization of geothermal energy 2020 worldwide review[J]. Geothermics,2021,90:101915. doi: 10.1016/j.geothermics.2020.101915
[2]	GAO Qing,LI Ming,YU Ming. Experiment and simulation of temperature characteristics of intermittently-controlled ground heat exchanges[J]. Renewable Energy,2010,35(6):1169 − 1174. doi: 10.1016/j.renene.2009.10.039
[3]	NIU Fuxin, NI Long, YAO Yang, et al. Thermal accumulation effect of ground-coupled heat pump system[C]//2011 International Conference on Electric Technology and Civil Engineering （ICETCE）. IEEE, 2011: 1805-1807.
[4]	CAO Xiaoling,YUAN Yanping,SUN Liangliang,et al. Restoration performance of vertical ground heat exchanger with various intermittent ratios[J]. Geothermics,2015,54:115 − 121. doi: 10.1016/j.geothermics.2014.12.005
[5]	BIGLARIAN H,ABBASPOUR M,SAIDI M H. Evaluation of a transient borehole heat exchanger model in dynamic simulation of a ground source heat pump system[J]. Energy,2018,147:81 − 93. doi: 10.1016/j.energy.2018.01.031
[6]	BAEK S H,YEO M S,KIM K W. Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger[J]. Energy and Buildings,2017,136:63 − 72. doi: 10.1016/j.enbuild.2016.11.056
[7]	官燕玲,江超,黄雪婷,等. 地源热泵竖直地埋管动态负荷下换热特性解析分析方法[J]. 暖通空调,2013,43(11):87 − 91. [GUAN Yanling,JIANG Chao,HUANG Xueting,et al. Analytical method for heat transfer characteristics of vertical ground heat exchangers in ground-source heat pump under dynamic load[J]. Heating Ventilating & Air Conditioning,2013,43(11):87 − 91. (in Chinese with English abstract)
[8]	柳晓雷,王德林,方肇洪. 垂直埋管地源热泵的圆柱面传热模型及简化计算[J]. 山东建筑工程学院学报,2001,16(1):47 − 51. [LIU Xiaolei,WANG Delin,FANG Zhaohong. Modeling of heat transfer of a vertical bore in ground-source heat pumps[J]. Journal of Shandong Institute of Architecture and Engineering,2001,16(1):47 − 51. (in Chinese with English abstract)
[9]	CARSLAW H S, JAEGER J C. Conduction of Heat in Solids[M]. 2nd ed. London: Oxford University Press, 1959.
[10]	ZENG H Y,DIAO N R,FANG Z H. A finite line-source model for boreholes in geothermal heat exchangers[J]. Heat Transfer—Asian Research:Co-sponsored by the Society of Chemical Engineers of Japan and the Heat Transfer Division of ASME,2002,31(7):558 − 567.
[11]	MAN Yi,YANG Hongxing,DIAO Nairen,et al. A new model and analytical solutions for borehole and pile ground heat exchangers[J]. International Journal of Heat and Mass Transfer,2010,53(13/14):2593 − 2601.
[12]	ESKILSON P. Thermal analysis of heat extraction boreholes[D]. Lund: University of Lund, 1987.
[13]	BERNIER M A. Ground-coupled heat pump system simulation[J]. ASHRAE Transactions,2001,107(1):605 − 616.
[14]	BERNIER M A,PINEL P,LABIB R,et al. A multiple load aggregation algorithm for annual hourly simulations of GCHP systems[J]. HVAC& R Research,2004,10(4):471 − 487.
[15]	MARCOTTE D,PASQUIER P. Fast fluid and ground temperature computation for geothermal ground-loop heat exchanger systems[J]. Geothermics,2008,37(6):651 − 665. doi: 10.1016/j.geothermics.2008.08.003
[16]	MAN Yi,YANG Hongxing,WANG Jinggang,et al. Operation performance investigation of ground-coupled heat-pump system for temperate region[J]. International Journal of Low-Carbon Technologies,2011,6(2):107 − 118. doi: 10.1093/ijlct/ctq047
[17]	ZHANG Linfeng,ZHANG Quan,LI Min,et al. A new analytical model for the underground temperature profile under the intermittent operation for ground-coupled heat pump systems[J]. Energy Procedia,2015,75:840 − 846. doi: 10.1016/j.egypro.2015.07.170
[18]	ZHANG Linlin,ZHAO Lei,YANG Liu,et al. Analyses on soil temperature responses to intermittent heat rejection from BHEs in soils with groundwater advection[J]. Energy and Buildings,2015,107:355 − 365. doi: 10.1016/j.enbuild.2015.08.040
[19]	WANG Enqi,ZHANG Fangfang,ZHANG Yuanyuan,et al. Influence investigation of thermal load imbalance on geothermal heat exchanger[J]. Procedia Engineering,2017,205:3846 − 3851. doi: 10.1016/j.proeng.2017.10.072
[20]	杨露梅,鄂建,朱明君,等. 典型地埋管系统模拟工况地温场特征研究[J]. 水文地质工程地质,2017,44(2):178 − 183. [YANG Lumei,E Jian,ZHU Mingjun,et al. Characteristics of the ground temperature of the typical Ground-Source heat pumps system in Nanjing[J]. Hydrogeology & Engineering Geology,2017,44(2):178 − 183. (in Chinese with English abstract) doi: 10.16030/j.cnki.issn.1000-3665.2017.02.27
[21]	刘爱华,佟红兵,冉伟彦. 北京某垂直地埋管区地温场变化规律研究[J]. 水文地质工程地质,2016,43(4):165 − 170. [LIU Aihua,TONG Hongbing,RAN Weiyan. A study of ground temperature changes in a vertical heat exchanger area of Beijing[J]. Hydrogeology & Engineering Geology,2016,43(4):165 − 170. (in Chinese with English abstract)
[22]	杨卫波,张来军,汪峰. 桩埋管参数对渗流下能量桩热-力耦合特性的影响[J]. 水文地质工程地质,2022,49(5):176 − 185. [YANG Weibo,ZHANG Laijun,WANG Feng. Effects of the pile buried pipe parameters on the thermal-mechanical coupling characteristics of energy pile under the groundwater seepage[J]. Hydrogeology & Engineering Geology,2022,49(5):176 − 185. (in Chinese with English abstract)
[23]	陈宝义,岳韬,曹品鲁,等. 挤密条件下U型地埋管换热器换热效率的理论分析及数值模拟[J]. 吉林大学学报(地球科学版),2016,46(6):1808 − 1814. [CHEN Baoyi,YUE Tao,CAO Pinlu,et al. Theoretical analysis and numerical simulation of heat exchange efficiency of U-tube ground heat exchanger under the condition of soil compaction[J]. Journal of Jilin University (Earth Science Edition),2016,46(6):1808 − 1814. (in Chinese with English abstract)
[24]	张延军, 张通, 殷仁朝, 等. 基于2 m测温法的地热异常区探测及地温预测[J]. 吉林大学学报（地球科学版）, 2017, 47（1）: 189−196 ZHANG Yanjun, ZHANG Tong, YIN Renchao, et al. Geothermal anomaly areas exploration and ground temperature prediction based on 2-meter temperature survey[J]. Journal of Jilin University （Earth Science Edition）, 2017, 47（1）: 189−196. （in Chinese with English abstract）
[25]	赵德印,范宏武,潘黎. 气象参数与建筑冷热负荷相关性分析[J]. 绿色建筑,2019,11(1):47 − 50. [ZHAO Deyin,FAN Hongwu,PAN Li. Relevance between climate parameter and building heating & cooling load[J]. Green Building,2019,11(1):47 − 50. (in Chinese with English abstract) doi: 10.3969/j.issn.1004-1672.2019.01.017