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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (11): 2244-2253    DOI: 10.3785/j.issn.1008-973X.2023.11.012
环境与土木工程     
花岗岩裂隙中的水-岩换热
刘若涛1(),荣冠1,2,*(),武延迪1,李博文1
1. 武汉大学 水资源与水电工程科学国家重点实验室，湖北 武汉 430072
2. 武汉大学 水工岩石力学教育部重点实验室，湖北 武汉 430072
Water-rock heat exchange in granite fractures
Ruo-tao LIU1(),Guan RONG1,2,*(),Yan-di WU1,Bo-wen LI1
1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2. Key Laboratory of Hydraulic Rock Mechanics, Ministry of Education, Wuhan University, Wuhan 430072, China
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摘要：

为了研究裂隙岩体中的渗流传热问题，研发岩石裂隙水-岩换热试验系统，采用控制变量法对花岗岩裂隙试样开展不同温度、体积流量、水力开度下的对流换热试验. 基于Forchheimer方程分析裂隙渗流流态，计算换热系数，定量研究温度、体积流量、水力开度的影响，并进行各影响因素的敏感性分析. 结果表明，在体积流量和水力开度不变的情况下，随着裂隙试样温度由70 ℃升高到100 ℃，出口水流温度和换热系数均提高；在裂隙试样温度与水力开度不变的情况下，体积流量从10 mL/min 增大到80 mL/min，出口水流温度线性降低，换热系数与体积流量增长关系为幂函数关系，且随着体积流量增大其增长速度减缓；裂隙试样温度与体积流量保持不变，裂隙水力开度增大，换热系数线性减小，裂隙粗糙度增大，换热系数增大. 利用敏感性函数对换热系数进行影响因素的敏感性分析，换热系数受裂隙试样温度的影响最大，其次是裂隙体积流量，影响最小的是水力开度.
关键词： 地热开发;  花岗岩;  裂隙;  换热系数;  渗流传热    
Abstract:

A rock fracture water-rock heat exchange test system was developed to study the seepage heat transfer in fractured rock masses. Convective heat transfer tests were carried out on granite fissure specimens at different temperatures, volume flow rates and hydraulic openings using the controlled variable method. The fracture seepage flow pattern was analyzed based on the Forchheimer equation, and the effects of temperature, volume flow rate, and hydraulic opening were quantitatively studied by heat transfer coefficient calculation. Sensitivity analysis of each influencing factor was conducted. Results showed that, under the condition of constant volume flow rate and hydraulic opening, the outlet flow temperature and heat transfer coefficient increased as the temperature of the fractured sample increased from 70 ℃ to 100 ℃. Under the condition that the temperature and hydraulic opening of the crack sample remained unchanged, when the volume flow rate changed from 10 mL/min to 80 mL/min, the outlet flow temperature decreased linearly, and the heat transfer coefficient had a power function relationship with the volume flow rate, and its growth rate slowed down with the increase of the volume flow rate. When the temperature and volume flow rate of the crack sample remained unchanged, the heat transfer coefficient decreased linearly when the hydraulic opening of the fissure increased. The heat transfer coefficient increased with the fissure roughness increasing. Sensitivity analysis of influencing factors on the heat transfer coefficient was conducted by the sensitivity function, and results show that the heat transfer coefficient is most affected by the temperature of the crack sample, followed by the volume flow rate of the crack, and least affected by the hydraulic opening.
Key words: geothermal development    granite    fissure    heat transfer coefficient    seepage heat transfer
收稿日期: 2022-08-23 出版日期: 2023-12-11
CLC:  TU 458  
基金资助: 国家自然科学基金资助项目( 41772305，51579189)
通讯作者: 荣冠     E-mail: liuruotao@whu.edu.cn;rg_mail@163.com
作者简介: 刘若涛（1999—），男，硕士生，从事裂隙岩石渗流换热研究. orcid.org/0000-0002-4174-1628. E-mail： liuruotao@whu.edu.cn
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引用本文:

刘若涛,荣冠,武延迪,李博文. 花岗岩裂隙中的水-岩换热[J]. 浙江大学学报(工学版), 2023, 57(11): 2244-2253.

Ruo-tao LIU,Guan RONG,Yan-di WU,Bo-wen LI. Water-rock heat exchange in granite fractures. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2244-2253.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.11.012    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I11/2244

图 1  裂隙水-岩换热试验系统实物图
图 2  裂隙水-岩换热试验流程图
图 3  裂隙出口水流温度随体积流量的变化
图 4  裂隙压力梯度随体积流量的变化
qV/
(mL·min?1) 		h/(W·m?2·K?1)
θ0=70 ℃ θ0=80 ℃ θ0=90 ℃ θ0=100 ℃
10 140.90 176.37 213.94 256.79
20 334.97 370.93 455.73 515.61
30 472.10 555.96 633.69 705.97
40 599.58 708.38 702.37 911.37
50 723.75 780.62 875.88 1011.54
60 738.22 852.37 1031.18 1126.29
70 835.52 960.93 1072.72 1284.38
80 918.01 1178.87 1218.06 1313.51
表 1  不同裂隙试样温度下换热系数随体积流量的变化
图 5  不同体积流量下换热系数随裂隙试样温度的变化
图 6  不同裂隙试样温度下换热系数差值随体积流量的变化
图 7  裂隙试样归一化换热系数和归一化流速的关系
图 8  努塞尔数、普朗特数和雷诺数的无量纲分析
图 9  不同体积流量下换热系数随裂隙水力开度的变化
图 10  不同体积流量下换热系数随裂隙粗糙度的变化
图 11  换热系数与体积流量的函数关系
图 12  换热系数与裂隙水力开度的函数关系
θ0/℃ S( $q_V^* $) S( $e_{\rm{h}}^* $)
70 0.489 0.204
80 0.574 0.100
90 0.656 0.064
100 0.686 0.129
表 2  不同裂隙试样温度下换热系数关于体积流量和裂隙水力开度的敏感性因子
岩样编号 S( $q_V^* $) S( $\theta _0^* $)
H1 0.628 0.967
H2 0.686 1.173
H3 0.709 1.190
H4 0.711 1.239
表 3  不同岩样换热系数关于体积流量和裂隙试样温度的敏感性因子
1 BRONICKI L Y. Power stations using locally available energy sources [M]. New York: Springer, 2018.
2 KOLDITZ O Modelling flow and heat transfer in fractured rocks: conceptual model of a 3-D deterministic fracture network[J]. Geothermics, 1995, 24 (3): 451- 470
doi: 10.1016/0375-6505(95)00020-Q
3 ZHOU X P, ZHANG J Z, YANG S Q, et al Compression-induced crack initiation and growth in flawed rocks: a review[J]. Fatigue and Fracture of Engineering Materials and Structures, 2021, 44 (7): 1681- 1707
doi: 10.1111/ffe.13477
4 ZHOU X P, ZHANG J Z, WONG L N Y Experimental study on the growth, coalescence and wrapping behaviors of 3D cross-embedded flaws under uniaxial compression[J]. Rock Mechanics and Rock Engineering, 2018, 51: 1379- 1400
doi: 10.1007/s00603-018-1406-4
5 ZHOU X P, WANG Y T, ZHANG J Z, et al Fracturing behavior study of three-flawed specimens by uniaxial compression and 3D digital image correlation: sensitivity to brittleness[J]. Rock Mechanics and Rock Engineering, 2019, 52: 691- 718
doi: 10.1007/s00603-018-1600-4
6 MA Y, ZHANG Y, HUANG Y, et al Experimental study on flow and heat transfer characteristics of water flowing through a rock fracture induced by hydraulic fracturing for an enhanced geothermal system[J]. Applied Thermal Engineering, 2019, 154: 433- 441
doi: 10.1016/j.applthermaleng.2019.03.114
7 FRANK S, HEINZE T, POLLAK S, et al Transient heat transfer processes in a single rock fracture at high volume flow rates[J]. Geothermics, 2021, 89: 101989
doi: 10.1016/j.geothermics.2020.101989
8 王家华, 郭恒 不同围压下粗糙裂隙渗流规律试验研究[J]. 矿业研究与开发, 2022, 42 (9): 99- 104
WANG Jia-hua, GUO Heng Experimental study on seepage law of rough fractures under different confining pressures[J]. Mining Research and Development, 2022, 42 (9): 99- 104
9 赵坚 岩石裂隙中的水流-岩石热传导[J]. 岩石力学与工程学报, 1999, 18 (2): 119- 123
ZHAO Jian Experimental study of flow-rock heat transfer in rock fractures[J]. Chinese Journal of Rock Mechanics and Engineering, 1999, 18 (2): 119- 123
10 BAI B, HE Y Y, LI X C, et al Experimental and analytical study of the overall heat transfer coefficient of water flowing through a single fracture in a granite core[J]. Applied Thermal Engineering, 2017, 116: 79- 90
11 李正伟, 张延军, 张驰, 等 花岗岩单裂隙渗流传热特性试验[J]. 岩土力学, 2018, 39 (9): 3261- 3269
LI Zheng-wei, ZHANG Yan-jun, ZHANG Chi, et al Experiment on convection heat transfer characteristics in a single granite fracture[J]. Rock and Soil Mechanics, 2018, 39 (9): 3261- 3269
12 黄奕斌, 张延军, 于子望, 等 考虑多级流速下的岩石粗糙单裂隙渗流传热特性试验研究[J]. 岩石力学与工程学报, 2019, 38 (Suppl.1): 2654- 2667
HUANG Yi-bin, ZHANG Yan-jun, YU Zi-wang, et al Experimental study of convection heat transfer characteristics in single rough rock fracture considering multi-level flow rates[J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38 (Suppl.1): 2654- 2667
13 HUANG Y, ZHANG Y, YU Z, et al Experimental investigation of seepage and heat transfer in rough fractures for enhanced geothermal systems[J]. Renewable Energy, 2018, 135: 846- 855
14 MA Y, ZHANG Y, HU Z, et al Numerical investigation of heat transfer performance of water flowing through a reservoir with two intersecting fractures[J]. Renewable Energy, 2020, 153: 93- 107
doi: 10.1016/j.renene.2020.01.141
15 CHAPMAN A J. Heat transfer, 4th edition[M]. London: Macmilan Publishing Company, 1989.
16 BAI B, HE Y Y, HU S B An analytical method for determining the convection heat transfer coefficient between flowing fluid and rock fracture walls[J]. Rock Mechanics and Rock Engineering, 2017, 50 (7): 1787- 1799
doi: 10.1007/s00603-017-1202-6
17 朱家玲, 张国伟, 李君, 等 裂隙通道内流固换热系数解析解及敏感性分析[J]. 太阳能学报, 2016, 37 (8): 2019- 2025
ZHU Jia-lin, ZHANG Guo-wei, LI Jun, et al Analytical solution and sensitivity analysis of fluid-solid heat transfer coefficient in fracture channel[J]. Acta Energiae Solaris Sinica, 2016, 37 (8): 2019- 2025
18 ZHANG G, ZHU J, LI J, et al. The analytical solution of the water-rock heat transfer coefficient and sensitivity analyses of parameters [C]// Proceedings World Geothermal Congress. Melbourne: Thermal Engineering, 2015.
19 JIANG Y, YAO H, CUI Y, et al Evaluative analysis of formulas of heat transfer coefficient of rock fracture[J]. International Journal of Thermophysics, 2020, 41 (8): 104
doi: 10.1007/s10765-020-02679-8
20 ZHAO Z H On the heat transfer coefficient between rock fracture walls and flowing fluid[J]. Computers and Geotechnics, 2014, 59: 105- 111
doi: 10.1016/j.compgeo.2014.03.002
21 姚池, 邵玉龙, 杨建华, 等 非线性渗流对裂隙岩体渗流传热过程的影响[J]. 岩土工程学报, 2020, 42 (6): 1050- 1058
YAO Chi, SHAO Yu-long, YANG Jian-hua, et al Effect of nonlinear seepage on flow and heat transfer process of fractured rocks[J]. Chinese Journal of Geotechnical Engineering, 2020, 42 (6): 1050- 1058
22 TAN J, RONG G, HE R H, et al Numerical investigation of heat transfer effect on flow behavior in a single fracture[J]. Arabian Journal of Geosciences, 2020, 13 (17): 368- 374
23 杜利, 唐果, 詹洪阳, 等 碳酸盐岩酸蚀裂缝渗流-传热特性[J]. 科学技术与工程, 2021, 21 (33): 14333- 14344
DU Li, TANG Guo, ZHAN Hong-yang, et al Seepage and heat transfer characteristics of acid corroded fractures in carbonate rock[J]. Science Technology and Engineering, 2021, 21 (33): 14333- 14344
24 惠峥, 冯子军, 武治盛, 等 多级围压下砂岩单裂隙渗流传热试验研究[J]. 矿业研究与开发, 2020, 40 (9): 105- 110
HUI Zheng, FENG Zi-jun, WU Zhi-sheng, et al Experimental study on seepage and heat transfer of sandstone with single fracture under multi-level confining pressure[J]. Mining Research and Development, 2020, 40 (9): 105- 110
25 ZHOU J Q, CHEN Y, TANG H, et al Disentangling the simultaneous effects of inertial losses and fracture dilation on permeability of pressurized fractured rocks[J]. Geophysical Research Letters, 2019, 46 (15): 8862- 8871
doi: 10.1029/2019GL083355
26 CHEN Y, LIAN H, LIANG W, et al The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses[J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 113: 59- 71
doi: 10.1016/j.ijrmms.2018.11.017
27 刘建, 杨巧艳, 白雪, 等 Forchheimer方程参数量化及达西—非达西转变临界点[J]. 西南交通大学学报, 2020, 55 (1): 218- 224
LIU Jian, YANG Qiao-yan, BAI Xue, et al Parameters quantification of Forchheimer equation and critical point of transition from Darcian to non-Darcian flow[J]. Journal of Southwest Jiaotong University, 2020, 55 (1): 218- 224
28 ZENG Z, GRIGG R A criterion for non-Darcy flow in porous media[J]. Transport in Porous Media, 2006, 63 (1): 57- 69
doi: 10.1007/s11242-005-2720-3
29 CHEN Y, LIANG W, LIAN H, et al Experimental study on the effect of fracture geometric characteristics on the permeability in deformable rough-walled fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 98: 121- 140
doi: 10.1016/j.ijrmms.2017.07.003
30 XIAO W, XIA C, WEI W, et al Combined effect of tortuosity and surface roughness on estimation of volume flow rate through a single rough joint[J]. Journal of Geophysics and Engineering, 2013, 10 (4): 045015
doi: 10.1088/1742-2132/10/4/045015
31 崔溦, 邹旭, 李正, 等 分形岩石裂隙中渗流扩散运动的试验研究[J]. 岩土力学, 2020, 41 (11): 3553- 3562
CUI Wei, ZOU Xu, LI Zheng, et al Experimental study on seepage diffusion movement in fractal rock fractures[J]. Rock and Soil Mechanics, 2020, 41 (11): 3553- 3562
32 LUO S, ZHAO Z, PENG H, et al The role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 87: 29- 38
doi: 10.1016/j.ijrmms.2016.05.006
33 TSO C P, ZHAO J A study in forced convection of water in a single uneven planar rock fracture for geothermal application[J]. Renewable Energy, 1994, 4 (4): 371- 375
doi: 10.1016/0960-1481(94)90043-4
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