Advances in research on the mechanical responses of hot dry granites under varying cooling conditions in China
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摘要:意义
增强型地热系统(EGS)是目前开发干热岩的关键技术手段，在EGS的建设与运行过程中，储层岩石会遇到高温冷却、循环冷却、遇水冷却等多种冷却条件。因此，研究不同冷却条件下花岗岩(典型干热岩)的力学响应特征意义重大。
进展(1) 总结并分析了不同冷却条件(高温自然冷却、遇水冷却、循环冷却)下我国典型花岗岩在力学响应(单轴抗压强度σc、弹性模量E、抗拉强度σt和泊松比ν)方面的实验数据，指出温度低于200或300 ℃时，高温自然冷却后花岗岩的σc、E和σt略有降低；温度高于200或300 ℃时，σc、E和σt随温度升高近线性减小。(2) 在任意温度下，遇水冷却后花岗岩σc、E和σt随温度的升高近线性减小。循环冷却下，在经历第1次循环后花岗岩σc、E和σt迅速降低，而当循环次数大于5时，σc、E和σt逐渐趋于定值。高温自然冷却下，ν随温度升高而降低，其降幅大于高温遇水冷却条件下的ν。(3) 高温花岗岩在不同冷却条件下力学性能劣化的主因是内部微裂纹的起裂和扩展。统计了不同冷却条件下干热花岗岩力学响应数据并分析其内在机理，对力学参数归一化值与温度的关系进行拟合，并提出了经验公式。
展望提出高温花岗岩岩石力学研究的未来发展趋势，包括干热岩开采与CO2地质封存结合过程中的力学响应、多场−多相−多过程耦合作用下干热岩力学响应、基于干热岩开发过程中的实际条件开展实验研究等，以期为干热岩开发的相关设计、计算和数值模拟提供理论支撑。
Abstract:SignificanceEnhanced geothermal systems (EGSs) serve as a key technique for exploiting hot dry rocks (HDRs) presently. During the construction and operation of EGSs, rocks of the HDR reservoirs will experience various cooling conditions, such as natural cooling, cyclic cooling, and water cooling, rendering it greatly significant to investigate the mechanical response characteristics of granites—typical HDRs—under varying cooling conditions.
AdvancesThis study offers a summary and analysis of experimental data about the mechanical responses, i.e., uniaxial compressive strength (σc), elastic modulus (E), tensile strength (σt), and Poisson's ratio (ν), of typical granites in China under varying cooling conditions including natural, water, and cyclic cooling. The results reveal that after natural cooling, the σc, E, and σt values of the granites decrease slightly at temperatures below 200 ℃ or 300 ℃ but decrease nearly linearly with an increase in temperature at temperatures greater than 200 ℃ or 300 ℃. After water cooling, these values decrease nearly linearly with an increase in the temperature at any temperature. Under cyclic cooling, these values decrease rapidly after cooling for the first time and then gradually tend to remain constant after more than five times of cooling. Under natural cooling, the value of ν decreases with a rise in temperature, with the decreasing amplitude greater than that under water cooling. The deterioration of the mechanical properties of high-temperature granites under varying cooling conditions is primarily due to the generation and propagation of microcracks in them. Based on the statistics and the internal mechanism analysis of the mechanical response data on hot dry granites under varying cooling conditions, this study conducts the fitting of normalized mechanical parameters with temperature and proposes relevant empirical formulas.
ProspectsThis study proposes that future research on the mechanical properties of high-temperature granites will focus on the mechanical responses of HDR during their exploitation combined with CO2 sequestration, the mechanical responses of HDRs under the coupling effects of multiple fields, phases, and processes, and experimental studies based on the actual conditions of HDR exploitation. All these are expected to provide some theoretical support for the design, calculation, and numerical simulation of HDR exploitation.
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图 2 EGS系统、现场照片及干热岩岩心
Fig. 2 Schematic diagram of the EGS system and images of the site and HDR cores of an EGS project
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图 3 高温后花岗岩σc归一化值随温度变化关系
注：图例中的数字对应表1中的序号。
Fig. 3 Normalized σc values of granites after cooling vaying with temperature (numbers in the legend correspond to the S. N. in Table 1
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图 4 花岗岩E归一化值随温度变化关系
注：图例中的数字对应表1中的序号。
Fig. 4 Temperature-varying normalized E value of granites
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图 5 高温循环后花岗岩力学特性归一化值随循环次数变化关系
注：图例中括号内数字对应表1中的序号。
Fig. 5 Normalized values of the mechanical properties of granites varying with the number of cycles of cooling (numbers in the legend correspond to the S. N. in Table 1
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图 6 花岗岩σt归一化值随温度变化关系
注：图例中的数字对应表1中的序号。
Fig. 6 Normalized σt values of granites varying with temperature
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图 7 花岗岩泊松比归一化值随温度变化关系
注：图例中的数字对应表1中的序号。
Fig. 7 Normalized Poisson’s ratio of granites varying with temperature (numbers in the legend correspond to the S. N. in Table 1
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图 8 高温液氮冷却后花岗岩单轴抗压强度和弹性模量归一化值随温度变化关系
注：图例中的数字对应表1中的序号。
Fig. 8 Normalized σc and E values of granites after liquid nitrogen cooling varying with temperature
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图 9 不同冷却方式下花岗岩单轴抗压强度和弹性模量归一化值平均值随温度变化关系
Fig. 9 Average normalized σc and E values of granites varying with temperature (t) under varying cooling modes
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图 10 不同循环水冷却条件下花岗岩温度与微裂纹密度(ρf)的关系
Fig. 10 Relationship between temperature (t) and the microcrack density (ρf) of granites under varying numbers of water cooling cycles
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图 11 不同高温条件下花岗岩循环次数与微裂纹密度(ρf)的关系
Fig. 11 Relationship between the number of water cooling cycles and the microcrack density (ρf) of granites under varying high temperature conditions
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表 1 不同冷却条件下高温花岗岩力学参数
Table 1 Mechanical parameters of high-temperature granites under different cooling conditions
序号 试样产地 σc0/MPa E0/GPa σt0/MPa 加热速率/
(℃·min−1)恒温
时长/h试样
个数冷却
方式尺寸/
(mm×mm)试样形状 参考文献 1 河南焦作 162.0 27.7 10/3 3 2 自然 50×100 圆柱 杜守继等[17] 2 河南焦作 152.3 34.7 10/3 3 5 自然 50×100 圆柱 邱一平等[18] 3 山东平邑 130.5 16.7 17.90 4 3 遇水 50×100 &
50×25圆柱 郤保平等[19] 4 浙江宁波 85.5 14.8 10 6 3 自然 40×80 圆柱 陈有亮等[20] 5 陕西秦岭 8.89 10 2 3 自然 50×25 圆柱 支乐鹏等[21] 6 山东潍坊 120.4 14.2 2 1 自然 50×100 圆柱 徐小丽等[22] 7 陕西秦岭 90.4 8.94 10 3 3 自然 50×25 圆柱 Liu Shi等[23] 8 华北燕山 63.7 23.4 2 1 自然 50×100 圆柱 Wang Yu等[24] 9 福建晋江 123.0 29.1 10 4 1 自然 25×50 圆柱 蔡燕燕等[25] 10 陕西秦岭 90.4 39.3 10 2 1 自然 50×100 圆柱 Liu Shi等[26] 11 陕西秦岭 8.96 10 3 3 自然 50×25 圆柱 方新宇等[27] 12 甘肃北山 155.7 39.5 5 4 1 自然 50×100 圆柱 胡少华等[28] 13 北京房山 83.3 26.6 5 4 3 自然 25×50 圆柱 田红等[29] 14 福建泉州 165.2 51.6 5 4 1 自然 30×80×160 立方柱 Huang Yanhua等[30] 15 山东日照 80.1 37.4 5 2 1 自然 50×100 圆柱 Yang Shengqi等[31] 16 湖北大别山 150.0 33.9 5 4 3 遇水 50×100 圆柱 操旺进[32] 17 山东日照 130.1 12.8 7.93 2 2 3 遇水 50×100 &
50×25圆柱 靳佩桦等[33] 18 福建晋江 5.20 5 2 1 自然&遇水 50×25 圆柱 梁铭等[34] 19 未明采样地 196.6 10.59 5 2 4 自然 50×25 圆柱 吴顺川等[35] 20 湖北随州 189.1 21.2 5 2 3 遇水 50×100 圆柱 朱振南等[36] 21 山东日照 125.0 10 1 1 遇水&循环 50×100 圆柱 Ge Zhenlong等[37] 22 福建晋江 168.7 39.8 10 4 3 自然&循环 50×100 圆柱 Rong Guan等[38] 23 山东兖州 120.4 31.3 10 2 1 自然 50×100 圆柱 Xu Xiaoliang等[39] 24 湖北大别山 168.0 11.3 5 1 1 自然 50×100 圆柱 Zhang Fan等[40] 25 北京房山 79.9 16.0 3 2 3 遇水 25×50 圆柱 陈宇等[41] 26 辽宁松辽盆地 164.7 44.6 14.30 30 4 3 自然&遇水 50×100 &
50×25圆柱 崔翰博等[42] 27 北京房山 153.6 33.7 9.89 5 12 3 自然&液氮 25×50 &
50×25圆柱 黄中伟等 [43] 28 山东某地 130.1 12.8 7.93 2 2 3 自然&遇水 50×25 圆柱 Jin Peihua等[44] 29 山东某地 154.2 33.2 9.91 5 10 3 自然&遇水 50×25 圆柱 Wu Xiaoguang等[45] 30 湖北汝城 107.3 30.3 8.78 6 3 自然&遇水 50×25 圆柱 Wu Qiuhong等[46] 31 山东某地 147.8 33.8 5 10 2 液氮 25×50 圆柱 Wu Xiaoguang等[47] 32 未明采样地 14.00 8 2 1 自然&遇水 50×25 圆柱 邓龙传等[48] 33 青海共和 115.2 37.6 5 2 1 自然 25×50 圆柱 卢运虎等[49] 34 青海共和 152.7 8.2 2 2 3 自然 50×100 圆柱 罗生银等[50] 35 甘肃北山 9.59 5 2 1 自然 50×25 圆柱 闵明等[51] 36 青海共和 132.2 14.8 3 3 3 自然 50×100 圆柱 吴阳春等[52] 37 青海共和 173.4 5 3 1 自然&遇水 50×100 圆柱 郤保平等[53] 38 福建漳州 123.1 69.3 4.76 10 2 2 遇水 50×100 &
50×25圆柱 朱栋等[54] 39 山东潍坊 120.7 36.4 2 3 自然 50×100 圆柱 Guo Hongjun等 [55] 40 未指明采样地 144.0 7.2 4 8 4 自然&遇水 50×100 圆柱 Li Chun等 [56] 41 北京房山 84.8 14.0 3 2 1 自然 25×50 圆柱 Qin Yan等[57] 42 湖南汪罗 174.0 23.0 5 4 3 液氮 25×50 圆柱 Shao Zuliang等[58] 43 甘肃北山 158.6 5 2 5 自然 80×80×80 立方体 Tang Zhicheng等[59] 44 山东日照 97.0 22.3 5 2 1 自然 50×100 圆柱 Yang Shengqi等[60] 45 湖南某地 195.0 37.7 9.43 5 2 3 遇水 50×100 圆柱 Yang Fujian等[61] 46 甘肃北山 134.2 34.0 3 2 3 自然&循环 50×100 圆柱 Yu Peiyang等[62] 47 湖北大别山 151.4 33.0 5 3 3 自然&遇水 37×74 圆柱 Zhang Fan等[63] 48 湖北麻城 161.4 40.9 3 4 1 自然 50×100 圆柱 Zhang Zhenyu等[64] 49 湖北随州 118.6 18.4 5 2 3 遇水&循环 50×100 圆柱 Zhu Zhennan等 [65] 50 辽宁锦州 238.9 20.2 2 4 3 遇水 50×100 圆柱 贾蓬等[66] 51 河南泌阳 7.27 5 2 2 自然 50×25 圆柱 杨圣奇等[67] 52 山东汶上 5.86 5 2 2 自然 50×25 圆柱 杨圣奇等[67] 53 广东珠江 116.1 12.1 5 2 3 自然 50×100 圆柱 Ding Qile等 [68] 54 江西铅山 10.59 5 2 3 自然 50×25 圆柱 Guo Pei等[69] 55 山东某地 242.3 42.7 9.31 5 2 1 遇水 50×100 &
50×25圆柱 Kang Fangchao等[70] 56 山东某地 115.4 32.6 9.24 5 2 3 自然&遇水&液氮 50×100 &
50×25圆柱 Kang Fangchao等[71] 57 湖北罗田 148.0 20.8 20 4 2 自然 50×100 圆柱 Ma Tianshou等[72] 58 甘肃北山 115.7 34.4 5 4 2 自然 100×50×30 长方体 Miao Shuting等[73] 59 山东济宁 157.6 16.6 5 2 3 遇水 50×100 圆柱 Ning Pei等[74] 60 湖北麻城 160.4 70.1 5.42 5 4 1 自然&液氮 50×100 &
50×25圆柱 Rong Guan等 [75] 61 湖南某地 185.3 20.4 2 2 1 液氮 50×100 圆柱 Wang Tianzuo等[76] 62 甘肃玉门 114.0 8 4 1 自然 50×100 圆柱 Wu Yun等[77] 63 甘肃北山 151.0 6.20 8 2 1 自然 50×100 &
50×25圆柱 Wu Yun等[78] 64 江苏徐州 101.7 8.1 6.13 5 2 3 自然&遇水 50×100 圆柱 Xiao Pei等[79] 65 湖南船山坪 138.0 25.9 10.20 5 2 3 遇水 50×100 &
50×25圆柱 Zhang Fan等[80] 66 福建南安 163.7 24.0 5 2 3 自然&遇水 50×100 圆柱 Zhu Zhennan等[81] 67 湖北麻城 178.5 68.8 5.42 5 4 1 自然&液氮 50×100 圆柱 Chen Zhiheng等[82] 68 广东东莞 110.1 11.4 1.00 5 2 3 自然 50×100 圆柱 Ding Qile等[83] 69 河南驻马店 180.6 16.7 6.52 2 2 1 自然 50×25 圆柱 Hu Yuefei等[84] 70 湖北某地 178.7 20.1 2 2 1 自然 50×100 圆柱 Zhang Xiaowu等[85] 71 山东临沂 190.8 48.9 10 1 1 自然&遇水 30×80×160 立方体 Zhao Fei等[86] 注：σc0、E0和σt0分别表示岩石初始单轴抗压强度、初始弹性模量和初始抗拉强度。 
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表 2 高温自然和遇水冷却后花岗岩力学参数归一化值与温度的拟合曲线方程
Table 2 Fitted equations of temperature-varying normalized mechanical parameters of granites after natural cooling and water cooling
力学参数 自然冷却 遇水冷却 液氮冷却 单轴抗压强度 ${ {\sigma } }_{ {\mathrm{c} } }/{ {\sigma } }_{ {\mathrm{c} }0}=\left\{\begin{aligned}& 1,\qquad\qquad\qquad\qquad\quad t\leqslant 300 \;{\text{℃} }\\& -0.001\;23t+1.361\;9\quad t > 300 \;{\text{℃} }\text{，}{ {R} }^{2}=0.977\;2\end{aligned}\right.$ ${ {\sigma } }_{{\rm{c}}}/{ {\sigma } }_{{\rm{c}}0}=-0.000\;9t+0.997\;6$
${{R} }^{2}=0.971\;6$${ {\sigma } }_{{\rm{c}}}/{ {\sigma } }_{{\rm{c}}0}=-0.000\;9t+1.074\;3$
${{R} }^{2}=0.931\;8$弹性模量 $E/{E}_{0}=\left\{\begin{aligned}& 1,\qquad\qquad\qquad\qquad\;\; t\leqslant 300 \;{\text{℃} }\\&-0.001\;48t+1.444\quad t > 300 \;{\text{℃} }\text{，}{ {R} }^{2}=0.994\;9\end{aligned}\right.$ $E/{E}_{0}=-0.001t+0.967\;6$
${{R} }^{2}=0.969\;2$$E/{E}_{0}=-0.001\;1t+1.163\;3$
${ {R} }^{2}=0.878\;0$抗拉强度 ${ {\sigma } }_{ {\rm{t} } }/{ {\sigma } }_{ {\rm{t} }0}=\left\{\begin{aligned}& 1,\qquad\qquad\qquad\qquad\;\; t\leqslant 200 \;{\text{℃} }\\& -0.001\;31t+1.262\;7\quad t > 200 \;{\text{℃} }\text{，}{{R} }^{2}=0.975\;9\end{aligned}\right.$ ${ {\sigma } }_{ {\rm{t} } }/{ {\sigma } }_{ {\rm{t} }0}=-0.001\;16t+1.007\;6$
${ {R} }^{2}=0.988\;2$
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