A Comprehensive Brittleness Evaluation Method for Deep Coal Reservoirs Based on Pre- and Post-Peak Energy Characteristics under Confining Pressure Constraints
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摘要: 深部煤岩储层压裂开发中，脆性评价的准确性直接影响压裂效果，但现有方法多针对页岩设计，难以适用于煤岩复杂的原生裂隙和围压敏感特性.通过三轴压缩试验获取煤岩应力‒应变曲线，引入损伤变量量化峰前裂纹演化对能量分配的非线性影响，构建损伤‒能量双参数峰前脆性指标Bpre；结合围压动态约束效应，建立应力降速率‒围压耦合的峰后脆性指数Bpost，并采用调和平均法得到了基于峰前‒峰后能量特征与围压约束的煤岩脆性指数Bcoal.试验结果表明，Bcoal能有效区分不同围压下煤岩的脆性差异，在5~20 MPa围压下评价结果可靠，且相较于传统方法具有更高的敏感性和可靠性.该研究提升了煤岩脆性评价准确性，为煤层气压裂优化提供重要理论支撑.Abstract: The accuracy of brittleness evaluation critically influences the effectiveness of hydraulic fracturing in deep coal reservoirs; however, conventional methods, largely developed for shale, are inadequate for coal rocks owing to their complex cleat systems and pronounced sensitivity to confining pressure. To address this, triaxial compression tests were conducted to obtain the stress-strain curves of coal rocks. A damage variable was introduced to quantify the nonlinear impact of pre-peak crack evolution on energy distribution, formulating a dual-parameter pre-peak brittleness index, Bpre, based on damage and energy. Incorporating the dynamic constraint effect of confining pressure, a post-peak brittleness index, Bpost, was established by coupling the stress drop rate with confining pressure. Subsequently, a comprehensive coal brittleness index, Bcoal, was derived by employing the harmonic mean method, integrating both pre- and post-peak energy characteristics and confining pressure constraints. Experimental results demonstrate that Bcoal effectively differentiates the brittleness of coal rocks across varying confining pressures, demonstrating reliable evaluation within the confining pressure range of 5 to 20 MPa, and exhibiting superior sensitivity and reliability over traditional methods. This study enhances the accuracy of coal brittleness evaluation, thereby providing crucial theoretical support for the optimization of coalbed methane fracturing strategies.
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图 1 同脆性异损伤煤岩应力‒应变对比
Fig. 1. Comparative analysis of stress-strain curves for coal-rock specimens with identical brittleness but varying damage levels
图 3 煤岩微观结构扫描电镜图
a. 放大100倍；b. 放大1 000倍；c. 放大2 000倍；d. 放大10 000倍
Fig. 3. Scanning electron microscope images of coal-rock microstructure
图 4 试验所用标准岩心柱样品
Fig. 4. Representative standard core plug samples utilized in the testing
图 6 不同围压条件下煤岩压缩试验破坏特征
Fig. 6. Failure characteristics of coal-rock under triaxial compression at varying confining pressures
图 7 F-T33-4D岩心在不同围压下的破坏形态
Fig. 7. Failure morphology of core F-T33-4D under varying confining pressures
a. 5 MPa; b. 10 MPa; c. 15 MPa; d.20 MPa
图 8 S-72-9D岩心在不同围压下的破坏形态
Fig. 8. Failure morphology of core S-72-9D under varying confining pressures
a. 5 MPa; b. 10 MPa; c. 15 MPa; d.20 MPa
图 9 岩石应力‒应变曲线及能量转化示意图
Fig. 9. Schematic of rock stress-strain behavior and associated energy conversion
图 10 不同围压下应力应变曲线
Fig. 10. Stress-strain curves under varying confining pressures
a. L-90-3D; b. L-102; c. L-112; d. L-69-1D; e. L-55-7D; f. S-37-1D; g. S-85-6D; h. F-T33-4D; i. S-72-9D
图 11 不同围压下煤岩力学参数
a. 偏应力；b. 弹性模量
Fig. 11. Mechanical parameters of coal and rock under different confining pressures
图 12 不同围压条件下煤岩的脆性指标评价结果
Fig. 12. Evaluation of coal-rock brittleness indices under varying confining pressures
图 13 不同围压下两组煤岩的脆性指数对比
Fig. 13. Comparison of brittleness indices between two coal-rock groups under varying confining pressures
图 14 不同围压下7组煤岩的脆性指数
Fig. 14. Brittleness indices for seven coal-rock groups under varying confining pressures
表 1 已有岩石脆性评价方法
Table 1. Rock brittleness evaluation methodologies
类别 公式 公式来源 公式说明 基于应力‒应变曲线特征 $ {B}_{1}=\frac{({\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}})/{\sigma }_{\mathrm{p}}}{|\left({\epsilon }_{\mathrm{c}\mathrm{r}}-{\epsilon }_{\mathrm{c}\mathrm{p}}\right)/{\epsilon }_{\mathrm{c}\mathrm{p}}|} $ 杨景祥等(2022) $ {\epsilon }_{\mathrm{c}\mathrm{p}} $为侧向峰值应变；$ {\epsilon }_{\mathrm{c}\mathrm{r}} $为侧向残余应变；$ {\sigma }_{p} $为峰值应力；$ {\sigma }_{r} $为残余应力；$ {{k}_{\mathrm{a}\mathrm{c}}}_{\left(AC\right)} $从屈服起始点到残余起始点的连线的斜率；$ {\sigma }_{\mathrm{c}\mathrm{i}} $为起裂应力；$ {\epsilon }_{\mathrm{c}\mathrm{i}} $为起裂应变；$ {\epsilon }_{p} $为峰值应变；$ \mathrm{\Delta }S $为峰后特定区域面积 $ {B}_{2}=\frac{S}{S+{S}_{w}}\cdot {\mathrm{e}}^{\frac{\left|{\epsilon }_{\mathrm{c}\mathrm{r}}-{\epsilon }_{\mathrm{c}\mathrm{p}}\right|}{{\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}}}} $ 宋昊等(2023) $ {B}_{3}=\frac{1}{{\epsilon }_{\mathrm{p}}}\cdot \frac{{\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{c}\mathrm{i}}}{{\epsilon }_{\mathrm{p}}-{\epsilon }_{\mathrm{c}\mathrm{i}}}\cdot {\mathrm{e}}^{\frac{10({\epsilon }_{\mathrm{p}}-{\epsilon }_{\mathrm{r}})}{{\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}}}} $ 匡智浩等(2022) $ {B}_{4}=\frac{{\epsilon }_{\mathrm{p}}({\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{i}})}{{\sigma }_{\mathrm{p}}({\epsilon }_{\mathrm{p}}-{\epsilon }_{\mathrm{i}})}+\frac{{\epsilon }_{\mathrm{p}}({\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}})}{{\sigma }_{\mathrm{p}}({\epsilon }_{\mathrm{r}}-{\epsilon }_{\mathrm{p}})} $ 陈国庆等(2018) $ {B}_{5}=(S\times {\epsilon }_{\mathrm{c}\mathrm{i}})/\left(\mathrm{\Delta }S\times ({\epsilon }_{\mathrm{p}}-{\epsilon }_{\mathrm{c}\mathrm{i}})\right) $ 高美奔等(2022) $ {B}_{6}=\frac{({\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}})}{({\epsilon }_{\mathrm{r}}-{\epsilon }_{\mathrm{p}})}+\frac{({\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}})({\epsilon }_{\mathrm{r}}-{\epsilon }_{\mathrm{p}})}{{\sigma }_{\mathrm{p}}{\epsilon }_{\mathrm{p}}} $ Xia et al. (2017) $ {B}_{7}=({\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{r}})\mathrm{l}\mathrm{g}\frac{\left|{k}_{\mathrm{a}\mathrm{c}\left(AC\right)}\right|}{10} $ Meng(2015) 基于能量演化机制 $ {B}_{8}=\frac{\mathrm{d}{W}_{\mathrm{d}}^{\mathrm{*}}}{\mathrm{d}{W}_{\mathrm{e}\left(B\right)}-\mathrm{d}{W}_{\mathrm{e}\left(A\right)}}\frac{\mathrm{d}{W}_{\mathrm{f}}}{\mathrm{d}{W}_{\mathrm{e}\left(B\right)}-\mathrm{d}{W}_{\mathrm{e}\left(C\right)}} $ 张军等(2017) $ \mathrm{d}{W}_{\mathrm{d}}^{\mathrm{*}} $为塑性屈服阶段的能量增量；$ \mathrm{d}{W}_{\mathrm{e}\left(i\right)} $为岩石内部积累的弹性能增量；$ \mathrm{d}{W}_{\mathrm{d}} $为峰前耗散能；$ \mathrm{d}{W}_{\mathrm{f}} $为破坏所需的断裂能；$ \mathrm{d}{W}_{\mathrm{r}} $为发生宏观断裂的断裂能；$ {W}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{\mathrm{c}\mathrm{e}} $、$ {W}_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}^{\mathrm{r}\mathrm{e}} $为峰前积聚的弹性能密度、岩样内部的残余弹性能；M为峰后模量；E1、E2、t1、t2分别为屈服前累积能量、破坏后残余能量、裂纹损伤及最终破坏时间 $ {B}_{9}=\frac{\mathrm{d}{W}_{\mathrm{r}}}{\mathrm{d}W({\epsilon }_{\mathrm{a}\mathrm{r}}, {\epsilon }_{\mathrm{r}\mathrm{r}})}\times \frac{\mathrm{d}{W}_{\mathrm{r}}}{\mathrm{d}{W}_{\mathrm{e}}({\epsilon }_{\mathrm{a}\mathrm{p}}, {\epsilon }_{\mathrm{r}\mathrm{p}})}+\frac{\mathrm{d}{W}_{\mathrm{d}}}{\mathrm{d}{W}_{\mathrm{e}}({\epsilon }_{\mathrm{a}\mathrm{p}}, {\epsilon }_{\mathrm{r}\mathrm{p}})} $ 刘俊新等(2022) $ {B}_{10}=2/\left(1/\frac{{c}_{\mathrm{b}\mathrm{i}\mathrm{t}}{W}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{\mathrm{c}\mathrm{e}}}{{c}_{\mathrm{b}\mathrm{i}\mathrm{t}}{W}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{\mathrm{c}\mathrm{e}}+{c}_{\mathrm{i}\mathrm{n}\mathrm{b}\mathrm{i}\mathrm{t}}{W}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{\mathrm{o}\mathrm{u}\mathrm{t}}}+1/\frac{{c}_{\mathrm{b}\mathrm{i}\mathrm{t}}\left({W}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{\mathrm{c}\mathrm{e}}-{W}_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}^{\mathrm{r}\mathrm{e}}\right)}{{c}_{\mathrm{b}\mathrm{i}\mathrm{t}}\left({W}_{\mathrm{p}\mathrm{r}\mathrm{e}}^{\mathrm{c}\mathrm{e}}-{W}_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}^{\mathrm{r}\mathrm{e}}\right)+{c}_{\mathrm{i}\mathrm{n}\mathrm{b}\mathrm{i}\mathrm{t}}{W}_{\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{t}}^{\mathrm{i}\mathrm{n}}}\right) $ 任岚等(2023) $ {B}_{11}=(M-E)/M $ Tarasov et al. (2013) $ {B}_{12}=E/M $ Tarasov et al. (2013) $ {B}_{13}=\frac{{E}_{2}-{E}_{1}}{{E}_{2}}\mathrm{l}\mathrm{g}\frac{{E}_{2}-{E}_{1}}{{t}_{2}-{t}_{1}} $ 侯鹏等(2016) $ {B}_{14}=\frac{{W}_{\mathrm{d}2}-{W}_{\mathrm{d}1}+{W}_{\mathrm{e}2}-{W}_{\mathrm{e}1}}{{W}_{\mathrm{e}2}-{W}_{\mathrm{e}1}}\times \frac{{W}_{\mathrm{e}2}-{W}_{\mathrm{e}3}}{{W}_{\mathrm{e}2}-{W}_{\mathrm{e}3}+{W}_{1}-{W}_{2}} $ 温韬等(2021) 基于矿物组分与弹性参数 $ {B}_{15}=\frac{E+\mu }{2} $ Rickman et al. (2008) qz为石英含量；car为碳酸盐矿物含量；fels为长石含量；clay为黏土含量；dol为白云石含量；lm为方解石含量；TOC为总有机碳含量；ω为粒径小于0.6 mm的岩屑颗粒含量 $ {B}_{16}=\frac{qz+car}{qz+fels+car+clay}\times 100 $ Lai et al. (2015) $ {B}_{17}=50\left(\frac{E-{E}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{E}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{E}_{\mathrm{m}\mathrm{i}\mathrm{n}}}+\frac{\mu -{\mu }_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mu }_{\mathrm{m}\mathrm{i}\mathrm{n}}-{\mu }_{\mathrm{m}\mathrm{a}\mathrm{x}}}\right) $ 郭京哲等(2023) 基于强度参数与破坏特征 $ {B}_{18}=({\sigma }_{\mathrm{c}}\cdot {\sigma }_{\mathrm{t}})/2 $ Yarali et al. (2011) σc、σt分别为岩石的单轴抗压强度和抗拉强度；Fmax为在岩石样品上的最大施加力；P为最大力对应的穿透深度；ρ为岩石密度；εf、εb为峰前、后应变；H为硬度；KIC为断裂韧性 $ {B}_{19}={F}_{\mathrm{m}\mathrm{a}\mathrm{x}}/P $ Yagiz (2009) $ {B}_{20}=0.198{\sigma }_{\mathrm{c}}-2.174{\sigma }_{\mathrm{t}}+0.913\rho -3.807 $ Yagiz (2009) $ {B}_{21}=(\alpha \cdot {\sigma }_{\mathrm{c}}\cdot {\epsilon }_{\mathrm{f}})/{\sigma }_{\mathrm{t}}{\epsilon }_{\mathrm{b}} $ 冯涛等(2000) $ {B}_{22}={\sigma }_{\mathrm{c}}/{\sigma }_{\mathrm{t}} $ Hucka et al. (1974) $ {B}_{23}=({\sigma }_{\mathrm{c}}-{\sigma }_{\mathrm{t}})/({\sigma }_{\mathrm{c}}+{\sigma }_{\mathrm{t}}) $ Hucka et al. (1974) $ {B}_{24}=H/{K}_{\mathrm{I}\mathrm{C}} $ Lawn et al. (1979) $ {B}_{25}=(H\cdot E)/{K}_{\mathrm{I}\mathrm{C}}^{2} $ Quinn et al. (1997) 
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表 2 试样的物性参数
Table 2. Physical properties of the tested specimens
编号 围压(MPa) 平均高度(mm) 平均直径(mm) 平均密度(g/cm³) 平均质量(g) 实验组数 1 5 46.80 25.23 1.36 31.03 9 2 10 47.76 25.25 1.35 32.34 9 3 15 46.71 25.26 1.39 32.55 2 4 20 49.46 25.24 1.43 35.30 2
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表 3 三轴压缩试验结果
Table 3. Triaxial compression test results
岩心号 围压
(MPa)偏应力(MPa) 弹性模量(GPa) 泊松比 L-90-3D-2 5 50.15 5.29 0.402 L-90-3D 10 66.15 5.48 0.399 L-102-2 5 43.68 4.66 0.385 L-102 10 58.99 4.85 0.383 L-112-2 5 36.76 3.85 0.419 L-112 10 50.23 4.11 0.426 L-69-1D-2 5 23.92 2.52 0.383 L-69-1D 10 40.20 4.73 0.380 L-55-7D-2 5 33.14 4.02 0.370 L-55-7D 10 52.47 4.83 0.396 S-37-1D-2 5 42.69 5.22 0.402 S-37-1D 10 58.93 5.29 0.390 S-85-6D-2 5 37.82 3.67 0.398 S-85-6D 10 67.79 4.99 0.389 F-T33-4D 5 39.14 4.59 0.385 F-T33-4D-3 10 60.79 5.65 0.372 F-T33-4D-2 15 63.85 5.69 0.383 F-T33-6D 20 72.11 7.16 0.387 S-72-9D-4 5 37.41 4.28 0.377 S-72-9D 10 56.60 5.32 0.386 S-72-9D-2 15 63.57 5.53 0.394 S-72-9D-3 20 76.45 5.72 0.408
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