• 论文
主办单位:煤炭科学研究总院有限公司、中国煤炭学会学术期刊工作委员会
基于体积应变的煤体渗透率模型及影响参数分析
  • Title

    Analysis of coal permeability model and influencing parameters based on volume strain

  • 作者

    王伟余金昊方志明李小春李琦陈向军王亮

  • Author

    WANG Wei;YU Jinhao;FANG Zhiming;LI Xiaochun;LI Qi;CHEN Xiangjun;WANG Liang

  • 单位

    河南大学 土木建筑学院中国科学院武汉岩土力学研究所 岩土力学与工程国家重点实验室河南理工大学 河南省瓦斯地质与瓦斯治理重点实验室—省部共建国家重点实验室培育基地煤矿瓦斯与火灾防治教育部重点实验室

  • Organization
    School of Civil Architecture, Henan University
    State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences
    State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University
    Key Laboratory of Gas and Fire Control for Coal Mines (China University of Mining and Technology), Ministry of Education
  • 摘要

    为研究瓦斯压力变化过程中渗透率演化规律,基于煤体代表性单元体(REV)细观尺度参数与体积应变关联特征推导了4种不同形式渗透率模型。利用实验数据对模型进行了可靠性验证,分析了有效应力引起的应变和吸附应变的变化规律,并与经典渗透率模型(P-M模型、S-D模型、CONNELL模型)进行对比验证。讨论了模型参数的敏感性,明确了REV细观尺度参数与裂隙率、渗透率的相关关系,并分析了吸附应变系数影响机理,进而对国内主要矿井渗透率极值压力进行了研究。结果表明:基于REV体积应变与REV裂隙体积应变的4种渗透率模型,其REV体积应变与REV裂隙体积应变线性相关,相关系数为初始裂隙率;体积模量与吸附应变系数分别控制有效应力和吸附应变对渗透率的影响;恒定围压、恒定孔压、恒定差压3种实验条件下,相比经典渗透率模型,4种渗透率模型对实验数据都有较好的匹配效果,但双参数拟合(体积模量与吸附应变系数)相比单参数拟合(吸附应变系数),参数的拟合误差较大,由参数敏感性分析可知,当参数变化时(< 10%)渗透率预测结果相比真实值也有较大偏差;以沁水盆地为例,计算的煤体REV细观尺度参数a0b0范围分别为1.73~46.31 μm和0.06~0.49 μm;恒定围压与恒定差压条件下,吸附应变系数与差压大小、气体类型及初始裂隙率有关;国内主要矿井CO2极值压力在0.94~5.33 MPa,CH4极值压力在1.06~6.94 MPa。

  • Abstract

    To investigate the evolution of coal permeability during the process of gas pressure change, four different forms of permeability models were derived based on the correlation between mesoscale parameters of coal representative elementary volume (REV) and strain-related characteristics. The reliability of the models was verified using experimental data, and the variation law of strain caused by effective stress and adsorption strain was analyzed and compared with classical permeability models (P-M model, S-D model, Connell model). The sensitivity of model parameters was discussed, the relationship between REV mesoscale parameters and fracture porosity and permeability was clarified, and the influence mechanism of adsorption strain coefficient was analyzed. Furthermore, the extreme values of permeability of major coal mines in China were studied. Results show that for the four permeability models derived in this paper, the REV volume strain satisfies a linear relationship with its fracture volume strain, and the correlation coefficient is the initial fracture porosity. The bulk modulus and adsorption strain coefficient control the influence of effective stress and adsorption strain on permeability, respectively. Under three different experimental conditions of constant confining pressure, constant pore pressure, and constant differential pressure, the four permeability models have shown a better matching effect on the experimental data compared with the classical permeability models. However, compared with single-parameter fitting, the parameter error in the double-parameter fitting (bulk modulus and adsorption strain coefficient) is larger. From the sensitivity analysis of parameters, it is observed that when the parameters change within 10%, the predicted permeability deviates significantly from the true value. Therefore, for the double or multiple-parameter fitting of permeability models, the parameter fitting errors could lead to serious distortion of the predicted permeability results. Taking the experimental data of coal samples from the Qinshui Basin as an example, the mesoscopic scale parameters a0 and b0 of REV were calculated to range from 1.73 to 46.31 μm and from 0.06 to 0.49 μm, respectively. Under constant confining pressure and constant differential pressure conditions, the adsorption strain coefficient was related to differential pressure, gas types, and initial fracture porosity. Furthermore, the extreme values of CO2 gas and CH4 gas in major coal mines in China are within the ranges of 0.94−5.33 MPa and 1.06−6.94 MPa, respectively.

  • 关键词

    渗透率表征单元体多实验条件模型参数敏感性吸附应变系数

  • KeyWords

    permeability;REV;multi-experimental condition model;parameter sensitivity;adsorption strain coefficient

  • 基金项目(Foundation)
    内蒙古自治区科技厅中央引导地方科技发展资金资助项目(2022ZY0018);河南省青年基金资助项目(242300420594)
  • DOI
  • 引用格式
    王伟,余金昊,方志明,等. 基于体积应变的煤体渗透率模型及影响参数分析[J]. 煤炭学报,2024,49(6):2741−2756.
  • Citation
    WANG Wei,YU Jinhao,FANG Zhiming,et al. Analysis of coal permeability model and influencing parameters based on volume strain[J]. Journal of China Coal Society,2024,49(6):2741−2756.
  • 相关文章
  • 图表

    Table1

    4组渗透率实验数据的基本情况[38-40]
    实验方法 编号 实验条件 取样地点 测定气体 气体压力变化范围/MPa
    稳态法Expdata1围压3 MPa润红矿CH40.30~1.85
    Expdata2围压6 MPa新田湾矿CH40.10~3.00
    瞬态法Expdata3围压10 MPaMonte Sinni矿CO20.49~7.75
    Expdata4围压10 MPaMonte Sinni矿N21.01~7.36

    Table2

    4组煤样的属性参数
    编号 实验数据来源[38-40] ϕf0/% K/MPa εL/10−2 b/MPa−1 α
    Expdata1 魏建平等 4.25 1.60×104 0.318 1.120 0 0.85
    Expdata2 王刚等 6.82 1.89×103 2.943 1.092 0 1.00
    Expdata3 PINI等 0.42 7.78×102 4.900 0.380 0 1.00
    Expdata4 PINI等 0.42 7.78×102 1.700 0.051 9 1.00

    Table3

    基于REV体积应变的渗透率模型匹配参数
    编号 k模型 kVb模型
    K1/MPa fV1 R2 K2/MPa fV2 R2
    Expdata1 9.66×103 0.83 0.99 1.00×104 0.80 0.99
    Expdata2 4.03×104 0.41 1.00 7.81×104 0.39 1.00
    Expdata3 9.19×102 0.16 0.99 9.23×102 0.16 0.99
    Expdata4 4.11×102 2.67 1.00 4.15×102 2.64 1.00

    Table4

    基于REV裂隙体积应变的渗透率模型匹配参数
    编号 kfϕ模型 kfb模型
    Kf1/MPa fVb1 R2 Kf2/MPa fVb2 R2
    Expdata1 4.11×102 19.43 0.99 4.25×102 18.88 0.99
    Expdata2 2.75×103 5.97 1.00 5.32×103 5.71 1.00
    Expdata3 3.86 39.16 0.99 3.88 38.96 0.99
    Expdata4 1.73 636.05 1.00 1.74 628.20 1.00

    Table5

    拟合与计算的体积模量及其误差
    编号 K1/MPa(k模型) K2/MPa(kVb模型) \(K'_1 \)/MPa(kfϕ模型) \(K'_2 \)/MPa(kfb模型) eK/%
    Expdata1 9.66×103 1.00×104 9.67×103 1.00×104 37.50~39.63
    Expdata2 4.03×104 7.81×104 4.03×104 7.80×104 2 032.28~4 032.28
    Expdata3 9.19×102 9.23×102 9.19×102 9.24×102 18.12~18.77
    Expdata4 4.11×102 4.15×102 4.12×102 4.14×102 46.66~47.17

    Table6

    吸附应变系数拟合值及误差分析
    编号 f'V1(k模型) f'V2(kVb模型) \({f}_{Vb1}' \)(kfϕ模型) \({f}_{Vb2}' \)(kfb模型) ef/%
    Expdata1 0.79 0.77 18.65 18.15 3.90~5.06
    Expdata2 0.47 0.45 6.81 6.57 12.33~13.33
    Expdata3 0.21 0.21 49.42 49.51 20.76~23.81
    Expdata4 0.83 0.84 198.36 200.01 214.08~221.69

    Table7

    CONNELL模型、P-M模型和S-D模型拟合参数
    编号CONNELL指数模型CONNELL立方模型P-M模型S-D模型
    Cf/MPa−1γγCm/MPa−1Cf/MPa−1
    Expdata11.77×10−318.570.771.00×10−163.93×10−3
    Expdata22.12×10−155.840.441.00×10−159.20×10−3
    Expdata31.87×10−127.300.218.64×10−41.00×10−3
    Expdata41.86×10−198.800.848.49×10−48.13×10−3

    Table8

    定孔压条件与定差压条件实验煤样属性参数
    气体类型 α ϕf0 pL/MPa εL
    CO2 0.8 0.03 0.83 0.036 2
    N2 0.8 0.03 2.61 0.005 8
    参数来源 [42] [21] [43] [43]

    Table9

    国内主要矿井渗透率极值
    地区方位 取样地点 气体类型 极值压力/MPa 数据来源[1,45-54]
    华中地区 郑煤白坪矿 CH4 4.95 王登科等
    西南地区 重庆松藻煤矿 CH4 4.95 赵源
    华中地区 焦作中马村煤矿 CH4 2.73 陈月霞
    华中地区 平煤八矿 N2 无极值 赵宇
    西南地区 贵州玉舍煤矿 CH4 1.47 袁梅
    华中地区 安阳红岭煤矿 CH4 6.94 蒋一峰
    华北地区 鄂尔多斯盆地 CO2 0.94~4.87 侯世辉
    华东地区 淮北矿区祁南煤矿 CH4 2.52~2.73 董骏等
    华北地区 山西寺河矿 CH4 4.19 王向浩
    华北地区 山西寺河矿 CO2 5.33 王向浩
    西北地区 陕西永陇煤矿 CH4 4.86 陈明义
    华中地区 平煤十矿 CH4 1.06 李文璞
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