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考虑微观孔隙几何的砂岩自发渗吸理论模型

董川龙 滕腾 李志虎 张文涛

董川龙, 滕腾, 李志虎, 张文涛. 考虑微观孔隙几何的砂岩自发渗吸理论模型[J]. 矿业科学学报, 2021, 6(4): 418-428. doi: 10.19606/j.cnki.jmst.2021.04.006
引用本文: 董川龙, 滕腾, 李志虎, 张文涛. 考虑微观孔隙几何的砂岩自发渗吸理论模型[J]. 矿业科学学报, 2021, 6(4): 418-428. doi: 10.19606/j.cnki.jmst.2021.04.006
Dong Chuanlong, Teng Teng, Li Zhihu, Zhang Wentao. Theoretical model of water spontaneous imbibition of sandstone considering microscopic pore geometry[J]. Journal of Mining Science and Technology, 2021, 6(4): 418-428. doi: 10.19606/j.cnki.jmst.2021.04.006
Citation: Dong Chuanlong, Teng Teng, Li Zhihu, Zhang Wentao. Theoretical model of water spontaneous imbibition of sandstone considering microscopic pore geometry[J]. Journal of Mining Science and Technology, 2021, 6(4): 418-428. doi: 10.19606/j.cnki.jmst.2021.04.006

考虑微观孔隙几何的砂岩自发渗吸理论模型

doi: 10.19606/j.cnki.jmst.2021.04.006
基金项目: 

国家自然科学基金重大国际(地区)合作研究项目 51861145403

中央高校基本科研业务费专项资金 2021YQNY06

详细信息
    作者简介:

    董川龙(1987—),男,内蒙古凉城人,博士研究生,主要从事裂隙岩体非饱和渗流等方面的研究工作。Tel:13593052170,E-mail:dtdcl@163.com

    通讯作者:

    滕腾(1989—),男,江苏丰县人,博士,讲师,主要从事煤岩力学特性与计算方法等方面的研究工作。Tel:15210994168,E-mail:T.Teng@cumtb.edu.cn

  • 中图分类号: TD745

Theoretical model of water spontaneous imbibition of sandstone considering microscopic pore geometry

  • 摘要: 为研究砂岩微观孔隙结构几何对其吸水特性的影响机理,应用Hagen-Poiseuille方程、Laplace-Young方程、分形几何理论,考虑孔隙的截面形态、大小分布和通道迂曲3种几何特性,建立了平均几何与分形几何表征的毛细管吸水模型,并对模型的适用性、有效性进行了验证。对比已有模型,分析了各几何参数影响孔隙结构吸水特征的敏感性。研究结果表明:①吸水性特征参量与孔隙几何、迂曲度、孔隙率、最大孔隙尺寸有关,孔隙几何形状越不规整、连通孔隙通道越迂曲、孔隙结构非均质性与各向异性越强,孔隙结构吸水性相对较弱;②平均几何表征的模型中等效平均孔隙直径的物理意义不明确,代入空间平均孔隙尺寸的计算结果大于实测值,而分形几何表征的模型各参数物理意义明确,得到与实测值相近的结果;③对于三维孔隙连通性以及孔吼特征性较弱的孔隙结构,模型适用性较强,相比程序复杂的IFU(Pia)模型、BEA模型,能得到相近甚至更精确的理论预测结果。
  • 图  1  孔隙几何特征影响吸水特性及等效模型

    Df—孔隙尺寸分布分形维数;z—孔隙拓扑结构配位数;τ—孔隙结构迂曲度;b—孔吼单元体孔吼比;δ—孔隙截面不规则形状几何因子;ΦV—孔隙结构体积孔隙率;drep—等效毛管束水力直径。

    Figure  1.  Influence of pore geometry on water absorption characteristics and its equivalent model

    图  2  模型预测值与实验值的对比

    Figure  2.  Comparison between the model predicted and experimental values

    图  3  模型预测值与实验值的对比

    Figure  3.  Comparison between model predicted and experimental values

    图  4  孔隙迂曲因子与形状因子影响吸水性系数规律

    Figure  4.  Diagram of influence law of pore geometry on water absorption characteristics

    图  5  孔隙迂曲因子与分形维数对平均等效孔隙直径影响规律

    Figure  5.  Average equivalent pore diameter vs.heterogeneity and anisotropy for pores

    图  6  孔隙迂曲因子与分形维数对平均等效孔隙直径影响规律

    Figure  6.  Average equivalent pore diameter vs.heterogeneity and anisotropy for pores

    表  1  模型计算参数以及计算所得吸水性系数

    Table  1.   Model calculation parameters and calculated water absorption coefficient

    试样 Sex/(kg·m-2·h-0.5) SB/(kg·m-2·h-0.5) ReB/% Spg/(kg·m-2·h-0.5) Repg /% Spf/(kg·m-2·h-0.5) β Repf /%
    BR-1 3.81 7.79 104.4 3.56 6.5 5.13 0.0001 34.6
    BR-2 6.11 5.14 15.8 2.60 57.4 5.86 0.001 4.0
    BC-1 0.91 1.96 115.3 0.90 0.9 0.92 0.0001 0.6
    BC-2 1.00 1.69 69 1.27 27 0.91 0.01 9.2
    BC-3 0.97 2.97 206.1 1.37 41.2 0.98 0.001 0.5
    BC-4 3.17 2.28 28.0 2.49 21.4 3.40 0.01 7.2
    BC-5 1.12 1.95 69.1 0.99 11.1 0.67 0.01 40.1
    SS-1 1.96 3.48 77.5 1.61 18.0 4.11 0.0001 111.3
    SS-2 2.71 3.14 15.8 1.41 47.9 4.90 0.0001 80.8
    SS-3 1.18 1.57 33.0 0.58 50.8 1.78 0.0001 50.9
    SS-4 0.73 3.62 395.8 1.91 161.6 2.83 0.0001 288.6
    SS-5 2.61 6.43 146.3 2.60 0.3 3.05 0.0001 16.8
    下载: 导出CSV

    表  2  模型计算参数以及计算所得吸水性系数

    Table  2.   Model calculation parameters and calculated water absorption coefficient

    试样 Sex/(mg·cm-2·s-0.5) SIFU/(mg·cm-2·s-0.5) ReIFU/% Spg/(mg·cm-2·s-0.5) Repg /% Spf/(mg·cm-2·s-0.5) β Repf /%
    S1 14.70 12.50 14.9 18.28 24.3 11.45 0.01 22.1
    S2 1.30 1.32 0.1 7.14 449.2 3.57 0.0001 170.4
    S3 2.55 3.14 23.1 9.78 283.5 5.00 0.0001 96.0
    S4 1.92 1.90 1.0 4.37 127.6 2.24 0.0001 16.6
    S5 1.59 1.77 11.3 7.47 369.8 1.73 0.0001 8.8
    S6 0.98 1.06 8.1 0.96 2.0 1.36 0.0001 38.7
    S7 0.73 0.46 36.9 1.43 95.8 0.81 0.0001 10.9
    S8 0.53 0.35 33.9 0.34 35.8 0.25 0.01 52.8
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-08-01
  • 修回日期:  2021-01-14
  • 刊出日期:  2021-08-01

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