Calculation of multi-fractal dimension of coal measure sedimentary rock and analysis of influencing factors
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摘要: 为表征煤系沉积岩的孔隙结构与分形特征，选取中侏罗统页岩、泥岩和砂岩3种典型沉积岩进行了X射线衍射(XRD)分析、核磁共振(NMR)实验，运用分形理论讨论了NMR分形维数与矿物组成、物性参数之间的相互关系。结果表明：①基于弛豫时间截止值T2C，可将页岩、泥岩NMR分形维数划分为吸附孔隙分形维数DA(T2≤3 ms)和渗流孔隙分形维数DS(T2>3 ms)。②储层物性方面，NMR分形维数Df与孔隙率、渗透率、储层质量指数呈良好的线性负相关关系，说明NMR分形维数能够作为衡量岩石物性的重要指标。③矿物成分方面，石英、长石含量与分形维数Df呈弱负相关关系，黏土矿物由于受到沉积环境、理化性质和矿物本身含量等多因素作用，对分形维数的影响差异较为显著。Abstract: In order to characterize the pore structure and fractal characteristics of coal-measure sedimentary rocks, three types of typical sedimentary rocks of the Middle Jurassic shale, mudstone and sandstone were selected as the research objects. Through X-ray diffraction(XRD)analysis and nuclear magnetic resonance(NMR)experiment, the correlation between NMR fractal dimension, mineral composition and physical property parameters was discussed by using fractal theory. The results are as follows: ① Based on the relaxation time cut-off value T2C, the NMR fractal dimension of shale and mudstone can be divided into the fractal dimension of adsorption pore DA(T2 ≤3 ms)and the fractal dimension of seepage pore DS (T2 >3 ms). ② In terms of reservoir physical properties, NMR fractal dimension Df has a good linear negative correlation with porosity, permeability, and reservoir quality index, indicating that NMR fractal dimension can be used as an important indicator of rock physical properties. ③ In terms of mineral composition, the content of quartz and feldspar has a weak negative correlation with the fractal dimension Df, and clay minerals have different influences on the fractal dimension due to multiple factors such as sedimentary environment, physical and chemical properties and mineral content.
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图 1 核磁共振与岩样饱和实验设备
Figure 1. Experimental equipment for nuclear magnetic resonance and sample saturation
图 2 岩石样本的T2和Sv的双对数关系
Figure 2. Double logarithmic relationship between T2 and Sv of rock sample
图 3 孔隙率、渗透率、RQI与Df之间的相关性
Figure 3. Correlation between porosity, permeability, RQI and Df
图 4 脆性矿物含量与分形维数相关关系
Figure 4. Correlation between brittle minerals content and fractal dimension
图 5 黏土矿物含量与分形维数相关关系
Figure 5. Correlation between clay minerals content and fractal dimension
表 1 岩石样品的基本物理参数
Table 1. Basic geophysical descriptions of the rock samples
样品编号 岩性 干重/g 岩样描述 SH-1 页岩 92.59 灰色，结构密实，周身光滑，表面有少量微裂纹和纹理 SH-2 页岩 76.72 灰黑相间，表面光滑，纹理层次分明 MS-1 泥岩 84.47 灰绿色，结构密实，表面混有少量白色矿物 MS-2 泥岩 72.61 灰色，结构密实，表面有少量微裂纹 SS-1 砂岩 75.83 灰色，颗粒均匀分布，表面较粗糙 
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表 2 岩石样品的矿物成分及含量
Table 2. Mineralogical compositions of the investigated rock samples
样品编号 全岩矿物成分含量/% 黏土矿物组成/% 黏土矿物 石英 钾长石 斜长石 菱铁矿 高岭石 绿泥石 伊利石 伊/蒙混层 SH-1 34 24 3 6 33 55 23 11 11 SH-2 43 41 4 12 — 49 20 9 22 MS-1 42 39 4 12 3 45 26 10 19 MS-2 44 41 3 12 — 44 25 12 19 SS-1 12 54 11 17 — 89 6 3 2
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表 3 NMR分形维数计算结果
Table 3. NMR fractal dimension calculation result
样品编号 孔隙率φ /% 渗透率K /mD RQI Df Df相关系数 DA(T2 ≤3 ms) DA相关系数 DS(T2 >3 ms) DS相关系数 SH-1 3.20 0.000 57 0.004 2 2.775 0.316 2.031 0.952 2.905 0.821 SH-2 7.15 0.068 60 0.030 9 2.736 0.375 2.016 0.946 2.907 0.861 MS-1 7.33 0.004 54 0.007 8 2.577 0.455 2.020 0.936 2.758 0.746 MS-2 7.64 0.006 85 0.009 4 2.668 0.367 2.032 0.922 2.827 0.696 SS-1 14.25 49.588 22 0.589 9 2.564 0.628 — — — —
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