Fractal theory-based investigation of the optimal interval of minimum pore radius of sandstone

Authors

XU Lulu, College of Construction Engineering, Jilin University, Changchun 130026, China
DONG Shuning, Xi'an Research Institute Co. Ltd., China Coal Technology and Engineering Group Corp., Xi'an 710077, ChinaFollow
DAI Zhenxue, College of Construction Engineering, Jilin University, Changchun 130026, China
XU Bin, Xi'an Research Institute Co. Ltd., China Coal Technology and Engineering Group Corp., Xi'an 710077, China; College of Geoscience and Surveying Engineering, China University of Mining&Technology, Beijing 100083, China
YIN Shangxian, College of Safety Engineering, North China Institute of Science and Technology, Beijing 101601, China
ZHOU Yan, College of Construction Engineering, Jilin University, Changchun 130026, China
CHEN Junjun, College of Construction Engineering, Jilin University, Changchun 130026, China

Abstract

Permeability is a main parameter for evaluation of water conductivity of porous media, and it is a macroscopic feature of micro-pore structure of water-conducting media. To obtain the geometry parameters of microscopic pores, we performed scanning electron microscopy(SEM) on sandstone samples. The image processing techniques were also applied in calculation of different statistical parameters(e.g., fractal dimensions) and geometrical parameters. Then, fractal theory was introduced to investigate the influence of micro pore structure on permeability. At the same time, the minimum pore radius r_min interval acting on the seepage was obtained by the measured permeability values. This interval can be used as the optimal interval of the minimum pore radius r_min when we have a prediction for permeability. The corresponding percentage of pore accumulation interval was also determined. The results show that:the value of minimum pore radius r_min of sandstone has a great influence on permeability. With increase of the value of minimum pore radius, its permeability decreases sharply at first, then tends to be stable gradually, is finally accompanied by an upward trend. In compact sandstone, when theoretical permeability is equivalent to measured one, the minimum pore radius r_min falls within the interval of 15%-25% of the cumulative percentage of pore radius, and the corresponding pore radius interval can be used as the optimal interval of the minimum pore radius r_min when we calculate the theoretical permeability of sandstone. Meanwhile, with the increase of the permeability of sandstone, corresponding to the minimum pore radius, the cumulative percentage of pore radius increases.

Keywords

fractal theory, permeability, micro-pore structure, minimum pore radius rmin, image processing technology

DOI

10.3969/j.issn.1001-1986.2019.05.003

Recommended Citation

XU Lulu, DONG Shuning, DAI Zhenxue, et al. (2019) "Fractal theory-based investigation of the optimal interval of minimum pore radius of sandstone," Coal Geology & Exploration: Vol. 47: Iss. 5, Article 4.
DOI: 10.3969/j.issn.1001-1986.2019.05.003
Available at: https://cge.researchcommons.org/journal/vol47/iss5/4

Reference

[1] ZHANG Maohua,LI Hui. Pore structure and chloride permeability of concrete containing nano-particles for pavement[J]. Construction & Building Materials,2011,25(2):608-616.

[2] 朱华,姬翠翠. 分形理论及其应用[M]. 北京:科学出版社,2011.

[3] SPARROW C. The fractal geometry of nature. by B. Man-delbrot[J]. Journal of the Royal Statistical Society,1984,147(4):616-618.

[4] AVNIR D,FARIN D,PFEIFER P. Chemistry in noninteger dimensions between two and three. II. Fractal surfaces of adsorbents[J]. the Journal of Chemical Physics,1983,79(7):3566-3571.

[5] HANSEN J P,SKJELTORP A T. Fractal pore space and rock permeability implications[J]. Physical Review B Condensed Matter,1988,38(4):2635-2638.

[6] KATZ A J,THOMPSON A H. Fractal sandstone pores:Implications for conductivity and pore formation[J]. Physical Review Letters,1985,54(12):1325-1328.

[7] KROHN C E. Sandstone fractal and euclidean pore volume distributions[J]. Journal of Geophysical Research:Solid Earth,1988,93(B4):3286-3296.

[8] XU Peng,YU Boming. Developing a new form of permeability and Kozeny-Carman constant for homogeneous porous media by means of fractal geometry[J]. Advances in Water Resources,2008,31(1):74-81.

[9] 郑斌,李菊花. 基于Kozeny-Carman方程的渗透率分形模型[J]. 天然气地球科学,2015,26(1):193-198. ZHENG Bin,LI Juhua. A new fractal permeability model for porous media based on Kozeny-Carman equation[J]. Natural Gas Geoscience,2015,26(1):193-198.

[10] 徐艳玲,徐斌,尹尚先. 砂岩渗透性能微观图像分形分析[J]. 工程勘察,2014,42(6):45-49. XU Yanlin,XU Bin,YIN Shangxian. Analysis on the permeability of sandstone with fractal theory[J]. Geotechnical Investigation & Surveying,2014,42(6):45-49.

[11] 蔡建超,胡祥云. 多孔介质分形理论与应用[M]. 北京:科学出版社,2015.

[12] LIU Chun,SHI Bin,ZHOU Jian,et al. Quantification and characterization of microporosity by image processing,geometric measurement and statistical methods:Application on SEM images of clay materials[J]. Applied Clay Science,2011,54(1):97-106.

[13] 尹尚先,张祥维,徐慧,等. "大井法"中渗透系数及含水层厚度的优化[J]. 煤田地质与勘探,2015,43(5):53-56. YIN Shangxian,ZAHNG Xiangwei,XU Hui,et al. Opti-mization of permeability coefficient and aquifer thickness in large-well-method[J]. Coal Geology & Exploration,2015,43(5):53-56.

[14] 杨靖,汪吉林. 砂性土渗流的分形特征研究[J]. 煤田地质与勘探,2010,38(2):42-45. YAN Jing,WANG Jilin. Research on fractal characteristics of permeability of sandy soil[J]. Coal Geology & Exploration,2010,38(2):42-45.

[15] 李保国. 分形理论在土壤科学中的应用及其展望[J]. 土壤学进展,1994,22(1):1-10. LI Baoguo. Application of fractal theory in soil science and its prospects[J]. Progress in Soil Science,1994,22(1):1-10.

[16] 郁伯铭. 多孔介质输运性质的分形分析研究进展[J]. 力学进展,2003,33(3):333-346. YU Boming. Advance of fractal analysis of transport properties for porous media[J]. Advances in Mechanics,2003,33,33(3):333-346.

[17] 陈永平,施明恒. 基于分形理论的多孔介质渗透率的研究[J]. 清华大学学报(自然科学版),2000,40(12):94-97. CHEN Yongping,SHI Mingheng. Study on permeability of porous media based on fractal theory[J]. Journal of Tsinghua University(Science and Technology),2000,40(12):94-97.

[18] CRAWFORD J W,MATSUI N. Heterogeneity of the pore and solid volume of soil:Distinguishing a fractal space from its non-fractal complement[J]. Geoderma,1996,73(3/4):183-195.

[19] LI Jianhua,YU Boming. Tortuosity of flow paths through a Sierpinski carpet[J]. Chinese Physics Letters,2011,28(3):117-119.

[20] FERANIE S,FAUZI U,BIJAKSANA S. 3D fractal dimension and flow properties in the pore structure of geological rocks[J]. Fractals,2011,19(3):291-297.

[21] KHABBAZI A,HINEBAUGH J,BAZYLAK A. Analytical tortuosity-porosity correlations for Sierpinski carpet fractal geometries[J]. Chaos Solitons & Fractals,2015,78:124-133.

[22] LUO Liang,YU Boming,CAI Jianchao,et al. Numerical simulation of tortuosity for fluid flow in two-dimensional pore fractal models of porous media[J]. Fractals,2014,22(4):1-7.