Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(5): 054701    DOI: 10.1088/1674-1056/ab7b53

Numerical study on permeability characteristics of fractal porous media

Yongping Huang(黄永平)1, Feng Yao(姚峰)2, Bo Zhou(周博)2, Chengbin Zhang(张程宾)1
1 Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China;
2 Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, School of Environmental Science and Engineering, Suzhou University of Science and Technology, Suzhou 215009, China
Abstract  The fractal Brownian motion is utilized to describe pore structures in porous media. A numerical model of laminar flow in porous media is developed, and the flow characteristics are comprehensively analyzed and compared with those of homogeneous porous media. Moreover, the roles of the fractal dimension and porosity in permeability are quantitatively described. The results indicate that the pore structures of porous media significantly affect their seepage behaviors. The distributions of pressure and velocity in fractal porous media are both non-uniform; the streamline is no longer straight but tortuous. When Reynolds number Re < 1, the dimensionless permeability is independent of Reynolds number, but its further increase will lead to a smaller permeability. Moreover, due to the higher connectivity and enlarged equivalent aperture of internal channel network, the augment in porosity leads to the permeability enhancement, while it is small and insensitive to porosity variation when ε < 0.6. Fractal dimension also plays a significant role in the permeability of porous media. The increase in fractal dimension leads to the enhancement in pore connectivity and a decrease in channel tortuosity, which reduces the flow resistance and improves the transport capacity of porous media.
Keywords:  seepage      fractal Brownian motion      porous media      fractal dimension  
Received:  19 December 2019      Revised:  19 January 2020      Accepted manuscript online: 
PACS:  47.15.-x (Laminar flows)  
  47.56.+r (Flows through porous media)  
  47.53.+n (Fractals in fluid dynamics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51776037 and 51806147) and Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170082).
Corresponding Authors:  Chengbin Zhang     E-mail:

Cite this article: 

Yongping Huang(黄永平), Feng Yao(姚峰), Bo Zhou(周博), Chengbin Zhang(张程宾) Numerical study on permeability characteristics of fractal porous media 2020 Chin. Phys. B 29 054701

[1] Ding H R, Liu J X, Cui Z W and Kundu T 2017 Chin. Phys. B 26 124301
[2] Xu P, Li C H, Qiu S X and Sasmito A P 2016 Fractals. 24 1650018
[3] Chen Y P, Gao W, Zhang C B and Zhao Y J 2016 Lab Chip 16 1332
[4] Chen Y P, Shen C Q, Lu P F and Huang Y P 2015 Chem. Eng. Process. 87 75
[5] Zou H, Deng S C and Li H B 2019 Chin. Phys. B 28 030202
[6] Hansen A, Sinha S, Bedeaux D, Kjelstrup S, Gjennestad M A and Vassvik M 2018 Transport. Porous. Med. 125 565
[7] Li B, Zhang Z W, He Z B et al 2015 High Power Laser Part. Beams 27 032024 (in Chinese)
[8] Wang T, Zheng K C, Jia Y P, Fu C L, Gong Z J and Wu W F 2017 Chin. Phys. B 26 074701
[9] Chen Y P, Liu X D and Shi M H 2013 Appl. Phys. Lett. 102 051609
[10] Whitaker S 1986 Transport. Porous. Med. 1 3
[11] Bhatti M M, Zeeshan A, Ellahi R and Shit G C 2018 Adv. Powder Technol. 29 1189
[12] Mandelbort B B, Passoja D E and Paullay A J 1984 Nature 308 721
[13] Chen Y P and Deng Z L 2017 J. Fluid Mech. 819 401
[14] Huo Y T, Guo Y Q and Rao Z H 2019 Int. J. Energ. Res. 43 767
[15] Pitchumani R and Yao S C 1991 J. Heat Transfer. 113 788
[16] Miao T J, Chen A M, Xu Y, Cheng S J and Yu B M 2019 Fractals 27 1950121
[17] Shen X W, Cui W Z and Feng Y 2018 Int. J. Heat Mass Transf. 121 1307
[18] Reis F D A A 2019 Adv. Water Res. 134 103428
[19] Yang Y, Feng Y T and Yu Y H 2017 Fractals. 25 1750040
[20] Kikkinides E S and Burganos V N 1999 Phys. Rev. E 59 7185
[21] Türk C, Carbone A and Chiaia B M 2010 Phys. Rev. E 81 026706
[22] Lv C Y and Yu F 2018 Math. Probl. Eng. 2018 8641471
[23] Qin R F, Lin L Z, Kuang C P, Su T C, Mao X M and Zhou Y S 2017 Environ. Model. Softw. 92 252
[24] Kumar M, Kumar S, Das M K, Budhiraja R and Singh S 2018 J. Inf. Secur. Appl. 40 134
[25] Kikkinides E S and Burganous V N 2000 Phys. Rev. Lett. 62 6906
[26] Ma Q and Chen Z Q 2014 Int. J. Heat Mass Transf. 79 925
[27] Rubio M A, Edwards C A, Dougherty A and Gollub J P 1989 Phys. Rev. Lett. 63 1685
[28] Timothy J J and Meschke G 2018 Transport. Porous. Med. 125 413
[29] Mandelbrot B B 1985 Phys. Scripta. 32 257
[30] Xu W, Liang Y J, Chen W and Cushman J H 2019 Int. J. Heat Mass Transf. 139 39
[31] Liu S J, Afacan A and Masliyah J 1994 Chem. Eng. Sci. 49 3565
[32] Schulz R, Ray N, Zech S, Rupp A and Knabner P 2019 Transport. Porous. Med. 130 487
[33] Koponen A, Kataja M and Tomonen J 1997 Phys. Rev. E 56 3319
[1] Dynamic crossover in [VIO2+][Tf2N-]2 ionic liquid
Gan Ren(任淦). Chin. Phys. B, 2021, 30(1): 016105.
[2] Shear-horizontal transverse-electric seismoelectric waves in cylindrical double layer porous media
Wei-Hao Wang(王伟豪), Xiao-Yan Zhu(朱晓焱), Jin-Xia Liu(刘金霞), and Zhi-Wen Cui(崔志文). Chin. Phys. B, 2021, 30(1): 014301.
[3] Frequency-dependent reflection of elastic wave from thin bed in porous media
Hong-Xing Li(李红星), Chun-Hui Tao(陶春辉), Cai Liu(刘财), Guang-Nan Huang(黄光南), Zhen-An Yao(姚振岸). Chin. Phys. B, 2020, 29(6): 064301.
[4] Polaron effects in cylindrical GaAs/AlxGa1-xAs core-shell nanowires
Hui Sun(孙慧), Bing-Can Liu(刘炳灿), Qiang Tian(田强). Chin. Phys. B, 2017, 26(9): 097302.
[5] Molecular dynamics simulation of decomposition and thermal conductivity of methane hydrate in porous media
Ping Guo(郭平), Yi-Kun Pan(潘意坤), Long-Long Li(李龙龙), Bin Tang(唐斌). Chin. Phys. B, 2017, 26(7): 073101.
[6] Experimental study and theoretical analysis of fluid resistance in porous media of glass spheres
Tong Wang(王彤), Kun-Can Zheng(郑坤灿), Yu-Peng Jia(贾宇鹏), Cheng-Lu Fu(付承鹭), Zhi-Jun Gong(龚志军), Wen-Fei Wu(武文斐). Chin. Phys. B, 2017, 26(7): 074701.
[7] Fractal dynamics in the ionization of helium Rydberg atoms
Xiulan Xu(徐秀兰), Yanhui Zhang(张延惠), Xiangji Cai(蔡祥吉), Guopeng Zhao(赵国鹏), Lisha Kang(康丽莎). Chin. Phys. B, 2016, 25(11): 110301.
[8] Biometric feature extraction using local fractal auto-correlation
Chen Xi, Zhang Jia-Shu. Chin. Phys. B, 2014, 23(9): 096401.
[9] A fractal approach to low velocity non-Darcy flow in a low permeability porous medium
Cai Jian-Chao. Chin. Phys. B, 2014, 23(4): 044701.
[10] Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid
Sadegh Khalili, Saeed Dinarvand, Reza Hosseini, Hossein Tamim, Ioan Pop. Chin. Phys. B, 2014, 23(4): 048203.
[11] Cross-diffusive effects on the onset of the double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above
Rajib Basu, G. C. Layek. Chin. Phys. B, 2013, 22(5): 054702.
[12] Tortuosity for streamlines in porous media
Kou Jian-Long,Tang Xue-Ming,Zhang Hai-Yan,Lu Hang-Jun,Wu Feng-Min,Xu You-Sheng,Dong Yong-Sheng. Chin. Phys. B, 2012, 21(4): 044701.
[13] Simulation of the relationship between porosity and tortuosity in porous media with cubic particles
Tang Xiao-Wu, Sun Zu-Feng, Cheng Guan-Chu. Chin. Phys. B, 2012, 21(10): 100201.
[14] Universal critical properties of the Eulerian bond-cubic model
Ding Cheng-Xiang, Yao Gui-Yuan, Li Song, Deng You-Jin, Guo Wen-An. Chin. Phys. B, 2011, 20(7): 070504.
[15] Acousto-electric well logging by eccentric source and extraction of shear wave
Sun Jian-Guo, Wang Ke-Xie, Cui Zhi-Wen, Hu Heng-Shan. Chin. Phys. B, 2007, 16(3): 746-752.
No Suggested Reading articles found!