Skip to main content
SpringerLink
Log in

The effects of fractality on hydrogen permeability across meso-porous membrane

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

A fractal theory employing a box-counting method was used to describe hydrogen gas diffusion into membrane pores in the meso-porosity regime. The diffusion of the gas into the membrane pore network confirmed the existence of fractal structure in the system. Two fractal identities to represent irregularity and roughness of pore surface and tortuosity of the membrane were obtained and analyzed. Their influences on hydrogen permeability were also evaluated. The fractal permeability model that reflects different hydrogen diffusion mechanisms was calculated and compared with that of the state of the art Kozeny–Carman equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Abbreviations

Ao :

The unit membrane area, cm2

C:

Kozeny–Carman constant defined by Eq. (29)

De:

Effective diffusivity, cm2 s−1

dE :

Euclid dimension

Df:

Area fractal dimension

dg :

Molecular collision diameter of gas, cm

Dt:

Tortuosity fractal dimension

F:

Gas flow through a single pore, cm3 s−1

К :

Permeability, mol cm cm−2 s−1 Pa−1

kB :

Boltzmann constant, 1.38 × 10−23 J K−1

Kn :

Knudsen number

L:

Length scale, cm

Lo:

Representative length of a straight capillary, cm

ls :

Length of the cell space, cm

M:

Mole molecule weight, g mol−1

N:

Number of pores

n:

Kozeny–Carman constant defined by Eq. (28)

P:

Total pressure, Pa

P:

Partial pressure, Pa

Q:

Total gas flow through a membrane, m3 s−1

R:

Gas constant, 8.314 × 107 g cm2 s−2 mol−1 K−1

T:

Temperature, K

V:

Volume, ml g−1

x:

Pore diameter, cm

f :

Loading factor, mol g−1, defined by Eq. (30)

r or rp :

Membrane pore radius, cm defined by Eq. (30)

rg :

Molecular radius of gas species, cm, defined by Eq. (30)

Δ:

Different

λ:

Mean free path, cm

μ:

Viscosity, Pa s

ρ:

Density, g cm−3

ε:

Porosity

A:

Gas A

K:

Knudsen

m:

Mean

max:

Maximum

min:

Minimum

mn:

Membrane

P:

Poiseulle

p:

Pore

References

  1. Krohn CE, Thompson AH (1986) Fractal sandstone pores: automated measurements using scanning-electron-microscope images. Phys Rev B 33:63

    Article  Google Scholar 

  2. Mandelbrot BB (1982) The fractal geometry of nature. WH Freeman, New York, 23–57, 117–119

  3. Warren TL, Krajcinovic D (1996) Random cantor set models for the elastic–perfectly plastic contact of rough surfaces. Wear 196:1

    Article  Google Scholar 

  4. Borodich FM, Mosolov AB (1992) Fractal roughness in contact problems. J Appl Math 56:681

    MathSciNet  Google Scholar 

  5. Majumdar A, Bhushan B (1990) Role of mechanical properties and surface texture in the real area of contact of magnetic rigid disks. J Tribol 112:205

    Article  Google Scholar 

  6. Pitchumani R, Ramakrishnan B (1999) A fractal geometry model for evaluating permeabilities of porous preforms used in liquid composite molding. Int J Heat Mass Transf 42:2219

    Article  MATH  Google Scholar 

  7. Yu BM (2001) Comments on a fractal geometry model for evaluating permeabilities of porous preforms used in liquid composite molding. Int J Heat Mass Transf 44:2787

    Article  MATH  Google Scholar 

  8. Yu B, Li J (2001) Some fractal characters of porous media. Fractals 9:365

    Article  Google Scholar 

  9. Yu B, Cheng P (2002) A fractal permeability model for bi-dispersed porous media. Int J Heat Mass Transf 45:2983–2993

    Article  MATH  Google Scholar 

  10. Yu BM, Lee LJ (2002) A fractal in-plane perme- ability model for fabrics. Polym Compos 23:201

    Article  Google Scholar 

  11. Yu BM, Li JH, Zhang DM (2003) A fractal trans-plane permeability model for textile fabrics. Int Commun Heat Mass Transf 30:127

    Article  Google Scholar 

  12. Yu BM, Lee LJ (2000) A simplified in-plane permeability model for textile fabrics. Polym Compos 21:660

    Article  Google Scholar 

  13. Yu BY, Liu W (2004) Fractal analysis of permeabilities for porous media. AIChE J 50:46

    Article  Google Scholar 

  14. Yu BM, Zou MQ, Feng YJ (2005) Permeability of fractal porous media by monte carlo simulations. Int J Heat Mass Transf 48:2787

    Article  MATH  Google Scholar 

  15. Meng FG, Zhang HM, Li YS, Zhang XW, Yang FL (2005) Application of fractal permeation model to investigate membrane fouling in membrane bioreactor. J Membr Sci 262:107

    Article  Google Scholar 

  16. He GL, Zhao ZC, Ming PW, Abuliti A, Yin CY (2007) A fractal model for predicting permeability and liquid water relative permeability in the gas diffusion layer (GDL) of PEMFCs. J Power Sources 163:846

    Article  Google Scholar 

  17. Zhang LZ (2008) A fractal model for gas permeation through porous membranes. Int J Heat Mass Transf 51:5288

    Article  MATH  Google Scholar 

  18. Wiheeb AD et al (2013) Pore morphological identification of hydrotalcite from nitrogen adsorption. Chaos Soliton Fract 49:7

    Article  MathSciNet  Google Scholar 

  19. Cussler EL (2000) Diffusion-mass transfer in fluid systems. Cambridge University Press, Cambridge

    Google Scholar 

  20. Baker RW (2000) Membrane technology and applications. McGraw-Hill, New York

    Google Scholar 

  21. Ahmad AL, Othman MR, Mukhtar H (2004) H2 separation from binary gas mixture using coated alumina-titania membrane by sol-gel technique at high temperature region. Int J Hydrogen Energy 29:817

    Article  Google Scholar 

  22. Acosta JL, Comacho AF (2009) Heat and mass transfer, transport and mechanics. Nova Science Publishers, New York

  23. Othman MR, Kim J (2008) Permeation characteristics of H2, N2 and CO2 in a binary mixture across meso-porous Al2O3 and Pd-Al2O3 asymmetric composites. Micro Meso Mater 112:403

    Article  Google Scholar 

  24. Othman MR, Mukhtar H, Ahmad AL (2001) Permeabilities of gases in porous inorganic membrane. Int Conf Adv Strategic Technol Proc 1:475

    Google Scholar 

  25. Wiheeb AD, Ahmad MA, Murat MN, Kim J, Othman MR (2014) Identification of Molecular Transport Mechanisms in Micro-Porous Hydrotalcite–Silica Membrane Transp Porous Med.104:133

  26. Wiheeb AD, Ahmad MA, Murat MN, Kim J, Othman MR (2014) Predominant Gas transport in microporous hydrotalcite–silica membrane. Transp Porous Med 102:59

    Article  MathSciNet  Google Scholar 

  27. Wiheeb AD, Ahmad MA, Murat MN, Kim J, Othman MR (2014) The effect of hydrotalcite content in microporous composite membrane on gas permeability and selectivity. Sep Sci Technol 49:1309

    Article  Google Scholar 

  28. Wiheeb AD, Ahmad MA, Murat MN, Kim J, Othman MR (2014) The declining affinity of microporous hydrotalcite-silica membrane for carbon dioxide. J Porous Med 17:159

    Article  Google Scholar 

  29. Shi Y, Shiao J, Pan M, Yuan R (2006) A fractal permeability model for the gas diffusion layer of PEM fuel cells. J Power Sources 160:277

    Article  Google Scholar 

  30. Othman MR, Helwani Z, Martunus (2010) Simulated fractal permeability for porous membranes. Appl Math Model 34:2452

    Article  MATH  Google Scholar 

  31. Othman MR, Martunus, Fernando WJN, Kim J (2010) Fractal rate of adsorption and surface diffusivity of carbon dioxide across mesoporous adsorbents. Adsorpt Sci Technol 27:893

  32. Othman MR, Martunus, Fernando WJN, Kim J (2010) Thermodynamic functions of temperature/pressure induced sorption across micro-porous membranes: Case study of methane and carbon dioxide. Adsorpt Sci Technol 28:179

  33. Othman MR, Tan SC, Bhatia S, Fernando WJN (2011) Separability of hydrogen from hydrogen-carbon dioxide mixture across silica-silicalite-1 film. Fuel Proc Technol 92:428

    Article  Google Scholar 

  34. Martunus, Helwani Z, Wiheeb AD, Kim J, Othman MR (2012) A flow through behavior of gas across meso-porous membranes. Micro Meso Mater 163:115

Download references

Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A2A2A01014540).

Author information

Authors and Affiliations

  1. School of Chemical Engineering, Universiti Sains Malaysia, 14300, Nibong Tebal, Penang, Malaysia

    Z. Helwani, A. D. Wiheeb, I. K. Shamsudin & M. R. Othman

  2. Department of Chemical Engineering, Riau University, Pekanbaru, 28293, Indonesia

    Z. Helwani

  3. Department of Chemical Engineering, College of Engineering, University of Tikrit, Salah ad Din, Iraq

    A. D. Wiheeb

  4. Department of Chemical Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701, Republic of Korea

    J. Kim & M. R. Othman

Authors
  1. Z. Helwani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Wiheeb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. K. Shamsudin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. R. Othman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to J. Kim or M. R. Othman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Helwani, Z., Wiheeb, A.D., Shamsudin, I.K. et al. The effects of fractality on hydrogen permeability across meso-porous membrane. Heat Mass Transfer 51, 751–758 (2015). https://doi.org/10.1007/s00231-014-1445-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-014-1445-7

Keywords

Search

Navigation