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Fractal Analysis of Shear-thinning Fluid Flow through Porous Media

Year 2017, Volume: 12 Issue: 2, 1 - 21, 01.10.2017

Abstract

The fractal capillary
models for calculating the volumetric flow rates and permeabilities for
Newtonian, power-law, Ellis and Bingham fluids in packed beds are developed by
considering fractal nature of the tortuous capillary. The fractal permeability
models for Newtonian and non-Newtonian fluids are found to be a function of the
tortuosity fractal dimension, the pore-area fractal dimension, sizes of
particles and clusters, the effective porosity and the flow behavior of a
non-Newtonian fluid. The volumetric flow rate of each fluid as a function of
pressure drop are calculated from both the converging-diverging duct approach
and the derived expressions in order to compare two models with one another. In
addition, hydraulic conductivity is also obtained in terms of the fractal scaling
parameters. The volumetric flow rates of shear-thinning fluids, including
power-law and Ellis fluids decrease with increasing the tortuosity fractal
dimension. It is found that the fractal capillary model for the Newtonian and
the Ellis fluids is in good agreement with the converging-diverging duct
approach for the considered values of the tortuosity fractal dimension.

References

  • 1. Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2008). Transport phenomena, Revised 2nd Edition, Wiley, New York.
  • 2. Sabiri, N. and Comiti, J. (1995). Pressure drop in non-Newtonian purely viscous fluid flow through porous media. Chem. Eng. Sci., 50: 1193-1201.
  • 3. Eslami, A. and Taghavi, S.M. (2017). Viscous fingering regimes in elasto-visco-plastic fluids. J. Non-Newt. Fluid Mech., 243: 79–94.
  • 4. Tijani, H.I., Abdullah, N., Yuzir, A. and Ujang, Z. (2015). Rheological and fractal hydrodynamics of aerobic granules. Bioresource Techn., 186: 276–285.
  • 5. Shokri, H., Kayhani, M. H. and Norouzi, M. (2017). Nonlinear simulation and linear stability analysis of viscous fingering instability of viscoelastic liquids. Physics of Fluids, 29: 033101 http://dx.doi.org/10.1063/ 1.4977443
  • 6. Balhoff, M.T. and Thompson, K.E. (2006). A macroscopic model for shear-thinning flow in packed beds based on netweork modeling. Chem. Eng. Sci., 61: 698-719.
  • 7. Chhabra, R.P., Comiti, J. and Machac, I. (2001). Flow of non-Newtonian fluids in fixed and fluidized beds. Chem. Eng. Sci., 56: 1-27.
  • 8. Yu, B. and Liu, W. (2004). Fractal analysis of permeability for porous media. AIChE J., 50: 46-57.
  • 9. Yu, B. and Cheng, P. (2002). A fractal permeability model for bi-dispersed porous media. Int. J. Heat Mass Transfer, 45: 2983-2993.
  • 10. Pearson, J.R.A. and Tardy, P.M.J. (2002). Models for flow of non-Newtonian and complex fluids through porous media. J. Non-Newt. Fluid Mech., 102: 447-473.
  • 11. Bird, R.B., Armstrong, R.C. and Hassager, O. (1987). Dynamics of polymeric liquids, Wiley, New York.
  • 12. Comiti, J. and Renaud, M. (1989). A new model for determining mean structure parameters of fixed beds from pressure drop measurements: Application to beds packed with parallel pipedal particles. Chem. Eng. Sci., 44: 1539-1545.
  • 13. Dharamadhikari, R.V. and Kale, D.D. (1985). Flows of non-Newtonian fluids through porous media, Chem. Eng. Sci., 40: 527-529.
  • 14. Yu, B.M. (2005). Fractal character for tortuous stream tubes in porous media. Chinese Physics Letters, 22:158-160.
Year 2017, Volume: 12 Issue: 2, 1 - 21, 01.10.2017

Abstract

References

  • 1. Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2008). Transport phenomena, Revised 2nd Edition, Wiley, New York.
  • 2. Sabiri, N. and Comiti, J. (1995). Pressure drop in non-Newtonian purely viscous fluid flow through porous media. Chem. Eng. Sci., 50: 1193-1201.
  • 3. Eslami, A. and Taghavi, S.M. (2017). Viscous fingering regimes in elasto-visco-plastic fluids. J. Non-Newt. Fluid Mech., 243: 79–94.
  • 4. Tijani, H.I., Abdullah, N., Yuzir, A. and Ujang, Z. (2015). Rheological and fractal hydrodynamics of aerobic granules. Bioresource Techn., 186: 276–285.
  • 5. Shokri, H., Kayhani, M. H. and Norouzi, M. (2017). Nonlinear simulation and linear stability analysis of viscous fingering instability of viscoelastic liquids. Physics of Fluids, 29: 033101 http://dx.doi.org/10.1063/ 1.4977443
  • 6. Balhoff, M.T. and Thompson, K.E. (2006). A macroscopic model for shear-thinning flow in packed beds based on netweork modeling. Chem. Eng. Sci., 61: 698-719.
  • 7. Chhabra, R.P., Comiti, J. and Machac, I. (2001). Flow of non-Newtonian fluids in fixed and fluidized beds. Chem. Eng. Sci., 56: 1-27.
  • 8. Yu, B. and Liu, W. (2004). Fractal analysis of permeability for porous media. AIChE J., 50: 46-57.
  • 9. Yu, B. and Cheng, P. (2002). A fractal permeability model for bi-dispersed porous media. Int. J. Heat Mass Transfer, 45: 2983-2993.
  • 10. Pearson, J.R.A. and Tardy, P.M.J. (2002). Models for flow of non-Newtonian and complex fluids through porous media. J. Non-Newt. Fluid Mech., 102: 447-473.
  • 11. Bird, R.B., Armstrong, R.C. and Hassager, O. (1987). Dynamics of polymeric liquids, Wiley, New York.
  • 12. Comiti, J. and Renaud, M. (1989). A new model for determining mean structure parameters of fixed beds from pressure drop measurements: Application to beds packed with parallel pipedal particles. Chem. Eng. Sci., 44: 1539-1545.
  • 13. Dharamadhikari, R.V. and Kale, D.D. (1985). Flows of non-Newtonian fluids through porous media, Chem. Eng. Sci., 40: 527-529.
  • 14. Yu, B.M. (2005). Fractal character for tortuous stream tubes in porous media. Chinese Physics Letters, 22:158-160.
There are 14 citations in total.

Details

Subjects Engineering
Journal Section TJST
Authors

Fethi Kamışlı

Publication Date October 1, 2017
Submission Date September 28, 2017
Published in Issue Year 2017 Volume: 12 Issue: 2

Cite

APA Kamışlı, F. (2017). Fractal Analysis of Shear-thinning Fluid Flow through Porous Media. Turkish Journal of Science and Technology, 12(2), 1-21.
AMA Kamışlı F. Fractal Analysis of Shear-thinning Fluid Flow through Porous Media. TJST. October 2017;12(2):1-21.
Chicago Kamışlı, Fethi. “Fractal Analysis of Shear-Thinning Fluid Flow through Porous Media”. Turkish Journal of Science and Technology 12, no. 2 (October 2017): 1-21.
EndNote Kamışlı F (October 1, 2017) Fractal Analysis of Shear-thinning Fluid Flow through Porous Media. Turkish Journal of Science and Technology 12 2 1–21.
IEEE F. Kamışlı, “Fractal Analysis of Shear-thinning Fluid Flow through Porous Media”, TJST, vol. 12, no. 2, pp. 1–21, 2017.
ISNAD Kamışlı, Fethi. “Fractal Analysis of Shear-Thinning Fluid Flow through Porous Media”. Turkish Journal of Science and Technology 12/2 (October 2017), 1-21.
JAMA Kamışlı F. Fractal Analysis of Shear-thinning Fluid Flow through Porous Media. TJST. 2017;12:1–21.
MLA Kamışlı, Fethi. “Fractal Analysis of Shear-Thinning Fluid Flow through Porous Media”. Turkish Journal of Science and Technology, vol. 12, no. 2, 2017, pp. 1-21.
Vancouver Kamışlı F. Fractal Analysis of Shear-thinning Fluid Flow through Porous Media. TJST. 2017;12(2):1-21.