Transport in Porous Media

, Volume 99, Issue 2, pp 391–411 | Cite as

Analysis of Two Ultrafiltration Fouling Models and Estimation of Model Parameters as a Function of Operational Conditions

  • María-José Corbatón-Báguena
  • María-Cinta Vincent-Vela
  • Silvia Álvarez-Blanco
  • Jaime Lora-García


This work analyses the measure of fit of experimental data of permeate flux decline with time for ultrafiltration experiments performed with polyethylene glycol aqueous solutions to two different ultrafiltration models. A feed solution of 5 kg/m\(^{3}\) of polyethylene glycol and a monotubular ceramic membrane of \({\mathrm{ZrO}}_{2}\)\({\mathrm{TiO}}_{2}\) were used in the experiments. The first model considered was developed by Ho and Zydney and it considers two different fouling mechanisms: pore blocking and gel layer formation. The second model was proposed by Yee et al. It is an exponential model that considers three stages: concentration polarization, molecule deposition on the membrane surface and long-term fouling. The results show that both models give very accurate predictions for the severe fouling conditions (high transmembrane pressures and low crossflow velocities). However, both models cannot explain the experimental results obtained for all the experimental conditions tested. An equation for Ho and Zydney’s model parameters as a function of operating conditions was obtained by means of multiple regression analysis.


Fouling dynamics Ultrafiltration Flux decline Multiple regression analysis Model parameters 

List of Symbols



Transport area (\({\mathrm{m}}^{2}\))


Membrane area blocked by a single aggregate (\({\mathrm{m}}^{2}\))


Region of membrane area with open pores (\({\mathrm{m}}^{2}\))


Region of membrane area with partially blocked pores (\({\mathrm{m}}^{2}\))


Membrane area (\({\mathrm{m}}^{2}\))


Constant in complete blocking law (\({\mathrm{s}}^{-1}\))


Rate constant for the decrease in flux decline in each stage of fouling (\({\mathrm{s}}^{-1}\))


Constant in standard blocking law (\({\mathrm{s}}^{-1}\))


Bulk concentration (\({\mathrm{kg}}/{\mathrm{m}}^{3}\))


Gel concentration (\({\mathrm{kg}}/{\mathrm{m}}^{3}\))


Permeate concentration (\({\mathrm{kg}}/{\mathrm{m}}^{3}\))


Particle diffusion coefficient


Fractional amount of the total solute present as aggregate (dimensionless)

\(f^{\prime }\)

Fractional amount of the total solute that contributes to the deposit growth (dimensionless)


Permeate flux (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}}\))


Average permeate flux (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)

\(J_\mathrm{eq }\)

Local equilibrium permeate flux (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)


Permeate flux through the open pores (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)

\(J_\mathrm{blocked }\)

Permeate flux trough the partially blocked pores (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)


Initial permeate flux (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)

\(J_{\infty }\)

Steady-state permeate flux (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)

\(J_\mathrm{w }\)

Deionized water flux (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)


Back-transport coefficient


Exponential factor for each stage of fouling (\({\mathrm{m}}^{3}/{\mathrm{m}}^{2}\,{\mathrm{s}})\)


Membrane length (m)

\(M_\mathrm{agg }\)

Mass of a single aggregate (kg)


Permeability coefficient

\(\Delta P\)

Transmembrane pressure (MPa)


Volumetric permeate flow rate through open pores \(({\mathrm{m}}^{3}/{\mathrm{s}})\)


Volumetric permeate flow rate through partially blocked pores (\({\mathrm{m}}^{3}/{\mathrm{s}})\)


Resistance of the irreversible adsorbed protein deposit (\({\mathrm{m}}^{-1}\))

\(R_\mathrm{m }\)

Resistance of the clean membrane (\({\mathrm{m}}^{-1}\))


Resistance of the solute deposit (\({\mathrm{m}}^{-1}\))


Resistance of a single solute aggregate (\({\mathrm{m}}^{-1}\))

\(R^{\prime }\)

Specific layer resistance (m/kg)


Filtration time (s)


Transition time between fouling stages 1 and 2 (s)


Transition time between fouling stages 2 and 3 (s)


Steady-state time (s)


Total volume collected (\({\mathrm{m}}^{3}\))


Distance from the membrane entrance (m)

Greek letters

\(\alpha \)

Pore blockage parameter (\({\mathrm{m}}^{2}/{\mathrm{kg}}\))

\(\beta \)

Fraction of pores susceptible to be completely blocked (dimensionless)

\(\gamma \)

Shear rate

\(\mu \)

Feed solution viscosity (\({\mathrm{kg}}/ {\mathrm{m}}/{\mathrm{s}})\)

\(\sigma \)


\(\omega \)

Angular velocity (\({\mathrm{rad}}/{\mathrm{s}}\))

\(\Delta \pi \)

Osmotic pressure





Polyethylene glycol


Multiple regression analysis



The authors of this work wish to gratefully acknowledge the financial support of the Universidad Politécnica de Valencia through the Project No. 2010.1009 and the Spanish Ministry of Science and Technology through the project CTM2010-20186.


  1. Alventosa-deLara, E., Barredo-Damas, S., Alcaina-Miranda, M.I., Iborra-Clar, M.I.: Ultrafiltration technology with a ceramic membrane for reactive dye removal: optimization of membrane performance. J. Hazard. Mater. 209–210, 492–500 (2012)CrossRefGoogle Scholar
  2. Baldasso, C., Barros, T.C., Tessaro, I.C.: Concentration and purification of whey proteins by ultrafiltration. Desalination 278, 381–386 (2011)CrossRefGoogle Scholar
  3. Bhattacharjee, C., Datta, S.: Analysis of polarized layer resistance during ultrafiltration of PEG-6000: an approach based on filtration theory. Sep. Purif. Technol. 33, 115–126 (2003)CrossRefGoogle Scholar
  4. Buetehorn, S., Carstensen, F., Wintgens, T., Melin, T., Volmering, D., Vossenkaul, K.: Permeate flux decline in crossflow microfiltration at constant pressure. Desalination 250, 985–990 (2010)CrossRefGoogle Scholar
  5. Chan, R., Chen, V.: Characterization of protein fouling on membranes: opportunities and challenges. J. Membr. Sci. 242, 169–188 (2004)CrossRefGoogle Scholar
  6. Cheryan, M.: Ultrafiltration and Microfiltration Handbook. Technomic Publishing Company, Inc., Lancaster (1998)Google Scholar
  7. de Barros, S.T.D., Andrade, C.M.G., Mendes, E.S., Peres, L.: Study of fouling mechanism in pineapple juice clarification by ultrafiltration. J. Membr. Sci. 215, 213–224 (2003)CrossRefGoogle Scholar
  8. de la Casa, E.J., Guadix, A., Ibáñez, R., Camacho, F., Guadix, E.M.: A combined fouling model to describe the influence of the electrostatic environment on the cross-flow microfiltration of BSA. J. Membr. Sci. 318, 247–254 (2008)CrossRefGoogle Scholar
  9. Espina, V., Jaffrin, M.Y., Ding, L., Cancino, B.: Fractionation of pasteurized skim milk proteins by dynamic filtration. Food Res. Int. 43, 1335–1346 (2010)CrossRefGoogle Scholar
  10. Fernández-Sempere, J., Ruiz-Beviá, F., García-Algado, P., Salcedo-Díaz, R.: Visualization and modeling of the polarization layer and a reversible adsorption process in PEG-10000 dead-end ultrafiltration. J. Membr. Sci. 342, 279–290 (2009)CrossRefGoogle Scholar
  11. Field, R.W., Wu, D., Howell, J.A., Gupta, B.B.: Critical flux concept for microfiltration fouling. J. Membr. Sci. 100, 259–272 (1995)CrossRefGoogle Scholar
  12. Hermia, J.: Constant pressure blocking filtration laws—application to powerlaw non-Newtonian fluids. Trans. IChemE 60, 183–187 (1982)Google Scholar
  13. Ho, C.-C., Zydney, A.L.: A combined pore blockage and cake filtration model for protein fouling during microfiltration. J. Colloid Interface Sci. 232, 389–399 (2000)CrossRefGoogle Scholar
  14. Karasu, K., Yoshikawa, S., Ookawara, S., Ogawa, K., Kentish, S.E., Stevens, G.W.: A combined model for the prediction of the permeation flux during the cross-flow ultrafiltration of a whey suspension. J. Membr. Sci. 361, 71–77 (2010)CrossRefGoogle Scholar
  15. Ko, M.K., Pellegrino, J.J.: Determination of osmotic pressure and fouling resistances and their effects on performance of ultrafiltration membranes. J. Membr. Sci. 74, 141–157 (1992)CrossRefGoogle Scholar
  16. Lin, S.-H., Hung, C.-L., Juang, R.-S.: Applicability of the exponential time dependence of flux decline during dead-end ultrafiltration of binary protein solutions. Chem. Eng. J. 145, 211–217 (2008)CrossRefGoogle Scholar
  17. Mondal, S., De, S.: A fouling model for steady state crossflow membrane filtration considering sequential intermediate pore blocking and cake formation. Sep. Purif. Technol. 75, 222–228 (2010)CrossRefGoogle Scholar
  18. Mondor, M., Girard, B., Moresoli, C.: Modeling flux behaviour for membrane filtration of apple juice. Food Res. Int. 33, 539–548 (2000)CrossRefGoogle Scholar
  19. Muthukumaran, S., Kentish, S.E., Ashokkumar, M., Stevens, G.W.: Mechanisms for the ultrasonic enhancement of dairy whey ultrafiltration. J. Membr. Sci. 258, 106–114 (2005)CrossRefGoogle Scholar
  20. Peng, H., Tremblay, A.Y.: Membrane regeneration and filtration modeling in treating oily wastewaters. J. Membr. Sci. 324, 59–66 (2008)CrossRefGoogle Scholar
  21. Popović, S., Milanović, S., Iličić, M., Djurić, M., Tekić, M.: Flux recovery of tubular ceramic membranes fouled with whey proteins. Desalination 249, 293–300 (2009)CrossRefGoogle Scholar
  22. Purkait, M.K., DasGupta, S., De, S.: Resistance in series model for micellar enhanced ultrafiltration of eosin dye. J. Colloid Interface Sci. 270, 496–506 (2004)CrossRefGoogle Scholar
  23. Rinaldoni, A.N., Taragaza, C.C., Campderrós, M.E., Pérez, Padilla A.: Assessing performance of skim milk ultrafiltration by using technical parameters. J. Food Eng. 92, 226–232 (2009)CrossRefGoogle Scholar
  24. Santafé-Moros, A., Gozálvez-Zafrilla, J.M.: Nanofiltration study of the interaction between bicarbonate and nitrate ions. Desalination 250, 773–777 (2010)CrossRefGoogle Scholar
  25. Song, L.: Flux decline in crossflow microfiltration and ultrafiltration: mechanisms and modeling of membrane fouling. J. Membr. Sci. 139, 183–200 (1998)CrossRefGoogle Scholar
  26. Vincent Vela, M.C., Álvarez, Blanco S., Lora, García J., Gozálvez Zafrilla, J.M., Bergantiños, Rodríguez E.: Modelling of flux decline in crossflow ultrafiltration of macromolecules: comparison between predicted and experimental results. Desalination 204, 328–334 (2007a)CrossRefGoogle Scholar
  27. Vincent Vela, M.C., Álvarez, Blanco S., Lora, García J., Gozálvez Zafrilla, J.M., Bergantiños, Rodríguez E.: Utilization of a shear induced diffusion model to predict permeate flux in the crossflow ultrafiltration of macromolecules. Desalination 206, 61–68 (2007b)CrossRefGoogle Scholar
  28. Vincent Vela, M.C., Álvarez, Blanco S., Lora, García J., Bergantiños, Rodríguez E.: Analysis of membrane pore blocking models applied to the ultrafiltration of PEG. Sep. Purif. Technol. 62, 489–498 (2008a)CrossRefGoogle Scholar
  29. Vincent Vela, M.C., Álvarez, Blanco S., Lora, García J., Bergantiños, Rodríguez E.: Fouling dynamics modelling in the ultrafiltration of PEGs. Desalination 222, 451–456 (2008b)CrossRefGoogle Scholar
  30. Vincent Vela, M.C., Álvarez, Blanco S., Lora, García J., Bergantiños, Rodríguez E.: Analysis of membrane pore blocking models to crossflow ultrafiltration in the ultrafiltration of PEG. Chem. Eng. J. 149, 232–241 (2009)CrossRefGoogle Scholar
  31. Vincent-Vela, C., Cuartas-Uribe, B., Álvarez-Blanco, S., Lora-García, J., Bergantiños-Rodríguez, E.: Analysis of ultrafiltration processes with dilatant macromolecular solutions by means of dimensionless numbers and hydrodynamic parameters. Sep. Purif. Technol. 75, 332–339 (2010)CrossRefGoogle Scholar
  32. Wang, L., Song, L.: Flux decline in crossflow microfiltration and ultrafiltration: experimental verification of fouling dynamics. J. Membr. Sci. 160, 41–50 (1999)CrossRefGoogle Scholar
  33. Yee, K.W.K., Wiley, D.E., Bao, J.: A unified model of the time dependence of flux decline for the long-term ultrafiltration of whey. J. Membr. Sci. 332, 69–70 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • María-José Corbatón-Báguena
    • 1
  • María-Cinta Vincent-Vela
    • 1
  • Silvia Álvarez-Blanco
    • 1
  • Jaime Lora-García
    • 1
  1. 1.Department of Chemical and Nuclear EngineeringUniversidad Politécnica de ValenciaValenciaSpain

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