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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
Article

Abstract

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.

Keywords

Fouling dynamics Ultrafiltration Flux decline Multiple regression analysis Model parameters 

List of Symbols

Variables

\(A\)

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

\(A_\mathrm{agg}\)

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

\(A_\mathrm{open}\)

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

\(A_\mathrm{blocked}\)

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

\(A_\mathrm{m}\)

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

\(B\)

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

\(b_\mathrm{f}\)

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

\(C\)

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

\(C_\mathrm{b}\)

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

\(C_\mathrm{g}\)

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

\(C_\mathrm{p}\)

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

\(D\)

Particle diffusion coefficient

\(f\)

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)

\(J\)

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

\({\overline{J}}\)

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

\(J_\mathrm{eq }\)

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

\(J_\mathrm{open}\)

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

\(J_\mathrm{blocked }\)

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

\(J_{0}\)

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

\(k_\mathrm{b}\)

Back-transport coefficient

\(k_\mathrm{f}\)

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

\(L\)

Membrane length (m)

\(M_\mathrm{agg }\)

Mass of a single aggregate (kg)

\(P_\mathrm{m}\)

Permeability coefficient

\(\Delta P\)

Transmembrane pressure (MPa)

\(Q_\mathrm{open}\)

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

\(Q_\mathrm{blocked}\)

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

\(R_\mathrm{a}\)

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

\(R_\mathrm{m }\)

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

\(R_\mathrm{p}\)

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

\(R_\mathrm{p0}\)

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

\(R^{\prime }\)

Specific layer resistance (m/kg)

\(t\)

Filtration time (s)

\(t_{1}\)

Transition time between fouling stages 1 and 2 (s)

\(t_{2}\)

Transition time between fouling stages 2 and 3 (s)

\(t_\mathrm{ss}\)

Steady-state time (s)

\(V\)

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

\(x\)

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 (\({\mathrm{kg}}/ {\mathrm{m}}/{\mathrm{s}})\)

\(\sigma \)

Rejection

\(\omega \)

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

\(\Delta \pi \)

Osmotic pressure

Abbreviations

UF

Ultrafiltration

PEG

Polyethylene glycol

MRA

Multiple regression analysis

Notes

Acknowledgments

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.

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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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