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Modeling equilibrium and kinetics of metal uptake by algal biomass in continuous stirred and packed bed adsorbers

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Abstract

Physical and chemical characterization of algae Gelidium particles shows a gel structure, with two major binding groups, carboxylic and hydroxyl groups, with an affinity constant distribution for protons, well described by a Quasi-Gaussian distribution suggested by Sips. A continuous model, considering a heterogeneous distribution of the carboxylic groups, determined by potentiometric titration experiments, was able to predict equilibrium data at different pH. The metal uptake capacity decreases with the solution pH, suggesting that competition exists between hydrogen ions, present in high concentrations for low pH values, and metal ions. For high ionic strengths, adsorption sites will be surrounded by counter ions and partially lose their charge, which weakens the contribution of the electrostatic binding and decreases the overall adsorption. A small influence of the temperature in the adsorption process was observed. Batch kinetic experiments were also performed, at different pH values, and results were well fitted by a mass transfer model, considering the intraparticle diffusion resistance given by the linear driving force model (LDF). Continuous stirred adsorber (CSTA) and packed bed column configurations were also tested for metal adsorption. The biosorbent regeneration was achieved by contacting it with strong acid (0.1 M HNO3). A mass transfer model was applied with success to describe the biosorption/desorption process in CSTA and packed bed column, considering the equilibrium given by the Langmuir equation/mass action law and film and intraparticle diffusion resistances.

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Abbreviations

a p :

Specific area for thin plates particles

C b :

Metal concentration in the bulk (mg or mmol metal/l fluid)

\(C_{b_{0}}\) :

Initial metal concentration in the bulk (mg or mmol metal/l fluid)

C E :

Feed concentration (mg or mmol metal/l fluid)

C f :

Metal concentration in the film (mg or mmol metal/l fluid)

C final :

Metal concentration in the solution at the end of the saturation or elution process (mg or mmol metal/l fluid)

C CI :

Initial metal concentration in the solution (elution process) (mmol metal/l fluid)

C H :

Equilibrium concentration of proton in the fluid phase (mmol proton/l fluid)

C M :

Equilibrium concentration of metal in the fluid phase (mmol metal/l fluid)

C T :

Total (metal + acid) liquid concentration (mmol/l fluid)

\(C_{T_{0}}\) :

Initial total (metal + acid) liquid concentration (mmol/l fluid)

\(C_{T_{E}}\) :

Total feed (acid) liquid concentration (mmol/l fluid)

D ax :

Axial dispersion coefficient (cm2/s)

D h :

Homogeneous diffusion coefficient (cm2/s)

IS:

Ionic strength (M)

k f :

Film mass transfer coefficient (cm/s)

k p :

Mass transfer coefficient for intraparticle diffusion (cm/s)

K H :

Equilibrium proton constant (l fluid/mmol H)

K M :

Equilibrium metal constant (l fluid/mmol M)

K H ′:

Average value of the affinity constant distribution for the proton (l fluid/mmol H)

K M ′:

Average value of the affinity constant distribution for the metal (l fluid/mmol M)

K L :

Equilibrium constant of Langmuir (l fluid/mg M)

K M H :

Selectivity coefficient between ion M in the particle and ion H in solution

L :

Bed length (cm)

n :

Empirical dimensionless parameter

n M and n H :

Constants that reflect the overall non-ideality of metal and proton

N d :

Number of mass transfer units by intraparticle diffusion

N f :

Number of mass transfer units by film diffusion

p :

Represents the intrinsic heterogeneity of the biosorbent

Pe :

Axial Peclet number based on the bed length

Pe p :

Axial Peclet number based on the particle diameter (spherical) or width (thin plate)

pH SE :

pH of feed solution

〈q〉:

Average metal concentration in the solid phase (mg or mmol metal/g biomass)

q E :

Solid phase concentration in equilibrium with C E (mg or mmol metal/g biomass)

q H :

Equilibrium concentration of proton in the biomass (mmol metal/g biomass)

q L e q LF :

Maximum amount of metal per g of adsorbent (mg/l)

q M :

Equilibrium concentration of metal in the biomass (mg or mmol metal/g biomass)

\(q_{M_{0}}\) :

Metal concentration in the solid phase in equilibrium with \(C_{b_{o}}\) (mg or mmol metal/g biomass)

q * :

Solid phase concentration in equilibrium with C f (mg or mmol metal/g biomass)

q t :

Concentration of ion species in the sorbent at time t (mg metal g biosorbent−1)

Q max  :

Concentration of carboxylic groups or maximum capacity of biomass (mmol/g biomass)

r :

The dimensionless axial coordinate inside the particle

R :

Half of thickness of the thin plate (cm)

Sh :

Sherwood number

t :

Time (s)

t b :

Breakthrough time (s)

t st :

Stoichiometric time (s)

T :

Temperature (°C)

u i :

Interstitial fluid velocity (cm/s)

V :

Metal solution volume (l)

V r :

Volume of the adsorber (CSTA) (cm3)

x :

Axial position normalized by the bed length

〈y〉:

Dimensionless average concentration in the solid phase

y b ′ or y b :

Dimensionless concentration in the fluid phase

y f ′:

Dimensionless concentration in the fluid phase at the film

y T :

Dimensionless total concentration in the fluid phase

y* or y M :

Dimensionless concentration in the solid phase at the particle surface

z :

The distance to the symmetry plane (cm)

z′:

Bed axial position (cm)

W :

Mass of biosorbent (g)

ε :

Porosity of the bed

τ :

Space time (s)

τ d :

Time constant for intraparticle diffusion

τ f :

Time constant for film diffusion

θ :

Dimensionless time

ρ ap :

Apparent density of particles (g solid/cm3 particle)

ξ :

The batch capacity factor

ξ′:

Adsorber capacity factor for saturation

ξ″:

Adsorber capacity factor for desorption

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Authors and Affiliations

  1. LSRE Laboratory of Separation and Reaction Engineering, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Vítor J. P. Vilar, Cidália M. S. Botelho & Rui A. R. Boaventura

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  1. Vítor J. P. Vilar
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  2. Cidália M. S. Botelho
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  3. Rui A. R. Boaventura
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Correspondence to Rui A. R. Boaventura.

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Vilar, V.J.P., Botelho, C.M.S. & Boaventura, R.A.R. Modeling equilibrium and kinetics of metal uptake by algal biomass in continuous stirred and packed bed adsorbers. Adsorption 13, 587–601 (2007). https://doi.org/10.1007/s10450-007-9029-1

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  • DOI: https://doi.org/10.1007/s10450-007-9029-1

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