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Adsorptive removal of Pb(II) using nanostructured γ-alumina in a packed bed adsorber: Simulation using gPROMS

  • Sustainable Technologies in Water Treatment and Desalination
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Abstract

In this work, convective–dispersive and pore volume and surface diffusion models have been used to analyze Pb(II) adsorption from an aqueous solution over a nanostructured γ-alumina adsorbent in a packed bed adsorber. The models encompassing partial differential equation and a linear algebraic equation coupled with isotherm have been simulated in gPROMS using the backward finite difference approach. The predicted breakthrough curves of Pb(II) adsorption concerning flow rate, initial metal concentration, and bed height were matched with the experimental data. The accuracy of model predictions was analyzed through statistical measures such as coefficient of determination (R2), root mean square error, and chi-squared value. The simulation results also predicted the axial dispersion, distribution coefficient, mass transfer coefficient, pore volume, and surface diffusion coefficient, which are, otherwise, difficult to measure experimentally and, in turn, have been used to assess the mass transfer characteristics of continuous Pb(II) adsorption. Additionally, the values of breakthrough time, exhaustion time, adsorption column capacity, and mass transfer zone were determined as a function of flow rate, bed height, and initial metal concentration. Surface and pore volume diffusions (10−11–10−10 m2/s) apparently controlled the continuous adsorption process, with surface diffusion being dominant. The transport parameters evaluated in the current study could be beneficial for the large-scale Pb(II)/nanostructured γ-alumina adsorption system. As evident from the successful simulation, the developed gPROMS program can also be applied to other adsorbate/adsorbent systems with a slight modification concerning the operating parameters.

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Data availability

Code developed during this study is available from the corresponding author upon reasonable request.

Abbreviations

\(C\) :

Heavy metal ion concentration in bulk liquid phase (mg/L)

\({C}_{0}\) :

Initial heavy metal ion concentration in bulk liquid phase (mg/L)

\({C}_{P}\) :

Heavy metal ion concentration within the adsorbent (mg/L)

\({D}_{AB}\) :

Molecular diffusivity of heavy metal in aqueous solution (m2/s)

\({D}_{L}\) :

Axial dispersion coefficient (m2/s)

\({D}_{\mathrm{p}}\) :

Pore volume diffusion coefficient (m2/s)

\({D}_{\mathrm{s}}\) :

Surface diffusion coefficient (m2/s)

\({K}_{\mathrm{d}}\) :

Distribution coefficient (m3/kg)

\({k}_{L}\) :

Mass transfer coefficient (m/s)

\({k}_{\mathrm{Th}}\) :

Thomas model constant (mL/min/mg)

\({k}_{\mathrm{YN}}\) :

Yoon-Nelson rate constant (min−1)

\(L\) :

Length of packed bed adsorber (m)

\(m\) :

Mass of adsorbent (g)

\({M}_{B}\) :

Molecular weight of water (g/mol)

\({N}_{\mathrm{p}}\) :

Mass transport due to pore volume diffusion (mg/m2/s)

\({N}_{\mathrm{s}}\) :

Mass transport due to surface diffusion (mg/m2/s)

\(Q\) :

Volumetric flow rate (mL/min)

\(q\) :

Adsorption capacity at equilibrium (mg/g)

\({q}_{\mathrm{p}}\) :

Adsorption capacity within the particle (mg/g)

\({q}_{\mathrm{eq}}\) :

Adsorption capacity of the packed bed adsorber (mg/g)

\({q}_{\mathrm{Th}}\) :

Maximum adsorption capacity (mg/g)

\({q}_{\mathrm{total}}\) :

Total Pb(II) adsorbed in the column (g)

\(R\) :

Radius of the adsorbent particle (m)

\(r\) :

Radial distance within the adsorbent particle (m)

\(Re\) :

Reynolds number

\(S\) :

External surface area of adsorbent per unit mass (m2/kg)

\(Sc\) :

Schmidt number

\(Sh\) :

Sherwood number

\(t\) :

Time (min)

\({t}_{\mathrm{b}}\) :

Breakthrough time (min)

\({t}_{\mathrm{e}}\) :

Exhaustion time (min)

\(T\) :

Temperature (K)

\(V\) :

Volume of heavy metal solution (mL)

\({V}_{A}\) :

Molal volume of heavy metals at normal boiling point (cm3/g/mol)

\({v}_{z}\) :

Interstitial velocity (m/s)

\(z\) :

Axial distance (m)

\({\varepsilon }_{\mathrm{b}}\) :

Bed voidage

\({\varepsilon }_{\mathrm{p}}\) :

Porosity of particle

\({\rho }_{\mathrm{p}}\) :

Density of the adsorbent (kg/m3)

\({\rho }_{\mathrm{water}}\) :

Density of the water (kg/m3)

\(\tau\) :

Tortuosity factor

\({\tau }_{\mathrm{YN}}\) :

Time required for 50% adsorbate breakthrough (min)

\({\mu }_{\mathrm{s}}\) :

Viscosity of solution (kg/m/s)

\({\mu }_{\mathrm{water}}\) :

Viscosity of water (kg/m/s)

\(\phi\) :

Association parameter for water

\({\chi }^{2}\) :

Chi-squared value

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Acknowledgements

The first author acknowledges the University Grant Commission (UGC) for the non-NET financial support.

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  1. Department of Chemical Engineering, Zakir Husain College of Engineering and Technology, Aligarh Muslim University, Uttar Pradesh, Aligarh, 202001, India

    Mohd Danish, Khursheed B. Ansari & Mohammad Danish

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  1. Mohd Danish
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Contributions

Mohd Danish: gPROMS-driven modeling of Pb(II) adsorption and initial draft preparation; Khursheed B. Ansari: conceptualization, draft editing, and revision; Mohammad Danish: initial concept of the work, visualization, and supervision.

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Correspondence to Mohammad Danish.

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Danish, M., Ansari, K.B. & Danish, M. Adsorptive removal of Pb(II) using nanostructured γ-alumina in a packed bed adsorber: Simulation using gPROMS. Environ Sci Pollut Res 30, 42629–42642 (2023). https://doi.org/10.1007/s11356-022-20175-4

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