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Prediction of half-life for adsorption kinetics in a batch reactor

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Abstract

Besides adsorption rate constant, the half-life was also a basic factor that described the characteristics of adsorption kinetics. However, the direct prediction of the half-life was still a problem to be addressed urgently. In this work, the parameter τ was introduced into the pseudo-first-order (PFO), pseudo-second-order (PSO), pseudo-nth-order (PNO), and the corresponding fractal-like kinetic models (fractal-like PFO, fractal-like PSO, and fractal-like PNO) to directly predict the half-life by changing the boundary condition, i.e., the replacement of qt = 0, t = 0 by qt = qe/2, t = τ. The fitting performance of these kinetic models after modification was evaluated by nitrate adsorption on polyaniline-modified activated carbon (PAN/AC) and phosphate adsorption on zirconium-loaded Ca-montmorillonite. The results indicated that this type of model modifications did not influence the fitting performance and that the half-life was easily obtained only by the curve fitting. The practical significance of this work was to simultaneously predict the adsorption rate constant and half-life using the modified kinetic models.

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Abbreviations

C 0 :

Concentration of adsorbate at initial time (mg L−1)

C e :

Concentration of adsorbate at equilibrium (mg L−1)

F :

Adsorption progress (F = qt/qe)

h :

Fractal-like exponent (dimensionless)

k 1 :

Pseudo-first-order rate constant (min−1)

k 2 :

Pseudo-second-order rate constant (g mg−1 min−1)

k n :

pseudo-nth-order rate constant (gn − 1 mg1 − n min−1)

\( {k}_1^0 \) :

Fractal-like pseudo-first-order rate constant (minh − 1)

\( {k}_2^0 \) :

Fractal-like pseudo-second-order rate constant (g mg−1 minh − 1)

\( {k}_n^0 \) :

Fractal-like pseudo-nth-order rate constant (gn − 1 mg1 − n minh − 1)

q e :

Amount of adsorbate uptake per unit mass of adsorbent at equilibrium (mg g−1)

q t :

Amount of adsorbate uptake per unit mass of adsorbent at time t (mg g−1)

t :

Adsorption time (min)

τ :

Half-life (min)

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Funding

The authors gratefully acknowledge the financial support from the Scientific Research Foundation (10912-KYQD2019-08165).

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Authors and Affiliations

  1. College of Ecology and Environment, Chengdu University of Technology, Chengdu, 610059, China

    Qili Hu

  2. Graduate School of Life and Environmental Sciences, University of Tsukuba, Ibaraki, 305-8572, Japan

    Qili Hu & Zhenya Zhang

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  1. Qili Hu
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  2. Zhenya Zhang
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Correspondence to Qili Hu.

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Hu, Q., Zhang, Z. Prediction of half-life for adsorption kinetics in a batch reactor. Environ Sci Pollut Res 27, 43865–43869 (2020). https://doi.org/10.1007/s11356-020-10228-x

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