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Comparative study of adsorptive removal of Cr(VI) ion from aqueous solution in fixed bed column by peanut shell and almond shell using empirical models and ANN

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Abstract

Cr(VI) is a toxic water pollutant, which causes cancer and mutation in living organisms. Adsorption has become the most preferred method for removal of Cr(VI) due to its high efficiency and low cost. Peanut and almond shells were used as adsorbents in downflow fixed bed continuous column operation for Cr(VI) removal. The experiments were carried out to scrutinise the adsorptive capacity of the peanut shells and almond shells, as well as to find out the effect of various operating parameters such as column bed depth (5–10 cm), influent flow rate (10–22 ml min−1) and influent Cr(VI) concentration (10–20 mg L−1) on the Cr(VI) removal. The fixed bed column operation for Cr(VI) adsorption the equilibrium was illustrated by Langmuir isotherm. Different well-known mathematical models were applied to the experimental data to identify the best-fitted model to explain the bed dynamics. Prediction of the bed dynamics by Yan et al. model was found to be satisfactory. Applicability of artificial neural network (ANN) modelling is also reported. An ANN modelling of multilayer perceptron with gradient descent and Levenberg-Marquardt algorithms have also been tried to predict the percentage removal of Cr(VI). This study indicates that these adsorbents have an excellent potential and are useful for water treatment particularly small- and medium-sized industries of third world countries. Almond shell represents better adsorptive capacity as breakthrough time and exhaustion time are longer in comparison to peanut shell.

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Abbreviations

a :

Modified dose–response model parameter

A :

Cross-sectional area of the bed (cm2)

AARE:

Average absolute relative error, \( \mathrm{AARE}=\frac{1}{N}\sum_{i=1}^N\left|\frac{\left({y}_1-{x}_i\right)}{x_i}\right| \), dimensionless

C 0 :

Influent Cr(VI) concentration (mg L−1)

C t :

Effluent concentration at time t (mg L−1)

C eq :

Equilibrium concentration (mg L−1)

K B :

Rate constant (L mg−1 min−1)

K L :

Langmuir isotherm constant (L mg−1)

K Y :

Yan et al. model kinetic rate constant (ml mg−1 min−1)

k AB :

Kinetic constant in Bohart-Adams model (L mg−1 min−1)

k Th :

Thomas model rate constant (ml mg−1 min−1)

k YN :

Rate constant in Yoon-Nelson model (min−1)

m :

Mass of the adsorbent (g)

MSE:

Mean square error, \( \mathrm{MSE}=\frac{1}{N}\sum_{i=1}^N{\left({x}_i-{y}_i\right)}^2 \), dimensionless

SE:

Standard error, \( \mathrm{SE}=\sqrt{\sum \frac{{\left({q}_{0\left( \exp \right)}-{q}_{0\left(\mathrm{cal}\right)}\right)}^2}{N}} \), dimensionless

m total :

Total amount of Cr(VI) ion sent to the column (mg)

N 0 :

Adsorption capacity (mg L−1)

N :

Number of experimental points run

Q :

Volumetric flow rate (ml min−1)

q 0 :

Adsorption capacity (mg g−1)

q 0(exp) :

Experimental adsorption capacity (mg g−1)

q 0(cal) :

Adsorption capacity calculated using theoretical kinetic models (mg g−1)

q Y :

Maximum adsorption capacity in Yan et al. model (mg g−1)

q exp :

Equilibrium Cr(VI) uptake (mg g−1)

q max :

Maximum adsorption capacity (mg g−1)

q mdr :

Adsorption capacity in modified dose–response model (mg g−1)

q total :

Total Cr(VI) adsorbed (mg)

R 2 :

Correlation coefficient, \( R=\frac{\sum_{i=1}^N\left({x}_i-\overline{x}\right)\left({y}_i-\overline{y}\right)}{\sqrt{\sum_{i=1}^N{\left({x}_i-\overline{x}\right)}^2\sum_{i=1}^N{\left({y}_i-\overline{y}\right)}^2}} \), dimensionless

t :

Time (min)

t total :

Total flow time (min)

TF1 :

Transfer function 1 in hidden layer, \( {f}_{1\mathrm{h}}(x)= \tanh \beta x=\frac{e^{\beta x}-{e}^{-\beta x}}{e^{\beta x}+{e}^{-\beta x}} \), dimensionless

TF2 :

Transfer function 2 in hidden layer, \( {f}_{2\mathrm{h}}(x)=\beta x,\kern0.5em \mathrm{where}\kern0.24em \begin{array}{l}\beta x=1\;\mathrm{for}\;\beta x>1\hfill \\ {}\beta x=-1\;\mathrm{for}\;\beta x>-1\hfill \end{array} \), dimensionless

TF3 :

Transfer function 3 in hidden layer, \( {f}_{3\mathrm{h}}(x)=\beta x,\kern0.5em \mathrm{where}\;\begin{array}{l}\beta x=0\;\mathrm{for}\;\beta x>0\hfill \\ {}\beta x=1\;\mathrm{for}\;\beta x>1\hfill \end{array} \), dimensionless

TF4 :

Transfer function 4 in hidden layer, \( {f}_{4\mathrm{h}}(x)=\frac{1}{1+{e}^{-\beta x}} \), dimensionless

U 0 :

Superficial velocity (cm min−1)

V eff :

Effluent volume (L)

Z :

Bed depth (cm)

β :

Kinetic coefficient of external mass transfer in Wolborska model (min−1)

τ :

Fifty percent breakthrough time (min)

χ 2 :

\( {\chi}^2=\sum_{i=1}^N\frac{{\left({x}_i-{y}_i\right)}^2}{y_i} \), dimensionless

σ :

\( \sigma =\sqrt{\sum_{i=1}^N\frac{1}{N-1}\left[\left|\frac{\left({y}_i-{x}_i\right)}{x_i}\right|-\mathrm{AARE}\right]} \), dimensionless

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Acknowledgements

The authors are gratefully acknowledging the Department of Science & Technology, West Bengal (Sanction No. 21 (Sanc)/ST/P/S&T/13G-1/2013 dt. 06.06.2014) for providing the research fund.

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Authors and Affiliations

  1. Chemical Engineering Department, University of Calcutta, 92, APC Road, Kolkata, 700009, India

    Munmun Banerjee, Nirjhar Bar, Ranjan Kumar Basu & Sudip Kumar Das

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  1. Munmun Banerjee
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  2. Nirjhar Bar
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  3. Ranjan Kumar Basu
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Correspondence to Sudip Kumar Das.

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Banerjee, M., Bar, N., Basu, R.K. et al. Comparative study of adsorptive removal of Cr(VI) ion from aqueous solution in fixed bed column by peanut shell and almond shell using empirical models and ANN. Environ Sci Pollut Res 24, 10604–10620 (2017). https://doi.org/10.1007/s11356-017-8582-8

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