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Prediction of coefficients of the Langmuir adsorption isotherm using various artificial intelligence (AI) techniques

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Abstract

Adsorption is a process that utilizes porous solid materials to separate some solutes from gas or liquid mixtures. The extent of this separation is often determined using the adsorption isotherms, i.e., semi-empirical correlation for relating the amount of adsorbed substances by the solid medium to its associated concentration in fluid phase at constant temperature. Prior to employing an adsorption isotherm, its coefficients should be adjusted using experimental data of a considered adsorption system. In this study, the coefficients of Langmuir model have been predicted using various types of artificial neural networks (ANNs), support vector machines, and adaptive neuro fuzzy interface systems, and coupled scheme of ANN-genetic algorithm. The employed ANN types are multi-layer perceptron neural network (MLPNN), radial basis function neural network, cascade feedforward neural network, and generalized neural network. The considered coefficients tried to be modeled as functions of temperature, pH, adsorbent density, and adsorbate molecular weight. Predictive accuracies of the AI techniques have been compared utilizing different statistical indices such as correlation coefficient (R2), mean square error, and absolute average relative deviation (AARD%). The results indicated that MLPNN was the most accurate model for predicting the coefficients of Langmuir isotherm, due to its AARDs of 24.64 and 22.40% for the first and second coefficients, respectively.

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Abbreviations

AARD:

Absolute average relative deviation

AI:

Artificial intelligence

ANFIS:

Adaptive neuro fuzzy interface systems

ANN:

Artificial neural network

CFNN:

Cascade-forward neural network

GA:

Genetic algorithm

GRNN:

Generalized regression neural network

LAI:

Langmuir adsorption isotherm

LM:

Levenberg–Marquardt

MLP:

Multi-layer perceptron

MLPNN:

Multi-layer perceptron neural network

MSE:

Mean square errors

M w :

Molecular weight

RBFNN:

Radial basis function neural network

SVM:

Support vector machines

\({q_{\rm{max} }}\) :

First coefficient of the Langmuir adsorption isotherm

\(b\) :

Second coefficient of the Langmuir adsorption isotherm

\(q\) :

Concentration of adsorbate in the solid phase

\({C_{\text{f}}}\) :

Concentration of adsorbate in the fluid phase

n :

Number of entry signals to the neuron

x r :

Entry signals to the neuron

w r :

Weight parameter

B :

Bias parameter

f :

Activation function

Out:

Neuron output

N :

Number of available data points

CoL:

Coefficient of Langmuir isotherm

CoLact :

Actual values of coefficients of Langmuir isotherm

CoLest :

Values of coefficients of Langmuir isotherm estimated by AI techniques

\(\overline {{{\text{CoL}}}}\) :

Average values of coefficients of Langmuir isotherm

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Authors and Affiliations

  1. Department of Chemical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran

    F. Mahmoodi

  2. Department of Chemical Engineering, Yasouj University, Yasouj, Iran

    P. Darvishi

  3. Young Researchers and Elite Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran

    B. Vaferi

Authors
  1. F. Mahmoodi
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  2. P. Darvishi
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  3. B. Vaferi
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Correspondence to B. Vaferi.

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Mahmoodi, F., Darvishi, P. & Vaferi, B. Prediction of coefficients of the Langmuir adsorption isotherm using various artificial intelligence (AI) techniques. J IRAN CHEM SOC 15, 2747–2757 (2018). https://doi.org/10.1007/s13738-018-1462-4

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