Neural network modelling of adsorption isotherms
- PDF / 688,066 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 94 Downloads / 227 Views
Neural network modelling of adsorption isotherms Graham Morse · Rudy Jones · Jules Thibault · F. Handan Tezel
Received: 19 March 2008 / Accepted: 20 October 2010 / Published online: 4 November 2010 © Springer Science+Business Media, LLC 2010
Abstract This paper examines the possibility to use a single neural network to model and predict a wide array of standard adsorption isotherm behaviour. Series of isotherm data were generated from the four most common isotherm equations (Langmuir, Freundlich, Sips and Toth) and the data were fitted with a unique neural network structure. Results showed that a single neural network with a hidden layer having three neurons, including the bias neuron, was able to represent very accurately the adsorption isotherm data in all cases. Similarly, a neural network with four hidden neurons, including the bias, was able to predict very accurately the temperature dependency of adsorption data. Keywords Isotherms · Neural networks · Langmuir · Freundlich · Sips · Toth Nomenclature A constant for Freundlich equation (kg ethanol/ kg adsorbent) (m3 /kg ethanol)1/n b constant for Langmuir, Toth and Sips equations; temperature dependent variable for the TD-Toth equation (m3 /kg adsorbate) constant for the TD-Toth equation (m3 / bo kg adsorbate) c fluid adsorbate concentration (kg adsorbate/m3 ) n constant for the Freundlich and Sips equations (dimensionless)
G. Morse · R. Jones · J. Thibault () · F.H. Tezel Department of Chemical Engineering, University of Ottawa, Ottawa, ON, Canada K1N 6N5 e-mail: [email protected]
q qs
qso Q R t to T To W W
solid adsorbate concentration (kg adsorbate/ kg solids) saturation capacity—constant for Langmuir, Sips, Toth equations; temperature dependent variable for the TD-Toth equation (kg adsorbate/kg solids) constant for the TD-Toth equation (kg adsorbate/ kg solids) heat of adsorption (J/mol adsorbed) gas constant (8.314 Pa m3 /(mol K) or 8.314 J/(mol K)) temperature dependent variable for TD-Toth equation (dimensionless) constant for the TD-Toth equation (dimensionless) temperature (°C or K) reference temperature (°C or K) neural network weights between the input and hidden layers parameters of (6) neural network weights between the hidden and output layers
Greek symbols α constant for the TD-Toth equation (dimensionless) χ constant for the TD-Toth equation (dimensionless)
Upperscript – normalized values
Subscripts i neuron number in input layer j neuron number in hidden layer k neuron number in output layer
304
Abbreviations ANN Artificial Neural networks BDDT Brunauer, Deming, Deming and Teller FFNN Feed-forward neural networks IUPAC International Union of Pure and Applied Chemistry TD Temperature Dependent
1 Introduction Adsorption is a commonly used chemical engineering separation process. It is a process whereby two or more components of a fluid (gas or liquid) stream are separated through contact with a solid surface. The quantity of the component which can bind to the surface of the adsorbent will depend on the temperature and the co
Data Loading...
