Separation of lead ions from wastewater using electrodialysis: Comparing mathematical and neural network modeling

Abstract

This paper presents experimental data, an artificial neural network (ANN) model and a mathematical model (MM) for a laboratory scale electrodialysis (ED) cell. The aim was to predict separation percent (SP) of Pb2+ ions as a function of concentration, temperature, flow rate and voltage. The MM started from a differential equation of steady state mass balance. Neglecting resistances of ion exchange membranes compared with resistances of bulk solutions in dilute and concentrate compartments and deriving a relation for solution resistance as a function of operating parameters, the final one-parameter model was obtained. The applied ANN was a multilayer perceptron (MLP) network with two hidden layers. The fast Levenberg–Marquardt (LM) optimization technique was employed for training the ANN. MM and ANN were able to predict the performance of ED desalination with correlation coefficients of 0.97 and 0.99, respectively. Comparing MM and ANN model results, it was found that ANN model is more capable than MM to predict nonlinear behavior of ED process. However, MM is more efficient at higher feed flow rates and lower voltages, temperatures and feed concentrations. ANN is found out to be an efficient tool to model the complicated ion transfer mechanism in an electrical field.