Modeling of CaCl2 removal by positively charged polysulfone-based nanofiltration membrane using artificial neural network and genetic programming

Artificial neural network (ANN) and genetic programming (GP) models were used to predict rejection (R) and permeability coefficient of water flux (L-p) with respect to CaCl2 in nanofiltration (NF) membrane process. The model inputs were concentration of the poly(ethylene imine) (PEI), p-xylene dichloride (XDC) and methyl iodide (MI), coating and crosslinking time of PEI, and pH of the solution. With this respect, ANN with 3:17:1 and 3:23:1 neurons, the lowest mean squad error (MSE) of 0.0023 and 0.000028 and the highest coefficient of determination (R-2) values of 0.9830 and 0.9990 for R and L-p, respectively, was found. In addition, the sensitivity analysis suggested that PEI coating time and pH had the significant effect on R and L-p, respectively. GP was used to make a mathematical function for prediction of R and L-p in terms of the input parameters. The GP model successfully described the R and L-p as function of input parameters. The GP results with R-2 values of more than 0.99 had an excellent preciseness.