Neural networks simulation of the filtraton of sodium chloride and magnesium chloride solutions using nanofiltration membranes

Artificial neural network (ANN) simulation is used to predict the rejection of two salts (NaCl and MgCl₂) at typical seawater concentrations in a cross-flow nanofiltration membrane process. Rejections are predicted as a function of feed pressure and permeate flux with the salt concentration as a parameter. ANN predictions of the two salts' rejections are compared with experimental results obtained using three different nanofiltration membranes (NF90, NF270 and N30F) in a cross flow filtration set-up. The experimental program spans a concentration range of 5000 to 25 000 ppm for NaCl solution and of 5000 to 20 000 ppm for MgCl₂ solution at pressures covering the range of 2-9 bars. The effects of the training algorithm, neural network architectures and transfer function on the ANN performance, as reflected by the percentage average absolute deviation are discussed. A network with one hidden layer comprising four neurones is found to be adequate for mapping input-output relationships and providing a good interpolative tool. Algorithms based on the conjugate gradient, regularization and quasi-Newton principles were found to outperform those based on the gradient descent and variable momentum gradient descent. The former algorithms gave an average absolute percentage deviation up to 5% whereas deviations up to 20% are obtained from the latter algorithms. For most of the cases considered, the ANN proved to be an adequate interpolation tool, where an excellent prediction was obtained for some concentration levels not represented in the training data set. For very limited cases, the ANN predictive performance was poor. However, the network's performance in these extreme cases didn't improve even with increasing the data points in the training data set.