Mid Sweden University

This study explains the modeling of synthesized membranes using the Donnan Steric Pore model (DSPM) based on the Extended Nernst Planck Equation (ENP). Conventionally, structural parameters required to predict the performance of the membranes were determined through tedious experimentation, which in this study are found using a new MATLAB technique. A MATLAB program is used to determine the unknown structural parameters such as effective charge density (Xd), effective pore radius (rp), and effective membrane thickness to porosity ratio (Δx/Ak) by using the single solute rejection and permeation data. It was found that the model predicted the rejection of studied membranes accurately, with the E5C1 membrane exceeding the others (E5, E5C5) for rejection of single and divalent salt's aqueous solutions. The rejection of 100 ppm aqueous solution of NaCl for E5C1 was around 60%, whereas, for an aqueous solution of 100 ppm, CaCl2 rejection reached up to 80% at 10 bar feed pressure. The trend of salt rejection for all three membranes was found to be in the following order: E5C1 > E5C5 > E5, confirming that their structural parameters-controlled ion transport in these membranes. The structural parameters, such as effective pore radius, effective membrane thickness to porosity ratio, and effective charge density for the best performing membrane, i.e., E5C1, were determined to be 0.5 nm, 16 μm, and −6.04 mol/m3,respectively. Finally, it can be asserted that this method can be used to predict the real performance of membranes by significantly reducing the number of experiments previously required for the predictive modeling of nanofiltration-type membranes.