Crossed mixture–process design approach to model nanofiltration rejection for non-dilute multi-ionic solutions in a given range of solution compositions

The goal of the present work is to illustrate the applicability of crossed mixture–process design to predict the rejection of the nanofiltration membranes when treating non-dilute solutions. The method used in this work is based on the use of mixture factors derived from the fractions of equivalents of the major ions present in solution combined with the total concentration as a process variable. In this way, polynomial models for permselectivity properties can be obtained. Model accuracy is improved by using pseudo-components to restrict the range of the composition variables to that expected for the feed water compositions. The experimental plan uses the D-optimal criterion. As an application example, the procedure was used to model the performance of the nanofiltration membrane NF270 (Dow-Filmtec) with ionic mixtures containing chloride, nitrate, sulfate, sodium and calcium. The experiments were carried out in a pilot plant with solutions of total concentration ranging from 2480 to 4050 mg/L. The obtained polynomial models could satisfactorily describe individual ion rejection despite the solutions not being dilute. The polynomial models can be useful for design and operation purposes as an alternative to physical-based nanofiltration models.

► Crossed mixture design was useful to describe the ionic rejection of a NF membrane.
► Cation and anion composition were crossed with total concentration as process variable.
► The experimental plan was performed using the D-optimal criterion.
► A linear × linear model was suitable to fit the data in a restricted composition range.
► The response surfaces obtained were analyzed in terms of physical explanation.