Improved lumped solutions for mass transfer analysis in membrane separation process of metals

A mixed lumped-differential mathematical model is proposed to analyze the metals extraction in membrane separation processes. The Coupled Integral Equations Approach (CIEA) is employed to reformulate and simplify the associated equations of species conservation and obtain improved lumped formulations by reducing the number of space variables with the use of Hermite’s approximations for integrals. The approach is illustrated in the extraction of Au (III) and Pd (II) present in a hydrochloric acid medium employing polymeric liquid membrane with Aliquat 336 as extractant and immobilized in PVC (polyvinylchloride), which was also used to analyze the extraction of Zn (II) with di-(2-ethylhexyl) phosphoric acid (D2EHPA) as extractant. From the constructed model, the behavior of the metal concentration profiles to be extracted from the feeding phase is discussed in light of the influence of relevant parameters in the extraction process, such as membrane composition and thickness, diffusion coefficient and extraction constant.