Expanding the Graphical Concepts of the Minimum and Maximum Solvent-to-Feed Ratios in Solvent Extraction

The minimum (S/F)min and maximum (S/F)max solvent-to-feed ratios with their respective number of stages are essential in designing countercurrent solvent extraction processes, as they define the operating limits of the separation task. The (S/F)min is typically associated with an infinite number of stages, and the common state-of-the-art method to graphically determine it for ternary systems depends on finding the limiting tie line that passes through a known feed composition. However, the method applicability ceases when solute concentration in the feed is high enough so that no limiting tie lines exist anymore. This work comes to extend for the first time the said method beyond its validity region to cover feed compositions for which it fails. To support the presented theory, rigorous simulations are performed that clearly show the typical asymptotic behavior at infinite stages when the graphical (S/F)min is approached. For (S/F)max, although it is associated in literature with one required stage, it is not clear how this applies and whether the term “stage” is even applicable. By discussing it from different perspectives, this work shows how the corresponding minimum stages can be obtained and that they can be different from one. The latter is also supported by simulations.