Minimum amount of extracting solvent of two-component extraction separation in a complex feeding pattern

• Greatly advancing countercurrent extraction theory.
• Introducing the in-with-out feeding pattern for countercurrent extraction.
• Giving equations of minimum use of chemicals for A/B unit in in-with-out feeding.
• Presenting a theoretical basis for optimizing a multi-component separation.

For a given countercurrent extraction separation, minimum amounts of extraction solvent and scrubbing agent solution indicating the limits of chemical consumptions are critical parameters for process design. The article derives the equations of those two minimum amounts for a two-component separation in a complex feeding pattern called “in-with-out” feeding by us. This feeding pattern leads out an organic stream from the stage that an aqueous feed enters or an aqueous stream from the stage that an organic feed enters. The exiting streams will serve as extracting solvent or scrubbing agent solution in other separation units, by which the overall chemical consumptions of an entire process can be decreased. Therefore the in-with-out feeding pattern is necessarily employed, especially in hyperlink extraction technology which has been widely applied to the rare earth separation industry in China with the aim of saving the use of chemicals. This work may significantly contribute to the theory of countercurrent extraction.