An optimization based algorithm for solving design problems of counter-current multistage batch solid–liquid extractors for complex systems: Application to vanilla extract

• A new counter-current N-stage solid-liquid extraction model was conceptualized.
• Differences between thermodynamic and apparent equilibrium were demonstrated.
• An optimization based algorithm for model solution was proposed.
• Equilibrium properties of vanilla-ethanol-water system were evaluated experimentally.
• The model was validated with experimental vanilla solid-liquid extraction in 3 stages.

Solid–liquid extraction is one of the aged unit operations in chemical engineering. However the process design models, universally included in textbooks, continue considering infinite dilution of extractable material and single component solvent. Extraction processes of bioactive compounds with composite solvents (ethanol–water) from plants or foods products require a better understanding of equilibrium between phases of bioactive compounds and their role in the process design. Then, a general mathematical model of counter-current ideal multi-stages batch solid–liquid extractors was developed. The model considers composite solvents and the two equilibrium relations required for the total description of a solid–liquid extraction system. An optimization based algorithm was proposed for solving the design problems. Experimental equilibrium relations were obtained for vanilla–ethanol–water system and used as example of model application. Additionally, the prediction of a particular component (vanillin) concentration in extract was included and experimentally validated.

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