Optimal synthesis of liquid liquid multi

This paper presents the optimal synthesis of liquid-liquid multistage extractors utilizing Generalized Disjunctive Programming (GDP) for designing effective extraction sequences. The primary objective is to establish a systematic approach to determining the necessary number of extraction stages and solvent flow rates to achieve desired separation outcomes such as purity and recovery. The methodology encompasses a comprehensive model incorporating the general superstructure and specific stage existence conditions, which include mass transfer balances and equilibrium equations for both existing and non-existing stages. Numerical examples are provided to illustrate the application of the developed GDP model, demonstrating its efficacy in optimizing extraction processes and improving operational performance. The results indicate that the proposed approach enables better resource utilization and enhances extraction efficiency, thereby contributing significantly to the field of chemical engineering and process design. This work has implications for industrial applications where liquid-liquid extraction processes are employed to separate complex mixtures efficiently.