Redefining Stage Efficiency in Liquid-Liquid Extraction: Development and Application of a Modified Murphree Efficiency

Liquid-liquid extraction stages often deviate from equilibrium due to factors like insufficient mixing, making accurate efficiency modeling essential for process simulation. This study addresses the limitations of Aspen Plus (AP), which distorts equilibrium calculations by directly multiplying efficiency with the distribution coefficient. A modified Murphree efficiency definition, more suitable for liquid-liquid systems but absent in AP's Extraction Column module, was implemented using Aspen Custom Modeler (ACM). The custom multi-stage extraction column model replaces mole fractions with mole flows to better represent mass transfer and phase interactions, enhancing simulation accuracy when imported into AP. Two test cases validated the custom model's effectiveness. Test Case I, utilizing the UNIQ-RK thermodynamic model, compared the ACM model to AP's built-in module, revealing that the ACM model provides a more realistic representation of extraction processes under varying stage efficiencies. It captured gradual efficiency changes and aligned with expected mass transfer behavior, while the built-in module showed reduced sensitivity and accuracy. Test Case II, using the UNIF-LL thermodynamic model, demonstrated the model's robustness across different thermodynamic frameworks. It highlighted how varying Murphree efficiency from 0 to 1 directly affects separation performance, with higher efficiencies leading to better separation and increased extract phase composition. These findings confirm that the modified Murphree efficiency is a reliable and effective approach, enabling engineers to optimize liquid-liquid extraction processes with greater accuracy and efficiency.