Optimal Design of Extraction-Distillation Hybrid Processes by Combining Equilibrium and Rate-Based Modeling

Liquid-liquid extraction (LLX) is an essential technique for separating heat-sensitive, highly diluted, or azeotropic mixtures. However, the design and optimization of LLX processes can be challenging due to mass transfer limitations and complex fluid dynamics. While distillation can often be modeled using equilibrium-based (EQ-based) approaches with (constant) height equivalent to theoretical stage (HETS) values, these kinetic effects can limit the applicability of EQ-based LLX models for conceptual design. Non-equilibrium (NEQ) or rate-based modeling can account for detailed mass transfer and fluid dynamics but further increases the nonlinearity and complexity of the respective optimization problems, which should account for closed-loop solvent recovery. To successfully address these complexities, we propose an integrated methodology combining NEQ-based simulation with EQ-based superstructure optimization to design a hybrid extraction-distillation process. An NEQ model is first used to derive operation-dependent HETS correlations, which are then incorporated into an EQ-based superstructure model for techno-economic optimization targeting total annualized cost. This approach balances model fidelity and computational efficiency, providing more reliable solutions by capturing the solvent-specific mass transfer behavior. We illustrate the methodology for a dilute acetone-water system with different solvents.