Optimization-based Separation System Synthesis

Abstract

We propose optimization-based approaches for the synthesis of separation processes using liquid-liquid extraction, membrane separation, and distillation. First, we present two optimization models for designing multistage liquid extractors.The models are motivated by the McCabe-Thiele method where mass transfer in the liquid extractor is represented graphically. Our approach allows complex thermodynamics to be represented by inexpensive yet accurate piece-wise linear functions. We demonstrate the applicability of the models through various examples (dilute systems, systems with immiscible solvents, and extractors with non-ideal stages). Next, we propose optimization models for membrane systems for multicomponent gas mixture separation. To represent the membrane systems, we employ a superstructure with rich connectivity. We use physics-based surrogate unit models to describe the mass transfer in the crossflow and counter-current flow permeators. We also develop optimization models to simultaneously synthesize membrane systems and design membrane materials. We consider three types of systems: (1) systems with the same membrane material, (2) systems with potentially different membrane materials, and (3) systems with property-targeting membrane materials. In the first two types of systems, the selection of membrane material is a decision. In the third type of system, membrane permeances are subject to optimization. Furthermore, we study the separation of homogeneous azeotropic mixtures using distillation. To synthesize the optimal distillation system, we develop an optimization-based approach. Numerous possible system configurations are represented using a network-based superstructure generated via a matrix method. The distillation columns are modeled using the modified Underwood equations. We extend the approach to account for curved separatrices by implementing corrections via piece-wise linear functions and collinearity properties. Finally, we address separation system synthesis when multiple technologies are considered. Since different technologies exploit different properties, we use a component ranking system based on those properties. Using these rankings, we construct matrices that identify possible separation splits and generate a network-based superstructure that encompasses numerous promising configurations comprising multiple separation technologies.