A pseudo‐transient optimization framework for periodic processes: Pressure swing adsorption and simulated moving bed chromatography

Abstract

Periodic systems are widely used in separation processes and in reaction engineering. They are designed for and operated at a cyclic steady state (CSS). Identifying and optimizing the CSS has proven to be computationally challenging. A novel framework for equation-oriented simulation and optimization of cyclic processes is introduced. A two-step reformulation of the process model is proposed, comprising, (1) a full discretization of the time and spatial domains and (2) recasting the discretized model as a differential-algebraic equation system, for which theoretical stability guarantees are provided. Additionally, a mathematical, structural connection between the CSS constraints and material recycling is established, which allows us to deal with these conditions via a "tearing" procedure. These developments are integrated in a pseudo-transient design optimization framework and two extensive case studies are presented: a simulated moving bed chromatography system and a pressure swing adsorption process.From (34), we see that the derivative @F1 @/ 1 is made negative if a small enough value of temporal discretization step Dt is used (the function / has Lipschitz continuous first and

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