(373c) Sequential Dynamic Optimization of Multi-Stage Vacuum Swing Adsorption

Vacuum Swing Adsorption (VSA) is an energy-efficient gas separation technology. The process of a VSA can be described by a set of dynamic mass/energy/momentum balance equations. These are stiff partial differential equations and additionally, the continuous switch between adsorption and desorption leads to a periodic pattern until a cyclic steady state is reached. Simulation of a VSA is thus computationally expensive making optimization very challenging. Stochastic algorithms for simulation-based optimization can be used for such optimization problems [1]. However, these are slow and there is no guaranteed convergence to an optimal solution. The direct simultaneous approach (discretize both spatial and temporal domain) has been applied to the optimization of VSA [2, 3], but this method leads to a computationally expensive large-scale nonlinear program (NLP). Thus, simplification methods are required, which may reduce accuracy.

Sequential dynamic optimization is well-suited to problems with few decision variables and many state variables. The integrator solves the large-scale VSA model and provides function and gradient information to the NLP solver, which in turn solves a rather small-scale NLP. However, sequential dynamic optimization has not yet been applied to VSA processes. In this contribution, we optimize a VSA using DyOS [4], a framework for adaptive direct sequential (single shooting) multi-stage dynamic optimization. We develop the model in Modelica [5] and export the model via the Functional Mock-up Interface (FMI) for use within DyOS. Using simultaneous state and direct sensitivity integration over the time horizon of all stages, we calculate function and gradient values for the NLP solver. This method successfully optimizes the flow velocity and operating pressures to local optimality.

Reference

1. Haghpanah R., Majumder A., Nilam, R., Rajendran, A., Farooq, S., Karimi, I. A., & Amanullah, M. Industrial & Engineering Chemistry Research2013 52 (11), 4249-4265
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3. Tsay, C., Pattison, R. C., & Baldea, M. AIChE Journal2018 64 (8), 2982-2996.
4. Caspari, A., Hannemann-Tam, R., Bremen, A., Faust M. M. J., Jung, F., Kappatou, D. C., Sass, S., Vaupel, Y., Mhamdi, A., Mitsos, A. A Framework for Optimization of Large Scale Differential Algebraic Equation Systems. 29^th European Symposium on Computer-Aided Process Engineering (ESCAPE-29) 2019
5. Fritzson, P., & Engelson, V. Modelica - A unified object-oriented language for system modeling and simulation. In European Conference on Object-Oriented Programming (pp. 67-90). Springer 1998