# (66c) Hybrid Mechanistic Data-Driven Modelling for Real-Time Dynamic Optimization of Large-Scale Rectification Systems: Application to Air Separation Units

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Monday, November 11, 2019 - 8:42am-9:09am

Model size is still the main bottleneck for the use of dynamic optimization methods in real-time, e.g., in distillation columns due to MESH equations for each stage. Therefore, there is a need to develop process models of substantially decreased complexity that retain accurate prediction abilities. In the context of distillation systems, model reduction approaches may be classified into three categories: (i) nonlinear wave models [12], (ii) collocation-based models [13], and (iii) compartment models [14]. All of these approaches have been applied to operational optimization of ASUs [15,16,17]. However, there is still an interest in more efficient model reduction approaches. For this purpose, we have recently proposed an advanced compartment model formulation that combines the aggregation of single stage dynamics with machine learning techniques using artificial neural networks (ANNs) [18]. More precisely, we replace the complex nonlinear input-output relations for the compartments with ANNs. We herein present the derivation of the ANN-based compartment model (ANNCM) â€“ starting from well-known full-order stage-by-stage models (FSM) for distillation columns. We analyze and discuss thoroughly the properties of the ANNCM (compliance with integral balance relations, stationary and dynamic errors compared to an FSM, etc.). We further demonstrate that by using the ANNCM as rectification model, we achieve reductions of the computational time for state and sensitivity integration of more than one order of magnitude whilst not introducing substantial errors compared to using an FSM.

We also present the utilization of the model for a closed-loop single-layer eNMPC framework. Therein, the computational time for solving the dynamic optimization problem is controlled by restricting to a fixed number of optimizer iterations. We consider a nitrogen plant from literature as an in-silico case study and use our in-house software for sequential dynamic optimization DyOS [19]. We explicitly consider (i) model-plant mismatch, (ii) erroneous forecasts for the development of the electricity price, (iii) unmeasured disturbances influencing the process, and (iv) time delays in updating the control signals caused by the computational time for solution of the dynamic optimization problems. The computational results from this study demonstrate the real-time applicability of the suggested framework for eNMPC purposes subject to time-variable electricity prices.

**Acknowledgements:**

The authors gratefully acknowledge the financial support of the Kopernikus project SynErgie by the Federal Ministry of Education and Research (BMBF) and the project supervision by the project management organization Projektträger Jülich. Furthermore, the authors thank Anna-Maria Ecker, Florian Schliebitz, Bernd Wunderlich, Andreas Peschel and Gerhard Zapp from Linde Engineering as well as Robert Kender from TU München for valuable discussions concerning modeling and control of cryogenic rectification columns.

**References:**

[1] Mitsos A, Asprion N, Floudas CA, Bortz M, Baldea M, Bonvin D, Caspari A, Schäfer P. Challenges in process optimization for new feedstocks and energy sources. *Comput Chem Eng.* 2018;113:209-221.

[2] Zhang Q, Grossmann IE. Enterprise-wide optimization for industrial demand side management: Fundamentals, advances, and perspectives. *Chem Eng Res Des.* 2016;116:114-131.

[3] Baldea M, Harjunkoski I. Integrated production scheduling and process control: A systematic review. *Comput Chem Eng.* 2014;71:377-390.

[4] Pattison RC, Touretzky CR, Johansson T, Harjunkoski I, Baldea M. Optimal process operations in fast-changing electricity markets: Framework for scheduling with low-order dynamic models and an air separation application. *Indus Eng Chem Res.* 2016;55:4562-4,584.

[5] Kelley MT, Pattison RC, Baldick R, Baldea M. An MILP framework for optimizing demand response operation of air separation units. *Appl Energy.* 2018;222:951-966.

[6] Engell S. Feedback control for optimal process operation. *J Process Control.* 2007;17(3):203-219.

[7] Amrit R, Rawlings JB, Biegler LT. Optimizing process economics online using model predictive control. *Comput Chem Eng.* 2013;58:334-343.

[8] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. *IEEE Trans Automat Contr*. 2012;57(7):1615-1626.

[9] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. *AIChE J*. 2012;58(3):855-870.

[10] Huang R, Biegler LT. Economic NMPC for energy intensive applications with electricity price prediction. *Comput Aided Chem Eng.* 2012;31:1612-1616.

[11] Caspari A, Faust JMM, Schäfer P, Mhamdi A, Mitsos A. Economic nonlinear model predictive control for flexible operation of air separation units. *IFAC-PapersOnLine.* 2018;51:295-300.

[12] Marquardt W. Nonlinear model reduction for binary distillation. Dynamics and Control of Chemical Reactors and Distillation Columns. 1988.

[13] Cho YS, Joseph B. Reduced-order steady-state and dynamic models for separation processes. Part II. Application to nonlinear multicomponent systems. *AIChE J.* 1983;29:270-276.

[14] Benallou A, Seborg DE, Mellichamp DA. Dynamic compartmental models for separation processes. *AIChE J.* 1986;32:1067-1078.

[15] Chen Z, Henson MA, Belanger P, Megan L. Nonlinear model predictive control of high purity distillation columns for cryogenic air separation. *IEEE Trans Control Syst Technol.* 2010;18:811-821.

[16] Fu Y, Liu X. An advanced control of heat integrated air separation column based on simplified wave model. *J Process Control.* 2017;49:45-55.

[17] Cao Y, Swartz CLE, Flores-Cerrillo J. Optimal dynamic operation of a high-purity air separation plant under varying market conditions. *Indus Eng Chem Res.* 2016;55:9956-9970.

[18] Schäfer P, Caspari A, Kleinhans K, Mhamdi A, Mitsos A. Reduced dynamic modeling approach for rectification columns based on compartmentalization and artificial neural networks. *AIChE J.* 2019; e16568.

[19] Caspari A, Bremen AM, Faust JMM, Jung F, Kappatou CD, Sass S, Vaupel Y, Hannemann-Tamas R, Mhamdi A, Mitsos A. DyOS - A framework for optimization of large-scale differential algebraic equation systems. Accepted for publication in: *Comput Aided Chem Eng.* 2019.