Optimal Laypunov exponent parameters for stability analysis of batch reactors with Model Predictive Control

Abstract Thermal runaways in exothermic batch reactions are a major economic, health and safety risk in industry. In literature most stability criteria for such behaviour are not reliable for nonlinear non-steady state systems. In this work, Lyapunov exponents are shown to predict the instability of highly nonlinear batch processes reliably and are hence incorporated in standard MPC schemes, leading to the intensification of such processes. The computational time is of major importance for systems controlled by MPC. The optimal tuning of the initial perturbation and the time frame reduces the computational time when embedded in MPC schemes for the control of complex batch reactions. The optimal tuning of the initial perturbation and time horizon, defining Lyapunov exponents, has not been carried out in literature so far and is here derived through sensitivity analyses. The computational time required for this control scheme is analysed for the intensification of complex reaction schemes.

[1]  C. F. Curtiss,et al.  Molecular Theory Of Gases And Liquids , 1954 .

[2]  Fahad Albalawi,et al.  A feedback control framework for safe and economically‐optimal operation of nonlinear processes , 2016 .

[3]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[4]  Fahad Albalawi,et al.  Process operational safety using model predictive control based on a process Safeness Index , 2017, Comput. Chem. Eng..

[5]  Fernanda Strozzi,et al.  On-Line Runaway Detection in Batch Reactors Using Chaos Theory Techniques. , 1999 .

[6]  A. Hurwitz.  Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt , 1895 .

[7]  Zhe Wu,et al.  On integration of feedback control and safety systems: Analyzing two chemical process applications , 2018 .

[8]  E. J. Routh.  A Treatise on the Stability of a Given State of Motion: Particularly Steady Motion , 2010 .

[9]  Fahad Albalawi,et al.  Process operational safety via model predictive control: Recent results and future research directions , 2017, Comput. Chem. Eng..

[10]  A. V. Apolenis,et al.  Synthesis of Iron Aluminates and New Modification of Alumina at Impact of Explosive , 2010 .

[11]  Jay H. Lee,et al.  Model predictive control: Review of the three decades of development , 2011 .

[12]  Sebastian Engell,et al.  Economics optimizing control of a multi-product reactive distillation process under model uncertainty , 2018, Comput. Chem. Eng..

[13]  Vassilios S. Vassiliadis,et al.  Thermal stability criterion integrated in model predictive control for batch reactors , 2018, Chemical Engineering Science.

[14]  K. Luo,et al.  The stability of toluene mononitration in reaction calorimeter reactor , 1998 .

[15]  Mawardi Rahmani.  The Nitration of Monoalkyl Benzene and the Separation of its Isomers by Gas Chromatography , 1982 .

[16]  Victor M. Zavala,et al.  Robustly stable economic NMPC for non-dissipative stage costs , 2017 .

[17]  Amyn S. Teja,et al.  Simple method for the calculation of heat capacities of liquid mixtures , 1983 .

[18]  David Banjerdpongchai,et al.  Comparison of PID control and linear model predictive control application to regenerative thermal oxidizer system , 2015, 2015 10th Asian Control Conference (ASCC).

[19]  Flavio Manenti,et al.  Online model-based optimization and control for the combined optimal operation and runaway prediction and prevention in (fed-)batch systems , 2015 .

[20]  Lawrence F. Shampine,et al.  Solving Index-1 DAEs in MATLAB and Simulink , 1999, SIAM Rev..

[21]  Ray Sinnott,et al.  Chemical Engineering Design , 2007 .

[22]  A. Oroskar,et al.  Stability of chemical reactors , 1979 .

[23]  Vassilis M. Charitopoulos,et al.  Explicit model predictive control of hybrid systems and multiparametric mixed integer polynomial programming , 2016 .

[24]  Vincent A Akpan,et al.  Nonlinear model identification and adaptive model predictive control using neural networks. , 2011, ISA transactions.

[25]  Fernanda Strozzi,et al.  A general method for assessing the thermal stability of batch chemical reactors by sensitivity calculation based on Lyapunov exponents , 1994 .

[26]  Manfred Morari,et al.  State-space interpretation of model predictive control , 1994, Autom..

[27]  David Q. Mayne,et al.  Model predictive control: Recent developments and future promise , 2014, Autom..

[28]  George F. Sheats,et al.  Rates and activation energies of nitronium ion formation and reaction in the nitration of toluene in ∼78% sulphuric acid , 1978 .

[29]  D. D. Perlmutter.  Stability of chemical reactors , 1972 .

[30]  Mark E. Davis,et al.  Fundamentals of Chemical Reaction Engineering , 2002 .

[31]  E. Obermeier,et al.  Thermal, Conductivity, Density, Viscosity, and Prandtl-Numbers of Ethylene Glycol-Water Mixtures , 1984 .

[32]  Andreas Potschka,et al.  Partial stability for nonlinear model predictive control , 2017, Autom..

[33]  Don W. Green,et al.  Perry's Chemical Engineers' Handbook , 2007 .

[34]  L. Biegler,et al.  Robust stability of economically oriented infinite horizon NMPC that include cyclic processes , 2012 .

[35]  Walter Kähm,et al.  Lyapunov exponents with Model Predictive Control for exothermic batch reactors , 2018 .

[36]  Panagiotis D. Christofides,et al.  Networked and Distributed Predictive Control , 2011 .

[37]  Adeniyi Lawal,et al.  Nitration of toluene in a microreactor , 2007 .

[38]  N. N. Semenov,et al.  Thermal Theory of Combustion and Explosion , 1942 .

[39]  Kerry J. Howe,et al.  MWH's Water Treatment: Principles and Design , 2012 .

[40]  Charles A. Desoer,et al.  An elementary proof of the Routh-Hurwitz stability criterion , 1990 .

[41]  Amy E. Theis,et al.  Case study: T2 Laboratories explosion , 2014 .