(105h) Application of Model Predictive Control to Wormlike Micelles Production: A Case Study of CTAB and NaCl
AIChE Annual Meeting
2021
2021 Annual Meeting
Computing and Systems Technology Division
Advances in Process Control I
Monday, November 8, 2021 - 2:43pm to 3:02pm
Model predictive control (MPC) has been widely employed in chemical processes such as polymer production as it can efficiently handle complex multi-input-multi-output problems with constraints [5]. Specifically, viscosity, as one of the crucial polymer properties, can be regulated to acquire the desired rheology of the final polymer products. Although the MPC control techniques have been widely implemented in industrial applications to control such variables [6], no studies have been executed regarding the control of the WLMs production. Moreover, owing to the unique âlivingâ nature (i.e., dynamic union and scission) of the WLMs, it is infeasible to directly extend the control strategies of conventional polymers to the production of WLMs.
Hence, in this work, a MPC scheme which elucidates the dynamic behavior of the WLMs was formulated and applied to a CTAB and NaCl system as a case study. First, a mathematical model was developed by integrating a kinetic micelle growth model [7,8], a thermodynamic model [9], and a tube-reptation-based rheology model [10]. Subsequently, in order to alleviate the high computational complexity of the integrated model, a state-space model was derived and employed in developing the model-based control system. Herein, the manipulated variables are surfactant concentrations, salt concentrations, and temperature to attain the target viscosity. In addition, a state estimator was implemented in the control loop since online measurement of viscosity was not presented in this system. Consequently, this feedback controller is capable of obtaining the required input sequences to attain the target viscosity of the WLMs.
Keywords: Wormlike micelle (WLM); model predictive control (MPC); reduced-order model (ROM)
References
[1] Nagarajan R, Ruckenstein E. Theory of Surfactant Self-Assembly: A Predictive Molecular Thermodynamic Approach. Langmuir 1991;7:2934â69. https://doi.org/10.1021/la00060a012.
[2] Jiang Yang. Viscoelastic wormlike micelles and their applications. Curr Opin Colloid Interface Sci 2002;7:276â81.
[3] Feng Y, Chu Z, Dreiss CA. Smart Wormlike Micelles Design , Characteristics and Applications. 2015.
[4] Chu Z, Dreiss CA, Feng Y. Smart wormlike micelles. Chem Soc Rev 2013;42:7174â203. https://doi.org/10.1039/c3cs35490c.
[5] Lee JH. Model predictive control: Review of the three decades of development. Int J Control Autom Syst 2011;9:415â24. https://doi.org/10.1007/s12555-011-0300-6.
[6] Bindlish R. Nonlinear model predictive control of an industrial polymerization process. Comput Chem Eng 2015;73:43â8. https://doi.org/10.1016/j.compchemeng.2014.11.001.
[7] Lund R, Willner L, Monkenbusch M, Panine P, Narayanan T, Colmenero J, et al. Structural observation and kinetic pathway in the formation of polymeric micelles. Phys Rev Lett 2009;102:1â4. https://doi.org/10.1103/PhysRevLett.102.188301.
[8] Jensen GV, Lund R, Gummel J, Monkenbusch M, Narayanan T, Pedersen JS. Direct observation of the formation of surfactant micelles under nonisothermal conditions by synchrotron SAXS. J Am Chem Soc 2013;135:7214â22. https://doi.org/10.1021/ja312469n.
[9] Danov KD, Kralchevsky PA, Stoyanov SD, Cook JL, Stott IP. Analytical modeling of micelle growth. 2. Molecular thermodynamics of mixed aggregates and scission energy in wormlike micelles. J Colloid Interface Sci 2019;551:227â41. https://doi.org/10.1016/j.jcis.2019.05.017.
[10] Zou W, Larson RG. A mesoscopic simulation method for predicting the rheology of semi-dilute wormlike micellar solutions. J Rheol (N Y N Y) 2014;58:681â721. https://doi.org/10.1122/1.4868875.