Model predictive control for wormlike micelles (WLMs): Application to a system of CTAB and NaCl

Abstract Wormlike micelles (WLMs), which are the self-assemblies of amphiphilic surfactants, have gained attention in various applications due to their unique ‘living’ nature (i.e., union-scission). However, the industrial production of the WLMs has rarely been discussed. Moreover, given that the system hardly reaches the desired viscosity without appropriate control actions within a reasonable operation time, a model-based controller has been implemented to the production of WLMs where CTAB/NaCl in a semi-batch reactor is used as a case study. For this, a high-fidelity model was developed by integrating thermodynamic, kinetic, and rheology models and validated with experimental results. Subsequently, to alleviate the computational burden of such a high-fidelity model, the model reduction was carried out by the multivariable output error state space algorithm. The developed reduced-order model (ROM) was able to reproduce the essential features of the high-fidelity model and utilized in the formulated model predictive control (MPC) system. Herein, the manipulated variables (i.e., surfactant volume fraction, salt concentration, and temperature) are adjusted to give the desired WLM length of 3700 nm (i.e., a zero-shear viscosity of 100 Pa-s). Finally, the developed MPC scheme resulted in optimal input sequences to successfully reach the setpoint within practical constraints.