(105h) Application of Model Predictive Control to Wormlike Micelles Production: A Case Study of CTAB and NaCl

Wormlike micelles (WLMs) are one of the supramolecular self-assemblies, which are elongated aggregates of amphiphilic surfactants in polar solvents [1]. Owing to the entanglements of the chains, these threadlike nanostructures exhibit remarkable viscoelasticity and thus have gained extensive research and industrial attention [2]. Specifically, in this non-covalent system, the WLMs continuously break and recombine, enabling instantaneous change in rheological properties via various external stimuli such as pH, salt concentration, temperature, and light [3]. Recently, such responsive WLMs have been employed in a broad range of industrial applications, for instance, personal care products, enhanced oil recovery, and pharmaceuticals [4]. Moreover, with the increasing demands of these macromolecular end-products, an advanced control technique can be utilized to produce the WLMs with desired properties.

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 ‘living’ 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

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