(250d) Advancing Polymerization Process Control: A Dnn-Accelerated Kmc for Multimodal Molecular Weight Distribution

Model predictive control (MPC) is renowned for its exceptional ability to guide multiple system variables to their respective set-points within the specified constraints [1]. To achieve the control objective, the use of various models – including a linear state-space model [2], stochastic partial differential equations [3], and simplified model with the method of moments [4] – has advanced the control capabilities. While such MPCs built on simplified models showed excellent control performance, there was an inevitable trade-off in the detail of information.

In the example of copolymerization processes, the end-product quality is determined by several factors, including the molecular weight distribution (MWD) and their monomeric configurations. In this regard, the kinetic Monte Carlo (kMC) algorithm has been widely used owing to its accurate and precise representation of the system from reactor to molecular scales. For example, the kMC model can capture both the full MWDs, including multi-modal distributions, and the monomeric configuration of existing polymer chains. Delicate control over these properties is essential for managing feedstock variability, but this becomes impractical without a high-fidelity model. However, embedding the standard kMC into the model-based control frameworks is still challenging due to limited computational efficiency in iterative calculations [3].

To address this issue, we identified the computationally demanding task within the kMC algorithm. While the algorithm requires the rates of each reaction in every time step to execute the events, evaluating the reaction rates takes a significant part of the computation time. Hence, we substituted this step with the deep neural network (DNN), trained to predict the reaction rates based on the current system configuration. This approach, which avoids scanning every polymer chain in the system, achieves a comparable improvement in computational efficiency to that reported in existing studies [5]. The simulation time was reduced to around 1% of the standard kMC simulation without sacrificing the simulation accuracy.

Consequently, we seamlessly incorporated the DNN-accelerated kMC scheme into the MPC framework. Notably, this novel control framework not only exhibited excellent performance but also retained the intricacy of the reacting system. To see its feasibility, we employed this framework in the lignocellulosic fractionation reactor and biopolymer production process. We achieved the delicate control of properties such as their full MWD and monomeric compositions, which provides richer information beyond the collective characteristics like the average values.

Literature cited:

[1] Morari M., & Lee J.H., (1999). Model predictive control: past, present and future. Comput. Chem. Eng., 23, 667-682.

[2] Kim J., Pahari S., Ryu J., Zhang M., Yang Q., Yoo C.G., & Kwon J.S.-I., (2024). Advancing biomass fractionation with real-time prediction of lignin content and MWd: A kMC-based multiscale model for optimized lignin extraction. Chem. Eng. J., 479, 147226.

[3] Lou Y., Hu G., & Christofides P.D., (2008). Model predictive control of nonlinear stochastic partial differential equations with application to a sputtering process. AIChE J., 54, 2065-2081.

[4] Bradford E., Reble M., & Imsland L., (2019). Output feedback stochastic nonlinear model predictive control of a polymerization batch process. 18^th European Control Conference, Naples, Italy, pp. 3144-3151.

[5] Fang Y., & Gao H., (2023). Scaling acceleration algorithm for hybrid kinetic Monte Carlo simulation of linear radical polymerization. Macromolecules, 56, 8484-8496.