2020 Young Investigator Grant Winner Report

Multiscale modeling and model predictive control of pulp digester

The pulp and paper industry is undergoing rapid modernization and is ripe for disruption. In fact, despite a decline in graphic paper demand due to digitalization, the demand for packing paper has seen a steady rise due to changing customer preferences toward online shopping resulting in an overall increase. Moreover, in the aftermath of the recent pandemic, since the demand on certain paper products (e.g., toilet tissue and hygienic paper) has skyrocketed, swift grade changes were required for pulp digesters. In Kraft pulping processes, more than 90% of chemical pulp is produced, and the grade transitions can take a long time to complete, which may lead to production of a large amount of off-grade pulp [2]. To deal with such growing paper demand and economic loss due to frequent grade changes, modernization and intensification of the PPI have received much attention, which may provide enormous opportunities for maximized efficiency and optimized energy usage. To this end, strong efforts have been allocated to develop process modeling and control framework for the pulping process in the past decades [3, 4].

However, even though previously developed kinetic models and control schemes have significantly contributed to the optimization and process control of pulp digesters, they have an inbuilt limitation as they only considered macroscopic equations; important paper properties such as density, ink holdout, surface smoothness, strength and absorbability are inherently dependent on the fiber morphology (e.g., fiber length and cell wall thickness) (Figure 1) [5]. Therefore, microscopic properties of pulp were not accurately captured by conventional approaches (i.e., mathematical models), thereby necessitating a robust kinetic model that can explain the variation of the fiber morphology change during the pulping process. Furthermore, recently, fibers are collected from unconventional sources (i.e., recycled fibers) and combined with virgin fiber during pulping, which may lead to fiber-to-fiber heterogeneity [6]. Although the heterogeneous characteristics must be properly regulated to produce pulps with constant quality, the conventional models are limited in describing the multiscale nature of pulping dynamics (Figure 2). While several model-based process control approaches have been proposed particularly for pulp digesters, the absence of such a robust model is critical as the performance of a model-based control framework is highly dependent on the accuracy of employed models. 

Motivated by the limitation, we developed a multiscale model of pulp digester to describe the evolution of fiber length during the pulping process [7 – 9]. Specifically, one of the widely employed pulping model (i.e., extended Purdue model) that captures the macroscopic phenomena (i.e., mass and energy transfer) was hybridized with a kinetic Monte Carlo (kMC) algorithm to capture microscopic events during the thermal degradation of wood chips. A set of nonlinear partial differential equations (PDEs) that depicts macroscopic dynamics in a continuous pulp digester was numerically solved by the finite difference method (FDM), and a kMC algorithm was employed to execute microscopic events such as degradation of the solid components in wood chips. The developed multiscale model was extensively validated by comparing against experimental data under identical operating conditions. Then, a soft sensor was developed via Kalman filtering to infer the state variables and primary measurement (i.e., blow-line Kappa number and cell wall thickness) by utilizing the secondary measurements. Lastly, an inferential offset-free model predictive control system was designed to regulate both the macroscopic and microscopic properties of pulp, and to achieve an optimal grade transition. Ultimately, the developed multiscale modeling and control framework will accelerate manufacturing innovation in the PPI. In addition, the new knowledge created by the proposed research will lower breakeven price with respect to paper and drive growth towards sustainable operations by making efficient use of renewable resources (i.e., lignocellulosic biomass). As such, it will improve manufacturing efficiencies, leading to reduced waste production, harmful emissions, and fossil fuel consumption.

References

[1] Särkkä, T., Gutiérrez-Poch, M., & Kuhlberg, M. (Eds.). (2018). Technological transformation in the global pulp and paper industry 1800–2018: comparative perspectives (Vol. 23). Springer.

[2] Bhartiya, S., Dufour, P., & Doyle III, F. J. (2003). Fundamental thermal‐hydraulic pulp digester model with grade transition. AIChE journal, 49(2), 411-425.

[3] Wisnewski, P. A., Doyle III, F. J., & Kayihan, F. (1997). Fundamental continuous‐pulp‐digester model for simulation and control. AIChE journal, 43(12), 3175-3192.

[4] Galicia, H. J., He, Q. P., & Wang, J. (2011). A reduced order soft sensor approach and its application to a continuous digester. Journal of Process Control, 21(4), 489-500.

[5] Brändström, J. (2001). Micro-and ultrastructural aspects of Norway spruce tracheids: a review. IAWA journal, 22(4), 333-353.

[6] Lindström, H. (1997). Fiber length, tracheid diameter, and latewood percentage in Norway spruce: development from pith outward. Wood and Fiber Science, 29(1), 21-34.

[7] Choi, H. K., & Kwon, J. S. I. (2019). Multiscale modeling and control of Kappa number and porosity in a batch‐type pulp digester. AIChE Journal, 65(6), e16589.

[8] Choi, H. K., Son, S. H., & Sang-Il Kwon, J. (2021). Inferential Model Predictive Control of Continuous Pulping under Grade Transition. Industrial & Engineering Chemistry Research, 60(9), 3699-3710..

[9] Son, S. H., Choi, H. K., & Kwon, J. S. I. (2020). Multiscale modeling and control of pulp digester under fiber-to-fiber heterogeneity. Computers & Chemical Engineering, 143, 107117.