(716a) The Emerging Role of Multiscale Modeling and Process Control to Effectively Handle the Panic-Buying of Toilet Paper amid Coronavirus Pandemic

Over the last couple of decades, the global production volume of packaging paper has steadily increased and reached 235 million tons per year owing to an unprecedented growing rate of e-commerce across the world [1]. It is widely known that the fiber morphology such as fiber length and cell wall thickness regulates the mechanical properties (i.e., tensile and burst strengths of paper) of final paper products as the interfiber bonding area is determined by the morphology of fibers. [2-3]. Therefore, a specific fiber morphology is required for each paper product type (e.g., toilet paper, high quality printing paper, etc.). As shown in the recent historical pandemic case, where the demand in toilet paper has surged instantaneously [4], customers’ demands on paper products can drastically change, thereby suddenly changing the corresponding desired pulp morphology. In this case, pulp mills need to recalibrate digester operation to make a specific pulp morphology because of the fixed production capacity. While model-based control strategies may facilitate optimal operation by minimizing production of off-spec paper during this sudden (but in practice very frequent) transition, their application has been bottlenecked by the absence of accurate kinetic model that can explain the evolution of fiber morphology during continuous pulping processes [5-10].

Motivated by this limitation, we developed a multiscale model that is capable of describing both macroscopic and microscopic phenomena in a continuous pulp digester. Specifically, a set of nonlinear partial differential equations (PDEs) are solved using a finite difference approach, and a kMC algorithm is used to describe evolution of solid component concentrations, Kappa number, cell wall thickness and fiber length. Then, a reduced-order model is identified using the high-fidelity input/output data of the proposed multiscale model to handle the computational requirement of the developed model [11]. Additionally, as the nominal model predictive control (MPC) framework cannot handle an offset caused by set-point change, the identified model is augmented with a disturbance model to achieve offset-free reference tracking, followed by the design of an observer which estimates both states and disturbances based on the augmented model [12]. Lastly, the developed model is implemented to a model-based predictive controller to minimize the off-spec product in the transition period using the upper heating temperature as a manipulated input when the set-point has altered.

References

[1] U.S. Bureau of Labor Statistics. Producer Price Index by Commodity for Pulp, Paper, and Allied Products: Wood Pulp [WPU0911] Retrieved from FRED, Federal Reserve Bank of St. Louis. https://fred.stlouisfed.org/series/WPU0911. Accessed March 31, 2020.

[2] Dinwoodie JM. The relation between fiber morphology and paper properties. TAPPI J. 1965;48(8):440-447.

[3] Xu F.; Zhong X.; Sun R.; Lu Q.; Jones GL. Chemical composition fiber morphology, and pulping of P. bolleana lauche. Wood Fiber Sci. 2006; 38(3):512-519

[4] Kavilanz P. Toilet paper makers: 'What we are dealing with here is uncharted'. CNN Business, Retrieved from https://www.cnn.com. Accessed March 31, 2020.

[5] Facada MJ. Influence of Kraft paper quality on the performance of an industrial paper impregnation process. Ph.D. thesis, Universidade Tecnica de Lisboa, Lisboa, Portugal, 2015.

[6] Funkquist J. Grey-box identification of a continuous digester – a distributed-parameter process. Control Eng. Pract., 1997, 5, 919-930.

[7] Wisnewski PA.; Doyle FJ. Fundamental continuous pulp-digester model for simulation and control. AIChE J., 1997, 43, 3175-3192.

[8] Smith C. Studies of the mathematical modeling simulation and control of the operation of Kamyr continuous digester for the Kraft process. Ph.D. thesis, Purdue University, West Lafayette, IN, 1974.

[9] Bhartiya S.; Dufour P.; Doyle FJ. Fundamental thermal-hydraulic pulp digester model with grade transition. AIChE J., 2003, 49, 411-425.

[10] Choi HK.; Kwon JSI. Modeling and control of cell wall thickness in batch delignification. Comput. Chem. Eng. 2019, 128, 512-523.

[11] Chou CT.; Verhaegen M. Subspace algorithms for the identification of multivariable dynamic errors-in-variables model. Automatica, 1997, 33, 1857-1869.

[12] Maeder U.; Borrelli F.; Morari M. Liner offset-free model predictive control, Automatica, 2009, 45, 2214-2222.