(744b) Handling Fiber-to-Fiber Heterogeneity in Pulp and Paper Industry Via Stochastic Multiscale Modeling and Model Predictive Control

Sang Hwan Son^1,2, Hyun-Kyu Choi^1,2, and Joseph Sang-Il Kwon^1,2

1) Artie McFerrin Department of Chemical Engineering, Texas A&M University College Station, TX

2) Texas A&M Energy Institute, Texas A&M University, College Station, TX

Contrary to the expectation that the demand for paper will decrease due to the development of the digital industry, the pulp and paper industry is steadily increasing [1]. Specifically, over the past decade, the global demand for document paper has decreased from 151 to 122 million tons per year as the display industry developed, but the demand for packaging paper has increased from 190 to 235 million tons per year because of online shopping booms [2]. As the plastic or styrofoam packaging materials are replaced with paper in accordance with eco-friendly policies, the pulp and paper industry is also expected to continuously grow. Therefore, to deal with the growing demand for various quality of papers, the need for maximizing yields and minimizing energy consumption in pulp and paper manufacturing processes has received much attention recently.

In order to manufacture pulp from a wood chip, the lignin component that adheres to cellulose microfibrils must be removed through a delignification process. The degree of delignification is expressed numerically through an index called Kappa number. The extended Purdue model, which considers mass transport and heat transfer phenomena during delignification via differential equations, has been widely used to describe macroscopic variables such as the process temperatures and concentrations at the solid, entrapped-liquor and free-liquor phases [3-5]. However, this macroscopic model was not able to explain the evolution of microscopic characteristics such as pore size distribution, porosity and cell wall thickness (CWT), while these attributes significantly affect the physical properties of the paper such as density, ink holdup, surface smoothness, strength and absorbability.

Recent studies proposed multiscale pulp digester models which integrate the kinetic Monte Carlo (kMC) algorithm (to describe the microscopic characteristics) with the extended Purdue model [6-8]. Although the proposed multiscale models are able to describe macroscopic and microscopic characteristics concurrently, they only studied the evolution of a single-fiber morphology without considering the fiber-to-fiber heterogeneity (e.g., variation in CWT and wood chip composition, etc. [9]); this heterogeneity is mainly due to the intrinsic source from stochastic fluctuations in dissolution kinetics and the extrinsic source from collection of fibers from multiple sources and recycling. In this study, we present a new multiscale modeling framework of batch pulp digester under fiber-to-fiber variation. Specifically, we run a number of kMC simulations in parallel by incorporating fiber-to-fiber heterogeneity via heterogeneous morphology evolution for each fiber and distributions of CWT and wood chip composition, while simultaneously running the Purdue model to describe the macroscopic variables. To effectively reduce the computational load of this parallel computation, we developed a novel coarse-grained kinetic Monte Carlo (CGMC) scheme, where neighboring microscopic particles are grouped together into coarse-grained (CG) cells (or meso-particles) [10,11]. More specifically, unlike the existing studies that consider a single dissolution event taking place at each solid lattice site separately, we simultaneously considered a number of dissolution events occurring at a group of solid lattice sites to reduce the computational requirement. Based on this multiscale pulp digester model, we designed a model-based control system to regulate the CWT as well as other macroscopic variables to desired set-point values.

REFERENCES

[1] Watson, A., (2019). Unit sales of printed books in the United States from 2004 to 2018 (in millions). Publishers Weekly Statistics, https://www.statista.com/statistics/422595/print-book- sales-usa/..

[2] (2019). Producer price index by commodity for pulp, paper, and allied products: wood pulp [WPU0911], U.S. Bureau of Labor Statistics, retrieved from FRED, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/series/WPU0911.

[3] Christensen, T., Albright, L.F., Williams, T.J., (1982). A Mathematical Model of the Kraft Pulping Process. Ph.D. thesis. Purdue University, West Lafayette, IN.

[4] 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.

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

[6] 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.

[7] Choi, H. K., & Kwon, J. S. I. (2019). Modeling and control of cell wall thickness in batch delignification. Computers & Chemical Engineering, 128, 512-523.

[8] Choi, H. K., & Kwon, J. S. I. (2020). Multiscale modeling and multiobjective control of wood fiber morphology in batch pulp digester. AIChE Journal, in press.

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

[10] Drews, T. O., Braatz, R. D., & Alkire, R. C. (2004). Coarse-grained kinetic Monte Carlo simulation of copper electrodeposition with additives. International Journal for Multiscale Computational Engineering, 2(2).

[11] Collins, S. D., Chatterjee, A., & Vlachos, D. G. (2008). Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level. The Journal of chemical physics, 129(18), 184101.