Multiscale modeling and control of Kappa number and porosity in a batch‐type pulp digester

Abstract

This work proposes a multiscale modeling and model-based feedback control framework for the delignification process in a batch-type pulp digester. Specifically, we focus on a hardwood chip in the digester and develop a multiscale model capturing both the evolution of microscopic properties such as the pore size and shape distributions in the solid phase and the dynamic changes in the temperature and component concentrations in the liquor phase. While the macroscopic model adopts the continuum hypothesis based on the Purdue model, a novel microscopic model is developed using a kinetic Monte Carlo algorithm, accounting for the dissolution of lignin, cellulose, and hemicellulose contacting the liquor phase. A reduced-order model was built to design a Luenberger observer for state estimation, which is then used to develop a model-based control system. The simulation results demonstrated that the proposed methodology was able to regulate both the Kappa number and porosity to desired values.

Multiscale modeling and multiobjective control of wood fiber morphology in batch pulp digester

“…In this work, a multiscale model for a batch pulp digester is established by improving the previously developed multiscale model 29,30 . Figure 1 clearly shows the pulping process is indeed a multiscale problem.…”

“…One novel aspect of this work is that important fiber morphological properties such as cell wall thickness and fiber length are microscopically described by integrating the macroscopic model with a microscopic model (i.e., kMC algorithm). Even though Choi and Kwon 29,30 successfully modeled and controlled the cell wall thickness evolution in a pulp cooking process, the fiber length evolution was not studied. It is important to note that the modeling of fiber length evolution is indeed a multiscale problem as the dimension of fiber length (mm) is much greater than that of cell wall thickness (μm).…”

Application of offset‐free Koopman‐based model predictive control to a batch pulp digester

“…However, these studies have a crucial limitation; specifically, only the evolution of macroscopic properties (i.e., temperature and concentration of components in wood chip and liquor phases) is studied without considering the microscopic properties of fibers (i.e., pore size, porosity, cell wall thickness [CWT], and fiber length), which directly influence the delignification rate in pulp digesters 17 and physical properties of paper products such as density, strength, and absorbability 18,19 . To handle this limitation, Choi and Kwon 20 developed a multiscale modeling framework for pulp digesters that combines a kinetic Monte Carlo (kMC) model 21–24 with the extended Purdue model, 25 which is the most commonly used macroscopic model for pulp digesters, to describe the evolution of microscopic attributes of fibers as well as that of macroscopic phenomena during pulping. Based on this multiscale modeling framework, Choi and Kwon 26 developed a multiscale model that tracks the CWT value of fibers and considers the fiber collapse phenomenon.…”

A computational approach to characterize formation of a passivation layer in lithium metal anodes

“…This requires a strong combination between the microscopic and macroscopic phenomena occurring in the battery. The existing literature shows that KMC simulations are powerful and versatile enough to tackle the above problem 12‐17 . This is possible because KMC describes spatio‐temporal evolution of chemical and biological systems at a reasonable computational cost 18‐22 .…”