(110e) Multiscale Modeling of Porosity and Cell Wall Thickness of Wood Chips in Pulp Digester

Several efforts have been made over the last two decades to achieve a precise understanding of pulp digester to estimate the produced pulp quality [1-3]. However, the developed mathematical models are limited in describing the microscopic properties of wood, which include wood chip porosity and cell wall thickness (CWT), that ultimately affect paper attributes such as density, surface smoothness and stiffness [4-5]. Specifically, depending on the bending stiffness, tear strength and ink holdout of end-use paper, the paper type can range from a soft tissue to a cartonboard [5]. For the above reasons, a precise modeling of wood chip microscopic properties is required for the production of paper with desired properties in the pulping process.

Motivated by this consideration, we developed a multiscale model that is capable of describing both macroscopic and microscopic phenomena of the pulping process. Specifically, by integrating the most widely used mathematical model (i.e., the Purdue model) and a kinetic Monte Carlo (kMC) algorithm [2-3, 6-8], the evolutions of both the Kappa number (i.e., residual lignin content in pulp), wood chip porosity and CWT are described accurately. The mass and energy balance equations are computed through the Purdue model, whereas microscopic events such as dissolution of solid molecules are executed by the kMC algorithm. As a novel aspect of the proposed model, practical considerations like the water vessels and cell wall structure (e.g., chemical composition of cell wall layers) were considered in the simulation lattice to accurately describe the realistic evolutions of porosity and CWT of wood chips [9]. Furthermore, several other industrially important delignification processes can benefit from the proposed multiscale model. For example, biomass pretreatment and nanocellulose production are fundamentally identical with wood pulping as they also remove the lignin from lignocellulosic fibers [10]; the proposed multiscale model can be employed in these processes to enable molecular-level analysis and to accurately calculate the important factors that determines the product yield and quality such as cellulose digestibility and accessibility. The proposed multiscale model is also used to design a model predictive control system that drives the porosity, CWT and Kappa number to desired values.

References

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

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

[3] 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.

[4] Johansson A. Correlations between fibre properties and paper properties. Master's thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2011.

[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] Lee D.; Mohr A.; Kwon JSI. Kinetic Monte Carlo modeling of multivariant binding of CTB proteins with GM1 receptor. Comp. Chem. Eng., 2018, 118, 283-295.

[7] Kwon JSI.; Nayhouse M.; Christofides PD.; Orkoulas G. Protein crystal shape and size control in batch crystallization: Comparing model predictive control with conventional operating policies. Ind. Eng. Chem. Res., 2014, 53, 5002-5014.

[8] Choi HK.; Kwon JSI. Multiscale modeling and control of Kappa umber and porosity in a batch-type pulp digester. AIChE J. (In press), 2019.

[9] Rowell RM.; Pettersen R.; Tshabalala MA.; Handbook of wood chemistry and wood composites, second ed. CRC Press, Boca Raton, Florida. 2012.

[10] Nakagaito AN.; Yano H.; Novel high-strength biocomposites based on microfibrillated cellulose having nano-order-unit web-like network structure. Applied Physics A, 2005, 80, 155-159.