(187d) Multiscale Modeling of Pulp Fiber Length in Batch Pulping Process

During the last two decades, several efforts have been made to recover fibers from used paper and increase the recycling rate, thus achieving a recycling rate of 64.7 percent (paper and paperboard product) in the United States [1]. However, paper products cannot be recycled permanently as the fiber length will be shortened after every recycling process and eventually become too short to make papers (generally, recycle up to six times). Since the fiber length governs the interfiber bonding capability which is associated with tensile and burst strengths of paper, the shortened fibers cannot be the source of high quality paper but can be used for newspaper or egg cartons [2-4]. Accordingly, a precise modeling of fiber length is required to elucidate its evolution during the pulping process which may increase the paper recycling efficiency. However, the existing mathematical models are limited in describing the evolution of pulp microscopic properties such as fiber length, cell wall thickness (CWT) and porosity [5-7].

Motivated by this limitation, we developed a multiscale model that is capable of describing both macroscopic and microscopic phenomena of the batch pulping process. Specifically, by integrating the most widely used mathematical model for pulping process (i.e., the Purdue model) [8] and a multiscale coarse-grained Monte Carlo (CGMC) algorithm [9], the evolution of both the Kappa number (i.e., residual lignin content in pulp), fiber length and CWT are captured accurately. The mass continuity and thermal energy balance equations are adopted from a modified “extended Purdue model”, and microscopic events such as dissolution of solid molecules are executed by the kinetic Monte Carlo algorithm [10-11]. Since the fiber length (mm) and CWT ( ) have different length scales, multiscale CGMC algorithm is implemented to calculate the probability density function of both the fine-grid and coarse-grid scales by separately operating two lengths and two time scales. Additionally, as a novel aspect of the proposed model, practical considerations like the water vessels and cell wall ultrastructure (e.g., chemical composition of cell wall layers) of wood chip were considered in the simulation lattice to precisely describe the realistic evolution of aforementioned microscopic properties. Furthermore, several other important fiber morphological parameter measurements can be estimated by the proposed multiscale model. For example, an increase in fines is generally observed during the recycling operation which can improve strength by improved interfiber bonding capability. However, only indirect determination methods are available, providing a potential application to our proposed model as a soft sensor for the properties that are not measured real-time.

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