(461b) Multiobjective Control of Fiber Morphology in Pulping Process Via Multiscale Modeling

It is well known that the mechanical properties of paper products are mainly dependent upon the morphological characteristics of wood pulp due to the interfacial adhesion of individual fibers [1]. Particularly, cell wall thickness and length of fibers are important parameters as they are closely related to the tensile and burst strengths of final paper products [1-2]. Despite the importance of fiber morphology, the regulation of fiber morphology to desired values during pulping process has not been enabled because of two challenges. First, even though wood fibers undergo broad morphological changes under conditions of Kraft pulping, online measurements of the properties are unavailable due to the harsh operating conditions such as high cooking temperature and corrosive liquor. Second, given the increasing PPI’s (Pulp and Paper Industry) reliance on model-based technology to optimally adjust the process while conforming the strengthened environmental regulation, several kinetic models have been developed to describe the kinetics and transport behavior of the Kraft pulping process [3-9]. Nevertheless, as the models are derived from macroscopic equations (i.e., differential equations) that are proven to fully capture the bulk phase dynamics, they come with an inbuilt weakness; elementary mechanisms that occur on very small scales such as degradation of cell wall and fiber breakage are hardly described by them.

Motivated by the limitations, in this work, a multiscale model is developed to simulate the evolution of fiber morphology in a pulp digester. Specifically, by integrating the most widely used mathematical model for pulping process (i.e., the Purdue model) with a kinetic Monte Carlo (kMC) algorithm, the evolution of both the Kappa number (i.e., residual lignin content in pulps), and fiber morphology (i.e., cell wall thickness and fiber length) are accurately captured; degradation events of cell wall components are executed based on the kMC algorithm, and the pit distribution and fiber breakage probability model are utilized to compute the fiber length. Then, a reduced-order model is identified using the high-fidelity input/output data from the proposed multiscale model to handle the computational requirement of the developed model [10]. While incorporating the developed multiscale model into a model-based controller design, an interesting process control problem is found; particularly, simultaneously driving both the Kappa number and fiber length is infeasible as they are two conflicting objectives. In order to accomplish the low Kappa number which is typically required from most of paper grades, it is unavoidable to produce fibers with thin cell wall thickness, which in turn leads to fiber breakage. Therefore, we employed the epsilon-constraint method to find the Pareto optimal solutions which allow decision makers to choose a preferred operating condition depending on a target product quality. Based on the optimal solutions, a model-based controller is designed to achieve them while minimizing the heat usage during Kraft pulping.

References

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