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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.

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The growing demand for various types of paper highlights the importance of optimizing the kraft pulping process to achieve desired paper properties. This work proposes a novel multiscale model to optimize the kraft pulping process and obtain desired paper properties. The model combines mass and energy balance equations with a layered kinetic Monte Carlo (kMC) algorithm to predict the degradation of wood chips, the depolymerization of cellulose, and the spatio-temporal evolution of the Kappa number and cellulose degree of polymerization (DP). A surrogate LSTM-ANN model is trained on data generated from the multiscale model under different operating conditions, dealing with both time-varying and time-invariant inputs, and an LSTM-ANN-based model predictive controller is designed to achieve desired set-point values of the Kappa number and cellulose DP while considering process constraints. The results show that the LSTM-ANN-based controller is able to drive the process to desired set-point values with the use of a computationally faster surrogate model with high accuracy and low offset.

Even though it is widely known that mechanical properties of papers are dependent upon fiber morphology such as fiber length and cell wall thickness, existing macroscopic models are limited in describing the microscopic traits of pulp. Thus, we proposed a multiscale model by integrating a macroscopic model (i.e., Purdue model) and a microscopic model (i.e., kinetic Monte Carlo algorithm) to capture the dynamic evolution of the fiber morphology as well as conventional pulp quality index such as Kappa number. Then, a reduced‐order model is identified to handle the computational requirement of the multiscale model, and implemented to a model‐based controller to regulate both the fiber length and the Kappa number which are expressed in the forms of conflicting objective functions. The epsilon‐constraint method is employed to find the Pareto optimal sets to provide decision makers with the degree of freedom to choose one according to their preferred end‐use paper properties.

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Even though continuous pulp processes have been studied for many years, the absence of a model that can accurately describe the evolution of fiber morphology has impeded the application of advanced control techniques. In this study, a multiscale model for continuous Kraft pulping processes, which can capture the spatiotemporal evolution of wood chips and cooking liquor, is developed by integrating a macroscopic model (i.e., Purdue model) with a microscopic model (i.e., kinetic Monte Carlo algorithm). Then, an approximate model is identified to circumvent the high computational requirement of the multiscale model and to handle the input time-delay, followed by designing a soft sensor to infer state variables and primary measurements. This allows the use of an inferential model predictive control strategy in a continuous pulp digester to regulate the blow-line pulp properties (i.e., Kappa number and cell wall thickness) and achieve optimal grade transitions.

This work presents the application of a Koopman operator approach to a batch pulp digester. To manufacture paper products with desired properties, it is essential to consider both macroscopic and microscopic attributes of pulp. However, the complexity of multiscale dynamics of pulping processes hinders proper control system design. Therefore, we utilize extended dynamic mode decomposition (EDMD), which is based on Koopman operator theory, to derive a global linear representation of a pulp digester. Then, we design an offset‐free Koopman‐based model predictive control (KMPC) system to regulate the Kappa number and cell wall thickness (CWT) of fibers at a batch pulp digester while compensating for the influence of plant‐model mismatch and disturbance during operation. The numerical experiments demonstrate that the linear state‐space model, obtained via EDMD, properly predicts the behavior of a batch pulp digester, and the designed offset‐free KMPC system successfully drives the Kappa number and CWT to set‐point values.