Processes 2023 , 11 , 809
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discuss how reaction conditions affect the cellulose DP . Additionally, there are few studies in the literature on using machine-learning-based predictive controllers for the pulping process to obtain optimal operating conditions and achieve desired paper properties. To address these limitations, we propose the development of a novel layered multiscale model that combines the kMC algorithm and extended Purdue model equations. This model aims to describe the temporal evolution of important paper properties, such as the Kappa number and cellulose DP . By building on a previously developed multiscale model, which describes the degradation of solid components at the mesoscale, we further modify it to model the depolymerization kinetics at the microscopic level. Specifically, we take into account that the degradation process occurs on a much faster time scale than depolymerization, and thus multiple depolymerization events occur over a single degradation event, thereby, resulting in a layered multiscale model. Realistic chemical process models, such as the proposed layered multiscale model, can be too complex to be solved in real-time operations. To overcome this challenge, machine learning (ML) and other system-identification methods are employed to learn mathematical models from data and discover patterns without explicit programming [29–32]. In this work, we construct a surrogate long short-term memory (LSTM)-artificial neural network (ANN) model using input–output data generated from the multiscale model by running it offline under different operating conditions [33–36]. We select the LSTM-ANN network to handle a combination of time-varying (i.e., temperature) and time-invariant (i.e., cooking time and NaOH concentration) inputs, which are commonly encountered in chemical processes, particularly the pulping process. LSTMs are known for accurately learning temporal dependencies in sequence data, while ANNs are better at extracting information from time-invariant features [37–39]. After obtaining an optimal network through hyperparameter tuning and overfitting analysis, the surrogate model is used as an internal evaluator in an LSTM-ANN-based model predictive controller (MPC). This controller is computationally more efficient as it utilizes a well-trained neural network to obtain the optimal input profiles and achieve the desired set-point values for the Kappa number and cellulose DP while considering the process constraints. The performance of the closed-loop controller is demonstrated through a representative case. The structure of this article is as follows: In Section 2, the mathematical model for the kraft pulping process is presented. In Section 3, the training of the LSTM-ANN model and the design of the controller are discussed. The results of the multiscale model and controller are presented in Section 4. Finally, our conclusions are presented in Section 5. 2. Layered Multiscale kMC Modeling of a Batch Pulp Digester The multiscale modeling framework is designed to describe the temporal evolution of microscopic properties (such as the Kappa number, cell morphology, pore size distribution, CWT, and cellulose DP ) and macroscopic properties (such as the temperature and con- centration profiles). The proposed model is built upon previous multiscale models [7,23] developed for the kraft pulping process, and further modified them to take into account the effect of both the degradation of wood solid components and the depolymerization of cellulose on the tensile strength of paper [14]. This is motivated by the understanding that these properties play a critical role in determining the quality and strength of the final paper product. The multiscale model comprises three phases: the solid, entrapped-liquor, and free- liquor phases as illustrated in Figure 2 [40]. The free-liquor phase represents the bulk liquor surrounding the chip phase, which comprises both the solid and entrapped-liquor phases. As the components of the solid phase react with those of the entrapped-liquor phase, they dissolve and transform into components of the liquor phase. The extended Purdue model is used to describe macroscopic phenomena, such as energy balance and mass transport, while microscopic properties, such as the Kappa number and cellulose DP , are described by kMC simulations [19,20]. The multiscale model captures the dynamic interaction between
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