(562d) Application of Discrete-Time Infinite-Dimensional Model for Optimal Control and Estimation of a Continuous Pulp Digester

In recent years, the interests of the pulp industry and academia have focused on simultaneously producing paper with superior grades and value-added chemicals, owing to the rise of e-commerce and emerging markets worldwide. This growth has led to a need for improved pulping efficiency to mitigate the negative environmental impact of the paper-making industry. Wood chips are important raw materials in this process, and also valuable resources for lignocellulosic biomass, which can be used as alternative fuels and green materials due to its renewable and sustainable nature [1] [2]. Hence, the development of an accurate dynamic model and reliable controllers for the digester system could have a significant impact on the quality and efficiency of the pulping process.

The digester system continuously cooks and washes wood chips from the chip storage before further refining them in the mill and paper-making operations. However, most of the delignification reaction occurs only after the wood chips and white liquor flow down into the subsequent cooking zone, where the mixture is heated to reaction temperatures achieved by liquor circulation through external heaters [3]. Hence, the temperature in the cooking zone is particularly crucial as it greatly affects the quality of the pulp, including the cooking degree and pulp viscosity. In general, the delignification process can be described by a system of nonlinear partial differential equations (PDEs) [4] [5]. Most of the existing contributions design the controller based on the approximated models which are obtained using model reduction or other approximation methods. Motivated by these considerations, this work aims at developing a reliable controller to optimize the temperature of the delignification reaction for cooking wood chips based on the infinite-dimensional properties of PDEs.

As usual in large chemical processes, measurements of process variables in pulping plants are limited and often noisy. Therefore, in this work, a model predictive controller consisting of a state estimator is designed for continuous pulp digester using infinite-dimensional control theories. The underlying model of interest in a pulp digester is modeled by a system of coupled hyperbolic PDEs and ordinary differential equations [6]. Output measurements are considered with delay due to the possible low sampling rate. The Cayley-Tustin transform is utilized to convert the continuous infinite-dimensional system into a discrete one without spatial discretization or model order reduction [7]. A numerical example is provided to demonstrate the feasibility and applicability of the proposed controller designs. The proposed design can be readily extended to the cases of accounting for multiple objective functions to achieve a good balance between biomass recovery and paper production grade.

References:

[1] D. Gavrilescu. Energy from biomass in pulp and paper mills. Environmental Engineering & Management Journal (EEMJ). 2008 Sep 1;7(5).

[2] J. Kim, S. Pahari, J. Sang-Il Kwon. Modeling Biomass Degradation with Multiscale kMC Simulations. In Energy Systems and Processes: Recent Advances in Design and Control 2023 Mar 17 (pp. 11-1). Melville, New York: AIP Publishing LLC.

[3] S. Bhartiya, P. Dufour, FJ. Doyle III. Fundamental thermal‐hydraulic pulp digester model with grade transition. AIChE journal. 2003 Feb;49(2):411-25.

[4] HK. Choi, SH. Son, J. Sang-Il Kwon. Inferential model predictive control of continuous pulping under grade transition. Industrial & Engineering Chemistry Research. 2021 Feb 24;60(9):3699-710.

[5] L. Ding, T. Gustafsson, A. Johansson. Model parameter estimation of simplified linear models for a continuous paper pulp digester. Journal of Process Control. 2007;17(2):115-127.

[6] L. Zhang, J. Xie, S. Dubljevic. Dynamic modeling and model predictive control of a continuous pulp digester. AIChE Journal. 2022 Mar;68(3):e17534.

[7] S. Dubljevic, and J.P. Humaloja. Model predictive control for regular linear systems. Automatica. 2020;119, p.109066.