(199c) Model Predictive Control of Phthalic Anhydride Synthesis in a Fixed-Bed Catalytic Reactor Via Machine Learning Modeling

Modeling, control and optimization of fixed-bed reactors (FBRs) has long been an active research area for both academia and industry as FBRs are building blocks of the petrochemical and refining industries. FBRs with highly exothermic reactions give rise to some of the most challenging control problems in chemical engineering owing to extreme nonlinearity, nonlinear spatially-distributed dynamics, moving hot spots, high risk of thermal runaway, constraints on manipulated inputs and state variables, and limited on-line measurements with high uncertainty and long delays [1]. The development of high-fidelity first-principles models has been recognized by many and has led to the development of powerful computing platforms, i.e., computational fluid dynamic (CFD) solvers, such as ANSYS Fluent. However, the communication between CFD solvers and other computing platforms for real-time control has not yet been explored.

This work proposes a general framework for linking a state-of-the-art computational fluid dynamics (CFD) solver, ANSYS Fluent, and other computing platforms using the lock synchronization mechanism in an effort to extend the utilities of CFD solvers from strictly modeling and design to also control and optimization applications. To demonstrate the effectiveness of the proposed approach, a challenging control problem in chemical engineering, i.e., maximizing the product yield and suppressing the hot-spot temperature in a fixed-bed reactor (FBR) with a highly exothermic reaction, is considered. Specifically, phthalic anhydride (PA) synthesis is chosen for this investigation because of its industrial significance and its extreme high exothermicity.

Initially, a high-fidelity two-dimensional axisymmetric heterogeneous CFD model for an industrial-scale FBR is developed in ANSYS Fluent. Next, the CFD model is used to explore a wide operating regime of the FBR to create a database, from which recurrent neural network and ensemble learning techniques are used to derive a homogeneous ensemble regression model using a state-of-the-art application program interface (API), i.e., Keras. Then, a model predictive control (MPC) formulation that drives the process output to the desired set-point and suppresses the magnitude of the hot-spot temperature to avoid catalyst deactivation is developed using the ensemble regression model. Subsequently, the CFD model, the ensemble regression model and the MPC are combined to create a closed-loop system by linking ANSYS Fluent to PyIpopt (a robust optimization subroutine in python) via a message-passing interface (MPI) with lock synchronization mechanism. Finally, the simulation data generated by the closed-loop system are used to demonstrate the robustness and effectiveness of the proposed approach.

[1] Wu, W., and Huang, M. Y. Nonlinear inferential control for an exothermic packed-bed reactor: Geometric approaches. Chemical engineering science, 58, 2023-2034, 2003.

[2] Anastasov, A. I. An investigation of the kinetic parameters of the o-xylene oxidation process carried out in a fixed bed of high-productive vanadia–titania catalyst. Chemical engineering science, 58, 89-98, 2003.

[3] Wu, Z., Tran, A., Ren, Y. M., Barnes, C. S., Chen, S., and Christofides, P. D. Model Predictive Control of Phthalic Anhydride Synthesis in a Fixed-Bed Catalytic Reactor via Machine Learning Modeling. Chem. Eng. Res. & Des., 145, 173-183, 2019.