(586g) Optimization Modeling for Advanced Syngas to Olefin Reactive Systems Under Parameter Uncertainty

Reactor designs with mixed catalysts play an important role transforming a multiple reactor system to single-shot reactors. In addition to savings in capital and ease of implementation, single-shot reactors are useful to break equilibrium limitations, therefore increasing the yield and selectivity of desired product as shown in [1, 2]. However, the nonlinear and highly exothermic nature of mixed-catalyst systems makes it difficult for commercial process simulation and optimization tools to optimize these systems. This talk describes the development and application of optimization strategies for mixed-catalyst, single-shot reactors for syngas to olefin (STO) processes.

Finding the optimal catalyst distribution is challenging and requires advanced solution strategies for singular optimal control problems, which are poorly conditioned and often lead to flat response surfaces. The graded bed approach is applicable to these problems for preliminary results, but more sophisticated solution approaches are needed in order to find the exact optimal profiles. To determine these profiles, we develop a partial moving finite element approach, which decreases the complexity and solution times significantly compared to previous singular optimal control optimization strategies [3].

The resulting optimal control strategy is applied to a comprehensive STO reaction mechanism with detailed rate expressions. However, the experimentally obtained kinetic parameters come with some level of uncertainty due to measurement and estimation errors. If not considered, the uncertainty in the parameters may lead to violations in hard constraints, like thermal runaways or bad product quality. Nominal control of the STO problem cannot account for the parameter uncertainty and thus, robust optimization algorithms are needed. A two-stage multi-scenario approach is implemented to the STO problem [4]. In the first stage, the optimal control profile is found given a certain number of scenarios. With the fixed control profile, the largest sum of constraint violations is solved in the second stage. The scenario corresponding to the largest violation is added to the problem in the first stage, and the algorithm stops when no constraints are violated in the second stage.

The overall goal of this RAPID project is to find the optimal catalyst mixing ratio along the bed for the mixed catalyst STO reactor, respecting safety constraints, like avoiding thermal runaways. The two optimization approaches (graded bed and partial moving grid) are applied to the STO reaction model. Moreover, uncertainties in the form of confidence regions for the model parameters will be considered in the optimization problem for a robust reactor design.

[1] D. L. S. Nieskens, A. Ciftci, P. E. Groenendijk, M. F. Wielemaker, A. Malek, “Production of Light Hydrocarbons from Syngas Using a Hybrid Catalyst” I&EC Research, 2017

[2] S. K. Mazidi, M. T. Sadeghi, M. A. Marvast, “Optimization of Fischer‐Tropsch Process in a Fixed‐Bed Reactor Using Non‐Uniform Catalysts” Chem. Eng. Technol., 2013

[3] W-F. Chen, L. T. Biegler, “A Simultaneous Approach for Singular Optimal Control Based on Partial Moving Grid" AIChE Journal, 2019

[4] Y. Wang, L. T. Biegler, M. Patel, J. Wassick, “Robust Optimization of Solid-Liquid Batch Reactors under Parameter Uncertainty” Chemical Engineering Science, 2020