Optimization of Syngas to Olefin (STO) Reactors Under Model 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. Starting from an equally spaced coarse grid and calculating the errors on non-collocation points, fixed elements are introduced at points where error constraints are violated and moving elements to determine optimal breakpoint locations. Finally, the spikes are detected and eliminated, in order to ensure that optimality conditions are satisfied. Embedded within a nonlinear optimization strategy, this approach 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 that extends the mixed-catalyst STO reaction mechanism in [4]. Moreover, a parallel experimental study to reaction mechanism is currently underway for better understanding and representation of the phenomena.

Finally, 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. Moreover, uncertainties in the form of confidence regions for the model parameters will be considered in the optimization problem for a robust reactor design. The two optimization approaches (graded bed and partial moving grid) will be applied to an evolving to STO reaction model, with updates due to possible changes in reaction mechanism as parallel experimental studies continue.

[1] D.L.S. Nieskens, A. Ciftci, P.E. Groenendijk, M.F. Wielemaker, A. Malek, I&EC Research, 56, 2722−2732 (2017)

[2] S. K. Mazidi, M. T. Sadeghi, M. A. Marvast, Chem. Eng. Technol. 2013, 36, No. 1, 62–72

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

[4] Alexey V. Kirilin, Joseph F. Dewilde, Vera Santos, Adam Chojecki, Kinga Scieranka, and Andrzej Malek, Ind. Eng. Chem. Res. 2017, 56, 13392-13401