(462c) Multi-Model Operability Approach for Process Design, Intensification and Modularity: Application to Nonlinear and High-Dimensional Membrane Reactors

Membrane reactors (MRs) have arisen as alternatives for conventional reactors, enabling previously economically unfavorable processes. MRs are also intensified processes that are candidates for modular applications. Such reactors provide a built-in membrane separation layer along the entire reactor length, where one or more reaction products can be selectively removed. This removal shifts the reaction equilibrium towards the products, increasing reactants conversion and production rate. However, the process design of MRs is intrinsically challenging. MRs combine chemical reactions with separation transport phenomena, which results in models of complex and nonlinear nature for their representation. MRs are also commonly placed in highly constrained environments, which poses an additional difficulty to the process design task, especially if process integration is needed for modularity. In this presentation, a multi-model operability approach is proposed to address these challenges. Operability was first introduced as a tool for the design and control interface to calculate the inputs that are needed to achieve specified desired outputs in a process ^[1]. Here, the operability pathway is extended to provide a framework able to tackle nonlinear high-dimensional and constrained systems. This framework attains process intensification, ensuring high efficiency units, suitable for modular systems applications.

In the past decades, process operability has been traditionally applied to low-dimensional nonlinear systems. The implementation of operability for high-dimensional nonlinear systems was successfully performed by employing optimization algorithms based on nonlinear programming (NLP) ^[2,3]. The novelty of this work derives from the fully utilization of linear programming (LP) tools to handle systems of the same complexity, with the advantage of computational time reduction. In particular, the original nonlinear system is divided into several subsystems and a linear model is calculated for each subsystem. The properties of all linear models are then analyzed, such as the eigenvalues (or singular values), so that the minimum number of model sets that adequately represents the process nonlinearity is obtained. A multi-level optimization algorithm is then formulated based on LP concepts, aiming intensification and control targets, while considering process requirements and constraints.

The developed framework is applied to a membrane reactor for the direct methane aromatization conversion (DMA-MR) to hydrogen and benzene. DMA-MR corresponds to a candidate system for modular natural gas utilization onsite at stranded gas fields without the need of building expensive pipelines ^[2]. Preliminary results for a low-dimensional system show that benzene production can be optimized and the membrane reactor footprint reduced by 60% in terms of volume (catalyst zone) and 80% in membrane area. These results indicate the potential of the proposed framework to facilitate process intensification towards modularity. In this presentation, a comparison will be established between this approach and previously developed NLP-based approaches ^[4] to analyze the trade-off between accuracy and computational expense. The expansion to a higher dimensional system will then be discussed, contemplating membrane parameters, design and operating conditions that are critical for process intensification and modularity.

References:

1. Vinson D. R. and Georgakis C. “A new measure of process output controllability”. J. Proc. Cont. 2000, 10(2-3), 185-194.
2. Carrasco J. C. and Lima F.V. “An optimization-based operability framework for process design and intensification of modular natural gas utilization systems”. Accepted for publication in Comput. Chem. Eng. 2017; DOI: CACE-5645.
3. Carrasco J. C. and Lima F. V. “Novel operability-based approach for process design and intensification: application to a membrane reactor for direct methane aromatization”. AIChE J. 2017; 63(3): 975-983.
4. Carrasco J.C. and Lima F. V. “Operability-based approach for process design, intensification, and control: application to high-dimensional and nonlinear membrane reactors”. In proceedings of the FOCAPO/CPC, 2017.