(583e) An MILP-Based Operability Approach for Process Design, Intensification and Modularity of Nonlinear and High-Dimensional Energy Systems

Operability emerged as a tool for the selection of the necessary inputs to achieve specified desired outputs in a given process ^[1]. In a previously developed mixed-integer linear programming (MILP)-based operability approach ^[2], the operability concept was extended to attain process intensification towards obtaining modular designs for energy systems. While a computational time improvement was achieved, the developed framework is still restricted to computational geometry techniques applied in two-dimensional spaces. The extension of this approach to systems with input and output spaces of higher dimensions consists of a challenge that still remains to be addressed. High dimensions give rise to new concerns such as volume of simulated data and overall increase in algorithm computational complexity, potentially impacting the computational cost. In this work, an improved MILP-based operability framework is derived with the utilization of computational geometry techniques suitable for higher-dimensional and nonlinear systems. This presentation will be focused on the discussion of the feasibility of the new approach to produce intensified modular designs for energy systems applications.

Process operability has been successfully applied to high-dimensional and nonlinear systems by the utilization of nonlinear programming (NLP) tools ^[3]. Potential tractability issues associated with the high computational expense of nonlinear algorithms have been tackled with the employment of parallel computing ^[4]. In the proposed framework, the addressed high-dimensional and nonlinear system is decomposed into several linearized subsystems. These subsystems are obtained using spatial discretization techniques that produce a set of convex polytopes in each n-dimensional space. Then, an MILP optimization problem is formulated based on spatial search and barycentric interpolation. For this application, the goal of the optimization problem is to minimize physical size, satisfying all process constraints and intensification targets. The outcome of this optimization problem is a modular design of high efficiency, associated with the most intensified operating point. As MILP tools have higher computational efficiency than NLP tools, a single processor will be considered for the proposed framework calculations, in contrast to the parallel workers present in the NLP approach.

The developed framework will be tested and compared to past NLP approaches for two case-studies: a membrane reactor for the direct methane aromatization conversion to hydrogen and benzene and a natural gas combined cycle (NGCC) process. These systems are characterized by dimensionalities as high as 5x5 and 8x8 dimensions, respectively ^[4]. The trade-off between accuracy and computational cost will be discussed for the validation of the proposed framework when compared to NLP approaches for high-dimensional system extrapolations.

References

1. Vinson D. R. and Georgakis C. “A new measure of process output controllability”. J. Proc. Cont., 10(2-3), 185-194 (2000).
2. Gazzaneo V., Carrasco J.C. and Lima F. V. “An MILP-based operability approach for process intensification and design of modular energy systems.” Accepted for publication in Proceedings of Process Systems Engineering (PSE), July (2018).
3. 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).
4. Carrasco J.C. and Lima F. V. “Bilevel and parallel programming-based operability approaches for process intensification and modularity.” Accepted for publication in AIChE Journal. DOI10.1002/aic.16113 (2018).