| Affiliation: | 1. Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada Contribution: Conceptualization (equal), Formal analysis (lead), Investigation (equal), Methodology (lead), Software (lead), Writing - original draft (lead), Writing - review & editing (equal);2. Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada |
| Abstract: | In this work, we propose a /methodology for the selection and refinement of finite elements for the integration of process design and control. The proposed methodology is based on the selection criteria of the Hamiltonian function through the implementation of the Pontryagin's minimum principle. The Hamiltonian function features to be continuous and constant over time for autonomous systems; nevertheless, the Hamiltonian function shows a nonconstant profile for underestimated discretization meshes, which is exploited in this work for the refinement of the discretization. Furthermore, the residuals at noncollocation points are evaluated to estimate the collocation error, this is used as a second refinement criterion in the proposed framework. The methodology is illustrated using two case studies featuring a reaction system with two CSTRs in series and the Williams–Otto reactor, respectively. The results showed that an accurate selection of the finite elements return economically attractive designs with fewer elements than those obtained with equidistributed finite element strategies. |
