Dynamic Optimization of a Batch Reactor using capabilities of an MINLP process synthesizer MIPSYN
Systematic methods and tools for managing the complexity
Advances in Computational & Numerical Methods (T4-4P)
Keywords: Batch reactor, orthogonal collocation, NLP, MINLP, process synthesis
Abstract
This contribution describes the development of various strategies for the dynamic optimization of a batch reactor in order to obtain a robust model, suitable for nonlinear (NLP) or mixed-integer nonlinear programming (MINLP) problems. Different schemes of Orthogonal Collocation on Finite Element (OCFE) and various model formulations have been studied to increase the robustness of the model. Various strategies have been applied to NLP and MINLP models, and in addition, their efficiencies and robustnesses have been compared.
Scope
In a recent research (Ropotar and Kravanja, 2006) NLP and MINLP models were developed for the dynamic optimization of batch reactors. Differential-algebraic equations were converted into an algebraic system of equations by the use of Orthogonal Collocation on Finite Element (OCFE).
Different OCFE schemes with a fixed (NLP) or changing number of finite elements (MINLP), with moving or fixed finite elements, and with an end and/or inner optimal point in the Legendre polynomial representation are investigated in order to further increase the efficiency of the NLP and MINLP models. In the case of NLP optimization, the number of finite elements has to be set in advance and is thus usually oversized in order to satisfy a given error tolerance, whereas in the MINLP cases it is explicitly modeled in order to adjust it simultaneously during the optimization process to the minimal number of the elements. Finally, in the case of the MINLP model, the robustness of the model is studied with respect to the use of different model formulations rooted in disjunctive programming and convex hull representations. Different model formulations are then compared in order to find out which of them are more efficient and robust.
Conclusions
The results represent optimal time-operation (concentration, temperature, etc.) and control (utility) profiles, optimal raw material consumption, and optimal number of batches. The NLP model with a fixed number of moving finite elements is most suitable for the optimization of stand alone reactors even if the number of final elements is overestimated, whilst the disjunctive MINLP model could be more efficient for MINLP synthesis of reactors within the overall process schemes where it is important not to burden the NLP computation by carrying the unnecessary final elements through the MINLP iterations.
ROPOTAR M., KRAVANJA Z., Optimization of a Batch Reactor using NLP and MINLP. Proceedings of ICCMSE 2006, Chania, Crete, Greece, 27 October - 1 November 2006.
See the full pdf manuscript of the abstract.
Presented Tuesday 18, 13:30 to 15:00, in session Advances in Computational & Numerical Methods (T4-4P).
