Načrtovanje in sinteza kemijskih procesov z uporabo učinkovitih modelnih tehnik in rešitvenih strategij : doktorska disertacija

slovenian

doktorska dela

2009

Univerza v Mariboru, Fakulteta za kemijo in kemijsko tehnologijo

This PhD thesis deals with modelling techniques and strategies for solving synthesis problems, which give rise to complex models that are very difficult to solve, highly combinatorial, nonlinear, and/or non-convex. Therefore, more efficient strategies and methods have to be developed despite that several advanced methods, algorithms, and professional software tools already exist. In the first part of the PhD thesis, alternative convex hull formulation based on mixed-integer transformation is presented. Transformation of variables transforms zero-lower-bounded variables into nonzero-lower-bounded variables. Optimization is, thus, performed in narrowed lifted space of local variables (i.e. variables representing alternative process units). Therefore, variables with nonzero lower bounds can be used when solving mixed-integer linear (MILP) or nonlinear optimization (MINLP) problems. Using nonzero-lower-bounded variables division by zero and other mathematical singularities are avoided. Additionally, nonzero-lower-bounded variables are useful when variables cannot have non-zero values even when process unit is not selected (e.g. temperature and flow). Transformation of variables has been used for: i) transforming conventional convex hull into alternative convexhull and ii) transforming conventional OA algorithm into alternative one. Several studies were performed and three different large-scale synthesis problems were solved to compare the performance and efficiency of Big-M formulation, convex hull and alternative convex hull formulation. Preliminary results with the alternative convex hull representation indicate that the alternative convex hull representation is, in most cases, the most efficient with respect to the non-linear programming (NLP) and MILP steps. The results indicate that the selection of arbitrarily-forced values to which local variables are fixed when the corresponding alternatives are rejected is very important. An inappropriate selection of these values could severely decrease the efficiency of the MINLP search. Most likely the best and the most obvious choice for arbitrarily-forced value is lower bound. Alternative formulation and outer approximation algorithm were implemented in the process synthesizer MIPSYN and, additionally, new logical interconnection nodes have been modelled and new pre-processor for outer approximation was programmed. Longer solution times of process synthesis problems are often a result of complicated reactor models. Therefore, efficient numerical procedure for solving reactor problems with orthogonal collocation was proposed. Within the procedure, the model for dynamic optimization of a batch reactor was developed and, additionally, different schemes and strategies utilized in order to increase the model's robustness. Finally, a batch reactor model for the design under uncertainty was developed. In the case of the motivating example of a batch reactor, the most efficient model was the one with moving finite elements. This model was then used to model the train of reactor elements in the plug flow reactor, and MINLP synthesis of allyl chloride production was performed. Additionally, the economic region was obtained by the one-parametric optimization. Using the proposed alternative formulation, new strategies and robust models for optimization of reactors, solving complicated synthesis models is now possible; moreover, process synthesizer MIPSYN was efficiently upgraded to solve process synthesis and other engineering problems.

07.08.2023