Process design and optimization has been part of the dyn research portfolio for many years, starting from projects on the optimization of reactive distillation columns. Initially, rigorous mixed-integer nonlinear programming methods were applied, and robust model formulations were developed that ensured convergence for arbitrary initial values. Later, our focus shifted to memetic algorithms and to the support of process design in the early phase of process development.

**Memetic algorithms for flowsheet optimization**

In the work on the optimization of reactive distillation columns, it turned out that such optimization problems exhibit a significant number of different local optima. The combination of meta-heuristics (evolution strategies) and gradient-based local search algorithms in memetic algorithms was developed as a promising approach to the robust and efficient computation of many of these local optima. The evolution strategy performs a global search in the space of the discrete and continuous design decisions and a local rigorous optimization of the continuous design parameters improves the solution that is proposed by the evolutionary algorithm. The memetic algorithm has been applied successfully to the optimization of a process for the production of Methyl-tert-butyl-ether (MTBE) using a reactive distillation column with an optional external reactor.

Publications

Barkmann, S., Sand, G., Engell, S.: Modellierungsansätze für die Design-Optimierung von reaktiven Rektifkationskolonnen. Chemie Ingenieur Tech-nik.80, 2008, 107–117.

Urselmann M., Barkmann S., Sand, G., Engell, S.: A memetic algorithm for global optimization in chemical process synthesis problems. IEEE Trans. Evol. Comput, 15, 2011, 659–683.

Urselmann, M., Barkmann, S., Sand, S., Engell, S.: Optimization-based design of reactive distillation columns using a memetic algorithm. Comput. Chem. Eng., 35, 2011, 787–805.

Urselmann, M., Engell, S.: Design of memetic algorithms for the efficient optimization of chemical process synthesis problems with structural restrictions. Comput. Chem. Eng., 72, 2015, 87-108.

Design optimization by memetic algorithms coupled to Aspen Plus® process simulations

Design optimization by memetic algorithms is transferred to applications by the research project „CHEMAX – Maximization of the energy efficiency of chemical processes” funded by BMBF. Via ZEDO e. V., the dyn group collaborates in this project with divis intelligent solutions and SUPREN.

To improve the flexibility and the acceptance of the optimization software in industry, a memetic algorithm is coupled to the process simulator Aspen Plus® which provides large data-bases for physical properties and model libraries for many process units and facilitates setting up and simulating complex flowsheets. As Aspen Plus® does not provide information about derivatives, the gradient-based local optimization is replaced by a derivative-free method that is tailored to handle simulation failures and constraints. The robustness and the computation time needed for the optimization are improved by providing initial values for the simulation using data that was collected during the search.

Urselmann, M., Foussette, C., Janus, T., Tlatlik, S., Gottschalk, A., Emmerich, M., Bäck, T., Engell, S.: Derivative-Free Design Optimization of Chemical Pro-cesses by a Memetic Algorithm. Proc. of the UK Workshop on Computational Intelligence, Exeter, 2015.

Within the collaborative research center (SFB Transregio 63) *InPROMPT* funded by the German Research Foundation (DFG), the dyn group is developing methods and software for the optimization-based support of process design in the early phase of process development. The goal of the SFB Transregio InPROMPT is to develop novel liquid multiphase processes. Currently, the research focuses on the functionalization of long-chain olefins and esters.

The goal of the sub-project C1 “Model-based control of the development of novel chemical production processes“ is to provide information about which process alternatives are most promising in the presence of significant uncertainties in the available models, and what experimental work should be performed to reduce the uncertainty in those parameters which are most important for the design decisions.

**Two-stage stochastic programming formulation**

In order to deal with the model uncertainty and to take the operational degrees of freedom of the plant into account, the process synthesis problem is decomposed into two stages: In the first stage, the design decisions are taken considering a set of discrete uncertainties. In the second stage, it is assumed that the values of the uncertain parameters are known and that the operational degrees of freedom can be adapted to the real situation.

The resulting large-scale optimization problem is decomposed by stages and solved using a hybrid algorithm that employs local gradient-based optimization algorithms for the evaluation of the mass and energy balances and of the operational degrees of freedom.

**The flowsheet superstructure optimization tool FSOpt**

During the course of the InPROMPT project a novel computer tool called FSOpt was developed with the goal to provide an integrated development environment for chemical process superstructures. FSOpt provides the user with capabilities for graphical and text-based modeling, as well as the automatic translation of the models into source code fit for execution and export into commercial optimization tools like GAMS® or MATLAB®.

**Approximation of complex thermodynamic models in process synthesis**

For process optimization, predictive thermodynamic models are indispensable. The more complex the phenomena are, e.g. if miscibility gaps exist, the more important are high-quality thermodynamic models. An example of this class of models is the Perturbed-Chain Associating Fluid Theory (PC-SAFT). But these models often use algorithmic procedures to solve large sets of coupled nonlinear equations, which are not compatible with equation-based optimization. If the model is reformulated in algebraic form and integrated into the flowsheet optimization, the computational effort increases significantly. In order to integrate advanced thermodynamic models into optimization-based flowsheet optimization, surrogate models can be used. As an example, one of the reactions considered in the InPROMPT project is the hydroformylation of 1-Dodecene in a thermomorphic multicomponent solvent system. The reaction medium is a 6-component-system and the solubility of CO and H2 depends on pressure, temperature, and the composition of the liquid phase. Using a perceptron neural network fitted to solubility data calculated by the original PC-SAFT model, the mean relative deviations from the original model predictions are 0.05% for CO and 0.09% for H2, while the computation time per phase equilibrium is reduced from 1.5 s to 0.005 s.

Publications

Steimel, J., Harrmann, M., Schembecker, G., Engell, S.: A framework for the modeling and optimization of process superstructures under uncertainty. Chem. Eng. Sci., 115, 2014, 225–237.

Steimel, J., Engell, S.: Conceptual design and optimization of chemical processes under uncertainty by two-stage programming. Comput. Chem. Eng., 81, 2015, 200–217.

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