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The present work deals with the determination of the optimal operating conditions of lactic acid synthesis by the alkaline degradation of fructose. It is a complex transformation for which detailed knowledge is not available. It is carried out in a batch or semi-batch reactor. The ‘‘Tendency Modeling’’ approach, which consists of the development of...
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In the article a Multi-Step Solution Technique were used. This technique enables to translate a complex optimal control problem to easier
nonlinear programming problems. Efficiency of the designed algorithm was verified on a real-live optimal control problem of a stiff and highly nonlinear
differential-algebraic system with constraints. One of the al...
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... To accommodate such a lack of detailed understanding, our research group introduced the concept of Tendency Modelling (Fotopoulos, Georgakis, & Stenger, 1996, 1998 which has been applied to several processes with significant success. See for example (Cabassud et al., 2005;Martinez, 2005). On the other hand, François et al. (François, Srinivasan, & Bonvin, 2005) have also introduced a methodology in which the feedback control concept is used to evolve from an initial batch operation to operations that are incrementally better and, after several cycles, arrive at an optimum operation. ...
The new methodology presented provides a way to optimize the operation of a variety of batch processes (chemical, pharmaceutical, food processing, etc.) especially when at least one time-varying operating decision function needs to be selected. This methodology calculates the optimal operation without the use of an a priori model that describes in some accuracy the internal process characteristics. The approach generalizes the classical and widely used Design of Experiments (DoE), which is limited in its consideration of decision variables that are constant with time. The new approach, called the Design of Dynamic Experiments (DoDE), systematically designs experiments that explore a considerable number of dynamic signatures in the time variation of the unknown decision function(s). Constrained optimization of the interpolated response surface model, calculated from the performance of the experiments, leads to the selection of the optimal operating conditions. Two examples demonstrate the powerful utility of the method. The first examines a simple reversible reaction in a batch reactor, where the time-dependant reactor temperature is the decision function. The second example examines the optimization of a penicillin fermentation process, where the feeding profile of the substrate is the decision variable. In both cases, a finite number of experiments (4 or 16, respectively) lead to the very quick and efficient optimization of the process.
... The general procedure of optimization is formulated as the following [22]: ...
... The thermal flux evacuated out of the reactor is expressed by Eq. (22). It is proportional to a temperature difference between reacting solution and coolant fluid, exchange area and global heat transfer coefficient. ...
The condensation reaction of furfural (F) on acetone (Ac) gives a high added value product, the 4-(2-furyl)-3-buten-2-one (FAc), used as aroma in alcohol free drinks, ice, candies, gelatines and other products of current life. This synthesis valorises the residues of sugar cane treatment since furfural is obtained by hydrolysis of sugar cane bagasse followed by vapor training extraction. In the face of numerous and complex reactions involved in this synthesis, it is very complicated to define the kinetic laws from exact stoichiometry. A solution allowing to cope the problem consists in identifying an appropriate stoichiometric model. It does not attempt to represent exactly all the reaction mechanisms, but proposes a mathematical support to integrate available knowledge on the transformation. The aim of this work is the determination of stoichiometric and kinetic models of the condensation reaction of furfural on acetone. Concentrations of reagents and products are determined by gas and liquid chromatography. Concentration profiles obtained at different temperatures are used to identify kinetic parameters. The model is then used for the optimization of the production of FAc. The interest of such tool is also shown for the scale up of laboratory reactor to a large scale. The anticipation of the reaction behaviour in large scale is crucial especially when the reactor presents important limitations of thermal exchange capacity.
An unconventional modelling methodology based on artificial neural networks is proposed to rapidly develop a model from data obtained during different batch experiments.
The objective of the global model is to predict time evolution of concentrations of all species present in the reaction medium. For this, different recurrent neural networks are elaborated to estimate a particular species as a function of operating parameters and concentrations of all species and then assembled in a complex global model.
To validate the approach, the esterification reaction of methanol by acetic acid, which presents equilibrium, has been chosen. The kinetic evolution of the chemical species during experiments conducted in batch mode are correctly represented whatever the operating conditions. Finally, the global model based on neural networks is integrated in a hybrid model. This permits to transpose the reaction to a semi-batch chemical reactor which has not been considered during the learning phase.
A new methodology for the design of experiments is presented that provides a way to optimize the operation of a variety of batch and semibatch or fed-batch processes without the use of a knowledge-driven or fundamental model describing the inner workings of the process, when one or more time-varying decision variables must be selected. The types of processes that can benefit from this approach include those producing specialty chemical, pharmaceutical, or food products whose production rate is not high enough to justify the development of a knowledge-driven model. The approach generalizes the classical and widely used Design of Experiments (DoE), which considers only decision variables, or factors, which are constant with time. The new approach, called the Design of Dynamic Experiments (DoDE), systematically designs experiments that explore a considerable number of dynamic signatures, called dynamic subfactors (DSFs), in the time dependency of the unknown decision variables or factors. Two example processes—a batch nonisothermal reactor and a semibatch penicillin fermentation process—amply demonstrate the utility of the method. In both cases, a small number of experiments lead to the quick and accurate optimization of the process. The calculated optimal operating conditions through the proposed DoDE approach are only slightly different from the optimum that would have been obtained if a knowledge-driven model were available.
