# A hybrid mathematical model for a three-phase industrial hydrogenation reactor

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- DOI: 10.1016/s1570-7946(01)80042-0
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## Abstract

Publisher Summary This chapter presents a hybrid mathematical model to describe a three-phase reactor behavior that combines neural network architecture––as a predictor block for the liquid solid mass-transfer coefficient––and phenomenological equations describing the mass-conservation principle. The optimization procedure used in the network training was based on the Fletcher–Powell algorithm. Results of the network training and validation showed the predictive capacity of the proposed model and its great potential to be used as a support for process modeling and control. To explore the potentialities of the artificial neural network (ANN), two different approaches were tested: (i) standard ANN modeling (also called “black-box”), where ANN was used to represent the whole process behavior by mapping its input to output process data and (ii) hybrid ANN modeling, where ANN was used to predict the liquid–solid mass transfer coefficient that is a parameter for the determinist model. The hybrid neural network model is composed of two blocks. The ANN block estimates a process parameter––the liquid–solid mass transfer coefficient––which is used as input to the second block, represented by the deterministic equations of the process––mass and energy balance equations.

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