NDLI: Minimal state representation for open fluid-fluid reaction systems

Content Provider	IEEE Xplore Digital Library
Author	Bhatt, N. Amrhein, M. Srinivasan, B. Mullhaupt, P. Bonvin, D.
Copyright Year	2012
Description	Author affiliation: Dept. of Chem. Eng., Ecole Polytech. Montreal, Montreal, QC, Canada (Srinivasan, B.) \|\| Lab. d'Autom., Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland (Bhatt, N.; Mullhaupt, P.; Bonvin, D.) \|\| Online Control Ltd., Lausanne, Switzerland (Amrhein, M.)
Abstract	Reaction systems can be represented by first-principles models that describe the evolution of the states (typically concentrations, volume and temperature) by means of conservation equations of differential nature and constitutive equations of algebraic nature. The resulting models often contain redundant states since the various concentrations are not all linearly independent; indeed, the variability observed in the concentrations is caused by the reactions, the mass transferred between phases, the inlet and outlet streams. A minimal state representation is a dynamic model that exhibits the same behavior as the original model but has no redundant state. This paper considers the material balance equations associated with an open fluid-fluid reaction system that involves $S_{l}$ species, R independent reactions, $p_{l}$ independent inlets and one outlet in the first fluid phase (e.g. the liquid phase) and $S_{g}$ species, $p_{g}$ independent inlets and one outlet in the second fluid phase (e.g. the gas phase). In addition, there are $p_{m}$ species transferring between the two phases. The $(S_{l}+S_{g})-dimensional$ model is transformed to q = R + $2p_{m}$ + $p_{l}$ + $p_{g}$ +2 variant states and $S_{l}$ $+S_{g}$ -q invariant states. Then, using the concept of accessibility of nonlinear systems, the conditions under which the transformed model is a minimal state representation are derived. It will be shown that the minimal number of concentration measurements needed to reconstruct the full state without kinetic information is R + $p_{m}.$ The simulated chlorination of butanoic acid is used to illustrate the various concepts developed in the paper.
Sponsorship	IEEE Control Syst. Soc.
Starting Page	3496
Ending Page	3502
File Size	244043
Page Count	7
File Format	PDF
ISBN	9781457710957
ISSN	07431619
e-ISBN	9781457710964
e-ISBN	9781467321020
DOI	10.1109/ACC.2012.6315195
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-27
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Mathematical model Vectors Equations Nonlinear systems Kinetic theory Current measurement Transforms
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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