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Journal of Non-Equilibrium Thermodynamics

Founded by Keller, Jürgen U.

Editor-in-Chief: Hoffmann, Karl Heinz

Managing Editor: Prehl, Janett / Schwalbe, Karsten

Ed. by Michaelides, Efstathios E. / Rubi, J. Miguel

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1437-4358
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Volume 43, Issue 2

Issues

Systematic Constraint Selection Strategy for Rate-Controlled Constrained-Equilibrium Modeling of Complex Nonequilibrium Chemical Kinetics

An Automatable and Thermodynamically Consistent, Quasi-Equilibrium Model of Far Nonequilibrium States of Complex Reacting Systems Based on Probing the Fully Detailed Model and Taking a Truncated Singular Value Decomposition of the Resulting Evolution of the Degrees of Disequilibrium

Gian Paolo Beretta / Luca Rivadossi / Mohammad Janbozorgi
Published Online: 2018-03-17 | DOI: https://doi.org/10.1515/jnet-2017-0055

Abstract

Rate-Controlled Constrained-Equilibrium (RCCE) modeling of complex chemical kinetics provides acceptable accuracies with much fewer differential equations than for the fully Detailed Kinetic Model (DKM). Since its introduction by James C. Keck, a drawback of the RCCE scheme has been the absence of an automatable, systematic procedure to identify the constraints that most effectively warrant a desired level of approximation for a given range of initial, boundary, and thermodynamic conditions. An optimal constraint identification has been recently proposed. Given a DKM with S species, E elements, and R reactions, the procedure starts by running a probe DKM simulation to compute an S-vector that we call overall degree of disequilibrium (ODoD) because its scalar product with the S-vector formed by the stoichiometric coefficients of any reaction yields its degree of disequilibrium (DoD). The ODoD vector evolves in the same (S-E)-dimensional stoichiometric subspace spanned by the R stoichiometric S-vectors. Next we construct the rank-(S-E) matrix of ODoD traces obtained from the probe DKM numerical simulation and compute its singular value decomposition (SVD). By retaining only the first C largest singular values of the SVD and setting to zero all the others we obtain the best rank-C approximation of the matrix of ODoD traces whereby its columns span a C-dimensional subspace of the stoichiometric subspace. This in turn yields the best approximation of the evolution of the ODoD vector in terms of only C parameters that we call the constraint potentials. The resulting order-C RCCE approximate model reduces the number of independent differential equations related to species, mass, and energy balances from S+2 to C+E+2, with substantial computational savings when C ≪ S-E.

Keywords: model reduction in nonequilibrium thermodynamics; rate-controlled constrained equilibrium; RCCE constraints; degrees of disequilibrium; singular value decomposition; principal component analysis

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About the article

Received: 2017-09-28

Revised: 2018-02-08

Accepted: 2018-02-26

Published Online: 2018-03-17

Published in Print: 2018-04-25


Citation Information: Journal of Non-Equilibrium Thermodynamics, Volume 43, Issue 2, Pages 121–130, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204, DOI: https://doi.org/10.1515/jnet-2017-0055.

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