Introducing mechanistic kinetics to the Lagrangian Gibbs energy calculation

Pertti Koukkari (Corresponding Author), Risto Pajarre

Research output: Contribution to journalArticleScientificpeer-review

42 Citations (Scopus)

Abstract

The Gibbs free energy minimum is usually calculated with the method of Lagrangian multipliers with the mass balance conditions as the necessary subsidiary conditions. Solution of the partial derivatives of the Lagrangian function provides the equilibrium condition of zero affinity for all stoichiometric equilibrium reactions in the multi-phase system. By extension of the stoichiometric matrix, reaction rate constraints can be included in the Gibbsian calculation. Zero affinity remains as the condition for equilibrium reactions, while kinetic reactions receive a non-zero affinity value, defined by an additional Lagrange multiplier. This can be algorithmically connected to a known reaction rate for each kinetically constrained species in the system. The presented method allows for several kinetically controlled reactions in the multi-phase Gibbs energy calculation.
Original languageEnglish
Pages (from-to)1189-1196
Number of pages8
JournalComputers and Chemical Engineering
Volume30
Issue number6-7
DOIs
Publication statusPublished - 2006
MoE publication typeA1 Journal article-refereed

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Gibbs free energy
Reaction rates
Kinetics
Lagrange multipliers
Reaction kinetics
Derivatives

Keywords

  • Gibbs energy minimization
  • Lagrange multipliers
  • kinetic constraints
  • reaction rate
  • process modeling

Cite this

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title = "Introducing mechanistic kinetics to the Lagrangian Gibbs energy calculation",
abstract = "The Gibbs free energy minimum is usually calculated with the method of Lagrangian multipliers with the mass balance conditions as the necessary subsidiary conditions. Solution of the partial derivatives of the Lagrangian function provides the equilibrium condition of zero affinity for all stoichiometric equilibrium reactions in the multi-phase system. By extension of the stoichiometric matrix, reaction rate constraints can be included in the Gibbsian calculation. Zero affinity remains as the condition for equilibrium reactions, while kinetic reactions receive a non-zero affinity value, defined by an additional Lagrange multiplier. This can be algorithmically connected to a known reaction rate for each kinetically constrained species in the system. The presented method allows for several kinetically controlled reactions in the multi-phase Gibbs energy calculation.",
keywords = "Gibbs energy minimization, Lagrange multipliers, kinetic constraints, reaction rate, process modeling",
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Introducing mechanistic kinetics to the Lagrangian Gibbs energy calculation. / Koukkari, Pertti (Corresponding Author); Pajarre, Risto.

In: Computers and Chemical Engineering, Vol. 30, No. 6-7, 2006, p. 1189-1196.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Introducing mechanistic kinetics to the Lagrangian Gibbs energy calculation

AU - Koukkari, Pertti

AU - Pajarre, Risto

PY - 2006

Y1 - 2006

N2 - The Gibbs free energy minimum is usually calculated with the method of Lagrangian multipliers with the mass balance conditions as the necessary subsidiary conditions. Solution of the partial derivatives of the Lagrangian function provides the equilibrium condition of zero affinity for all stoichiometric equilibrium reactions in the multi-phase system. By extension of the stoichiometric matrix, reaction rate constraints can be included in the Gibbsian calculation. Zero affinity remains as the condition for equilibrium reactions, while kinetic reactions receive a non-zero affinity value, defined by an additional Lagrange multiplier. This can be algorithmically connected to a known reaction rate for each kinetically constrained species in the system. The presented method allows for several kinetically controlled reactions in the multi-phase Gibbs energy calculation.

AB - The Gibbs free energy minimum is usually calculated with the method of Lagrangian multipliers with the mass balance conditions as the necessary subsidiary conditions. Solution of the partial derivatives of the Lagrangian function provides the equilibrium condition of zero affinity for all stoichiometric equilibrium reactions in the multi-phase system. By extension of the stoichiometric matrix, reaction rate constraints can be included in the Gibbsian calculation. Zero affinity remains as the condition for equilibrium reactions, while kinetic reactions receive a non-zero affinity value, defined by an additional Lagrange multiplier. This can be algorithmically connected to a known reaction rate for each kinetically constrained species in the system. The presented method allows for several kinetically controlled reactions in the multi-phase Gibbs energy calculation.

KW - Gibbs energy minimization

KW - Lagrange multipliers

KW - kinetic constraints

KW - reaction rate

KW - process modeling

U2 - 10.1016/j.compchemeng.2006.03.001

DO - 10.1016/j.compchemeng.2006.03.001

M3 - Article

VL - 30

SP - 1189

EP - 1196

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 0098-1354

IS - 6-7

ER -