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Exploiting the Gibbs‐Duhem equation in separation calculations
Author(s) -
Venkataraman S.,
Lucia Angelo
Publication year - 1986
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690320702
Subject(s) - gibbs–helmholtz equation , mathematics , iterated function , helmholtz equation , gibbs free energy , mathematical analysis , physics , thermodynamics , boundary value problem
Various ways of building quasi‐Newton matrix approximations that satisfy the special form of the Gibbs‐Duhem equation are studied. Partition symmetry, the separability of the functions in γ and in ϕ, and the method of iterated projections are used in order to develop thermodynamically consistent matrix approximations with good secant information. Many examples are presented which show that exploiting the special form of the Gibbs‐Duhem equation results in improved numerical performance. Ways of exploiting the Gibbs‐Helmholtz equation in addition to the special form of Gibbs‐Duhem equation, and thus the isobaric form of the Gibbs‐Duhem equation, are also discussed.