Mathematical formulation

[Amirreza Hesabi Shotorbani]

Hello,

When using gas.equilibrate('TP') in Cantera, what is the underlying mathematical formulation and which solver does Cantera use? How can I access detailed information about these methods?

Thank you.

[Amirreza Hesabi Shotorbani]

Specifically, I am looking for the mathematical formulation of the Gibbs free energy and the objective function that is minimized during equilibrium calculations.

[Ray Speth]

Hi,

The calculation of the Gibbs free energy depends on the thermodynamic model selected and on how the thermodynamics of the individual species are parameterized. In probably the most common case, the thermodynamic functions of the ideal-gas model are used with 7-coefficient NASA polynomials describing the standard-state thermodynamics of each species.

In the case of equilibrium at constant temperature and pressure, the thermodynamic potential that is minimized is the Gibbs free energy of the mixture, calculated as the dot product of the species chemical potentials and the moles of each species. There are a few different equilibrium solvers present in Cantera, as described in the documentation. Which one is used will depend on options passed to the equilibrate method. The default behavior is to try the ChemEquil element potential solver first for problems where it is applicable, and then to fall back to the implementations of the VCS algorithm in the MultiPhaseEquil or vcs_MultiPhaseEquil classes.

Regards,
Ray

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