Cantera/Reaction Rate Source Terms

Notes

• Reaction rates are a functon of TPX, thermodynamic state of gas
• phase object wraps an equation of state and wraps kinetic object
• use phase to obtain reaction rates

• Definition of reaction rate
  • for a component: sum over each reaction rate

• Cantera phase object - calls
  • production rate for component i
  • production rate for reaction j
  • production rate for ij
  • species production rate for component i
  • species production rate for reaction j
  • species production rate for ij

Definition of Rates

Species Production Rate

In a differential, perfectly uniform control volume in which a chemical reaction is the only phenomena occurring, the species rate of production (species i) can be defined as the change in moles of i with time:

$ \frac{d c_i}{dt} = R_i \qquad i = 1 \dots N_{sp} $

where:

• $ c_i $ is molar volume (units of $ \frac{\text{mol}}{\text{m}^3} $)
• $ R_i $ is the volume-specific species rate of production (units of $ \frac{\text{mol}}{\text{m}^3 \text{s}} $)

Reaction Production Rate

A species production rate can be further broken up into its contributions from each reaction. These rates of production are stoichiometric and known as the reaction rates of production:

$ R_i = \sum_{j=1}^{N_{rxns}} \nu_{ij} \mathfrak{R}_j $

where:

• $ \nu_{ij} $ - stoichiometric coeff of species i in rxn j
• $ \mathfrak{R}_j $ - volume-specific stoichiometric reaction rate for reaction j

Phases

Gas Only: Volumetric Reaction Rates

Volumetric reaction rate is: (volume) x (rate of production per unit volume)

Rate of production per unit volume is: (stoichiometric coefficient) x (rate of production of reaction)

Gas and Surface: Surface Reaction Rates

Surface reaction rates are: (area) x (rate of production per unit area)

Rate of production per area is: (mass cat) x (surface area per mass cat) x (surface density of active sites) x (fractional coverage of surface species) x (rate of production of surface reaction)

See Cantera/Surface_Coverage