Reaction Rates#
Here, we describe how Cantera calculates chemical reaction rates for various reaction types.
Elementary Reactions#
The basic reaction type is a homogeneous reaction with a pressure-independent rate coefficient and mass action kinetics. For example:
where A and B are reactant species, C and D are product species, and
The forward reaction rate is then calculated as:
where
YAML Usage
An elementary reaction with an Arrhenius reaction rate can be defined in the YAML format
using the elementary
reaction type
, or by omitting the
reaction type
entry, as it represents the default. An exception to this default is
when the same species occurs on both sides of the reaction equation, in which case the
reaction is treated as a
three-body reaction for a specific collider.
Three-Body Reactions#
A three-body reaction is a gas-phase reaction of the form:
Here
Different species may be more or less effective in acting as the collision partner. A
species that is much lighter than
These effects can be accounted for by defining a collision efficiency
where
where
Added in version 3.0: The rate coefficient
Collider-specific rate parameterizations#
Sometimes, accounting for a particular third body’s collision efficiency may require an alternate set of rate parameters entirely. In this case, two reactions are written:
where the third-body efficiency for C in the first reaction should be explicitly set to zero. For the second reaction, the efficiencies will automatically be set to one for C and zero for all other colliders.
YAML Usage
A three-body reaction may be defined in the YAML format using the
three-body
reaction type
or, if no type
is specified,
identified automatically by the presence of the generic third body M or a specific
non-reactive species (for example, C in R2 above).
Pressure-dependent Reactions#
For pressure-dependent reactions where the behavior is more complex than described by the three-body form, the pressure dependency is folded into the calculation of the rate constant. Cantera supports several ways of representing pressure-dependent reactions:
Electrochemical Reactions#
In an electrochemical reaction (one that moves electrical charge from one phase of
matter to another), the electric potential difference
The free energy of the reaction equals the electrochemical potential change:
where
Cantera’s charge transfer treatment assumes a reversible reaction with a linear energy
profile in the region of the transition state. From above, for any
This means that the activation energy for the reaction changes:
The barrier height for the forward reaction increases by
.The reverse reaction barrier height decreases by
.
Note that
From transition state theory, the forward and reverse reaction rates are therefore calculated as:
and
respectively, where
Note that Cantera’s actual software implementation looks quite different from the description above, which is meant solely to give a clearer understanding of the science behind Cantera’s calculations.
YAML Usage
Electrochemical reactions only occur at phase boundaries and therefore use the standard
interface
reaction rate implementation.Charge transfer is automatically detected, and
automatically calculated. If no value forbeta
is provided, anelectrochemical
reaction assumes a default ofbeta = 0.5
.
The Butler-Volmer Form#
Cantera’s electrochemical reaction rate calculation is equivalent to the commonly-used
Butler-Volmer rate form. In Butler-Volmer, the net rate of progress,
where the kinetic rate constant
To convert between the two forms, the exchange current density varies with the chemical state and can be calculated as:
YAML Usage
One can explicitly provide an exchange current density, rather than the exchange-current-density-formulation
field to true
.
- equation: LiC6 <=> Li+(e) + C6
rate-constant: [5.74, 0.0, 0.0]
beta: 0.4
exchange-current-density-formulation: true
Here, the rate constant Arrhenius parameters will be used to calculate the exchange current density.
Reaction Orders#
Explicit reaction orders different from the stoichiometric coefficients are sometimes used for non-elementary reactions. For example, consider the global reaction:
the forward rate constant might be given as [Westbrook and Dryer, 1981]:
Special care is required in this case since the units of the pre-exponential factor depend on the sum of the reaction orders, which may not be an integer.
Note that you can change reaction orders only for irreversible reactions.
Normally, reaction orders are required to be positive. However, in some cases negative reaction orders are found to be better fits for experimental data. In these cases, the default behavior may be overridden in the input file.
YAML Usage
To include explicit orders for the reaction above, it can be written in the YAML format as:
- equation: C8H18 + 12.5 O2 => 8 CO2 + 9 H2O
units: {length: cm, quantity: mol, activation-energy: kcal/mol}
rate-constant: {A: 4.5e+11, b: 0.0, Ea: 30.0}
orders: {C8H18: 0.25, O2: 1.5}