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 \(a, b, c, \) and \(d\) are stoichiometric coefficients.
The forward reaction rate is then calculated as:
where \(k_f\) is the forward rate constant, calculated using one of the available rate parameterizations such as the modified Arrhenius form.
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 \(\t{M}\) is an unspecified collision partner that carries away excess energy to stabilize the \(\t{AB}\) molecule (forward direction) or supplies energy to break the \(\t{AB}\) bond (reverse direction). In addition to the generic collision partner \(\t{M}\), it is also possible to explicitly specify a colliding species. In both cases, the reaction type can be automatically inferred by Cantera and does not need to be explicitly specified by the user.
Different species may be more or less effective in acting as the collision partner. A species that is much lighter than \(\t{A}\) and \(\t{B}\) may not be able to transfer much of its kinetic energy, and so would be inefficient as a collision partner. On the other hand, a species with a transition from its ground state that is nearly resonant with one in the \(\t{AB^*}\) activated complex may be much more effective at exchanging energy than would otherwise be expected.
These effects can be accounted for by defining a collision efficiency \(\epsilon\) for each species, defined such that the forward reaction rate is
where
where \(C_k\) is the concentration of species \(k\). Since any constant collision efficiency can be absorbed into the rate coefficient \(k_f(T)\), the default collision efficiency is 1.0.
Added in version 3.0: The rate coefficient \(k_f(T)\) may be implemented using any rate parameterization supported by Cantera, not just the modified Arrhenius form.
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:
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}