Gasphase chemistry
The input file
The gas chemistry input file generally follows the chemkin input format. The following section briefly describes the setting up of the gasphase mechanism input file. For a complete example, the users may refer to the home pages of GRI Mech (http://combustion.berkeley.edu/gri-mech/) or the mechanisms hosted by Lawrence Livermore national lab (https://combustion.llnl.gov/mechanisms)
The general structure of the input file is shown below.
! GRI-Mech Version 3.0 7/30/99 CHEMKIN-II format
! See README30 file at anonymous FTP site unix.sri.com, directory gri;
! WorldWideWeb home page http://www.me.berkeley.edu/gri_mech/ or
! through http://www.gri.org, under 'Basic Research',
! for additional information, contacts, and disclaimer
ELEMENTS
O H C N AR
END
SPECIES
H2 H O O2 OH H2O HO2 H2O2
C CH CH2 CH2(S) CH3 CH4 CO CO2
HCO CH2O CH2OH CH3O CH3OH C2H C2H2 C2H3
C2H4 C2H5 C2H6 HCCO CH2CO HCCOH N NH
NH2 NH3 NNH NO NO2 N2O HNO CN
HCN H2CN HCNN HCNO HOCN HNCO NCO N2
AR C3H7 C3H8 CH2CHO CH3CHO
END
!THERMO
! Insert GRI-Mech thermodynamics here or use in the default file
!END
REACTIONS
2O+M<=>O2+M 1.200E+17 -1.000 .00
H2/ 2.40/ H2O/15.40/ CH4/ 2.00/ CO/ 1.75/ CO2/ 3.60/ C2H6/ 3.00/ AR/ .83/
...
...
O+CO(+M)<=>CO2(+M) 1.800E+10 .000 2385.00
LOW/ 6.020E+14 .000 3000.00/
H2/2.00/ O2/6.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/3.50/ C2H6/3.00/ AR/ .50/
...
...
H+CH2(+M)<=>CH3(+M) 6.000E+14 .000 .00
LOW / 1.040E+26 -2.760 1600.00/
TROE/ .5620 91.00 5836.00 8552.00/
H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/ .70/
...
...
2HO2<=>O2+H2O2 1.300E+11 .000 -1630.00
DUPLICATE
2HO2<=>O2+H2O2 4.200E+14 .000 12000.00
DUPLICATE
END Any line starting with ! is treated as a comment line. The actual mechanism specification begins with the ELEMENT keyword. Instead of ELEMENT, ELEM may also be used. The element specification ends with the keyword END, which is not mandatory. However, there shall be only one instance of ELEMENT or ELEM keyword. This part is entirely ignored by ReactionEngine. i.e. it does not read and stores the element information provided in the mechanism input file. The species specification follows the element specification. The species specification starts with the keyword SPECIES or SPEC and ends with END. The END keyword is not mandatory. The species names may be specified either in uppercase or lowercase letters. The reactions follow the species definition and start with the keyword REACTIONS or REAC and ends with the keyword END. The default values of the activation energy are CAL/MOL. If the activation energy units are different from CAL/MOL, that must follow the keyword REACTION or REAC. The activation energy units may be specified in CAL/MOLE, KCAL/MOLE, JOULES/MOLE, KELVINS, or EVOLTS. An example specification is shown below.
REACTION JOULES/MOLThe units of pre-exponential factors by default are cm-mol-s-K. Instead of cm-mol-s-K, cm-molecule-s-K may be used. An example specification is shown below
REACTION JOULES/MOL MOLECULESSpecifying a reaction
An example of reaction stoichiometry is as follows.
H+O2+H2O<=>HO2+H2O 11.26E+18 -.760 .00There are two parts to this reaction specification. The first part is the stoichiometric equation, and the second part is the reaction parameters. The stoichiometric equation represents the chemical transformation happening, which may be reversible or irreversible. A reversible reaction is represented by <=> as shown in the above example. Instead of <=>, = may also be used for denoting a reversible reaction. An irreversible reaction, on the other hand, is represented by the symbol =>. An example is shown below.
O2+C3H7=>OH+C2H5+CH2O 2.410E+13 .000 .00The + symbol separates the reactant species. There may be space between the different participating species. The reaction's stoichiometry may be specified either in the uppercase or lowercase letter. The reaction parameters follow the stoichiometric equation. These are the Arrhenius parameters. The first is the pre-exponential factor, the second is the temperature exponent, and the third is the activation energy. All the three parameters must be specified for the mechanism parser to work.
The rate of progress of the reaction $i$, $r_i$ for an Arrhenius reaction is calculated according to
\[r_i = k_{fi} \prod_{k=1}^{N_g} [X_k]^{\nu_{ki}^{\prime}} - k_{ri} \prod_{k=1}^{N_g} [X_k]^{\nu_{ki}^{\prime\prime}}\]
where
\[k_{fi} = A_{fi} T^\beta \exp(-E/RT)\]
The reverse reaction rate constant for a reversible reaction is calculated from the thermodynamic information. i.e
\[k_{ri} = \frac{k_{fi}}{K_{ci}}\]
The equilibrium constant $K_{ci}$ is related to $K_{pi}$ according to
\[K_{ci} = K_{pi} \left( \frac{p_\mathrm{atm}}{RT} \right)^{\sum_{k=1}^{N_g}\nu_{ki}}\]
The equilibrium constant $K_{pi}$ is calculated from the Gibb's free energy change of the reaction. $N_g$ is the number of gasphase species and $\nu_{ki} = \nu_{ki}^{\prime\prime}-\nu_{ki}^{\prime}$
Auxiliary information
The chemkin gasphase mechanism format allows several auxiliary information to alter the rate of a reaction. The ones that are supported by ReactionEngine is described below.
Third body reactions
An example of a third body reaction is shown below.
2O+M<=>O2+M 1.200E+17 -1.000 .00
H2/ 2.40/ H2O/15.40/ CH4/ 2.00/ CO/ 1.75/ CO2/ 3.60/ C2H6/ 3.00/ AR/ .83/Here M is the third body. By default the third body collision efficiency is treated as 1. Any species that contribute differently (i.e efficiency is not 1) as a third body must be specified in a separate line that follows the reaction specification line. The species and its enhanced third body efficiency are separated by '/'. For instance, in the above example, the enhanced third body efficiency of H2 is 2.4.
In the case of third body reactions, the Arrhenius rate is modified by the concentrations of the third body species. The rate of progress then becomes
\[r_i = \sum_{k=1}^{N_g}\left( \alpha_{ki}[X_k] \right) \left( k_{fi} \prod_{k=1}^{N_g} [X_k]^{\nu_{ki}^{\prime}} - k_{ri} \prod_{k=1}^{N_g} [X_k]^{\nu_{ki}^{\prime\prime}} \right)\]
Reaction order
The order of a reaction with respect to a species may be altered by specifying the FORD and RORD keywords. An example is shown below.
2H2+O2<=>2H2O 3.0e13 0.0e-16 0.0e-16
FORD/H2 2.0/O2 1.0/
RORD/H2O 1.0/In the above example, the order of the forward reaction w.r.t $H_2$ is 2. By default the order of the reaction w.r.t the concentration of $H_2$ is 2 due to the value of the stoichiometric coefficient. The additional specification of order 2 w.r.t $H_2$ will make the reaction 4th order w.r.t. H$_2$. In ReactionEngine the rate for the above reaction translates into the following
\[r = A_f \exp\left(\frac{-E}{RT}\right) [H_2]^2[H_2]^2[O_2] - \frac{k_f}{K_c} [H_2O][H_2O]\]
Pressure dependent reactions
***ReactionEngine*** implements three different models for the rate calculation of pressure dependent reactions. The pressure dependent reactions auxiliary information line must follow the reaction specification. For fall off reactions, the LOW keyword follows the reaction information, and the parameters correspond $A_0, \beta_0$, and $E_0$. For chemically activated bi-molecular reactions, the auxiliary information for the HIGH keyword must be provided. The parameters correspond to $A_{\infty}, \beta_{\infty}$, and $E_{\infty}$.
With the high pressure and low pressure parameters, the rate constant is calculated as follows.
\[k_0 = A_0 T^{\beta_0} \exp(-E_0/RT)\]
\[k_{\infty} = A_{\infty} T^{\beta_{\infty}} \exp(-E_{\infty}/RT)\]
\[k = k_{\infty} \left( \frac{Pr}{1+Pr} \right)F\]
The reduced pressure $Pr$ is given by
\[Pr = \frac{k_0[M]}{k_{}\infty}\]
where $[M]$ is the concentration of the mixture, including third body efficiencies. For the Lindemaan form $F=1$
Troe reactions
In the case of Troe reactions, in addition to the high pressure and low pressure parameters, the parameters following the TROE keyword must be provided. The parameters are assumed to be in the following order $a, T^{***}, T^*$, and $T^{**}$. The fourth parameter is optional.
The value of $F$ in Troe form is calculated as follows
\[log F = \left[ 1+ \left( \frac{log Pr + c}{n-d(log Pr + c)} \right)^2 \right]^{-1} log F_\mathrm{cent}\]
\[c = -0.4-0.67log F_\mathrm{cent}\]
\[n = 0.75 -1.27 log F_\mathrm{cent}\]
\[d = 0.14\]
\[F_\mathrm{cent} = (1-\alpha) \exp(-T/T^{***}) + \alpha \exp( -T/T^*) +\exp(-T^{**}/T)\]
Sri reactions
In the case of SRI reactions, in addition to the low and high pressure limit parameters, the parameters following the SRI keyword must be provided. Either 3 or 5 parameters must be provided. The parameters are assumed in the following order $a, b, c, d$ and $e$. If only first three are specified, then $d=1$ and $e=0$. The F value in the case of Sri fall off reaction is calculated as follows
\[x = 1/(1+log^2 Pr)\]
\[F = d\left[ a \exp(-b/T)+\exp(-T/c) \right]^{x} T^e\]