3.6.4. Usage of Multiple Bath-gas Species

The typical usage of the reaction types outlined in Unimolecular/Recombination Fall-off Reactions through General Pressure Dependence Using Logarithmic Interpolation is with a specific species present as the "bath" gas. Many times the reactions for different bath-gas species are all included in the same mechanism. Note that the reaction rate computed at the high or low pressure limit would, in theory, be identical regardless of which species acts as the bath gas. However, if multiple instances of the same reaction with different bath-gas species are present in a given mechanism, then the net rate reaction rate is computed by summing up the individual rates. If each rate expressiongives the reaction rate at the limiting pressure as Randsuppose that there are nsuchrate expressions (for ndifferentbath-gas species), then the total rate is n*R (due to the summation). Note, however, that the expected value is R. To accommodate such cases, an enhanced way of specifying the reaction with multiple bath-gas species is provided. In particular, the rate expressions for different bath-gas species may be written together in the same reaction. For reactions written in this manner, the net rate is computed by summing the individual rates multiplied by the mole fraction of corresponding bath-gas species (or the mixture). Thus, the correct limiting rate is obtained.

Consider the following example:

H +O2 (+M) = HO2 +(M) 4.650e+012 0.440 0.0
LowMX/1.737e+019 -1.230 0.0/
TroeMX/ 6.700e-001 1.000e-030 1.000e+030 1.000e+030/ LowSP/ AR 6.810e+018 -1.200 0.0/
TroeSP/AR 7.000e-001 1.000e-030 1.000e+030 1.000e+030/ LowSP/ HE 9.192e+018 -1.200 0.0/
TroeSP/HE 5.900e-001 1.000e-030 1.000e+030 1.000e+030/ HE / 1.0 / AR / 1.0 / H2/ 1.30/ H2O/ 10.00/

Note that the keywords LOW and TROE (see the Chemkin Input Manual) here are augmented by SP and MX; which indicate the rate expressions for a particular species (such as Argon (AR) and Helium (HE) in this case) and the rest of the mixture. The net rate for this reaction is then

(3–38)

where and indicate rate and mole fraction, respectively, and

is the mole fraction of the "rest" of the mixture. In the example above, each rate expression makes use of the third-body efficiencies. For the specific bath-gas species (that is, and in this example) non-unity third-body efficiency cannot be specified.

This formulation is also available when (a) the reaction line input is for the low- pressure limit, that is, for individual species and for a mixture, the rates are indicated by the keyword HIGHMX and HIGHSP and (b) for general logarithmic pressure dependence use keywords PLOGMX and PLOGSP as shown in the example below:

H + O2 = HO2         1.0 0. 0.
    PLOGMX/1.      2.48E+17 -2.226  36. /
    PLOGMX/10.     1.90E+18 -2.194   6. /
    PLOGMX/100.    6.05E+19 -2.330 635. /
    PLOGSP/HE 1.   2.48E+17 -2.226  36. /
    PLOGSP/HE 10.  1.90E+18 -2.194   6. /
    PLOGSP/HE 100. 6.05E+19 -2.330 635. /

For PLOG input, third-body enhancements are not allowed. In the example above, the rates for the specific species (HE in this case) and for the rest of the mixture are first computed by appropriate interpolation for the specified pressure. The net rate is then computed by multiplying by the corresponding mole fractions as shown in Equation 3–38.