Determination of rate parameters based on both direct and indirect measurements

The determination of rate parameters of gas-phase elementary reactions is usually based on direct measurements. The rate parameters obtained in many independent direct measurements are then used in reaction mechanisms, which are tested against the results of indirect experiments, like time-to-ignition or laminar flame velocity measurements. We suggest a new approach that takes into account both direct and indirect measurements and optimizes all influential rate parameters. First, the domain of feasibility of the Arrhenius parameters is determined from all of the available direct measurements. Thereafter, the optimal Arrhenius parameters are sought within this domain to reproduce the selected direct and indirect measurements. Other parameters of a complex mechanism (third-body efficiencies, enthalpies of formation, parameters of pressure dependence, etc.) can also be taken into account in a similar way. A new fitting algorithm and a new method for error calculation were developed to determine the optimal mean values and the covariance matrix of all parameters. The approach is demonstrated on the calculation of Arrhenius parameters of reactions (R1): H + O2 = OH + O and (R2): H + O2 + M = HO2 + M (low-pressure limit, M = N2 or Ar). In total, 9 direct measurements for reaction (R1) (745 data points), 10 direct measurements for reaction (R2) (258 data points), and 11 ignition time measurements (79 data points) were taken into account. The application of the method resulted in the following rate parameters for the investigated reactions—(R1): A = 3.003 × 1010 cm3 mol-1 s-1, n = 0.965, E/R = 6158 K (T = 950–3550 K) and (R2): A = 7.856 × 1018 cm6 mol-2 s-1, n = -1.100, E/R = 0 K (low-pressure limit, M = N2, T = 300–1850 K). The optimized third-body efficiency of Ar relative to N2 is m = 0.494 (standard deviation s = 0.010). The uncertainty parameter f as a function of temperature was also calculated. Average uncertainty parameter values are f = 0.025 and 0.049 for reactions (R1) and (R2) (corresponding to 6% and 12%), respectively, which are much lower than those of the previous evaluations