Dependence of CO emissions on the rate of product cooling

Abstract

Detailed chemical kinetics simulations of the cooling of hydrocarbon combustion products show that the mole fraction of CO freezes well above equilibrium levels at a value that depends on the cooling rate. The frozen mole fraction of CO can be expressed as a function of the system pressure and the mole fractions of CO 2, O 2, and H 2O X CO, f = 2.0 × 10 −9[ X CO 2 /( X O 2 X H 2O )]( Pτ) −1.6where τ is the temperature relaxation time, inversely proportional to the cooling rate. The ratio of mole fractions in this result can also be derived by partial equilibrium analysis. However, this derivation yields X CO, f proportional to X OH 2 rather than ( Pτ) −1.6. The dependence on cooling rate is shown to be a kinetic effect due to the relatively slow forward rate of the principal CO oxidation reaction. This rate is proportional to PX OH, and X CO freezes when X OH is too small to maintain the consumption rate for CO that is needed to keep X CO near equilibrium at a given cooling rate. Partial equilibrium analysis shows that X OH, f , the value of X OH when X CO freezes, is proportional to ( Pτ) −1. The temperature, T f where X OH equals X OH, f is found by setting X OH, f = X OH,0 exp(−γ OH/ T f ), where γ OH is a fitting parameter related to equilibrium constants. Using T f and the equilibrium value of γ OH with the temperature-dependent result of the partial equilibrium analysis gives X CO proportional to ( Pτ) −1.56. This gives values of frozen X CO in reasonable agreement with the detailed chemical kinetics results. At high cooling rates, γ OH is a function of τ that can be found by a curve fit to X OH vs. T data from detailed kinetics calculations. Using this function to calculate T f improves the agreement with the detailed chemical kinetics results.