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18.1.4 Prompt NOx Formation

It is known that during combustion of hydrocarbon fuels, the NOx formation rate can exceed that produced from direct oxidation of nitrogen molecules (i.e., thermal NOx).

Where and When Prompt NOx Occurs

The presence of a second mechanism leading to NOx formation was first identified by Fenimore [ 71] and was termed ``prompt NOx''. There is good evidence that prompt NOx can be formed in a significant quantity in some combustion environments, such as in low-temperature, fuel-rich conditions and where residence times are short. Surface burners, staged combustion systems, and gas turbines can create such conditions [ 7].

At present the prompt NOx contribution to total NOx from stationary combustors is small. However, as NOx emissions are reduced to very low levels by employing new strategies (burner design or furnace geometry modification), the relative importance of the prompt NOx can be expected to increase.

Prompt NOx Mechanism

Prompt NOx is most prevalent in rich flames. The actual formation involves a complex series of reactions and many possible intermediate species. The route now accepted is as follows:

$\displaystyle \mbox{CH} + \mbox{N}_{2}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{HCN} + \mbox{N}$ (18.1-21)
$\displaystyle \mbox{N} + \mbox{O}_{2}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{NO} + \mbox{O}$ (18.1-22)
$\displaystyle \mbox{HCN} + \mbox{OH}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{CN} + \mbox{H}_{2}\mbox{O}$ (18.1-23)
$\displaystyle \mbox{CN} + \mbox{O}_{2}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{NO} + \mbox{CO}$ (18.1-24)

A number of species resulting from fuel fragmentation have been suggested as the source of prompt NOx in hydrocarbon flames (e.g., CH, CH $_{2}$, C, C $_{2}$H), but the major contribution is from CH (Equation  18.1-21) and CH $_{2}$, via

\begin{displaymath} \mbox{CH}_{2} + \mbox{N}_{2} \rightleftharpoons \mbox{HCN} + \mbox{NH} \end{displaymath} (18.1-25)

The products of these reactions could lead to formation of amines and cyano compounds that subsequently react to form NO by reactions similar to those occurring in oxidation of fuel nitrogen, for example:

\begin{displaymath} \mbox{HCN} + \mbox{N} \rightleftharpoons \mbox{N}_{2} + ..... \end{displaymath} (18.1-26)

Factors of Prompt NOx Formation

Prompt NOx formation is proportional to the number of carbon atoms present per unit volume and is independent of the parent hydrocarbon identity. The quantity of HCN formed increases with the concentration of hydrocarbon radicals, which in turn increases with equivalence ratio. As the equivalence ratio increases, prompt NOx production increases at first, then passes a peak, and finally decreases due to a deficiency in oxygen.

Primary Reaction

Reaction 18.1-21 is of primary importance. In recent studies [ 224], comparison of probability density distributions for the location of the peak NOx with those obtained for the peak CH have shown close correspondence, indicating that the majority of the NOx at the flame base is prompt NOx formed by the CH reaction. Assuming that Reaction  18.1-21 controls the prompt NOx formation rate,

\begin{displaymath} \frac{d[{\rm NO}]}{dt} = k_{0} [\mbox{CH}] [\mbox{N}_{2}] \end{displaymath} (18.1-27)

Modeling Strategy

There are, however, uncertainties about the rate data for the above reaction. From Reactions  18.1-21- 18.1-25, it can be concluded that the prediction of prompt NOx formation within the flame requires coupling of the NOx kinetics to an actual hydrocarbon combustion mechanism. Hydrocarbon combustion mechanisms involve many steps and, as mentioned previously, are extremely complex and costly to compute. In the present NOx model, a global kinetic parameter derived by De Soete [ 248] is used. De Soete compared the experimental values of total NOx formation rate with the rate of formation calculated by numerical integration of the empirical overall reaction rates of NOx and N $_{2}$ formation. He showed that overall prompt formation rate can be predicted from the expression

\begin{displaymath} \frac{d [{\rm NO}]}{dt} = \mbox{(overall prompt {NOx} formation rate)} -\mbox{(overall prompt N$_{2}$\ formation rate)} \end{displaymath} (18.1-28)

In the early stages of the flame, where prompt NOx is formed under fuel-rich conditions, the O concentration is high and the N radical almost exclusively forms NOx rather than nitrogen. Therefore, the prompt NOx formation rate will be approximately equal to the overall prompt NOx formation rate:

\begin{displaymath} \frac{d[{\rm NO}]}{dt} = k_{pr} [\mbox{O}_{2}]^{a} [\mbox{N}_{2}] [\mbox{FUEL}] e^{-E_a/RT} \end{displaymath} (18.1-29)

For C $_2$H $_4$ (ethylene)-air flames,

$k_{pr}$ = $1.2 \times 10^{7} (RT/p)^{a+1}$
$E_{a}$ = 60 kcal/gmol

where $a$ is the oxygen reaction order, $R$ is the universal gas constant, and $p$ is pressure (all in SI units). The rate of prompt NOx formation is found to be of the first order with respect to nitrogen and fuel concentration, but the oxygen reaction order, $a$, depends on experimental conditions.

Rate for Most Hydrocarbon Fuels

Equation 18.1-29 was tested against the experimental data obtained by Backmier et al. [ 5] for different mixture strengths and fuel types. The predicted results indicated that the model performance declined significantly under fuel-rich conditions and for higher hydrocarbon fuels. To reduce this error and predict the prompt NOx adequately in all conditions, the De Soete model was modified using the available experimental data. A correction factor, $f$, was developed, which incorporates the effect of fuel type, i.e., number of carbon atoms, and air-to-fuel ratio for gaseous aliphatic hydrocarbons. Equation  18.1-29 now becomes

\begin{displaymath} \frac{d[{\rm NO}]}{dt} = f k'_{pr} [\mbox{O}_{2}]^{a} [\mbox{N}_{2}] [\mbox{FUEL}] e^{-E'_a/RT} \end{displaymath} (18.1-30)

so that the source term due to prompt NOx mechanism is

\begin{displaymath} S_{\rm prompt, NO} = M_{w,{\rm NO}} \frac{d[{\rm NO}]}{dt} \end{displaymath} (18.1-31)

In the above equations,

\begin{displaymath} f = 4.75 + 0.0819\ n - 23.2 \phi + 32 \phi^{2} - 12.2 \phi^{3} \end{displaymath} (18.1-32)

$n$ is the number of carbon atoms per molecule for the hydrocarbon fuel, and $\phi$ is the equivalence ratio. The correction factor is a curve fit for experimental data, valid for aliphatic alkane hydrocarbon fuels (C $_n$H $_{2n+2}$) and for equivalence ratios between 0.6 and 1.6. For values outside the range, the appropriate limit should be used. Values of $k'_{pr}$ and $E'_a$ are selected in accordance with reference [ 64].

Here the concept of equivalence ratio refers to an overall equivalence ratio for the flame, rather than any spatially varying quantity in the flow domain. In complex geometries with multiple burners this may lead to some uncertainty in the specification of $\phi$. However, since the contribution of prompt NOx to the total NOx emission is often very small, results are not likely to be biased significantly.

Oxygen Reaction Order

Oxygen reaction order depends on flame conditions. According to De Soete [ 248], oxygen reaction order is uniquely related to oxygen mole fraction in the flame:

\begin{displaymath} a = \left\{ \begin{array}{ll} 1.0, & X_{{\rm O}_2} \leq 4.1 ... ..._2} < 0.03 \\ 0, & X_{{\rm O}_2} \geq 0.03 \end{array}\right. \end{displaymath} (18.1-33)

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