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20.1.6 NOx Formation from Intermediate N $_2$O

Melte and Pratt [ 236] proposed the first intermediate mechanism for NOx formation from molecular nitrogen (N $_2$) via nitrous oxide (N $_2$O). Nitrogen enters combustion systems mainly as a component of the combustion and dilution air. Under favorable conditions, which are elevated pressures and oxygen-rich conditions, this intermediate mechanism can contribute as much as 90% of the NOx formed during combustion. This makes it particularly important in equipment such as gas turbines and compression-ignition engines. Because these devices are operated at increasingly low temperatures to prevent NOx formation via the thermal NOx mechanism, the relative importance of the N $_2$O-intermediate mechanism is increasing. It has been observed that about 30% of the NOx formed in these systems can be attributed to the N $_2$O-intermediate mechanism.

The N $_2$O-intermediate mechanism may also be of importance in systems operated in flameless mode (e.g., diluted combustion, flameless combustion, flameless oxidation, and FLOX systems). In a flameless mode, fuel and oxygen are highly diluted in inert gases so that the combustion reactions and resulting heat release are carried out in the diffuse zone. As a consequence, elevated peaks of temperature are avoided, which prevents thermal NOx. Research suggests that the N $_2$O-intermediate mechanism may contribute about 90% of the NOx formed in flameless mode, and that the remainder can be attributed to the prompt NOx mechanism. The relevance of NOx formation from N $_2$O has been observed indirectly, and theoretically speculated for a number of combustion systems and by a number of researchers [ 18, 68, 124, 356, 365].

N $_2$O-Intermediate NOx Mechanism

The simplest form of the mechanism [ 236] takes into account two reversible elementary reactions:

$\displaystyle \mbox{N$_2$} + \mbox{O} + \mbox{M}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{N$_2$O} + \mbox{M}$ (20.1-64)
$\displaystyle \mbox{N$_2$O} + \mbox{O}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{2NO}$ (20.1-65)

Here, M is a general third body. Because the first reaction involves third bodies, the mechanism is favored at elevated pressures. Both reactions involve the oxygen radical O, which makes the mechanism favored at oxygen-rich conditions. While not always justified, it is often assumed that the radical O atoms originate solely from the dissociation of molecular oxygen,

 \frac{1}{2} \mbox{O$_2$} \rightleftharpoons \mbox{O} (20.1-66)

According to the kinetic rate laws, the rate of NOx formation via the N $_2$O-intermediate mechanism is

 \frac{d[{\rm NO}]}{dt} = 2 \left( k_{f,2} [{\rm N}_2{\rm O}]... ...m O}] - k_{r,2}[{\rm NO}]^2 \right) \qquad \mbox{gmol/m$^3$-s} (20.1-67)

To solve Equation  20.1-67, you will need to have first calculated [O] and [N $_2$O].

It is often assumed that N $_2$O is at quasi-steady-state (i.e., $d[{\rm N}_2{\rm O}]/dt = 0$), which implies

[\mbox{N$_2$O}]= \frac{k_{f,1} [\mbox{N$_2$}][\mbox{O}][\mbox... ..._{r,2} [\mbox{NO}]^2} {k_{r,1} [\mbox{M}] +k_{f,2} [\mbox{O}]} (20.1-68)

The system of Equations  20.1-67- 20.1-68 can be solved for the rate of NOx formation when the concentration of N $_2$, O $_2$, and M, the kinetic rate constants for Equations  20.1-64 and 20.1-65, and the equilibrium constant of Equation  20.1-66 are known. The appearance of NO in Equation  20.1-65 entails that coupling of the N $_2$O mechanism with the thermal NOx mechanism (and other NOx mechanisms).

$k_{f,1}$ = $4.44 \times 10^{32} T^{-8.358} e^{-28234/T}$ $\phantom{X}$ $k_{r,1}$ = $4.00 \times 10^8 e^{-28234/T}$
$k_{f,2}$ = $2.90 \times 10^7 e^{-11651/T}$ $\phantom{X}$ $k_{r,2}$ = $1.45 \times 10^{-29} T^{9.259} e^{-11651/T}$

In the above expressions, $k_{f,1}$ and $k_{f,2}$ are the forward rate constants of Equations  20.1-64 and 20.1-65, and $k_{r,1}$ and $k_{r,2}$ are the corresponding reverse rate constants. The units for $k_{f,2}$, $k_{r,1}$, and $k_{r,2}$ are m $^3$/gmol-s, while $k_{f,1}$ has units of m $^6$/gmol $^2$-s.

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