Page 323 - Advanced Thermodynamics for Engineers, Second Edition

14.4 CHEMICAL KINETICS OF NO 313

reaction rates are available, although it should be recognised that most other pollutants are produced by
reactions between the oxygen in the air and a constituent of the fuel (e.g. carbon or sulfur). The
formation of NO in combustion processes can occur from two sources: thermal NO and prompt NO.
Thermal NO is formed by the combination of the oxygen and nitrogen in the air, and will be produced
even if there is no nitrogen in the fuel itself. This section will restrict itself to considering thermal NO.
Prompt NO is thought to be formed in the flame as a result of the combination of the nitrogen in the fuel
with the oxygen in the air. The amount of nitrogen in most conventional hydrocarbon fuels is usually
very low.
The governing equations for the mechanism of NO formation are (Lavoie et al. (1970))

3
ð1Þ N þ NO5N 2 þ O; k f1 ¼ 3:1 10 10 e ð 160=TÞ m =kmol s (14.19)
3
6
ð2Þ N þ O 2 5NO þ O; k f2 ¼ 6:4 10 T e ð 3125=TÞ m =kmol s (14.20)
ð3Þ N þ OH5NO þ H; k f3 ¼ 4:2 10 10 m 3 kmol s (14.21)
3
ð4Þ H þ N 2 O5N 2 þ OH; k f4 ¼ 3:0 10 10 e ð 5350=TÞ m =kmol s (14.22)
3
ð5Þ O þ N 2 O5N 2 þ O 2 ; k f5 ¼ 3:2 10 12 e ð 18900=TÞ m =kmol s (14.23)
ð6Þ O þ N 2 O5NO þ NO; k f6 ¼ k f5 (14.24)

3
ð7Þ N 2 O þ M5N 2 þ O þ M; k f7 ¼ 10 12 e ð 30500=TÞ m =kmol s: (14.25)
3
In these equations the rate constants (k fi ) are all in m /kmol s. M is a third body which may be
involved in the reactions, but is assumed to be unchanged by the reactions. These equations can be
applied to the zone containing ‘burned’ products, which exists after the passage of the flame through
the unburned mixture. It will be assumed that H and OH, and O and O 2 are in equilibrium with each
other: these values can be calculated by the methods described in Chapter 12.

14.4.1 RATE EQUATIONS FOR NITRIC OXIDE
The rate of formation of nitric oxide can be derived in the following manner. Consider reaction j, let k fj
be the forward reaction rate, k bj the backward rate and R j the ‘one way’ equilibrium rate. Also let

NOŠ ½NOŠ ¼ a; ½NŠ ½NŠ ¼ b; ½N 2 OŠ ½N 2 OŠ ¼ g:
e
e
e
where suffix e denotes equilibrium values. Then the following expressions are obtained for the burned
gas, or product, volume.

14.4.1.1 Expression for Nitric Oxide, NO
From Eqn (14.19) the net rate is

k f1 ½N NO þ k b1 N 2 O ¼ abk f1 ½NŠ ½NOŠ þ k b1 ½N 2 Š ½OŠ :
e e e e