Page 237 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

7.7 NO x 213

This equation can also be expressed in terms of dimensionless NO concentration,

½
a ¼ NOŠ NOŠ
½
e
2
da 1 2r 1 r 2 þ r 3 Þ 1 a Þ
ð
ð
¼ ð7:64Þ
dt ½NOŠ
e ar 1 þ r 2 þ r 3
Integration of this equation with an initial condition of a ¼ 0at t = 0 leads to the
description of the NO concentration at any time.

r 1 r 1 4r 1
1 ln 1 þ aÞ 1 þ ln 1 aÞ ¼ t ð7:65Þ
ð
ð
r 2 þ r 3 r 2 þ r 3 ½NOŠ
e
For easier expression, we can define the characteristic time for thermal NOx
formation as,
½NOŠ e
s NO ¼ ð7:66Þ
4r 1
and the reaction rate ratio,
r 1
q ¼ ð7:67Þ
r
r 2 þ r 3
By considering s NO and q , Eq. (7.65) becomes
r
ð
ð 1 q Þln 1 þ að Þ 1 þ q Þln 1 aÞ ¼ t=s NO ð7:68Þ
ð
r
r
In a typical combustion process, the residence time is shorter than the charac-
teristic time. As a result, NO does not reach its equilibrium concentration. There-
fore, it is better for the actual NO concentration in the flame to be determined using
this equation.

7.7.1.2 Prompt NO

Fenimore [12] found that some of the NO formed during combustion could not be
explained by the aforementioned Zeldovich mechanisms. When equivalence ratio is
greater than 1, the nitrogen in the air reacts to form hydrogen cyanide (HCN)
through the following chemical reaction,

N 2 þ CH $ HCN þ N ð7:69Þ

Since there are oxygen-containing compounds in the combustion system, HCN
produced in the above reaction and the nitrogen atom reacts further to produce NO
through several chain reactions.