Page 236 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

212 7 Combustion Process and Air Emission Formation

The net rate of NO formation under a constant pressure and temperature con-
dition can be calculated by considering all three step reactions in Table 7.5.

½
dNOŠ
f
r NO ¼ ¼ k 1f N 2 Š O½Š k 1b NO½ Š N½Šg
½
dt
ð7:57Þ
½
f
þ k 2f O 2 Š N½Š k 2b NO½ Š O½Šg
f
þ k 3f N½Š OH½ Š k 3b NOŠ H½Šg:
½
When all the reactions in Table 7.5 reach equilibrium state, the NO formation
rate attributed to each of three step reactions can be described as, respectively,
½
r 1 ¼ k 1f N 2 Š O½Š ¼ k 1b NO½ Š N½Š
e e e e
½
½
r 2 ¼ k 2f O 2 Š N½Š ¼ k 2b NOŠ O½Š e ð7:58Þ
e
e
e
½
½
r 3 ¼ k 3f N½Š OHŠ ¼ k 3b NOŠ H½Š e
e
e
e
where the subscript e stands for equilibrium. For easy analysis, we also define two
dimensionless concentrations as follows.
½NO] ½NŠ
a ¼ ; b ¼ ð7:59Þ
½ NOŠ ½NŠ
e e
Then the rate of NO formation before reaching equilibrium state Eq. (7.57) can
be rewritten as
r NO ¼ r 1 1 abð Þ þ r 2 b aÞ þ r 3 b aÞ ð7:60Þ
ð
ð
The concentration of N atoms is needed in order to solve this equation. By
similar approach, we can get the rate of N atom formation
ð
ð
r N ¼ r 1 1 abð Þ þ r 2 a bÞ þ r 3 a bÞ ð7:61Þ
By the pseudo-steady-state approximation, we can set the left hand side of
Eq. (7.61), r N ¼ 0, and it leads to
r 1 þ r 2 a þ r 3 a
b ¼ ð7:62Þ
r 1 a þ r 2 þ r 3
Substitute Eq. (7.62) into Eq. (7.60), and we have the corresponding rate of NO
formation as

2
ð
ð
2r 1 r 2 þ r 3 Þ 1 a Þ
r NO ¼ ð7:63Þ
ar 1 þ r 2 þ r 3