Environmental Engineering Reference
In-Depth Information
where
n
and
m
are the number of C and H atoms in the parent hydrocarbon. The
rates of reaction are
r
HC
=
k
1
[HC][O
2
],
r
CO
=
k
2
[CO][O
2
]−
nk
1
[HC][O
2
], and
r
CO
2
=
k
2
[CO][O
2
]. Combustion is frequently carried out in the presence of excess
air. The oxygen mole fraction is usually in the range 0.1-0.15 for a HC mole fraction
of 0.001. Hence,
r
HC
=
k
2
[CO]. In
Chapter 5, we saw that the above reaction rates reflect the following series reaction:
HC
k
1
k
1
[HC],
r
CO
=
k
2
[
nk
1
[HC], and
r
CO
2
=
CO
]−
CO
k
2
CO
2
.
It is to be expected that since reaction rates are sensitive to temperature, so is the
efficiencyofanincinerator.Sincereactionsinthermaloxidizersoccuratvaryingrates,
sufficienttimeshouldbegivenforthereactiontogotocompletion.Mixingintheincin-
erator should be sufficient to bring the reactants together. Thus, three important time
factorsaretobeconsideredinthedesignofanincinerator.Thesearethe
residencetime
,
τ
res
=
V
R
/G
=
Z
s
/V
g
,
chemical reaction time
,
τ
rxn
=
1
/k
, and
mixing time
,
τ
mix
=
Z
s
/D
e
.
V
R
is the total reactor volume (m
3
)
,
G
is the volumetric waste gas flow rate
at afterburner temperature (m
3
/s),
V
g
is the gas velocity (m/s),
Z
s
is the reaction zone
length (m), and
D
e
is the turbulent diffusivity (m
2
/s). The relative magnitudes of these
times are represented in terms of two dimensionless numbers: Peclet number,
Pe
−→
−→
=
Z
s
V
g
/D
e
, and Damköhler number,
Da
Z
s
k/V
g
.If
Pe
is large and
Da
is small, then
mixing is rate controlling in the thermal oxidizer, whereas for small
Pe
and large
Da
,
chemical kinetics controls the rate of oxidation. At most temperatures used in after-
burners, a reasonably moderate
V
g
is maintained so that mixing is not rate limiting.
The rate constant
k
for a reaction is related to its activation energy (Chapter 5),
=
k
E
a
/RT)
. For a variety of hydrocarbons, values of
A
and
E
a
are available
(Table 6.7), and hence
k
at any given temperature can be obtained.
=
A
exp
(
−
TABLE 6.7
Thermal Oxidation Reaction Rate Parameters
A
(s
−1
)
Compound
E
a
(kJ/mol)
3.3
×
10
10
Acrolein
150
7.4
×
10
21
Benzene
401
3.7
×
10
14
1-Butene
243
1.3
×
10
17
Chlorobenzene
321
5.6
×
10
14
Ethane
266
5.4
×
10
11
Ethanol
201
6.0
×
10
8
Hexane
143
1.7
×
10
11
Methane
218
7.3
×
10
8
Methyl chloride
171
1.6
×
10
12
Natural gas
206
5.2
×
10
19
Propane
356
2.3
×
10
13
Toluene
236
3.6
×
10
14
Vinyl chloride
265
Source:
From Buonicore, A.T. and Davis, W.T. (eds). 1992.
Air Pollution Engineering Manual
. New York, NY:
Van Nostrand Reinhold.
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