Modeling of Combustion Systems A Practical Approach 13 potx

421
5
Semiempirical Models
Chapter Overview
implications it had for flow of air and fuel in burners. This allowed
us to make good physical models requiring one or no adjustable
parameters. In this chapter, the physics become more complicated
and involve thermodynamic, chemical, and kinetic quantities. For
this reason, our semiempirical models will require more adjust-
able parameters. Notwithstanding, such expressions will be capa-
ble of correlating complicated behavior with engineering
accuracy. With the techniques the reader has already learned, he
will be able to regress such semiempirical models handily from
facility data or planned experiments.
We begin the chapter with a discussion of various NOx forma-
tion mechanisms. Along the way, we introduce the reader to what-
ever thermodynamics or kinetics the situation may require. NOx
formation naturally progresses to NOx reduction, so here we
discuss nearly a dozen such strategies. These lead to a generic
semiempirical model for NOx and NOx reduction. We then
develop a parallel approach for CO. Throughout, we focus on the
practical.
The heat flux profile from a combustion system has now gained
importance. Modeling of such profiles is important for certain
reactors such as ethylene cracking units (ECUs) and hydrogen
and ammonia reformers. We develop the general three-parameter
equation from a simplified analysis of fuel jets and the heat bal-
ance. We can reduce this to a two-parameter model by normaliz-
ing the heat flux. Such a model also allows us to consider the
qualitative response of heat flux to various operational factors.
Two important responses we consider are run length between

decoking cycles and process efficiency. The heat flux model also
allows us to develop a similarity criterion for test and field units.
© 2006 by Taylor & Francis Group, LLC
In Chapter 2, we discussed the mechanical energy balance and
422 Modeling of Combustion Systems: A Practical Approach
Next, we consider how one may measure flame length. We
discuss a flame model and show its semiempirical analog. Some
fuel and combustion characteristics also cause other problems,
such as plume formation and corrosion through acid dew point
elevation. We treat these briefly in the final section. By the con-
clusion of this chapter, the reader will have an arsenal of practical
techniques for modeling important aspects of fired units.
5.1 NOx and Kinetics
5.1.1 NOx: Some General Comments
NOx produced from combustion is a terribly inefficient process. The high-
temperature reaction of oxygen and nitrogen produces most of it. The com-
bustion air contains both. If we were trying to manufacture NOx in this way,
we would go broke. For every million volumes of air, we would produce
only a few hundred volumes of nitric oxide (NO) and only a few tens of
volumes of nitrogen dioxide (NO
2
). Collectively, we refer to these as NOx.
Notwithstanding this paucity, 100 ppm is above regulated limits for most
combustion sources; at the time of this writing, limits are 25 to 50 ppm for
most processes and ever declining.
5.1.2 The Thermal NOx Mechanism
At very high temperature, we may cause nitrogen to react with oxygen:
N
2
+ O

2
→ 2NO (5.1)
Many elemental reactions contribute to NO formation. In the simplest
analysis, we may look at two:
1
O + N
2
= NO + N (5.2)
N + O
2
= NO + O (5.3)
N
2
+ O
2
→ 2NO
Oxygen is the second most reactive gas in the periodic table. Only fluorine
is more reactive. Oxygen dissociates relatively easily under high heat from
a diatomic molecule to an atomic entity:
1/2 O
2
= O (5.4)
© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 423
Atomic oxygen is very reactive and can rupture the very strong N≡N triple
bond. This frees a nitrogen atom in the process (Reaction 5.2). Atomic nitro-
gen goes on to attack the ambient oxygen (Reaction 5.3). The net reaction
produces NO (Reaction 5.1).
Since Reaction 5.2 involves the rupture of N≡N, it is the slowest reaction
and the rate-determining step. The rate-determining step is the slowest reac-

tion in a chain that paces the entire sequence. We always look for these where
possible because they reduce the analysis to fewer equations. Now we may
write the rate of the forward reaction in terms of the rate-limiting quantity
for a differential amount of substance:
where k
f
is the forward reaction rate constant and k
r
is the reverse reaction
rate constant. The brackets [ ] denote the concentration of the enclosed spe-
is a general kinetic expression. The forward reaction involves a forward rate
constant and the mathematical products of the reactant concentrations. From
this, we subtract the rate of the reverse reaction involving the reverse rate
constant and the mathematical product of the product concentrations.)
NO and N are present in very low concentrations. Therefore, we can safely
presume that the forward reaction will dwarf the reverse because N
2
is
present in a thousand times greater concentration. The equation simplifies to
The wet concentration of N
2
is practically constant throughout the com-
bustion reaction; subtracting a few ppm of NO via Reaction 5.2 from ~80,000
ppm (80%) nitrogen makes virtually no difference. However, the atomic
oxygen concentration is a different story.
To solve for this concentration, we presume an equilibrium relation
between molecular and atomic oxygen (called partial equilibrium because we
consider this part independent of the whole fabric of concurrent equilibrium
reactions). Equation 5.4 leads to the following equilibrium relation according
to:

(Equilibrium constants always involve the mathematical product of the reac-
tion products divided by the product of the reactants. Stoichiometric coeffi-
cients become exponents. Also, the equilibrium reaction is the ratio of the
forward to reverse reactions: .) Solving for [O] and combining con-
stants in k, we derive
d
dt
kk
fr
NO
ON NON
2
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
−
⎡
⎣
⎤
⎦

⎡
⎣
⎤
⎦
d
dt
k
f
NO
ON
2
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
K
O
=
⎡
⎣
⎤

⎦
⎡
⎣
⎤
⎦
O
O
2
1
2
Kkk
fr
=
© 2006 by Taylor & Francis Group, LLC
cies. (See Appendix G for a useful summary of formulating rate laws.) (This

424

Modeling of Combustion Systems: A Practical Approach

(5.5)
Now we may integrate this relation. Presuming [N

2

] is approximately
constant, we have
Finally, we note that

k

(like the equilibrium constant,

K

) has an Arrhenius
relation to temperature . With this substitution, we have the follow-
ing form:
(5.6)
where

A

is a preexponential coefficient termed the

frequency factor

, and in
this case it has the units of

√

[

L

3

/

N

], and

b

is a constant [

T

] related to the
activation energy of the reaction.
Equation 5.6 gives us a basic relation for NOx production. From it, we
may deduce that NOx is a strong (exponential) function of temperature, and
a weaker function of oxygen concentration and time.

5.1.3 The Fuel-Bound Nitrogen Mechanism

Most refinery fuels and natural gas do not contain significant amounts of
nitrogen bound in the fuel molecule. If that is the case, then the thermal NOx
mechanism described above will account for most of the NOx. If the fuel
contains significant nitrogen compounds, the

fuel-bound

mechanism predom-
inates. It is important to reemphasize that the fuel-bound mechanism sub-
sumes nitrogen bound as part of the fuel molecule. Diluting fuel gas with
diatomic nitrogen will not increase NOx, nor result in fuel-bound NOx, because
it is not chemically bound to the fuel. In fact, it will likely have the opposite

Some compounds can elevate NOx via the fuel-bound mechanism. They
include the following:
• Ammonia (NH

3

) and related compounds (e.g., ammonium hydroxide
also known as aqua ammonia — NH

4

OH and urea (NH

2

)

2

CO).
• Amines — there are three kinds.
– Primary amines have one organic group attached to the nitrogen
(R–NH

2

) where R stands for an organic group. In fuels, there are
usually hydrocarbons (e.g., if R is CH

3

CH

2

then R–NH

2

is ethyl-
amine CH

3

CH

2

NH

2

).
d
dt
k
NO
ON
2
⎡

⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
NO N O
2
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
⌠
⌡

⎮
kdt
2
()
(/ )
Ae
bT−
NO N O
2
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
−
⌠
⌡
⎮
⎮
Ae dt
b
T

2

© 2006 by Taylor & Francis Group, LLC
effect for reasons we will discuss in Section 5.2.6 and elsewhere.
Semiempirical Models 425
– Secondary amines have two organic groups attached to the ni-
trogen (R
1
R
2
NH). An example would be methyl ethylamine
(MEA), CH
3
NHCH
2
CH
3
. Since MEA is used in some refinery
operations, it may be entrained as a mist into the fuel supply,
termed amine carryover. This is expensive because the MEA
needs to be replaced, can exacerbate corrosion, and, most impor-
tantly for the topic of this chapter, can greatly elevate NOx from
the fuel-bound mechanism.
– Tertiary amines have no hydrogen atoms attached to the nitro-
gen. They may be of two types: R
1
R
2
R
3

N, for example, dimethyl
ethylamine (DMEA), (CH
3
)
2
NCH
2
CH
3
, or aromatic types, such
as pyridine C
6
H
5
N. Pyridine is often used as a surrogate to spike
the fuel-bound nitrogen content of a base oil for the purpose of
experimental investigations into fuel-bound NOx formation.
Heavy fuel oils contain related compounds that elevate NOx.
As far as the NOx chemistry is concerned, it makes little difference how
the fuel binds the nitrogen because it will pyrolyze to form HCN and CN
fuel fragments; that is, C
n
H
m
N → CN + HCN from the high heat radiating
from the downstream flame. The pyrolized fragments oxidize to hydrogen
and carbon monoxide. Finally, late in the process, the hydrogen and carbon
monoxide oxidize to H
2
O and CO

2
. This provides the bulk of the heat to
pyrolyze new fuel. If there is no nitrogen in the fuel, then there will be no
CN or HCN and there can be no fuel-bound NOx.
Returning to NOx formation, CN and HCN exist in partial equilibrium:
H + CN ↔ HCN. One fate of these fuel fragments is to generate atomic
nitrogen, which can oxidize to NO:
HCN = CH + N (5.7)
Then, NO formation occurs via N attack on diatomic oxygen; we gave this
relatively facile reaction earlier in Equation 5.3:
N + O
2
= NO + O
Because Equation 5.7 avoids the rupture of the N≡N triple bond, it has a
lower energy pathway for the generation of atomic N. Therefore, the pres-
ence of fuel-bound nitrogen greatly accelerates NOx kinetics. To formulate
a rate law, let us presume the following in Equation 5.3:
• The fuel pyrolysis is fast.
• The atomic nitrogen concentration is proportional to the concentra-
tion of nitrogen in the starting fuel.
• Reaction 5.3 is the rate-determining step.
© 2006 by Taylor & Francis Group, LLC
426 Modeling of Combustion Systems: A Practical Approach
Then a possible rate law is
(5.8)
5.1.4 The Prompt NOx Mechanism
If there is no fuel-bound nitrogen in the fuel, then there can be no fuel-bound
NOx. In such a case, the thermal-bound NOx mechanism discussed earlier
will generate most of the NOx. However, there is still another mechanism.
1

Suppose that a fuel fragment attacks diatomic nitrogen.
C
n
H
m
→ CH + C
n–1
H
m–1
CH + N
2
= HCN + N (5.9)
Reaction 5.9 is clearly rate limiting because it involves the rupture of an
N≡N triple bond by a fuel fragment. However, Reaction 5.2 is much faster.
But on the fuel side of the flame front, where there is no oxygen, Reaction
5.9 is the only real possibility. As one might imagine, N from this source is
meager and prompt NOx forms only 10 to 20 ppm NO at most. However,
modern ultra-low-NOx burners can produce 20 ppm NOx under some prac-
tical conditions. In such a case, prompt NOx must be a substantial contrib-
utor to the total NOx budget.
With the following presumptions, we may establish a rate law:
• The fuel pyrolysis is fast.
• CH is proportional to the number of carbons in the fuel molecule.
• Reaction 5.9 is the rate-limiting step.
This leads to the following rate equation:
(5.10)
Since [N
2
] is essentially constant, prompt NOx is proportional to the
amount of carbon in the fuel. Note that it is impossible for pure hydrogen

to form any prompt NOx even though it may generate much thermal NOx
(owing to hydrogen’s very high flame temperature). In fact, the thermal NOx
mechanism causes hydrogen-combusting vehicles to generate more NOx
than even gasoline engines.
d
dt
k
nm
NO
CH N O
2
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
d
dt
k
nm
n
NO

CH N
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
© 2006 by Taylor & Francis Group, LLC

Semiempirical Models

427

5.1.5 Chemical Kinetic Effects for NOx in Diffusion Flames

Diffusion flames require mixing of the fuel and air external to the burner. In
such a case, additional air not only increases the oxygen concentration, but
aids in fuel mixing. The additional facility of oxygen transport to the flame
zone increases the availability of oxygen for NOx production. Hence, addi-
tional air increases NOx. At some point, there is sufficient oxygen transport,
and the further addition of air does not increase the NOx production rate
enough to offset the cooling effect of more air. At this point, the NOx begins

to fall. This phenomenon occurs between 5 and 8% oxygen for most indus-
trial flames. At high bridgewall temperatures oxygen as high as 8% may still
increase NOx because the kinetics are still fast, whereas for low bridgewall
temperatures, oxygen above 5% tends to reduce NOx production, as it is
easier to cool the flame. With premixed flames, additional oxygen does not
significantly enhance the availability of oxygen for the NOx reaction — at
least not enough to offset the cooling effect of the additional air. Therefore,
additional air decreases NOx production in premixed flames.
We begin by considering the NOx response for diffusion flames to oxygen,
temperature, and fuel composition. Then we shift our attention to the behav-
ior of premixed flames regarding these factors.

5.1.5.1 NOx Response to Air in Diffusion Flames

The addition of oxygen has two effects on NOx: the first is the pure dilution
measured NOx concentration. We can account for this exactly using dilution
correction. A mass balance grounds the dilution correction on solid theoret-
ical footing without the need for any adjustable parameters in the final
equations. Additionally, oxygen participates in NOx chemistry. Unlike dilu-
tion correction, estimation of this effect (chemical kinetic) necessarily
involves some empiricism: the amount of excess air affects the availability
of oxygen and the flame temperature.
Small increases in excess air do not abstract significant heat from the flame
and they aid in flame mixing, thereby increasing the availability of oxygen
and increasing the NOx (see Equation 5.6). Theoretically, the local flame
stoichiometry remains at unity regardless of the global oxygen concentration
for a diffusion flame. This would certainly be so for normal variations in
excess air between 0 and 5%. If this is so, then we may place the temperature
effect outside the integral. Nitrogen will vary little for small differences in
oxygen, and we place it outside the integral as well. This was the basis for

Equation 5.6, developed earlier:
NO N O
2
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
−
⌠
⌡
⎮
⎮
Ae dt
b
T
2

© 2006 by Taylor & Francis Group, LLC
effect of adding air. As we have seen in Section 2.4.10, this acts to reduce the
428 Modeling of Combustion Systems: A Practical Approach
Making use of the ideal gas law, we may recast Equation 5.6 in terms of

mole fractions. This gives
or
(5.11)
We do not know precise oxygen–time history in a diffusion flame. How-
ever, we may define a dimensionless reaction coordinate, χ, such that
(5.12)
and , where y
O2,b
is the wet mole fraction of oxygen in the windbox
or burner plenum (initial O
2
), y
O2,wet
is the wet mole fraction of oxygen along
the reaction coordinate, y
O2,g
is the wet mole fraction of oxygen in the effluent
flue gas (final O
2
), t is the time along the reaction coordinate, and θ is the
total reaction time.
Then and . Making these substitutions
into Equation 5.11 gives
or
where
(5.13)
y
P
RT
Ae y

P
RT
P
RT
ydt
b
T
NO
=
−
⌠
⌡
⎮
⎮
⎮
N2
O2
yAey
P
RT
ydt
b
T
wet wetNO
=
−
⌠
⌡
⎮
⎮

N2, O2,
χ
θ
=
−
−
=
yy
yy
t
bwet
bg
OO
OO
22
22
,,
,,
01≤≤χ
yy y
wet b gOO O22 2
1
,, ,
=−
()
+χχdt d=θ χ
yAey
P
RT
yyd

b
T
bgNO N2 O2 O2
=−
()
+
−
⌠
⌡
⎮
⎮
θχχχ
,,
1
0
1
yAey
Py
RT
b
T
b
NO N2
O2
=+
()
−
⌠
⌡
⎮

⎮
θχζ
,
–11
0
1
ζ= =
y
y
y
y
wet
b
g
b
O2
O2
O2
O2
,
,
,
,
© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 429
where y
O2,g
is the final oxygen concentration (wet) of the flue gas. The integral
resolves to
(5.14)

Note that because ; likewise, because ; there-
fore, .
For practical combustion problems ζ is close to zero; e.g., for y
O2,b
= 21%
and y
O2,g
= 3%, ζ = 1/7 and . For small ζ, a two-term Taylor
series gives
This substitution reduces the equation to
If the total reaction time is an Arrhenius function of temperature, then we
may combine constants and take the log to give
(5.15)
There are strong theoretical reasons to use log NOx rather than NOx. For
example, data from planned experiments
2
show that the distribution of error
is lognormal. Hence, one should use the log transform to correlate NOx data
if fitting semiempirical correlations of NOx. Other statisticians have made
more general statements about the log transform for environmental data
3
;
such data have zero as their lower limit but no theoretical upper bound.
yAey
Py
RT
d
b
T
b

NO N2
O2
=− + −
()
⎡
⎣
⎤
⎦
+−
−
θχζχζ
,
1111
32
(()
⎡
⎣
⎤
⎦
⌠
⌡
⎮
⎮
1
0
yAey
Py
RT
b
T

b
NO N2
O2
=
−
−
⎛
⎝
⎜
⎞
⎠
⎟
−
2
3
1
1
32
θ
ζ
ζ
,
ζ<1 yy
gbO2 O2,,
< ζ>0
y
gO2,
> 0
01<<ζ
ζ

32
118 0<≈
ζ
ζ
ζ
32
1
1
1
−
−
≈+
yAy
Py
RT
e
b
b
T
NO N2
O2
=
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥

+
()
−
,
θζ
2
3
1
ln ln ln ln
,
yAy
Py
R
T
b
T
b
NO N2
O2
=
′
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
−−

′
+
1
2
2
3
11+
()
ζ
© 2006 by Taylor & Francis Group, LLC
430 Modeling of Combustion Systems: A Practical Approach
Therefore, the log-transformed data distribute more normally than untrans-
formed data for emissions.
From Equation 5.15, a semiempirical equation to correlate NOx with oxy-
gen from diffusion flames would have the form
where
For small ζ, we may even linearize the log function and write
(5.16)
If there is no flue gas recirculation to the windbox, then y
O2,a
= y
O2,g
and
. Letting , Equation 5.16 becomes
(without FGR) (5.17)
Then an estimate for NOx from one oxygen condition to a reference con-
dition becomes
With suitable adjustment of we may use either wet or dry concentrations
for oxygen. Theoretically, which is too low. However,
our goal was to find an approximate model and use the data to adjust the

parameter. Data for low-NOx burners using dry oxygen values yield
, and we shall use .
(without FGR) (5.18)
ln lnya
NO
=+ +
()
0
2
3
1 ζ
aAy
Py
R
T
b
T
b
0
1
2
=
′
⎡
⎣
⎢
⎢
⎤
⎦
⎥

⎥
−−
′
ln ln
,
N2
O2
ln ya
NO
=+
0
2
3
ζ
ζ=yy
gaO2 O2,,
ay
a1
23= ()
,O2
ln
,
yaay
gNO O
=+
012
ln
,,
y
y

ay y
ref
g ref
NO
NO,
OO2
⎛
⎝
⎜
⎞
⎠
⎟
=−
()
12
a
1
a
1
2 3 100 21 3=≈()( ),
12 16
1
<<a a
1
14=
ln
,,
y
y
yy

ref
O g ref
NO
NO,
O2
⎛
⎝
⎜
⎞
⎠
⎟
≈−
()
14
2
© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 431
Example 5.1 Estimation of the Chemical Kinetic
Effects of Oxygen
Problem statement: A high-temperature furnace generates 40
ppm corrected to 3% O
2
when using a state-of-the-art low-NOx
burner at 2% O
2
. Use Equation 5.18 to estimate the chemical
kinetic effect on NOx when oxygen increases from 2 to 3%. If the
reactor temperature remains constant due to a decrease in feed
rate, what are the actual NOx concentrations in ppm for each case?
Solution: Equation 5.18 becomes

Then
= 46 ppm
Note that even though the dilution correction for NOx is 3% O
2
,
we have used 2% O
2
as the chemical reference condition because
this is where we know the value of NOx. In other words, although
2% O
2
is the reference for dilution correction, it is not the reference
for the chemical kinetic correction based on the problem state-
ment.
Unlike dilution correction, this represents a real increase in cor-
rected NOx. That is, the NOx has gone from 40 ppm corrected to
3% O
2
to 46 ppm corrected to 3% O
2
. To find the actual concen-
trations (what one would actually measure with an analyzer), we
use the dilution correction formula (Equation 2.69):
Now 40 ppm NOx corrected to 3% O
2
must give the following if
corrected to 2% O
2
:
= 42.2 ppm

This makes sense. As the dilution air decreases, the mole fraction
NOx increases. There is no need to correct the 46 ppm number
because both the actual and dilution reference concentrations are
ln . .
y
NO
40
14 0 03 0 02
⎛
⎝
⎜
⎞
⎠
⎟
=−
()
ye
NO
ppm=
−
()
40
14 0 03 0 02
[]
y
y
yy
yy
NO i
NO e

Oa Oi
Oa Oe
,
,
,,
,,
=
−
−
22
22
y
NO
ppm=
−
−
⎛
⎝
⎜
⎞
⎠
⎟
21 2
21 3
40[ ]
© 2006 by Taylor & Francis Group, LLC
432 Modeling of Combustion Systems: A Practical Approach
3%. Therefore, we expect the actual flue gas analysis to be as
follows.
Before: NOx = 42.2 ppm, O

2
= 2%
After: NOx = 46 ppm, O
2
= 3%
The reduction in O
2
from 3 to 2% masks the true increase in NOx.
Looking only at raw (uncorrected) values, a 3.8 ppm increase in
NOx is apparent. But with both NOx values on the same basis,
the corrected NOx is actually 6 ppm greater at 3% O
2
reference
conditions.
5.1.5.2 Dimensional Units for NOx
One can see the potential for confusion when using concentration-based
NOx values. For this reason, other NOx units have arisen. The two most
common are milligrams per normal cubic meter (mg/Nm
3
) and pounds mass
per million BTUs (lbm/MMBtuh). The nomenclature is in wide use, but it
is equivocal; that is, N does not stand for Newtons as one might expect in
an SI quantity, and each M stands for thousand (not million) from the Latin
prefix mille. This is the source of the Roman numeral M, but unlike Roman
numerals, MM stands for 1000·1000 = 1,000,000. Because environmental engi-
neering is an emerging discipline, we can expect these kinds of equivocations
into the near future.
Moreover, even these units require reference conditions. For example, a
normal cubic meter must have reference to some oxygen concentration in
the flue gas, and the typical reference is 3% oxygen. The exact conversion at

reference conditions from ppm to mg/Nm
3
is
With respect to lb/MMBtu, the conversion depends on the actual fuel
stoichiometry, and it depends on whether we use the higher or lower heating
value. In the boiler industry, the higher heating value (HHV) is usually the
basis, while the refining industry typically uses the lower heating value
(LHV). A rule of thumb based on the HHV of natural gas (and similarly for
most hydrocarbon fuels) is
2 055
1
.
mg NOx
Nm
ppm NOx
3
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎤
⎦
=
40 0 05ppm NOx
lbm NOx
MMBtu

⎡
⎣
⎤
⎦
≈
⎡
⎣
⎢
⎤
⎦
⎥
.
© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 433
On an LHV basis, the lbm/MMBtu number is about 10% higher. We can
derive an exact expression using the following logic:
1. Convert the ppm reading of the emission (y
x,ref
) to 0% O
2
reference:
2. Solve for TDP at 0% O
2
, which gives the moles of dry flue-gas per
mole of fuel. From Equation 2.16b at 0% O
2
this is
3. Multiply item 2 by item 1 to obtain the moles of emission per mole
of fuel:
4. Multiply item 3 by the molecular weight of the emission (W

x
) to
obtain the mass of the emission per mole of fuel:
For NOx, most regulatory agencies use NO
2
for the molecular weight
calculation, regardless of the actual NO/NO
2
ratio in the flue gas.
5.
Regulatory districts may use either the higher or lower heating value
in this calculation. Therefore, one must use the proper metric. (For
the sake of calculations in this text, we will use the lower heating
value, but this will not always be the case in actual practice.)
6. Divide item 4 by item 5 to find the emission on a mass/heat release
basis.
(5.19)
y
y
y
x
ref
x ref,
,
,
%
%
0
2
21

21
=
−
⎛
⎝
⎜
⎞
⎠
⎟
O
TDP =+
⎛
⎝
⎜
⎞
⎠
⎟
−
100
21
1
44
ψψ
yTDPy
y
x x ref
ref
,,
,
%

%
0
2
21
21
100
21
1
()
=
−
⎛
⎝
⎜
⎞
⎠
⎟
+
O
ψψψ
44
⎛
⎝
⎜
⎞
⎠
⎟
−
⎡
⎣

⎢
⎤
⎦
⎥
yTDPWyW
y
x x x ref x
ref
,,
,
%
%
0
2
21
21
100
()
=
−
⎛
⎝
⎜
⎞
⎠
⎟
O
221
1
44

+
⎛
⎝
⎜
⎞
⎠
⎟
−
⎡
⎣
⎢
⎤
⎦
⎥
ψψ
y
TDP W
H
y
W
H
y
x
x
c
x ref
x
c
re
,,

,
ˆ
0
2
21
()
=
⎛
⎝
⎜
⎞
⎠
⎟
−
Δ
Δ

O ff
21
100
21
1
44
⎛
⎝
⎜
⎞
⎠
⎟
+

⎛
⎝
⎜
⎞
⎠
⎟
−
⎡
⎣
⎢
⎤
⎦
⎥
ψψ
© 2006 by Taylor & Francis Group, LLC
Find the heating value of the fuel per mole (Appendix A). Important:
434 Modeling of Combustion Systems: A Practical Approach
Example 5.2 Conversion of ppm to lb/MMBtu
Problem statement: Use Equation 5.19 to convert 40 ppm NOx
at 3% O
2
to its equivalent in lb/MMBtu for CH
4
combustion.
Compare the results using both the lower and higher heating
values and the rough rule of thumb.
Btu/lbm, which equates to
.
For methane, ψ = 4, and on an LHV basis, Equation 5.19 becomes
We can ratio this result by the LHV/HHV ratio to convert to an

HHV basis:
HHV basis
The rough rule of thumb gives 40 ppm ≈ 0.050 lbm/MMBtu
(HHV) and 0.055 lbm/MMBtu (LHV).
5.1.5.3 The Relation of Referent and Objective Forms
Earlier, we extrapolated NOx emissions behavior from one condition (the
reference condition) to another. We shall define this kind of equation as the
referent form of the equation: a referent form is a correlating equation com-
prising parameters derived from at least one known response factor pair —
the referent pair. We may then express the factors and responses as deviations
from the reference condition. For example, Equation 5.20 is the referent form
of an equation for a straight line.
(5.20)
21 495 16 04 344,. ,
Btu
lbm
lbm
lbmol
⎡
⎣
⎢
⎤
⎦
⎥
⋅
⎡
⎣
⎢
⎤
⎦

⎥
=
7780
Btu
lbmol
⎡
⎣
⎢
⎤
⎦
⎥
40
40 10 10 46 01
66
ppm
Btu
MMBtu
lbm
lb
→
⋅⋅
⎡
⎣
⎢
⎤
⎦
⎥
⋅
−
.

mmol
Btu
lbmol
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎢
⎤
⎦
⎥
−
⎛
⎝
⎜
⎞
⎠
⎟
344 780
21
21 3
,
1100
21
1
4

4
4
4
0 053+
⎛
⎝
⎜
⎞
⎠
⎟
−
⎡
⎣
⎢
⎤
⎦
⎥
=
⎡
⎣
⎢
⎤
.
lbm
MMBtu
⎦⎦
⎥
0 053
21 495
23 845

0 048.
,
,
.
lbm
MMBtu
lbm
MM
⎡
⎣
⎢
⎤
⎦
⎥
⋅=
BBtu
⎡
⎣
⎢
⎤
⎦
⎥
yy
xx
m
ref
ref
−
−
=

© 2006 by Taylor & Francis Group, LLC
Solution: From the table in Appendix A we have LHV = 21,495
Semiempirical Models 435
In the above equation, y is the response, x is a factor, y
ref
is a known value
of the response at x
ref
, a known value of the factor, and m is the slope of the
line (rise-to-run ratio). We also know this particular equation form as the
point–slope form of a line because it derives from a point (x
ref
, y
ref
) and a slope
(m).
In contrast, an objective form is a correlating equation relating a response
to a function of one or more factors without any declaration of known
factor–response pairs. For example, the same equation in objective form is
(5.21)
where b is the offset. In comparing the two equations, we see that
. When we have known reference conditions, the referent form
will be the most convenient to use. It also has the advantage of eliminating
the offset. The offset in Equation 5.20 is implicit (undeclared). Obviously, it
is always possible to transform a referent form into an objective form and
of pertinent factors for various emissions reduction strategies. One may
convert between forms as required.
5.1.5.4 NOx Response to Temperature in Diffusion Flames
One can conduct experiments with burners and furnaces to reach any desired
target oxygen concentration for any given heat release. This is merely a

matter of controlling the air/fuel ratio. However, matching the actual heat
profile of a heater is much more difficult. Experimentally, one must add or
remove insulation to achieve the proper bridgewall temperature. This is a
cumbersome job for a test heater of any size. Current practice requires full-
scale testing of at least one or two burners. Two-burner testing has the
advantage of quantifying burner–burner and burner–furnace interactions.
art simulator for ethylene cracking capable of firing two floor burners and
several levels of wall burners at full scale. The internal firebox is more than
12 m tall.
The general test procedure comprises matching the bridgewall tempera-
ture for the maximum heat release case and recording emissions. Then, at
lower loads, one must correct the NOx to the target temperature. To derive
such a correction, we begin with Equation 5.15:
ymxb=+
by mx
ref ref
=−()
ln ln ln ln
,
yAy
Py
R
T
b
T
b
NO N2
O2
=
′

⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
−−
′
+
1
2
2
3
11+
()
ζ
© 2006 by Taylor & Francis Group, LLC
These can be strong for low-NOx burners. Figure 5.1 shows a state-of-the-
vice versa. Sections 5.1.5 and 5.1.6 list some equations for NOx in referent
form. In Section 5.2, we will list objective forms for emissions as a function
436 Modeling of Combustion Systems: A Practical Approach
Usually, one applies these kinds of corrections over no more than ±100°C.
Over such a range, we can linearize the foregoing equation to two terms
with either
(5.22)
or
(5.23)
Over small ranges, either equation is acceptable, and we shall choose the

simpler (Equation 5.23). Theoretically, over larger ranges, Equation 5.22
should be preferred, but we are unlikely to see a large difference in practice.
For extended ranges, Equation 5.15 suggests
(5.24)
FIGURE 5.1
An ECU simulator. The figure is a picture of a state-of-the-art ECU simulator capable of firing
up to 8 MW using up to two floor burners and six sidewall burners in three rows. (From Baukal,
C.E., Jr., Ed., The John Zink Combustion Handbook, CRC Press, Boca Raton, FL, 2001.)
ln ya
a
T
NO
=−
0
1
ln yaaT
NO
=+
01
ln ln
,
yaaT
a
T
ay
gNO O
=− −+
01
2
32

© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 437
For small temperature excursions, we may recast Equation 5.23 with com-
parison to some reference condition.
(5.25)
Then, if we know y
NO,ref
for a given burner and bridgewall temperature, we
may find y
NO
for a new bridgewall temperature. An empirical value is a
1
≈
1/1000 [K].
A purely empirical and dimensional NOx correction equation that has
been in use for more than 20 years* is
(5.26a)
or
(5.26b)
This equation derives from empirical NOx behavior of first-generation
low-NOx burners and conventional burners.** Because it does not capture
any exponential behavior whatsoever, we can expect that it is applicable
within ± 50°C or so.
Example 5.3 Correcting NOx for Temperature
Problem statement: A furnace generates 40 ppm (corrected to 3%
O
2
) at 2190°F. However, the target temperature is actually 2246°F.
Estimate the corrected NOx at the target temperature. If the cor-
rected NOx limit were 50 ppm, would you be satisfied with the

burner’s NOx performance?
Solution: We may use either Equation 5.25 or Equation 5.26. We
begin with Equation 5.26, leading to
= 41.3 ppm
* Developed by John Zink LLC, Tulsa, OK.
** Claxton, M., private communication, 2004.
ln
y
y
aT T
ref
BWT ref
NO
NO,
⎛
⎝
⎜
⎞
⎠
⎟
=−
()
1
y
y
t
t
ref ref
NO
NO

FF
FF
,
[]
[]
=
°− °
°− °
400
400
y
y
t
t
ref
ref
NO
NO
CC
CC
,
=
°
⎡
⎣
⎤
⎦
−°
°
⎡

⎣
⎤
⎦
−°
204
204
y
NO
FF
FF
ppm=
°− °
°− °
⎛
⎝
⎜
⎞
⎠
⎟
2246 400
2190 400
40[ ]
© 2006 by Taylor & Francis Group, LLC
438 Modeling of Combustion Systems: A Practical Approach
Equation 5.25 leads to
= 42.3
So both corrections lead approximately to the same results. If the
maximum emissions limit is 50 ppm, then the burner is safely
under the limit, being less than 85% of the requirement. However,
if the requirement were 45 ppm, neither equation would estimate

an adequate safety margin. Generally, one would like test emis-
sions to be less than 90% of the statutory limit to account for
deviations in fuel and operation.
5.1.5.5 NOx Response to Fuel Composition
The flame temperature significantly affects the thermal NOx. In turn, hydro-
gen concentration has the most profound influence on the flame temperature.
Since we are considering fuel composition effects only, we may look at
adiabatic flame temperature as an indication of the true flame temperature
and the major NOx influence for composition changes. That is, for a given
furnace temperature, the flame temperature should scale as a linear function
of the adiabatic flame temperature. Therefore, we may consider adiabatic
flame temperature ratios as indicators of relative NOx production from the
fuels. If we presume that the temperature effect dominates the NOx produc-
tion, then we may start with Equation 5.22:
and
Presuming the flame temperature is an average of the bridgewall and
adiabatic flame temperatures, we have T = (T
AFT
+ T
BWT
)/2. Substituting this
relation gives
(5.27)
ye
NO
ppm=
⎡
⎣
⎤
⎦

−
⎛
⎝
⎜
⎞
⎠
⎟
40
2246 2190
1000
ln ya
a
T
NO
=−
0
1
ln
y
y
a
TT
ref ref
NO
NO,
⎛
⎝
⎜
⎞
⎠

⎟
=−
⎛
⎝
⎜
⎞
⎠
⎟
1
11
ln
y
y
a
TT T
ref ref AFT BWT
NO
NO,
⎛
⎝
⎜
⎞
⎠
⎟
=−
+
⎛
⎝
⎜
⎞

⎠
⎟
1
12
© 2006 by Taylor & Francis Group, LLC
thermal mechanism. Appendix A, Table A.2 shows the difference among
Semiempirical Models 439
5.1.5.6 Chemical NOx When Prompt NOx Is Important
All of these approaches ignore the prompt NOx contribution of hydrocarbon
fuels, and the effect can be significant for ultra-low-NOx burners that dilute
the fuel with lots of flue gas before combustion. Therefore, ultra-low-NOx
burners are often less sensitive to adiabatic flame temperature differences,
but more sensitive to hydrocarbon concentrations. For prompt NOx, Equa-
tion 5.10 states
Or in terms of mole fraction, we obtain
In order to integrate it we will use a parameter, χ, such that
and , where θ is the time to complete the reaction
and y
CnHm,0
is the concentration of C
n
H
m
at time zero. Here n is the average
carbon chain length and , where is the average H/C ratio. These
give
=
or
(5.28)
Theoretically,

Combining Equations 5.22 and 5.28 and consolidating constants gives
d
dt
k
nm
n
NO
CH N
⎡
⎣
⎤
⎦
=
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
2
yk
P
RT
yy dt
n
nm
n
NO N C H

=
⎛
⎝
⎜
⎞
⎠
⎟
+
⌠
⌡
⎮
⎮
1
2
yy
nm nmCH CH
=−
,
()
0
1 χ t =θχ
mn=ψ ψ
yk
P
RT
yy d
n
nm
n
n

NO N C H ,
=
⎛
⎝
⎜
⎞
⎠
⎟
−
()
−
()
+
θχχ
1
20
1
0
11
⌠⌠
⌡
⎮
⎮
nk
P
RT
yy
n
nm
n

θ
⎛
⎝
⎜
⎞
⎠
⎟
+1
20NCH,
ln
NO C H ,
yany
nm
()
=+
00
ak
P
RT
y
n
0
1
2
=
⎛
⎝
⎜
⎞
⎠

⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
+
ln
N
θ
ln
CH ,
yany
a
T
nmNO
=+ −
00
1
© 2006 by Taylor & Francis Group, LLC
440 Modeling of Combustion Systems: A Practical Approach
Substituting T = (T
AFT
+ T
BWT
)/2 for T we have
(5.29)

One problem is determining the actual fuel concentration. For that, we
will need to construct some kind of fuel concentration history so that we
can define an average concentration for Equation 5.29. Fuel jets scale with a
length-to-diameter ratio (L/d
o
), where L is the length of the jet until it contacts
the airstream and d
o
is the diameter of the orifice. The sum of all such jets
is proportional to the area (or d
o
2
). Multiplying the two contributions, we
have Ld
o
, the sum being ΣLd
o
. Then Equation 5.29 becomes
(5.30)
where k is an index from 1 to n
o
, the total number of all burner fuel orifices,
L
k
is the length of the k
th
fuel jet before contacting the airstream, and d
o,k
is
the diameter of the k

th
fuel orifice. Since we know T
AFT
and T
BWT
, we may
regress all of the constants from the data.
5.1.6 Chemical Kinetic Effects for NOx in Premixed Flames
NOx in premix flames behaves similarly to that of diffusion flames with
respect to temperature, but differently with respect to air.
5.1.6.1 NOx Response to Temperature in Premixed Flames
For premix burners, we can use the temperature equations we developed
earlier to correlate temperature behavior, e.g., Equations 5.22, 5.24, or 5.25.
Therefore, these are still valid for premix burners. However, the behavior of
NOx in response to air for premixed burners is dramatically different from
that of diffusion flames.
5.1.6.2 NOx Response to Air in Premixed Burners
Premixed burners intimately mix fuel and air. Therefore, additional air does
not substantially increase oxygen availability; actually, increased airflow
removes heat from the flame. The overall effect is to reduce NOx with
increasing air/fuel ratio via flame cooling. We begin as before with Equation
5.22.
ln
CH ,
yany
a
TT
nm
AFT BWT
NO

=+ −
+
00
2
ln
,
yaaLd
a
TT
kok
k
n
AFT BWT
o
NO
=+ −
+
=
∑
01
1
2
© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 441
However, to solve this equation in terms of air effects, we will need expres-
sions for T and ζ in terms of some measure of air/fuel ratio, say, α
w
. In fact,
this is useful for its own sake, so we digress to list these expressions below.
5.1.6.3 Solving for ζζ

ζζ
as a Function of αα
αα
w
By combining Equations 2.16a and 2.32, we obtain . Solving
Equation 2.85 for α
w
and substituting into the former equation yields
Rearranging Equation 2.32 to solve for ε gives
w
Substituting the expressions for α
w
into Equation 2.17b gives y
O2,wet
as a
function of α
w
:
(5.31)
Substituting Equation 5.31 into Equation 5.13 gives
(5.32)
5.1.6.4 Solving for T as a Function of αα
αα
w
Now we know from Equation 2.93 that
TWP =+αψ4
TWP
W
W
w

f
a
=+α
ψ
4
ε
α
ψ
=
+
()
−
84
100 4
1
ε
α
ψ
=
+
()
−
84
100 4
1
wf
a
W
W
y

WW W
WW
Owet
wf a a
wf a
2
084 4
4
,
.
=
−−
+
αψψ
αψ
ζ
αψψ
αψ
=
−−
+
⎛
⎝
⎜
⎞
⎠
⎟
1
084 4
4

2
y
WW W
WW
b
wf a a
wf aO,
.
T
H
C
T
AFT
c
pw
a
=
+
()
+
Δ
1 α
© 2006 by Taylor & Francis Group, LLC
or in terms of α (Section 2.5.4):
442 Modeling of Combustion Systems: A Practical Approach
where α
w
is a function only of fuel composition (ψ) and excess air rate (ε),
and T
a

is the air temperature. Presuming once again that the flame temper-
ature is given by T = (T
AFT
+ T
BWT
)/2, we obtain
(5.33)
5.1.6.5 Log NOx as a Function of αα
αα
w
Substituting Equation 5.33 into Equation 5.22 gives
(5.34)
or letting
and
we have
(5.35)
Then
(5.36)
This makes NOx a weak but decreasing function of α
w
. If we desire a
numerical approximation, however, we cannot regress the coefficients of
Equation 5.36 from a data set via least squares — the equation is nonlinear
in the coefficients. A two-coefficient function that has the same behavior at
the limits is
(5.37)
We may derive this by noting that
T
H
C

TT
HCT T
pw
aBWT
pa BWT w
≈
+
()
+
+
=
++
()
+
()
Δ
Δ
21
2
1
α
α
221C
pw
+
()
α
ln ya
aC
HCT T

pw
pa BWT w
NO
=−
+
()
++
()
+
()
0
1
21
1
α
αΔ
β
0
11
22
=+
+
()
ΔH
aC
TT
a
p
aBWT
β

1
1
2
=
+
()
TT
a
aBWT
ln ya
w
w
NO
=−
+
+
0
01
1 α
ββα
ln
,
,
y
y
ref
w ref
w ref
wNO
NO,

⎛
⎝
⎜
⎞
⎠
⎟
=
+
+
−
+
1
1
01
α
ββα
α
βββα
01
+
w
ln
y
y
ref w
NO
NO,
⎛
⎝
⎜

⎞
⎠
⎟
=+
+
δ
δ
α
0
1
1
lim
ln
,
,
α
α
ββα
w
ref
w ref
wr
y
y
→∞
⎛
⎝
⎜
⎞
⎠

⎟
=
+
+
NO
NO,
1
01eef
−
1
1
β
© 2006 by Taylor & Francis Group, LLC
Semiempirical Models 443
and
where
and
or, conversely,
and
5.2 Overview of NOx Reduction Strategies
Ultimately, we wish to derive equations to correlate the effects of various
NOx reduction strategies. In order to do that, we first shall give a general
overview of these. Afterward, we shall meld our knowledge of NOx reduc-
tion with the NOx formation models we have already developed. This will
arrive at our destination — semiempirical equations for NOx in response to
NOx reduction methods.
5.2.1 Low Excess Air (LEA) Operation
Low excess air (LEA) reduces the available oxygen concentration, thereby
reducing thermal and fuel-bound contributions to NOx. The reduction strat-
egy is global in the sense that the entire furnace environment operates under

low excess oxygen conditions, not just the near-burner region. CO trim is the
strategy of reducing oxygen until the onset of CO formation. CO trim is
especially effective for boilers burning natural gas or other constant-compo-
sition fuels or for those fuels whose composition changes only slowly. The
strategy requires automated furnace stack dampers (or automated fan) and
automated burner registers. Usually, refinery process heaters lack automatic
airflow control and use manual burner registers.
ln
,
,
y
y
ref
w ref
w ref
w
NO
NO,
⎛
⎝
⎜
⎞
⎠
⎟
=
+
+
−
=α
α

ββα
0
01
1
11
0
β
δ
ββ
1
10
11
=−
δ
α
ββα β
0
01 1
1
1
=
+
+
−
w ref
w ref
,
,
β
δ

αδ
δδ
0
1
0
01
1
1=−
+
+
⎛
⎝
⎜
⎞
⎠
⎟
w ref,
β
δα δδ
1
101
1111
=+ +
⎛
⎝
⎜
⎞
⎠
⎟
w ref,

© 2006 by Taylor & Francis Group, LLC
444 Modeling of Combustion Systems: A Practical Approach
Figure 5.2 shows a schematic of the general CO trim concept. The air/fuel
controller attempts to maintain a constant air/fuel ratio. Oxygen control
biases this air/fuel ratio based on a target oxygen concentration. Thus, as
the air density or fuel composition varies over the course of the day, oxygen
control maintains oxygen level and furnace efficiency. However, at higher
furnace temperatures, one can tolerate lower oxygen levels without gener-
ating significant CO.
The CO trim controller works by comparing the CO in the furnace to some
target, say, 200 ppm. If the CO is low or nonexistent, then the CO trim
controller biases the oxygen setpoint downward. The CO trim controller can
be a typical proportional-integral-derivative (PID) controller. However, with
distributed control systems (DCSs) and programmable logic controllers
(PLCs) one may use a CO–O
2
relation, φ(x), built directly into the logic. One
may develop an O
2
–CO relation by collecting data at various temperatures
in a designed experiment. We develop the actual semiempirical model in
ward model modified response surface methodology (MRSM). Feedforward con-
trol provides superior process control to feedback-only strategies. However,
accurate feedforward control requires accurate feedforward models,
4
and
MRSM is ideal for this function. (This strategy is also useful for feedforward
control of NOx
5
in fired equipment such as boilers.

6
) The reader should note
that the difference between 200 and 1000 ppm CO is often 0.2% O
2
or less.
That is, if 1.1% O
2
gives 200 ppm, 0.9% will give about 1000 ppm. Since an
extra 0.2% O
2
represents only a trivial energy penalty, a 200 ppm CO target
is adequate to ratchet down the O
2
to its minimal level.
FIGURE 5.2
A CO trim strategy. The air/fuel controller attempts to maintain a constant air/fuel ratio.
Oxygen control biases the input to the air/fuel controller to account for changes in fuel com-
position and airflow. If the fuel composition varies slowly enough, one may also trim O
2
to its
minimum level by biasing the O
2
controller setpoint based on a CO analysis of the furnace flue gas.
from CO
analyzer
CO Trim
Controller
from O
2
analyzer

O
2
Controller
Air/Fuel
Controller
to air
damper
PID
PID
Σ
Σ
(y
CO
)
φ
CO
SP
O
2
SP
Firing
Rate
© 2006 by Taylor & Francis Group, LLC
Section 5.4. We shall call feedforward control with a semiempirical feedfor-
Semiempirical Models 445
CO trim is often impossible with refinery gas because the fuel may change
composition drastically. In turn, changing fuel composition can alter the
theoretical air requirements significantly. If the fuel composition undergoes
significant variation in hydrogen content, then the required air changes
dramatically. The result is that for a given heat release and airflow, O

2
can swing
2
of CO and dangerous heater operation. With these kinds of swings in oxygen
fraction, minor adjustments (trim) to the O
2
setpoint is useless. Therefore, CO
trim is usually not appropriate for process heaters in the refinery.
Another reason most process heaters cannot use CO trim is because in
addition to automated stack damper control, one must also have automated
air register adjustment of the burners — automated stack damper control
alone is insufficient. It stands to reason that if one seeks to control both draft
and oxygen level, one needs two control elements: stack damper and burner
registers, or airflow and draft control. Manual CO trim adjustments are not
possible because the furnace requires many adjustments to maintain precise
oxygen levels on a continual basis.
One must measure CO in the furnace in order to use CO trim. The stack
CO does not meaningfully relate to the combustion in the furnace because
CO will further oxidize to CO
2
before reaching the stack and underreport
the actual furnace CO level. Additionally, stacks leak, drafting in oxygen, in
natural and balanced draft systems. Air preheaters leak too, so CO measure-
ment after this point is prone to error as well. Besides, in situ CO analyzers
for furnaces are inexpensive. The only proper function of stack analyzers is
to measure emissions leaving the unit. One should not use them to control
combustion. Most process heaters do not have CO trim control. However,
boilers or heaters with a constant-composition fuel supply can use CO trim
to maximize unit efficiency.
5.2.2 Air Staging

In contrast to LEA, air staging is a local NOx reduction strategy. Dividing
the combustion into two zones can reduce NOx. In the first zone, all of the
fuel meets some of the air producing very low NOx and high levels of
combustibles. A second zone adds air to complete the combustion. Since the
flame will transfer some heat to the process before encountering the second
zone, the flame temperature will be lower, thus reducing thermal and fuel-
bound NOx. Air staging is an effective strategy for reducing NOx from fuel-
bound nitrogen because it minimizes contact with air as the fuel pyrolyzes
(see Equation 5.8). Fuel-bound nitrogen converts to N
2
rather than NO in
the absence of sufficient oxygen.
5.2.3 Overfire Air
Overfire air is the global version of air staging. Rather than staging the air
only in the burner, one divides the entire furnace volume into two zones.
© 2006 by Taylor & Francis Group, LLC
from 3 to 0% (see Chapter 2). Obviously, 0% O will generate copious quantities