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20.1.5 Fuel NOx Formation



Fuel-Bound Nitrogen


It is well known that nitrogen-containing organic compounds present in liquid or solid fossil fuel can contribute to the total NOx formed during the combustion process. This fuel nitrogen is a particularly important source of nitrogen oxide emissions for residual fuel oil and coal, which typically contain 0.3-2% nitrogen by weight. Studies have shown that most of the nitrogen in heavy fuel oils is in the form of heterocycles and it is thought that the nitrogen components of coal are similar [ 169]. It is believed that pyridine, quinoline, and amine type heterocyclic ring structures are of importance.



Reaction Pathways


The extent of conversion of fuel nitrogen to NOx is dependent on the local combustion characteristics and the initial concentration of nitrogen-bound compounds. Fuel-bound compounds that contain nitrogen are released into the gas phase when the fuel droplets or particles are heated during the devolatilization stage. From the thermal decomposition of these compounds, (aniline, pyridine, pyrroles, etc.) in the reaction zone, radicals such as HCN, NH $_3$, N, CN, and NH can be formed and converted to NOx. The above free radicals (i.e., secondary intermediate nitrogen compounds) are subject to a double competitive reaction path. This chemical mechanism has been subject to several detailed investigations [ 244]. Although the route leading to fuel NOx formation and destruction is still not completely understood, different investigators seem to agree on a simplified model:

figure

Recent investigations [ 147] have shown that hydrogen cyanide appears to be the principal product if fuel nitrogen is present in aromatic or cyclic form. However, when fuel nitrogen is present in the form of aliphatic amines, ammonia becomes the principal product of fuel nitrogen conversion.

In the FLUENT NOx model, sources of NOx emission for gaseous, liquid and coal fuels are considered separately. The nitrogen-containing intermediates are grouped as HCN, NH $_3$, or a combination of both. Transport equations ( 20.1-1 and 20.1-2 or 20.1-3) are solved, after which the source terms $S_{\rm HCN}$, $S_{\rm NH_3}$, and $S_{\rm NO}$ are determined for different fuel types. Discussions to follow refer to fuel NOx sources for $S_{\rm NO}$ and intermediate $\rm HCN$, $\rm NH_3$ sources for $S_{\rm HCN}$ and $S_{\rm NH_3}$. Contributions from thermal and prompt mechanisms have been discussed in previous sections.



Fuel NOx from Gaseous and Liquid Fuels


The fuel NOx mechanisms for gaseous and liquid fuels are based on different physics but the same chemical reaction pathways.

Fuel NOx from Intermediate Hydrogen Cyanide (HCN)

When HCN is used as the intermediate species:

figure

The source terms in the transport equations can be written as follows:


$\displaystyle S_{\rm HCN}$ $\textstyle =$ $\displaystyle S_{\rm pl, HCN} + S_{\rm HCN-1} + S_{\rm HCN-2}$ (20.1-29)
$\displaystyle S_{\rm NO}$ $\textstyle =$ $\displaystyle S_{\rm NO-1} + S_{\rm NO-2}$ (20.1-30)

HCN Production in a Gaseous Fuel

The rate of HCN production is equivalent to the rate of combustion of the fuel:


 S_{\rm pl, HCN} = \frac{{\cal R}_{\rm cf} \; Y_{\rm N, fuel} \; M_{w,{\rm HCN}}}{M_{w,{\rm N}}} (20.1-31)


where $S_{\rm pl, HCN}$ = source of HCN (kg/m $^3$-s)
  ${\cal R}_{\rm cf}$ = mean limiting reaction rate of fuel (kg/m $^3$-s)
  $Y_{\rm N, fuel}$ = mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, ${\cal R}_{\rm cf}$, is calculated from the Magnussen combustion model, so the gaseous fuel NOx option is available only when the generalized finite-rate model is used.

HCN Production in a Liquid Fuel

The rate of HCN production is equivalent to the rate of fuel release into the gas phase through droplet evaporation:


 S_{\rm pl, HCN} = \frac{S_{\rm fuel} \; Y_{\rm N, fuel} \; M_{w,{\rm HCN}}}{M_{w,{\rm N}} V} (20.1-32)


where $S_{\rm pl, HCN}$ = source of HCN (kg/m $^3$-s)
  $S_{\rm fuel}$ = rate of fuel release from the liquid droplets to the gas (kg/s)
  $Y_{\rm N, fuel}$ = mass fraction of nitrogen in the fuel
  $V$ = cell volume (m $^3$)

HCN Consumption

The HCN depletion rates from reactions (1) and (2) in the above mechanism are the same for both gaseous and liquid fuels, and are given by De Soete [ 77] as


$\displaystyle {\cal R}_1$ $\textstyle =$ $\displaystyle A_1\ X_{\rm HCN}\ X^{a}_{\rm O_2}\ e^{-E_1/RT}$ (20.1-33)
$\displaystyle {\cal R}_2$ $\textstyle =$ $\displaystyle A_2\ X_{\rm HCN}\ X_{\rm NO}\ e^{-E_2/RT}$ (20.1-34)


where ${\cal R}_1$, ${\cal R}_2$ = conversion rates of HCN (s $^{-1}$)
  $T$ = instantaneous temperature (K)
  $X$ = mole fractions
  $A_1$ = 1.0 $\times 10^{10}$ s $^{-1}$
  $A_2$ = 3.0 $\times 10^{12}$ s $^{-1}$
  $E_1$ = 280451.95 J/gmol
  $E_2$ = 251151 J/gmol

The oxygen reaction order, $a$, is calculated from Equation  20.1-28.

Since mole fraction is related to mass fraction through molecular weights of the species ( $M_{w,i}$) and the mixture ( $M_{w,m}$),


 X_i = Y_i \frac{M_{w,m}}{M_{w,i}} = \frac{Y_i}{M_{w,i}} \left(\frac{\rho R T}{p}\right) (20.1-35)

HCN Sources in the Transport Equation

The mass consumption rates of HCN which appear in Equation  20.1-29 are calculated as


 S_{\rm HCN-1} = -{\cal R}_1 \frac{M_{w,{\rm HCN}} \; p}{R\overline{T}} (20.1-36)


 S_{\rm HCN-2} = -{\cal R}_2 \frac{M_{w,{\rm HCN}} \; p}{R\overline{T}} (20.1-37)


where $S_{\rm HCN-1}$ = consumption rates of HCN in
  $S_{\rm HCN-2}$   reactions 1 and 2 respectively (kg/m $^3$-s)
  $p$ = pressure (Pa)
  $\overline{T}$ = mean temperature (K)
  $R$ = universal gas constant

NOx Sources in the Transport Equation

NOx is produced in reaction 1 but destroyed in reaction 2. The sources for Equation  20.1-30 are the same for a gaseous as for a liquid fuel, and are evaluated as follows:


 S_{\rm NO-1} = - S_{\rm HCN-1} \frac{M_{w,{\rm NO}}}{M_{w,{\rm HCN}}} = {\cal R}_1 \frac{M_{w,{\rm NO}} \; p}{R\overline{T}} (20.1-38)


 S_{\rm NO-2} = S_{\rm HCN-2} \frac{M_{w,{\rm NO}}}{M_{w,{\rm HCN}}} = - {\cal R}_2 \frac{M_{w,{\rm NO}} \; p}{R\overline{T}} (20.1-39)

Fuel NOx from Intermediate Ammonia (NH $_3$)

When NH $_3$ is used as the intermediate species:

figure

The source terms in the transport equations can be written as follows:


$\displaystyle S_{\rm NH_3}$ $\textstyle =$ $\displaystyle S_{\rm pl, NH_3} + S_{\rm NH_3-1} + S_{\rm NH_3-2}$ (20.1-40)
$\displaystyle S_{\rm NO}$ $\textstyle =$ $\displaystyle S_{\rm NO-1} + S_{\rm NO-2}$ (20.1-41)

NH $_3$ Production in a Gaseous Fuel

The rate of NH $_3$ production is equivalent to the rate of combustion of the fuel:


 S_{\rm pl, NH_3} = \frac{{\cal R}_{\rm cf} \; Y_{\rm N, fuel} \; M_{w,{\rm NH_3}}}{M_{w,{\rm N}}} (20.1-42)


where $S_{\rm pl, NH_3}$ = source of NH $_3$ (kg/m $^3$-s)
  ${\cal R}_{\rm cf}$ = mean limiting reaction rate of fuel (kg/m $^3$-s)
  $Y_{\rm N, fuel}$ = mass fraction of nitrogen in the fuel

The mean limiting reaction rate of fuel, ${\cal R}_{\rm cf}$, is calculated from the Magnussen combustion model, so the gaseous fuel NOx option is available only when the generalized finite-rate model is used.

NH $_3$ Production in a Liquid Fuel

The rate of NH $_3$ production is equivalent to the rate of fuel release into the gas phase through droplet evaporation:


 S_{\rm pl, NH_3} = \frac{S_{\rm fuel} \; Y_{\rm N, fuel} \; M_{w,{\rm NH_3}}}{M_{w,{\rm N}} V} (20.1-43)


where $S_{\rm pl, NH_3}$ = source of NH $_3$ (kg/m $^3$-s)
  $S_{\rm fuel}$ = rate of fuel release from the liquid droplets to the gas (kg/s)
  $Y_{\rm N, fuel}$ = mass fraction of nitrogen in the fuel
  $V$ = cell volume (m $^3$)

NH $_3$ Consumption

The NH $_3$ depletion rates from reactions (1) and (2) in the above mechanism are the same for both gaseous and liquid fuels, and are given by De Soete [ 77] as


$\displaystyle {\cal R}_1$ $\textstyle =$ $\displaystyle A_1\ X_{\rm NH_3}\ X^{a}_{\rm O_2}\ e^{-E_1/RT}$ (20.1-44)
$\displaystyle {\cal R}_2$ $\textstyle =$ $\displaystyle A_2\ X_{\rm NH_3}\ X_{\rm NO}\ e^{-E_2/RT}$ (20.1-45)


where ${\cal R}_1$, ${\cal R}_2$ = conversion rates of NH $_3$ (s $^{-1}$)
  $T$ = instantaneous temperature (K)
  $X$ = mole fractions
  $A_1$ = 4.0 $\times 10^{6}$ s $^{-1}$
  $A_2$ = 1.8 $\times 10^{8}$ s $^{-1}$
  $E_1$ = 133947.2 J/gmol
  $E_2$ = 113017.95 J/gmol

The oxygen reaction order, $a$, is calculated from Equation  20.1-28.

Since mole fraction is related to mass fraction through molecular weights of the species ( $M_{w,i}$) and the mixture ( $M_{w,m}$), $X_i$ can be calculated using Equation  20.1-35.

NH $_3$ Sources in the Transport Equation

The mass consumption rates of NH $_3$ which appear in Equation  20.1-40 are calculated as


 S_{\rm NH_3-1} = -{\cal R}_1 \frac{M_{w,{\rm NH_3}} \; p}{R\overline{T}} (20.1-46)


 S_{\rm NH_3-2} = -{\cal R}_2 \frac{M_{w,{\rm NH_3}} \; p}{R\overline{T}} (20.1-47)


where $S_{\rm NH_3-1}$ = consumption rates of NH $_3$ in
  $S_{\rm NH_3-2}$   reactions 1 and 2 respectively (kg/m $^3$-s)
  $p$ = pressure (Pa)
  $\overline{T}$ = mean temperature (K)
  $R$ = universal gas constant

NOx Sources in the Transport Equation

NOx is produced in reaction 1 but destroyed in reaction 2. The sources for Equation  20.1-41 are the same for a gaseous as for a liquid fuel, and are evaluated as follows:


 S_{\rm NO-1} = - S_{\rm NH_3-1} \frac{M_{w,{\rm NO}}}{M_{w,{... ...NH_3}}} = {\cal R}_1 \frac{M_{w,{\rm NO}} \; p}{R\overline{T}} (20.1-48)


 S_{\rm NO-2} = S_{\rm NH_3-2} \frac{M_{w,{\rm NO}}}{M_{w,{\r... ..._3}}} = - {\cal R}_2 \frac{M_{w,{\rm NO}} \; p}{R\overline{T}} (20.1-49)



Fuel NOx from Coal


Nitrogen in Char and in Volatiles

For the coal it is assumed that fuel nitrogen is distributed between the volatiles and the char. Since there is no reason to assume that N is equally distributed between the volatiles and the char the fraction of N in the volatiles and the char should be specified separately.

When HCN is used as the intermediate species, two variations of fuel NOx mechanisms for coal are included. When NH $_3$ is used as the intermediate species, two variations of fuel NOx mechanisms for coal are included, much like in the calculation of NOx production from the coal via HCN. It is assumed that fuel nitrogen is distributed between the volatiles and the char.

Coal Fuel NOx Scheme A

The first HCN mechanism assumes that all char N converts to HCN which is then converted partially to NO [ 345]. The reaction pathway is described as follows:

figure

With the first scheme, all char-bound nitrogen converts to HCN. Thus,


$\displaystyle S_{\rm char, HCN}$ $\textstyle =$ $\displaystyle \frac{S_{c} Y_{\rm N, char} M_{w,{\rm HCN}}}{M_{w,{\rm N}} V}$ (20.1-50)
$\displaystyle S_{\rm char, NO}$ $\textstyle =$ $\displaystyle 0$ (20.1-51)


where $S_{c}$ = char burnout rate (kg/s)
  $Y_{\rm N, char}$ = mass fraction of nitrogen in char
  $V$ = cell volume (m $^{3}$)

Coal Fuel NOx Scheme B

The second HCN mechanism assumes that all char N converts to NO directly [ 221]. The reaction pathway is described as follows:

figure

According to Lockwood [ 221], the char nitrogen is released to the gas phase as NO directly, mainly as a desorption product from oxidized char nitrogen atoms. If this approach is followed, then


$\displaystyle S_{\rm char, HCN}$ $\textstyle =$ $\displaystyle 0$ (20.1-52)
$\displaystyle S_{\rm char, NO}$ $\textstyle =$ $\displaystyle \frac{S_{c} Y_{\rm N, char} M_{w,{\rm NO}}}{M_{w,{\rm N}} V}$ (20.1-53)

HCN Scheme Selection

The second HCN mechanism tends to produce more NOx emission than the first. In general, however, it is difficult to say which one outperforms the other.

The source terms for the transport equations are


$\displaystyle S_{\rm HCN}$ $\textstyle =$ $\displaystyle S_{\rm pvc, HCN} + S_{\rm HCN-1} + S_{\rm HCN-2}$ (20.1-54)
$\displaystyle S_{\rm NO}$ $\textstyle =$ $\displaystyle S_{\rm char, NO} + S_{\rm NO-1} + S_{\rm NO-2} + S_{\rm NO-3}$ (20.1-55)

Source contributions $S_{\rm HCN-1}$, $S_{\rm HCN-2}$, $S_{\rm NO-1}$, and $S_{\rm NO-2}$ are described previously. Therefore, only the heterogeneous reaction source, $S_{\rm NO-3}$, the char NOx source, $S_{\rm char, NO}$, and the HCN production source, $S_{\rm pvc, HCN}$, need to be considered.

NOx Reduction on Char Surface

The heterogeneous reaction of NO reduction on the char surface has been modeled according to the following [ 204]:


 {\cal R}_3 = A_3 e^{-E_3/R\overline{T}} \; \overline{p}_{\rm NO} (20.1-56)


where ${\cal R}_{3}$ = rate of NO reduction (gmol/m $^2_{\rm BET}$-s)
  $\overline{p}_{\rm NO}$ = mean NO partial pressure (atm)
  $E_3$ = 142737.485 J/gmol
  $A_3$ = 230 gmol/m $^2_{\rm BET}$-s-atm
  $\overline{T}$ = mean temperature (K)

The partial pressure $\overline{p}_{\rm NO}$ is calculated using Dalton's law:


\overline{p}_{\rm NO} = \overline{p} X_{\rm NO}

The rate of NO consumption due to reaction 3 will then be


S_{\rm NO-3} = c_s A_{\rm BET} M_{w,{\rm NO}} {\cal R}_{3}


where $A_{\rm BET}$ = BET surface area (m $^{2}$/kg)
  $c_s$ = concentration of particles (kg/m $^3$)
  $S_{\rm NO-3}$ = NO consumption (kg/m $^3$-s)

BET Surface Area

The heterogeneous reaction involving char is mainly an adsorption process whose rate is directly proportional to the pore surface area. The pore surface area is also known as the BET surface area due to the researchers who pioneered the adsorption theory (Brunauer, Emmett and Teller [ 45]). For commercial adsorbents, the pore (BET) surface areas range from 100,000 to 2 million square meters per kilogram, depending on the microscopic structure. For coal, the BET area is typically 25,000 m $^2$/kg which is used as the default in FLUENT. The overall source of HCN ( $S_{\rm pvc, HCN}$) is a combination of volatile contribution ( $S_{\rm vol, HCN}$) and char contribution ( $S_{\rm char, HCN}$):


S_{\rm pvc, HCN} = S_{\rm vol, HCN} + S_{\rm char, HCN}

HCN from Volatiles

The source of HCN from the volatiles is related to the rate of volatile release:


S_{\rm vol, HCN} = \frac{S_{\rm vol} \; Y_{\rm N, vol} M_{w,{\rm HCN}}} {M_{w,{\rm N}} V}


where $S_{\rm vol}$ = source of volatiles originating from
      the coal particles into the gas phase (kg/s)
  $Y_{\rm N, vol}$ = mass fraction of nitrogen in the volatiles
  $V$ = cell volume (m $^{3}$)

Calculation of sources related to char-bound nitrogen depends on the fuel NOx scheme selection.

Coal Fuel NOx Scheme C

The first NH $_3$ mechanism assumes that all char N converts to NH $_3$ which is then converted partially to NO [ 345]. The reaction pathway is described as follows:

figure

In this scheme, all char-bound nitrogen converts to NH $_3$. Thus,


$\displaystyle S_{\rm char, NH_3}$ $\textstyle =$ $\displaystyle \frac{S_{c} Y_{\rm N, char} M_{w,{\rm NH_3}}}{M_{w,{\rm N}} V}$ (20.1-57)
$\displaystyle S_{\rm char, NO}$ $\textstyle =$ $\displaystyle 0$ (20.1-58)


where $S_{c}$ = char burnout rate (kg/s)
  $Y_{\rm N, char}$ = mass fraction of nitrogen in char
  $V$ = cell volume (m $^{3}$)

Coal Fuel NOx Scheme D

The second NH $_3$ mechanism assumes that all char N converts to NO directly [ 221]. The reaction pathway is described as follows:

figure

According to Lockwood [ 221], the char nitrogen is released to the gas phase as NO directly, mainly as a desorption product from oxidized char nitrogen atoms. If this approach is followed, then


$\displaystyle S_{\rm char, NH_3}$ $\textstyle =$ $\displaystyle 0$ (20.1-59)
$\displaystyle S_{\rm char, NO}$ $\textstyle =$ $\displaystyle \frac{S_{c} Y_{\rm N, char} M_{w,{\rm NO}}}{M_{w,{\rm N}} V}$ (20.1-60)

NH $_3$ Scheme Selection

The second NH $_3$ mechanism tends to produce more NOx emission than the first. In general, however, it is difficult to say which one outperforms the other.

The source terms for the transport equations are


$\displaystyle S_{\rm NH_3}$ $\textstyle =$ $\displaystyle S_{\rm pvc, NH_3} + S_{\rm NH_3-1} + S_{\rm NH_3-2}$ (20.1-61)
$\displaystyle S_{\rm NO}$ $\textstyle =$ $\displaystyle S_{\rm char, NO} + S_{\rm NO-1} + S_{\rm NO-2} + S_{\rm NO-3}$ (20.1-62)

Source contributions $S_{\rm NH_3-1}$, $S_{\rm NH_3-2}$, $S_{\rm NO-1}$, $S_{\rm NO-2}$, $S_{\rm NO-3}$, $S_{\rm char, NO}$ are described previously. Therefore, only the NH $_3$ production source, $S_{\rm pvc, NH_3}$, needs to be considered.

The overall production source of NH $_3$ is a combination of volatile contribution ( $S_{\rm vol, NH_3}$), and char contribution ( $S_{\rm char, NH_3}$):


 S_{\rm pvc, NH_3} = S_{\rm vol, NH_3} + S_{\rm char, NH_3} (20.1-63)

NH $_3$ from Volatiles

The source of NH $_3$ from the volatiles is related to the rate of volatile release:


S_{\rm vol, NH_3} = \frac{S_{\rm vol} \; Y_{\rm N, vol} M_{w,{\rm NH_3}}} {M_{w,{\rm N}} V}


where $S_{\rm vol}$ = source of volatiles originating from
      the coal particles into the gas phase (kg/s)
  $Y_{\rm N, vol}$ = mass fraction of nitrogen in the volatiles
  $V$ = cell volume (m $^{3}$)

Calculation of sources related to char-bound nitrogen depends on the fuel NOx scheme selection.



Fuel Nitrogen Partitioning for HCN and NH $_3$ Intermediates


In certain cases, especially when the fuel is a solid, both HCN and NH $_3$ can be generated as intermediates at high enough temperatures [ 261]. In particular, low-ranking (lignite) coal has been shown to produce 10 times more NH $_3$ compared to the level of HCN, whereas higher-ranking (bituminous) coal has been shown to produce only HCN [ 260]. Studies by Winter et al. [ 405] have shown that for bituminous coal, using an HCN/NH $_3$ partition ratio of 9:1 gave better NOx predictions when compared to measurements than specifying only a single intermediate species. Liu and Gibbs [ 219] work with woody-biomass (pine wood chips), on the other hand, has suggested an HCN/NH $_3$ ratio of 1:9 due to the younger age of the fuel.

In total, the above work suggests the importance of being able to specify that portions of the fuel nitrogen will be converted to both HCN and NH $_3$ intermediates at the same time. In FLUENT, fuel nitrogen partitioning can be used whenever HCN or NH $_3$ are intermediates for NOx production, though it is mainly applicable to solid fuels such as coal and biomass. The reaction pathways and source terms for HCN and NH $_3$ were discussed in previous sections.


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