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20.1.7 NOx Reduction by Reburning

The design of complex combustion systems for utility boilers, based on air- and fuel-staging technologies, involves many parameters and their mutual interdependence. These parameters include local stoichiometry, temperature and chemical concentration field, residence time distribution, velocity field, and mixing pattern. A successful application of the in-furnace reduction techniques requires control of these parameters in an optimum manner so as to avoid impairing the boiler performance. In the mid 1990s, global models describing the kinetics of NOx destruction in the reburn zone of a staged combustion system became available. Two of these models are described below.

Instantaneous Approach

The instantaneous NOx reburning mechanism is a pathway whereby NO reacts with hydrocarbons and is subsequently reduced. In general:

 \mbox{CH}_i + \mbox{NO} \rightarrow \mbox{HCN} + \mbox{products} (20.1-69)

Three reburn reactions are modeled by FLUENT for $1600 \leq T \leq 2100$:

$\displaystyle \mbox{CH} + \mbox{NO}$ $\textstyle \stackrel{k_1}{\rightarrow}$ $\displaystyle \mbox{HCN} + \mbox{O}$ (20.1-70)
$\displaystyle \mbox{CH}_2 + \mbox{NO}$ $\textstyle \stackrel{k_2}{\rightarrow}$ $\displaystyle \mbox{HCN} + \mbox{OH}$ (20.1-71)
$\displaystyle \mbox{CH}_3 + \mbox{NO}$ $\textstyle \stackrel{k_3}{\rightarrow}$ $\displaystyle \mbox{HCN} + \mbox{H}_2\mbox{O}$ (20.1-72)


If the temperature is outside of this range, NO reburn will not be computed.

The rate constants for these reactions are taken from Bowman [ 38] and have units of m $^{3}$/gmol-s:

 k_1 = 1 \times 10^8; \;\;\; k_2 = 1.4 \times 10^6 e^{-550/T}; \;\;\; k_3 = 2 \times 10^5

The NO depletion rate due to reburn is expressed as

 \frac{d[\mbox{NO}]}{dt} = - k_1 [\mbox{CH}][\mbox{NO}] - k_2 [\mbox{CH}_2][\mbox{NO}] - k_3 [\mbox{CH}_3][\mbox{NO}] (20.1-73)

and the source term for the reburning mechanism in the NO transport equation can be calculated as

 S_{\rm reburn,NO} = -M_{w,{\rm NO}} \frac{d[\mbox{NO}]}{dt} (20.1-74)


To calculate the NO depletion rate due to reburning, FLUENT will obtain the concentrations of CH, CH $_2$, and CH $_3$ from the species mass fraction results of the combustion calculation. When you use this method, you must be sure to include the species CH, CH $_2$, and CH $_3$ in your problem definition.

Partial Equilibrium Approach

The partial equilibrium approach is based on the model proposed by Kandamby et al. [ 171] and [ 12]. The model adds a reduction path to De Soete's global model [ 77] that describes the NOx formation/destruction mechanism in a pulverized coal flame. The additional reduction path accounts for the NOx destruction in the fuel-rich reburn zone by CH radicals (see Figure  20.1.1).

Figure 20.1.1: De Soete's Global NOx Mechanism with Additional Reduction Path

This model can be used in conjunction with the eddy-dissipation combustion model and does not require the specification of CH radical concentrations, since they are computed based on the CH-radical partial equilibrium. The reburn fuel itself can be an equivalent of CH $_4$, CH $_3$, CH $_2$, or CH. How this equivalent fuel is determined is open for debate and an approximate guide would be to consider the C/H ratio of the fuel itself. A multiplicative constant of $4.0 \times 10^{-4}$ has been developed for the partial equilibrium of CH radicals to reduce the rates of HCN and NO in the reburn model. This value was obtained by researchers, who developed the model, by way of predicting NOx values for a number of test cases for which experimental data exists.

NOx Reduction Mechanism

In the fuel-rich reburn zone, the HCN oxidation is suppressed and the amount of NO formed in the primary combustion zone is decreased by the reduction reaction from HCN to N $_2$. However, the NO concentration may also decrease due to reactions with CH radicals, which are available in significant amounts in the reburn zone. The following are considered to be the most important reactions of NO reduction by CH radicals:

$\displaystyle \mbox{NO} + \mbox{CH$_2$}$ $\textstyle \longrightarrow$ $\displaystyle \mbox{HCN} + \mbox{OH}$ (20.1-75)
$\displaystyle \mbox{NO} + \mbox{CH}$ $\textstyle \longrightarrow$ $\displaystyle \mbox{HCN} + \mbox{O}$ (20.1-76)
$\displaystyle \mbox{NO} + \mbox{C}$ $\textstyle \longrightarrow$ $\displaystyle \mbox{CN} + \mbox{O}$ (20.1-77)

These reactions may be globally described by the addition of pathways (4) and (5) in Figure  20.1.1, leading respectively to the formation of HCN and of minor intermediate nitrogen radicals. Assuming that methane is the reburning gas, the global NO reduction rates are then expressed as

$\displaystyle {\cal R}_4$ $\textstyle =$ $\displaystyle (k_a \chi_1 +k_b \chi_1^2) [\mbox{CH$_4$}][\mbox{NO}]$ (20.1-78)
$\displaystyle {\cal R}_5$ $\textstyle =$ $\displaystyle k_c \chi_1^3 \chi_2 [\mbox{CH$_4$}][\mbox{NO}]$ (20.1-79)


\chi_1 = \frac{[\mbox{H}]}{[\mbox{H$_2$}]}; \; \; \; \chi_2 = \frac{[\mbox{OH}]}{[\mbox{H$_2$O}]}

Therefore, the additional source terms of the HCN and NO transport equations due to reburn reactions are given by

$\displaystyle \frac{d[\mbox{HCN}]}{dt}$ $\textstyle =$ $\displaystyle 4 \times 10^{-4}{\cal R}_4$ (20.1-80)
$\displaystyle \frac{d[\mbox{NO}]}{dt}$ $\textstyle =$ $\displaystyle -4 \times 10^{-4}({\cal R}_4 +{\cal R}_5)$ (20.1-81)

Certain assumptions are required to evaluate the rate constants $k_a$, $k_b$, and $k_c$ and the factors $\chi_1$ and $\chi_2$. For hydrocarbon diffusion flames, the following reaction set can be reasonably considered to be in partial equilibrium:

$\displaystyle \mbox{CH$_4$} + \mbox{H}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{CH$_3$} + \mbox{H$_2$}$ (20.1-82)
$\displaystyle \mbox{CH$_3$} + \mbox{OH}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{CH$_2$} + \mbox{H$_2$O}$ (20.1-83)
$\displaystyle \mbox{CH$_2$} + \mbox{H}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{CH} + \mbox{H$_2$}$ (20.1-84)
$\displaystyle \mbox{CH} + \mbox{H}$ $\textstyle \rightleftharpoons$ $\displaystyle \mbox{C} + \mbox{H$_2$}$ (20.1-85)

Thus, the rate constants may be computed as

k_a = k_1 \frac{k_{f,4} k_{f,5}}{k_{r,4} k_{r,5}}; \; \; \; k... ...{f,4} k_{f,5} k_{f,6} k_{f,7}}{k_{r,4} k_{r,5} k_{r,6} k_{r,7}}

where $k_1$, $k_2$, and $k_3$ are the rate constants for Equations  20.1-75- 20.1-77. The forward and reverse rate constants for Equations  20.1-82- 20.1-85 are $k_{f,4}$- $k_{f,7}$ and $k_{r,4}$- $k_{r,7}$, respectively. In addition, it is assumed that $\chi_1=1$, because the H-radical concentration in the post-flame region of a hydrocarbon diffusion flame has been observed to be of the same order as [H $_2$]. Finally, the OH-radical concentration is estimated by considering the reaction

 \mbox{OH} + \mbox{H$_2$} \rightleftharpoons \mbox{H$_2$O} + \mbox{H} (20.1-86)

to be partially equilibrated, leading to the relationship

\chi_2 = \frac{k_{r,8}}{k_{f,8}}

Values for the rate constants $k_a$, $k_b$, and $k_c$ for different equivalent fuel types are given in Arrhenius form ( $A T^b e^{-E/RT}$) in Table  20.1.1 [ 203]. All rate constants have units of m $^3$/gmol-s, and all values of $E$ have units of J/gmol.

Table 20.1.1: Rate Constants for Different Reburn Fuels
Equivalent   ${k_a}$     $k_b$     $k_c$  
Fuel Type $A$ $b$ $E$ $A$ $b$ $E$ $A$ $b$ $E$
CH $_4$ $5.30 \times 10^9$ -1.54 27977 $3.31 \times 10^{13}$ -3.33 15090 $3.06 \times 10^{11}$ -2.64 77077
CH $_3$ $0.37 \times 10^9$ -1.54 27977 $0.23 \times 10^{13}$ -3.33 15090 $0.21 \times 10^{11}$ -2.64 77077
CH $_2$ $0.23 \times 10^7$ -1.54 27977 $0.14 \times 10^{11}$ -3.33 15090 $0.13 \times 10^9$ -2.64 77077
CH 0.0 0.0 0.0 $0.63 \times 10^8$ -3.33 15090 $0.58 \times 10^6$ -2.64 77077

For Equation  20.1-86,

 k_{f,8} = 1.02 \times 10^5 T^{1.60} e^{-13802/RT}; \;\;\; k_{r,8} = 4.52 \times 10^5 T^{1.60} e^{-80815/RT}

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