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20.2.3 Reaction Mechanisms for Sulfur Oxidation

A detailed reaction mechanism for sulfur oxidation has been proposed by Kramlich [ 187]. The mechanism consists of 20 reversible reactions and includes 12 species (S, $S_2$, SH, SO, $SO_2$, $H{_2}S$, H, $H_2$, OH, $H{_2}O$, O and $O_2$). However, such a detailed mechanism is not practical for CFD applications unless used in a flamelet based model. An attempt was made therefore to reduce the number of reactions and species to a manageable level while predicting the major species concentration levels within acceptable tolerance. The need to retain the minor intermediate species SH and SO has been the major constraint and as such, an eight-step mechanism has been identified using PSR (a Fortran program for modeling well stirred reactors with gas reactions) and SENKIN (a Fortran program for predicting homogeneous gas phase chemical kinetics). The rationale behind the selection of an eight-step mechanism was to remove species S and $S_2$ from the detailed mechanism. Table  20.2.1 lists the reduced mechanism, which has been developed in-house, with the modified rate constants. For reduction calculations O and OH concentrations have been calculated through partial equilibrium assumptions based on $O_2$ and $H{_2}O$ concentrations respectively. $N_2$ was used as the dilutant. Since each reaction of the eight-step reduced mechanism is reversible, for each adjacent pair of reactions given in Table  20.2.1, the second reaction is in fact the reverse reaction of the first.

The reduced mechanism given in Table  20.2.1 closely follows the $SO_2$ concentration levels but slightly overpredicts the $H{_2}S$ concentrations at temperatures below 1500 K. Above 1500 K, both mechanisms are in close agreement for $SO_2$ and $H{_2}S$ concentration predictions. However, SO and SH are not well correlated by the reduced mechanism when compared against the predictions using the original detailed mechanism.

A major concern in these mechanisms is the presence of H radical and the method in which to calculate its concentration in the flow field. At present, the concentration of H radical is assumed to be proportional to the O radical concentration, which can be evaluated from one of the existing methods in FLUENT; viz. Partial Equilibrium (Section  20.1.3) or Equilibrium (Section  20.1.3). The user is then given the option to vary the proportionality constant. Although this assumption is open to debate, the lack of simple relation to calculate the H radical concentration in a flame has prompted the present choice.

Present implementation allows the user to either include or remove SO $_3$ from the calculations. Also, depending on the form of fuel sulfur release (e.g., $H{_2}S$ or SO $_2$) the species $H{_2}S$ may or may not be present for the calculation. The user is also given the extended option of partitioning the intermediate fuel sulfur species to $H{_2}S$ and $SO_2$. However, there is no literature to guide the user on how to select a correct partition fraction.

Table 20.2.1: Eight-Step Reduced Mechanism (Rate Constant $k = A T^b exp(-E/RT)$)
Reaction A b E
$H{_2}S + H \rightarrow SH + H_2$ 1.819702E+07 0.0E+00 7.484300E+03
$SH + H_2 \rightarrow H{_2}S + H$ 9.375623E+06 0.0E+00 6.253660E+04
$OH + H{_2}S \rightarrow H{_2}O + SH$ 1.380385E+02 0.0E+00 3.742150E+03
$H{_2}O + SH \rightarrow OH + H{_2}S$ 3.104557E+07 0.0E+00 1.218543E+05
$SO + OH \rightarrow H + SO_2$ 1.621810E+08 0.0E+00 2.565926E+03
$H + SO_2 \rightarrow SO + OH$ 7.691299E+09 0.0E+00 1.187023E+05
$SH + O \rightarrow SO + H$ 3.548135E+08 0.0E+00 2.687316E+03
$SO + H \rightarrow SH + O$ 2.985385E+09 0.0E+00 1.694600E+05
$O + H{_2}S \rightarrow SH + OH$ 4.365162E+03 0.0E+00 1.380493E+04
$SH + OH \rightarrow O + H{_2}S$ 9.885528E+08 0.0E+00 6.035996E+04
$SO + O_2 \rightarrow SO_2 + O$ 4.466832E+05 0.0E+00 2.703222E+04
$SO_2 + O \rightarrow SO + O_2$ 1.663412E+06 0.0E+00 7.613643E+04
$H + SH + M \rightarrow H{_2}S + M$ 1.096478E+03 0.0E+00 0.000000E+00
$H{_2}S + M \rightarrow H + SH + M$ 8.669613E+14 0.0E+00 3.819463E+05
$SO + O + M \rightarrow SO_2 + M$ 8.709647E+09 k -1.8E+00 0.000000E+00
$SO_2 + M \rightarrow SO + O + M$ 1.905464E+14 0.0E+00 5.207365E+05

A is in m $^3$/gmol-s, E is J/gmol (assumed 1 cal = 4.18585 J), A units for the thirteenth reaction is m $^6$/gmol $^2$-s, and A units for the fifteenth reaction is m $^6$/gmol $^2$-s.

In addition, the following two reactions were included in FLUENT to complete the SOx mechanism, with the rate constants taken from Hunter's work [ 150].

 SO_2 + O + M \Longleftrightarrow SO_3 + M (20.2-6)

M = argon, nitrogen, oxygen
k $_{f1}$ = $3.63$ x $10^{2}$ exp(+4185.85/RT) m $^6$/gmol $^2$/sec

where R = 8.313 J/gmol-K

k $_{r1}$ = $7.41$ x $10^{14}$ exp(-346123.75/RT) m $^3$/gmol/sec

 SO_3 + O \Longleftrightarrow SO_2 + O_2 (20.2-7)

k $_{f2}$ = $1.2$ x $10^{6}$ exp(-39765.575/RT) m $^3$/gmol/sec

The reverse rate of Equation  20.2-7 was determined through the equilibrium constant for that equation.

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