Thermal NO mechanisms: For premixed combustion systems a conservative estimate of the thermal contribution to NO formation can be made by considering the equilibrium system given by reaction (8.48):

As is undoubtedly apparent, the kinetic route of NO formation is not the attack of an oxygen molecule on a nitrogen molecule. Mechanistically, as described in Chapter 3, oxygen atoms form from the H₂–O₂ radical pool, or possibly from the dissociation of O₂, and these oxygen atoms attack nitrogen molecules to start the simple chain shown by reactions (8.49) and (8.50):

If one invokes the steady-state approximation described in Chapter 2 for the N atom concentration and makes the partial equilibrium assumption also described in Chapter 2 for the reaction system,

To calculate the thermal NO formation rate from the preceding expression, it is necessary to know the concentrations of O₂, N₂, O, and OH. But the characteristic time for the forward reaction (8.49) always exceeds the characteristic times for the reaction systems that make up the processes in fuel−oxidizer flame systems; thus, it would appear possible to decouple the thermal NO process from the flame process. Using such an assumption, the NO formation can be calculated from Eqn (8.52) using local equilibrium values of temperature and concentrations of O₂, N₂, O, and OH.

From examination of Eqn (8.52), one sees that the maximum NO formation rate is given by

The strong dependence of thermal NO formation on the combustion temperature and the lesser dependence on the oxygen concentration are evident from Eqn (8.54). Thus, considering the large activation energy of reaction (8.49), the best practical means of controlling NO is to reduce the combustion gas temperature and, to a lesser extent, the oxygen concentration. For a condition of constant temperature and varying pressure, Eqn (8.53) suggests that the O atom concentration will decrease as the pressure is raised according to Le Chatelier's principle, and the maximum rate will decrease. Indeed, this trend is found in fluidized bed reactors.

To determine the errors that may be introduced by the Zeldovich model, Miller and Bowman [6] calculated the maximum (initial) NO formation rates from the model and compared them with the maximum NO formation rates calculated from a detailed kinetics model for a fuel-rich (ϕ = 1.37) methane−air system. To allow independent variation of temperature, an isothermal system was assumed and the type of prompt NO reactions to be discussed next were omitted. Thus, the observed differences in NO formation rates are due entirely to the nonequilibrium radical concentrations that exist during the combustion process. Their results are shown in Figure 8.1, which indicates a noticeable acceleration of the maximum NO formation rate above that calculated using the Zeldovich model during the initial stages of the reaction owing to nonequilibrium effects, with the departures from the Zeldovich model results decreasing with increasing temperature. As the lower curve in Figure 8.1 indicates, while nonequilibrium effects are evident over a wide range of temperature, the accelerated rates are sufficiently low that little NO is formed by the accelerated nonequilibrium component. Examining the lower curve, as discussed in Chapter 1, one sees that most hydrocarbon−air combustion systems operate in the range of 2100–2600 K.

Prompt NO mechanisms: In dealing with the presentation of prompt NO mechanisms, much can be learned by considering the historical development of the concept of prompt NO. With the development of the Zeldovich mechanism, many investigators followed the concept that in premixed flame systems, NO would form only in the post-flame or burned-gas zone. Thus, it was thought possible to experimentally determine thermal NO formation rates and, from these rates, to find the rate constant of Eqn (8.49) by measurement of the NO concentration profiles in the post-flame zone. Such measurements can be performed readily on flat flame burners. Of course, to make these determinations, it is necessary to know the O atom concentrations. Since hydrocarbon−air flames were always considered, the nitrogen concentration was always in large excess. As discussed in the preceding subsection, the O atom concentration was taken as the equilibrium concentration at the flame temperature and all other reactions were assumed to be very fast compared with the Zeldovich mechanism.

These experimental measurements on flat flame burners revealed that when the NO concentration profiles are extrapolated to the flame-front position, the NO concentration goes not to zero, but to some finite value. Such results were most frequently observed with fuel-rich flames. Fenimore [9] argued that reactions other than the Zeldovich mechanism were playing a role in the flame and that some NO was being formed in the flame region. He called this NO, “prompt” NO. He noted that prompt NO was not found in nonhydrocarbon CO−air and H₂−air flames, which were analyzed experimentally in the same manner as the hydrocarbon flames. The reaction scheme he suggested to explain the NO found in the flame zone involved a hydrocarbon species and atmospheric nitrogen. The nitrogen compound was formed via the following mechanism:

The N atoms could form NO, in part at least, by reactions (8.50) and (8.51), and the CN could yield NO by oxygen or oxygen atom attack. It is well known that CH exists in flames and indeed, as stated in Chapter 4, is the molecule that gives the deep violet color to a Bunsen flame.

To verify whether reactions other than the Zeldovich mechanism were effective in NO formation, various investigators undertook the study of NO formation kinetics by use of shock tubes. The primary work in this area was that of Bowman and Seery [10], who studied the CH₄–O₂–N₂ system. Complex kinetic calculations of the CH₄–O₂–N₂ reacting system based on early kinetic rate data at a fixed high temperature and pressure similar to those obtained in a shock tube [11] for T = 2477 K and P = 10 atm are shown in Figure 8.2. Even though more recent kinetic rate data would modify the product−time distribution somewhat, the general trends of the product distribution are important and are relatively unaffected by some changes in rates. These results are worth considering in their own right, for they show explicitly much that has been implied. Examination of Figure 8.2 shows that at about 5 × 10⁻⁵ s, all the energy–release reactions will have equilibrated before any significant amounts of NO have formed; and, indeed, even at 10⁻² s the NO has not reached its equilibrium concentration for T = 2477 K. These results show that for such homogeneous or near-homogeneous reacting systems, it would be possible to quench the NO reactions, obtain the chemical heat release, and prevent NO formation. This procedure has been put into practice in certain combustion schemes.

Equally important is the fact that Figure 8.2 reveals large overshoots within the reaction zone. If these occur within the reaction zone, the O atom concentration could be orders of magnitude greater than its equilibrium value, in which case this condition could lead to the prompt NO found in flames. The mechanism analyzed to obtain the results depicted in Figure 8.2 was essentially that given in Chapter 3, Section 3.7.2, with the Zeldovich reactions. Thus, it was thought possible that the Zeldovich mechanism could account for the prompt NO.

The early experiments of Bowman and Seery appeared to confirm this conclusion. Some of their results are shown in Figure 8.3. In this figure the experimental points compared well with the analytical calculations based on the Zeldovich mechanisms alone. The same computational program as that of Martenay [11] was used. Figure 8.3 also depicts another result frequently observed: fuel-rich systems approach NO equilibrium much faster than do fuel-lean systems [12].

Although Bowman and Seery’s results would seem at first to refute the suggestion by Fenimore that prompt NO forms by reactions other than the Zeldovich mechanism, one must remember that flames and shock tube–initiated reacting systems are distinctively different processes. In a flame there is a temperature profile that begins at the ambient temperature and proceeds to the flame temperature. Thus, although flame temperatures may be simulated in shock tubes, the reactions in flames are initiated at much lower temperatures than those in shock tubes. As stressed many times before, the temperature history frequently determines the kinetic route and the products. Therefore, shock tube results do not prove that the Zeldovich mechanism alone determines prompt NO formation. The prompt NO could arise from other reactions in flames, as suggested by Fenimore.

Bachmeier et al. [13] appeared to confirm Fenimore’s initial postulates and to shed greater light on the flame NO problem. These investigators measured the prompt NO formed as a function of equivalence ratio for many hydrocarbon compounds. Their results are shown in Figure 8.4. What is significant about these results is that the maximum prompt NO is reached on the fuel-rich side of stoichiometric, remains at a high level through a fuel-rich region, and then drops off sharply at an equivalence ratio of about 1.4.

Bachmeier et al. also measured the HCN concentrations through propane−air flames. These results, which are shown in Figure 8.5, show that HCN concentrations rise sharply somewhere in the flame, reach a maximum, and then decrease sharply. However, for an equivalence ratio of 1.5, a fuel-rich condition for which little prompt NO is found, the HCN continues to rise and is not depleted. The explanation offered for this trend is that HCN forms in all the rich hydrocarbon flames; however, below an equivalence ratio of 1.4, O radicals are present in sufficient abundance to deplete HCN and form the NO. Since the sampling and analysis techniques used by Bachmeier et al. [13] did not permit the identification of the cyanogen radical CN, the HCN concentrations found most likely represent the sum of CN and HCN as they exist in the flame. The CN and HCN in the flame are related through the rapid equilibrium reactions [14].

The HCN concentration is probably reduced mainly by the oxidation of the CN radicals [14,15].

From other more recent studies of NO formation in the combustion of lean and slightly rich methane−oxygen−nitrogen mixtures as well as lean and very rich hydrocarbon−oxygen−nitrogen mixtures, it must be concluded that some of the prompt NO is the result of the overshoot of O and OH radicals above their equilibrium values, as the Bowman and Seery results suggested. But even though O radical overshoot is found on the fuel-rich side of stoichiometric, this overshoot cannot explain the prompt NO formation in fuel-rich systems. It would appear that both the Zeldovich and Fenimore mechanisms are feasible.

Some interesting experiments by Eberius and Just [16] seem to clarify what is happening in the flame zone with regard to NO formation. Eberius and Just's experiments were performed on a flat flame burner with propane as the fuel. Measurements were made of the prompt NO at various fuel−oxygen equivalence ratios whose flame temperatures were controlled by dilution with nitrogen. Thus, a range of temperatures could be obtained for a given propane−oxygen equivalence ratio. The results obtained are shown in Figure 8.6. The highest temperature point for each equivalence ratio corresponds to zero dilution.

The shapes of the plots in Figure 8.6 are revealing. At both the low- and high-temperature ends, all the plots seem nearly parallel. The slopes at the low-temperature end are much less than the slopes at the high-temperature end, thereby indicating two mechanisms for the formation of prompt NO. The two mechanisms are not related solely to the fuel-rich and fuel-lean stoichiometry, as many investigators thought, but also to the flame temperature. These results suggest two routes: a high-temperature, high-activation route and a lower-temperature, low-activation route.

The systematic appearance of these data led Eberius and Just to estimate the activation energy for the two regions. Without correcting for diffusion, they obtained an activation energy of the order of 270 kJ/mol for the high-temperature zone. This value is remarkably close to the 315 kJ/mol activation energy required for the initiating step in the Zeldovich mechanism. Furthermore, diffusion corrections would raise the experimental value somewhat. The low-temperature region has an activation energy of the order of 50–60 kJ/mol. As will be shown later, radical attack on the cyano species is faster than oxygen radical attack on hydrogen. The activation energy of O + H₂ is about 33 kJ/mol; therefore, the HCN reaction should be less. Again, diffusion corrections for the oxygen atom concentration could lower the apparent activities of activation energies of 50–60 kJ/mol to below 34 kJ/mol. This crude estimate of the activation energy from Eberius and Just’s low-temperature region, together with the formation of HCN found by the same group [13] in their other flame studies with propane (Figure 8.5), appears to indicate that the Fenimore mechanism [9] would hold in the lower-temperature region.

The kinetic details for prompt NO formation must begin with the possible reactions between N₂ and hydrocarbon fragments, as Fenimore [9] originally suggested. Hayhurst and Vance [17] suggested that two other likely candidate reactions may be added to those posited by Fenimore. The four candidate reactions would then be

As discussed in the introduction to Chapter 4, the existence of C₂ and CH in hydrocarbon−air flames is well established. Methylene (CH₂) arises in most combustion systems by OH and H attack on the methyl radical (CH₃). Similar attack on CH₂ creates CH.

Hayhurst and Vance [17] established that the amount of prompt NO in moderately fuel-rich systems is proportional to the number of carbon atoms present per unit volume and is independent of the original parent hydrocarbon identity. This result indicates that reactions (8.59) and (8.60) are not primary contributors because it is unlikely that C₂ or C₂H could derive from CH₄ with an efficiency one-half that from C₂H₂ or one-third that from C₃H₆ or C₃H₈. In their complete model Miller and Bowman [6] introduced the reactions

They concluded from estimated rates that reaction (8.63) is an insignificant contributor to prompt NO. However, they also pointed out that the reverse reaction (8.64) is fast at room temperature and under shock tube conditions. Hence, this step is a minor, but nonnegligible contributor to prompt NO, and because of the large endothermicity of reaction (8.64), its importance with respect to reaction (8.61) increases with increasing temperature.

The major products of reactions (8.61) and (8.62) are HCN and NH. In the experimental work of Bachmeier et al. [13], HCN and CN were indistinguishable because of the equilibrium reactions (8.57) and (8.58) mentioned and the analysis methods applied. In consideration of the work of Ref. [1], the major kinetic route to prompt NO would then appear to be

Following the conclusions of Bowman [1], then, from the definition of prompt NO, these sources of prompt NO in hydrocarbon fuel combustion can be identified: (1) nonequilibrium O and OH concentrations in the reaction zone and burned gas, which accelerate the rate of the thermal NO mechanism; (2) a reaction sequence, shown in Figure 8.7, that is initiated by reactions of hydrocarbon radicals, present in and near the reaction zone, with molecular nitrogen (the Fenimore prompt−NO mechanism); and (3) reaction of O atoms with N₂ to form N₂O via the three-body recombination reaction

The relative importance of these three mechanisms in NO formation and the total amount of prompt NO formed depend on conditions in the combustor. Acceleration of NO formation by nonequilibrium radical concentrations appears to be more important in non-premixed flames, in stirred reactors for lean conditions, and in low-pressure premixed flames, accounting for up to 80% of the total NO formation. Prompt NO formation by the hydrocarbon radical−molecular nitrogen mechanism is dominant in fuel-rich premixed hydrocarbon combustion and in hydrocarbon diffusion flames, accounting for greater than 50% of the total NO formation. Nitric oxide formation by the N₂O mechanism increases in importance as the fuel−air ratio decreases, as the burned gas temperature decreases, or as pressure increases. The N₂O mechanism is most important under conditions where the total NO formation rate is relatively low [1].

Bozzelli and Dean [18] proposed that NO can also form through the formation of NNH radicals and their subsequent oxidation via the reaction sequence

Experimental evidence for this mechanism has been found in low-pressure H₂/air flames, fuel-rich H₂/O₂/N₂ and CH₄/O₂/N₂ flames at atmospheric pressure, and lean H₂–air mixtures in stirred reactors. Modeling of these systems by Konnov et al. [19] supports the importance of this mechanism. Through modeling and experimental studies of jet stirred reactors fuels with various hydrocarbons, Ruter et al. [20] found that prompt and NNH pathways dominate the formation of NO in the flame, whereas Zeldovich and nitrous oxide are primary contributors to the NO formation in the post flame. While some uncertainty exists in the NNH rate constants, the NNH mechanism appears to play a role in NO formation.

Fuel-bound nitrogen NO mechanisms: In several experiments, it was shown that NO emissions from combustion devices that operate with nitrogen-containing compounds in the fuel are high; in other words, fuel-bound nitrogen is an important source of NO. The initial experiments of Martin and Berkau [21] commanded the greatest interest. These investigators added 0.5% pyridine to base oil and found almost an order of magnitude increase over the NO formed from base oil alone. Their results are shown in Figure 8.8.

During the combustion of fuels containing bound nitrogen compounds, the nitrogen compounds most likely undergo some thermal decomposition prior to entering the combustion zone. Hence, the precursors to NO formation will, in general, be low-molecular-weight, nitrogen-containing compounds or radicals (NH₃, NH₂, NH, HCN, CN, etc.). All indications are that the oxidation of fuel-bound nitrogen compounds to NO is rapid and occurs on a time scale comparable to the energy–release reactions in the combustion systems. This conclusion arises from the fact that the NH and CN oxidation reactions discussed in the previous section are faster [22,23] than the important chain branching reaction

Thus, the reaction system cannot be quenched to prevent NO formation from fuel-bound nitrogen, as is the case with atmospheric nitrogen. In fact, in the vicinity of the combustion zone, observed NO concentrations significantly exceed calculated equilibrium values. In the post-combustion zone, the NO concentration decreases relatively slowly for fuel-lean mixtures and more rapidly for fuel-rich mixtures. Recall Bowman and Seery's results (Figure 8.3) showing that fuel-rich systems approach equilibrium faster. When fuel−nitrogen compounds are present, high NO yields are obtained for lean and stoichiometric mixtures and relatively lower yields are found for fuel-rich mixtures. The NO yields appear to depend only slightly on temperature, thus indicating a low activation energy step. This result should be compared to the strong temperature dependence of NO formation from atmospheric nitrogen.

The high yields on the lean side of stoichiometric pose a dilemma. It is desirable to operate lean to reduce hydrocarbon and carbon monoxide emissions; but with fuel containing bound nitrogen, high NO yields would be obtained. The reason for the superequilibrium yields is that the reactions leading to the reduction of NO to its equilibrium concentration, namely

The extent of conversion of fuel nitrogen to NO is nearly independent of the parent fuel molecule, but is strongly dependent on the local combustion environment and on the initial fuel nitrogen in the reactant. Unlike sulfur in the fuel molecule, nitrogen is much more tightly bound in the molecule and, for the most part, in an aromatic ring [24]. Regardless, all fuel−nitrogen compounds exhibit solely carbon−nitrogen or nitrogen−hydrogen bonding. Thus, it is not surprising that in the oxidation of fuel−nitrogen compounds, the major intermediates are HCN and CN and amine radicals stemming from an ammonia structure: that is, NH₂, NH, and N.

In a large radical pool, there exists an equilibrium

Consequently, reactions (8.61) and (8.62) can be written as a generalized reaction

Thus, there is great similarity between the prompt NO reactions discussed and the fuel−nitrogen reactions.

In the combustion of fuel−nitrogen compounds, the equilibrium of

The general scheme of the fuel−nitrogen reactions is also represented in Figure 8.7.

In fuel-rich systems, there is evidence [8,25,26] that the fuel−nitrogen intermediate reacts not only with oxidizing species in the manner represented, but also competitively with NO (or another nitrogen intermediate) to form N₂. This second step, of course, is the reason that NO yields are lower in fuel-rich systems. The fraction of fuel nitrogen converted to NO in fuel-rich systems can be as much as an order of magnitude less than that of lean or near-stoichiometric systems. One should realize, however, that even in fuel-rich systems, the exhaust NO concentration is substantially greater than its equilibrium value at the combustion temperature.

Haynes et al. [14] showed that when small amounts of pyridine are added to a premixed, rich (ϕ = 1.68; T = 2030 K) ethylene−air flame, the amount of NO increases with little decay of NO in the post-flame gases. However, when larger amounts of pyridine are added, significant decay of NO is observed after the reaction zone. When increasingly higher amounts of pyridine are added, high concentrations of NO leave the reaction zone, but this concentration drops appreciably in the post-flame gases to a value characteristic of the flame, but well above the calculated equilibrium value. Actual experimental results are shown in Figure 8.9.

In fuel-rich systems, the conversion reactions of the fuel−nitrogen intermediates are subject to doubt, mainly because the normal oxidizing species O₂, O, and OH are present only in small concentrations, particularly near the end of the reaction zone. Haynes et al. [14] offered the interesting suggestion that the CN can be oxidized by CO₂ since the reaction

However, in the case of sampling from gas turbines, NO₂ can vary from 15% to 50% of the total NO_x, depending on the NO level [24,27,28]. In the case of range-type burners, the NO_x has been reported as high as 15−20 times the NO levels in parts of the flame surrounding the burner top [29,30].

Merryman and Levy [31] examined both NO and NO₂ formation in a flat flame burner operated near stoichiometric. In the low-temperature regime of visible flames, they found large concentrations of HO₂ that can react with the NO formed in the high-temperature regime and diffuse back to the lower-temperature zone. Their measurements showed that NO₂ is produced in the visible regime of all air flames (with and without fuel-bound nitrogen) and that NO is observed only in the visible region when fuel-bound nitrogen is present. Furthermore, these investigators found that NO₂ is consumed rapidly in the near–post-flame zone, whereupon the NO concentration rises correspondingly. They postulated the following scheme to represent their findings:

In light of Figure 8.7, whether reaction (8.81) should be the representative reaction for NO formation is irrelevant.

The significant step is represented by reaction (8.82). One should recall that there can be appreciable amounts of HO₂ in the early parts of a flame. The appearance of the NO₂ is supported further by the fact that reaction (8.82) is two orders of magnitude faster than reaction (8.83). The importance of the hydroperoxy radical attack on NO appeared to be verified by the addition of NO to the cold-fuel mixtures in some experiments. In these tests, the NO disappeared before the visible region was reached in oxygen-rich and stoichiometric flames: that is, flames that would produce HO₂. The NO₂ persists because, as mentioned previously, its reduction to N₂ and O₂ is slow. The role of HO₂ would not normally be observed in shock tube experiments owing to the high temperatures at which they usually operate.

The Merryman−Levy sequence could explain the experimental results that show high NO₂/NO ratios. For the experiments in which these high ratios were found, it is possible that reaction (8.83) is quenched, in which case the NO₂ is not reduced. Cernansky and Sawyer [32], in experiments with turbulent diffusion flames, also concluded that the high levels of NO₂ found were due to the reactions of NO with HO₂ and O atoms.

The experimental efforts reporting high NO₂ levels have come into question because of the possibility that much of the NO₂ actually forms in sampling tubes [33,34]. Optical techniques are now being applied; but unfortunately, the low concentrations of NO₂ that exist make resolution of the controversy difficult.

In natural gas combustion an increasingly important contribution from

Calculated lifetimes of N₂O in combustion products indicate that for temperatures above 1500 K, the lifetime of N₂O typically is less than 10 ms, suggesting that except for low-temperature combustion, as found in fluidized bed combustors and in some post-combustion NO removal systems, N₂O emissions should not be significant, a conclusion that is in agreement with the most recent measurements of N₂O emissions from combustion devices.