Periodic cool-flames

Three requirements must be fulfilled before any mechanism can be accepted. Firstly, it must be capable of explaining the mode of formation of the reaction products secondly, it must be acceptable from thermo-kinetic considerations and finally it must be capable of explaining phenomena such as the negative temperature coefficient and periodic cool flames. It was recently pointed out [38] that many mechanisms have been proposed in recent years which do not take the second consideration into account. Whilst this is a valid criticism, the reverse is also true, i.e. many mechanisms have been suggested which are based on inaccurate thermo-kinetic considerations and have not been confirmed experimentally. In any event, the system under consideration must be defined by experiment, which in this case requires extensive knowledge of the kinetics, the yields and nature of the products formed and their variation with the extent of reaction and the reaction conditions. Modern techniques have allowed the system to be reasonably well defined in these terms and this has led to two principal theories regarding chain-propagation. 

The mole fraction versus time profiles from the sub-atmospheric pressure studies by Wilk et al. [13] in a closed vessel, shown in Figs 6.24 and 6.25, are rather typical of the records obtained by many different workers subsequent to the seminal work by Newitt and Thornes [8,134] in 1937. The results in Fig. 6.24 were obtained by Wilk et al. [13] during the occurrence of periodic cool-flames. The associated temperature changes were measured by a thermocouple. 

Early among the isothermal models used to ex ain periodic cool flames was the Lotka-Volterrascheme invoked - as a possible prototype by Frank-Kamenetskii. Two active intermediates X and Y are postulated in the scheme ... 

At present it would seem as if detailed modelling is most profitable after vindication of a generalized approadi and is not a realistic indepraident altmiativc. Progress 1 both paths has deepened understanding in the study of hydrocarbon oxidation. From being the most mysterious, periodic cool flames have become the best undostood of oscillatory chemical reactions. 

Cool Flames. An intriguing phenomenon known as "cool" flames or oscillations appears to be intimately associated with NTC relationships. A cool flame occurs in static systems at certain compositions of hydrocarbon and oxygen mixtures over certain ranges of temperature and pressure. After an induction period of a few minutes, a pale blue flame may propagate slowly outward from the center of the reaction vessel. Depending on conditions, several such flames may be seen in succession. As many as five have been reported for propane (75) and for methyl ethyl ketone (76) six have been reported for butane (77). As many as 10 cool flames have been reported for some alkanes (60). The relationships of cool flames to other VPO domains are depicted in Figure 6. 

Propane. The VPO of propane [74-98-6] is the classic case (66,89,131—137). The low temperature oxidation (beginning at ca 300°C) readily produces oxygenated products. A prominent NTC region is encountered on raising the temperature (see Fig. 4) and cool flames and oscillations are extensively reported as compHcated functions of composition, pressure, and temperature (see Fig. 6) (96,128,138—140). There can be a marked induction period. Product distributions for propane oxidation are given in Table 1. 

Cool Flames. Cool flames are confined, roughly speaking, to the temperature regime which exhibits the negative temperature coefficient of the rate. The flames are clearly nonisothermal, and the light emission which is most intense at the end of the maximum rate period is probably caused by radical-radical reactions (27, 28) such as... 

Figure 4. Regions of ignition, cool flames, slow oxidation with and without the pic darret in an equimolar propane-oxygen mixture. Bars on the boundaries represent experimental points, and numbers on these curves signify the duration of induction periods (in seconds). Numbered regions are defined in the text...

Above 250°C. we approach, in the gas phase, what is known as the cool flame regime. This is characterized by induction periods and by the appearance of pressure peaks and luminescent phenomena in the oxygen-hydrocarbon system. The consensus of present data seems to support the contention that these cool flames arise from the secondary decomposition of the hydroperoxides produced by the low temperature chain. The unimolecular decomposition of the hydroperoxide yields active alkoxy and hydroxyl radicals ... 

Increased induction period Lengthened time to appearance of cool flame Increased induction period Increased induction period... 

Provided (f - g) > 0, the chain carrier concentration, and hence, the reaction velocity will increase exponentially with time. However, (/ - g) may be small enough so that t, corresponding to the induction period, r, may be very long. If (f — g) < 0, a true explosion never develops. A slow change from — to + values of (/ - g) has been observed for hydrocarbon-oxygen systems. These phenomena are sometimes referred to as degenerate chain-branching explosions or cool flames (44, ) ... 

For aliphatic hydrocarbons a close relationship exists between knock and low-temperature, two-stage ignition (110). In both cases two induction periods are observed. One, Ti, extends up to cool flame formation. The other, r2, follows ti and lasts up to autoignition. 

The t2 period includes the cool flame reaction, which may be followed by a period of decreased reaction velocity, and leads up to autoignition. Lewis and von Elbe (108, 110) believe that in the r2 region unbranched chains are initiated by reaction of formaldehyde and perhaps other aldehydes with oxygen. Second-stage ignition is not believed to be of the branched-chain type but occurs as a result of unbalancing of thermal equilibrium. 

This delayed decomposition of the metastable peroxides has been termed degenerate chain branching by Semenoff and has been used by him to account for the ignition limits of hydrocarbon oxidations, in particular for the long induction periods preceding the cool flames. 

The cool flame phenomenon seems to be closely tied to the formation of aldehydes and peroxides in oxidation systems. In Fig. XIV. 10 is shown a typical example of the explosion limits for a hydrocarbon-oxygen mixture. The explosion region, except for a region of positive slope, resembles the limit curve for a thermal explosion. The transition between slow combustion and explosion is characterized by an intense luminous blue flame which appears after a short induction period and is followed by explosion. The induction periods are not more than a few seconds. 

The region of cool flames, which also has a region of positive slope (and is in this sense analogous to the second explosion limits for H2 and CO), has been the subject of much interest. The cool flames are most arresting because of the very long induction periods that precede them. Andrew" found that, in n-butane + O2 mixtures, the induction period decreased ex-... 

The periodicity of the cool flames and their merging into the region of explosion with increasing pressure are features on which there has been much speculation but as yet little clear-cut evidence. Chamberlain and Walsh have proposed that the catalytic agents responsible for the cool flames are hydroxy alkyl peroxides arising from the condensation of peroxides and aldehydes on surfaces. Frank-Kamenetskii,- on the other hand, has made the rather intriguing proposal that the mechanism itself is responsible for the periodicity.This requires that peroxides and aldehydes catalyze each others production and disappearance in a set of second-order processes such as... 

Associated with the low temperature (200—450 °C) oxidation of hydrocarbons are the phenomena of the negative temperature coefficient, cool flames and their periodicity, and multiple-stage ignitions. Any mechanism must, therefore, be able to account for these phenomena in addition to explaining the modes of product formation. 

Under suitable initial reaction conditions the intermediate can lead to multiple cool flames if AH21 > 1 AH and E2 > E. Thus, as X accumulates the second reaction becomes more rapid and hence increases the temperature. Since E2 > 1, its rate is therefore accelerated relative to the first reaction and [X] falls. This in turn leads to a decrease in temperature and the first reaction is accelerated relative to the second leading to another increase in [X] and thus to a periodic thermokinetic phenomenon. The second theory is purely kinetic and depends on the production of critical concentrations of two different intermediate products which enter into branching reactions [30]. The reaction scheme may be represented as (where A and B are the reactant and final product, respectively, and X and Y are the intermediates)... 

When [X] reaches the critical value k [A]/k, d[Y]/df becomes positive and [Y] increases at the expense of [X]. Similarly, when [Y] in turn reaches the critical value k. [A]/k, d[X]/dt becomes negative and [X] eventually falls below the value [A] jk, . [Y] will then begin to fall and when it becomes less than [A] /feb. [X] will increase again. Thus if the criteria for the odd-numbered cool flames is that [X] > [X]crit and the criteria for even-numbered cool flames is that [Y] >[Y] ri, the periodicity is explained. This two-product theory has been discussed elsewhere [6, 14, 31, 32]. Not unexpectedly the identities of X and Y are thought to be hydroperoxides and aldehydes, respectively. 

VIV propene to equimolar mixtures of propane + oxygen reduced the cool-flame induction period by ca. 18 % at 300 °C. Like the previous work, these results showed the importance of the conjugate alkene in the autocatalytic oxidation of propane. However, at 247 °C, the yield of cyclohexene just prior to the cool flame was < 1 % of the total products. In contrast, at temperatures above 300 °C, it becomes the major product and is formed in roughly equal amounts with hydrogen peroxide prior to a stabilized cool flame [52]. Tipper concluded that above 300 °C reaction (2) occurs to an appreciable extent until well after the initial stage of oxidation since the differential yield of the alkene (d[C H2 ]/ d [C Hj 2 ]) was > 25 % over at least a quarter of the reaction. 

Further support for the attainment of a critical concentration of hydroperoxide prior to the passage of a cool flame at temperatures corresponding to the Lq and L, lobes has been obtained by Taylor [131], and more recently by Pollard and co-workers [68,132], who determined the maximum concentrations of tert-butyl hydroperoxide found during the cool-flame oxidation of isobutane. Again, the concentration of hydroperoxide increased prior to the cool flame and it was almost entirely consumed during its passage (Fig. 12). Also, in common with other hydrocarbon + oxygen systems, (e.g. refs. 55, 65, 78,133) the induction period to the first cool flame (r,) was related to the initial reactant pressure (po) by the expression... 

Values of the coefficients for the set of differential equations were chosen to give cool flames at realistic initial pressures and temperatures. Further restrictions on the choice of coefficients were imposed by requiring that the fuel conversion should not exceed 25 % at the maximum of the temperature pulse, that the induction period should be between 15 and 20 sec, and that the thermal relaxation time should be 0,25 sec. To achieve this the rate coefficients of reactions (d), (f), (h) and (g) were varied about reasonable estimates of their likely values. The parameters chosen for the model are given in Table 24. The computer was used in a conversational mode to map out an ignition diagram (Fig. 26) which compares favourably with that found experimentally [191] (Fig. 27). 

Cool flames are difficult subjects for quantitative study since the time scale of events is generally too short to allow the use of conventional sampling. In addition, their non-isothermal character (which implies rate coefficients which change as reaction progresses) makes it difficult to develop theoretical models which satisfactorily describe the more important features (the periodicity and temperature rise). It is outside the scope of this review to discuss the more general theoretical aspects of cool-flame phenomena, and the reader is referred to VoL 2, Chap. 2 of this Series and also to the work of Yang and Gray [113], Halstead et al. [114, 115] and others [112,116,117]. 

Recently Halstead et aL [122, 122a] have proposed a model for acetaldehyde cool flame combustion which is basically similar to that described above. Their treatment accounts for the periodicity and the self-quenching which is attributed to a thermal switch in which the decomposition of CH3CO... 

Although the addition of small amounts of acetaldehyde reduced the induction period markedly, the acceleration period and (p were unaffected until the pressure added exceeded that present just before the cool flame. In contrast, apparently, to the results of Cullis and Newitt [16], the addition of quite large amounts of acetaldehyde did not eliminate the induction period completely and only reduced the acceleration period by less than 25 %. 

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