Explosion limits second

One problem in the determination of second limits is that water, a product of the slow reaction, is also a powerful inhibitor of the explosion. In order to reduce errors due to water formation, much of the earlier work on this limit was carried out with potassium chloride coated vessels. With these, and in vessels coated with certain other salts, the limit is much less sensitive to withdrawal rate than it is with a clean Pyrex or a boric acid coated vessel, for example. Pease [19] first noted that potassium chloride coating produces a marked suppression of the slow reaction rate. More recent work by Baldwin et al. [20, 21], which will be discussed later, suggests that the suppression of the limit at low withdrawal rates in 

Second limits for 2Hz + O2 in potassium chloride coated vessels 

The second limits are quite reproducible over long periods using the same apparatus, and the limits from independent investigations also agree well. This is shown by Table 6, wliich quotes limits for stoichiometric mixtures in potassium chloride coated vessels. According to Willboum and Hinshelwood [27] the use of a number of similar coatings (KCl, KI, CsCl, Csl) does not alter the limit much. The results of Lewis and von Elbe [23] and Warren [25] in Table 6 also show that the limit is virtually independent of vessel diameter, provided the latter is greater than 4—5 cm. Clearly the limits are not determined primarily by competition between gas phase and wall effects. 

There have been a number of measurements of the effects of mixture composition and temperature on the hydrogen—oxygen second limits in potassium chloride coated vessels (e.g. refs. 28,14, 23, 25, 30). Typical of the results are the explosion regions shown in Figs. 3 and 4. They all 

The general form of eqn. (4), as well as the lack of dependence of the limit on vessel surface and diameter, is readily understood if the gas phase deactivation term in the denominator of eqn. (1) is dominant. Let it be assumed that the reaction of a chain carrier X with Oj can give rise to different products according to whether it reacts in a bimolecular or termolecular collision thus 

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In step (1) and step (2) there is an increase from one to two chain carriers . (For brevity, step (x) is used to refer to equation (A3.14.V) tliroughout.) Under typical experimental conditions close to the first and second explosion limits (see section A3.14.2.3). step (2) and step (3) are fast relative to the rate detemiining step (1). 

At this point an explosion will occur corresponding to the second explosion limit in Figure 4.1. 

The second explosion limit must be explained by gas-phase production and destruction of radicals. This limit is found to be independent of vessel diameter. For it to exist, the most effective chain branching reaction (3.17) must be overridden by another reaction step. When a system at a fixed temperature moves from a lower to higher pressure, the system goes from an explosive to a steady reaction condition, so the reaction step that overrides the chain branching step must be more pressure-sensitive. This reasoning leads one to propose a third-order reaction in which the species involved are in large concentration [2], The accepted reaction that satisfies these prerequisites is... 

Indeed, in developing complete mechanisms for the oxidation of CO and hydrocarbons applicable to practical systems over a wide range of temperatures and high pressures, it is important to examine the effect of the H02 reactions when the ratio is as high as 10 or as low as 0.1. Considering that for air combustion the total concentration (M) can be that of nitrogen, the boundaries of this ratio are depicted in Fig. 3.3, as derived from the data in Appendix C. These modem rate data indicate that the second explosion limit, as determined... 

FIGURE 3.4 The extended second explosion limit of IF—02 (after Ref. [6a]). 

The location of the second explosion limit, around 50 Torr, is determined by the competition between the chain-branching reaction,... 

The H + O2 competition is responsible for several important aspects of combustion phenomena. For example, the second explosion limit for hydrogen-oxygen mixtures is explained by the competition between H + O2 branching and termination (Section 13.2.6). The observed reduction in hydrocarbon-air flame speeds with increased pressure between 1 and 10 atm is caused by the branching-termination competition. For a given temperature, as the pressure increases, the concentration of [M] increases, which favors the termination reaction. Thus the chain branching competes less favorably for a greater portion of the flame, which diminishes the flame speed [427]. 

Therefore, at constant temperature, the second explosion limit pressures for a scries of mixture compositions can be used to obtain ratios of rate constants. In addition, Equation 41 serves as a check on the validity of the proposed reaction scheme. Alternatively, explosion-limit temperatures at constant pressure may be compared. Equation 40 can be rewritten as... 

If the activation energy difference, (E34 — E32), is known, rate constant ratios may be evaluated. Conversely, if the latter are known, (E34 - E32) may be evaluated. If second explosion limits for a series of undiluted mixtures of hydrogen and oxygen are compared, Equation 42 becomes... 

The occurrence of Reactions 45 through 48 will modify the second explosion limit. This has been offered in explanation of the observed dependence of the hydrogen-oxygen second-explosion limit on the nature of the vessel surface. 

A vessel is filled at room temperature to a pressure above the explosion limit. The temperature is then raised to a known value and the mixture is slowly withdrawn until explosion occurs. The pressure just prior to explosion is measured. This is commonly referred to as the withdrawal method 45,56), and is applicable only to situations where upper (or second) explosion limits exist. 

Kach method suffers from one or more inherent sources of error. Method 1 is not readily adaptable to the determination of second explosion limits. If temperature equilibrium is reached very quickly by the gas flowing into the vessel, as the continued flow causes the pressure to increase, the system must first intersect the lower explosion limit. Method 2 can lead to large errors if explosion is preceded by an induction period. In the carbon monoxide-oxygen reaction, for example, it was found that the heating rate could considerably affect the results owing to the existence of a zone of slow reaction adjacent to the second limit and inhibition of the reaction by the product, carbon dioxide... 

The feature which is unique to the chain-branching system is the paradoxical, upper, or second explosion limit. Plere one observes that a reaction proceeding with explosive speed at pressures below the limit is effectively (picnched on raising the pressure. In addition, the pressure limit increases if the temperature increases, just opposite to the behavior at the first and third limits. It is the existence of this limit that is the real evidence of the branching chain. It is observed that the limit is much less sensitive to surface-volume effects than is the first limit, while added inert gases always tend here to lower the limit (i.e., quench the explosion). 

If we add this reaction to our chain-termination system [Eq. (XIV.5.1)] by writing it as a termination step in the form kti G)P f thou above the second explosion limit we have... 

At pressures below the second limit, this higher-order termination process cannot keep pace with chain branching and we have chain explosion. Tlic equation for the second explosion limit is thus given by the equality of these two processes, or... 

At regions near the junction of the first and second explosion limits this is a poor approximation and the more exact equation defining both the first and second limits is given by the positive root of the equation — kbP ktJi/V = 0. At thc turn-... 

Below the first explosion limit the rate of reaction seems to be negligibly slow. Above the second explosion limit, studies of the rate of the normal" reaction have shown considerable irreproducibility among different laboratories and even in the same laboratory. The rates are remarkably sensitive... 

In the region above the second explosion limit, since all surface reactions are diffusion-controlled and decrease in relative importance with increasing pressure (including it is likely that the terms in and fc ,oH are small, and the expression can be somewhat simplified by ignoring them. However, at those pressures, additional termination reactions of IIO2 become important, which indicates that water poisons the active centers and inhibits initiation, or that H2O has an enormous cross section for the transfer reaction 5 (which is not too likely), or finally that homogeneous termination of H and OH replace wall termination and thus continue the importance of the inhibition reaction 4. ... 

Because of the appearance of a second explosion limit it is necessary to find a branching chain reaction for the system, and two have been proposed. 

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-... 

Measurements by Lewis and von Elbe [23] of initial reaction rates at 530 °C in a KCl coated Pyrex reaction vessel of diameter 7.4 cm are shown in Fig. 6. For constant total pressure, the rate varies little in hydrogen-rich mixtures but diminishes when the oxygen content increases. The reaction seems more sensitive to the total pressure than it is to mixture composition. The rate diminishes with pressure until the neighbourhood of the second explosion limit is reached. At the limit itself the rate becomes infinite, and very near the limit, within a few torr, Lewis... 

Second explosion limits and the slow reaction in vessels having very low surface destruction efficiencies for hydroperoxyl and hydrogen peroxide... 

Fig. 12. Second explosion limits of + O2 in boric acid coated Pyrex vessel, 7.4 cm diameter (after Egerton and Warren [24]). (By courtesy of The Royal Society.)...

Since the ratio 2fe2/ 4 is reliably known from second explosion limit work, the three kinetic unknowns in the system are now 3/ 20 smd 17. Again initially, 2 was assigned the fixed value 2.05 x 10 exp (—8,250/T). It was found that the best fit of the burning velocity, the relative H atom concentration decay profile in the recombination region (measured by intensity of sodium chemiluminescence), and the temperature and composition profiles were obtained with feg /fe2 0 = 5 1 and fej 7 = (4.5 1.5) X 10, assuming equal efficiencies of all the molecules in the... 

To obtain the expression for fe4,H 2 values at 773 K were related with k2 by way of the second explosion limit result that 2fe2/ 4,Hi 67.0... 

Compared with the reaction between hydrogen and oxygen, there have been relatively few studies of the deuterium—oxygen system. Early studies by Hinshelwood et al. [243] dealt with the second explosion limits and the slow reaction in silica vessels while at about the same time Frost and Alyea [14] measured the second limits in a KCl coated Pyrex vessel of 20 mm diameter. More recently Linnett and Selley [244] have determined the relative efficiencies of a number of molecules in reaction (ivD) D + O2 + M = DO2 + M (ivD)... 

Of greater interest here are the inhibition phenomena at the first and second explosion limits, and certain other experiments in which traces of hydrocarbons are added to slowly reacting H2 + N2 + O2 mixtures at around 773 K in aged boric acid coated vessels. Both types of measurement open up the possibility of examining the reactions of the radicals of the H2 + O2 system with the additive. 

Fig. 58. Second explosion limits of CO + 2O2 mixture in packed and unpacked cylindrical quartz vessels (after Dickens et al. [358]). o, Unpacked vessel, 9.9 cm long, 8.0 cm diameter packed vessel, 8.0 cm long, 6.0 cm diameter. (By courtesy of The Faraday Society.)...

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