The Reaction between Hydrocarbons and Oxygen

CHAPTER IV

The Reaction between Hydrocarbons and Oxygen

1. Slow Oxidation, Cool Flames, and High-Temperature Explosive Reaction The general features of the oxidation kinetics of methane and higher hydrocarbons are illustrated in Fig. 22 by the explosion limit curves 5-8 which have been obtained by Townend and co-workers. Curve 5 applies to a mixture of methane and air; it shows that the pressure at the explosion limit decreases monotonously with increasing temperature as occurs in branched-chain explosions if the rate of chain breaking is controlled by diffusion of chain carriers to the vessel wall, and if the rate of chain branching is a function of temperature of the form exp[—E/RT\. Curves 6 and 7 apply specifically to hexane and air but are characteristic for paraffinic hydrocarbons and related compounds in general. At temperatures above about 400°C such limits are of the same type as the methane limit, though the explosion temperatures or pressures are lower than for methane, but as shown in Fig. 22, below about 400°C the limits are grossly changed by a mechanism of chain branching that generates explosion limits roughly bounded by an upper and lower limit temperature, more or less independent of pressure. It is known that this mechanism involves the formation and subsequent reaction of the peroxidic free radicals ROO that are produced by association of 0 with alkyl radicals R, as for example propyl radicals, C H ; butyl radicals, C4H9; or hexyl radicals, CôHI . Chain branching of this type occurs generally with compounds that contain alkyl groups, including in particular acetaldehyde and higher aldehydes, R · CHO, and notably ethers, R · Ο · R, which are highly susceptible to peroxidation. It does not occur with methane C H 4 , methyl alcohol CH OH, formaldehyde HCHO, or with unsaturates and aromatics such as ethylene CH :CH , acetylene CH : CH, and benzene CeH . As shown in Fig. 23, it occurs only marginally with ethane CH · C H , but the reaction becomes strongly developed when a small quantity of acetaldehyde, CH · CHO, is added to the ethane-air mixture. Further­ more, as shown by the curve 8 in Fig. 22, it occurs only marginally with isobutane HC(CH ) , whereas η-butane CH · CH · CH · C H , is known to have an explosion region similar to the peninsula outlined by the curves 6 and 7 for hexane. 1

2

3

7

3

3

2

2

6

3

3

3

3

3

3

2

2

3

It has become customary to refer to this peninsula region as the cool flame region, inasmuch as the reaction that occurs just outside the peninsula or within the peninsula during induction periods preceding explosion produces a blueish, more or less intense luminosity which tends to fluctuate and to traverse the reacting gas volume as a wave, 96

97

1. FLOW OXIDATION, COOL FLAMES, AND EXPLOSIVE REACTION 6

I

8

7\ CO LU CC LU X CL CO

11 11 11

Ο S

l u

il t \ 11 11

LU CC D CO CO LU CC Q.

\\

/ /

Λ

\ \

\

V

\ \ \ \ \ \ \ \ N

. K

\Co< 3l Flames >^ \

(

3*

0« 200

400

800

600

TEMPERATURE, °C FIG. 22. Explosion regions of hydrocarbon-oxygen mixtures. Lower curves: 1, CFU + 2 0 , quartz vessel (Neumann and Serbinow ); 2, CH + 2 0 , quartz vessel (Sagulin ); 3, C H + 3 . 5 0 , pyrex vessel (Taylor and Riblett ); 4, C H -I- 3 . 5 0 , quartz vessel (Sagulin ); Upper curves: 5, 15% methane in air, quartz vessel (Townend and Chamberlain ); 6, 1.8% hexane in air, glass vessel; 7, 1.8% hexane in air, steel vessel; 8, 2.6% isobutane in air, steel vessel (Townend, Cohen, and Mandlekar'). 2

4

5

4

2

6

2

6

2

5

2

6

2

1

and which is attributable to excited formaldehyde, HCHO*, that is formed in traces by certain free-radical reactions as a by-product of the chain-branching process. The further discussion of cool flame chemistry and kinetics is deferred to later sections. Here it is noted that above the upper temperature limit of the explosion peninsula the peroxidic free radicals vanish and the reaction proceeds via a plethora of nonperoxidic free radicals that are generated by fragmentation and oxygenation of the original hydrocarbon. Thus, whereas the reaction within and to the "west" of the peninsula is governed by peroxidic free radicals, to the "east" it is increasingly governed by nonperoxidic free radicals. Furthermore, chain breaking by free-radical diffusion to the vesssel wall intrudes into the cool flame region from the "south," i.e., toward low pressures, thus narrowing the explosion peninsula and establishing a low-pressure explosion limit. In sum, the chemistry and kinetics of the reaction of paraffinic hydrocarbons with oxygen comprise: (1) slow peroxidation at low temperatures, (2) peroxidic explosive and nonexplosive cool flame reaction at temperatures ranging roughly from 250° to 400°C, (3) a regime of slow oxidation via nonperoxidic free radicals at higher temperatures, and finally (4) high-temperature explosive reaction.

98

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

1

25

4000

12(V

---1-

-

-

20|

CO LU CC LU I Q. CO Ο 15 LU

3200

i 1

\84

w\

i

22'

!

1 1

y

1 1

ΠQ.

Ί

2

\

Ε Ε 2400?= CO CO LU CC 0. Ζ 1600g >Χ

ο

\

\ \ 5 " \

N

\

3

oL 200

en I

2"/I

2

y

/

y

27/ 400

1

800

600

TEMPERATURE, °C

FIG. 2 3 . Explosion regions and ignition lags in ethane-air mixtures; effect of adding acetaldehyde. 1 3 % ethane in air. (Townend and Chamberlain.) 1, No acetaldehyde. 2 , 1% acetaldehyde. 3 , 2 % acetal­ dehyde. Induction periods are marked along 1 and 2 in min. and sec.

2. Chemical Kinetics of the High-Temperature Explosive Reaction A multitude of elementary reactions involving a multitude of free-radical and other molecular species are initiated by rapidly heating a hydrocarbon-oxygen mixture to temperatures above approximately 800°K. This may be brought about either by rapid admission to a heated reaction vessel or some high-temperature flow system, or by rapid compression which may be adiabatic (isentropic) or may proceed as a shock or detonation wave, or simply by some local ignition source such as a spark or hot wire from which the reaction propagates by thermal and molecular diffusion as a combustion wave. Furthermore, explosive reaction that is induced at temperatures in the cool flame region rapidly passes from peroxidic to nonperoxidic free-radical chains, and conversely, even rapid heating of a hydrocarbon-oxygen mixture may not completely eliminate the initial formation of peroxidic free radicals. The availability of large amounts of elementary kinetic and thermochemical data and of techniques for estimating such data where no measurements exist, together with the development of efficient "stiff equation" solution techniques for computer

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

99

programming, have made this enormously complex reaction the most prominent subject of chemical-kinetic combustion research. Elaborate reaction mechanisms comprising more than one hundred elementary reactions have been proposed and tested in computational models of combustion processes, by comparing computed data with experimental measurements. A review of the subject including 162 literature references has been published by Westbrook and Dryer. They have also compiled another detailed review including 497 literature references. To quote these authors, reaction mechanisms for hydrocarbon fuels include within them submechanisms for the combustion of simpler molecules, which suggests that each mechanism can be built on a "hierarchical" sequence of reaction mechanisms for simpler molecules. Thus, starting with H , the mechanism involves hydrogenoxygen kinetics, and adding CO one obtains the combined C O - H - 0 mechanism. This in turn is part of the oxidation of formaldehyde, HCHO, which is part of the mechanism of C H oxidation, and so on through C , C , etc., hydrocarbons. Follow­ ing such a sequential path can, according to these authors, simplify the task of validating a proposed reaction mechanism, since only those reactions and rates which have been added to account for the next level of complexity require special attention. Hydrogen-oxygen kinetics is unmistakably evident in curve 1 of Fig. 22, which is the record of an explosion limit for methane and oxygen obtained in early work on this reaction. The curve shows the characteristic explosion peninsula bounded by an upper and lower pressure limit, indicating that in this case the limit was primarily dependent on competition between chain branching via H + 0 —» OH 4- Ο and chain breaking via H + 0 + M —» H 0 + M followed by diffusion of H 0 to the vessel wall. The effect is also slightly discernible in the curve 4 for ethane but is not shown by the curve 2 for methane or the curve 3 for ethane, which suggests that diffusion and surface reactions of molecular species may complicate the already complex reaction mechanism beyond analysis. Furthermore, explosion limits such as curve 5 are no doubt affected by reaction and heat release during preceeding induction periods much as shown for the third explosion limit of hydrogen and oxygen in Fig. 5, and thus do not conform to isothermal branched-chain theory. Understandably therefore, the literature that is quoted by Westbrook and Dryer includes no reference to explosion limits in heated reaction vessels. Instead, test data for validation of proposed reaction mechanisms are obtained principally from ex­ periments with shock tubes and "plug flow" reactors. Shock tube experiments are generally performed as described by Burcat, Lifshitz, Scheller, and Skinner in their study of the propane-oxygen reaction. The text mixture of hydrocarbon and oxygen is diluted by approximately 90% argon, which has a low heat capacity favoring high shock temperatures and provides sufficient dilution to prevent the shock wave from becoming a detonation wave. Shock temperatures and pressures are calculated from the measured shock Mach number. The reflection of the shock wave at the tube end temporarily produces a zone of stagnant, highly compressed test gas, allowing the explosive reaction that develops in this zone to be 2

3

2

2

4

2

2

3

4

2

2

2

5

2

5

7

6

100

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

monitored spectroscopically. The entire reaction is divided roughly into three phases: initiation, consumption of the hydrocarbon, and CO oxidation. Depending on the fuel and the initial temperature and pressure the first two phases may overlap, but the CO oxidation phase is usually very distinct and produces most of the heat release of the overall reaction. The corresponding rapid temperature and pressure transients are often used to define the end of the ignition delay or induction period, with the subsequent CO oxidation usually taking less than 1 to 5% of the duration of the overall reaction. The reaction time is so short that heat loss and diffusion processes play no role. This also applies to plug flow reactors. In this type of reactor a stream of fuel gas is injected into a heated stream of oxygen and inert gas, and the reacting mixture then passes through a tube at such rate that characteristic times for heat loss and diffusion are much longer than the residence time. Operating at steady state, this condition expands the reaction zone often over more than a meter in length. As in shock tube experiments, the fuel consumption and CO oxidation phases are usually distinct and the progress of the reaction is monitored along the reaction zone. This type of reactor is used for studies at the relatively low temperatures of about 800 to 1300°K, where reaction times are too long for shock tube experiments. Shock tube data generally extend over a range from about 1500 to 2200°K. Plug flow reactors are instrumented to yield profiles of the temperature and the concentrations of reactants and reaction products over the length of the steady-state reaction zone. Shock tubes are generally instrumented to focus on a narrow test section near the tube end. The incident shock passes through the section but the temperature behind the shock front is too low to generate a signal. Then, as the reflected shock passes, the gas becomes stagnant, its temperature nearly doubles, and emission and absorption spectra are recorded which sharply mark the beginning of chemical reaction but leave it to the experimenter to decide which part of the record should be considered the ignition delay or induction period. Fortunately, it seems that different criteria do not give substantially different results. Thus, in separate shock-tube investigations of the methanol-oxygen reaction, Bowman uses the at­ tainment of maximum 3700 Â emission and Cooke, Dodson, and Williams use the onset of 4.3 μ infrared emission as the respective end points of the induction period. The 3700 Â emission is attributed to the reaction between CO and Ο and the maximum correspondingly indicates the maximum of the product of the CO and Ο concentra­ tions, whereas 4.3 μ emission indicates C 0 which is largely produced by reaction of CO and OH and may be expected to appear ahead of the 3700 À maximum. However, the two sets of data conform almost identically to the equation 8

9

2

τ - 2.1 X 1 0 ( e x p [ 3 6 , 2 0 0 / / ? r ] ) [ C H O H ] - ' [ O , ] " 13

0

3

05

sec,

(1)

which has been empirically developed and provides an excellent correlation of the measured induction periods τ with the shock temperatures Τ in degrees Kelvin and the concentrations of CH OH and 0 in the shock-compressed gas, in units of moles 3

2

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

101

per cubic centimeter (the argon concentration has no effect). This suggests that the arbitrariness of the end point of the induction period is unimportant, inasmuch as at any chosen end point the reaction has become or is about to become very rapid. Numerous investigators are involved in ongoing experimentation with shock tubes and plug flow reactors, and imaginative modeling of hydrocarbon-oxygen reaction mechanisms comprising enormous numbers of known or postulated elementary reactions. They are determining individual rate coefficients by a variety of experi­ mental methods or theoretical considerations, programming computers for the solu­ tion of the kinetic equations governing the formation and disappearance of molec­ ular species and the change of temperature, and by changes and adjustments finally arriving at a model of the reaction mechanism that is judged to yield acceptable agreement between computed and experimental data. A prime example of such work is the comprehensive mechanism of the methanol-oxygen reaction shown in Table 1, which has been compiled by Westbrook and Dryer on the basis of a formidable array of publications as well as their own work and extensive use of computers. For details of this compilation, including the references used by Westbrook and Dryer, the reader is referred to these authors. The "hierarchical" structure of the mechanism is shown by reactions (1) to (8), which are the only reactions involving C H O H . The total mechanism of 84 reactions was obtained by adding these reactions and reactions 9 and 10 for C H O H to a previous mechanism for methane-ethane-oxygen mixtures, which in turn was built on various earlier mechanisms with a view of reproducing flow reactor data for methane and oxygen as well as shock tube data that were determined for methane, ethane, and oxygen. The mechanism in Table 1 is intended to reproduce the shock tube data and flow reactor data on methanol and oxygen. For the latter data the agreement between experiment and theory is illustrated in Fig. 24. For the shock tube data the agreement is illustrated in Fig. 25 by means of a data correlation based on Eq. (1). This equation is written in the form 10

3

2

11

8

12

T[CH OH]° [0 ] a

3

2

0 5

= 2.1 x 1 0 "

1 3

exp[36,200//?r],

(2)

and a straight line corresponding to the function on the right side of the equation is drawn in Fig. 25 as shown. All values of the function on the left side, computed from experimental values of τ for given sets of conditions [ C H O H ] , [ 0 ] , and Γ, cluster very closely around this line. This is shown elsewhere. The question is whether this holds true when computed values of τ are substituted for the experimental values. An apparently positive answer is found in the cluster of data points that are shown in the figure. These points correspond to Bowman's experiments with com­ puted values of τ substituted for the experimental ones. The end point of the computed time τ is the attainment of the maximum of the product of the C O and Ο concentra­ tions, which conforms to Bowman's criterion. There are six compositions of methanol-oxygen-argon mixture ranging from fuel-lean to fuel-rich, and for each 3

2

8

8

102

IV.

THE REACTION BETWEEN HYDROCARBONS A N D

OXYGEN

TABLE 1 METHANOL OXIDATION MECHANISMAB

Reaction

log A

Rate η

E

a

1

CH OH + M -» CH

M

18.5

0

80.0

2

CH3OH + 0 ^ C H O H + H 0 CH3OH + O H - * C H O H + H 0 CH3OH + Ο - > C H O H + O H

13.6

0

50.9

3 4

3

+ OH +

3

2

2

2

2

2

2

5

CH OH + H -* CH OH +

6 7

CH3OH + H - > C H + H 0 CH3OH + C H - > C H O H + C H

8

CH3OH + H 0

9

3

H

2

3

3

2

2

2

2

-> CH OH +

2

CH OH + M -» CH OH + H + 2

2

10

CH OH + 0

11

CH

2

-> CH 0 +

2

4

+ M -> CH

+ H +

3

12

CH

4

+ H -> CH

13

CH

4

+ OH -> CH

3

14

CH

4

+ Ο -> CH

+

4

+

3

3

H

OH

CH

17

CH

3

+ OH -» C H 0 +

18

CH

3

+ Ο -> CH 0 +

19

CH

-* CH

2

2

+

2

H 0

2.0

0

9.2

2.0

CH

+

4

HCO

+

4

CO

+

4

0

2

24

CH3O + 0

25

C H 0 + M -> HCO + H +

M

CH 0 +

H0

2

2

M

2

26

C H 0 + OH

27

C H 0 + H —» H C O +

H

28

CH 0 + Ο

OH

29

CH 0 + H0

30

HCO

+ OH

31

HCO

+ M - ^ H

32

HCO

+ H

33

HCO

+ Ο —» C O +

34

HCO

+ H0

35

HCO

+ 0

HCO +

H 0 2

2

HCO +

2

-> HCO + CO +

H 0 2

H 0 2

+ CO +

CO +

H

M

2

OH

CH 0 +

0

CO

+ OH -> CO, +

CO

+ H0

38

CO

+ Ο + M —» C 0

39

co

+ Ο —> C O +

40

H + 0

41

H

42

H 0

+ Ο -> OH +

43

H 0

+ H -» H

o

12.0

0

0.4

13.7

0

21.0

12.0

0

6.0

16.7

0

72.0

14.7

0

6.3

12.6

0

3.8

13.7

0

4.6

12.0

0

8.0

14.0

0

0.0

14.2

0

19.0

14.3

0

0.0

14.0

0

0.0

0

3.0

0

7.0

OH

14.0

0

15.8

0

4.1

12.4

0

43.8 16.8

+

2

6.0 0.0

14.0

H

-> CO, +

0.5 0.5

12.5

H0

36

2

10.0 11.5

2

2

CO +

37

2

11.9

3.08

29.0

2

2

0

0

+ H0

2

2

7.1 M

1.3

-0.8 23.0

+

OH

14.3

0

+ Ο -> H +

OH

10.3

1

8.9

13.5

0

18.4

14.0

0

20.3

2

^ 0

14.1

13.4

3

2

88.4

0.0

CH3O + M - > C H 0 + H +

2

0

0

CH

2

6.0

17.1

14.1

H

23

2

29.0

0

0.0

CH

2

0

12.0

0

2

22

2

13.4

12.6

H

+ HCO -> CH

2

M

18.0

3

2

19.4

0

C H 0 + CH

2

9.8

0

0

CH

2

0

13.3

20

2

11.3 12.8

13.2

2

21

3

7.0 5.3

2

3

- > CH3O + Ο

2

0 0

CH3O + O H

2

+ 0

13.5 12.7

13.2

2

3

2.0 2.3

3.5

2

CH

+ H0

M

H 0

15

+ H0

2

2

+

16

3

H0

2

0 0

2

4

H 0

2

12.6 12.2

2

+

OH OH

2.

CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

TABLE

1 (Continued)

Reaction 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

H 0 + OH —» H 0 + H 0 H 0 + M - + H + OH + M H + 0 + M —> H 0 + M H0 + Ο OH + 0 H0 + Η OH + OH H 0 + Η -> H + 0 H 0 + OH - > H 0 + 0 H 0 + 0 -> H 0 + H 0 H 0 + M - > OH + OH + M H 0 + H —> H 0 + H O + H + M^OH + M 0 + M-*0 + 0 + M H + M->H + H + M 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

C H - > CH + CH C H + CH C H + CH C H + H -> C H + H C H + OH - > C H + H 0 C H + Ο - * C H + OH C H5 —> C H + Η C H + 0 C H + H0 C H + C H -> C H + C H C H + Ο - > CH + HCO C H + M -> C H + H + M C H 4- H —» C H + H C H + OH C H + H 0 C H + Ο C H 0 + CH C H + M -> C H + H + M C H + M —> C H + H + M C H + 0 HCO + HCO C H + H -> C H + H C H + OH - > C H + H 0 C H + Ο - > C H + OH C H + Ο - > CH + CO C H + 0 - > HCO + CO CH + Ο CO + CH CH + 0 HCO + OH CH + Ο CH + OH CH + Η - > CH + H CH + OH —» CH + H 0 CH + 0 CO + OH CH + 0 HCO + Ο 2

6

2

6

2

6

2

6

2

6

3

3

3

2

2

5

2

2

5

2

2

2

2

5

2

2

5

2

2

4

2

4

2

4

2

4

2

4

2

3

2

2

2

2

2

2

2

2

2

2

2

2

4

5

2

5

4

2

4

3

2

2

4

2

3

2

3

2

3

2

2

3

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

4

log A

Rate η

13.0 16.3 15.2 13.7 14.4 13.4 13.7 13.6 17.1 12.2 16.0 15.7 14.3 19.4 -0.3 2.7 13.8 13.4 13.6 12.0 17.5 13.0 17.6 13.8 14.0 13.4 16.5 14.0 12.6 14.3 12.8 15.5 13.8 13.0 13.7 14.0 11.3 11.4 11.4 11.1 13.0

0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 3.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.6 0 0 0 0 0.68 0.67 0.67 0.67 0

^Reaction rates in cm /mole sec units, k = AT" e\p(-EJRT). C. K. Westbrook and F. L. Dryer. 3

b

10

E in kcal/mole. a

E

n

1.8 105.1 -1.0 1.0 1.9 0.7 1.0 42.6 45.5 3.8 0.0 115.0 96.0 88.3 8.3 5.2 2.4 6.4 38.0 5.0 35.6 1.1 98.2 6.0 3.5 5.0 40.5 114.0 28.0 19.0 7.0 17.0 4.0 7.0 0.0 3.7 25.0 25.7 25.7 25.7 0.0

103

104

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN 1140

X Ο ο

I

ι

ι

•

π .

£

4

Ο

Ε CM

Ο ο ο ο

ο 2

0

ι

I

I

20

40

60

80

20

40

60

80

POSITION — CM

POSITION — CM

FIG. 2 4 . Comparison between experimental data (open symbols) and computed species and temper­ ature profiles for lean methanol oxidation in a plug flow reactor. Position is measured from the inlet duct of the flow system. (Westbrook & Dryer ). 2,10

composition there are four to six data points representing temperatures from about 1550°K to nearly 2200°K and pressures from about one to five atmosphere in the zone of shock reflection at the tube end. Westbrook and Dryer have also computed the burning velocity S of a stoichio­ metric methanol-air mixture, using the above reaction mechanism in conjunction with the appropriate thermochemical data and equations governing thermal and molecular diffusion and mass and energy conservation. A system of equations for computing burning velocities has been developed by Hirschfelder and Curtis and is shown on p. 222 of this book; Westbrook and Dryer use a computer code developed by Lund. Their value of S , computed for a mixture at 298°K and atmospheric pressure, is 44 cm/sec. This agrees well with published experimental values which are in the range from 44 to 46 cm/sec. Accordingly, Westbrook and Dryer consider their comprehensive mechanism of methanol oxidation to be well validated, but they have not addressed a problem that 10

u

13

210

14

u

15

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

105

shows up when the data points in Fig. 25 are examined in detail. It is found that these points conflict with Bowman's careful determination of the effect of changes of concentrations of methanol, oxygen, and argon on the induction periods τ. Bowman performed the experiments in such way that in any run of four to six experiments not only the composition of the methanol-oxygen-argon mixture re­ mained constant, but also the concentrations of methanol, oxygen, and argon in the zone of shock reflection remained nearly constant, though the temperature varied from about 1550°K to nearly 2200°K. Table 2 shows these concentrations for the six sets of data points corresponding to mixtures 1-6 in Fig. 25. In runs with mixtures 1 to 3 Bowman found that a nearly threefold increase of the argon concentration had no effect on the induction period, a result that he symbolized by inserting the term

106

IV.

THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

TABLE 2 CONCENTRATION OF METHANOL, OXYGEN AND ARGON IN THE ZONE OF SHOCK REFLECTION FOR THE DATA POINTS IN FIG. 25 (BOWMAN) 8

Mixture, ΙΟ" mole/cm 7

CH OH 3

Ar

1

2

3

4

5

6

2.1 4.1 95

2.1 4.3 210

2.1 4.3 276

2.1 2.1 200

2.1 8.4 200

4.1 2.1 200

3

[Ar]° into Eq. (1). From runs with mixtures 4 and 6 and an additional mixture with [CH3OH] = 8.4 x 10~ moles/cm , Bowman determined the exponent - 0 . 1 ± 0.1 for the methanol term in Eq. 1, and the runs with mixtures 2, 4, and 5 yielded the exponent - 0 . 5 ± 0.15 for the oxygen term. The experimental data are accordingly almost precisely correlated by the function T [ C H O H ] ° [ 0 ] ' as shown in Eq. (2). If now computed values of τ are substituted for the experimental ones, the data points in Fig. 25 are seen to break away from the curve that represents the function 2.1 x 1 0 " exp[36,200//?r] on the right side of Eq. (2), except for those points that have been put onto the curve in the course of adjusting the reaction mechanism to yield the best data fit. Each set of points now forms its own line with a slope that differs from the slope of the correlation function except for one or two of the six sets. The points show that the computed valves of τ are not independent of the argon concentration but increase as the argon concentration decreases; that they do not decrease like the experimental T'S when [ 0 ] is increased, but increase instead; and that an increase of [ C H O H ] causes the computed T'S to decrease at low temperatures and to increase at high temperatures. In other words, changes of the concentrations of the mixture components have totally different effects on the computed and the experimental T'S. This suggests that there are major flaws in the reaction mechanism. It is not sufficient that the theoretical model should yield merely a rough agreement between computed and experimental values of τ, for such agreement can be achieved with a faulty reaction mechanism by adjusting rate coefficients and activation ener­ gies. Rather, the correct theoretical model should yield values of τ that would place all the data points in Fig. 25 exactly on the line that represents the correlation function. 7

3

a

3

0

5

2

13

2

3

The argument is supported by the fact that shock tube data of hydrocarbon-oxygen induction periods are generally found to conform to equations of the form of Eq. (1), and that hence such equations can hardly be taken to be mere empirical correlations but most likely have chemical-kinetic significance, comparable to the relations between the molecular concentrations and temperature that govern branchedchain explosion limits. It is therefore important to determine in which way the chemical kinetics of induction generates these τ equations.

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

107

The present authors have studied this problem in connection with the τ equation that Burcat, Lifshitz, Scheller, and Skinner have developed for the propane-oxygen reaction. This equation reads 16

7

τ = 4.4 χ l O ^ i e x p ^ ^ O / ^ r D t C s H s ]

0 5

7

^ ] '

1

2

2

sec

(3)

with concentrations in units of moles per cubic centimeter. The precision of the data correlation is indicated by the decimals in the exponents of the concentration terms, which are 4-0.57 for propane and - 1.22 for oxygen. The theory that is presented here contains the following elements. 1. The initial free-radical concentration in the shock-compressed gas is zero. The shock compression activates the chain-initiating reaction which generates free radicals C3H7 at the constant rate d[C H ]/<# - /. 3

7

In the subsequent chain reaction C H is always rapidly regenerated, so that during the induction period it is the principal free radical present, and since during most of this period the chain-branching rate is small compared to the rate I, the concentration [C H ] is substantially It, where t ^ τ. 2. C H generates H at the rate d[H ]/dt = «[C H ]. During the induction period the consumption of H by reaction with Ο and OH is very small because the concentrations of these species are very small, so that by integration one obtains 3

3

7

7

3

7

2

2

3

7

2

[H ] =

(i)Iat , 2

2

where t ^ τ. 3. [OH] and [C H ] are in equilibrium corresponding to reactions C H 4- 0 —> • · · OH and OH + C H - > · · · C H . Thus, 3

7

3

3

8

3

7

2

7

[OH] = M C H ] - Ibt. 3

7

Η atoms are generated by OH + H —> H 0 + Η and destroyed principally by H 4- C H —» C H + H . The generation of H by the latter reaction is insignificant at the low Η concentrations during the induction period. By equating the rates of formation and destruction of Η one obtains [H] = c[H ][OH], or 2

3

8

3

7

2

2

2

2

[H] =

(k)I abct\ 2

4. Ο atoms are generated by Η 4- 0 —» OH 4- Ο and destroyed principally by Ο 4- C H —> C H 4- H 0 or by some kinetically equivalent reaction path. By equating the rates of formation and destruction one obtains [O] = d[H] or 2

3

8

3

6

2

[O] =

(h)I abcdt\ 2

5. Chain branching occurs by the reaction Ο 4- H —» OH 4- H, which adds two new free radicals to the free-radical concentration n. The rate of chain branching is 2

108 {dnldt)

IV.

br

THE REACTION

BETWEEN

HYDROCARBONS

AND

OXYGEN

= AT[H ][0] or 2

{dnldt)

=

br

{\)Pa bcdKt\ 2

and the total rate of increase of the free-radical concentration is {dnldt) = / +

{\)Pa bcdKt . 2

5

The rate of chain branching is initially zero but increases at a high order, and becomes explosive shortly after it has overtaken the rate of chain initiation. The end point of the induction period may thus be defined as the instant at which the rates of chain initiation and chain branching become equal, so that / =

{\)Pa bcdKi 2

5

and /

4 \Pa bcdK

7

2

The specific reaction mechanism that is proposed in Table 3 generates the exponents + 0.6 and — 1.20, respectively, for the propane and oxygen terms. The positive sign indicates that propane inhibits the reaction thus causing the induction period to increase with increasing propane concentration, whereas the negative sign indicates that oxygen promotes the reaction. The difference between the theoretical exponents + 0.6 and — 1.20 and the experimental exponents +0.57 and — 1.22 may reflect the different end points of the theoretical and experimental induction periods: the experi­ mental T'S extend beyond the theoretical T'S into the regime of high-order acceleration and thus are slightly distorted in the sense that the inhibiting effect of propane is diminished and the promoting effect of oxygen is enhanced. The mechanism does not include any reactions involving collisions between two free radicals, inasmuch

TABLE 3 PROPOSED REACTION MECHANISM OF PROPANE AND OXYGEN DURING SHOCK-INDUCED INDUCTION PERIODS (i)

C H 3

8

(1)

C H

7

7

3

(2)

C H

(3)

CH

(4)

CH

3

3

3

-» C H 3

+ 0

-* C H 2

+ 0

^

2

7

+

H0

—> ·

2

+ C H 3

4

2

· OH

+ CH

3

CH 00 8

-> CH

4

+

(5)

OH + C H

(6)

OH + H - > H 0 + H

3

2

H 0 +

8

2

(7)

H + 0

H + C H

(9)

Ο + H - > OH + Η

(10)

8

3

3

C H 3

- » OH + Ο

3

8

C H 3

7

+

H

2

2

Ο + C H 3

8

—» C H 3

6

+

>C H

C H

2

(8)

2

"

C 3

3

H 0 2

7

7

7

+ CH OOH - > HCOOH + H 3

2

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

109

as such collisions are far too infrequent in the early stage of increase of the freeradical concentration. Except for reactions 3 and 10 the proposed elementary reactions are not controversial. The generation of hydrogen via reaction 3 is suggested by studies of the decomposition of alkyl hydroperoxides RCH OOH, which shows that the reaction in part takes the course RCH OOH —» RCOOH + H . The reaction (10) between Ο and C H is commonly assumed to yield OH and C H , but as discussed below, this is not proven. The equation for τ is obtained from this scheme as follows: 17

2

2

3

2

8

3

7

1. From reaction (i) one obtains I = 2&;[0 ][C H ], assuming that H 0 and C H react to form H 0 and C H . 2. H is generated by reaction (3) at the rate d[H ]/dt = & [0 ][CH ] and consumed by reactions (6) and (9). However, during the induction period the latter reactions do not significantly retard the buildup of the hydrogen concentration because the concentrations of OH and Ο are very small. CH is generated by reaction 2 and destroyed by reactions (3) and (4). Equating the rates of formation and destruction of CH and taking £ [C H ] to be much larger than & [0 ], one obtains [CH ] = fe[C H ]/£ [C H ]. This yields 2

2

2

3

3

8

2

3

8

7

2

2

3

2

3

3

3

3

4

7

4

3

3

8

3

2

3

8

fl = Jfc2*3[02]/*4[C H ]. 3

8

3. Reaction (1) generates OH from C H and 0 and reaction (5) regenerates C H from OH and C H . Equating the reaction rates yields fc [C H ][OH] = ^[0 ][C H ]and 3

3

7

2

3

3

7

2

8

5

3

8

7

* = *i[0 ]/* [C H ]. 2

5

3

8

During the induction period the effect of reactions (6), (7), and (9) on the OH concentration is negligible because the concentrations of H, H , and Ο are very small. However, Η is generated by reaction (6) and destroyed by reactions (7) and (8). Reaction (7) can be neglected relative to (8) because it has a much larger activation energy, 17 kcal/mole versus 8 kcal/mole. Thus £ [H ][OH] ~ & [C H ][H]. This yields 2

6

2

8

3

8

c = k/* [C H ]. 8

3

8

4. From reactions (7) and (10) one obtains rf = * [ O ] / * [ C H ] . 7

2

I0

3

8

Reaction 9 is neglected relative to reaction 10 because during the induction period the concentration of H is much smaller than the concentration of C H . 5. The rate of free-radical generation by chain branching is 2£ [H ][0]. This yields Κ = 2k and hence 2

3

8

9

2

9

1/5

l_

klk k k

2

kjklklkxkekjkg,

5

s

6\l/5

l0

([C H ] [0 r ) 3

3

8

6

2

(4)

110

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

This makes τ ~ [C H ]° [ 0 ] ~ (mole/cm ) ~ . The exponents of the concentration terms thus correspond to the power of τ that is obtained by multiplying the time integrals of the various concentrations that determine the rate of chain branching. Furthermore, by using the function k = A exp[—E/RT] one obtains from Eq. (3) 6

3

1 2

8

3

0 6

2

. , ,

= 4.4 x 10

ΧΙΑΪΑΙΑΙΑ,Α^Α,)

(cm /mole)

15

3

sec

u 0

and i[2(Ei + E + E ) +Ε +Ε 2

3

= 42,000

χ

+ Ε + Ε-

β

Ί

2E - E - E -

9

4

5

E]

%

l0

cal/mole.

Thus, the proposed branched-chain mechanism in Table 3 yields a τ equation that is fully consistent with the experimental τ equation. This result is not obtainable without inclusion of reactions 3 and 10 into the mechanism, or of kinetically equiv­ alent reactions if they can be found. However, there seems to be at present no definitive independent information available on either reaction. Concerning reaction (3), CH is known to react with 0 to yield C H 0 + O. However, this reaction has an activation energy of about 29 kcal/mole and is therefore infrequent compared to the association reaction CH + 0 - > C H 0 0 which is included in the Table. The latter has no activation energy, and since it is exothermic by about 31 kcal/mole, the equilibrium CH + 0 —» C H 0 0 favors the formation of C H 0 0 . The hydrogen bond energies in C H 0 0 - H and C H - H have been reported to be about 87.6 kcal/mole and 96.2 kcal/mole, respectively, which makes the postulated reaction C H 0 0 + C H - > CH OOH + C H in Table 3 a likely occurrence. The subsequent gas-phase reaction CH OOH —> HCOOH + H is inferred from experience with other alkyl hydroperoxides. It is also known that the explosive decomposition of liquid CH OOH yields H and C 0 , the latter presumably being formed by further decomposition of formic acid HCOOH. Reaction (10) violates the generally held belief that Ο atoms react with hydro­ carbon molecules to yield a hydrocarbon free radical and OH. An exception is known to occur only with electronically excited singlet oxygen atoms which are capable of slipping into the CH bonds of propane to form C H OH, whereas for normal Ο atoms in the triplet ground state this reaction is forbidden by the spin conservation rule. However, whereas methane apparently reacts with Ο to form CH and OH, it is generally assumed, rather than known, that higher hydrocarbons also react in this way and not as shown in reaction (10), to yield H 0 and a carbon double bond. A review of the subject by Huie and Herron shows that numerous investigators have reacted Ο atoms with hydrocarbons at room temperature, but there is no conclusive evidence that OH has been generated, and even if this were the case one may ask whether at high temperatures the reaction might produce H 0 rather than OH. Furthermore, one may argue that reaction (10) is just as plausible as the reaction 18

3

2

3

3

2

3

19

3

2

3

3

3

3

19

7

20

3

3

8

3

3

7

3

3

2

2

2

21

3

7

3

2

22

2

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

111

Ο + H + M —» H 0 + M, whose occurrence is confirmed by explosion limit data (p. 71). An Ο atom in collision with a C H molecule impacts on two neighboring Η atoms that are about as closely spaced as the atoms in an H molecule; the formation of a double bond - C = C - assists in the break-away of the Η atoms, and the bulk of the hydrocarbon molecule acts as a stabilizing third body. If one agrees that the experimental τ equation is not just an adhoc data correlation but is composed of the rate coefficients of the elementary reactions in the chainbranching mechanism, one also concedes the reality of the reactions (3) and (10), or perhaps of kinetically equivalent alternative reactions that have not yet been thought of; otherwise there would be no agreement between theory and experiment. Further­ more, induction periods are seen to depend on comparatively few elementary reac­ tions, which makes it possible to arrive at solutions of the chemical-kinetic equations without introducing numerical values and solving the equations numerically by computer programs. In this respect there is a wide difference between shock-tube data on induction periods and data obtained with flow systems such as plug flow reactors. The former data are limited to the process of ignition in which the system undergoes transition from zero reaction to incipient explosive reaction, whereas the latter data encompass the total reaction from beginning to end, with emphasis generally on the later stages in which concentrations of free radicals and other intermediate reaction products are high, chain branching fades out and a host of encounters between reaction inter­ mediates occurs. Hence, the computer offers a tool to test giant reaction schemes and to adjust the model in many an hour of computer time until computation and experiment can be deemed to be in reasonable agreement. Whenever this is accom­ plished one may expect the scheme also to be satisfactory for combustion wave calculations. A combustion wave is after all just another flow system, the difference being that a combustion wave is maintained by a feedback cycle in which the incoming explosive gas is ignited by diffusion of heat and free radicals from the reaction zone, whereas in a plug flow reactor there is no such feedback, and ignition occurs as fuel gas is injected into a hot stream of oxygen and inert gas. Thus, a reaction scheme that performs well with plug flow reactors should also perform well in computations of burning velocities of combustion waves, particularly since such computations are not overly sensitive to imperfections in the scheme. Some experimenters have used shock tubes as flow reactors. Whereas shock tube experiments on induction periods are so conducted that the incident shock is too weak to ignite the argon-diluted test mixture, and ignition occurs only in the zone of shock reflection at the tube end, it is also feasible to make the incident shock sufficiently strong for ignition while keeping the argon dilution so high that there is no significant feedback of pressure from the reaction zone to the shock front and hence no detonation wave develops. Thus, the shock tube can be operated as a flow reactor in which reaction occurs in the gas flow behind an incident shock of experi­ mentally controllable strength. Experiments of this type have been performed by 2

2

3

8

2

112

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

McLain and Jachimowski, using propane and oxygen in 94% argon and spectroscopically monitoring the concentration profiles of CO and C 0 and the rate of the chemiluminescent reaction Ο + CO —» C 0 + hv behind the shock front. These investigators have developed a scheme of 59 elementary reactions for a computer program that predicts experimentally measured concentration profiles and reaction times "quite well." They also made computations of induction periods in an attempt to match the experimental τ equation of Burcat et al., but they did not obtain the scatter-free match that one would obtain if the computation were based on the reac­ tion scheme in Table 3 above. It seems that with suitable numerical values for the rate coefficients and activation energies in the scheme of Table 3 one might combine the two schemes with certain adjustments, such as eliminating the reaction Ο + C H —» C H + OH, and obtain a scheme that fits all the data "quite well" or better, and that might be further perfected by consulting additional experimental and modeling studies. The numerical solutions of the theoretical τ equation that would be obtained in this way would be mathematically rigorous as compared to the approximations that have been made in arriving at Eq. (4) above. In a mathematically rigorous approach one would construct and solve a fifth-order differential equation at the cost of sacrificing the perception of the chemical mechanism that makes it possible to recognize the need for introducing unknown, unreported reactions such as reactions 3 and 10 into the scheme. The gain in such a procedure would be merely a nugatory change of a numerical coefficient. This is illustrated below by a mechanistic inter­ pretation of Eq. (1), which is the experimental τ equation for the C H O H - 0 system. As mentioned, this equation fits Bowman's data very closely, but the data fit is hardly changed if the term [CH OH] ~ ° is omitted and the equation is written in the form 23

2

2

1

3

8

3

7

24

3

2

8

1

3

τ = 2.1 x 1 0 " ( e x p [ 3 , 2 0 0 / / ? r ] ) [ O ] 13

sec.

05

2

(la)

Indeed, Bowman himself places an error limit of ±0.1 on the exponent - 0 . 1 of the CH OH term, which shows that the effect of the CH OH concentration of the induction period can be neglected. One should thus search for a reaction mechanism that yields an equation of the form 3

3

dn/dt = I + C [ 0 ] i , 2

2

where dn/dt is the rate of increase of the free-radical concentration during the induction period, / is the rate of the chain-initiating reaction, and C [ 0 ] / is the rate of the chain-branching reaction. The induction period ends when the rates of chain initiation and chain branching become equal, so that / = C[Q ]t or 2

2

2

2

T = (I/C)-°- [0 ]" - . 5

0

2

5

2. CHEMICAL KINETICS OF THE HIGH-TEMPERATURE EXPLOSIVE REACTION

113

A scheme that meets this specification might comprise the steps (i)

CH3OH + 0

-> CH (OH) +

(a)

CH (OH) + 0

(b)

H 0

2

2

2

dissociation 2

H0 ,

2

2

HCHO + H 0

2

> 20H

2 C H 3

°

C H 3 2

°

>H 0

H

2

+ CH (OH),

2

2

> 2 H 0 + 2CH (OH).

H

2

2

This yields the equations d[CH (OH)]/dt

= I + 2fc[H 0 ]

2

2

(5)

2

and d[H 0 ]/dt 2

= U 0 ] [ C H ( O H ) ] - k [H 0 l

2

2

2

b

2

(6)

2

For the larger part of the induction period the rate / is large compared to so that approximately

11 dt =

[CH (OH)] 2

2k [U 0 ], b

2

2

It,

Jo

and since, as discussed below, the rate of formation of H 0 by reaction (a) is much larger than the rate of dissociation by reaction (b), one may write 2

2

rt

= k [0 ]I r I / Jo

d[H 0 ]/dt 2

t

2

a

d

t

\

=

2

k [Q ]It . 2

a

2

At t = τ, iU*[0 ]/T ,

/ - 2fc[H 0 ] 2

so that IIC =

kk a

b

2

2

2

and T = (k k y [O ] 05

a

b

(7)

05

2

This becomes Eq. (la) if kk a

b

= 0.227 x 1 0

26

e x p t - 7 2 , 4 0 0 / ^ 7 ] cm /mole sec . 3

2

Changing from units of mole to molecule, the preexponential factor 0.227 Χ 10 in this equation becomes 6.2 Χ Κ Γ or roughly 10~ cm /molecule sec . This is consistent with the usual order of magnitude of the preexponential factors A of binary and unimolecular reactions, namely, a factor A — 10~ cm /molecule sec for the bimolecular reaction (a) and a factor A — 10 ~ sec for the unimolecular reaction (b), to yield the product A A — 10 cm /molecule sec . The energy of 72.4 kcal/ mole in the exponential term represents the sum E + E of the activation energies of reactions (a) and (b). If E is the dissociation energy of H 0 , which is 51.3 kcal/ mole, E becomes 21.1 kcal/mole. This corresponds to the energy required by the 26

2 4

23

3

2

10

3

a

13

- 1

b

2 3

a

3

2

b

a

b

a

b

2

2

114

IV.

THE REACTION BETWEEN

HYDROCARBONS

AND

OXYGEN

endothermic reaction CH (OH) —> HCHO + H 4- 20.5 kcal/mole, which is calcu­ lated from 3.9 kcal/mole for the heat of formation of C H 0 and similarly also of CH (OH), and the values of -27.7 kcal/mole for HCHO and 52.1 kcal/mole for H that are listed in the JANAF tables. It suggests that reaction (a) requires sufficiently energetic collisions of CH (OH) and 0 to break CH (OH) into HCHO and H. The subsequent reaction H 0 4- CH OH —> H 0 4- CH (OH) is exothermic by about 6 kcal/mole and involves CH OH in the scheme, which might possibly be connected to the term [ C H O H ] " in Bowman's τ equation [(Eq. (1)]. If, in line with a contemporary trend toward "mathematical" combustion, one objects to the approximation that has been made by taking [CH (OH)] = It, one may replace the term d[CW (OW)]ldt in Eq. (5) by the term (d [H 0 ]/dt )/k [0 ] = 4 C H ( O H ) M , which is obtained from Eq. (6) with U 0 ] [ C H ( O H ) ] > fe[H 0 ]. Equation (5) may then be transformed to 2

1 9

2

2

2

2

2

2

3

2

2

2

3

01

3

2

2

2

2

2

2

2

2

2

a

2

2

2

d y/dt 2

- cy = c,

2

where y = 2fc,[H 0 ]// and c = 2k [0 ]k . With the boundary conditions y = 0; t = 0, and dy/dt = 0, t = 0, one obtains by integration 2

2

a

At t = τ, y becomes 1. This yields ^ (k k ) [O ] T 05

a

b

2

b

T

+ e ^ _V

= 4, or VCT = 1.32, so that

T

= 1.32/V2 = .93 and

05

2

T =

0.93(* fe)-°- [O ]-°- , 5

5

e

2

which is virtually the same as the result obtained with the simplifying approximation [CH (OH)] = It. Among the 84 reactions of the C H O H - 0 system that are listed in Table 1, reaction (a) is included as number 10, but the preexponential factor is given as 10 cm /mole sec, or 1.7 x 1 0 " cnrVmolecule sec, instead of about 10~ cm / molecule sec, and the activation energy is given as 6 kcal/mole instead of about 21 kcal/mole. The unimolecular reaction (b) is not included; instead, the list includes the binary reaction (51) ( H 0 + 0 - » 2 H 0 ) and reaction (52) ( H 0 + M -> 2 0 H 4- M). Any of these changes would make it necessary to revise the scheme of reactions (i), (a), and (b) proposed above for the induction period, which might be done with no change of Eq. (7) for τ as follows: 2

3

12

3

2

12

2

2

10

2

2

(i)

C H O H 4 - 0 - > CH (OH) + H 0

(a)

CH (OH) + 0

(b)

CH (OH)OOH

3

2

2

2

2

-> C H ( O H ) 0 0 2

dissociation

2

2

3

2

2

C H 3

° > CH (OH)OOH + CH (OH) H

2

2

> , etc. · · · 2CH (OH) 2

Here it is assumed that 0 attaches itself to the free carbon bond of a methoxyl radical to form the corresponding peroxidic free radical. This is unreported and unproven, but it is analogous to the reaction CH + 0 —> CH3OO and conforms 2

3

2

3. OXIDATION OF METHANE AND FORMALDEHYDE

115

to the general experience of 0 attachment to a free carbon bond. It is thus hardly less plausible than the assumption that CH (OH) and 0 yield HCHO and H 0 , which is also not proven. The foregoing discussions illustrate the difference between the induction phase of high-temperature explosive reaction, in which an initially nonreacting fuel-oxygen mixture is activated to reaction by temperature increase, and the subsequent phases of rapid reaction and burn out. The elementary reactions that govern the induction phase are relatively few in number but they are not necessarily catalogued in contem­ porary compilations of chemical-kinetic data; whereas in subsequent phases the system becomes so loaded with an array of free radicals and other reaction inter­ mediates that the scheme of elementary reactions expands to giant proportions, and quantitative reaction-kinetic predictions must be entrusted to computer programs that are instructed with respect to the chemical-kinetic details as best as possible. It appears that such schemes perform well in flow systems, even though they are not necessarily faultless in detail, and thus it becomes possible to compute the structure and velocity of combustion waves where the induction phase is cut short by diffusion of free radicals from the reaction zone into the preheat zone, and chain-initiation kinetics does not apply. Such computations may offer tempting vistas for exercises in mathematical combustion, including in particular combustion waves perturbed by heat sinks, by gradients of gas velocity and by turbulence, which may make it possible with liberal input of computer time to describe burner flames of premixed fuel gas and air in elaborate if not absolutely correct detail. The range of computations might be extended to include laminar and turbulent diffusion flames, and by including carbon-forming reactions in the scheme it might be possible to solve, if not ameliorate, such problems as the onset of smoke in overcharged diesel engines. In this way one would pursue the multitude of possible combustion systems relentlessly in all the details of their formidable complexities, eschewing the use of simplifying concepts that may be workable but lack the satisfaction of attacking problems with every means available in natural science, mathematics, and computer technology. However, this book relies by preference on a basic understanding of combustion systems which makes it possible, for example, to develop such simplifying concepts as flame stretch and the Karlovitz number and others that are presented in later chapters. 2

2

2

2

3. Oxidation of Methane and Formaldehyde in Heated Reaction Vessels As discussed in the preceding section, current interest is focused principally on the multitude of free-radical reactions that cause the rapid consumption of fuel and oxygen in flames and explosions. This probing into flames and explosions has been made possible by high-technology data-gathering apparatus and computer facilities, whereas former research had been substantially restricted to regimes of slow reactions

116

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

where experimental techniques are less demanding. Thus, in the usual experimental procedure a test mixture of gases containing hydrocarbon and oxygen is admitted to a heated vessel and the reaction is monitored by readings of pressure and temperature, by analysis of samples of the reacting gas and occasionally by other similarly manageable procedures. Such work has produced much experimental information, but in virtually no instance has there been a definitive chemical-kinetic analysis of the data based on a well-established mechanism of free-radical reactions. In our view, as expressed in the preceding section, this also applies to the computer-aided analysis from shock-tube and flow-reactor experiments. In particular, the giant mechanisms that have been evolved do not fit the data on initiation of chemical reaction in shockheated hydrocarbon-oxygen mixtures, and although they may seem to be in satis­ factory agreement with experimental data on flow reactors and combustion waves it has not been demonstrated that there are no other mechanisms that yield similar agreements. It seems to us that a secure and comprehensive knowledge of hydrocar­ bon-oxygen systems can be expected only from continued experimentation aimed at the kinetics of individual free-radical reactions, coupled with continued reexami­ nation of all the data, new and old, until postulated reaction mechanisms not only fit the data from some particular experiment, but are also consistent with all other evidence. An illustration of this approach is found below. It is shown that reactions involving the exotic free radical C H ( O H ) 0 0 not only account for Bowman's previously discussed shock-tube data on preexplosion induction periods in methyl alcohol-oxygen mixtures, but also account for the data of Norrish and co-workers on the steady-state rate of methane oxidation in cylindrical glass vessels. 8

2

A.

SLOW OXIDATION OF METHANE AT 8 0 0 ° K

Norrish and Foord and Norrish and Reagh have studied the reaction between methane and oxygen in small cylindrical vessels of soda glass and pyrex glass at various pressures, mixture ratios, and vessel diameters in the temperature range of 4 8 0 to 5 3 0 ° C , i.e., at about 800°K. The reaction is preceded by an induction period and subsequently proceeds at a steady-state rate that is gradually declining as the reactants are consumed. It was found that the initial steady-state rate immediately following the induction period is represented by the empirical equation 25

26

J[CH ] dt 4

ad

2

1 + bd

4

(8)

where d is the vessel diameter, and a and b are functions of pressure and mixture composition. The coefficient a is proportional to the fourth power of the pressure and the coefficient b to the first power of the pressure. Coefficient a is furthermore proportional to the square of the mole fraction of methane and the first power of the mole fraction of oxygen and b appears to be independent of mixture composition as far as the data permit judgment. Experiments with added nitrogen show the rate to

117

3. OXIDATION OF METHANE AND FORMALDEHYDE

increase with increasing partial pressure of inert gas, but the curve of reaction rate versus inert gas pressure has a declining slope, as is expected if both a and b are linearly dependent on [N ]. Figure 26 shows reaction data in millimeters of mercury per minute of Norrish and coworkers as function of vessel diameter in millimeters and pressure in millimeters of mercury The data of Norrish and Foord are seen to agree with those of Norrish and Reagh in smaller vessels, whereas in larger vessels Norrish and Reagh observed significantly larger rates. Curves fitting the data of Norrish and Reagh are obtained if a is taken to be equal to 0.228(f7300) mm Hg m i n m m and b equal to 0.00548(77300) m m . Concerning the pressure de­ pendence of b, the second power might be tolerated but it does not provide as good 2

4

- 1

- 2

2

35

30

UJ 25 Ζ

Χ

ai UJ Α.

, 20 χ/

^15

Χ

χ ο I

χ

i

10

200

m' ο

χ

150 mm j g

Χ χ

χ 25

10

30

VESSEL DIAMETER, m m

FIG. 26. Reaction rate of methane and oxygen as function of vessel diameter.

ICH4 + l O , 5 3 0 ° C . 2

Θ Data of Norrish and Reagh.

26

x Data of Norrish and Foord.

, , .A ffrom equation .· Curves calculated a = 0.288(P/300) mm Hg m i n - mm 4

1

2

- j

ο

χ

25

* dt

d [ C H

]

=

a

d

l

1 + bd

2

; b = 0.00548(P/300) m m - . 2

35

118

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

a representation of the facts. The above-stated dependence of a on mixture compo­ sition appears to be well substantiated. The discrepancy between the earlier data of Norrish and Foord and the later data of Norrish and Reagh may be ascribed to an erratic influence of the nature of the vessel surface ' on the rate, which is not easily eliminated. Thus Norrish and Foord report that they obtain concordant and repro­ ducible results only by carrying out a complete series of experiments without allowing the reaction vessel to cool, and pumping out the vessel for at least half an hour between successive experiments. Previous admittance of air lowered the rate consid­ erably. In Norrish and Reagh's experiments the previous experience was fully utilized so that these data may be more representative of a trouble-free surface. Another fact is that there exists a critical lower limit of vessel diameter below which reaction is not observed at all, and the methane-oxygen system appears to be stable for an indefinite period. Eq. (8) should therefore be modified by adding a negative term of such form that the rate reduces to zero at some critical small value of d. This is done by inserting the term -f(l/d) into the numerator, so that the equation becomes 26

25 27

d[CH ] 4

dt

_ ad

-

2

~

(8')

1 + +bd

2

Other investigators have sampled and analyzed the reaction product at various stages of the reaction. Thus, Bone and Gardner as well as Norrish and Foord have shown that formaldehyde C H 0 accumulates during the induction period and that it attains a steady-state concentration at the end of the induction period. The increase of the formaldehyde concentration with time is initially exponential, and during this period the pressure remains constant. Toward the end of the induction period CO and H 0 appear in quantity, and in later stages of the reaction C 0 appears also. No hydrogen and no peroxides have been detected. Methyl alcohol, CH OH also has not been detected in mixtures of CH and 0 reacting in a heated vessel at atmospheric pressure, ' but Newitt and Gardner have obtained methyl alcohol as well as formaldehyde by forcing mixtures of methane and oxygen through the pores of an unglazed porcelain tube at atmospheric pressure and 440°C. In rich mixtures at high pressures and comparatively low temperatures, substantial amounts of methyl alcohol are formed; in addition, the ratio of C 0 to CO sharply increases and the yield of formaldehyde decreases. 27

25

2

28

2

2

28

3

4

28 29

2

29

30

2

The chain-initiating role of formaldehyde is demonstrated by the observation that addition of formaldehyde in a concentration equal to its steady-state concentration eliminates the induction period. ' Smaller additions of formaldehyde decrease the induction period without changing the subsequent steady-state rate of the reaction, but if the amount exceeds the steady-state concentration the rate is initially larger than normal and in time reverts to the normal rate. Table 4 shows a generalized reaction mechanism, containing two unspecified free radicals X and Y, that can be shown to be consistent with the empirical rate Eq. (8') 25 27

3.

OXIDATION OF METHANE

AND

FORMALDEHYDE

TABLE 4 GENERALIZED REACTION MECHANISM CORRESPONDING TO THE EMPIRICAL RATE EQ.

(a) (i) (1) (2) (3) (4)

(8')

A trace of C H 0 is formed by slow reaction of CH with 0 C H 0 + 0 - > · · · nX X + CH -> · · CH 0 + X X + CH 0 · •· y X " > · · · destruction X -2L*?L+ . . . destruction 2

2

4

2

2

4

2

2

s

a c e

(5)

Y + C H —> · · · X

(6)

CH 0 + 0

4

2

surface 2

> · · · destruction of C H 0 2

if the rates of reactions (i) and (6) are taken to be small compared to reaction (1), and if the rate of reaction 4 is taken to be small compared to reaction (5). With these specifications one may write « £ [CH 0][X] - Jfc,[CH ][X]

fc [CH ][Y] 5

4

2

2

4

so that d[CH ] 4

= k [CH ][X]

dt

x

+ fe[CH ][Y] - 2*,[CH ][X]

4

4

(9)

4

Using the symbol Κ to denote the rate coefficients of surface reactions as was done in previous chapters, one obtains for steady-state reaction (d[X\/dt and d[Y]/dt = 0) rvi 1

f

=

K /k [CH 0]

J

3

2

+ Jc /k [CH ]

2

4

5

v

}

4

where

K

_ 1 + .5(1 + jr/*,-)(Mfc5[CH])

3

6

k [CH 0] 2

4

(11)

tifCHJ/ATa - .5(1 + K /kd

2

6

If it is further specified that the surface reaction (3) (the destruction of free radicals X) proceeds with e > λ/d and the surface reaction (6) with e <^ k/d, one may write K = k /[M]d and K = k /d as was done analogously in Chapter Π. K depends on the nature of the surface which thus has an influence on the overall reaction. Combining Eq. (11) with Eq. (10) and inserting [X] into Eq. (9), one obtains 2

3

3

6

6

6

d[CH ] 4

dt 2«(A:^/A: A:3)[CH ] [0 ][M]i/ - n(kik\/& )[CH ][0 ](.5 2

2

4

2

2

1 +

2

4

(k k lk k )[M\d

2

x

4

3

5

2

+

kJhd)

(12)

120

IV.

THE REACTION BETWEEN HYDROCARBONS A N D

OXYGEN

This corresponds to Eq. (8') if [ C H ] [ 0 ] [ M ] = a,

(13)

2

4

2

TT

(14)

[M] = b,

and

5^1

[CT4

][0 ](.5 2

+

|i)

( 1 5 )

In agreement with the experimental facts, the coefficient a is proportional to the fourth power of pressure, to the square of the mole fraction of methane and to the first power of the mole fraction of oxygen; the coefficient b is proportional to the first power of pressure and independent of the mixture composition; and there is a critical lower limit of the vessel diameter at which ad becomes equal to f(l/d) and the reaction rate becomes zero. According to Walsh the change of the reaction rate with temperature corresponds to an overall activation energy of approximately 51 kcal/mole, and experiments by van Tiggelen and Bone and Allum suggest an even higher value. The response of the reaction rate to a change of temperature is governed principally by the temperature dependence of the coefficient a in Eq. (8) or (8') and hence corresponds principally to the overall activation energy of the term kik lk in Eq. (13), bearing in mind that the coefficient k represents a diffusion rate which has no activation energy. Using the general equation k = A exp[—E/RT] for bimolecular rate coefficients and taking η = 2 (see Table 5) one obtains from Eq. (13) 2

31

31

28

2

2

3

e x p [ - ( £ ; + 2Ei - E )/RT] = 2

* ° 4 A , A [M] [ C H ] [ 0 ]

1

A l

3

2

2

4

2

For a mixture of ICH4 + 10 at 803°K (530°C) and 300 mm Hg Norrish and Reagh report a = 0.288 mm Hg min" m m , which translates to a = 5.8 Χ 10 molecules c m s e c c m . The concentrations [CH ] and [ 0 ] are both 1.8 x 10 molecules c m " . From gas-kinetic equations given earlier one obtains 2

1

- 3

1

- 2

15

2

18

4

2

3

k /[M] = (|)ττ /ν,λι

cm sec"

2

2

3

V! = 14,500V77m,

1

cm s e c "

1

λ, = 1/ττ[Μ]σ , [1 + ( m , / m ) ] 2

2

2

1/2

cm.

Τ is 803°K, m\ is the molecular weight of 47 of the diffusing free radical X, which is identified as CH3OO, and [M] is 3.6 x 10 molecules c m " . σ , is the average of the square of the molecular diameters of the diffusing species CH3OO and the gas through which it is diffusing, which is an equimolar mixture of CtU and 0 . Taking 18

3

2

2

2

3.

OXIDATION OF METHANE A N DFORMALDEHYDE

121

TABLE 5 SPECIFIC REACTIONS FOR THE SCHEME IN TABLE 4 (a)

A trace of C H 0 is formed by slow reaction of C H with 0 2

(i)

CH 0

(1)

C H

+ 0

2

3

4

-> · · · 2 C H 0 0

2

3

0 0 + CH

Τ

4

C

3 ° O H

H

-> C H (2)

H

0+

CH 0 2

CH3OO

3

HCOOH

CH3OO + C H 0 -

2

(-* C O + H 0 ? ) 2

2

CH3O +± C H ( O H )

CH (OH)00

2

2

(3)

CH3OO

( )

C H ( O H ) 0 0 - > unimolecular decomposition - > H

4

2

surface

> destruction

2

CH (OH)OOH

D E C O M P

2

(5)

CH (OH)00 + CH

(6)

2CH 0 + 0

2

2

2

2

0+

0 = C O H ?

>CO+

S I T L O N

2H 0 2

p

4

-> C H SURFAC

°

% 2CO +

C H 0 0

3

3

2H 0 2

the molecular diameters of C H 0 0 , CH4, and 0 as 5, 4, and 3 x 1 0 " cm, respectively, σ becomes 17 x 1 0 " cm . Similarly, the molecular weight m of the CH4-O2 mixture is taken to be the average weight of 24. With these data one obtains approximately 8

3

2

2

16

2

2

2

(i)(fe/[M])a/[CH ] [0 ] - 1 0 " 2

4

3 8

2

c m molecules" s e c " 6

2

2

The preexponential factors A of binary rate coefficients are typically of the order of 1 0 " cm molecules" sec" . Thus, A /A;A is roughly of the order of 10 molecules c m " sec , and hence at Τ = 803°K 11

3

1

1

2

22

2

2

6

2

e x p [ - ( £ , + 2E - E )/RT] - 1 0 " 22

X

38

2

= 10" . 16

This yields —58 kcal/mole for the overall activation energy E + 2E — E , which is sufficiently close to the experimental data to show that the reaction mechanism is consistent with numerical reaction kinetic calculations. In order to apply the reaction mechanism in Table 4 to the induction period, it is assumed that at the start of the reaction a trace of C H 0 is formed by some slow reaction of CH4 with 0 . Subsequently, free radicals X are formed and the concen­ tration [CH 0] increases at the rate t

X

2

2

2

2

d[CH 0] r 2

= (*i[CH ] 4

fe[CH 0])[X] 2

By equating the rate of formation of X in reaction / with its rate of destruction in

122

IV.

THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

reaction (3) one obtains [X] = -

[CH 0][0 ],

1

2

2

and hence d[CU Q]

nki[0 ]

2

(MCH4] - £ [ C H 0 ] ) [ C H 0 ] .

2

2

dt

2

2

This shows that in the early stage of the reaction, when &1ΙΧΙΉ4] > & [CH 0], the formaldehyde concentration increases exponentially with time according to 2

2

[ C H 0 ] = [ C H O ] e x p ( ^ l , [ 0 ] [ C H 4 ] ( / - / )/fe) 2

2

0

2

0

and later attains a steady state corresponding to d[CY{ 0\ldt - » 0 as fc [CH 0] approaches k\ [CH4]. The free radical X was formerly thought to be OH and the chain reaction (1) in Table 4 was believed to comprise the reaction OH + CH4 —» H 0 + C H , followed by reaction of 0 with the methyl radical CH to yield formaldehyde and OH according to 0 + CH —» C H 0 + OH. However, experiments by Baldwin and Golden in which CH and 0 were passed through a flow system have shown that up to 1200°K the latter reaction either does not occur at all or has a rate coefficient of less than 0.5 x 10~ cm molecules" s e c , which is by far too small to be consistent with the reaction rates in Norrish and co-workers' experiments. Brabbs and Brokaw have obtained data from shock-tube experiments which show that the reaction CH + 0 —> C H 0 + Ο occurs with an activation energy of 29 kcal/ mole, and that C H 0 probably dissociates at high temperatures into C H 0 and H. However, the high activation energy of 29 kcal/mole makes this reaction much too slow to be significant in Norrish and co-workers' experiments. On the other hand, the association reaction CH + 0 —» CH 00——31 kcal/mole (see p. 110) occurs readily in the pressure range of these experiments and is sufficiently exothermic to make the reverse reaction C H 0 0 -> CH + 0 insignificant at the experimental temperature of ~800°K. Thus, CH becomes C H 0 0 . Furthermore, the reaction C H 0 0 + CH4 - > CH OOH + CH is endothermic by only about 15 kcal/mole and should therefore occur readily at 800°K; and since CH OOH decomposes into C H 0 and H 0 and CH becomes C H 0 0 it is apparent that C H 0 0 is the free radical X in reaction (1). Concerning the free radical Y, it is noted that reaction (2) does not regenerate C H 0 . This eliminates the reaction 2

2

2

2

2

3

3

32

2

3

2

3

2

17

3

1

- 1

18

3

2

3

3

2

3

2

3

3

3

3

3

2

3

3

3

3

2

2

3

3

3

2

CH3OO + C H 0 - > CH3OOH + CHO 2

because CH OOH would regenerate C H 0 by decomposing into C H 0 and H 0 , and thus eliminates the radical CHO from the reaction path that generates radicals Y. An obvious alternative reaction is the transfer of an Ο atom from CH3OO to 3

2

2

2

123

3. OXIDATION OF METHANE AND FORMALDEHYDE

C H 0 , producing formic acid HCOOH, which decomposes into CO and H 0 , and generating a methoxyl radical C H 0 . The latter cannot be the radical Y in reaction (4) because in no way can the reaction chain be broken by gas-phase unimolecular decomposition of C H 0 , as is demanded by reaction (4). However, C H 0 may change to the isomer CH (OH) and by association with 0 become the free radical C H ( O H ) 0 0 , which takes the role of the free radical Y because no plausible alternative can be found. This oxymethyl peroxide radical has already been introduced on page 114 in a mechanism that accounts for Bowman's shock-tube data on the ignition of C H O H - 0 mixtures. In that mechanism C H ( O H ) 0 0 reacts with CH OH to form CH (OH) and CH (OH)OOH, whereas in the present mechanism it reacts with CH4 to form CH and CH (OH)OOH, but the two reactions are nearly identical because the C - H bond energies are nearly identical. Concerning reaction (4) it may be proposed that the gas-phase decomposition of C H ( O H ) 0 0 produces a neutral molecule and a free radical that at the high temperatures of Bowman's experiments would continue the reaction chain, but at the comparatively low tem­ perature of the present experiments it diffuses to the vessel wall and is destroyed, thus making reaction (4) a chain-breaking reaction. From experiments that will be discussed in Section B, it is found that reaction (4) is not disturbed by introducing NO into the system. This rules out the decomposition of C H ( O H ) 0 0 into C H 0 and H 0 , because NO would convert the inert radical H 0 into the active radical OH by the reaction NO + H 0 —> N 0 + OH, and chain-breaking would not occur. Hence it may be suggested that C H ( O H ) 0 0 decomposes into H 0 and the formyl radical 0 = C O H , which is not well known and may be rather inert. Table 5 shows the specific reactions that replace the generalized reactions of Table 4. There are some additional comments on this scheme. The formulation of reaction / does not indicate in which way the colliding molecules C H 0 and 0 break up into free radicals. If there were a transfer of H from C H 0 to 0 to form CHO and H 0 , it would be certain, as is shown in Section C, that in the temperature range of Norrish and co-workers' experiments CHO would react with 0 to form CO and H 0 , so that H 0 would be the only free-radical species generated in reaction (i). The reaction H 0 + CH4 —» H 0 + CH followed by CH + 0 —» C H 0 0 would occur and chains would be initiated, but it is certain that H 0 would also diffuse to the vessel wall and be destroyed at a significant rate, so that the rate of chain initiation would depend on the concentration [M] and the vessel diameter d. This is incompatible with the experimental facts and elminates the concept that reaction (i) involves a transfer of H from C H 0 to 0 . Instead, it may be proposed that the reaction involves a transfer of Ο from 0 to C H 0 analogous to the transfer of Ο from CH3OO to C H 0 in reaction (2) of Table 5, yielding formic acid and an oxygen atom according to C H 0 + 0 —» HCOOH + O. This has already been proposed by Harding and Norrish, who have pointed out that this reaction is approximately thermoneutral and thus may have a fairly low activation energy. The Ο atom would react with CH4 to form CH and OH, followed in rapid 2

2

3

3

3

2

2

2

3

2

3

2

2

2

3

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

2

2

2

3

3

2

2

2

2

33

3

2

2

2

2

124

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

sequence by OH + CH4 - > H 0 + CH and CH + 0 - » C H 0 0 to yield 2 C H 0 0 as shown in Table 5. Another comment concerns the break-up of oxymethyl peroxide CH (OH)OOH that is formed in reaction (5). The interpretation of Bowman's shock tube experiments on page 114 shows the peroxide to dissociate into free radicals, whereas in the present mechanism it decomposes into neutral molecules. There is no contradiction, considering that Bowman's data apply to temperatures from 1500°K upward whereas the present mechanism applies to temperatures close to 800°K, and that dissociation no doubt requires a substantially larger activation energy than decomposition. Thus, dissociation becomes increasingly significant as the temperature is raised above 800°K, and at some critical temperature that depends on pressure, vessel parameters and mixture composition the steady-state reaction of methane and oxygen changes to branched-chain explosion. This implies that a methane-oxygen explosion limit such as curve 5 in Fig. 22 is of the branched-chain type, although it no doubt includes a thermal contribution due to heat release in the induction period, as does the third explosion limit of hydrogen and oxygen in Chapter Π. 2

3

3

2

3

3

2

B. SENSITIZATION OF THE METHANE-OXYGEN REACTION BY N 0

2

Figure 27 shows data by Norrish and Wallace on the decrease of the ignition temperature of C H + 0 mixtures by addition of N 0 . These experiments were performed before it had become known that the similar sensitization of hydrogen-oxygen mixtures is caused not by N 0 but by formation of NO from N 0 , followed by conversion of unreactive H 0 radicals into reactive OH by the very rapid reaction NO + H 0 N 0 + OH. Being unaware of this fact, Norrish and Wallace did not use NO but only N 0 in their experiments but it is reasonable to suppose that N 0 is reduced to NO by the formaldehyde generated from C H and 0 and that NO reacts with C H 0 0 as it does with H 0 , to form N 0 and C H 0 . On this basis the induction periods that have been observed by Norrish and Wallace to precede ignition represent the time required for accumulation of formaldehyde and generation of NO, and the scheme of radiations in Table 5 is expanded to include the following numbered reactions: 34

4

2

2

2

2

2

2

2

2

2

4

2

3

2

2

3

(7)

CH (OH)OOH

d i s s o c i a t i o n

(8)

CH (OH)OOH

d e c o m p o s i t i o n

(9)

C H 0 0 + NO - > N 0 + C H 0 .

2

> OH + C H ( O H ) 0 - » C H 0 + OH 2

2

-> · · · 2 C H 0 0 , 3

2

3

> CO + 2 H 0 , 2

2

3

The reaction (8) has already been included in the scheme but not numbered; it is now seen to compete with the chain-branching reaction (7) which is the previously discussed dissociation of oxymethyl peroxide into free radicals. Reaction (7) has a high activation energy and is thus very slow at 800°K, but at a sufficiently high temperature causes the mixture to explode. Figure 27 shows that in the series of

125

3. OXIDATION OF METHANE AND FORMALDEHYDE

°
700

PRESSURE OF N 0

2

(mm)

FIG. 27. Effect of N 0 on the ignition temperature of equimolar mixtures of CH and 0 (Norrish and Wallace). Cylindrical quartz vessel, 2.5 cm diameter. Constant concentrations of CH and 0 correspond­ ing to the following pressures of the C H 4 + 0 mixture at 500°C: Curve 1, 229.7 mm Hg; Curve 2, 88.6 mm Hg; Curve 3, 360.0 mm Hg. The N 0 pressures are the actual pressures in the reaction vessel at the temperature of ignition, representing all the added nitrogen peroxide as N 0 . 2

4

2

34

4

2

2

2

2

experiments represented by curve 1 the ignition temperature at zero concentration of N 0 is about 740°C, or more than 1000°K. The mixture explodes because at this temperature the rate of destruction of free radicals in the chain-breaking reactions (3) and (4) is exceeded by the rate of generation of free radicals in the chain-branching reaction (7). When N 0 is added, NO is generated; free radicals CH3OO become CH3O and are thus taken out of the reaction path 3 that leads to chain breaking. The chain-breaking rate is accordingly reduced and ignition occurs at a lower rate of chain branching, viz., at a lower temperature. The date in Fig. 27 shows that a large reduction of the ignition temperature is obtained with extremely small additions of N 0 , as is also the case in the hydrogen-oxygen system. Figure 27 also shows that the ignition temperature drops to about 500°C and then 2

2

2

126

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

becomes virtually independent of the N 0 pressure. This is explained if it is assumed that, unlike C H 0 0 , the radical C H ( O H ) 0 0 does not significantly react with NO or N 0 . In that case the chain-breaking reaction (4) remains operative and places a lower limit on the ignition temperature. It is implied in this explanation that the gas phase decomposition of C H ( O H ) 0 0 does not produce C H 0 + H 0 because NO would convert H 0 into the active radical OH and the reaction would not be chain breaking. Hence it is suggested that the decomposition produces H 0 and the formicacid radical 0 = C O H which is believed to be unreactive towards CH* and NO. On this basis the explosion limit is defined by the equation 2

3

2

2

2

2

2

2

2

2Jfc k + k 7

7

k + k [CH ] 4

s

5

fc [CH 0]

4

2

+ k [NO]

2

9

It is reasonable to assume that reaction (7) has a much larger activation energy than reaction (8) and that k is thus much smaller than & · Furthermore, the analysis of the steady-state reaction has shown that k is small compared to ^[CK*]. It may be noted here that the rate of reaction (5) is so large that the rate of destruction of C H ( O H ) 0 0 at the vessel wall is negligible in comparison and does not appear in Table 5. It can also be reasonably assumed that the virtually zero activation energy of reaction (9) makes the term £ [NO] larger than the term & [CH 0] even at NO concentrations that are much smaller than the small C H 0 concentration. Therefore, in the temperature range above 500°C, where k /k$ is large compared to kJk [CYU\, the explosion limit equation becomes approximately 7

8

4

2

9

2

2

2

7

2k /k 7

s

=

5

K /k [NO], 3

9

and introducing the Arrhenius equation k = A cxp[E/RT] one obtains (£ ~ E )/RT = In [NO] + const. 7

S

Norrish and Wallace were able to determine the small N 0 pressures in the steep part of curve 1 in Fig. 27 with such precision that a plot of log p versus 1/7 could be made. This yielded a straight-line relation corresponding to the activation energy 2

NOl

Ε — Es = 34.3 kcal/mole. η

Other correlations of experiment and theory are qualitative rather than quantitative. Thus, if the rate coefficient K of the surface chain-breaking reaction (3) is of the form k [M]d , K is increased by a decrease of [M], i.e., of the pressure of the C H 4 - 0 mixture, and the concentration [NO] at a given ignition temperature is therefore increased. This applies to the relation between the curves 1 and 2 in Fig. 27. The mixture pressure along curve 1 is larger than the pressure along curve 2 by a factor of 2.6 and curve 2 correspondingly lies above curve 1. Furthermore, using a series of reaction vessels with diameters ranging from 3.4 to 1.5 cm it was found that a decrease of the vessel diameter produced only a slight increase of the ignition temperature when the test mixture was composed of 4.1 mm Hg of N 0 and 229.7 3

2

3

3

2

2

127

3. OXIDATION OF METHANE AND FORMALDEHYDE

mm Hg of CH4 4- 0 , but that the increase was large for a rnixture of 8.8 mm Hg of N 0 and 88.6 mm Hg of CH4 + 0 . The first mixture corresponds to a point at the beginning of the flat part of curve 1 in Fig. 27 where the explosion limit becomes 2& /£ = k /k [C¥{4\ and the ignition temperature is thus independent of the vessel diameter. The other mixture corresponds to a point on curve 2 where the explosion limit depends on K /k [NO] and the ignition temperature accordingly changes in­ versely with the change of vessel diameter according to the inverse relation between K and the vessel diameter. However, the data do not permit quantitative correlations. In particular, the separation of curve 2 in Fig. 27 from curve 1 is larger than can be accounted for by the change of K alone. There is an additional contribution from the term k lk [CYU\ which also increases as the pressure is decreased, but it is not sufficient to account for the separation of the curves. Further, contributions are possibly hidden in changing conditions at the surface of the quartz reaction vessel, of the type that has been discussed in Chapter HI in connection with the C O - 0 reaction, and in gas phase and surface reactions of NO and N 0 that have not been identified. A significant role of the vessel surface and hence of surface reactions is indicated in the observation made by Norrish and Wallace that ignition data obtained "in the first run of the day" tended to be erratic. This shows that the data depend on the condition of the vessel surface, which changes spontaneously between runs and must be reconditioned by repeated explosions in order to obtain reproducible data. 2

2

7

2

8

4

5

3

9

3

3

4

5

2

2

C. FORMALDEHYDE AND OXYGEN AT 550 τ ο ~1000°K

The products that are formed during slow reaction of formaldehyde and oxygen have been determined by Bone and Gardner. The kinetics of the reaction has been studied by Axford and Norrish, by Spence and by Snowden and Style in the temperature range from about 300 to 370°C, and by Vardanyan, Sachyan, and Nalbandyan at temperatures ranging from 500 to 700°C, or up to nearly 1000°K. As will be shown, the chemical mechanism that underlies the multitude and diversity of the experimental observations is in principle quite simple. Free radicals CHO are formed by reaction between C H 0 and 0 . At low temperatures CHO associates with 0 to form performyl radicals CHO-OO and performic acid CHO · OOH in a chain reaction with C H 0 . At high temperatures CHO reacts with 0 to form CO and H 0 , and hydrogen peroxide is formed in a chain reaction of H 0 with C H 0 . In detail, there are complexities. As has been discussed, the mechanism of the methane-oxygen reaction excludes the reaction C H 0 + 0 —» CHO + H 0 and points instead to the reaction C H 0 + 0 —» HCOOH + O. It may be proposed that Ο combines with C H 0 to form a highly energized molecule HCOOH that dissociates into CHO and OH, the overall process being exothermic by about 25 kcal/mole, and that OH reacts with CHO to form H 0 and another radical CHO, so that the reaction becomes C H 0 + 0 —> · · · 2CHO. Concerning the low-temper27

35

36

37

38

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

128

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

ature production of performic acid in a chain reaction, it is found from reactionkinetic data quoted below that the radicals CHO · 0 0 , analogous to H 0 are too inert to react with C H 0 at low temperatures and are instead destroyed at the vessel wall. It appears that CHO and 0 associate in ternary collisions CHO + 0 + M - » CHO · 0 0 + M, where M may be 0 or some inert molecule like N , but that with C H 0 as the third molecule there is also an exchange of an hydrogen atom, so that the chain reaction occurs in the single step CHO + 0 + C H 0 —» CHO-OOH + CHO. There are no complexities at high temperatures where H 0 reacts readily with C H 0 to form hydrogen peroxide and the chain reaction correspondingly comprises the sequence 2

2

2

2

2

2

2

2

2

2

2

H0 + CH 0 2

H 0 + CHO,

2

2

2

CHO + 0 - ^ CO + H 0 . 2

2

However, at high as well as at low temperatures there are side reactions involving the peroxidic reaction products, and the overall reaction kinetics becomes quite complicated unless the experimental conditions are such that peroxides are rapidly destroyed. In particular, the data on the low-temperature reaction indicate that per­ formic acid reacts in the gas phase with CHO in such way that ultimately the freeradical chain is broken and CHO · OOH is destroyed. The details of this reaction path are uncertain and must be left open for the present. Also, at high temperatures chain branching may occur by dissociation of H 0 into the 2 0 H . Following this overview of the formaldehyde-oxygen reaction the individual experimental investigations will now be discussed. Bone and Gardner performed three experiments in which the reacting mixture of formaldehyde and oxygen was suddenly cooled by plunging the reaction vessel into ice water, and then was extensively analyzed. The results of these experiments are shown in Table 6. It is seen that when the reaction was stopped, the formaldehyde and oxygen had largely reacted. On the other hand, after the shortest of the three runs, the pressure rise was by no means complete. This is due to the large yield of performic acid and another peroxide, believed by Bone and Gardner to be dioxydimethyl peroxide, CH (OH) · OO · CH (OH), which can be synthesized from formal­ dehyde and hydrogen peroxide and which may decompose into two moles of formic acid and 1 mole of hydrogen. The two peroxide substances disappear and the pressure increases as the duration of the reaction is extended from A\ to 30 min. This is accompanied by a large percentage increase in the yields of C 0 , H , and formic acid. Traces of methane also appear. The data and the chemistry of the system suggest, as has already been pointed out by Bone and Gardner and other investigators, that the primary product of the reaction is performic acid, or hydrogen peroxide derived from performic acid by loss of CO, and that all other products result from secondary reactions. If an agent were present in the system that efficiently promotes the decomposition of peroxides, these products would be mostly CO and H 0 and in lesser yield also C 0 and H . Such 2

2

27

2

2

39

2

2

40

2

2

2

129

3. OXIDATION OF METHANE AND FORMALDEHYDE

TABLE 6

REACTION PRODUCTS OF 2 C H 0 2

+ 0

AT 215°C -

a b

2

Reaction 2

3

14

30

508.4 238.9

515.8 232.0

502.2 237.8

55.7 20.1 16.5 305.5 261.3 39.4 nil 35.0 49.3 23.2 8

12.8 7.9 55.2 365.5 305.2 63.5' 2.3 61.5 13.7 2.4 19

5.9 9.0 47.5 365.8 314.8 65.8 1.5 81.5 nil nil 20

1 Duration of reaction, min Initial pressure, mm CH 0 o Unchanged reactants, mm CH 0 o co CO H 0 H CH HCOOH CHOOOH (CH OH) 0 Total pressure increase, % 2

2

2

2

2

2

2

4

2

2

2

4.5

£

"Bone and Gardner. A\\ pressures are partial pressures in mm Hg at 275°C. 'Considered somewhat too small by Bone and Gardner. 27

b

agent is mercury which in Axford and Norrish's experiments was used as a sealant, and this may explain why these investigators found no peroxides in their product samples. Working with cylindrical pyrex vessels of 2.8, 5.0, 11.1, and 23.6 mm diameter, with C H 0 + 0 mixtures at 337°C and 150-300 mm Hg pressure and with widely varying mixture ratios, they measured well-reproducable rates of pressure rise that could be translated into reaction rates, -d[CH 0]/dt. They found that reaction occurs immediately on admission of the test gas to the reaction vessel without induction period, and that the initial reaction rate conforms to the equation 35

2

2

2

-d[CH 0]/dt 2

= const[CH 0]

2

2

independent of mixture ratio and vessel diameter. After some time, when reaction products have accumulated and the rate is slowing down, the rate becomes dependent on the oxygen concentration in the sense that the slowdown is accelerated when the initial oxygen concentration is decreased. Addition of nitrogen moderately decreases the rate over the whole course of the reaction. The data obtained with the several reaction vessels indicate no effect of vessel diameter and are sufficiently consistent to indicate only a mild sensitivity of the rate to the nature of the surface. These facts

130

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

are explained by the following reaction mechanism which is unique in the sense that no viable alternative mechanism can be proposed: (i)

C H 0 + 0 -> · · · 2CHO,

(a)

CHO + 0

2

(b)

CHO + 0

2

+ 0 -^0

(b') CHO + 0

2

+ M —> M 4- C H O O O

2

2

+ C H 0 - » CHO + CHO · OOH -> products CO, H 0 , etc., 2

2

2

+ CHO 0 0

2

> products CO, H 0 , etc.,

surface

2

surface

> products CO, H 0 , etc. 2

Here M is either an inert addictive like N or a reaction product such as CO, H 0 , etc. The scheme yields the equation 2

2

[CHO] = 2 £ [ C H 0 ] / [ ( M 0 ] + M M ] ) , /

2

2

and since the consumption of reactants by reaction (i) is negligible compared to the chain reaction (a), - d[CH 0]/dt 2

= UCH 0][0 ][CHO]. 2

2

If no inert gas has been added [M] is initially zero and the reaction proceeds without induction period initially at the rate -d[CH 0]/dt 2

-

imual

(2t * /fe)[CH 0] /

e

2

2

in agreement with the experiments. In general, the rate is represented by the equation
2

dt

2

~

2

W0 ]+fo[M] ' 2

which shows that at later stages of the reaction the rate becomes increasingly dependent on the remaining oxygen concentration and that addition of inert gas decreases the rate over the whole course of the reaction, as found experimentally. It is possible, though not shown here, to fit the theoretical rate equation numerically to the experimental data. The experiments of Spence and Snowden and Style were similar to those of Axford and Norrish, but neither Spence nor Snowden and Style used mercury seals and thus there was no mercury vapor present in the reaction vessel. It seems that for this reason the rate of decomposition of performic acid in their experiments was much lower than in Axford and Norrish's experiments and hence the simplicity of the reaction kinetics was lost due to secondary performic acid reactions. Thus, the steady-state reaction rates of Snowden and Style are empirically expressed by an equation of the form 36

37

35

-d[CH 0]/dt 2

= AT[CH 0]([CH 0] - C) 2

2

The "constants" Κ and C of this expression show a tendency to vary erratically. This is particularly true of C which is markedly affected by the nature of the surface. Κ

131

3. OXIDATION OF METHANE AND FORMALDEHYDE

and C show a tendency toward an inverse relationship, i.e., C decreases as Κ increases. The effect of vessel size is noted mainly in the value of C which is larger in a smaller vessel. Increase of oxygen concentration had a tendency to increase Κ but this was not always observable. The effect of oxygen on C is even less certain. To describe results of an experimental series in which only the formaldehyde concentration was varied, Spence proposed a similar empirical equation but containing an added constant term. We may write his equation in the form 36

- r f [ C H 0 ] / A - / a C H 0 ] ( [ C H 0 ] - C) + K'. 2

2

2

In order to accommodate their data the previous reaction mechanism that accounts for Axford and Norrish's data is modified to include the following performic acid reactions: (c)

C H O O O H + CHO -> · · · CO, H 0 ,

(d)

CHOOOH

etc.

2

>

surface

-

CO, H 0 ,

etc.

2

The modified mechanism yields the equation [CHO] - a[CHO] = b, 2

where 2fc[CH 0]

/

2

U C H 0 ] + k [0 ] 2

and b =

b

b

b

V

2

2k U C H 0 ] + k [0 ] 2

k [Q ] K , —— - — - — —

1

2

2k Κ c

3

molecules/cm

MCH 0] 2

[CH 0]

molecules /cm .

2

2

2

k [CU 0]

2

d

6

2

Solving the quadratic equation for the case 4b/a <^ 1, one obtains 2

[CHO] - a + b/a, and by neglecting b altogether one obtains [CHO] = a. Substitution of the function a for [CHO] in the reaction rate equation -d[CH 0]/dt = £ [CH 0][0 ][CHO] yields Snowden and Style's form of equation, where 2

Κ - 2 ^ [ 0 ] / ( Â : [ C H 0 ] + k [0 ]) 2

a

2

b

fl

2

cm m o l e c u l e s s e c " 3

2

1

2

1

and C = k [0 ]K /2kik b

2

d

molecules/cm . 3

c

It is seen that the coefficient k appears in the numerator of Κ and the product of the coefficients £,· and k appears in the denominator of C. These rate coefficients, and ki in particular, presumably have substantial activation energies, whereas the coefficients of the ternary reactions (a) and (b) and of the surface reaction (d) have little or no activation energies. Thus, Κ and C are in inverse relation: an increase of c

132

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

temperature increases Κ and decreases C, and vice versa. Furthermore, C is propor­ tional to the surface reaction coefficient K ; hence, C increases with decreasing vessel diameter and is dependent on the nature of the surface. The equations are thus consistent with the main features of the experimental observations. Both Κ and C are seen to be proportional to the oxygen concentration; however, if the unspecified reaction (c) is not a binary reaction but a ternary reaction involving 0 as a third body, the constant C becomes independent of oxygen. Inasmuch as an increase of Κ increases the reaction rate and an increase of C decreases the reaction rate it is obviously very difficult to make an experimental determination of the oxygen de­ pendence of Κ and C. There is also the consideration that with changing parameters the condition 4b/a < 1 may become invalid and the experimental data become undecipherable. For the case that hia is not negligible compared to a the rate equation contains the additional term fc [CH 0] [0 ]b/a, whose dependence on the experimental param­ eters is difficult to determine and which apparently represents the term K' in Spence's equation. It is seen that Spence and Snowden and Style have been plagued by complicating side reactions of the peroxidic intermediate, whereas a stroke of luck has enabled Axford and Norrish to avoid these complications and to demonstrate the basic simplicity of the reactions kinetics. Their data include the change of the reaction rate with temperature which yields an activation energy of 21.0 kcal/mole. The rate is proportional to kikjk , but since the ternary reactions (a) and (b) presumably have little or no activation energies the measured value applies essentially to the chaininitiating reaction (i). Simplicity of the reaction kinetics is also found in the experiments of Vardanyan et ai, * though in this instance it might be attributed to design rather than to luck, due to foreknowledge that at the high temperatures in these experiments CHO reacts rapidly with 0 to yield CO and H 0 , and that for the familiar radical H 0 the effects of surface coatings are quite predictable. However, whereas in Axford and Norrish's experiments the progress of the reaction was monitored in time intervals on the order of minutes, in the experiments of Vardanyan et al. these intervals had to be shortened to the order of tenths and even hundredths of a second. This is consistent with the activation energy of 21 kcal/mole, which corresponds to some 1000-fold increase of the reaction rate at the elevated temperatures of the present experiments. The investigators accordingly used a flow system, passing a stream of reactant gas through the reactor—a quartz tube of 1 cm diameter and 17 cm length— at varying residence times and collecting the reaction products in scrubbers at the outlet. In this way they obtained reproducible data on the progress of the reaction, using a test mixture of 1 % formaldehyde in air. With uncoated quartz or with a boric acid coating it was found that hydrogen peroxide accumulates in the mixture and accelerates the formaldehyde consumption, presumably by generating free radicals in the dissociation reaction H 0 + M - » 20H + M. A small quantity of performic d

2

2

â

2

2

b

3

2

2

2

2

2

4.

133

HIGHER HYDROCARBONS AND OXYGEN BELOW 900°K

acid also accumulates, which shows that the ternary reactions (a) and (b) which are dominant in Axford and Norrish's experiments are not totally suppressed by the binary reaction CHO + 0 —» CO + H 0 that dominates the present experiments. With a coating such as KBr, no peroxides were recovered and the reaction was much slower and nonaccelerating. An elegant proof of the identity of H 0 as the freeradical chain carrier was obtained by the method of electron spin resonance (ESR), in which free radicals trapped in an electromagnetic resonance cavity are identified by the spin frequencies of their unpaired valence electrons. A small sample of the mixture stream was passed from the reactor to the resonance cavity by means of a boric acid-coated capillary scoop that extended through the reactor wall into the stream. A strong ESR signal characteristic of H 0 was obtained when the reactor surface was uncoated quartz or quartz coated with boric acid, whereas with coatings known to be destructive of H 0 no signal or only a weak signal was received. The reaction CO + H 0 —> C 0 + OH also occurs in these experiments but is hardly significant, since it is not a chain-branching reaction and CO is not originally present in the system. In conclusion it may be stated that perhaps the most significant aspect of the various investigations of the formaldehyde-oxygen reaction is the information they furnish on the reaction of oxygen with the formyl radical CHO. At low temperatures 0 associates with CHO to yield CHO · 0 0 radicals which may react further to yield perforrnic acid. At high temperatures 0 reacts with CHO to yield H 0 radicals and, further, hydrogen peroxide. It is thus evident that the reaction CHO + 0 —> CO + H 0 has a substantial activation energy, but it seems that this fact has not been generally recognized in assigning rate coefficients to this reaction for use in com­ bustion processes and atmospheric chemistry. 2

2

2

2

2

2

2

2

2

2

2

2

4. Higher Hydrocarbons and Oxygen below 900°K. A.

CHAIN BRANCHING BY PEROXIDATION OF ALKANE

HYDROCARBONS,

COOL FLAMES, AND TWO-STAGE IGNITION

As has already been mentioned in the introductory Section 1 of this chapter, the oxidation kinetics of higher hydrocarbons includes branched-chain reactions at low temperatures that produce regimes of cool flames and low-temperature explosion peninsulas as illustrated in Figs. 22 and 23. These reactions involve peroxidic free radicals ROO in which one of the two oxygen atoms is bonded to a carbon atom to form the group OO— —CHz—C—

I H

134

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

Bennet, Mile, and Thomas have obtained electron spin resonance (ESR) spectra of ROO radicals that were prepared by the method illustrated in Fig. 28. The vapor of a halohydrocarbon RC1 or RF was condensed as a solid on the surface of a stainlesssteel drum which was cooled to 77°K by liquid nitrogen and rotated rapidly (2400 rpm) in a high vacuum (10" mm Hg). The freshly deposited halide was carried around on the drum past a region where it was lightly bombarded with a stream of sodium atoms such that few sodium atoms would alight adjacent to each other. The sodium extracted the halogen atom from the halohydrocarbon molecules to produce free radicals R according to the reaction RC1 + Na —> R + NaCl. These radicals were trapped on the cold surface and, if no 0 was admitted, were subsequently covered by further deposition of RC1 or RF at the completion of a whole revolution of the drum. The whole process was repeated in every revolution and specific free radicals R were thus prepared frozen in a matrix of excess RC1 or RF. The deposit was then transferred from the drum, still at 77°K and under high vacuum, into a glass tube suitable for ESR measurements. 41

4

2

RX (THICK LAYER) I I

SPINNING DRUM CONTAINING

DIFFUSION PUMP FIG. 28. Scheme of preparation of peroxidic free radicals ROO. (Bennett, Mile, and Thomas ). RX is a compound of a radical R with a halogen atom X. A layer of RX is frozen on the rotating drum at liquid-nitrogen temperature. A beam of sodium atoms is directed at the drum and generates free radicals R by the reaction RX + Na —> R 4- NaX. A subsequent beam of 0 generates ROO. 41

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

135

In subsequent experiments, before the radicals were covered up, they were bom­ barded with a stream of oxygen molecules from a third jet as indicated in Fig. 28. The reaction R + 0 —» ROO could thus take place and the radicals that were now covered up and preserved at the end of a revolution were radicals ROO together with any unconverted R. It was also possible to prepare the radicals in other matrices that were laid down by an additional jet. The ESR spectrum of a peroxy alkyl radical ROO was found to be very different from the spectrum of the corresponding radical R. It was thus not difficult to estimate the amounts of each type of radical in the deposits and hence to estimate the extent of conversion of R to ROO. Some 15 radicals covering a wide range of molecular weights and chemical structures were studied and in each case complete conversion was obtained when sufficient oxygen was used, indicating a high efficiency of the reaction. From these data the activation energy was estimated to be smaller than 2 - 3 kcal/mole. It was already known from photochemical studies ' that ethyl and methyl radicals combine with 0 very rapidly and the ESR data extend this obser­ vation to free radicals R in general. Whereas the ESR spectra of the various free radicals R in this investigation were found to be substantially different from each other, the ROO spectra were all found to be closely similar. This shows that in ROO the orbital occupied by the unpaired electron is almost unaffected by the nature of the attached R group which means that apart from steric effects, all such peroxide free radicals should have similar reactiv­ ities. This applies in particular to the chain reaction 2

42 43

2

ROO + RH - > ROOH + R

ROO

which produces hydroperoxides ROOH as a major product of slow oxidation outside the regimes of cool flames and low-temperature explosion. As will be shown later, there is also a competing chain reaction that generate olefins and H 0 , as illus­ trated by 2

RCHCH + 0 3

2

- > RCH = CH + H 0 2

R C H 2 C H 3 2

2

> H 0 + RCHCH . 2

2

3

Furthermore, more than one mode of chain branching is inherent in the polyatomic structure of higher hydrocarbons. The simplest branching mode is the thermal dissociation, or fission, of hydro­ peroxide ROOH into the free radicals RO and OH. However, the high dissociation energy, namely, 44.6 kcal/mole according to Benson, makes this chain-branching reaction rather ineffective at low temperatures. Benson estimates that the lifetime of ROOH prior to fission is of the order of 10 sec at a temperature above 300°C, which makes the chain-branching rate slow even at high concentrations of hydroperoxide and relatively high temperatures of the typical explosion peninsula. A branching mode that is much more efficient is suggested by the ability of the larger aklyl free radicals to undergo double peroxidation. 44

45

136

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

An illustration of this latter mode has been given by Tipper and co-workers ' who have studied the peroxides formed by slow oxidation of higher hydrocarbons. They describe the formation and possible break-up of the double peroxide dihydroperoxyheptane as follows: An w-heptyl radical /z-C Hi combines with 0 to form an /z-peroxyheptyl radical. Within the radical the peroxy group - O O - abstracts an H atom from a neighboring carbon atom, thus exposing a free carbon bond that captures another 0 molecule, viz., 46 47

7

5

2

2

CH CHCH CHCH CH CH 3

2

2

2

CH CHCH CHCH CH CH .

3

3

OO— Η

2

ΟΟΗ

2

2

3

OO—

Another heptane molecule may react with the doubly peroxidized radical to yield a heptyl radical and dihydroperoxyheptane which have indeed been found among the products of slow oxidation of heptane. Alternatively, the doubly peroxidized free radical may decompose and form C = 0 double bonds from single-bonded O, which would generate sufficient energy to form additional free radicals, as illustrated by the possible reaction products (CH ) CO, CO, 2 0 H , C H . Bonner and Tipper suggest that this mode of chain branching enhances the cool-flame intensity and explosivity of a high-molecular hydrocarbon such as heptane, as compared with a relatively lowmolecular hydrocarbon such as propane. They do not suggest that it is the only or even the dominant branching mode, and they even consider the possibility that the doubly peroxidized free radical may decompose in a chain-breaking instead of chainbranching mode. In particular, if the two peroxidic groups - O O H and - O O - were to split off to form the neutral molecules H 0 and 0 , the remaining skeleton would 46

47

3

2

3

ι

2

2

7

2

be a structure such as CH CH=CH-CH(CH ) CH , which is a resonance-stabilized free radical and hence presumably quite unreactive. Nevertheless, the principle of chain branching via double peroxidation furnishes an attractive explanation of the high reactivity of mixtures of ethers with oxygen, and as shown below, it also explains the role of aldehydes in the regime of cool flame and low-temperature explosion. Figure 29 shows cool flame limits of a diethyl ether-oxygen mixture based on a paper by Chamberlain and Walsh. The experimenters report that the cool-flame flash occurs "on admitting the gases to the heated reaction vessel," i.e., before the entering gas has attained pressure and temperature equilibrium, and hence the curve that is reproduced in Fig. 29 represents the experimenters' estimate of what the limits would be if admission and equilibration of the gas could be made instantaneous. One notes that there is no induction period of sufficient length to be observable in these experiments, and that free-radical concentrations of sufficient magnitude to produce the cool flame effect are generated already at temperatures lower than 200°C and at pressures as low as 10 mm Hg. This high reactivity is consistent with the concept that a free radical formed by abstraction of an H atom from an ether molecule undergoes a sequence of peroxidation, internal hydrogen transfer, second peroxida3

2

48

2

3

137

4 . HIGHER HYDROCARBONS AND OXYGEN BELOW 9 0 0 ° K 350

tion, and break-up, as follows: CH CHOCH CH 3

2

3

C H C H O C H C H -> C H C H O C H C H 3

2

3

3

OO—

3

OOH

C H C H O C H C H - » 2CO + 2CH + 3 0 H . I I OOH O O — 3

3

3

The free radicals that are formed, assumed here to comprise both OH and C H , abstract atoms from other ether molecules, and each such event leads to chain branching, which is thus a rapid process occurring instantaneously via reactions of low activation energies. It should be noted here that ether peroxides are notoriously unstable. Whereas dihydroperoxyheptane can be synthesized by slow oxidation of heptane, it does not seem possible to synthesize the corresponding ether product. Apparently the doubleperoxidized ether radical decomposes instantly as indicated above. The further pursuit of this concept leads to an explanation of the remarkable enhancement of the low-temperature explosion region of ethane, C H C H , and air 3

46

3

3

138

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

by small additions of acetaldehyde CH CHO, as shown previously in Fig. 23. It is known that aldehydes and peroxides may combine to form an adduct. With CH CHO and the ethyl peroxide radical C H C H 0 0 this adduct is an isomer of and may even be identical to the ether peroxide radical, viz., 3

3

3

2

CH CH + 0 = C H C H -> C H C H O C H C H , 3

2

3

3

OO—

2

3

OO—

•and thus the adduct equally reacts in the described chain-branching mode. If no acetaldehyde is present in the ethane-air mixture, explosive reaction depends on the gradual accumulation of acetaldehyde by slow oxidation of ethane, as observed by Bone and Hill in their study of the ethane-oxygen reaction. But only small quantities of aldehyde are produced by the reaction and most of the aldehyde is formaldehyde, which is known to inhibit rather than promote the explosion reaction. Thus, with no addition of acetaldehyde the explosion region is only marginally developed as shown by the curve in Fig. 23. Acetaldehyde and other higher aldehydes not only promote the explosion of ethane and oxygen but also enlarge the cool flame and explosion regions of hydrocarbons above ethane, though the effect is not as spectacular as it is with ethane. This is shown by the diagrams for propane-air and hexane in Figs. 30 and 31 which have been obtained by Townend and co-workers. Evidently, the mechanism of chain branching by ether-type peroxidation of aldehyde-peroxide adducts is a generic mechanism of all hydrocarbons, and even with large hydrocarbon molecules such as heptane chain branching via double peroxidation of aldehyde-peroxide adducts is the predominant mechanism in the generation of cool flames and low-temperature explosion. It follows that the cool flames of hydrocarbons and hydrocarbon compounds other than ethers are preceded by a period of accumulation of aldehydes RCHO and hydroperoxides ROOH and their radicals ROO, until chain branching by adduct formation and double peroxidation exceeds chain breaking. The free-radical concen­ tration rises to levels at which the gas is made luminous by electronically excited molecules such as C H 0 * that are formed in energetic free-radical reactions. How­ ever, as discussed in detail later, there is also a temperature rise and the temperature rise effectively inhibits the formation of ROO radicals by promoting the dissociation reaction ROO —» R + 0 . In this way chain branching by adduct formation and double peroxidation is arrested. However, most of the chemical enthalpy of the gas remains unexpended, the gas is at an elevated temperature, and it contains active species in the form of free radicals, aldehydes, and peroxides. Now another chainbranching mechanism becomes operative, identified in Section Ε as chain branching by alkoxyperoxide dissociation. At low pressures this mechanism fades out so that the reaction does not proceed beyond the cool flame stage, but at high pressures it carries through to ignition. The ignition process accordingly comprises two stages. The first stage extends over a period τι from the start of the reaction to cool flame, 49

49

1

2

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

139

OXYGEN P R E S S U R E , mm Hg 400

2

600

3

800

4

5

1000

1200

6

PRESSURE, ATMOSPHERES FIG. 3 0 . Effect of adding aldehydes on the "cool flame" and explosion region of a 7.5% propane-air mixture. Curve 1, no aldehyde; 2 , 1% propionaldehyde; 3 , 2 % propionaldehyde; 4 , 1% acetaldehyde; 5 , 2 % acetaldehyde (Townend and Chamberlain ). 1

and the second stage extends over a period τ from the sudden but relatively small temperature rise in the cool flame reaction to the sudden and large temperature rise in the explosive reaction. Figure 32 shows experiments by Kane on the ignition of a mixture of propane and air in a heated reaction vessel. The upper part of the figure shows the regions of cool flame and low-temperature explosion in a Ρ, Τ diagram. The lower part shows 2

50

140

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

records of the increase of pressure in the reaction vessel prior to explosion, for conditions corresponding to the points A to D in the explosion region. The pressure increase monitors the progress of the reaction, and it is seen that there is indeed a period T i during which the reaction does not significantly progress beyond an inter­ mediate stage, viz., the cool flame stage, and a period τ during which the reaction gradually accelerates to explosion. The records were obtained for a series of initial pressures at constant initial temperature of 360°C. It is seen that with increasing pressure τ decreases at a higher order than Ti and thus τ eventually vanishes, so that at sufficiently high pressure there is only a single short induction period τ. Two-stage ignition also applies to ethers, although there is virtually no induction period preceding the onset of ether-oxygen reaction, but the regions of cool flame and explosion are at rather low pressures compared to other hydrocarbons. Figure 2

2

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

141

PRESSURE, ATMOSPHERES t

Il

I

I

0

1.2

1.4

I

I

I

I

1.6

1.8

2.0

2.2

τ

l_

1

τ

2

1.75

0.61

1.68

0.50

1.36

0.19

1.34

0.14

2.4

T I M E , SECONDS FIG. 3 2 . Two-Stage ignition of a 6 . 5 % propane-air mixture in a cylindrical steel vessel of 3 . 2 cm diameter (Kane ). Above: Cool flame and explosion limits. Below: Records of pressure rise preceding explosion showing periods τι and τ at points A, B, C and D in the limit diagram. 50

2

33 shows such regions for diisopropyl ether. An induction period is obtained when formaldehyde is added to the ether-oxygen mixture, which indicates that ether peroxide is reduced by formaldehyde and chain branching is delayed until the for­ maldehyde is consumed. With acetaldehyde, the cool flame and explosion regions are very similar to the regions obtained with methyl and ethyl ether, but there is an induction period preceding onset of reaction indicating that chain branching occurs via an aldehyde-peroxide adduct. The peroxide in this case seems to be peracetic acid, CH CO(OOH), and the induction period can accordingly be eliminated by adding peracetic-acid vapor to the aldehyde-oxygen mixture. 51

48

51

3

52

142

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

500

O

400

Ignition

ο

LU CC D < LU Pr 3 0 0 LU

200

0

0.44

0.88

1.32

1.76

2.20

PRESSURE, ATMOSPHERES FIG. 33. Cool flame and explosion limits for 2.5% diisopropyl ether in air. (Maccormac and Townend ). Pressures expressed as sum of partial pressures of ether and oxygen. 51

B. WAVE PROPAGATION OF COOL FLAMES, SECOND-STAGE IGNITION FLAMES, AND SPARK-IGNITED "NORMAL" FLAMES

Cool flames have originally been described as waves of luminosity that form spon­ taneously when a mixture of hydrocarbon and air is passed through a heated tube. Following earlier observations by Perkin and others, cool flames in mixtures of air with paraffins, olefins, napthenes, alcohols, aldehydes, and ethers were studied systematically by Prettre et al. Additional observations were made by Beauty and Edgar on heptane and air. To describe the type of experiment we quote the following example. A mixture of pentane and air is continuously passed through a reaction tube whose temperature is slowly increased by external heating. If pentane is in excess of stoichiometric and the pressure is maintained at atmospheric, a bluish luminosity develops at about 200°C. At 240°C, the luminosity increases strongly but uniformly while at approximately 260°C a fairly bright luminous wave is formed which starts at the exit of the tube and travels slowly against the stream at a rate of the order of 10 cm/sec. In the described experiment there is a succession of waves which form at the exit and disappear at the entrance to the tube. Evidently, the time of travel of a gas element from the entrance to the exit represents the induction period of the cool flame. With increasing temperature, the wave becomes more diffuse and travels more slowly. At about 290°C the discrete waves disappear leaving a luminous column in the tube with zones of greater brightness which move slowly against the 53

54

55

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

143

stream. At 350°C the luminosity has become uniform along the tube; at higher temperatures from about 670°C upward, ignition occurs with comparative brilliance at the tube entrance with the flame intermittently becoming extinct and re-igniting. Other fuels behave similarly. Neumann and Aivazov studied the pentane-oxygen system in a long cylindrical quartz vessel observing the luminosity effects visually and recording the pressure development by means of a sensitive glass diaphragm manometer. After the mixture had come to temperature equilibrium with the vessel, the pressure remained virtually constant for a while and then suddenly rose. Simultaneously, cool flames were observed to travel along the tube. The pressure passed through a minimum coincident with the disappearance of the cool flame but remained considerably above the original pressure. Following this, the pressure rose gradually with time. During the cool flame period an increase in the number of moles occurred and also some heat liberation. Evidently the drop in pressure following the maximum is attributable to dissipation of the heat developed in the passage of the cool flame through the vessel. Occasionally more than one wave was observed with corresponding irregularities in the pressure record. On repeating a standardized experiment some 20 times, it became possible to collect products of the reaction formed at various stages of the pressure rise. They were distinguished as aldehydes, peroxides, acids, and carbon monoxide. The composite data are shown in Fig. 34. Curve ABCD denotes the pressure and the other curves denote the yields of various compounds, CO expressed in volume percentage of gas mixture and the other compounds in percentage of pentane con­ sumed in the reaction. The rise of aldehyde and peroxide concentrations coincident 56

144

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

with the pressure increase is noted. The dip in the pressure curve is clearly a thermal effect because the number of moles increases rather than decreases during this period. The appearance of cool flame waves, characterized by sudden rise and fall of pressure, can be suppressed by lowering the pressure below some critical value, all other conditions being the same; and at a higher critical pressure the reaction following the cool flame terminates in explosion which, in stronger mixtures, is marked by considerable violence. An example of this is given in Table 7 which refers to an experiment with a mixture of 1 C H I and 4 0 at 3 4 0 mm Hg and 318°C. The first row of figures denotes the time in seconds from the beginning of the experiment and the second row, the pressure increase in millimeters of mercury. The record is another example of two-stage ignition as shown previously in Fig. 32. The period Ή is here about 8.2 sec and the period τ is about 2 sec. The development of waves of cool flames is linked to the fact that the chemical reaction accelerates in some volume elements more rapidly than elsewhere in the volume of reacting mixture. In this way centers of ignition are formed within which temperature and concentrations of active species are relatively high. From such centers heat and chain carriers flow to an adjacent layer by the processes of heat transfer and diffusion. The layer then becomes activated to chemical reaction and serves as a source of ignition for the next layer, and so on. Behind the cool flame wave there exists an accumulation of peroxides and aldehydes, and a large part of the chemical enthalpy of the mixture is still unexpended. In the wake of the cool flame, therefore, the reactions of the τ regime take place which accelerate to explosion. In the final stage of the latter process where the reaction had become very fast, discrete sources of ignition probably also appear. Since the process is very fast, it is difficult to resolve the details of the final explosion. Neumann and Aivazov believe that in the experiment quoted in Table 7 a hot flame wave developed which traveled with a velocity of the order of 5 0 0 to 1000 meters per second. Similar hot flame waves have been observed by Miller in high-speed schlieren photographs of knocking combustion in the internal combustion engine. When a cool flame propagates from a spontaneously formed ignition source, the mixture that is being overrun by the wave has itself progressed more or less along the same reaction path as the volume element that now constitutes the ignition source, and it may be surmised that the reaction, prior to the arrival of the cool flame wave, assists in the propagation process. There is, however, no reason to believe that a preparatory reaction is essential for the propagation of the cool flame. That is, it is a priori quite imaginable that cool flames may be induced in a nonreacting cold mixture by means of a suitable ignition source. This is fully borne out by experiment. 5

2

2

2

2

57

TABLE 7

INCREASE OF PRESSURE DURING REACTION OF PENTANE AND OXYGEN Seconds Δρ, mm Hg

0 0

8 0

8.2 2

8.4 35

8.6 48

8.8 52

9.0 54

9.2 57

9.21 Explosion

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

145

900°K

Such observations were made originally on diethylether-air mixtures by White and later extensive studies were carried out by Townend and his co-workers. The larger part of these studies was made on ethers because the low pressures at which the phenomena are observed afford ease of experimentation. However, the observation of Hsieh and Townend on propane, butane, and hexane in air have estblished that the same phenomena occur with these compounds at pressures of the order of 5 to 20 atm, and it may be concluded that the phenomena are quite general. In the earlier experiments of White and Townend and co-workers, the ignition source was a hot wire and the cool flame was observed at fuel percentages exceeding the limit of flammability for ignition by a high voltage electric spark. In later experiments of Spence and Townend it was found possible to produce cool flames in mixtures of ether and oxygen that explode when ignited by an electric spark. The ignition source is described as a ceramic body heated electrically to a carefully controlled temper­ ature. In a diagram of pressure versus fuel percentage the regions of flame propagation are thus represented by three approximately U-shaped curves as shown in Fig. 35. 58

59

700

600 k

Violent explosions

500 X

Ε Ε LU

400

ZD CO CO Lu CC

CL

300

200

100

0

10

20

30

40

ETHER IN AIR, PERCENT FIG. 35. Limits for propagation of normal, cool and second-stage flames in diethyl ether-air mixtures at room temperature. Closed tube of 5 cm diameter (Spence and Townend ). 59

146

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

One of these represents the region of "normal" flame, another a region of cool flames and a third a region of two-stage ignition. Concerning the normal flame, we shall see later in this book, in the discussion of spark ignition, that the depth of the U along the pressure coordinate depends essentially on the spark energy and length of spark gap, which were arbitrarily standardized in these experiments; the width of the U along the mixture composition coordinate represents the ordinary limits of flammability which change very little with spark characteristics. The normal flame constitutes a combustion wave within which the temperature rises steeply from the initial temperature of the mixture to the combustion temperature corresponding to approximately adiabatic transition to thermodynamic equilibrium. Within this wave there are no discontinuous stages of chemical transformation associated with different reaction mechanisms. A volume element of the original mixture which is overrun by the wave is quickly heated to temperatures at which cracking and dissociation reactions become rapid, so that there is no question of appreciable formation of peroxide capable of alternative reactions, or reactions of aldehydes and other inter­ mediates, as distinguished from reactions of the original molecules themselves. In other words, in the normal combustion wave the reaction is a straight run to the final products corresponding to complete transformation of chemical enthalpy to thermal energy. The driving force of the wave is the heat released in the reaction which creates a strong source of heat adjacent to the cold medium. In contrast, the driving force in the cool flame wave is the production of large concentrations of chains carriers by a chain-branching process, and the reaction is arrested, at least temporarily, at an intermediate chemical stage. Cool flame flammation is caused by a heat source of comparatively low temperature which induces in the adjacent medium the branch­ ing reactions by which the wave is propagated. Whether wave propagation does or does not occur depends on temperature, pressure, and composition of the medium in the sense that at a given composition a lower temperature can be compensated by higher pressure. This is illustrated by a family of curves determined by Hsieh and Townend and shown in Fig. 36. The second-stage ignition develops at an appropriate pressure in the wake of the cool flame wave. In experiments of this kind the wave character of the second-stage flame is readily observed. It travels as a luminous zone of increased brightness behind the cool flame. Outside the region of normal flames the second-stage flame wave is observed to maintain a constant distance from the cool flame wave over a considerable range of pressures and mixture compositions provided that the end of the tube is open so that the pressure is maintained constant. If the pressure is raised sufficiently above the critical pressure limits for the appearance of second-stage flame, the latter travels faster than the cool flame wave and eventually the two coalesce. When this occurs an appreciable increase in flame speed of the combined wave is observed. Within the region of normal flames the coalescence presumably results in a normal combustion wave. At high pressures and nearstoichiometric mixture such flames are rather violent. Although second-stage flames presumably result in complete release of chemical 59

enthalpy and establishment of thermodynamic equilibrium, they must not be confused with normal flame since they start in a medium that is greatly different from the original reactants. In a closed tube the appearance of second-stage flame produces a considerable increase of pressure and consequently an increase of its velocity relative to the cool flame. Curious phenomena have been observed here. For mixtures outside the limits of flammability for normal flames, the coalesced flame proved to be unstable and reverted to a cool flame after a short time. This propagated for some distance down the tube after which the process repeated itself, giving rise to an oscillatory propa­ gation. For mixtures near the limit of flammability the second-stage flame produced violent gas flow effects and on overtaking the cool flame has been commonly observed to extinguish the latter, so that in closed tubes under such conditions flame cannot travel the entire length of the tube. It has been found possible to stabilize the cool flame in burner-flame fashion in a gas stream. The experiment could be extended to include stabilization of the secondstage flame at some distance behind the cool flame as well as stabilization of the coalesced flame. This was accomplished by passing the gas mixture through a conically shaped tube whose temperature was kept constant by a water jacket. Along such a tube the gas velocity decreases monotonously, and the flame waves settle at

148

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

some region in which the rate of propagation matches the gas velocity. The flames do not occupy a cross-section normal to the tube axis but are considerably tilted as described in the second part of this book under combustion waves in tubes. A schematic diagram of a stabilized cool flame is shown in Fig. 37, together with data of the temperature distribution along the tube axis determined by thermocouple measurements. Figure 38 shows photographs of the stabilized cool flame: the cool flame a, a second-stage flame b following it, and a coalesced flame c. Some systematic data have been obtained on the cool flame threshold as a function of various parameters. The dependence of the cool flame limit on partial pressures of reactants and on temperature is typified by the series of curves in Fig. 39 for methyl propyl ether. There appear to be lower limits of the partial pressures which shift with temperature. A similar curve for second-stage ignition is apparently not affected by the initial temperature of the mixture. Other variables that have been investigated include addition of diluent gases, C 0 , N , and A, and the tube diameter. Diluent gases increase the cool flame limit pressures; the increase was found to be in proportion to the heat capacities of the diluents, suggesting that the temperature rise in the cool flame makes an important contribution to the propagation mechanism. 2

Side

u

2

Front

140 220 T E M P E R A T U R E , °C

300

380

FIG. 37. Temperature gradient in stabilized cool flame of acetaldehyde and oxygen (Spence and Townend ). 59

4.

149

HIGHER HYDROCARBONS AND OXYGEN BELOW 900°K

FIG. 38. Photographs of stabilized cool and second-stage flame waves. 4CH CHO + 0 (Spence and Townend ). A. Cool flame at 300 mm Hg. B . Cool and second-stage flames at 400 mm Hg. C. Coalesced cool and second-stage flame at 600 mm Hg. 3

2

59

Change of tube diameter showed the existence of a quenching diameter below which cool flames could not propagate. C.

THE UPPER TEMPERATURE LIMIT OF THE DOMAIN OF COOL FLAME AND TWO-STAGE IGNITION. BENSON'S THEORY

An overview of the domain of cool flame and two-stage ignition is obtained by plotting data from experiments in closed reaction vessels in a pressure-temperature diagram. In the literature the construction of such diagrams is marked by different preferences of the investigators concerning the choice of coordinates, some investi­ gators using pressure and temperature as abscissa and ordinate, respectively, and others as ordinate and abscissa. This tends to cause some inconvenience, but since it is ingrained in the literature the reader's indulgence is asked.

150

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN 4001

Τ

300

Ε Ε -200 ο >χ ο CL

χ

χ •20°

100 U

5f 100°

160° C 0

100

300

200

^ ETHER, m m Hg

FIG. 39. Influence of temperature on the partial pressures necessary for cool and second-stage flame propagation in mixtures of methylpropylether with air (Spence and Townend ). 59

Figure 40A, which is based on data obtained by Townend, Cohen, and Mandlekar, is one more example of such plot. The mixture composition is 3.1% hexane in air. For juxtaposition, Fig. 40B shows Neumann and Aivazov's curves of average rates of pressure rise in an 11.1% pentane-oxygen mixture, at pressures ranging from 15 to 25 cm Hg. They represent the reciprocal of the half-time from the beginning of the reaction to the completion of the pressure rise, at pressures below the ignition limit. It is seen that the upper temperature limit of the regime of intense chain branching, i.e., the domain of cool flame and two-stage ignition, is virtually the same in these very different experiments. Evidently, this limit is controlled by reactions that are generic to aliphatic hydrocarbons. Specifically, there is agreement that on approach to the limit, peroxidation via the reaction R + 0 —> ROO de­ creases and the alternative reaction R + 0 —> H 0 + olefin becomes increasingly prominent. Benson ' has developed the theory of this change-over on the basis of the mechanism* given in the accompanying tabulation. The theory acknowledges that 1

56

2

2

2

60

44,45

61

* Benson prefers units of liter/mole sec (1 liter/mole = 1.66 x 10" cm molecule" ). Also he writes the exponential terms as powers of 10; thus, k = io liters/mole sec, where θ = 4.575771000 and 6 is the activation energy in kcal/mole. 21

9

v

2_6/e

3

1

4 . HIGHER HYDROCARBONS AND OXYGEN BELOW 9 0 0 ° K

151

ι i\

2

ω sz

CL

Ε χ ρ I ο s i V €

35

r e gl i c) n

11 s i CL

C Ο

si

33

iR

,15 héL 4

Ψ

2

\ N,

\

\ \Cool flamesN \\ ^1

Ν cK K \ N N s i vr e ) η e χ ρ Iο

•—

r e g iο n

1

/

fl

η

25

/

cm j 7

20

cm / zir\J

Λ

1A 1 ί

300

400

Temperature, C

500

600

e

FIG. 4 0 . A. Ignition region of 3.1% hexane in air mixture. Region of "cool flames" marked by shaded area. Induction periods in seconds indicated by numbers along curve (Townend, Cohen, and Mandlekar ). B. Reaction rates of 11.1% pentane in oxygen mixture at different pressures (Neumann and Aivazov ). 1

56

the primary products of the chain reaction are hydroperoxides ROOH and olefins R'C=CH or R'C=CR"; furthermore, hydroperoxides or their free radicals are essen­ tial for low-temperature chain-branching and are known to be produced within the domain of cool flame and two-stage ignition. Olefins play no role in chain branching but they become the main product of the primary chain reaction as the hightemperature limit of the domain is approached. The theory thus describes the approach to the limit in terms of the ratio of the rate of production of olefin to the rate of 2

Biomolecular 1. R + 0 —» ROO 1'. R + 0 —» H 0 + olefin 2. ROO + RH ROOH + R 2

2

2

k, cm /molecules sec 3

0.5 x 1 0 " (£, « 0) 0.3 x ΙΟ"" e x p t - 3 0 0 0 / Γ ] 0.5 x ΚΓ e x p [ - 7 0 0 0 / 7 ] 12

Monomolecular -1.

ROO —» R + 0

2

k, s e c 3 x

- 1

10 exp[-14000/r] ,4

152

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

production of hydroperoxide. The two rates are, respectively, d[olefin]/A = M 0 ] [ R ] 2

and rftROOH]/A=

. ^ ™ [0 ][R]. k-\ + k [RH] 2

2

If ROOH does not exceed the order of 10 molecules/cm the term & [RH] becomes small compared to k- at temperatures above ~250°C and the ratio of the rates becomes 19

3

2

}

d [olefin] /dt d[ROOU]/dt

ky ~

(ki/k-i)k [RH] 2

Using [RH] ~ 10 molecules/cm and the rate coefficients that are tabulated above, one finds the following relation between the temperature Τ and the ratio of the rates: 19

3

Γ, °C Ratio

250 0.02

300 1

350 3.6

400 13

450 35

This places the upper temperature limit of the domain about halfway between 300 and 400°C in substantial agreement with experiment. Although the reactions involved are generic for aliphatic hydrocarbons, the activation energies depend somewhat on the nature of the hydrocarbon and introduce minor differences. It is particularly noteworthy that the rate coefficient k\ has virtually no activation energy, whereas ky has an activation energy and also a preexponential factor that is somewhat smaller than k . Hence the reaction R + 0 —> H 0 + olefin is always much slower than the reaction R + 0 - » ROO and the existence of an upper temperature limit of the cool flame and two-stage ignition domain is due entirely to the occurrence of the reverse reaction ROO —» 0 + R, which thus plays a profoundly significant role in hydrocarbon oxidation. In principle there may also be the reverse reaction H 0 + olefin —> 0 + R which reconverts olefin to the free radical R, but the chance of an occurrence of this reaction is negligible due to competing reactions of H 0 , including in particular the reaction H 0 + RH —» H 0 + R and also, as pointed out by Benson, the oxidation reaction H 0 + olefin —» epoxide + OH. There is experimental evidence for the inverse dependence of the ratio of rates on the concentration RH that is shown in the above equation. Furthermore, the change of reaction mechanism that occurs on transversing the upper temperature limit of the domain is clearly reflected in the effect of traces of N 0 on the explosion limit, as found by Kane and Townend and shown in Fig. 41. It is seen that below the limit the effect is small and above the limit it is large and similar to the effect on methane and oxygen that is shown in Fig. 27. Obviously, free-radical species that react rapidly with N 0 , or rather with NO, are rare below the limit and prevalent 45

{

2

2

2

2

2

2

2

44

2

2

2

2

45,61

2

62

2

above the limit, and one such species is H 0 which reacts with NO to yield N 0 and OH. However, the available information is not sufficient for determining the details of the reaction mechanism. 2

2

D . THE PERIODS TI AND T OF COOL FLAMES AND TWO-STAGE IGNITION 2

The time lag or induction period in two-stage ignition represents the sum Ti 4- τ . In Figs. 23 and 40A such periods τι + τ are inserted along the boundary of the ignition region. Townend and Chamberlain have constructed the diagram in Fig. 42 which shows induction periods preceding the onset of cool flames outside the ignition region and not only periods Τι + τ along the ignition region but also curves of constant τι + τ within the ignition region. The latter curves present an orderly pattern of S-shapes whereas the explosion boundary is marked by curious protrusions and indentations that are well documented experimentally but not readily explainable. 2

2

1

2

2

154

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN OXYGEN PRESSURE, mm Hg 0

400

800

1200

PRESSURE, ATMOSPHERES FIG. 4 2 . Time lags (induction periods) T! within the cool flame region and τ ι + τ within the ignition (explosion) region. 7.5% propane-air mixture. (Townend and Chamberlain ). 2

1

They do not occur with ethane, and as shown in Figs. 30 and 31 they disappear when aldehyde is added to the mixture. Evidently, the critical pressure at which two-stage ignition occurs is not a monotonous function of temperature, an effect that may be due to the degradation of the original hydrocarbon into smaller molecules with more or less different activation energies in free-radical reactions. But the pressures within the explosion region at which explosion occurs after a specified time τι + τ are shown by the diagram to be monotonous functions of temperature, reflecting the less-complicated reaction kinetics that governs the periods τι and τ . Prettre studied the reaction of pentane and oxygen in the τι regime in a closed vessel using the rise of pressure as a measure of the progress of the reaction. The rate was sufficiently slow so that substantially isothermal conditions were maintained. The rise of pressure in these experiments is, therefore, a measure only of the increase in the number of moles. Since it is not known how many moles of products are formed per mole of reactants consumed, the pressure rise cannot be taken a priori as a measure of the number of moles of reactants consumed. However, Prettre believed 2

2

63

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

155

that this was nevertheless admissible over a limited range of experimental conditions. He found that in the temperature range 260-300°C, the percentage pressure rise was proportional to the initial pressure for a given mixture composition or, in other words, the number of moles of products formed per mole of initial mixture remained constant. This was true when the reaction did not culminate in a cool flame and came slowly to a standstill, as well as when the reaction passed through a cool flame stage and went rapidly to completion. The rule was found valid in the stated temperature range when the vessel diameter was 30 mm or larger and when the pentane content was between 12 and 50%. Percentages beyond this do not appear to have been investigated. The percentage pressure rise, i.e., the moles of products per mole of initial mixture, was found to increase linearly with the oxygen percentage. Using the pressure under the stated range of conditions as a measure of the progress of the reaction, Prettre obtained exponential curves of pressure rise versus time which, below the cool flame range, turned and flattened out again, and above the cool flame range terminated in a reaction of explosive proportions. This is illustrated in Fig. 43 where curve 1 corresponds to a pressure below the cool flame range, curve 2 to a pressure within the cool flame range, and curves 3 and 4 to pressures within the range of two-stage ignition. On a logarithmic scale the curves of this figure become partly straight lines (see Fig. 44 with slopes φ corresponding to the equation p = A(e*'-

1),

where t is time and A is a proportionally factor). For the exponential factor φ Prettre has offered several relations. Thus, at constant temperature φ was supposedly pro­ portional to the partial pressure of pentane and the square of the total pressure: ψ ~

^pentane^ ·

A linear increase of φ with pentane pressures is observed only up to 50% pentane. For larger percentages φ decreases. The equimolar mixture therefore gives the largest value of φ. Under conditions in which cool flames develop, the product of φ and Ti was found to be fairly constant at temperatures within the range investigated (260300°C); thus φτι = const. Therefore, for the equimolar mixture Ti is a minimum. From the above equations T l P p e n t a n e / " = COnSt, 2

where the constant depends only on temperature. The temperature dependence of the product φτι is shown in Fig. 45 in which the log of φτι is plotted against the reciprocal of the absolute temperature. From the linearity of the curve between 260 and 280°C, it is seen that in this temperature range φτι is proportional to e~ Therefore in this temperature range EIRT

Φ ~

^pentane Ρ

&

Ε is found to be 40 to 50 kcal. Above about 280°C the product φτι is less than proportional to e~ . Extrapolation of the curve suggests that at about 310°C φτι passes through a minimum. An experimental point determined by Tizard and Pye by means of rapid adiabatic compression (τι = 0.5 sec, temperature = 295°C, pressure = 5 atm, 2% pentane in air) fits well onto the curve. Taken at face value, Fig. 45 indicates that between 260 and 280°C the induction period Ti at constant mixture composition and pressure is approximately proportional to ; at ternE/RT

64

2 5 0 0 0 / T

e

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

157

peratures above 280°C, τι decreases less and less and finally passes through a minimum at approximately 310°C. It is a question whether Prettre's observations above 280°C refer exclusively to the regime of τι or whether the regime or τ is included. Investigations of Andreev and Rogener, which will be discussed below, show that τι always decreases and τ always increases with increasing temperature so that the total induction period τ leading to two-stage ignition reflects a temperature dependence of the type shown in Fig. 45. Addition of nitrogen accelerated the reaction rate. The effect of nitrogen on the 2

2

158

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN T E M P E R A T U R E , °C 295 290 280 1 1 1

300 1

1 I

270 1

260 1 X

/

X

/

y V

Tizard and Pye ζ idiabatic compressior

—

ίο /

Γ( κ)

3

β

FIG. 45. Plot of log(cpT) versus reciprocal absolute temperature (Prettre ). φ = exponential factor in the equation ρ = Α(β - 1). τ = induction period preceding cool flame or ignition. 63

ψτ

exponential factor φ could be represented by the equation φ = φ (1 + 0

aP ), Nl

where φ refers to a nitrogen-free mixture. The coefficient α is a function of the sum of the pressures of pentane and oxygen and is of the form 0

1

α ~

^pentane

Ρθ

2

From the constancy of the product φτι is follows that Τι(1 + a P ) = const. N z

Similar results were found with argon. Other observations include the following. Whereas in the experiments below 300°C T i decreases on adding inert gas, above 300°C the sum of T i and τ is increased by inert gas. Surface conditions affect the rate of rise of the reaction rate. The experiments were 2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

159

900°K

carried out in clean pyrex vessels, and consistent results were obtained only after many consecutive runs had been made in the same vessel. In the temperature range below 300°C the rate was found to be much slower in a KCl-coated pyrex vessel. Above 30 mm diameter the vessel size did not affect the values of φ, but below this diameter the value of φ decreased approximately according to the relation φ ~ 1-

(k'/d ), 2

where k' is a constant for otherwise constant conditions. The proportionality is somewhat doubtful owing to frequent inconsistency of the results when one vessel is replaced by another. However, it appears true that a critical diameter exists at which φ becomes zero. Thus, at 270°C reaction was found to cease in a range of diameters from 7 to 10 mm. Some observations were also made in a packed vessel. The packing consisted of thin glass rods and the surface-to-volume ratio was 20 c m . Reaction became observable above 310°C and cool flames appeared above 320°C. With increasing temperature the induction period decreased and then increased after pass­ ing through a minimum of about 325°C. The minimum of the induction period is thus shifted from approximately 310°C in the empty vessel to about 325°C in the packed vessel. If, as suggested, the data refer to the sum of τι and τ it would appear that τ is somewhat more strongly affected by packing than τι. A set of data paralleling those of Prettre has been reported by Aivazov and Neumann. These authors did not follow the development of pressure in detail but determined induction periods and pressure limits of cool flames. As mentioned earlier the induction periods were recorded photographically by means of a glass diaphragm manometer and we may assume that they refer to the τι regime. Their results with pentane-oxygen mixtures were essentially similar to those of Prettre, but the empir­ ical formulation of the data is different. Thus, where Prettre writes an equation which at constant pentane percentage becomes 1

2

2

65

i\P

= const,

2

Aivazov and Neumann write τι(Ρ - P )

n

0

= const,

where P is the pressure limit of the cool flame region and η is a number. The temperature range of this investigation was considerably higher. The equation is illustrated by data on a 1C HI + 4 0 mixture at 350°C, P being 95 mm and η being 2 in this case. The temperature dependence is expressed by an equation of the form 0

5

2

2

τ β~ ι

Ί

ί

0

τ

=

const,

where 7 is dependent on pressure and has, for example, a value of 64,000 at 200 mm Hg and 56,000 at 150 mm Hg. The data on which the equation is based were obtained in a temperature range from 325 to 375°C, which is significantly higher

160

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

than Prettre's temperatures. It is noted though that there is no suggestion of a minimum induction period as in Fig. 45. For the effect of nitrogen on the induction period Aivazov and Neumann propose an equation of the form T i ( l + const PN ) = const. 2

2

The equation conforms to the data only approximately. The experiments were per­ formed with an equimolar mixture of butane and oxygen at 321 °C and at an initial pressure, before addition of nitrogen, of 162 mm Hg, Neumann and Tutakin similarly found τι to decrease with addition of nitrogen and even ammonia. In harmony with these observations, Pease observed an accelerating effect of nitrogen on propane oxidation in a KCl-coated pyrex vessel at 270-280°C which is certainly in the T i regime. On the other hand, in a clean pyrex vessel the inert gas effect vanished. In this vessel the induction periods were much shorter than in the KClcoated vessel. This appears to be a clear case of low chain-breaking efficiency at the clean pyrex surface. Here the rate of chain-carrier destruction is determined only by the chain-breaking efficiency e of the surface and not by the diffusion rate of chain carriers; hence inert gas can have no effect. In a KCl-coated vessel where the chainbreaking efficiency of the surface is high, the rate of chain-carrier destruction is deteirnined essentially by diffusion and can therefore be decreased by addition of inert gas. Aivazov and Neumann studied the effect of vessel diameter using a mixture of 1 C H + 4 0 at 300 mm Hg and 390°C. The vessel diameters ranged from 10 to 40 mm. The results are approximately represented by the equation 66

67

5

I2

2

but the authors consider the generalization of this equation uncertain. In agreement with Pettre the authors find the shortest induction periods for approximately equimolar mixtures. Andreev has studied both the Ti and τ regimes by following the pressure increase of an equimolar mixture of butane and oxygen in a quartz vessel, using a glass membrane manometer and a photographic recording system. A typical set of results at 380 mm Hg pressure is shown in Fig. 46. In agreement with Aivazov and Neumann T i is found to decrease continuously with increasing temperature. In striking contrast, τ (shown on a 100-fold increased scale) increases with temperature. The increase does not follow a simple law; thus, between 336 and 352°C the curve for τ is broken. In this range no second-stage ignition but only cool flames were obtained. Supple­ mentary information obtained by Neumann and Tutakin shows that τ steadily decreases relative to T i as the pressure of a given mixture is increased. This agrees with the data that have been obtained by Kane and are shown in Fig. 32. The range of data has been greatly extended by the work of Rogener. This investigator was able to observe very short induction periods Ti and τ , corresponding to high pressures 68

2

2

2

66

2

50

69

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

161

250

00 200 Q Ζ Ο

ο

LU 00 {Γ 150 Q

g

en

LU CL

1 loo ho

ZD

Q

z

50 0 270

320

370 420 TEMPERATURE, °C

470

FIG. 46. Induction periods Τι (scale on left) and τ (scale onright)for C H + 0 at 380 mm Hg (Andreev ). 2

4

10

2

68

and temperatures, by rapidly compressing the fuel-air mixtures to a precisely deter­ mined fraction of the original volume and recording the pressure developed in the subsequent chemical reaction by means of a piezoelectric gage in conjunction with a cathode-ray oscilloscope. The principle of rapid compression as a means of studying ignition lags at high pressures and temperatures was utilized originally by Tizard and Pye. This work was later continued by Jost and Teichmann ' and Scheuermeyer and Steigerwald who were able to observe very short induction periods but did not obtain clear-cut separations of the τι and τ regimes. The records obtained by Rôgener, on the other hand, show this separation very clearly; illustrations of such records together with a description of the technically interesting apparatus are found in a paper by Jost. The adiabatic compression temperatures attained in Rogener's ex­ periments range from approximately 400 to 500°C; the pressures range from 5 to 40 atm; and the observed induction periods from 1 0 ' to less than 10~ sec. The results are summarized by empirical equations for τι and τ in Table 8. Though no immediate kinetic significance attaches to the "activation energies" and other numerical values in these equations, it is seen that TJ always decreases and τ increases with temperature; and both τι and τ decrease with pressure. Concerning the relative magnitudes of 64

70 71

72

2

71

1

2

2

2

2

162

IV.

THE REACTION BETWEEN HYDROCARBONS A N D OXYGEN TABLE 8 EMPIRICAL EQUATIONS FOR τ, AND τ

α 2

(STOICHIOMETRIC MIXTURES OF FUEL IN AIR)

n-heptane

[T, = 8 . 1 Χ Ι Ο

1 2

[7 =

066

0.5xp- Xe- ' iS2

2

ίτ, = 2 . 7 Χ 1 ( T X p~

0

9

rc-pentane

[τ

2

=

4.5Χ/7-

, 5 4

Χ^- ·

Γτ, - 5 . 8 Χ 1 ( Γ Χ ρ{ί

135

= 2 . 3 5 Χ ΙΟ x ρ- · 4

2

l 4O0,T

69

3

6

rc-butane

x e,15,100/Γ

X p~

2 96

é ι i,600/r

X

0 3 0 / 7

x

"

é 5,330/7"

Χ e

-5,220/7·

From Rogener. τ is in seconds; ρ and Τ are pressure in atmos­ phere and temperature in degrees kelvin at the end of compression and before occurrence of appreciable chemical reaction. û

69

these effects it is noted that the decrease of Ti with temperature is more rapid then the corresponding increase of τ ; and that τ decreases with pressure more rapidly than T i . These relations indicate that the total induction period τ = τι + τ is dependent on temperature and pressure in a complex manner. This is illustrated by Kane and Townend's curves in Fig. 42 and further illustrated by measurements of Scheuermeyer and Steigerwald on ^-heptane and air at high pressures and temperatures. In Fig. 47 their data on TJ and τ are plotted on a logarithmic scale against the reciprocal of the absolute temperature at the end of the compression calculated with the assumption of adiabatic conditions. Three curves are shown corresponding to end pressures of 9, 15, and 20 atm. At low temperatures each curve conforms rather well to a straight line, that is, τ decreases by the factor , indicating that Ti is predominant. Toward high temperatures the curve turns up, the more so the lower the pressure. This conforms to the trend of τ which increases with increasing temperature but decreases with increasing pressure more rapidly than T i . Rogener also investigated the effect of fuel-air ratio on both induction periods. He used ^-heptane to which was added 2% by volume of Pb(Et) . The fuel-air ratios corresponded to 56, 100, and 183% of stoichiometric. Ti was found to be reasonably independent of the fuel-air ratio while τ decreased with increasing fuel-air ratio. The insensitivity of Ti toward mixture composition is not inconsistent with the data of Prettre and of Aivazov and Neumann when the nitrogen content of the mixture is considered. Extrapolation of their data to an 0 - N ratio corresponding to air suggests a similar insensitivity of τ toward fuel-air ratio. With respect to lead tetraethyl as an additive, the outstanding fact is the observation reported by Rogener that the induction period Ti is unchanged while the induction period τ is considerably lengthened. Thus, addition of 2% by volume of lead tetraethyl to liquid η-heptane left the equation for τι in Table 8 unaffected, but resulted 2

2

2

62

72

2

c o n s V T

e

2

4

2

2

2

2

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

163

T E M P E R A T U R E , °C

327

1000 ι

1

r

.1 I

477

1

427

1

527

1

1

577

627

1

1

Ι

ι

I

I

I

I

I

600

650

700

750

800

850

900

1

550

377

A D I A B A T I C C O M P R E S S I O N T E M P E R A T U R E , °K

FIG. 47. Ignition lags for stoichiometric mixture of «-heptane and air determined by rapid-compression method (Scheuermeyer and Steigerwald ). 72

in values of τ expressed by the empirical equation 2

τ = 2 x 10 x p~ 4

2

2

2 4

x ~

1 ( m / T

e

.

In the temperature and pressure range of Rogener's experiments this exceeds the value of τ obtained from the corresponding equation in Table 8 by a factor of the order of 10. The effect of lead tetraethyl on the pressure-temperature limits of twostage ignition is shown for pentane-air mixtures in Fig. 4 8 . This figure comprises the ignition limits as a function of temperature, pressure, mixture composition, and addition of P b ( C H ) in an amount of 0.05%. Along the vertical dotted lines no ignition is obtained. The figure shows that at constant pressure of the mixture (1? and 1 1 atm, respectively) the addition of lead tetraethyl shifts the ignition threshold to higher fuel percentages and higher temperatures. If the data for a mixture, for example 3.7% pentane, are plotted in a temperature-pressure diagram, the curves shown in Fig. 49 are obtained. It is seen that Pb(C H ) causes a displacement to higher temperatures and pressures, which appears moderate in a diagram of this type but might, in certain regions of the diagram, lead to very large temperature increases if the pressure remains constant, or very large pressure increases if the temperature remains constant. Similar curves have been obtained for butane, isobutane, and hexane with air. ' For isobutane and hexane, the Pb(C H ) curves are so displaced toward higher temperatures, without changing the peninsula shape, that they cross 2

73

2

5

4

2

5

4

1 74

2

5

4

164

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

J

PENTANE IN AIR, PERCENT

STOICHIMETRIC MIXTURE FIG. 4 8 . Effect of lead tetraethyl on two-stage ignition of pentane-air mixtures at various pressures (Townend and Mandlekar ). The dotted lines run outside the ignition region. 73

the curves for the nonleaded mixtures in several places. In such places the ignition pressure at constant temperature is actually lowered by addition of P b ( C H ) . Figure 49 also shows a set of iso-induction period curves for Τ ι + τ = 4 x 10~ sec calculated for /i-heptane from Rôgener's data. The displacement of these curves by Pb(C H ) is of similar character. It might be expected that the cool flame region similarly shifts with addition of Pb(C H ) . In experiments of this type performed by Prettre, described earlier in this section, where the pressure of the mixture remained 2

5

4

3

2

2

5

4

2

5

4

4.

PRESSURE, ATMOSPHERES 10 15

5

I

l

Ν

Ν.

165

HIGHER HYDROCARBONS AND OXYGEN BELOW 9 0 0 ° K

I

I

20

25

I

X \

-

\ \ \ PbCEt)

\ \^0.1%

2% Pb(Et)

1,

4

4

\ \ \ \ \ \ \ \ \ \

A

Β

\\

\ t /J / 1

/ / / /

// V\

ι

Ν

ι

1

ι

ι

I

Χ ΝΝ Χ Ν Χ ι II eg

ι

I

PRESSURE, ATMOSPHERES

FIG. 4 9 . Effect of lead tetraethyl on ignition limits and induction periods. A . Ignition limits of 3.7% pentane-air mixture with and without lead tetraethyl (Townend and Mandlekar ). B. Curves of equal induction periods τ of stoichiometric /i-heptane-air mixture with and without lead tetraethyl. τ = 4 x 1 0 " second (Rogener ). 73

3

69

constant as the temperature was changed, addition of Pb(C H ) might therefore cause dimunition of luminosity effects and even elimination of cool flames depending upon the amount of P b ( C H ) added. Such has been the experience of Prettre. The chemical processes that determine Τ ι and τ involve peroxides and hence inevitably include reactions of peroxides at the vessel surface. All experimeters report that in order to obtain reproducible values, treatment of the reaction vessel is nec­ essary. This treatment usually consists of a number of blank runs preceding the measurement. This applies to the glass vessel experiments at low pressures as well as to the high-pressure experiments of Rogener. The latter author reports that in the first series of experiments with pure η-heptane the scattering of data was very pronounced. Subsequent experiments with Pb(C H ) showed a much improved reproducibility. Following this, experiments were carried out with pure w-heptane, pentane, and butane which also showed greatly reduced scattering of points. It was further noted that occasionally in a series of experiments under identical conditions 2

2

5

4

2

2

5

4

5

4

166

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

the induction period decreased monotonously. The empirical equations of Rogener refer to experiments in which these effects were absent. Interesting photographs of the development of the ignition process have been obtained in a rapid compression apparatus by Taylor and co-workers. One of these is reproduced in Fig. 50. The camera views the end of the cylindrical compression chamber through a heavy glass window. The mixture was butane and air with a fuelair ratio of 0.065 by weight, initial temperature of 310°F; initial pressure of 80 cm Hg, and compression ratio of 10.04. The time of travel of the piston was 0.006 sec. The first frame, corresponding to zero time, was photographed at the end of the compression stroke. The times of subsequent frames are given in milliseconds. The striking fact is noted that luminous spots appear preferentially at the surface of the cylinder and that ignition develops inward toward the center. Not all exposures show this clear evidence of surface origin of the luminosity. Some luminous spots are frequently distributed at random over the field of vision. Whether these spots have their origin in the gas phase, at the face of the piston, or at the glass window, the photographs cannot reveal, as the camera does not provide stereoscopic vision. However, the spottiness and randomness of origin of the luminosity in itself indicates that reaction does not occur uniformly throughout the mixture. Figure 51 shows a 75

75

FIG. 5 0 . Ignition of butane-air mixture by rapid compression (Taylor et al. ). indicate milliseconds from end of compression. 15

Numbers below frames

168

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

succession of photographs of a heptane-air mixture synchronized with a pressuretime record. The two-stage character of the ignition is evident from the pressure record, whereas the photographs themselves give no indication of the termination of the induction period Τι. It appears that the process that leads to the small but rapid pressure increase at the end of the τ regime gives rise to a comparatively small amount of luminosity. However, during this regime some spotty luminosity develops. The sudden spread of luminosity over the field of vision seems to coincide with the end of the τ regime. Concerning the role played by surfaces, one is reminded of an observation of Beatty and Edgar who passed mixtures of η-heptane and air through a pyrex tube of 2.4 cm diameter at various temperatures. While the initial diffuse luminosity at about 250°C seemed to occupy the whole column of the mixture, the cool flames that formed at about 270°C appeared in the shape of rings in the sense that the luminosity was more intense near the wall than in the center. }

2

55

E.

CHEMISTRY AND KINETICS IN THE COOL FLAME DOMAIN

The low-temperature chain-branching reaction that culminates in cool flames has been related (in Section A) to the chemistry of ether and etherlike adducts of hydroperoxides with acetaldehyde CH CHO and other higher aldehydes. This concept implies that hydrocarbons and their compounds produce cool flames only if in the course of their oxidation not only hydroperoxides but also aldehydes other than formaldehyde, HCHO, are formed. An aldehyde such as CH CHO is formed by oxygen attack on a primary carbon atom - C H or a secondary carbon atom - C H in the carbon chain of an n-alkyl group, whereas oxygen attack on a tertiary atom - C H produces a ketone, such as (CH ) CO. Ketones do not form etherlike adducts with hydroperoxides and hence, as shown by curve 8 in Fig. 22, isobutane (CH ) CH does not produce cool flame. On the other hand, isooctane, such as 2,2,4-trimethyl pentane, produces cool flame and two-stage ignition because it contains a - C H group, but as shown by curves 1 and 3 in Fig. 52, the cool flame domain is narrow and displaced toward higher pressures compared to n-octane which abounds in such groups. Ethane CH CH generates formaldehyde and also small quantities of acetal­ dehyde (see below). With ethane, the domain is only weakly developed (see Fig. 53) but becomes fully developed when a percent of acetaldehyde is added to the mixture (Fig. 23). Ethylene CH CH can generate only formaldehyde and thus does not produce a cool flame (Fig. 54). This also applies to acetylene C H , benzene C H , and higher aromatics. It also applies to toluene C H C H (see below), but as shown in Fig. 54, the cool flame effect is obtained with propylene CH =CHCH as well as with other olefins that contain n-alkyl groups. Whereas, as discussed below, ethylene generates formaldehyde via the free-radical reaction sequence 3

3

3

3

2

2

3

3

51

2

3

3

76

2

2

2

6

5

2

6

6

3

2

3

62

CH CH 2

CH CHOO 2

€

" ™ > CH CH + CH CHOOH -> 2CH 0, 2

2

2

2

2

with propylene the analogous reaction generates C H 0 4- CH CHO and thus fur2

3

4.

900°K

HIGHER HYDROCARBONS AND OXYGEN BELOW

169

rushes acetaldehyde required to produce a cool flame. With toluene, such acetaldehyde-producing reaction is not possible. Newitt has studied the reaction of oxygen with olefins at temperatures and pressures just outside the cool flame domain. Among the reaction products he found mixed ethers. It may be suggested that these ethers are formed from aldehydehydroperoxide adducts via a reaction such as 77

CH CH · Ο · C H C H - > CH CH · Ο · C H C H + 0 . 3

2

3

3

2

3

2

OO—

The link between the molecular structure of a hydrocarbon and its capability or incapability of low-temperature chain branching is thus clearly evident, and it is also possible, as in the case of w-octane and isooctane, to identify from molecular structure the more reactive hydrocarbon, viz., the hydrocarbon that produces cool flame and two-stage ignition at lower temperatures and pressures than the other.

The confinement of the cool flame chain-branching mechanism to a limited domain of temperature, pressure and other variables has already been described, and an explanation has been given for the existence of a common upper temperature limit for the alkane hydrocarbons. But there are various other observations and data on the reaction within and outside the domain that need to be described and discussed. An indication of the complexity of the reaction kinetics is the odd shape of the boundary between the zones of cool flame and two-stage ignition, showing inden­ tations and protrusions that are well verified experimentally. This seeming irregularity can be seen in the explosion diagrams that are reproduced in various preceding figures, and it is further illustrated by the diagrams in Figs. 55 and 56 which were obtained by Townend and Chamberlain and Newitt and Thornes, respectively. Figure 55 shows data obtained with propane and air in a steel vessel, whereas the data in Fig. 56 were obtained with propane and oxygen in a silica vessel, but as shown by the scale of oxygen pressures in Fig. 55, the air data fall into the range of the oxygen pressures of the data in Fig. 56, so that neither the atmospheric nitrogen nor the vessel parameters make much difference and the principal parameter that sets the ignition curves apart is the ratio of propane to oxygen. This ratio increases from 0.13:1 along the curve 1 in Fig. 55 to a value of 1:1 in Fig. 56, and there is a corresponding expansion of the ignition region at the expense of the cool flame region. As the expansion of the region progresses toward lower temperatures and pressures much of the cool flame region becomes encircled by the ignition boundary. 1

78

172

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

A brief comment on this subject is found below, and numerous other details are noted that have been reported by Newitt and Thornes. Thus, on passing along the isobar DE in Fig. 56 the phenomena shown in the accompanying tabulation are observed. Temperature range (°C) 275--285 290

330--340

340 345--385

380--425

Observations After an induction period of several minutes, a faint luminosity develops and remains until reaction is substantially complete A faint luminosity develops followed by a pale blue cool flame which starts near the center of the vessel and spreads outward giving rise to a slight pressure pulse; the luminosity persists for some seconds after the flame The initial luminosity observed immediately on filling the vessel is succeeded by four or five separate cool flames at intervals of several seconds; each of these flames traverses the whole vessel before extinction Two cool flames only are formed Over this range only one cool flame is observed, the intensity of the cool flames increases as their number diminishes and in all cases they are succeeded by an intense uniform glow persisting for some seconds; between 350 and 385°C the single cool flames diminish in intensity while the general luminescence increases until eventually it becomes impossible to distinguish the flames Intense luminosity develops immediately on filling the vessel; at 425°C it is succeeded by a bright blue flame which, at a slightly higher temperature, changes to the char­ acteristic yellow flame usually associated with true ignition; the narrow shaded strip adjacent to the ignition curve defines the region in which these blue flames are formed

On traversing the isothermal line FH at 315°C, the observed phenomena are similar to those described above; the number of cool flames first increases from one at 180 mm Hg to four or five at 321 to 520 mm Hg and then diminishes. Ignition occurs at about 530 mm Hg sometimes after an interval of several seconds succeeding the passage of one or two separate cool flames and under these experimental conditions it is usually accompanied by carbon formation in the cool flame region. In a number of runs Newitt and Thornes have monitored the progress of the reaction by manometric observations, and at predetermined times the reaction was arrested by plunging the vessel into an ice bath. The products were analyzed for formaldehyde, total higher aldehydes (acetaldehyde and propionaldehyde), propylene, total peroxides, acetylene, CO, C 0 , and CH4. Alcohols, mostly methyl alcohol but also including ethyl and propyl alcohol, were monitored in some runs, and small quantities of organic acids, polymerized olefins and hydrogen were detected. Con­ cerning the peroxides, it seems that the primary peroxide, viz., propylhydroperoxide, does not survive and that only alkoxy peroxides derived from aldehydes and H 0 are recovered. This is inferred from flow reactor data on propane and oxygen that have been obtained by Pease at 260-300°C, by Harris and Egerton at 307-340°C, and by Cartlidge and Tipper at 327°C. 2

2

79

46

80

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

173

OXYGEN PRESSURE, mm Hg 200

400

600

800

1000

1200

1400

1600

1800

2000

PRESSURE, ATMOSPHERES FIG. 5 5 . Propane-air mixtures in a steel vessel. (Townend and Chamberlain ). Propane content in curve 1, 2 6 % ; in curve 2 , 5 . 0 % in curve 3 , 7.5%. Propane: oxygen ratio in curve 1, 0.13:1; in curve 2 , 59

0 . 2 5 : 1 ; in curve 3 , 0 . 3 9 : 1 .

The product yields were tabulated as percentages of the carbon of the propane consumed ("burned") and the development of the reaction is shown by plots of product yields versus time, omitting acetylene, CO, C 0 , and CH4. Figure 57 shows such plot for the reaction at 460 mm Hg at 274°C, which is at a temperature below the cool flame region. Figure 58 applies to 400 mm Hg at 294°C which according to the investigators generates four cool flames and is situated in the explosion diagram just above the lower cool flame boundary near the tip of the intruding tongue of the ignition region. The data extend to the second cool flame only; beyond this point the rate of the reaction ws found to be too high for taking samples. Figure 59 applies to 360 mm Hg and 400°C, which is above the cool flame region in a narrow region of arrested reaction between cool flame and ignition. Supplementary data on pressure change and product yields are found in the original paper. The slow reaction below the cool flame region (Fig. 57) is preceded by an induction period of 15 min during which no detectable pressure change and only a slight consumption of fuel and oxygen takes place. This is followed by production of higher 2

78

1

I 200

I

ι

ι

400 PRESSURE, mm Hg

ι 600

ι

1 800

FIG. 56. Cool flame and two-stage ignition limit of C H -I- 0 in a silica vessel of 5.5 cm diameter (Newitt and Thornes ). Propane:oxygen ratio, 1:1. 3

78

40

8

2

175

4 . HIGHER HYDROCARBONS AND OXYGEN BELOW 9 0 0 ° K

8.0

8.5

9.0

9.5

TIME, MINUTES FIG. 5 8 . Products from the reaction of a C H Thornes). 3

8

+ 0

2

mixture at 4 0 0 mm and 2 9 4 ° C . (Newitt and

aldehydes and propylene at an accelerating rate, aldehydes being produced in a chain reaction involving the step C H — ^ C3H7OO and propylene being formed in the competing reaction C H ° > C H + H 0 . In the present instance the two reac­ tions apparently proceed at nearly equal rates, and as the run is proceeding and the supply of C H is diminishing, the chain reaction shifts from production to con­ sumption of the higher aldehydes and propylene, so that their concentrations pass through a maximum almost simultaneously. The final products include formaldehyde and peroxides. Although cool flames were not generated in the experimental series of Fig. 57, some chain branching by double peroxidation of aldehyde-hydroperoxide adduct was 3

7

2

3

3

8

7

3

6

2

176

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

TIME, MINUTES

FIG. 5 9 . Products from the reaction of a C H Thornes). 3

8

+ 0

2

mixture at 3 6 0 mm and 4 0 0 ° C . (Newitt and

undoubtedly occurring. Accordingly, if one uses the simplified schematics dn/dt = n + (α + β)π, 0

where η is the free-radical concentration, α and β are the coefficients of chain branching and chain breaking, respectively, and n is the rate of "spontaneous" generation of free radicals, a is smaller than β in the present case and one would normally expect the reaction to proceed at a steady rate corresponding to the steadystate concentration. 0

η = η /(β — α). 0

But the reaction that is monitored in Fig. 57 certainly shows no sign of settling down to a steady state. We shall write instead dn/dt = n — (β — a)n, 0

which implies that the rate n , far from being some elementary reaction, represents a slow but self-accelerating production of free radicals by some mechanism other 0

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

177

900°K

than double peroxidation of aldehyde-hydroperoxide adducts. This mechanism will be discussed later. Here it is noted that Newitt and Thornes have performed experi­ ments with different vessel diameters which show that chain breaking occurs by diffusion of free radicals to the vessel wall. Thus, β is a manageable kinetic function. However, the chain branching coefficient α depends on the concentrations of aldehyde and hydroperoxide, both of which change with time, which makes α a complex timedependent function that is not further examined here. Figure 58 shows the progress of the reaction at lower pressure but higher tempera­ ture. Under these conditions the induction period is reduced to 8 min, and as α in­ creases the free-radical concentration becomes sufficiently large to produce the cool flame effect. But the heat that is released as oxygen is being consumed also raises the temperature of the mixture, so that the frequency of the dissociation reaction C3H7OO —> C3H7 + 0 increases and the chain reaction now increasingly produces propylene and H 0 instead of propylhydroperoxide and the higher aldehydes. Ac­ cordingly, the cool flame is quenched by a feedback cycle in which the rate of destruction of hydroperoxide by reaction with free radicals, now mostly H 0 , exceeds its rate of production from free radicals C3H7OO, so that the concentrations of hydroperoxide and higher aldehydes decrease, and hence α decreases, with cumulative effect on the decline of the concentrations, including the free-radical concentration and the reaction rate. 2

2

2

The process is reflected in Fig. 58 by the slower growth of the higher-aldehyde yield relative to the propylene yield as the first cool flame is being approached, and by the subsequent temporary arrest of the growth of the propylene yield and the simultaneous rapid loss of higher aldehydes. Presumably there is a rather complete loss of propylhydroperoxide, which is the parent substance of the higher aldehydes, but this information has not been obtained in Newitt and Thornes' experiments. It has, however, been obtained by Burgess and Laughlin for heptylhydroperoxide in the cool flame reaction of heptane and oxygen. Figure 60 shows the spectroscopically monitored formation and destruction of the hydroperoxide (specifically heptane2-hydroperoxide) in an equimolar mixture of η-heptane and oxygen at 100 mm Hg and 243°C. The hydroperoxide concentration, which is zero at the start of reaction, increases at an accelerating rate to a partial pressure of about 3 mm Hg. At this point, it seems, α becomes equal to β. In consequence the free-radical concentration and hence the heat evolution and temperature increase rapidly as shown by the sudden pressure increase (dashed curve), and the hydroperoxide concentration drops rapidly to a partial pressure of about 0.2 mm Hg. Subsequently, the mixture cools and the reaction recovers but this recovery takes place in a mixture that is altered not only by loss of oxygen and original hydrocarbon but also by accumulation of chemically active reaction products such as formaldehyde and peroxides derived from H 0 , so that concentration profiles are not repeated identically in successive cool flames. However, the common feature of cool flames throughout the range of hydrocarbons is the temperature rise that promotes the dissociation reaction ROO —» R + 0 and 81

2

2

2

178

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN 5 Δ

cool flame = 4 5 mm Hg

ρ

P p

0

0

(heptane) = 5 0 mm Hg (oxygen) = 5 0 mm Hg

-CL.

0

30

60

90

TIME, SECONDS FIG. 6 0 . Change of concentration of heptylhydroperoxide with time during cool flame reaction of heptane and oxygen (Burgess and Laughlin ). C Hi + 0 mixture at 242°C and 100 mm Hg. 81

7

6

2

correspondingly inhibits the formation of hydroperoxides and aldehydes, and thus makes the flame self-quenching by inhibiting chain branching via aldlehyde-peroxide adducts. This is confirmed by measurements of temperatures in cool flames that have been reported by various investigators and in particular by Burgess et al. who found that the temperature rise during cool flame combustion was always sufficient to inhibit hydroperoxide formation and to transport the system into the regime governed by the reaction R + 0 —> olefin + H 0 . This regime evidently dominates the reaction that is recorded in Fig. 59. The pressure and temperature correspond to a point midway between the zones of cool flame and ignition (see Fig. 56), in a region where according to Newitt and Thornes "intense luminosity develops immediately on filling the vessel." This is reminiscent of the glow reaction of carbon monoxide that is described in Chapter III. It shows that a high free-radical concentration is established that generates luminosity by reactions between free radicals. The concentration remains stationary and no ignition occurs because chain breaking occurs largely by recombination of free radicals, so that the rate of chain breaking takes the form βη + β ' η , whereas the rate of chain branching remains an; hence, chain breaking and branching are in equilibrium at the free-radical concentration η = (a — β)/β'. However, Fig. 56 shows that a small increase of temperature or pressure suffices to take the system into the ignition region. This is not a thermal explosion in as much as ignition limits of hydrocarbons even outside the cool flame domain are certainly branched-chain explosion limits similar to the limit for methane. In Section 3.B, methane ignition has been attributed to chain branching involving the formation of methoxyperoxide, CH (OH)OOH, folS2

2

2

2

2

179

4 . HIGHER HYDROCARBONS AND OXYGEN BELOW 9 0 0 ° K

lowed by dissociation to yield free radicals OH. Analogous reactions involving alkoxyperoxides may be proposed for hydrocarbons in general; and in as much as the combination of an aldehyde with H 0 yields an alkoxyperoxide one arrives at the following theory: The nonexplosive luminous reaction above the cool flame domain generates H 0 by the reactions C H + H 0 —» C H + H 0 and 2 H 0 —» H 0 + 0 ; it is the latter reaction that keeps the free-radical concentration stationary and prevents ignition; the aldehydes that are formed (see Fig. 59) react with H 0 to form alkoxyperoxides; and the ignition limit represents the condition at which the rate of chain branching by alkoxyperoxide dissociation becomes larger than the rate of chain breaking in the gas phase and at the vessel wall. Norrish and Reagh have extended their studies of the nonexplosive methaneoxygen reaction to the nonexplosive ethane-oxygen and propane-oxygen reactions at temperatures well above the cool flame domain. Under these conditions nearly the same relation between vessel diameter, reaction rate, and induction period was found for ethane and propane as had been found earlier for methane. It is thus shown that above the cool flame domain the oxidation kinetics of higher hydrocarbons becomes analogous to the oxidation kinetics of methane which has been discussed in Sec­ tion 3.A. Figure 61 shows records of the increase of pressure with time at constant initial pressure of 360 mm Hg and several temperatures. The experimental conditions correspond to points along the constant-pressure line DE in Fig. 56. The pressure increase reflects the increase of the number of moles in the reaction vessel, mostly due to formation of CO, C 0 , and H 0 , but in the cool flame zone the curves show sudden changes that are caused by the rapid heat release and temperature rise in the cool flames. The effect is particularly large in the curve Ε which is in the zone where Newitt and Thornes observed up to five successive cool flames. At any such peak the temperature has become so high that chain branching via aldehyde-peroxide adducts virtually ceases, but alkoxyperoxides that are being formed from aldehydes and H 0 initiate a second stage of chain branching that may culminate in ignition. Thus, two-stage ignition is attributed to chain branching via alkoxyperoxide dis­ sociation, occurring in a medium whose reactivity is boosted by heat, aldehydes, and the various peroxides generated by a preceding cool flame reaction. In Fig. 56 the domain of two-stage ignition extends roughly to a temperature corresponding to the point A on the ignition limit curve. At higher temperature there is no preceding cool flame reaction and the ignition limit becomes similar to the limit in a methaneoxygen mixture. An examination of the curves in Fig. 61 in reverse alphabetical order from Ε to A shows that with increasing temperature the time from the start of the reaction to the first cool flame becomes shorter, but as expected from the increasing inhibition of the cool flame reaction by the dissociation reaction ROO —> R + 0 , the cool flame peaks become weaker. In two-stage ignition the time from the start of reaction to the cool-flame stage is the period τι which accordingly decreases when the temperature 2

2

2

2

2

2

2

2

3

8

2

3

2

2

26

2

2

2

2

2

7

2

2

180

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

15

0 16

1 17

0

18

1 19

2

20

3 21

TIME, MINUTES FIG. 61. Pressure-time curves of C H + 0 at initially 360 mm Hg in a silica vessel of 5.5 cm diameter (Newitt and Thornes). The curves correspond to points along the line DE in Fig. 56. Curve F (lower time scale) is preceded by a 15-min period of no detectable pressure rise. All other curves start at zero time. 3

8

2

is increased; but since the cool flame reaction is increasingly inhibited its boost effect on the second-stage ignition decreases and the period τ correspondingly increases, as has been noted in the preceding section. The same mechanism may explain the shape of the boundary between the region of cool flame and two-stage ignition. In Fig. 56 the boundary is found to recede from a pressure of 380 mm Hg at 287°C to 530 mm Hg at 317°C. The pressure increase presumably compensates for the decreased boost effect of the cool flame reactions as the temperature is raised from 287 to 317°C, whereas at the latter temperature the boundary is so near to the limit for ignition without preceding cool flame that it does not recede further. Figure 62 shows curves of pressure increase that have been obtained by Newmann 2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

181

and Aivazov at increasing temperatures along the 200 mm Hg isobar that passes through the tip of the blunt-nosed cool flame peninsula of a pentane-oxygen mixture. These curves present another illustration of the weakening of the cool flame peaks and the shortening of the induction periods that is shown by Newitt and Thornes' propane curves in Fig. 61. The simplified schematic reaction kinetics that has been applied to the data plots in Figs. 57-59 utilizes the term n to represent the rate of free-radical generation by some mechanism other than double peroxidation of aldehyde-hydroperoxide adducts, and also other than alkoxyperoxide dissociation. This n mechanism, as it may be called, becomes operative on admission of the hydrocarbon-oxygen mixture to the heated reaction vessel and initiates a slow but self-accelerating reaction as illustrated by the family of curves in Fig. 61. Each curve shows an initial acceleration of the pressure rise that increases with increasing temperature and is thus initially larger in curve A than in curve B; but since curve Β is within the cool flame domain whereas curve A is outside the domain, the cool flame mechanism takes effect and subse­ quently curve Β rises more steeply than curve A. This also applies to the 450° and 350° curves in Fig. 62. The curves A and F in Fig. 61 and the 450° and 310° curves in Fig. 62 are outside the cool flame domain and thus are entirely governed by the no mechanism, whereas the intermediate curves are initially governed by the no mechanism and subsequently by the cool flame mechanism. It has been mentioned that at temperatures above the cool flame domain Norrish and Reagh have found a strong similarity of the oxidation kinetics of ethane and propane to that of methane. However, below the cool flame domain and also at low 56

0

0

182

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

temperatures within the domain one finds the seemingly discordant phenomenon that the admission of the hydrocarbon-oxygen mixture to the heated reaction vessel is followed by a period of imperceptible or barely perceptible reaction. The period is seen to persist for 15 min in curve F of Fig. 61, for 125 min in the 310° curve of Fig. 62, and for about 8 min in the cool flame reaction that is depicted in Fig. 58. In two-stage ignition the phenomenon is observable in the great length of the period τι at low temperatures, as shown by the plot of TJ versus temperature in Fig. 46 and as indicated in the explosion diagrams that are plotted in Figs. 40, 42, 52, and 55. Thus, while Norrish and Reagh's investigation strongly suggests that the no mecha­ nism is analogous to the methane mechanism, it may be questioned whether the analogy is preserved at temperatures near the lower temperature limit of the cool flame domain. The question is given an affirmative answer by the mechanism that is proposed in Table 9. The mechanism is structured in analogy to the methane oxidation mechanism in Table 5. It is however formulated without consideration of the reactions ROO —> R + 0 and R + 0 —» olefin + H 0 and thus applies only to low temperatures, showing the feature of self-acceleration and build-up of the concentrations of alde­ hydes and hydroperoxides in the early stage of the reaction, and the occurrence of preceding periods of imperceptible or barely perceptible reaction. Some of the reactions are not specified in detail and the oxidation and degradation of aldehyde by free-radical attack is neglected, implying that in the early stage of the reaction the free radicals react predominantly with hydrocarbon RH. Using the symbols K , K , and K for the rate coefficients of the surface reactions (a), (3), and (6), one obtains from Table 9 2

2

2

a

rf[R'CHO]/A

3

6

- *i[RH][ROO] - # [ R ' C H O ] [ 0 ] + ATJRH][0 ] 6

2Jfci[0 ][R'CHO] 2

2

2

tf [ROO] 3

so that «/[R'CHO]

[RH] - K

6

dt

[0 ][R'CHO] + K [RU][Q ]. 2

a

2

(16)

Also -d[RH]/dt

= ^[RH][ROO] + ATJRH][0 ], 2

so that d[RH]

[R'CHOJ+A,

dt

[RH][0 ]. 2

(17)

The lower temperature limit of the cool flame domain lies in the range of temperatures at which (2kik /K )[RR] and K are of comparable magnitude. The product of the rate coefficients k and k has a large activation energy E + E and is thus sensitive x

3

6

x

t

x

4.

HIGHER HYDROCARBONS A N D OXYGEN BELOW

900°K

183

TABLE 9 MECHANISM OF METHANE OXIDATION (TABLE 5 ) ADAPTED TO THE EARLY STAGE OF OXIDATION OF HIGHER HYDROCARBONS, R H

(a)

RH + 0

(i)

R'CHO + 0

> · · · a trace of aldehyde R ' C H O

surface 2

-> CO + H 0

2

+ R'

2

R O O H -> (1)

ROO +

· · · 2ROO

· · · mostly R ' C H O

RH R - ^ >

(3)

ROO

(6)

R'CHO + 0

surface

ROO

> destruction surface 2

> inert products

to temperature, so that below some temperature the first term in Eq. (16) is negative and only a trace quantity of aldehyde is produced corresponding to the concentration [R'CHO] = Κ [ΚΆ]/(Κ α

-

6

(2^/Κ )[ΚΗ]). 3

Under these conditions the reaction proceeds at an extremely low rate, but K is changing since theory as well as experience shows that on exposure to catalytic reaction the vessel surface undergoes a change. Generally, the adsorptivity decreases, so that the coefficient K becomes smaller and the first term in Eq. (16) eventually becomes positive. The reaction now proceeds at an accelerating rate which by integration of Eq. (16) and combining with Eq. (17) is found to be 6

6

dt

\

Φ

with 9 = ^[RH][0 ]-£ . 2

(18)

6

^3

For small values of K one obtains 6

=Ka{m[Q2]e

*

with φ =

^ ][0] (18)'

Ut

[ΚΗ

2

Λ3

Integration over a short period t yields Δ[ΚΗ], =

2kik\

(e* - 1)

(19)

where A[RH], represents the hydrocarbon that has been consumed by the reaction at a time t at which the concentrations [RH] and [ 0 ] have not decreased significantly. Figure 43 shows a sample of Prettre's curves of the pressure rise following admission 2

63

184

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

of a pentane-oxygen mixture to a cylindrical Pyrex vessel at 260°C, and Fig. 44 illustrates Prettre's method of assigning exponential factors φ to the initial slopes of the curves, so that the relation between the pressure rise ΔΡ and elapsed time t takes the form Δ Ρ - A{e*< - 1).

(20)

Prettre's curves seem to be free of preceding periods of imperceptible reaction, which in the context of the reaction mechanism in Table 9 probably means that the coefficient Κ β was small because the reaction vessel was large and well aged. Thus, Eq. (20) corresponds to Eq. (19) if the pressure rise Δ Ρ is assumed to be proportional to the hydrocarbon consumption A[RH], an assumption which Prettre believes to be justi­ fied. But Prettre's data correlation 9 ~ Ppentane^

(21)

2

is problematical inasmuch as it has no decipherable reaction-kinetic significance. In the reaction mechanism of Table 9 the coefficient K may take the form k /[M]d or k' ld depending on the chain-breaking efficiency e , and thus Eq. (18') becomes either 2

3

3

3

2kk\ φ = — — [RH][0 ][M]
(«'a)

2

2

or 9 = ^[RH][0 ] /~P „Po . 2

i

R

( 1 8

2

'

b )

k

3

Prettre's correlation disagrees with both (18'a) and (18'b). However, it is shown in Table 10 that Prettre's experimental data are not sufficiently definitive to discriminate between his correlation (21) and the correlations (18'a) or (18'b). The table is based on Prettre's original publication and contains all of his data on φ as a function of P PRH and Po . It is seen that all of the three ratios of φ/Ρ^Ρ , Ç/PRRPO P, and <Ç/PRHPO scatter around average values within acceptable limits. Thus, the data do not tell which correlation is correct and which is incorrect. However, there exists an independent criterion. It has been found for pentane by Prettre and for propane by Newitt and Thornes that for otherwise equal conditions the rate of pressure rise is largest for the equimolar mixture RH + 0 . Also, Bonner and Tipper report for cyclohexane, propane, and rc-heptane that at equal temperature the equimolar mixture RH + 0 yields the lowest pressure for cool flame appearance. It follows that for otherwise equal conditions the exponential factor φ is largest for the equimolar mixture and is thus proportional to the product [RH][0 ], viz., PRRPO This applies to either of the correlations (18'a) and (18'b) but not to Prettre's correlation (21). Prettre has extended his studies to include empirical correlations of φ with inertgas pressure and vessel diameter. They are found on p. 158 in the preceding section and in common with the correlation proposed in Eq. (21) they are problematical. f

2

2

2

2

63

78

47

2

2

2

2

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

185

TABLE 1 0 PRETTRE'S EXPERIMENTS WITH PENTANE AND OXYGEN AT 2 6 0 ° C ; COMPILATION OF THE A

RATIOS φ/Ρ Ρ ,

2

ΚΗ

φ, min

0.23 500 103 397 8.9 11.2 5.6

1

Ρ PRH

Po

2

Ψ/PRHP

2

φ/ PRHPQ P 2

0.29 500 155 345 7.5 10.8 5.4

0.36 500 181 319 8.0 12.5 6.2

RH

0.39 500 262 238 6.0 12.5 6.3

2

AND

0.426 500 230 270 7.4 13.7 6.8

1.10 746 265 481 7.5 11.6 8.6

RH

b 2

0.51 581 210 371 7.2 11.3 6.5

0.32 500 180 318 7.2 11.2 5.6

0.30 400 142 258 13.2 x 20.6 x 8.2 x

ψ/ΡκπΡο

2

Empirical correlation (Prettre): φ ~ Equation (18'a):

φ ~

Equation (18'b):

φ ~

P P

2

RH

P PP RH

0l

P Po RH

2

S e e Prettre. P , Ρ , and Ρ are the partial and total pressures in mm Hg.

a

63

b

RH

θ2

Thus, φ is shown to be increased by addition of nitrogen which is consistent with the correlation (18'a), but the correlation is given in the form φ = φ (1 + α Ρ ) , which is inconsistent with theory The second term in the correlation φ ~ 1 — (k'/d ) is consistent with the term —K in Eq. (18) which is an inverse function of vessel diameter, but the first term of this correlation is inconsistent inasmuch as it should be proportional to d or d according to Eq. (18'a) or (18'b). Thus, the chemical-kinetic significance of Prettre's correlations is not clearly established, and this also applies to the correlations proposed by Aivazov and Newmann that have been quoted in the preceding section. Perhaps these uncertainties are in some measure attributable to the assumption of a linear relation between the pressure rise Δ Ρ and the hydrocarbon consumption A[RH] which Prettre believes to be justified but which does not seem to be conclusively proven. However, Prettre's work does not contradict the essential validity of the reaction mechanism that is proposed in Table 9, and it merits to be viewed as an innovative excursion into the experimental aspects of the complicated non-steady-state kinetics of the mechanism. We have identified three generic reaction mechanisms that are operative in the oxidation of alkane hydrocarbons and related compounds over a temperature range between roughly 200°C and an upper bound of about 900°C. They comprise the mechanism of initiation and slow reaction that has been named the n mechanism; the mechanism of chain branching by double peroxidation, generally involving aldehyde-hydroperoxide adducts, that generates cool flame and is inhibited as the temperature rise promotes the dissociation reaction ROO —> R + 0 ; and the mechanism of chain branching by alkoxyperoxide dissociation which is operative in 0

Ν 2

2

6

2

0

2

186

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

two-stage ignition and in single-stage ignition above the cool-flame domain. These generic mechanisms provide a fairly comprehensive interpretation of the experimental observations, particularly observations made in closed-vessel experiments, without detailed examination of the organic chemistry of the elementary reactions that compose the mechanisms and of course are individually different for different hydrocarbon species. The identification and formulation of specific reactions that occur with spécifie hydrocarbons is an ongoing effort that is producing a volume of literature too large to be covered in this book. A broad review of the subject with comprehensive lists of references is found in a book by Hucknall, whereas the present purpose is served by a brief discussion of the differences in the oxidation kinetics of the higher and lower hydrocarbons. Thus, on comparing Newitt and Thornes's curve F in Fig. 61 with an analogous curve obtained by Bonner and Tipper for η-heptane one finds that with propane the initial period of imperceptible reaction is terminated by pressure increase whereas with η-heptane it is terrninated by a short period of pressure decrease followed by pressure increase. Furthermore, whereas Newitt and Thornes did not detect hydroperoxypropane among the reaction products, Bonner and Tipper found dihydroperoxyheptane and its aldehyde adduct being formed during the period of initial pressure decrease, which is thus attributable to the decrease of the number of moles in the generic chain reaction R ROO ROOH + R. Evidently, the propane peroxide C3H7OOH or its radical C3H7OO is rapidly converted into aldehyde and other products, whereas the n-heptane peroxide radical produces dihydroperoxide in the chain reaction 83

47

> C H OOH

C H 00 7

I 5

7

C H (OOH) + C H 7

14

2

C (00)H 00H

14

7

7

1 4

C 7

" > 1 6

C H 00,

15

7

! 5

and also produces aldehyde via one or more reaction paths involving decomposition of peroxide or peroxide radicals or both. With respect to propane, suggestive data have been obtained by Pease. In these experiments 400 cm of mixture were passed through KCl-coated pyrex reaction tubes at 260 to 300°C, the rate of passage being slow enough to allow the reaction to go to virtual completion. Results are shown in Table 11. The table shows that a prominent product of the reaction is methyl alcohol, the amount of which tends to approximate the amount of propane reacting as the percentage of oxygen in the initial mixture is decreased (see 10% runs). The sum of formaldehyde and higher aldehydes, the latter being mostly acetaldehyde, behaves similarly. The total aldehyde yield is close to the methanol yield. With Pease, we interpret the analytical data as a clue to the chain mechanism of propane oxidation. A free radical removes an H atom from a C H molecule, but the probability of this occurrence is different for the hydrogen on the end and middle carbons. From a variety of evidence, Walsh estimates attack on the middle carbon H to be about three times more probable than attack on the end carbon H in the 79

3

3

84

8

187

4 . HIGHE R HYDROCARBON S AN D OXYGE N BELO W 9 0 0 ° K TABLE 1 1 PRODUCTS O F REACTIO N BETWEE N C H AN D 0 3

8

I N A SINGL E PAS S O F 40 0 CM O F 3

2

MIXTURE THROUG H KC 1 COATE D PYRE X T U B E S

Reaction tub e Diam, cm

Formed , c m Used, c m

Length, Temp, Percent cm °C o2

2 3 4 6.5 3

30 22 12 6.5 22

6

28

0

300 300 300 300 300 300 300 260 260 260 300

0

20 20 20 20 10 20 30 10 20 30 20

2

77 79 78 76 39 79 119 39 77 116 76

3

3

C H * CO 2

40 41 50 46 19 41 47 17 44 65 48

Higher HCHO CHO

CH OH 2

8

28 38 37 38 14 38 48 16 33 47 45

21 23 24 20 16 23 27 12 22 28 20

14 12 11 13 9 12 12 7 12 14 9

7 8 8 5 4 8 11 4 5 5 5

co

2

15 10 12 11 4 10 17 7 11 19 10

CH

CH„

4

2

1 4 8 11 2 4 5 5 7 9 15

2

5 6 5 7 4 6 9 3 3 2 6

"From Pease. Subject t o erro r o f 3 t o 5 cm . 79

b

3

temperature rang e unde r consideratio n here . Thus , th e mos t frequen t propy l radica l is C H 3 C H C H 3 , an d it s associatio n wit h 0 lead s t o a peroxid e radica l C H C H ( 0 0 ) C H which , b y simpl e fissio n o f th e O - O bon d an d on e C - C bond , leads t o 2

3

3

C H C H ( 0 0 ) C H - * CH3CH O + CH3O . 3

3

The formatio n o f methy l alcoho l i s thu s readil y accounte d fo r b y th e reactio n CH3O + C H - » CH3O H + C H , 3

8

3

7

and wit h a competin g C H 0 + 0 reactio n formulate d analogou s t o th e reaction i n th e methan e schem e i n Tabl e 5 , namely , 3

CH3O + 0

2

2

CH3 O

- > C H ( O H ) 0 0 -^âïïs- * C H + CH (OH)OOH - > C H + C O + 2 H 0 , 2

3

7

2

3

7

2

The tren d o f equimola r proportion s o f propan e consume d an d methano l forme d wit h decreasing oxyge n percentag e i s clear . Likewise , i f on e assume s tha t formaldehyd e arises fro m th e furthe r oxidatio n o f acetaldehyd e an d tha t som e formaldehyd e under goes oxidation , th e tota l aldehyd e yiel d shoul d mor e o r les s equa l th e methano l yiel d and follo w a simila r trea d wit h respec t t o propan e consumed . Th e othe r entrie s i n Table 1 1 ar e hardl y significant ; C O an d C 0 ar e forme d b y furthe r oxidatio n o f aldehydes an d othe r intermediat e products , an d th e origi n o f C H 4 an d olefin s i s conjectural. The highe r aldehyde scompris e acetaldehyd e an d som epropionaldehyd e C H CHO 2

2

5

188

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

which is formed from the less frequent propyl radical CH CH CH via peroxidation and break-up, viz., 3

2

2

C H C H C H - * C H CHO + OH. 3

2

2

2

5

Newitt and Thornes' data in Figs. 57-59 confirm that the higher aldehydes are primary reaction products and that formaldehyde is a secondary product arising evidently from the further oxidation and degradation of the higher aldehydes. If the scheme of peroxidation and break-up is applied to the higher rc-alkanes it would seem that initial attack is possible with equal facility on any of the CH groups. We would therefore write in general 2

R'CHCH R" -22-» R'CH(00)CH R" - > R'CHO + R"CH 0. 2

2

2

Unlike propane where the methoxyl radical is stable and can react further to form methyl alcohol, the higher oxyalkyl radicals formed in this fashion are not stable. It has been shown in metal mirror experiments that these radicals decompose readily to yield formaldehyde according to 85

R"CH 0 - > R" + C H 0 . 2

2

Accordingly, one would expect that in the low-temperature oxidation of the higher fl-alkanes formaldehyde is a primary reaction product and that formaldehyde and higher aldehyde R'CHO are initially produced in equimolar yields. This has indeed been found in a study of the oxidation of w-hexane by Cullis and Hinshelwood, who originally proposed the above mechanism. One would also expect that an isoalkane reacts more slowly with oxygen than an Az-alkane because the reaction rate depends on the aldehyde concentration and the tertiary carbon atoms in iso-alkane do not produce aldehydes. This concept has been put to test by Pope et al. in one of the earliest investigations of the oxidation kinetics of higher hydrocarbons. In these experiments near-stoichiometric mixtures of all possible octane isomers with air were passed through a heated pyrex tube and the consumption of oxygen at identical contact times was measured. The data are shown in Fig. 63. They do not provide the wealth of information that is obtained from Maccormac and Townend's closed-vessel experiments (see Fig. 52), but they certainly demonstrate the preeminent oxidizability of η-octane and the oxidation resistance of 2,2,4-trimethyl pentane, which is the ideal isooctane of the fuel rating scale. With the higher w-alkanes there is certainly no dearth of aldehydes and hydroperoxides to generate cool flames, and this is reflected in comments made by Bonner and Tipper in their paper on the cool flames of propane and η-heptane, concerning the much greater ease of cool flame formation with n-heptane and the much stronger pressure pulses and the much higher luminosity of the η-heptane cool flames. The earliest investigations of hydrocarbon oxidation include the work of MondainMonval and Quanguin who discovered that streams of higher hydrocarbons and air at around 300°C produce organic peroxides including hydroperoxides in large yields. 86

9,1

47

88

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

200

300

400

900°K

189

500

600

TEMPERATURE, °C

FIG. 63. Oxygen consumption during passage of mixtures of various octanes and air through heated pyrex tube (Pope, Dykstra, and Edgar ). Tube diameter, 2.5 cm; constant flow. Contact times from 50 seconds at 200°C to 25 seconds at 650°C. 87

Cartlidge and Tipper have determined the yields and identities of peroxides from the oxidation of w-heptane, isoheptane (2,2,3-trimethyl butane), cyclohexane, nbutane and propane in flow reactors. As has been mentioned earlier, with propane no hydroperoxide but only oxyalkylperoxide derived from aldehydes and H 0 was obtained, which is in agreement with similar data by Pease and Harris and Egerton. This is relevant with respect to cool flame generation. Chain branching culminating in cool flame may occur via two possible reaction paths. One path involves reaction of hydroperoxide molecules ROOH with aldehyde molecules to yield etherlike mole­ cules of adduct that subsequently are attacked by free radicals and after such attack produce additional free radicals by double peroxidation and decomposition. The other path involves reaction of hydroperoxide radicals ROO with aldehyde molecules to yield free-radical adducts that are isomeric or even identical with free radicals of ether peroxides and instantly undergo double peroxidation and decomposition. It seems that with propane only the latter reaction path is operative whereas with the higher /z-alkanes both paths may be followed simultaneously. The latter reaction path is also the only possible one with ethane which, like propane, does not yield hydroxyperoxide in low-temperature oxidation. As was mentioned in Section A, ethane produces mostly formaldehyde and little acetalde­ hyde; thus, as shown in Fig. 23, the domain of cool flame and two-stage ignition is 46

2

79

2

80

190

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

only marginally developed but becomes a large explosion peninsula on addition of very small quantities of higher aldehydes to the ethane-oxygen mixture. This is documented in detail by data of Bone and Hill on the progress of the reaction of a C H H + 0 mixture in a silica vessel at 313°C and 695 mm Hg. There was an induction period of 26 min followed by gradual accumulation of reaction products as shown in Table 12. It is seen that the aldehyde yield is small and consists mostly of formaldehyde. Bone and Hill experimented with adding various gases in standard quantity of 1%, or about 3 mm Hg at 0°C, to the mixture. The induction period was shortened by H 0 which testifies to the role of the vessel surface, viz., reactions (3) and (6) of the mechanism in Table 9. It was also shortened or even eliminated by ethyl alcohol, formaldehyde, iodine, N 0 , and other additives. To the astonishment of the investigators, acetaldehyde produced an explosion. The overly rich mixture of C H + 0 was too weak to shatter the vessel but there was flame and a heavy deposit of carbon black. Table 12 shows that in the normal progress of the reaction the acetaldehyde yield rose to about 2 mm Hg (0°C) as compared to 3 mm Hg (0°C) for the aldehyde added at the start of the experiments, but there was also a yield ranging from about 5 to 7 mm Hg (0°C) of formaldehyde, and this probably prevented the reaction from becoming explosive. 49

2

6

2

2

2

2

6

2

F. ETHYLENE, ACETYLENE, AND AROMATICS

These hydrocarbons do not produce higher aldehydes and thus have explosion limits similar to methane and the third explosion limit of hydrogen governed by peroxide dissociation and thermal effects. Acetylene can decompose explosively into carbon and hydrogen and acetylene-oxygen mixtures are accordingly very shock-sensitive. To a lesser extent this also applies to ethylene.

TABLE 12 REACTION OF C H 2

6

+ 0

2

IN A SILICA VESSEL AT INITIALLY

313°C AND 695 MM

HG

ah

Time, min

26

32

34

41

60

C H o CO co H C H 0 HCHO CH CHO

161 167 1.2 0.1 0 0 0 0

149 150 12 2 0 0.2 4.2 1.4

139 132 23 3 6 0.5 5.5 1.9

108 69 59 10 6 1.0 6.7 2.3

81 1 100 20 5 0 4.3 0

2

6

2

2

2

2

4

3

3

"From Bone and Hill. *The tabulated data are partial pressures in mm Hg normalized to 0°C. The H 0 yield is not shown. C H 0 represents alkoxyperoxide. 49

2

2

4

3

4.

191

900°K

HIGHER HYDROCARBONS A N D OXYGEN BELOW

Systematic data on explosion limits are available for some aromatics, whereas for ethylene and acetylene the slow reaction with oxygen has been of primary interest. Ethylene. Ethylene oxidation has been studied by several authors. The char­ acteristics of the reaction are analogous to those of other hydrocarbons. An induction period is observed; the reaction rate is dependent on a power of the ethylene concen­ tration larger than 1 (the second power according to Thompson and Hinshelwood) and a power of the oxygen concentration equal to or less than 1; the reaction is inhibited by packing the vessel, consistent with its chain nature. Chemical analyses of the reaction products were made by Bone, Haffher, and Ranee, and by Lenher. The latter's work will be summarized. Experiments were performed by a flow method at atmospheric pressure in a Pyrex tube 2 cm in diameter and 20 cm long and in other tubes 5.5 cm in diameter and 40 cm long made of clean Pyrex, Pyrex coated with K S i 0 and KC1, quartz, stainless steel, and aluminum. A typical and repro­ ducible run in the small tube with 360 cm of a 1:1 ethylene-oxygen mixture at 400°C reacting in 75 sec gave the following products: 102.5 cm of CO, 11.4 cm of C 0 , 2.9 cm of H , and 0.1689 gm of condensibles consisting of ethylene oxide, ethylene glycol, glyoxal, formaldehyde, formic acid, and water. No evidence was obtained for the presence of acetaldehyde, glycolic aldehyde, glycolic acid, or oxalic acid. The experiments in the larger tube are summarized in Table 13. It was established that formic acid was generated by decomposition of dioxydimethyl peroxide which also produces hydrogen. The presence of H 0 was established in separate experi­ ments and this explains the presence of dioxydimethyl peroxide, which is formed from H 0 and formaldehyde. No peroxide was found in the salt-coated Pyrex tubes or in the metal tubes. 89

2

8

3

3

3

3

2

2

2

2

2

2

TABLE 1 3 REACTION OF ETHYLENE AND OXYGEN IN 5 . 5 cm

x 4 0 CM TUBES IN A SINGLE PASS;

YIELDS OF PRINCIPAL PRODUCTS

Per cent of C H consumed which goes to

Tube

Per cent of C H consumed

CO, C 0 and W

Pyrex Pyrex, 3 % steam added Pyrex, 3 % steam added Pyrex, KCl-coated Pyrex, K Si0 -coated Fused silica Stainless steel Aluminum

9.8 9.9 9.0 9.1 5.4 9.3 4.6 5.5

51.2 65.0 55.5 58.0 58.6 57.0 52.0 89.8

2

2

3

"From Lenher.

89

^Mostly C O . T

C

=

350°C.

Τ

=

c

4

365°C; 8 5 % C H , 15% 2

4

0

2

0 . 2

2

4

HCHO

(CH ) 0

HCOOH

10.2 11.6 10.8 27.7 31.7 27.1 41.8 9.6

13.7 14.7 14.4 13.5 9.7 11.7 5.1 0.0

24.8 8.5 19.2 0.8 0.0 4.3 1.1 0.8

2

2

192

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

Bone, Haffner, and Ranee found that the induction period is shortened and can practically be eliminated by addition of acetaldehyde. The main reaction is not noticeably accelerated by this substance, which agrees with similar observations of Steacie and Plewes. The main reaction chain may be visualized to yield CH CH · OOH as 2

Free radical + C H - > CH CH 2

4

CH CHOO

2

C 2

2

" > CH CHOOH + CH CH, 4

2

2

and the appearance of formaldehyde is most simply understood by assuming the reaction CH CHOOH = 2CH 0. 2

2

The formaldehyde is oxidized as discussed earlier, and the ethylene-oxygen and formaldehyde-oxygen systems thus appear closely interlinked in a manner reminis­ cent of the methane-oxygen system. This correspondence between the ethylene and methane systems has been emphasized by Norrish and Harding ' who arrive at a theoretical rate equation analogous to the equation for methane-oxygen and report experimental confirmation of the predicted diameter, pressure, and mixture compo­ sition dependencies. It was shown that ethylene oxide does not noticeably react with oxygen under the experimental conditions of Table 13, so that this substance appears to be a final product of the chain reaction rather than an intermediate product. Its formation may be explained by oxidation of formaldehyde to performic acid and reaction of performic acid with ethylene according to 33 90

Acetylene. The oxidation of acetylene appears to be unrelated to the reaction in other hydrocrabon-oxygen systems, except that traces of acetylene are frequently found among the products of partial oxidation of higher hydrocarbons. Early studies by Bone and Andrew in a temperature range of 200 to 350°C showed that CO and formaldehyde are the principal products. Kistiakowsky and Lenher studied the reaction in a single-pass flow system and analyzed the exit gas for oxides of carbon, H , and condensible products. Comparison of runs in empty and packed reaction tubes established the occurrence of a homogeneous chain reaction preceded by an induction period, and a slow heterogeneous reaction whose rate depended on the treatment of the surface of the vessel. The rate of the chain reaction was found to be proportional to the square of the acetylene concentration and practically independent of oxygen. Glyoxal was detected among the condensible products together with formic acid and formaldehyde. Of the oxides of carbon, CO was the main product. In the packed vessel where the reaction was heterogeneous, C 0 was the main product. Spence and Kistiakowsky made further studies in a closed circulatory system in which the condensible products were continuously removed by a freezing trap. They confirm the essential results of the former observations, particularly the 92

93

2

2

94

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

193

dependence of the rate on the square of the acetylene concentration and the kinetic ineffectiveness of oxygen if its concentration is not small compared to acetylene. Their results even suggest a small inhibitory effect of large amounts of oxygen. Addition of nitrogen had no or perhaps a slight retarding effect. The authors deter­ mined the rate by observing the initial rate of pressure rise. The decrease of the rate of pressure rise as the reaction proceeds corresponds fairly well to the consumption of acetylene assuming the rate to be proportional to the square of the acetylene concentration. Steacie and MacDonald investigated the reaction in closed silica and Pyrex vessels. The reaction was allowed to proceed for a given time when the products were withdrawn and analyzed for oxides of carbon and residual reactants. The degree of completion of reaction was determined from the total amount of carbon in the form of oxides of carbon and condensibles, and the residual acetylene. In agreement with earlier work the rate was found to be virtually independent of oxygen and of added inert gas such as nitrogen. The rate was found to be proportional to somewhat more than the square of the acetylene concentration, the calculated ex­ ponent being 2.7. Of interest were experiments on the addition of glyoxal and formaldehyde. The former produced a slight, if any, accelerating effect, whereas formaldehyde markedly slowed down the reaction. Spence found a diameter de­ pendence of the rate resembling that for the methane-oxygen system. On decreasing the diameter of the vessesl from 20 to 6 mm, the rate decreased to only about onethird. With further reduction of the diameter from 6 to 4 mm, the rate suddenly decreased to about one-thirtieth of its original value. This result is confirmed by the more extensive data of Norrish and Reagh, who determined the diameter effect at various pressures and obtained a family of curves analogous to that for methane. 95

96

26

On the basis of these facts it appears that the kinetics of acetylene oxidation is essentially a steady-state problem of the type encountered in the methane-oxygen system. Thus, an intermediate reaction product must be assumed that plays a role analogous to formaldehyde in the methane-oxygen system. Unlike the steady-state concentration of formaldehyde in the latter system, the concentration of the present intermediate must be independent of oxygen. We propose that the intermediate substance in glyoxal and that it is formed in the main chain, viz., I HC i CH + CHO · CO = CHOCHO + HC ! C — HCC— + 0

2

= CHOCO

I

and that glyoxal is destroyed by I CHO-CO + 0

2

+ CHOCHO = HCO(OOH) + 2CO + CHO.

Assuming that the radical CHO : CO is destroyed at the surface CHO · CO

a c e

> destruction,

194

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

and assuming as before that the radical CHO does not continue chains, one obtains for the reaction rate an expression analogous to the equation for methane, with the exception that the oxygen factor in the numerator is missing as is required by the facts. Benzene and Other Aromatics. According to Hinshelwood and Fort the oxi­ dation of benzene takes a course similar to other hydrocarbons; that is, the main reaction is preceded by an induction period during which the rate gradually increases. Studies of the reaction rate of a stoichiometric mixture of benzene and oxygen at atmospheric pressure in pyrex vessels were made by Amiel. The temperatures ranged from 380 to 565°C. The striking observation was made that over a large part of the total reaction period the rate of the reaction, expressed as percentage of carbon converted to CO and C 0 per hour, remained constant. Small amounts of phenol and benzoquinine, but no peroxides, were found among the reaction products. The ignition and slow reaction of mixtures of oxygen with benzene and its monoalkyl derivatives were also investigated by Burgoyne, Tang, and Newitt. Figure 64 shows ignition limits of mixtures of benzene, toluene, ethylbenzene, and propylbenzene with air. For comparison, a curve of methane is included. The fuel content of these mixtures 97

98

2

99

4.

HIGHER HYDROCARBONS AND OXYGEN BELOW

900°K

195

was 1.85 stoichiometric. It is seen that under such conditions a low-pressure peninsula and a weak cool flame is observed for w-propylbenzene only. In a higher pressure range the phenomenon might possibly be found with ethylbenzene. For benzene itself, as previously stated, no cool flame region has ever been observed. We mention here that compression-ignition experiments of Taylor et al. with benzene show smooth curves of pressure rise with no trace of two-stage ignition. Comparison of the methane and benzene curves suggests that the oxidizability of benzene is relatively low. However, measurements of Jost and Teichmann of ignition lags of benzene and aliphatic hydrocarbons in a rapid-compression apparatus show that the oxidiza­ bility of benzene increases more rapidly with temperature than the aliphatic hydro­ carbons. This is illustrated in Fig. 65. In the slow reaction of a mixture of 205 mm C H and 425 mm 0 at 487°C in a quartz vessel, Burgoyne found that the main products were CO, C 0 , and phenol; small amounts of formaldehyde, peroxides other than peracids, ethylene, acetylene, paraffins, hydrogen, and acids were also detected. The acids appeared to be aliphatic in character and included maleic and formic acids. The data show that during the reaction the ratio of CO and C 0 remains fairly constant between 2.4 and 3.5. The products obtained from aromatics with substituted aliphatic side chains are more complex, as may be expected, since they include products of partial oxidation of the side chain. 15

70

6

6

2

2

2

10

.01

.00 1 550

500

450

400

350

RECIPROCAL OF T E M P E R A T U R E ,

300°

C.

γ

FIG. 6 5 . Ignition lags for stoichiometric mixtures of benzene, isooctane and «-heptane as function of temperature at end of compression (uncorrected for cooling). Ε = activation energy (Jost and Teichmann ). 70

196

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

5. Engine Knock A.

DESCRIPTION OF THE PHENOMENON

The temperatures and pressures to which fuel-air mixtures have been subjected in rapid-compression experiments, such as those of Rogener, Jost and Teichmann, Scheuermeyer and Steigerwald, and Taylor and co-workers, are of the order of magnitude encountered in the Otto cycle engine. The important difference between the compression experiments and the engine is that in the latter, compression con­ tinues after the piston compression stroke is completed; this is due to the volume displacement of the spark-initiated flame, which begins shortly before the piston reaches top dead center. The unburned gas ahead of the flame is in fact subjected to higher temperatures and pressure than have thus far been attained in rapid-compres­ sion experiments. Consequently, the induction periods τι and τ that in many instances in the latter experiments have been found to be as low as 10" sec, may become of the order of 10" sec or less in the engine. Since the spark-initiated normal flame cannot complete its travel through the cylinder head in such short times, it is understandable that in some residual unburned fraction of the charge the reactions of the Ti and τ regimes will take their course. The disturbances caused by the greatly accelerated combustion of the charge in the end zone lead to the formation of shock waves and an increase of heat transfer from the burned gases to the engine. In airplane engines which are designed for low weight and high power, a substantial increase of heat transferred to the walls of the combustion chamber causes dangerous temperature rise and failure by overheating; in more liberally dimensioned engines of the auto­ mobile type the consequences are not necessarily serious. High-speed schlieren photographs have permitted a detailed visualization of the processes occurring in the engine h e a d . In these experiments a single-cylinder engine of the two-stroke, sleeve-valve type was used with a full-view thick glass window at the top of the combustion chamber. The piston top was ground to a schlieren mirror, and the photographs were taken through the window by means of externally supplied light that was reflected from the piston top back to the camera. In order to prevent contamination of the mirror and window, the engine was operated for only one power cycle. This was accomplished by injecting the fuel, w-heptane, directly into the cylinder, whose temperature was maintained at 210°F by externally heated glycerin. The engine was driven to an operating speed of 600 rpm by an electric motor. Air was supplied at a pressure of 34 in. Hg absolute and a temperature of 300Έ The compression ratio was 7. The fuel was injected early in the cycle to permit adequate vaporization. The spark passed 20° crank angle before top dead center. The fuel-air ratio was not known but was adjusted to cause fairly heavy knock starting early in the combustion process. Two high-speed cameras were used, one capable of taking pictures at the rate of 40,000 frames per second and the other at the rate of 500,000 frames per second. The 40,000-frame camera operated on the 69

70

72

75

2

3

4

2

57100

5.

ENGINE KNOCK

197

principle of a rotating film with a novel optical system, part moving and part stationary. In the 500,000-frame camera the film was stationary and a sequence of images was produced by an ingeniously designed optical system. Design details of the camera may be found in the original reports. The 40,000-frame camera covered the cycle from the spark ignition to well beyond the end of the combustion process. The 500,000-frame camera was used to resolve the phenomena occurring during knock. We produce here a part of the cycle commencing 1.8 msec after passage of the spark (Fig. 66). Up to this point of the cycle the flame has progressed as a turbulent combustion wave from the upper left of the field of view until it occupies approxi­ mately one-third of the field as shown in frame G-l. The hot flame gas stands out as a dark mottled area against the lighter field occupied by the unburned gas mixture. The four dark spots are screw heads. The flame progresses smoothly across the chamber and at frame H-ll the first indications of a disturbance in the center of the end zone are discernible in the original photographs. This develops until it becomes plainly visible in frame 1-6, whence a dark area spreads until it occupies the upper and central part of the end zone. A second disturbance is seen to develop in the lower part of the end zone from frame 1-8 onward, traveling upward and to the right until it merges with the other disturbance and fills the entire end zone at frame J-7. These disturbances do not appear to interfere materially with the progress of the normal flame, but since they are capable of changing the illumination in the field of vision it must be concluded that they produce density or temperature gradients. We believe, therefore, with Miller, that they are cool flames which, as may be judged from previously quoted work, release sufficient heat to produce schlieren effects.* Con­ cerning the appearance of these pictures it is noted that the camera views a depth of gas from the window to the piston head and that in the turbulent normal flame as well as in the cool flame region, the optical path leads through an irregular succession of zones of higher and lower density. In the normal flame these zones are formed by the irregularity of the boundary between the burned and unburned gases (pages 419423), and in the cool flame such inhomogeneities of density may be expected to result from the irregularity and spottiness of the flame origin, exemplified by the photographs in Figs. 50 and 51. The fact that these zones appear dark is a matter of optical arrangement. In the burned gas behind the turbulent combustion wave the field is bright and uniform corresponding to the uniform density prevailing there. 101

102

Beyond frame J-7 one is still able to distinguish the front of the normal flame which progresses without recognizable acceleration into the cool-flame region. The change of dlumination at frame J-12 is traceable to a schlieren reversal occasioned by the turning on of an additional light source to operate the 500,000 frames-persecond-camera. This new light source also produced the timing marks which appear from frame J-12 on. The latter frame is practically identical with frame J-ll except for this reversal, and with frame K-l in which the photographic contrast is deepened. *In the original reports this phase of the combustion sequence is referred to as auto-ignition.

199

5. ENGINE KNOCK

In the lower right area of frame K-2 there appears to be the first indication of onset of violent knock, which in the engineering literature is commonly referred to as detonation and which we believe to be second-stage ignition. This disturbance becomes plainly visible in frame K-3, but frame K-4 and subsequent frames are blurred due to passage of shock waves. These shock waves are made visible by the high time resolution of the 500,000-frame camera and are shown in Fig. 67. Only selected frames of this series are shown. Frame 5 corresponds to frame J-12 except for schlieren reversal in the latter; frame 44 corresponds roughly to frame K-3; frame 162 corresponds roughly to frame K-12. The waves A and Β in frames 44, 48 and 51 travel through the burned gas at speeds of approximately 1300 and 1700 m/sec. Wave C which develops later in frame 57 moves at a speed of approximately 1500 m/sec between frames 57 and 64. Reflections of waves A and C are shown in the remaining frames. The finer details of these motions can only be seen when the films are viewed as motion pictures. At some time following the onset of knock and during the passage of the waves, a bright luminosity appears which is interpreted as incandescent carbon. This is indicated in frame K-8. At a relatively much later stage, not shown in this sequence, there are indications of dark patches which are interpreted as soot formation. The appearance of free carbon in the end gas appears to be somewhat at variance with

FRAME

FRAME

FRAME

57

64

122

128

156

162

FIG. 67. Schlieren photographs at 500,000 frames per second showing shock waves formed during engine knock. Frame 5 corresponds to frame J-12 of previous figure (Male ). 100

200

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

the observation of Rassweiler and Withrow that in the emission spectrum of the knocking charge the bands of C - C and C H are rather weaker than in the emission of the normal flame. But this observation is not necessarily contradictory as emission spectra comprise only a very small fraction of the reacting molecules and their intensities may be unrelated to the main chemical process. The interpretation of knock as a rapid chemical reaction in the end gas preceded by relatively slow chemical changes in the charge was already established in a number of earlier investigations. Several of the investigators recognized the passage of high-velocity waves. Schnauffer reports velocities of about 300 m/sec; Surreys, about 500 m/sec; and Sokolik and Voinov as high as 2000 m/sec. 103

104

B. SPECTROSCOPIC AND CHEMICAL INVESTIGATION OF THE END GAS

Information on the chemical changes occurring in the end gas is furnished by spectroscopic studies and by analysis of samples withdrawn at predetermined stages of the cycle. Rassweiler and Withrow obtained absorption spectra by passing a continuous light source through two quartz windows on opposite sides of the combustion chamber. The windows were so arranged that the end gas came under observation. From the photographs it was possible to identify absorption bands of formaldehyde. A number of facts are of interest. Formaldehyde is always detected in the noninflamed charge which is about to knock. With increasing knock intensity, the formaldehyde absorption bands increase in intensity, and it is immaterial whether the knock is brought about by change of composition of the mixture (especially by leaning an over-rich mixture), by advancing the spark (which increases the pressure in the end gas), by preheating the mixture, by decreasing the engine speed (which decreases turbulence and therefore the normal flame speed), or by adding a proknock compound like isopropylnitrite. Formaldehyde also appears under nonknocking conditions, but under conditions where formaldehyde is not detectable knock is never observed. These facts are fully consistent with the previously discussed role of formaldehyde in the τ !-regime mechanism where formaldehyde is found to be a reaction product and an inhibitor rather than a promoter of the reaction. The appearance of formal­ dehyde is, therefore, only an indication that the reactions leading to second-stage ignition (knock) are occurring; and the increasing intensity of the formaldehyde bands merely shows that the oxygen attack on the fuel has progressed further. If knock is suppressed by addition of Pb(Et) formaldehyde always remains detectable, in accord with Rogener's observation that this compound increases the induction period T but has no noticeable effect on τι. Analyses of samples withdrawn from the engine are reported by Egerton and co­ workers. For the details of the technically interesting apparatus and the operating conditions of the engine the reader is referred to the original paper. We are interested in their finding that chemical reaction in the end zone before arrival of the flame is 105

4

69

2

106

5. ENGINE KNOCK

201

not inconsiderable. Formaldehydes and higher aldehydes were found in concentra­ tions up to 1 part in 150. Under their operating conditions some N 0 was formed, but they also were able to detect organic peroxides in concentrations of the order required to induce knocking by added peroxides. It was further shown that aldehydes were formed as a result of mechanical compression alone when the cycle was operated without ignition. Experiments of the latter type were also reported by Damkohler and Eggersgluss using a fuel consisting mainly of paraffins and about 20% naphthenes. They determined quantitatively C 0 , H 0 , acids, formaldehyde, acetal­ dehyde, and higher aldehydes. Peroxides were also found though not further identified. From their data which include measurements of oxygen consumption and water and heat generation in relation to quantities of reaction products, they conclude that the major part of formaldehyde is not formed by oxidative degradation of the carbon chains but is probably formed in radical chains involving original hydrocarbon molecules. This is consistent with the scheme of oxygen attack on radicals discussed earlier. 2

107

2

C.

2

EFFECT OF MOLECULAR STRUCTURE AND ADDITIVES

If an engine is operated under standardized conditions with various fuels and if only one knock-controlling parameter is adjusted so that incipient knock is obtained, the various fuels fall into a pattern that parallels that obtained on the basis of various oxidizability criteria mentioned earlier. Such a parameter is the compression ratio. Boyd and co-workers determined the critical compression ratios for incipient knock of a larger number of fuels in a variable compression engine similar to the CFR engine. The operating conditions were 600 rpm, jacket water 100°C full load, mixture ratio and spark timing for maximum power. In Table 14 a selected list is given of compounds tested, their critical compression ratios (ccr) and the increase of Δ of the ccr on adding 1 cc of Pb(Et) to a gallon of the fuel. Under some conditions Pb(Et) is found to be proknock rather than an antiknock. A number of regularities appear from the table, as pointed out by Jost. 108

4

4

109

(a) In the series of Η-paraffins, knock resistance increases with decreasing length of the carbon chain. (b) Olefins show a similar behavior. Since the position of the double bond for molecules of equal number of carbon atoms introduces differences, it is necessary to base the comparison on a fixed position of the double bond. For example, among the series of α-olefins the rule under (a) is immediately apparent. Displacement of the double bond toward the center of the molecule increases the knock resistance. For the acetylene series, the data are insufficient for drawing conclusions. Comparison of paraffins and olefins shows that the decrease of knock resistance with increasing numbers of carbon atoms does not occur in similar increments. Consequently, the curves for these series cross each other approximately at butane. Above butane

202

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN TABLE 14 CRITICAL COMPRESSION RATIOS (CCR) OF VARIOUS FUELS AND CHANGE (POSITIVE OR NEGATIVE) OF CCR BY ADDITION OF 1 CM Pb(Et) το 1 GAL OF F U E L 3

0

4

Paraffins ccr >15 14.0 12.0 6.4 8.9 3.8 5.7 3.3 2.8 3.9 5.0 13.0 12.0 7.7 3.3 3.9

Methane Ethane Propane n-Butane Isobutane «-Pentane 2-Methylbutane w-Hexane M-Heptane 3-Ethylpentane 2,4-Dimethylpentane 2,2,3-Trimethylbutane 2,2,3-Trimethy lpentane 2,2,4-Trimethylpentane 2,7-Dimethyloctane 3,4-Diethylhexane

Acer — — —

— — 0.50 0.95 0.20 0.20 0.20 0.80

— — 2.10 0.20 0.30

Olefins and Diolefins Ethylene Propylene 1-Pentene 2-Pentene 2-Methyl-2-butene 2,3-Dimethy lbutadiene 2,4-Hexadiene 1,5-Hexadiene 1-Hexene 2-Hexene 1-Heptene 3-Heptene 3-Ethyl-2-pentene 2,2-Dimethy 1-4-pentene 2,4-Dimethyl-2-pentene 2-Methyl-5-hexene 3-Methyl-5-hexene 2,2,3-Trimethy 1-3-butene 1-Octene 2,2,4-Trimethyl-3-pentene 2,2,4-Trimethyl-4-pentene

— —

8.5 8.4 5.8 7.0 7.0 8.6 6.6 4.8 4.6 5.4 3.7 4.9 6.6 10.0 8.8 4.7 5.0 12.6 3.4 10.0 11.3

0.15 0.35 0.25

4.6 4.9 3.4 4.0

0.33 0.10 0.10

0.30 0.50 0.70 0.10 0.10 0.25

— — 0.25 0.80 0.50 — 0.70 0.25 0.20

—

Acetylenes Acetylene 1-Heptine 3-Heptine 2-Octine

—

5.

203

ENGINE KNOCK

TABLE 14 (Continued) Naphthenes 10.8 Cyclopentane 3.9 Ethylcyclopentane 4.2 1,3-Dimethylcyclopentane 3.6 1,3-Methylethylcyclopentane 2.8 rc-Amylcyclopentane 4.5 Cyclohexane 4.6 Methylcyclohexane 5.1 1,2-Dimethylcyclohexane 4.4 1,3-Dimethylcyclohexane 4.3 1,4-Dimethylcyclohexane 3.8 Ethylcyclohexane 4.3 1,2-MethylethyIcyclohexane 3.8 1,3-Methylethylcyclohexane 3.7 1,4-Methylethylcyclohexane 3.3 H-Butylcyclohexane 3.6 sec-Butylcyclohexane 3.6 1,2-Methyl-H-propylcyclohexane 3.4 1,3-Methyl-«-propylcyclohexane 3.3 1,4-Methyl-n-propylcyclohexane 4.0 1,4-Methyl isopropylcyclohexane 3.2 1,3-Diethylcyclohexane 3.3 1,4-Diethylcyclohexane 3.1 fl-Diethylcyclohexane 3.3 Isoamylcyclohexane 4.2 teri-Amylcyclohexane 3.3 1,2-Methyl-n-butylcyclohexane 3.3 1,3-Methyl-n-butylcyclohexane 3.2 1,4-Methyl-n-butylcyclohexane 3.2 1,2-Methyl-«-amylcyclohexane 3.6 Decahydronaphthalene Unsaturated Cyclic Hydrocarbons 10.9 Cyclopentadiene 9.2 Dimethyl fulvene 11.2 Indene 11.0 Dicyclopentadiene 7.9 Cyclopentene 5.9 1,3-Cyclohexadiene 4.8 Cyclohexene 4.8 1 -Methylcyclohexene 5.9 Dipentene Aromatics >15 Benzene 13.6 Toluene 10.5 Ethylbenzene 9.6 6>-Xylene 13.6 m-Xylene

2.70

— — — — 0.65 0.30 0.35 0.21

— — 0.16 0.12 0.13

— — 0.12 0.12 0.12 0.26

— — — — — 0.10 0.10 0.10 0.10 0.13 -0.90 -0.13 -0.10 -0.30 0.20 -0.02 0.20

— 0.25

__ — 2.0

— —

204

IV.

THE REACTION BETWEEN HYDROCARBONS A N D

TABLE 14

(Continued)

p-Xylene /r-Propylbenzene Isopropylbenzene Mesitylene n-Butylbenzene sec-Butylbenzene tert-Butylbenzene /7-Cymene (1,4-methylisopropylbenzene) 1,3-Diethylbenzene 1,4-Diethylbenzene teri-Amylbenzene Phenylacetylene Phenylethylene Benzylacetylene Methylphenylacetylene Phenylbutadiene Trimethylphenylallene a

OXYGEN

14.2 10.1 11.9 14.8 7.7 10.1 12.5 11.1 10.8 9.3 12.1 12.4 14.0 7.4 11.8 9.5 8.3

— — — — —

— — 1.0 — — 2.0 -0.80 — 0.12 -0.30 0.00 -0.20

From Boyd et al.

introduction of a double or triple bond generally increases knock resistance for otherwise the same structure and number of carbon atoms. (c) In any series knock resistance increases as the hydrocarbon chains become more branched. These rules agree well with the rules of oxidizability found by other criteria. In Fig. 68 are plotted values of ccr versus Acer for a number of representative compounds in Table 14. The figure shows that for any critical compression ratio the increase due to added Pb(Et) is largest in the paraffin and naphthene series. Aromatics with saturated side chains are affected somewhat less, while α-olefins, diolefins, and acetylenes are hardly affected at all. Some aromatics and unsaturated cycles show a decrease on addition of Pb(Et) . For comparison the gasoline range is indicated by the circle. In explanation of the different lead susceptibilities of the various fuel groups Jost and von Muffling advance the following suggestion. It is probable that with regard to the initiation of chains olefins are more effective than paraffins. Thus, for example, peroxidation of the double bond and subsequent bond fission may occur so that under otherwise comparable conditions more chains are initiated in an olefin-oxygen system than in a paraffin-oxygen system. However, olefins are less oxidizable, viz., possess higher knock resistance, because the double bonds act as chain breakers. If it is the property of the antiknock compound to break chains, it is clear that the effect will be the larger the less frequent chain breaking occurs in the absence of the compound. Therefore, it affects the paraffins and saturated naphthenes more than 4

4

110

5. ENGINE KNOCK

205

14r

-0.8

-0.4 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 INCREASE IN COMPRESSION RATIO F O R 1 CC L E A D T E T R A E T H Y L P E R GALLON FIG . 68. Relative antiknock effect of lead tetraethyl in various types of hydrocarbons (Lovell, Campbell, and Boyd ). Dotted curve calculated by Jost and von Muffling. 108

110

the corresponding unsaturates. If it is granted further that PB(Et) not only destroys chains (by removal of peroxides) but also initiates chains (by dissociation into free radicals), it becomes understandable that in some cases where the chains are already very short and rapid reaction depends on a high rate of chain initiation, the effect of Pb(Et) is reversed. Jost, von Muffling, and Rohrmann have examined the possibility of a reactionkinetic interpretation of the values of Acer. They suggest a rather simple approach to the problem. Lead tetraethyl prevents knock because it decreases the average reaction rate; increase of the compression ratio by the amount Acer restores knock because the inhibiting effect of lead on the reaction is compensated by the higher temperature and pressure of the mixture. Assuming as a first approximation the reaction rate to be an Arrhenius function of temperature and not significantly de­ pendent on pressure, they derive the following relation between ccr and Acer: 4

4

111

Acer = const x (ccr) , 7

206

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

where 7 is the ratio of specific heats c lc . The constant is in principle calculable from reaction-kinetic data: it is found to be approximately equal to 4.57δΓ / E(y — 1), where δ is the logarithm of the ratio of reaction velocities before and after addition of lead tetraethyl; T is the temperature before compression, and Ε is the activation energy of the reaction. From our present viewpoint it appears that these considerations apply only insofar as τι is the larger part of the total induction period τ. The dotted curve in Fig. 68 is obtained from the equation with the value of the constant detenriined empirically to conform with the experimental points for paraffins and naphthenes. The fact that the experimental points cluster closely around the calculated curve indicates that the constant in the equation, and therefore the values δ and £ , are about the same for various members of this group of compounds. Of the thousands of compounds that have been investigated for their antiknock properties, lead tetraethyl, discovered by Midgley and Boyd in 1922, is the most effective. A sample of such compounds and some knock-resistant fuels used as additives is shown in Table 15. The table contains relative antiknock values from benzene to Pb(Et) expressed as reciprocal number of moles that cause the same antiknock effect as one mole of aniline. Concerning metallic antiknocks we mention the remark of Egerton that the metal must be oxidized, that it must preferably be molecularly dispersed, and that it must be capable of existing in several oxidation states. Thus, lead, thallium, and potassium, which in the vapor state are generally very effective antiknocks, form stable peroxides at high temperatures; sodium, which does not, is ineffective. The requirement that the metal must be oxidized is in apparent contradiction to the observation of Rassweiler and Withrow that, when knocking was eliminated by addition of Pb(Et) , absorption spectra of Pb, not PbO, could be observed in the end gas. This observation does not necessarily exclude the simultaneous presence of oxides of lead that escape detection both because of their low concentration and the weaker absorption bands of molecules compared to the line spectra of atoms. Fur­ thermore, free radicals formed from fuel molecules may be expected to constitute a powerful reducing agent for compounds such as lead oxide. With regard to the lead effect, the suggestion of Callendar that antiknock agents destroy peroxides appears to be most plausible. Following Egerton, one may imagine that the various oxidation states of lead are involved. The Pb(Et) by decomposition and reaction with oxygen may form P b 0 , which reacts destructively with organic peroxides forming PbO; the last is reduced to Pb by reaction with free radicals. There may also be a destructive reaction between Pb and peroxides leading to PbO, and P b 0 may be restored by reaction of oxygen with Pb or PbO. A number of chemical substances have been found to promote the knocking process. Among them are ozone, organic nitrites, and peroxides, particularly alkyl peroxides which are effective in very small concentrations in agreement with other observations on hydrocarbon-oxygen systems quoted earlier. Diethyl peroxide is considerably more effective than hydrogen peroxide, to produce the same knock p

v

0

0

112

4

114

4

115

4

2

2

116

117

5.

207

ENGINE KNOCK TABLE 1 5

RELATIVE EFFECTIVENESS OF ANTIKNOCK COMPOUNDS AND SOME ANTIKNOCK FUELS (BASED ON ANILINE =

Benzene Isooctane (2,2,4-trimethylpentane) Triphenylamine E t h y l alcohol Xylene D i m e t h y l aniline Diethylamine Aniline E t h y l iodide Toluidine Cadmium dimethyl m-Xylidine Triphenylarsine T i t a n i u m tetrachloride

.495 1.00 1.09 1.22 1.24 1.40 1.00

35 50 118

Lead t e t r a e t h y l From Calingaert.

0.085 .085 .090 .104 .142 .21

3.2 4.0 4.1 0.9 23.8 20.6

Tin tetraethyl S t a n n i c chloride D i e t h y l selenide B i s m u t h triethyl D i e t h y l telluride Nickel carhonyl Iron c a r h o n y l

a

1)

113

intensity a mole fraction of H 0 of 6 x 10 was found to be equivalent to a mole fraction of C H O O C H of 1.6 x 10" ; that is, the alkyl peroxide was about 40 times more effective. At the fairly high temperatures in the end gas preceding secondstage ignition, one may expect that 0 - 0 fission occurs to some extent with any peroxide, and if such fission leads to free radicals, the peroxide will be a knock promoter. It is nevertheless interesting that H 0 , which is formed in hydrocarbon oxidation, presumably in the oxidation of formaldehyde via performic acid is found to be considerably less effective than peroxides of the alkyl type. This again stresses the fact that the peroxide yields obtained from reacting hydrocarbon-oxygen mixtures are not necessarily representative of the active peroxides that are mainly responsible for chain initiation and chain branching, but constitute, in part, fairly unreactive intermediate products. In agreement with various observations mentioned earlier that acetaldehyde has only a moderate accelerating effect in the τι regime, this substance is found to be only a moderate knock promoter. The view has frequently been expressed in this chapter that formaldehyde tends to arrest the reaction in the τ ι regime; this harmonizes 4

2

2

5

2

5

2

5

2

117

2

208

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

with the observation that this substance has no knock-promoting properties and that, in fact, a motor could be run smoothly on pure formaldehyde. It will be recalled that formaldehyde does not produce cool flames. In contrast, acetaldehyde, which forms cool flames, produces knock in the motor. 117

References 1. D. T. A. Townend, L. L. Cohen, and M. R. Mandlekar, Proc Roy Soc, A146, 113 (1934); D. T. A. Townend and E. A. C. Chamberlain, ibid. A154, 95 (1936). 2. Ch. Κ. Westbrook and F. L. Dryer, "Eighteenth Symposium on Combustion," p. 749, The Com­ bustion Institute, 1981. 3. Ch. Κ. Westbrook and F. L. Dryer, Prog. Energy Combust. Sci. 10, 1-57 (1984). 4. M. B. Neumann and A. Serbinov, Phys. Z. (U.S.S.R.) 1, 536 (1932). 5. A. Sagulin, Z. Phys. Chem. Bl, 275 (1928). 6. H. A. Taylor and E. W. Riblett, J. Phys. Chem. 35, 2667 (1931). 7. A. Burcat, A. Lifshitz, K. Scheller, and G. B. Skinner, "Thirteenth Symposium on Combustion," p. 745, The Combustion Institute, 1971. 8. C. T. Bowman, Combustion & Flame 25, 343 (1975). 9. D. F Cooke, M. G. Dodson, and A. Williams, Combustion & Flame 16, 233 (1971). 10. Ch. Κ. Westbrook and F. L. Dryer, Combustion Science & Technology 20, 125 (1979). 11. Ch. Κ. Westbrook, Combustion Science & Technology 20, 5 (1979). 12. D. Aronowitz, R. J. Santoro, F. L. Dryer, and I. Glassman, "Seventeenth Symposium on Com­ bustion," p. 633, The Combustion Institute, 1979. 13. J. O. Hirschfelder and C. F. Curtiss, "Third Symposium on Combustion," p. 121, Williams & Wilkins, Baltimore, 1949. 14. C. Lund, Univ. of California, Lawrence Livermore Lab Report UCRL-52504, 1978. 15. W. H. Wiser and G. R. Hill, "Fifth Symposium on Combustion," p. 553, Reinhold, New York, 1955; Η. T. Henderson and G. R. Hill, J. Phys. Chem. 60, 874 (1956); M. Metghalchi and J. C. Keck, Paper presented at the Fall Meeting of the Eastern Section of the Combustion Institute, Nov. 10-11, Hartford, CT, 1977. 16. Unpublished. 17. E. G. E. Hawkins, "Organic Peroxides," pp. 12-13, Van Nostrand, Princeton, 1961. 18. T. A. Brabbs and R. S. Brokaw, "Fifteenth Symposium on Combustion," p. 893, The Combustion Institute, 1975. 19. S. W. Benson, Oxidation Communications, 2, 169 (1982). 20. R. R. Baldwin and R. W. Walker, Report, AFOSR 77-3215, 1979. 21. H. Yamazaki and R. J. Cventanovic, J. Chem. Phys. 41, 3703 (1964). 22. R. E. Huie and J. T. Herron, Prog. Reaction Kinetics, 8, 17 (1975). 23. A. G. McLain and C. J. Jachimowski, NASA Technical Note TN-D-8501, 1977. 24. M. Cathonnet, J. C. Boettner, and H. James, "Eighteenth Symposium on Combustion," p. 903, The Combustion Institute, 1981. 25. R. G. W. Norrish and S. G. Foord, Proc. Roy. Soc. A157, 503 (1936). 26. R. G. W. Norrish and J. D. Reagh, Proc. Roy. Soc. A176, 429 (1940). 27. W. A. Bone and J. B. Gardner, Proc. Roy. Soc. A154, 297 (1936). 28. W. A. Bone and R. E. Allum, Proc. Roy. Soc. A134, 578 (1932). 29. D. M. Newitt and J. B. Gardner, Proc. Roy. Soc. A154, 329 (1936). 30. D. M. Newitt and A. E. Haffner, Proc. Roy. Soc. A134, 591 (1932). 31. A. D. Walsh, "Cinétique et mécanisme des réactions d'inflammation et de combustion en phase

REFERENCES

209

gazeuse," Centre National de la Recherche Scientifique, Paris, 1948, discussion remark, p. 43; A. van Tiggelen, ibid, p. 44. 32. A. C. Baldwin and D. M. Golden, Chem. Phys. Letters 55, 350 (1978). 33. A. J. Harding and R. G. W. Norrish, Nature 163, 767 (1949). 34. R. W. G. Norrish and J. Wallace, Proc. Roy Soc. A145, 307 (1934). 35. D. W. E. Axford and R. G. W. Norrish, Proc. Roy. Soc. A192, 518 (1948). 36. R. Spence, J. Chem. Soc. 649 (1936). 37. F. F Snowden and D. W. G. Style, Trans. Faraday Soc. 35, 426 (1939). 38. I. A. Vardanyan, G. A. Sachayan, and A. B. Nalbandyan, Combustion and Flame 17, 315 (1971). 39. Cf. ref. 17, p. 139. 40. D. W. G. Style and D. Summers, Trans. Faraday Soc. 42, 388 (1946). 41. J. E. Bennett, B. Mile, and A. Thomas, "Eleventh Symposium on Combustion," p. 853, The Combustion Institute, 1967. 42. D. P. Dingledy and J. G. Calvert, J. Am. Chem. Soc. 85, 856 (1963); J. G. Calvert and W. C. Sleppy, ibid. 81,769(1959). 43. D. E. Hoare and A. D. Walsh, Trans. Faraday Soc. 53, 1102 (1957). 44. S. W. Benson, Prog. Energy Combust. Sci. 7, 125 (1981); Oxidation Communications, 2, 169 (1982). 45. S. W. Benson, "Thermochemical Kinetics," pp. 239-241, Wiley, New York, (1976). 46. J. Cartlidge and C. F. H. Tipper, Proc. Roy. Soc. A261, 388 (1961). 47. H. Bonner and C. F. H. Tipper, Combustion and Flame 9, 317, 387 (1965). 48. G. H. N. Chamberlain and A. D. Walsh, "Third Symposium on Combustion," p. 375, Williams and Wilkins, Baltimore, 1949. 49. W. A. Bone and S. G. Hill, Proc. Roy. Soc. A129, 434 (1930). 50. G. P. Kane, Proc. Roy. Soc. A167, 62 (1938). 51. M. Maccormac and D. T. A. Townend, J. Chem. Soc. 238 (1938). 52. Ε. V. Aivazov, N. P. Keyer, and M. B. Neumann, Acta Physicochim., U.R.S.S., 14, 201 (1941). 53. W. H. Perkin, J. Chem. Soc. 41, 363 (1882); G. S. Turpin, Brit. Assoc. Rpt. 75, 776 (1890); H. B. Dixon, J. Chem. Soc. 75, 600 (1899); Rev. trav. chim. 46, 305 (1925); A. Smithells, Brit. Assoc. Rpt. 93, 469, (1907); F. Gill, E. W. Mardles, and H. C. Tett, Trans. Faraday Soc. 24, 574 (1928). 54. M. Prettre, P. Dumanois, and P. Laffitte, Compt. rend. 191, 329, 414 (1930). M. Prettre, Ann. office natl. combustibles liquides 6, 7, 269, 533 (1931); 7, 699 (1932); 11, 669 (1936); Bull. soc. chim. France 51, 1132 (1932); "Science of Petroleum," Vol. 4, p. 295, Oxford, 1938. 55. H. A. Beatty and G. Edgar, J. Am. Chem. Soc. 56, 112 (1934). 56. M. B. Neumann and Ε. V. Aivazov, Nature 135, 655 (1935); Acta Physicochim. U.R.S.S. 4, 575 (1936); ibid. 6,279(1937). 57. C. D. Miller, Soc. Automotive Engrs. Quart. Trans. 1, 98 (1947); cf. Section 5 of this chapter. 58. A. G. White, J. Chem. Soc. p. 498 (1927). 59. J. E. C. Topps and D. T. A. Townend, Trans. Faraday Soc. 42, 345 (1946). Kate Spence and D. T. A. Townend, "Cinétique et mécanisme des réactions d'inflammation et de combustion en phase gazeuse," p. 113, Centre National de la Recherche scientifique, Paris, 1948. D. T. A. Townend and E. A. C. Chamberlain, Proc. Roy. Soc. (London) A158, 415 (1937). M. S. Hsieh and D. T. A. Townend, /. Chem. Soc. 332, 337, 341 (1939). M. Maccormac and D. T. A. Townend, J. Chem. Soc. 143, 151 (1940). Kate Spence and D. T. A. Townend, Nature 155, 339 (1945); "Third Symposium on Combustion and Flame and Explosion Phenomena," p. 404, Williams and Wilkins, Baltimore, 1949. 60. C. F. H. Tipper, Quart Rev. Chem. Soc. London 11, 313 (1957). 61. S. W. Benson, J. Am. Chem. Soc. 87, 972 (1965); Adv. Chem. 75, 76 (1968). 62. G. P. Kane and D. T. A. Townend, Proc. Roy. Soc. A160, 174 (1937). 63. M. Prettre, "Third Symposium on Combustion and Flame and Explosion Phenomena," p. 397, Williams and Wilklins, Baltimore, 1949.

210

IV. THE REACTION BETWEEN HYDROCARBONS AND OXYGEN

64. H. T. Tizard and D. R. Pye, Phil. Mag. 44 (VI), 79 (1922); 1 (VII), 1904 (1926). 65. Ε. V. Aivazov and M. B. Neumann, Z. Physik. Chem. B33, 349 (1936). 66. M. B. Neumann and P. Tutakin, Compt. rend. acad. sci., (U.R.S.S.) 4, 122 (1936). 67. R. N. Pease, Chem. Rev. 21, 279 (1937). 68. E. A. Andreev, Acta Physiocochim. (U.R.S.S.) 6, 57 (1937). 69. H. Rogener (in collaboration with W. Jost) U.S. Govt. Tech. Oil Mission microfilm reel 242; Photoduplication Service, Library of Congress (1945); Z. Elektrochem. 53, 389 (1949). 70. W. Jost and H. Teichmann, Naturwissenschaften 27, 318 (1939); Z. Elektrochem. 47, 262, 297 (1941). 71. W. Jost, "Third Symposium on Combustion and Flame and Explosion Phenomena," p. 424, Williams and Wilkins, Baltimore, 1949. 72. M. Scheuermeyer and H. Steigerwald, Motortech. Zeitschrift, Stuttgart, Vols. 8 - 9 (1943); cf. F. A. F. Schmidt, "Verbrennungsmotoren," Springer, Berlin, 2nd ed. with supplements, FIAT (U.S.) (Library of Congress) Rept. 709 (1946). 73. D. T. A. Townend and M. R. Mandlekar, Proc. Roy. Soc. A143, 168 (1934). 74. D. T. A. Townend and M. R. Mandlekar, Proc. Roy. Soc. A141, 484 (1933). 75. C. F. Taylor, E. S. Taylor, J. C. Livengood, W. A. Russell, and W. A. Leary, Soc. Automotive Engrs. Quart. Trans. 4, 232 (1950). 76. S. Lenher, / Am. Chem. Soc. 53, 3737, 3752 (1931). 77. D. M. Newitt, Proc. Roy Soc. A157, 348 (1936). 78. D. M. Newitt and L. S. Thornes, J. Chem. Soc. 1656, 1669, (1937). 79. R. N. Pease, J. Am. Chem. Soc. 51, 1839 (1929). R. N. Pease and W P. Munro, ibid. 56, 2034 (1934). R. N. Pease, ibid. 57, 2296 (1935); Chem. Rev. 21, 279 (1937). 80. E. J. Harris and A. Egerton, Chem. Rev. 21, 287 (1937). 81. A. R. Burgess and R. G. W. Laughlin, Chem. Soc. Chem. Commun, p. 769 (1967). 82. A. R. Burgess, R. G. W. Laughlin, and M. J. D. White, Proc. Symp. on Gas Kinetics, p. 379, Szeged, Hungarian Chem. Soc., 1969. 83. D. J. Hucknall, "Chemistry of Hydrocarbon Combustion," Chapman and Hall, London-New York, (1985). 84. A. D. Walsh, Trans. Faraday Soc. 42, 269 (1946). 85. F. O. Rice and E. L. Rodowskas, J. Am. Chem. Soc. 57, 350 (1935). 86. C. F. Cullis and C. N. Hinshelwood, Discussion of Faraday Soc. 2, 117 (1947). 87. J. C. Pope, F. J. Dykstra, and G. Edgar, J. Am. Chem. Soc. 51, 1875, 2203, 2213 (1929). 88. P. Mondain-Monval and B. Quanguin, Ann. Chim. 15, 309 (1931); Comp. Rend. 191, 299 (1930). 89. W. A. Bone and R. V. Wheeler, J. Chem. Soc. 85, 1637 (1904); E. W. Blair and T. S. Wheeler, J. Soc. Chem. Ind. (London), 41, 303 (1922); 42, 415 (1923); H. W. Thompson and C. N. Hinshelwood, Proc. Roy. Soc. A125, 277 (1929); S. Lenher, J. Am. Chem. Soc. 53, 3737, 3752 (1931); R. Spence and H. S. Taylor, ibid. 52, 2399, (1930); W. A. Bone, A. E. Haffner, and H. F. Ranee, Proc. Roy. Soc. A143, 16 (1933); E. W. R. Steacie and A. C. Plewes, ibid. A146, 72 (1934). 90. R. G. W. Norrish, "Cinétique et mécanisme des réactions d'inflammation et de combustion en phase gazeuse," p. 23, Centre Natl. Recherche Sci., Paris, 1948. 91. M. W. C. Smit, Rev. trav. chim. 49, 675, 691 (1930); J. Boeseken, Chem. Weekblad 31, 166 (1934); N. A. Milas and A. McAlevy, J. Am. Chem. Soc. 55, 352 (1933); J. Stuurman, Proc. Acad. Sci. Amsterdam 38, 450 (1935). 92. W. A. Bone and J. Andrew, J. Chem. Soc. 87, 1232 (1905). 93. G. B. Kistiakowsky and S. Lenher, J. Am. Chem. Soc. 52, 3785 (1929). 94. R. Spence and G. B. Kistiakowsky, J. Am. Chem. Soc. 52, 4837 (1930). 95. E. W R. Steacie and R. D. MacDonald, J. Chem. Phys. 4, 75 (1936). 96. R. Spence, / Chem. Soc, p. 6867 (1932). 97. C. N. Hinshelwood and R. Fort, Proc. Roy Soc. A127, 218 (1930).

REFERENCES

211

98. J . Amiel , Ann. Chim. 7 , 7 0 (1937) . 99. J . H . Burgoyne , T . L . Tang , an dD . M . Newitt , Proc. Roy. Soc. A174 , 37 9 (1940) ;J .H . Burgoyne , ibid. A174 , 39 4 (1940) ; A175 , 53 8 (1940) . 100. T . Male , "Thir d Symposiu m o n Combustio n an d Ram e an d Explosio n Phenomena, " p . 721 , Williams an d Wilkins , Baltimore , 1949 . 101. C . D . Miller , Phot. Soc. Am. 14 , 66 9 (1948) ; U.S . Pat . Nos . 240088 5 an d 2400887 , Ma y 28 , 1946;Natl. Advisory Comm. Aeronaut. Tech. Note, No . 1405 , 1947 ;J. Soc. Motion Picture Engrs. 53 , 479 (1949) . 102. C . D . Miller , Discussio n remark , "Thir d Symposiu m o n Combustio n an d Flam e an d Explosio n Phenomena," p . 414 , William s an d Wilkins , Baltimore , 1949 . 103. G . M . Rassweile r an d L . Withrow , Ind. Eng. Chem. 24 , 52 8 (1932) . 104. M . Auber t an d R . Duchêne , Compt. rend. 192 , 163 3 (1931) . M . Surreys , ibid. 197 , 22 4 (1933) ; Aircraft Eng. 10 , 14 3 (1938) . K . Schnauffer , Z. Ver. deut. Ing. 75,45 5 (1931) ;J. Soc. Automotive Engrs. 34, 1 7 (1934) ; G . M . Rassweile r an d L . Withrow , J. Soc. Automotive Engrs. 39 , 29 7 (1936) ; A . Sokoli k and A . Voinov , Tech. Phys. (U.S.S.R.) 3 , 80 3 (1936) ; A . Philippovich , Z . Elektrochem. 42 , 47 2 (1936) . 105. G . M . Rassweile r an d L . Withrow , Ind. Eng. Chem. 25 , 923 , 135 9 (1933) ; 26 , 125 6 (1934) ; 27 , 872 (1935) ; J. Applied Phys. 9 , 36 2 (1938) . 106. A . Egerton , F . Smith , an d A . R . Ubbelohde , Trans. Roy. Soc. A234 , 433-52 1 (1935) ; A . R . Ubbelohde, J . W . Drinkwater , an d A . Egerton , Proc. Roy. Soc. A153 , 10 3 (1936) . 107. G . Damkôhle r an d W . Eggersgluss , Z . physik. Chem. B51 , 15 7 (1942) . 108. J . M . Campbell , W . G . Lovell , an d T . A . Boyd , J. Soc. Automotive Engrs. 26 , 12 3 (1930) ; Ind. Eng. Chem. 23 , 26 , 55 5 (1931) ; 25 , 110 7 (1933) ; 26 , 475 , 110 5 (1934) ; 27 , 59 3 (1935) . 109. W . Jost , " Explosion s un d Verbrennungsvorgàng e i n Gasen, " p . 547 , Springer , Berlin , 1939 . 110. W . Jos t an d L . vo n Muffling , Z . Elektrochem. 45 , 9 3 (1939) . 111. W . Jost , L . vo n Muffling , an d W . Rohrmann , Z . Elektrochem. 42 , 48 8 (1936) . 112. T . Midgle y an d T . A . Boyd , Ind. Eng. Chem. 14 , 589 , 849 , 89 4 (1922) . 113. G . Calingeart , Science of Petroleum, 4 , 302 4 (1938) . 114. A . Egerto n an d S . F . Gates , J. Inst. Petroleum Technol. 13 , 24 4 (1927) ; A . Egerto n an d F . L . Smith, Phil. Trans. Roy. Soc. (London) , A234 , 50 7 (1935) . 115. H . L . Callendar , Aeronaut. Research Comm. (London) Rept . 116 2 (1927) . 116. H . L . Callendar , Engineering 123 , 147 , 182 , 21 0 (1927) . M . Holmes , Nature, 133 , 17 9 (1934) ; D. B . Brooks , J. Ind. Petroleum Technol. 19 , 83 5 (1933) ; A . Egerto n an d A . R . Ubbelohde , Nature 133 , 179 (1934) ; A . Egerton , F . L . Smit h an d A . R . Ubbelohde , Referenc e 106 . 117. A . Egerto n an d A . R . Ubbelohde , referenc e 116 .