Combustion studies of olefins and of their influence on hydrocarbon combustion processes

Combustion studies of olefins and of their influence on hydrocarbon combustion processes

COMBUSTION STUDIES OF OLEFINS AND OF THEIR INFLUENCE ON HYDROCARBON COMBUSTION PROCESSES K. C. S A L O O J A * 'Shell' Research Ltd. Th.wmon Research ...

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COMBUSTION STUDIES OF OLEFINS AND OF THEIR INFLUENCE ON HYDROCARBON COMBUSTION PROCESSES K. C. S A L O O J A * 'Shell' Research Ltd. Th.wmon Research Cot!ire. P ,'z,. Box 1. ( hestcr ('onlparative ~tudie~ of the pte-I]atne and ignititl.1 behaviours of ethylene, ptopenc, but-I -ene. tq~-bul-2-,:ne, traitshut-2-ene, i'.ohult'ne, hex-I-ene and hexad.5-diene have been made. Moreover. the ofreal of all thc,c olel/n~ oll tile i:l~lrlbtlstionill her.anu at di!~2renl oxidation Mage~,leading to ignition has been studied. "[he (d~er red lelalive order of case of combustion of some of the olefins is difl~erent from thai ohs,:r red in klborator 3 .iludies by other worker, but agrees with the relative order of knocking tendencies in engine~ It i~ drown lhLlt. H1 general oletins ;ire less prone to oxidative dogradiaion than the conitlgate alkanes, lind not ~i¢¢ vcr,a as ha~ b~2cn presuffled recently in proposals for a new mechanism for the combustion of hydrocarbons. All tile otel]llSat tidied illilrkedly alleet tile combustion [fl hexane Item Ihe earliest stage o[ ils oxidat loll 'fhc earliest pre-Ilanle ~dag¢i~.inhil)ited wJlihl the final stage leadillg to ignit iun is prtllllOtl:d. The natttre of Ibe t:l'l'ecI on tbe interveiling stagex, vitri¢', w,:lelg, however : ethylene and i.,obutene inhibit, while Ilex-l-ene. Ilextl-1.5-dtene and but-2-ene~ prOlllOte; propene and btlt-l-elle have a negligible efl¢ct. The results I~leildatt' undcrshlntlillg i)f tile m¢charlism of colnhttqion o[ o[¢lins and of their roll: as mlerllled;Zll0~ !n tile cltlllbtlstion el hydrocarbons ill general. Dlccbanlsnls arc prolx>vd to cxpll, n the variou, observation..

introduction

workers, hi general, olefins life less p r o n e to oxidative d e g r a d a t i o n than are the conjugate alk.anes, and not vice versa as has been presun'ted recently by Knox I in advancint, a new mechanism for the c o m b u s t i o n of h y d r o c a r b o n s . W c also find that olefins inhibit some oreflame stages of h y d r o c a r b o n c o m b u s t i o n a n d p r o m o t e others. Tile n a t a r e and the n l a g n i t u d e of tile effect on a given pre-Ilame stage often vary from olefin In olel'in.

AL~I HOUGH the c o m b u s t i o n b e h a v i o u r s of several o l e f n s have been studied individually, little effort ha~, been expended on fi) c o m p a r a t i v e studies to establish rcrationships between the m o l e c u l a r structure and combustion b e h a v i o n r of a n u m b e r of these c o m p o u n d s , or on (it) studies of the inflnenee of these olefms on hydroc a r b o n c o m b u s t i o n processes to elucidate their role as c o m b u s t i o n intermediates. W e have investigated the p r e - l l a m e and ignition b e h a v i o u r of ethylene, propene, but-I ° ene, ei.~'-but..2-ene, t r a n s - b n t - 2 - e n e , isobut~ne. h e x - l - e n e and hexa-l.5-diene. T h e influence of each olefin on the pre-flame and ignition beh a v i o u r of hexane was then studied. H e x a n e was chosen as the base fuel boentlse it clearly displays all the pre-flame regions of c o m b u s t i o n . and a l m o s t all the olefins stttdied are formed d u r i n g its combustion. O u r results show that the rchttive o r d e r of ease of oxidation of several of the olefins studied is different from that reported by earlier

Experlmentul T h e e>:perimental conditions Ic, r ths~c studies ~ e t ' e tile sanic as those used lor o a r p r m i o u s studies on h y d r o c a r b o n eolllbtlstion:. Briefly. the Sttldies were cat'ried Out at atnlospheric pressure ill it flow system ill which a ho[IIOgell@Ous mixture of fttel v.tpour ~Hld aic t.%~t.~ passed through a tltnarlz reaction vessel h d d ill a tlnilorm tenlperatur',.- Jaside a furaaee. T h e residence lime of the f a d air tnixtz~re in tile reaction splice was 0.69 sec at 5IR) (', I he prod uct gases froro the reaction vessel were Colltitlnottsly passed through infra-red (i.r.I atnalysers to d e t e r m i n e (i) c a r b o n dioxide, and (ih c a r b o n

* Present address: Esm I{¢seardlCentre. Abill~'don.Bcakshirc

401

K.C. SAL(X}JA

402

monoxide, and through a paramagnetic antF lyser to determine (iii) oxygen. The pattern of behaviour in terms of the three measurements was similar with every fuel and therefore the results in the paper are presented in terms of only one of the measurements made, namely the formation of carbon monoxide. A.q the hydrocarbons were very pure; the impurities, if any, were le~s than 0.1 per cent and consisted of isomeric hydrocarbons.

Vol, 12 i

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16

~ ~ Shows the onset of | | ignition in pre-fiame ~ studies 14

61

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Studies of olefins The results on the pre-flame and ignition of butenes have already been reported z, but some are presented here again for ease of comparisor, with those for the other olefins studied. The results for ethylene and propene (Figure 1) show that propene is far more resistant to pro-flame oxidation than ethylene is. As regards ignition, propene is again more resistant except when the ignition lag is greater than 5"5 seconds when propene ignites but ethylene does not. A comparison of the combustion heb~viours of ethylene and propene with those of the butenes (Figure 2) shows that but-l-one and the but-2enos are far more prone to oxidation than

a.

c ~u

Ethyten~Pr openeat 0 .-o --J'-'~°" , - -'~'~ /,50 500 550 - 600 Temperature,°C

FIGURe I. Pro-flame and ignition behaviours of ethylene and propene. Effect of temperature on (i) the extent of proflame reaction il1terms of carbon monoxide production, and (ii) ignition laB,from twices~ichiometric hydrocarbon-air mixture

t

trnns-But

Arrow shows ,gnit~on

-2-ene

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&70

500

530

2 0 650

560 Ten~6rit ure0 °C

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FIGURE 2. Pre-flame behavlours of ethylene, propene and butenes, Effect of temperature on extent of reaction, in terms of carbon monoxide production, from stolchiometric hydrocarb~,n-air mixture

620

October 1968

COMBUSTIONSTUDIESOFOLEFINS 4O3 however, hex-l-ene does not ignite while hexa1,5-diene does.

ethylene is, but isobutene is even more resistant to oxidation than propene. Although ethylene ignites at a lower temperature than do the but-2-enes, comparison of the ignition lag/ temperature relationships3 leaves little doubt that on the whole ethylene is more resistant to ignition than the but-2-enes. Hex-l-ene and bexa-l,5-diene (Figure 3), unlike the other oleflns studied, begin to oxidize in the cool-flame region. The ease of oxidation at different pre-flame stages is far greater for hex-l-ene than for hex-l,5-diene. Ignition lag/temperature relationships show that above 475°C hex-l-ene ignites more readily than hexa-l,5-diene; at lower temperatures.

Influence of olefins on the combustion processes of hexane The influence of each olefin was examined at a 20 per cent mole concentration in hexane. The effect of adding a similar amount of benzene was also studied; benzene is highly resistant to oxidation, the results thus providing an interesting comparison with those for the effects of olefins. The results are presented in Figures 4 and 5. For hexane (without admixture with the other hydrocarbons) results are presented for (i) a twice stoichiometric fuel-air mixture cortes-

the onset of Jonilion I shows in pre-flarn e stuclies He~ane

:~

o

o o

~3 '6

250

J300

350

L,O0 t, FjO CoO0 remper~,lure, °C Flc;cr~e 3. Pre-flame and ignition behaviours of hcxane, I~x.l.mle and hcxa-l,5.diene. Effect of temperature on

(i) the extentof pre-flamereactionin termsof carbon monoxideproduction,and (ii)ignitionlag,froma twicestoichio. metrichydrocarbon-airmixture

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H l x l n e ( I 6 x stolch )) hex-1-ene (0 4 $toich ) Hexlne 11 6 x slouch ) + h e x i +1,5 - d }lot' (0 ~ stoich )

350

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F=t~U~4. Influenceof ethylene,propcne, bex-I-ene,hexa1.5-diene and benzene on the combustion behaviour of hexane. Effec~of temperature on the extent of reaction. in terms of carbon monoxideproduction, up to ignition point pondin~ to that used for studies on mixtures of hexane with the other hydrocarbons, and (ii) a 1.6 times stoichiomr:tricmixture corresponding to the partial concentration of hexane in the mixtures. The results show that, whilst benzene has virtually noeffect at any stage, olefins, in general, exercise a marked influence. All olefins inhibit the initial stage of oxidation and promote the onset of ignition. T ~ r e are variations in the magnitude of inhibition in the initial st'~gcs of oxidation. Inhibition is least with hex-l-ene and greatest with hexa-l,5-diene; variations in the effects of the other olefins are only small. Effects on the intervening pre-flame ~tages, however, usually vary. Ethylene and isobutene inhibit markedly and propene only slightly, but but-lerie, but-2-enes, hex-l-ene and hexa-l,5-diene

promote combustion• The promoting effect is greatest for hex-l-ere; for bnt-2-enes it is much greater than for but-l-ene. Differences in the promoting effect of olefins on ignition are generally small, except for hexa-l,5-diene which effected greater promotion than the other olefins+ Discussion The observed relative order of ease of oxidation of several of the compounds studied is far different from that observed by other workers. For instance, Kerr, Lastra and TrotmanDickenson4 have reported that the ease of oxidation increases in the order ethylene < propcne < isobutene but this is the opposite of that observed in the present studies. Kerr et at. have further observed

October 1968

COMBUSTION STUDIES OF OLEIFINS

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Temperature, °C Fz¢zt:m~ 5. Influence of bot-I--cne, cis-but-2-cne..'rarLs-but-2eric a n d isobutene o n the c o m b u s t i o n b e h a v i o u r o f hexan'.. Effect o f temperature o n the extent o f reaction, in terms c f carbon m o n o x i d e production, up to ignition point

that the ease of oxidation of cis-but-2-ene is equal to that of isobutene. We, however, find cls-but-2-ene, and also the trans-isomer, to be very much more reactive than isobutene. Again, contrary to the observations of Norrish and Porter s, we find that but-l-erie oxidizes more readily than the but-2-enes. Blundell and Skirrows, and also Norrish and Porter, failed to observed any differences in the behaviours of cb- and trans-but-2-enes. Our studies, however, show that the behaviour of the two isomers is indistinguishable in the early pre-flame stages only; in the later stages the eis-isomer is more reactive and eventually ignites at a lower temperature. Recently Knox t has advanced a new mech. anism for the low temperature oxidation of hydrocarbons which is based largely on the

premise that conjugate olcfins are considerably more reactive than the parent alkanes. We find this premise to be generally incorrect. Isobutene oxidizes less readily than isobutane s. But-l-ene and but-2-enes oxidize far less readily than butane in the 'low temperature' region of combustion, although this order is reversed in the 'high temperature' region 3. The greater resistance to oxidation of olefins, particularly in the 'low temperature' region, is also shown by the results on hexane, bex-l-ene and hexa-1,5-diene (Figure 3). it is not readily apparent why our results are so different from those of previous workersL Our results agree well with those in gasoline engines7. The knocking tendencies of a large number of pure hydrocarbons have been compared in engines under identical, well-controlled

406

K. C. SALOOJA

Vo|. 12

varied in the nature and magnitude of their effect on the intervening pre-flame stages. Knox t ha~ presumed that olefms simply accelerate com.° bustion. His own studies9"t o limited to the effects of ethylene on ethane and ofpropene on propane, had shown that the olefins promoted combustion. However, these observations of Knox were not in agreement with those of earlier investigators. Satterfield and Reid tl had shown that propene accelerated the initial stage of oxidation of propane but inhibited most other stages. Bawn and Skirrow t2 had observed partial suppression of the oxidation of propene, but-l-ene a n d

conditions. The results expressed as the knocklimited compression ratios of the hydrocarbons under discussion ar presented in Table 1. We have shown previously for several hydrocarbons that the ami-knock performance, and a l ~ the changes in the performance that are brought about b y alterations in engine speed and/or operating temperature, can be interpreted from the pre-flame and ignition characteristics of the hydwcarbon s. In general, the greater the ease of oxidation and the extent of pre-flame reaction of a hydrocarbon, the greater is its tendency to knock (the lower its critical compression ratio).

TABLE I. Knock.limited c:ompression ratios in General Motors single cylinder

variablecompressionengineT

Critical co~rcsMo)l ratio at : Engine speed Jacket temperature Air temperature

Ethylene Propene Butane But-l-erie cis.But.2-ene trans.But-2-ene isobutane Isobutene Hexane Hex-I -ene Hexa-1,5-diene

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2000 rev/min

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350°F 150 °F

212~F 100 °F

350°F 150 °F

8.5 10.6 5.5 7.1 7.9 £'7 8-0 10.6 3.25 4,35 4.6

5.6 6.9 5.3 5.3 5.95 5'95 6.45 ~.0 3.0 3.6 3.55

6.5 7,85 7.55 6'4 6.95 7.0 8-45 9.1 4.05

4.25 5.7 5.85 4'8 5-35 5"4 6.5 6,25 3.55

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3~25

Furthermore, the higher the resistance to ignition of a hydrocarbon, the lower is the depreciation in its performance when the severity of engine operation is increased. It can now be seen that the observed differences in the combustion behaviours of the hydrocarbons studied accord well with the engine results. Our results on the effect of olefins on combustion processes show that even though some of the olefins are themselves highly resistant to oxidative degradation and oxidize only in the 'high temperature' region, they influence all the pre-flarae stages including the earliest one in the 'low temperature' region. All the olefins inhibited the earliest pre-flam¢ stage and prometed the final stage leading to ignition, but

hex-l-ene by an excess of the olefin. Thus, Knox's generalization is untenable.

Probable mechanismfor the combustionof olefins Ethylene and propene--Some investigators, notaLly Shtern t s and Kerr, Lastra and TrotmanDickenson4, consider that olefins oxidize primarily by hydrogen abstraction. While there is a strong case for this mode with propene, the explanation for ethylene must be different. Ethylene oxidizes more readily than propene despite hyd;cogen-abstraction being more difficult; the strength of the C - - H bond in ethylene is much greater than in propene (in the CH3 group) ta. With ethylene, addition reactions are likely to predominate. Some investigators t4' is

October 1968

COMBUSTION"STUDIESOFOL~INS

hold the view that the addition reaction occurs with molecular oxygen. However, the fact that, in general, olefins begin to oxidize far less readily than the conjugate alkanes indicates that the addition process involves free radicals rather than molecular oxygen. Knox and Wells9 have shown that the major intermediate in the oxidation of ethylene is formaldehyde, 80 per cent of the hydrocarbon consumed being converted into formaldehyde in the early stages of oxidation. They have proposed the following mechanism for its formation: CHzCH 2 + HO~ --* "CH:CH2OOH ['1"] "CH2CH2OOH -'-*CH20 + "CHzOH

[2"1

407

For the oxidation of propene Shtern 13 and Mullen and Skirrow 7 have. shown acetaldehyde to be the important chain-branching intermediate. The other aldehydes involved are acrolein and formaldehyde. The formation of acrolein is easy to explain as occurring by the reaction -ff allyl radicals with oxygen. However, the formation of acetaldehyde, which is formed in about ten times greater amounts than acrolein aT,is difficult to visualize if, as Shtern claims, propene molecules only undergo hydrogenabstraction reactions. More probably acetaldehyde is formed through free-radical addition to propene in a manner e~al~gous to that proposed above for the formation of formaldehyde from ethylene: HO

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2 CH20 + "OH ~ - - - . C H ~ - - C H 2 Molecular models show this scheme to he very plausible. Such a scheme has already succeSsfully explained the formation of the major intermediates in the oxidation of several oxygen derivatives of hydrocarbons16.

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It is difficult to see why propene undergoes oxidative degradation less readily than ethylene. Probably this is partly due to propene undergoing predominantly hydrogen-abstraction reactions rather than addition reactions. Although the hydrogen is abstracted readily, the allyl radical formed is stable. Partly the explanation could be that whereas the reaction of ethylene with free radicals formed during combustion produces another free radical. CH2=::~H2 -4- X" --+'CH2--CH2X that with allyl radicals from propene produces stable molecular species, CH2:---~H---CH2 + X" -~ CH2~--~CH--CH2X Butenes--The observed order of reactivities of the butenes, although in several cases different from that reported by the previous investigators,

408

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can be readily explained. It has been established that the abstraction of a hydrogen atom from an olefin generally occurs from the cz position to the double bond t3. Whereas but-l-ene has a methylene group in t he ct position, but-2-enes and isobutene have methyl groups. The strength of the C - - H bond in a methylene group being considerably less than in a methyl group Is, the ease of abstraction of hydrogen, and hence of oxidation, should be greater for but-l-enes than for the other hutches. That isobutene is more resistant to oxidative degradation than the but-2.enesis most probably du.~ to the differences in the reactivities of their principal intermediates. Acetaldehyde, the major intermediate from but-2-enes, is far more reactive than acetone and formaldehyde from isobutene. The observed reactivity of cis-but-2-ene being greater than that of trans-but-2-ene could be due to the intramoiecular reactions of the peroxy radical, which play a role in oxidation tg, being feasible only with the eis-isomer. The little difference between the combustion behaviours of the two isomers in the early pro-flame stages (at lower temperature) could be due to the intramolecular reaction involving abstraction of .hydrogen from fi methyl group not readily occurring at low temperatures.

Hex-l-ene and hexa-l,5-diene--Hex-l-ene, with three methylene groups including one adjacent to the ¢~oublebond, is, as expected, more reactive than *.he other olefins studied. The fact that it oxidizes less readily than bexane is probably due largely to: (i) The probability of intramoleeular reactions being less for peroxy radicals formed on the 3 position in bex-l-ene than on the 2 position in hexane. (ii) Differences in the amounts and relative proportions of reactive intermediates formed from them. Larger amounts, particularly of the more reactive intermediates, would be formed from hexane than from hex-i-ene. For instance, acrolein would be formed in greater amounts from hex-l-ene but the more reactive acetaldehyde and propionaldehyde would be formed in greater amounts from hexane. Off) Considerable self-inhibition of oxidation occurring with hex-l-ene. With hexane this

would occur mainly after olefinic products have formed. For similar reasons, hexa.-l,5-dienv should, as observed, be even less reactive than hex-l-ene.

Influence of olefins on combustion processes Since the influence of olefins often changes from one pre-flame stage to another, the effects on different stag~s will be discussed separately. Pre.cool-fiame stage--All the olefins inhibited the oxidation process in this stage. The effect of hexa-l,5-diene was considerably greater than that of hex-l-ene. Differences in the magnitude of the effect of the other olefins were only small. Inhibition must involve the conversion of reactive free radicals involved in combustion into less reactive free radicals or stable molecules. Such changes could be brought about either by the abstraction of a hydrogen atom from olefins or by an addition reaction : CH2=~H--R" + XH CH2==CH--RH + X ' - -

X

Withethylene theaddition reaction isexpected to predominate while with the other olefins both modes are likely to be involved though to different extents for different olefins. Cool-flame region--In this region olefins vary most in their effect. Ethylene and isobutene markedly inhibit, while hex-l-ene, bexa-l,5diene and but-2-enes strongly promote and prope~e and but-l-ene have a negligible effect. The differences in the effects of olefins are most probably due to the differences in the nature of the effects of their principal intermediates. Oxidative degradation of ethylene, following its reaction with reactive free radicals such as OH, would, as previously discussed, give rise to formaldehyde. A similar reaction with propene would produce largely formaldehyde and acetaldehyde. It has already been established for the oxidation of hexane under the present experimental conditions that while formaldehyde markedly inhibits oxidation acetaldehyde strongly promotes it 2°. Thus while the formation of formaldehyde from ethylene should cause

October 1968

COMBUSTIONSTUDIESOF OLESINS 409 inhibition, that of formaldehyde and acetaldeadjacent carbon atom. O n steric grounds the hyde from propene would tend to cancel the possibility of intramolecular abstraction of effects of the aldehydes and the net effect could, hydrogen in the peroxy radical, in the manner as observed, be negligible. depicted above for ethylene and propene resThe principal reactive intermediates from the pectively, will be greater than for the peroxy butenes are: acrolein and formaldehyde from radical formed from hexane. A further obstacle but-l-one, acetaldehyde from but-2-enes, and to hydrogen abstraction in the latter ease will acetone and formaldehyde from isobutene 3. arise from the hydrogen atoms nearest to the Our previous studies on the effect of carbonyl terminal oxygen atom being likely to include compounds on the combustion of hexane 2°' 2~ those in the strongly bonded CH3 group. have shown that whereas formaldehyde inhibits, High temperature region--In the region imacetaldehyde and acrolein--the former more mediately preceding ignition all the olefins than the latter--promote, and acetone has •studied tended to increase the extent of reaction virtually no effect. Thus, the observed effects and they all lowered the ignition temperature. of different butenes are well accounted for. This is in line with the combustion behaviour The reason for the promoting effects of of the olefins on their own. Compared with hex-l-one and bexa-l,5-diene is not so obvious alkanEs, conjugate olefins have a greater tenbecause most of the reactive intermediates dency to ignite despite, in several cases, a lower from these unsaturated compounds will be the tendency to undergo pro-flame oxidation. This same as those from bexane. However, the is probably because at high temperatures almost reason for the difference in the effectiveness of all the intermediates are prone to oxidative hex-l-ene and hexa-l,5-diene can be readily degradation and the overall ease of combustion visualized. Concurrent with the promoting is reflected more closely by the nature of the bonds comprising a molecule. The strength reactions, the inhibiting reactions, as evidenced of the C - - H bond in olerms (in a position to the in the pre-cool-flame region, must occur and these will take place to a greater extent with the double bond) is less than in the conjugate hexadiene than with the bexene and hence alkanes, and th~s would cause the olefins to largely account for the observed difference in the undergo chain reactions more readily and net promoting effects of the two compounds. eventually to ignite more readily. The principal promoting reactions with box- I one and bexa-l,5-diene are likely to be related The author wishes to than~ Mr C. P. Rimmer to the ease of formation of peroxides. Peroxides for his able assistance in the experimental work. are the most important intermediates in the coolflame region, their decomposition into RO and (Received October 1967; revised April 1968) OH radicals providing the principal chainbranching steps. The formation of peroxide is References dependent on the facility with which RO2 J KNox, J. H. Comb~aon & Flame, 9. 297 (1965) radicals can abstract a hydrogen atom either SALOOJA, K. C. Combustion & Flante. 4. 117 (1960); intermolecularly or intramolecularly. Either 6, 275 11962) of these processes is likely to occur more readily 3 SAI,OO/A,K. C. Combusaon d Flame. It. 511 (1967) 4 KERI~,J. A.. LASTRA,G. and TROrMAN-DICKEN~)N,A. F. in the presence of the unsaturated compounds J. chem. Soc. 3504 11964) because: s NORRISH, R. (~. W. and PORTER, K. Proc. Roy. Soc. A, (i) intermolecular abstraction of hydrogen will 272, 164 (1963) occur more readily from unsaturated compounds 6 BLUNDELL, A. and SKIRROW, G. Proc. Roy. Soc. A, than from hexane since olefins have the weakest 2414, 331 (1958) I ,Knocking characteristics of pure hydrocarbons', A S T M C - - H bonds (in CH2 groups u to the double Spec. Tech. Publ. No. 25511958) bond), and a SALtXXlA,K. C. Combustion & Flame. 4, 193 11960); 6, (it) following the addition of a reactive free 275 11962); 9,121 11965) radical, such as OH, to the olefin, a peroxy 9 KNOX, J. H. and WELLS,C. H. J. Trans. Faroday So¢. 59, 2786(1963) radical is formed when oxygen adds on to the

410

K. C. S^LOt,JA

l0 KNox, J. H. Trans. Farad¢¢r Sec..ftS. 1362 (1959) 11 SStTI-ERFIELD.C. N, and REID+ R. C. Fi/?h Symposmm ('=nternational) on Combustion, p 511, Reinhold: New York (1955) 12 BAWN, C. E. H. and SKIRROW, G, Fi/?h Symposium flnternational) on Comhwtioa, p 521. Reinhold: New York (1955) t3 SHTERN, V. YA. The Ga.~ Phase Oxidatian of Hydrocarbons, translated M, F. MULLINS.edited B. P. MULLINS. Pergamon: Oxford (1964) t¢ Doeatlezgm^, A. A. and NEUMANN. M. B. Dokl. Akad. .¥auk S.S.S.R. t~, 1919 (1947)

VoL 12

t~ CULLIS, C. F,, FISH, A. and TURNER, D. W. Proc. Roy. ,foe. ,4. 262. 318 (1961): 267. 433 41962) t~ SALOOJA.K. C, Combustion & Flume. 10. I I (1966) t ~ MULU!~. J. D, and SKiP,Row. G. Proc. R~9'. Sac./I. 244, 312 (1958) =s COT~rmiLL T. L. The Strength of Chemical Bonds. Butlerworths: London (1954) 19 FISH, A Quart, Rev. chem. Soc., Load, I$, 243 (1964) 2o SAI.OOJA,K. C. Coi1~|bu$/ion 4~ Flame, 9, 373 {1965) z~ S&t~UA. K. C. Combustion & Flame, 9. 219 (1965)