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2.2 Concepto y origen de la motivación laboral
Figures 8.1 and 8.2 show the consumption o f the reactants n-heptane and oxygen for the initial condition po = 110 torr, To = 515 K, RH:02 = 1:1 by volume, for both numerical simulation and experiment. For the time period shown one cool flame is observed experimentally while two are predicted by numerical simulation. The cool flame event is
è ' o 15-
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g o 20- 25- 30 100 0 20 40 60 80 3 5 15-II
2 0 - 25- 60 100 40 80 0 20 time (s) time (s)Figure 8.1 Pressure of n-heptane consumed with time, o experimental points. — numerical simulation. Po = 110 torr. To = 515 K. Reactants: n-heptane/oxygen. RH:02 = 1:1 by vol. Cylindrical batch reactor. Volume = 330 cm^. (experimental data from Laughlin, 1967).
Figure 8.2 Pressure of oxygen consumed with time. □ experimental points. — numerical simulation. Po = 110 torr. To = 515 K. Reactants: n-heptane/oxygen. RH:02 = 1:1 by vol. Cylindrical batch reactor. Volume = 330 cm^. (experimental data from Laughlin, 1967).
Chapter Eight Results and Discussion — Kinetic Analysis
identified by the sudden consumption o f reactants; for the experimental profile this is at approximately 45 s while for the numerically simulated profile this is at approximately 40s and 80 s. The small peak observed in the numerically simulated n-heptane and oxygen consumption prior to the first cool flame is due to an increase in the numerically simulated total pressure before significant consumption o f the reactants occurs.
The numerically simulated profiles compare reasonably well with the experimental ones, until the occurrence o f a second cool flame. However, the numerically simulated profiles show that there is negligible reactant consumption before and after the first cool flame, while experimentally consumption o f both reactants is seen to occur either side o f the cool flame.
Prior to the experimental cool flame, the consumption o f n-heptane and oxygen is equal suggesting that the initiation reaction,
RH + O2-> R -+ HOO- (8.1)
is principal in accounting for reactant consumption. During the passage o f the cool flame, more oxygen is consumed (approximately 6 torr compared to approx. 4 torr n- heptane consumed), mainly because o f other reactions involving oxygen, e.g. oxygen addition to alkyl radicals to form alkylperoxy radicals. As mentioned in the previous chapter, rapid reactant consumption during cool flame propagation is a result o f chain- branching, producing a large concentration o f radicals, particularly the highly reactive hydroxyl radical ( OH), accelerating the overall rate o f reaction. After the cool flame, the rate o f reactant consumption decreases, and a lower pressure o f oxygen than n- heptane (approximately 2 torr difference) is observed. With respect to the numerically simulated profiles, the difference between the pressure o f n-heptane and oxygen consumed (approx. 0.5 torr more oxygen is consumed than n-heptane) is not as large as the experimental case.
8,3 Hydroperoxides
Figures 8.3 and 8.4 show the partial pressure-time profiles for all hydroperoxides (excluding hydrogen peroxide), represented generally by R’OOH, obtained from numerical simulations and experiment, for two different initial conditions.
2.0- 2 Q. m.
II
1.0- 0.5- (x lO O) . — □ 0.0- 0 5 10 15 C L t (^0) 60 80 0 20 40 time (s) time (s)Figure 8.3 R ’OOH partial pressure-time profile. □ experimental points; — numerical simulation. Reactants; n-heptane/oxygen. RHiOz = 1:1 by volume. Po =
100 torr. To = 581 K (308 °C). Cylindrical batch reactor. Volume = 330 cm^. (experimental data from Laughlin, 1967).
Figure 8.4 R ’OOH partial pressure-time profile, -o - experimental points; — numerical simulation. Reactants: n-heptane/oxygen. RH:02 = 1:1 by volume, po =
110 torr. To = 515 K (242 °C). Cylindrical batch reactor. Volume = 330 cm^. (experimental data from Laughlin, 1967).
Chapter Eight Results and Discussion — Kinetic Analysis
The experimentally acquired profile was assumed, for convenience and lack o f more detailed information, to be monohydroperoxides only (Laughlin, 1967; Burgess & Laughlin, 1967; Burgess et al., 1969), ie heptylhydroperoxides. However, the method used to determine the experimental R’OOH concentrations was based on that o f Clover and Houghton (1904) and sought to detect the presence o f an hydroperoxide group. It may be possible that other species containing an hydroperoxide group, such as heptyldihydroperoxides and carbonyl alkylhydroperoxides, were unknowingly detected, and comprise part o f the final profile. Since alkyl monohydroperoxides, alkyl dihydroperoxides and carbonyl alkylhydroperoxides all form part o f the proposed reaction mechanism, these have all been included and presented as one curve.
Inspection o f figs. 8.3 and 8.4 reveal that very poor agreement between experiment and numerical simulation is found. For the initial condition po = 100 torr. To = 581 K, RH:02 = 1:1 by volume (fig. 8.3) two peaks in the R’OOH concentration profile were observed experimentally while four peaks are predicted from numerical simulation. Since a critical concentration o f chain-branching agent is produced prior to the propagation o f a cool flame (see previous chapter; Burgess and Laughlin, 1967; Falconer et al, 1983) the peaks in R’OOH concentration correspond to two experimental^ and four numerically simulated cool flames. More significantly, however, is that the numerically simulated R’OOH partial pressure is one hundred times smaller
than the experimental values. Similarly, for the initial condition po = 110 torr. To = 515 K, RH:02 = 1:1 by volume (fig. 8.4) two peaks in the numerically simulated ROOH partial pressure profile are predicted (two cool flames) while only one is seen from experiment (one cool flame). Again the magnitude o f the numerically simulated R ’OOH is lower than experiment but only by a factor o f ten.
It would seem plausible that the R’OOH concentration determined experimentally is composed o f a mixture o f hydroperoxide-based compounds. Such a mixture is not dissimilar to the “hydroperoxide complex” reported by Sahetchian (1990) and is composed o f three classes o f hydroperoxide compound. Each class o f hydroperoxide compound is formed via a different chemical pathway and represent different possible chain-branching agents. One would intuitively expect a particular chemical pathway leading to a particular class o f hydroperoxide compound to be dominant, a matter that
^ Interestingly, the experimentally determined pressure profile indicates four pressure pulses, suggesting four cool flames, which conflicts with the two pulses seen in the experimental R’OOH concentration profile, since production of a critical concentration of chain-branching agent is required before cool flame propagation. The discrepancy between the experimental pressure and R’OOH concentration profiles may be due to a low sampling rate of R’OOH.
may be revealed from the relative concentrations o f the different classes o f hydroperoxide compound.
The three classes o f hydroperoxide compound consist of;
(i) alkyl monohydroperoxides (ROOH), formed by external H-atom abstraction by the alkylperoxy radical (ROO ):
ROO + RH ^ ROOH + R (8.2)
(ii) ketoalkylhydroperoxides (0 = Q 0 0 H ), formed by a series o f internal isomérisation reactions and an oxygen addition reaction:
ROO ^ QOOH (+ O2) OOQOOH -> 0 = Q 0 0 H + OH (8.3)
(iii) alkyl dihydroperoxides (HOOQOOH), formed by external H-atom abstraction by the hydroperoxidealkylperoxy radical ( OOQOOH) produced in eqn. (8.3):
•OOQOOH + RH -> HOOQOOH + R (8.4)
With respect to n-heptane, four heptylmonohydroperoxides, eighteen ketoheptylhydroperoxides and seventeen heptyldihydroperoxides are possible.
An idea o f the composition o f the hydroperoxide mixture may be readily obtained from the numerical simulations. Table 8.1 shows the distribution o f the three classes o f hydroperoxide compound in the R’OOH mixture for the two initial conditions po = 100 torr. To = 581 K and po = 110 torr. To = 515 K (RH:02 = 1:1 by volume in both cases).
In Table 8.1 a distinction is made between the distribution before a particular (local) maximum in partial pressure is observed (values in italics), ie the induction time to a particular cool flame, and the (local) maximum attained, ie the propagation o f a cool flame. The distribution before a particular maximum remains approximately constant until just before the local maximum is reached.
Chapter Eight Results and Discussion — Kinetic Analysis
Po = B)0 torr, To == 5 81K Po = l l 0 torr, To = 5 1 5 K
% % % % % %
ROOH OQOOH Q (00H )2 ROOH OQOOH 0(OOH)2
before max 1.5 98.5 <0.002 1.2 91.4 <0.003 at l®^max 12.4 87.6 <0.001 8.6 91.4 <0.002 before max 4.5 95.5 <0.001 3.6 96.4 <0.002 at 2"^ max 6.8 93.2 <0.001 13.3 86.7 <0.001 before 3^^ max 5.7 94.3 <0.001 - - - at 3^^^ max 6.2 93.8 <0.001 - - - before max 5.7 94.3 <0.001 - - - at 4^^ max 5.9 94.1 <0.001 - - -
Table 8.1 Distribution of the three classes of hydroperoxide compound in the hydroperoxide mixture, R ’OOH. Numerical simulation.
From Table 8.1, one can see that heptyldihydroperoxides (Q (00H )2) constitute an insignificant portion o f the hydroperoxide mixture, R’OOH. This suggests that production and subsequent decomposition o f Q (00H )2 is o f minor, if any, importance in the low-temperature oxidation o f paraffins since relatively little heptyldihydroperoxide is produced. Allied with the observation that ketoheptylhydroperoxides (0 = Q 0 0 H ) clearly form the major proportion o f the hydroperoxide mixture, one may conclude that H-atom abstraction via internal isomérisation o f the hydroperoxideheptylperoxy radical ( OOQOOH) (reaction (8.3)), from which both Q (00H )2 and 0 = Q 0 0 H are derived, is favoured over external H-atom abstraction (reaction (8.4)). That 0 = Q 0 0 H constitutes the significant percentage o f the hydroperoxide mixture at any instant leads one to regard ketoheptylhydroperoxide as the chain-branching agent. However, the role o f the monohydroperoxides should not be immediately dismissed since they form a significant, albeit small, part o f the hydroperoxide mixture.
The distribution o f specific hydroperoxide compounds is also readily accessible from the numerical simulations. Table 8.2 shows the compounds present by more than 1% at a local maximum in the numerically simulated R ’OOH mixture profile.
The five compounds presented in Table 8.2 represent 95-98% o f total hydroperoxides in the R ’OOH mixture. By far the most abundant species are 4-ketoheptyl-2-hydroperoxide (4-0=C7Hi3-2-00H ) and 2-ketoheptyl-4-hydroperoxide (2-0=C7Hi3-4-00H), (a) and (b) respectively in Table 8.2 and leads one to propose that these are the chain-branching agents. The only other ketoheptylhydroperoxide produced in any significant amount is 3-ketoheptyl-5-hydroperoxide ((c). Table 8.2), while the only other hydroperoxide
compounds o f apparent significance are heptyl-4-hydroperoxide and heptyl-3-hydroperoxide. The results shown in Tables 8.1 and 8.2 would tend to agree with the results o f Sahetchian (1991), who showed that the “hydroperoxide complex” was composed o f ketoheptylhydroperoxide.
VW
0 OOH (a)v/V
HOO 0(b)
HOO 0vVV
(c)v y v
OOH(d)
OOHvW
(e) simulation A before max 43.8 43.8 8.7 0.3 1.1 at F‘ max 38.1 38.1 8.5 8.9 3.4 before 2"^^ max 40.3 40.3 9.5 0.9 2.6 at2"*^
max 40.2 40.2 9.2 4.5 1.5 before 3’’’^ max 40.4 40.4 9.2 1.2 3.7 at3'^'*
max 40.3 40.3 9.1 4.1 1.4 before max 40.5 40.5 9.1 1.2 3.8 at 4^ max 40.5 40.5 9.0 3.9 1.3 simulation B before max 45.3 45.3 6.7 0.2 1.0 at F‘max 41.5 41.5 6.9 6.8 1.4 before 2'^ max 43.9 43.9 7.0 0.5 2.9 at2"^
max 40.6 40.6 6.5 8.7 1.7Table 8.2 Distribution of the most prolific hydroperoxide species in the hydroperoxide mixture, R ’OOH. Numerical simulaion. Simulation A: po = 100 torr, To = 581 K. Simulation B: po = 110 torr, To = 515 K. RHiGi = 1:1 by vol. and reactor volume = 330 cm^ for both simulations, (a) 4-ketoheptyl-2- hydroperoxide. (b) 2-ketoheptyl-4-hydroperoxide. (c) 3-ketoheptyl-5-hydroperoxide. (d) heptyl-4- hydroperoxide. (e) heptyl-3-hydroperoxide.
Since only five o f the possible thirty-nine hydroperoxide compounds are produced in any significant amount suggests that certain chemical reactions leading to the formation o f hydroperoxide compounds are prominent. From reactions (8.2), (8.3) and (8.4), production o f any o f the three classes o f hydroperoxide compound requires formation o f the heptylperoxy radical (C7H15OO ), occurring via hydrogen-atom abstraction o f the fuel molecule and subsequent oxygen addition to the resulting heptyl radical:
Chapter Eight Results and Discussion — Kinetic Analysis