Effect of the molecular structure of olefin admixtures on the combustion and explosion of hydrogen-air mixtures

Article abstract of DOI:10.1134/S0023158407010028

Small admixtures of propylene, hexene, and isobutylene efficiently inhibit the combustion and explosion of hydrogen-air mixtures at an initial pressure of 1 bar. The inhibition effect depends on the chemical properties of the admixture. The difference bet

Full text of DOI:10.1134/S0023158407010028

ISSN 0023-1584, Kinetics and Catalysis, 2007, Vol. 48, No. 1, pp. 8–16. © MAIK “Nauka /Interperiodica” (Russia), 2007.
Original Russian Text © A.A. Avetisyan, V.V. Azatyan, V.I. Kalachev, V.V. Masalova, A.A. Piloyan, 2007, published in Kinetika i Kataliz, 2007, Vol. 48, No. 1, pp. 12–21.
Effect of the Molecular Structure of Olefin Admixtures
on the Combustion and Explosion of Hydrogen–Air Mixtures
a
b
b†
b
a
A. A. Avetisyan , V. V. Azatyan , V. I. Kalachev , V. V. Masalova , and A. A. Piloyan
a
Yerevan State University, Yerevan, 375049 Armenia
b
Institute of Structural Macrokinetics and Materials Research Problems,
Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia
e-mail: azatyan@ism.ac.ru
Received July 28, 2005
Abstract—Small admixtures of propylene, hexene, and isobutylene efficiently inhibit the combustion and
explosion of hydrogen–air mixtures at an initial pressure of 1 bar. The inhibition effect depends on the chemical
properties of the admixture. The difference between the effects produced by inhibitors manifests itself in all
combustion parameters. Since the chain avalanche plays the determining role in combustion, the inhibition effi-
ciency depends on both the length and the structure of the hydrocarbon chain in the inhibitor molecule. Taking
into account the competition between the branching and termination of reaction chains and the correlation
between the molecular structure and reactivity of the admixture makes it possible to explain and describe all of
the observed regularities of combustion.
DOI: 10.1134/S0023158407010028
†
Sensitivity to small amounts of reactive admixtures simultaneously: the heat generation rate (q ) exceeds
+
is among the most important features of chain combus- the heat dissipation rate (q–),
tion. Theoretical science shows increasing interest in
q > q ,
(1)
+
–
this phenomenon, because reactive admixtures enable
the researcher to distinguish and study the role of the
chain avalanche in combustion under gas self-heating
conditions [1, 2]. Such admixtures make it possible to
knowingly vary combustion parameters without chang-
ing any gas kinetic or thermal parameter of the reacting
gas mixture. This highlights the chemical factors deter-
mining the kinetics of the process. Furthermore, reac-
tive admixtures are of applied interest as means of com-
bustion and explosion control.
and, as the temperature increases, heat generation
accelerates more rapidly than the heat dissipation rate,
dq /dT > dq /dT,
(2)
+
–
where T is temperature [3, 4]. Ignition and combustion
caused by self-heating are conventionally called ther-
mal ignition and combustion.
The other factor that can cause ignition and combus-
tion is the avalanche multiplication of reactive interme-
diates (free atoms and radicals) in their multiply recur-
ring reactions with initial reactants and sometimes with
one another [3–7]. The multiply alternating regenera-
tion and multiplication of reactive intermediates form a
The purpose of this study is to elucidate the depen-
dence of the combustion and explosion of hydrogen–
air mixtures on the molecular structure of the inhibi-
tor (In).
Until recently, very little attention was given to the branched reaction chain. Ignition and combustion
inhibition of combustion accompanied by self-heating. caused by a chain avalanche are called chain ignition
The main reason for this neglect was the imperfection and combustion. The rate of a developed chain combus-
of combustion theory, which generally disregarded the tion reaction is given by
crucial role of the avalanche multiplication of reactive
intermediates in a reaction mixture undergoing self-
heating, as is the case in practical applications.
W = k [B]n,
(3)
p
where [B] is the concentration of the initial reactant B,
n is the concentration of the reactive intermediate, and
The progressive self-acceleration of the chemical
reaction responsible for combustion can arise from two
radically different factors. One is a positive feedback
between the self-heating rate of the reaction mixture
and the temperature. Ignition due to self-heating will
take place if the following two conditions are satisfied
kp is the rate constant of the rate-limiting step of the
consumption of B.
The rate of change of n is given by the following
equation, which was validated against isothermal chain
combustion data:
†
Deceased.
dn/dt = ω + (f – g)n,
(4)
0
8

EFFECT OF THE MOLECULAR STRUCTURE OF OLEFIN ADMIXTURES
9
where t is time and ω is the rate of generation of reac- non. Such calculations can agree with an experiment
0
tive species in the reactions involving only initial reac- only with respect to some particular features of com-
tants [3, 7].
bustion and only if they use empirical input data
obtained in the same experiment under similar condi-
tions. As was demonstrated in an earlier paper [2], the
rate constants thus calculated are usually physically
implausible. In this connection, it is noteworthy that
The chain ignition condition is that the chain
branching rate exceeds the chain termination rate:
f > g,
(5)
where f and g are, respectively, the chain branching and some authors [19, 20] represent the oxidation of H and
2
termination rates at a reactive species concentration CO as stoichiometric, single-step, trimolecular reac-
equal to unity [3].
tions involving only the initial compounds and the ulti-
mate products, ignoring the chain mechanism of these
processes. This representation implies that the self-
acceleration of a reaction can be due only to self-heat-
ing. Furthermore, empirical second-order “rate con-
stants” were assigned to both of the above overall reac-
tions [19, Tables 1, 2], and it was stated that this model
is in good agreement with experimental data. Kostenko
et al. [21] suggest that the ignition condition for a gas
mixture should be defined as the temperature at which
the heat generation rate is equal to the heat dissipation
rate. Thus, contrary to the principles of combustion the-
ory, Kostenko et al. [21] equate the self-heating condi-
tion with the ignition condition. Furthermore, it is sug-
gested the heat generation rate be described in terms of
a first-order rate equation [21, Eq. (4)] and the Arrhe-
nius law, although this formalism is inapplicable to the
chain process, including its heat generation kinetics,
because it is functionally inadequate for describing the
Until recently, chain combustion kinetics were stud-
ied only at pressures hundreds of times lower than
atmospheric, at which reaction mixture could undergo
only a slight, if any, self-heating. The theory of
branched-chain processes was limited to isothermic
processes (see, e.g., [3, 7]). At higher pressures such
that self-heating is significant, the role of the chain ava-
lanche in the initiation and development of combustion
was usually ignored and the self-heating was regarded
as the only factor responsible for ignition and combus-
tion (see, e.g., [3–13]). Even at present, the chemical
process is conventionally treated as a single-step reac-
tion when deriving analytical expressions relevant to
combustion. The temperature dependence of the reac-
tion rate is expressed in terms of an Arrhenius-like
function. Although kinetic networks used in the numer-
ical simulation of combustion sometimes abound with
insignificant reactions, they often include reactions that
can indeed constitute a reaction chain. However, in any
case, the roles of the chain and thermal factors are not
chain combustion of H and CO.
2
Some authors [22, 23] came to the point of stating
considered or, if the gas pressure is above several kilo- that self-heating is not unnecessary for ignition, thus
pascals, implying significant self-heating, ignition and denying the basic principle of the theory of branched-
combustion are regarded as resulting from a thermal chain processes.
avalanche rather than a chain avalanche (see, e.g., [14–
The denial of the significance of the chain ava-
1
6]). The authors of some publications recognize the
lanche in combustion accompanied by self-heating is
sometimes substantiated by noting that the reaction
rate is an exponential function of the gas temperature
and only a power-law function of the concentrations
importance of the chain mechanism in combustion
accompanied by self-heating. However, in the same or
subsequent publications by the same authors, the reac-
tion is written as a single step and, accordingly, ignition
and explosion are considered to result only from pro-
gressive temperature growth. In encyclopedias, mono-
graphs, treatises, and nearly all articles dealing with
chemical kinetics, the pressure range corresponding to
the branched-chain mechanism of ignition and combus-
tion is limited to pressures tens or hundreds of times
lower than atmospheric (see, e.g., [3–10, 13–18]). Fur-
thermore, the chain mechanism of the process is not
taken into account in some works devoted to gas com-
bustion under filtration conditions [19, 20].
(
see, e.g., [4–6]).
However, it was demonstrated that, as the tempera-
ture rises, the significance of the chain avalanche
increases rather than decreases [24, 25]. It was empha-
sized that the specific chain branching rate (f) increases
exponentially as the temperature increases. As this
takes place, the specific chain termination rate (g)
increases much more slowly. In the case of trimolecular
chain termination, g even decreases slightly. As a con-
sequence, the difference f – g, which determines the
feedback between dn/dt and n according to Eq. (4),
grows sharply as the temperature increases. This causes
a further speedup of the accelerating multiplication of
active species and results in a more rapid increase in the
rate of the overall chain process (W).
The role of the chain avalanche is frequently denied
by stating that the data calculated with neglect of the
chain branching and termination reactions are in agree-
ment with experimental data (see, e.g., [12, 13, 19–
2
1]). Obviously, this statement is equivalent to the
statement that the neglected chain factor is insignifi-
Furthermore, it was demonstrated that, even if there
cant. However, reaction networks ignoring the chain is no quadratic-law chain branching, chain ignition and
mechanism and calculations based on these false net- combustion can still occur in a reaction mixture under-
works are incapable of explaining some basic features going no self-heating and even in a mixture being
of combustion, including the autocatalysis phenome- monotonically cooled [2]. If the reaction proceeds by a
KINETICS AND CATALYSIS Vol. 48 No. 1 2007

1
0
AVETISYAN et al.
branched-chain mechanism, ignition can be caused
only by a chain avalanche. A fundamental feature of
branched-chain processes is that, outside the ignition
region, even near the third limit, the reaction rate is neg-
ligible and the characteristic reaction time is one order
of magnitude longer than the characteristic time of heat
dissipation from the reactor. Accordingly, the self-heat-
ing of the reaction mixture does not exceed a few
kelvins and can by no means cause thermal ignition. At
the same time, even at such a low extent of self-heating,
the chain branching rate can exceed the chain termina-
tion rate under these conditions, because f depends
more strongly on temperature than g. The change of the
sign of the difference f – g from negative to positive
causes chain ignition, which always happens earlier
than thermal ignition. The thermal avalanche condi-
tion (2) is met only in highly developed chain combus-
tion [2, 24].
EXPERIMENTAL
Reactions were carried out in an airtight, cylindri-
cal, stainless-steel reactor 12.6 cm in diameter and
2
5.2 cm in height. The components were mixed in the
reactor using a partial pressure–based method with an
accuracy of 0.5% for the H and air concentrations and
2
4
% for the inhibitor concentration. The components
were admitted into the reactor in the following order:
small admixture, hydrogen, and air. The initial mixture
pressure and temperature were 1.0 bar and 293 K,
respectively. The mixture was spark-ignited at the
lower end of the reactor after the time necessary for the
perfect mixing of the components (20 min). The spark
energy could be varied. In most runs, it was 3.6 J.
The gas pressure and luminescence were recorded
simultaneously starting at the ignition point up to the
completion of combustion. The signal from the piezo-
electric pressure gauge was amplified and was then
It was noted in earlier publications [2, 25] that gas- recorded with an S9-8 double-beam memory oscillo-
phase combustion has numerous features inexplicable scope. The discretization time was 2 µs. The chemilu-
in terms of the conventional thermal theory of combus- minescence of the flame in the wavelength range 300–
tion. These include the above-noted strong effect of 600 nm was recorded on the same oscilloscope with the
small admixtures on ignition, the absence of correlation use of an FEU-39 photomultiplier. After each run, the
between the heat of combustion and the combustibility reactor was pumped down to ~2 Pa. This experimental
procedure is detailed in an earlier publication [28].
of a given substance, and the hysteresis of the concen-
tration limits of flame propagation.
Since the number of moles of the gas mixture
decreases steadily during H oxidation, the increase in
These and other phenomena that were not explained
by thermal theory have recently been adequately
explained by accepting the key role of the competition
between chain branching and termination [1, 2, 25].
2
pressure (∆P) observed in the reactor during develop-
ing combustion is due only to the increasing tempera-
ture. Obviously, the gas temperature in the moving
flame, which is the place where heat is generated, is
By varying the rates of the competing branching and higher than the temperature of the unburnt gas. There-
termination reactions using small admixtures of certain fore, ∆P characterizes the temperature rise averaged
types, it is possible to control combustion, explosion, over the reactor volume (and the average temperature as
well). The temperature rise is determined by the ratio
between the rate of heat generation due to combustion
and the rate of heat dissipation. The volume-average
temperature is closer to the combustion zone tempera-
ture the shorter the characteristic time of the reaction in
comparison with the characteristic time of heat dissipa-
tion. Therefore, ∆P is a measure of the heat generation
rate and, accordingly, the combustion rate. This is the
reason why the chemiluminescence intensity and pres-
sure (Fig. 1), which grow at an increasing rate (the ini-
tial portions of their curves are convex downwards),
peak almost simultaneously.
and detonation of gases, for example, hydrogen and
carbon monoxide [1, 2, 25–29]. Inhibitors with similar
heats of combustion and combustion properties may
exert different effects, depending on their chain termi-
nation capacity. This was demonstrated by examining
propylene versus isopropanol [28]. These compounds
were found to act via different mechanisms and at dif-
ferent rates. These differences arise from the fact that,
as distinct from isopropanol, propylene has a π-bond
and is regenerated during H oxidation. Allyl alcohol
2
and isopropanol vapors also show different inhibition
efficiencies because of the presence of a π-bond in the
former and the absence of such a bond in the latter [29].
We studied the dependence of the energy necessary
for ignition, the upper concentration limit of flame
propagation, and the combustion rate on the amount
and structure of lower olefin admixtures. The upper
limit was determined as the average between the high-
In this study, we chose to examine different olefins
since chain processes primarily involve the π-bond
because of its high reactivity. Therefore, any difference
in the inhibiting capacity can arise only from the π-
bond being in different positions in the molecule. This
est H percentage at which the mixture could be ignited
2
and a higher H percentage starting at which the mix-
2
difference should be used as a measure of the sensitiv- ture could not be ignited any longer. The concentration
ity of combustion to this structural property of small of an olefin did not exceed the lower concentration limit
admixtures.
of flame propagation for this olefin in air.
KINETICS AND CATALYSIS Vol. 48 No. 1 2007

EFFECT OF THE MOLECULAR STRUCTURE OF OLEFIN ADMIXTURES
11
∆P, I, mV
[H ], %
2
4
3
2
1
00
00
00
00
4
4
3
3
5
0
5
0
1
25
2
2
1
1
0
5
0
5
2
1
0
1
2
3
4
5
6
7
8
3 6
9
0
100
200
300
400
t × 10 , s
[
C H ], %
3
Fig. 2. Effect of the propylene concentration on the concen-
tration limit of flame propagation in the hydrogen–air mix-
ture as a function at combustion initiation energies of (1)
0.07 and (2) 3.6 J.
Fig. 1. (1) Luminescence intensity (I) and (2) pressure rise
∆P) curves for the combustion of 7% H in air.
(
2
RESULTS AND DISCUSSION
Obviously, since the olefin concentration was
always below the lower ignition limit for the olefin–air
mixture, the ignition of the olefin was ruled out irre-
spective of whether hydrogen was burning. Further-
Effects of Admixtures: An Increase in the Power
Necessary for Initiation and Slowdown
of the Development of Combustion
more, since H does not ignite at all above a certain
2
Our data indicate that even olefin concentrations as
admixture concentration, implying that there is no O2
consumption, the hypothesis that combustion is
low as a fraction of a percent prevent the ignition of
hydrogen–air mixtures and raise the energy necessary
for ignition (Figs. 2, 3). Furthermore, the higher the
admixture concentration, the higher the minimum igni-
tion energy. Olefins decrease the upper concentration
limit of flame propagation (Fig. 3); that is, they hamper
ignition. They reduce the combustion development
rate: throughout the process, the pressure and chemilu-
minescence curves are flatter in the presence than in the
absence of an admixture (Fig. 4). Olefins reduce the
ultimate consumption of O and H ; that is, combustion
retarded because of a lack of O [30] is groundless. The
2
necessity of raising the spark energy in the presence of
an admixture is direct evidence that the spark initiates
the chain ignition, which is hampered by chain termina-
tion by the admixture.
It was demonstrated, using lean hydrogen combus-
tion in a tube as an example, that the characteristic time
2
2
[
H ], %
2
terminates sooner in the presence than in the absence of
an olefin.
5
4
3
2
1
0
0
0
0
0
Like the pressure variation curves (which are, in
essence, temperature variation curves), the lumines-
cence curves are also flatter in the presence of an inhib-
itor, and both indicate that the higher the olefin concen-
tration, the lower the combustion development rate.
Thus, olefins hamper combustion in all respects.
Because the amount of olefin in the mixture was no
larger than 2 vol %, the effect of the olefin cannot be
explained in terms of the increased in heat capacity or
dilution. Furthermore, since the heat dissipation from
the reactor does not increase as an admixture is progres-
sively added, the observed slowdown of self-heating
and the decrease in the maximum temperature rise are
due only to the slowdown of the chemical reaction. This
is also evident from the fact that equal amount of chem-
ically different inhibitors exert different effects on the
mixture ignition and the combustion rate.
2
1
0
1
2
3
4
5
6
7
[
i-C H ], %
4
8
Fig. 3. Effect of isobutylene on the concentration limit of
flame propagation in the hydrogen–air mixture as a function
at combustion initiation energies of (1) 1.0 and (2) 3.6 J.
KINETICS AND CATALYSIS Vol. 48 No. 1 2007

1
2
AVETISYAN et al.
∆
P, atm
involved in the competition between chain branching
and termination [3, 4, 31]:
(
‡)
8
.
H + O = H + HO ,
(0)
(I)
2
2
2
.
H + O = OH + O,
6
4
2
0
2
1
.
O + OH = O + H,
(–I)
(II)
2
3
.
OH + H = H O + H,
2
2
2
.
O + H = OH + H,
(III)
(IV)
2
.
H + O + M = HO + M,
2
2
.
HO
(HO ) ,
(V)
(VI)
2
2 s
0
10
20
b)
30
40
t, ms
.
∆
8
P, atm
HO + H = H O + H,
2
2
2
2
(
.
.
.
H + HO = OH + OH ,
(VII)
(VIII)
2
.
H + RH = R .
6
4
2
1
1
.
Here, RH is an olefin molecule, R is an alkyl (propyl,
1
2
isobutyl, or hexyl) radical, and (HO ) is an adsorbed
2 s
.
3
OH radical.
2
The alkyl radical is involved in the fast reaction
.
.
R + O = R O ,
(IX)
1
2
1
2
which is most likely followed by the olefin regeneration
.
0
10
20
30 t, ms
reaction yielding HO [32, 33]:
2
.
.
2
Fig. 4. (a) Combustion rate of 30% H in air (1) in the
R O = RH + HO .
(X)
2
1
2
absence of an admixture, (2) in the presence of 0.5% propy-
lene, and (3) in the presence of 0.5% isobutylene. (b) Com-
bustion rate of the same mixture (1) in the absence of an
admixture, (2) in the presence of 0.9% propylene, and (3) in
the presence of 0.9% isobutylene.
The σ–π* conjugation in the propylene molecule
increases the reactivity of the H atoms in the α-posi-
tion. This facilitates the abstraction of an H atom with
the formation of an allyl radical [34]:
.
H + CH CHCH = H + CH CHCH .
(XI)
3
2
2
2
2
of heat generation in a nonchain reaction is thousands
of times longer that the characteristic time of heat dis-
sipation [2]. Therefore, in the absence of reaction
chains, the extent of self-heating does not exceed a few
kelvins and can cause neither ignition nor flame propa-
gation. Thus, layer-by-layer ignition, which gives rise
to laminar flame propagation, is a chain, not thermal,
process, contrary to earlier beliefs. Accordingly, the
Nevertheless, the activation energy of the addition
of a hydrogen atom to the π-bond, which is no higher
than 6.5 kJ/mol [35, 36], is much lower than the activa-
tion energy of H abstraction, so inhibition is mainly due
to reaction (VIII). The increased chain termination
capacity of compounds having a π-bond as compared to
compounds without a π-bond manifests itself, for
flame velocity and the critical conditions for flame example, as the fact that propylene and allyl alcohol are
propagation are primarily determined by the competi- stronger inhibitors of hydrogen combustion than iso-
tion between chain branching and chain termination [1, propanol [28, 29], which has similar gas kinetic and
2
, 28] rather than by thermal ignition conditions. There- thermal properties.
fore, flame propagation is a chain, not thermal, process.
It is due to this fact that most of the observed regulari-
ties of combustion differ radically from those predicted
by thermal theory.
It is clear from the above mechanism that free
valences are multiplied only by reaction (I). Reac-
tions (II) and (III) multiply reactive intermediates, spe-
cifically, atoms and radicals. In stoichiometric and rich
hydrogen–air mixtures, nearly all of the O atoms and
Under the conditions examined, the key role in H2
combustion is played by the following reactions OH radicals react with H
.
because of the large rate
2
KINETICS AND CATALYSIS Vol. 48 No. 1 2007

EFFECT OF THE MOLECULAR STRUCTURE OF OLEFIN ADMIXTURES
13
constants of reactions (II) and (III) and the rather high spark-induced self-heating to a greater extent than the
H content. Therefore, the branching rate in such mix- chain termination reactions even if ξ did not decrease.
2
tures is limited by reaction (I) rather than reaction (II) In fact, as the initiation rate increases, ξ does decrease
or (III). The bimolecular, nonlinear, chain-termination primarily because of the increase in the H concentra-
reaction (–I) plays a significant role in the kinetics of tion, which appears in the denominator of Eq. (6).
developed combustion [31].At the same time, since this Furthermore, as the temperature increases, ξ
reaction is the reverse of the branching step and its rate decreases because of the increase in the rate constant
is proportional to the product of the concentrations of of reaction (VI), which appears in the denominator of
active species, which are scarce at the onset of combus- the right-hand member of Eq. (6).
tion, the ignition limit is independent of its rate.
Taking into account the competition between chain
Reaction (V) is adsorption eliminating free branching and chain termination makes it possible to
valences. This reaction competes with reaction (VI), explain the dependence of the initiation energy on the
which regenerate hydrogen atoms. The trimolecular inhibitor concentration. Indeed, in the presence of an
recombination reaction (IV) causes chain termination inhibitor, the right-hand side of the critical condition of
.
chain ignition contains the term k f . Therefore, as
8
In
only if the HO radical is adsorbed to react with O or
2
2
compared to the inhibitor-free mixture, the same mix-
ture containing an inhibitor requires a larger increase in
k1 and a greater reduction in ξ for ignition. This is
achieved by raising the initiation power, which results
in a temperature rise and higher H and O concentra-
tions. Note that, in the presence of an inhibitor, com-
bustion proceeds less rapidly and is less capable of
heating the adjacent layers of the fresh mixture. This is
one way in which inhibitors hamper the initiation of
combustion.
decompose instead of participating in reaction (VI) or
VII).
(
.
The reaction between a hydrogen atom and the HO
2
.
radical primarily yields the OH radical [36]. In view
of reactions (V)–(VII), we arrive at the following
expression for the fraction of reaction (IV) events
resulting in chain termination:
k
5
ξ = -----------------------------------------------,
(6)
The effect of an inhibitor on the necessary initiation
k + k [H ] + k [H]
5
6
2
7
power is determined by the k value for this inhibitor.
8
where rate constants are numbered in the same way as Since a π-bond at a tertiary carbon atom is more reac-
reactions in the above mechanism.
It follows from the above mechanism that the chain for isobutylene than for propylene. Therefore, at a
ignition condition (f > g) can be expressed as
tive than the same bond at a secondary atom, k is larger
8
given olefin concentration, the isobutylene-containing
mixture will require a higher initiation power for ine-
quality (7a) to be true (i.e., for ignition).
2
k [O ] ≥ k [O ][M]ξ + k [In].
(7)
1
2
4
2
8
Here, the equality sign corresponds to the ignition
Thus, accepting the determining role of the
branched-chain mechanism and the competition
between chain branching and termination makes it pos-
sible to explain the above effects of the inhibitors on the
minimum energy required for the initiation of combus-
tion and the difference between the inhibition efficien-
cies of olefins.
limit.
In this study, the initial concentration of the mixture
was the same in all runs and only the initial mole frac-
tions of components were varied. For this reason, the
component concentrations in Eq. (7) are conveniently
expressed in terms of mole fractions:
Let us compare the effects of isobutylene and propy-
lene on the development of combustion. The combus-
2
k1 f O2 ≥ k f [M]ξ + k f .
(7a)
4
O
8
In
2
Let us now consider the role of a temperature rise in tion kinetic curves are flatter for i-C H than for propy-
4 8
the spark initiation of combustion. It can readily be lene (Fig. 4); that is, combustion in the presence of
seen that, even if the last two terms in the dominator of isobutylene develops at a lower rate. Furthermore,
Eq. (6) are neglected, ξ at a temperature of, e.g., 900 K isobutylene produces a much stronger effect on the
will be smaller than unity by a factor of several hun- slope of the combustion curve of the pure mixture than
dreds. This temperature is established in the immediate do equal amounts of propylene. Curve slopes as a func-
proximity of the spark and causes chain ignition. This tion of the admixture concentration differ more widely
ignition, which is a fast exothermic reaction, causes for isobutylene than for propylene. The data obtained
self-heating capable of initiating layer-by-layer igni- for a mixture containing 40% H also indicate that
2
tion (i.e., flame propagation) under certain conditions.
The activation energy of reaction (I) is close to
isobutylene exerts a stronger effect on combustion. Fur-
thermore, the stronger effect of isobutylene on H com-
2
bustion manifests itself as a stronger dependence of the
7
0 kJ/mol, while that of reaction (VIII) is no higher
∆
Pmax and Imax values and of the ultimate oxygen con-
than a few kilojoules per mole [35, 36]. The value of k4
decreases slightly with increasing temperature since
reaction (IV) is trimolecular. As a consequence, the
sumption on the admixture concentration.
The decelerating effect of the inhibitors on combus-
chain branching reactions would be accelerated by tion and the difference between their efficiencies are
KINETICS AND CATALYSIS Vol. 48 No. 1 2007

1
4
AVETISYAN et al.
[
H ], %
Note that, in the oxidation of propyl and isobutyl
2
1
2
3
radicals, olefin regeneration is primarily due to the
8
0
0
0
0
reaction between the alkyl radical and O followed by
2
the decomposition of the resulting alkyl peroxy radical.
Therefore, to the extent to which the levels of regener-
ation of propylene and isobutylene are similar, the
observed difference between the effects of these olefins
is due to kinetic differences in the primary stage of the
process, specifically, the capture of a hydrogen atom.At
the same time, the difference between propylene and
isobutylene in terms of thermal and gas kinetic param-
eters is too small to be significant when small amounts
of an olefin are used.
7
6
5
4
3
2
1
0
0
0
0
2
1
3
Thus, although the combustible mixture undergoes
strong self-heating, which additionally speeds up the
combustion process, there is a marked difference
between the effects of propylene and isobutylene. This
difference arises only from the fact that the π-bonds at
the secondary and tertiary carbon atoms differ in reac-
tivity and is further evidence that the chain avalanche
plays the determining role in combustion even in the
case of strong self-heating.
0
1
2
3
4
5
6
7
8
9
10
[
ln], %
Fig. 5. Effects of (1) isobutylene, (2) propylene, and (3)
hexene on the upper concentration limit of flame propaga-
tion in the hydrogen–air mixture.
explicable in terms of the following formula for the rate
of a nonisothermal branched-chain process:
The Effects of the Admixtures on the Concentration
Limits of Flame Propagation
t
0
1
W/[O ] = k n exp {2k f exp(–E /RT)
The data presented in Fig. 5 indicate that C H and
4 8
at very low concentrations. For example, 1% propylene
changes the upper concentration limit from 75 to 50%.
An equal amount of isobutylene decreases this limit to
2
1
0
O
1
3
6
∫
2
(
8) i-C H decrease the upper limit by different values even
t
0
–
k f [M]ξ – k f }[M]dt.
4 O 8 In
2
In this expression, the indices given to rate constants 40%. It is also clear that, as the inhibitor concentration
are consistent with the above reaction numbering, k is
the preexponential factor of reaction (I), E is the acti-
vation energy of reaction (I), f O2 and f are the mole
0
1
is raised, the difference between the effects of C H and
3
6
i-C H increases. This finding is in good agreement
4
8
1
with Eqs. (7a) and (8). The effect of isobutylene
exceeds not only the effect of propylene but also the
In
fractions of O and the inhibitor, [M] is the mixture con- effect of n-hexene (Fig. 5). This result is quite consis-
2
tent with the well-known fact that the π-bond at a ter-
tiary carbon atom is more reactive than the same bond
at a secondary carbon atom. This regularity manifests
itself as differences in both critical ignition conditions
and combustion intensity.
centration, t is the time after which the contribution
0
from ω to the multiplication rate of reactive species is
0
insignificant, and n is the concentration of reactive
0
species at the time t0.
It is clear from Eq. (8) that an inhibitor, implying the
presence of a third term in the braces, reduces the inte-
grand and, accordingly, causes an exponential decrease
in the combustion reaction rate. This causes a decrease
in the self-heating of the mixture. It is equally impor-
tant that a decrease in the braced quantity causes an
exponential weakening of the temperature dependence
of the reaction rate (dW/dT). As a consequence, self-
heating exerts a much weaker speedup effect on com-
bustion.
Taking into account the crucially significant compe-
tition between chain branching and chain termination
makes it possible to explain the dependence of the
upper limit of flame propagation on the mole fraction of
the inhibitor (the shape of the curves plotted in Figs. 1–3).
Since the concentration limit is determined both by the
ignition condition and by the capacity of the burning
layer to ignite the adjacent layer of the fresh mixture,
we will consider the dependence of the combustion
reaction rate on the inhibitor concentration. A measure
of this dependence is the derivative of the reaction rate
It follows from Eq. (8) that the slowdown due to
with respect to f . It is clear from Eq. (8) that this deriv-
inhibition must increase with increasing k . Since the
In
8
rate constant is larger for the reaction between H and ative, as well as the reaction rate, is proportional to an
i-C H than for the reaction between H and C H , isobu- exponential function in which the inhibitor concentra-
4
8
3
6
tylene exerts a stronger effect on combustion, in accor- tion is in the exponent. Furthermore, it follows from
dance with expectations (Figs. 3, 4).
Eq. (8) that, as fIn increases, the integrand decreases,
KINETICS AND CATALYSIS Vol. 48 No. 1 2007

EFFECT OF THE MOLECULAR STRUCTURE OF OLEFIN ADMIXTURES
15
of nonisothermal chain reactions not only provides an
explanation for these facts but also enables the
researcher to predict and reveal the effects of admix-
tures by considering their molecular structures. The
correlation between the molecular structure and reac-
tivity in gas-phase chain combustion is so strong that
changing a single functional group in the molecule of
the admixture causes marked changes in the kinetic,
macrokinetic, and gas dynamic parameters of the pro-
cess as a whole.
∂
∂
W
f
In
implying an exponential decrease in --------- (a weakening
of the dependence of the combustion rate on the inhib-
itor concentration). The way in which the combustion
rate decreases with increasing f means that, as the
inhibitor concentration is raised, the progressively
greater increase in f is required to produce the desired
In
In
inhibiting effect. This inference is in good agreement
with the fact that the upper concentration limit was an
exponentially descending function of f in all runs,
In
including the runs presented in Fig. 3.
ACKNOWLEDGMENTS
This study was supported by the Presidium of the
Russian Academy of Sciences (program no. 7P) and by
the Russian Foundation for Basic Research (grant
no. 05-03-33050).
Suppression of the Chain Thermal Explosion
As is noted above, the pressure curve shows an
upward excursion in the absence of an inhibitor (Fig. 4).
As judged from the sound effect (plop) accompanying
ignition in these runs, as well as from the maximum
pressure value, the gas pressure is not uniformly dis-
tributed throughout the reactor. This nonuniformity is
due to the local gas compression caused by the rapidly
propagating combustion wave at the opposite end of the
chamber. This compression causes extra gas heating
before the combustion front and facilitates the fulfill-
ment of the thermal explosion condition (3) at already
fulfilled conditions (1) and (2). This leads to a chain
thermal explosion. Thus, the pressure at the moment of
the excursion of the first postinitiation point in Fig. 2 is,
in essence, the instantaneous explosion pressure. The
effect of the inhibitors on the chain thermal explosion
will be analyzed in terms of Eqs. (2) and (3). A quanti-
tative characteristic of the temperature dependence of
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KINETICS AND CATALYSIS Vol. 48 No. 1 2007