Kinetics of 2-methylbutene-2 epoxidation with 2-methylbutane hydroperoxide

Article abstract of DOI:10.1134/S0965544110050117

The kinetics of 2-methylbutene-2 epoxidation with 2-methylbutane hydroperoxide was studied in the presence of a molybdenum catalyst. The mathematical description of the hydroperoxide consumption and 2-methyl-butene-2 oxide formation was derived, and the most probable scheme of the process was suggested. The main kinetic constants were calculated.

Full text of DOI:10.1134/S0965544110050117

ISSN 0965ꢀ5441, Petroleum Chemistry, 2010, Vol. 50, No. 5, pp. 381–387. © Pleiades Publishing, Ltd., 2010.
Original Russian Text © L.A. Petukhova, V.N. Sapunov, Kh.E. Kharlampidi, A.A. Petukhov, 2010, published in Neftekhimiya, 2010, Vol. 50, No. 5, pp. 391–397.
Kinetics of 2ꢀMethylbuteneꢀ2 Epoxidation
with 2ꢀMethylbutane Hydroperoxide
L. A. Petukhovaa, V. N. Sapunovb, Kh. E. Kharlampidia, and A. A. Petukhovc
a Kazan Technical University, Kazan, Russia
b Mendeleev University of Chemical Technology, Moscow, Russia
c Nizhnekamsk Institute of Chemical Technology, Nizhnekamsk, Russia
eꢀmail: sapunovvals@gmail.ru
Received April 28, 2010
Abstract—The kinetics of 2ꢀmethylbuteneꢀ2 epoxidation with 2ꢀmethylbutane hydroperoxide was studied in
the presence of a molybdenum catalyst. The mathematical description of the hydroperoxide consumption
and 2ꢀmethylꢀbuteneꢀ2 oxide formation was derived, and the most probable scheme of the process was sugꢀ
gested. The main kinetic constants were calculated.
DOI: 10.1134/S0965544110050117
The synthesis of isoprene from isopentane via the prene, the final product. The key stage of the overall
reaction sequence involving 2ꢀmethylbuteneꢀ2 oxide process shown in the scheme is epoxidation, which
(OMB) is one of the most promising isoprene manuꢀ determines the isoprene production efficiency in
facturing processes [1, 2] (Scheme 1):
many respects. Various molybdenum compounds were
used as catalysts [3, 4].
In this work, we studied the general features of
2ꢀmethulbuteneꢀ2 epoxidation with 2ꢀmethylbutane
hydroperoxide in the presence of a molybdenumꢀconꢀ
taining catalyst. Revealing the trends in the characterꢀ
istics of the process and its mathematical description
are of great importance for both the design of a reacꢀ
tion unit for the commercial production of isoprene
according to the scheme given above and the epoxidaꢀ
tion theory. Moreover, it is quite unclear whether the
steric factor has an effect on the reaction mechanism,
as the reactants bear bulky substituents.
I
VI
OOH
OHOH
II
V
IV
O
EXPERIMENTAL
III
Experiments were carried out at a temperature of
30–40 С in a steady system with the use of a temperaꢀ
°
OH
Scheme 1.
tureꢀcontrolled glass vessel (50 ml) equipped with a
heating jacket, a thermostat, a stirring device, a conꢀ
denser, and a thermometer. The thermocatalytic
The specific feature of the process is the fact that decomposition of hydroperoxide was not observed at
the successive transformations of 2ꢀmethylbutane these temperatures, and OMB is formed almost quanꢀ
hydroperoxide (HPMB) into 2ꢀmethylbutanolꢀ2 titatively, thereby simplifying the study of the kinetics
(MBOL) (route II) and the OMB synthesis from 2ꢀ of the process in question. The reaction was carried
methylbuteneꢀ2 (OL) (route IV) are combined in one out in isopentane. As a catalyst, we used a freshly preꢀ
process, i.e., in the hydroperoxide epoxidation of oleꢀ pared solution of bis(2ꢀmethylbutanediolꢀ2,3) molybꢀ
fin. This is shown in the scheme by crossing of the date in MBD with 3.5 wt % of molybdenum, which
arrows referring to routes II and IV. The scheme also was obtained by solution of molybdenum anhydride in
involves the stages of HPMB synthesis (route I); OMB MBD according to the procedure described in [5].
hydration to 2ꢀmethylbutanediol (MBD) (route V); HPMB was synthesized according to the procedure
and the dehydration of the alcohols, namely, the conꢀ described in [6]. 2ꢀMethylbuteneꢀ2 was synthesized by
version of MBOL into the olefin and MBD into isoꢀ the dehydration of MBOL in the presence of a KUꢀ2
381

382
PETUKHOVA et al.
FPP catalyst. All the compounds were identified by the general scheme of epoxidation, which involves the
IR, NMR, electronic absorption spectroscopy, and fast equilibrium formation of a catalyst complex with
elemental analysis.
hydroperoxide and its slow reaction with the olefin:
The progress of the reaction course was monitored
by following the hydroperoxide consumption, because
the selectivity for the oxide was 93–97% in all cases.
The epoxidation reaction mixture was analyzed for
HPMB by iodometric titration. The concentration of
homogeneous molybdenum was determined by titraꢀ
tion with an ammonium metavanadate solution in the
presence of phenylanthranylic acid after molybdenum
conversion into the pentavalent form by heating with
an acidic phenylhydrazine solution. The concentraꢀ
tion of OMB in the reaction mixture was determined
by titration: an aliquot was added to a saturated MgCl2
solution containing a 0.02 N HCl solution, held for
15 min at an ambient temperature, and the residual
HCl was titrated with a KOH solution.
K
1
[ROOH] + [cat]
[cat
⋅
ROOH
]
(I)
к0
[cat ⋅ ROOH] + [OL]
[ROH] + [oxide].
[cat]
(II)
+
The reaction course is complicated by the formaꢀ
tion of various catalyst complexes with reaction prodꢀ
ucts, which causes the soꢀcalled simple, quadratic,
and crossed inhibition:
K
2
[ROH] + [cat]
2[ROH] + [cat
[ROH] +
[cat
[cat
⋅
ROH
]
(III)
(IV)
K
3
]
⋅
2ROH
]
[ROOH] + [cat]
(V)
K
4
[cat ⋅ ROOH ⋅ ROH].
Kinetic Studies of the Process
The formation of these complexes in the reaction
Many publications are devoted to the kinetics of mixture was established not only by the analysis of
the hydroperoxide epoxidation of olefins, and the proꢀ kinetic data, but also by physicochemical methods [8–
cess itself has been employed in industry for a long 10]. According to published data, the rate equation for
time [1, 7]. Despite some disagreements in the interꢀ olefin epoxidation by hydroperoxides described above
pretation of the details, most researchers agree with (reactions (I)~(V)) is a linearꢀfractional function
k0 ⋅ K1 ⋅ [cat] ⋅ [OL] ⋅ [ROOH]
d[ROOH]
–ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ,
(1)
2
dt
1 + K1[ROOH] + K2[ROH] + K3[ROH] + K4[ROOH] ⋅ [ROH]
where the terms in the denominator of Eq. (1) correꢀ
(ii) solution of the problem regarding whether the
spond to the formation of various complexes of the reaction of interest obeys the most widespread scheme
reactants and the products with the catalyst (soꢀcalled of metal complex catalysis, as the reaction centers of
catalyst complexation function).
both reactants OL and HPMB possess bulky substituꢀ
ents.
In order to simplify the solution of this problem, we
studied the reaction kinetics until ~50% hydroperoxꢀ
ide conversion, thereby diminishing the effect of the
quadratic and crossed inhibition.
Taking into account the material balance relation,
i.e., [ROH] = [ROОH]0 – [ROOH], Eq. 1 can be repꢀ
resented as a function of a single variable (2):
–d[ROOH]/dt
(2)
2
=
[ROOH]/(α + β[ROOH] + γ[ROOH] ),
RESULTS AND DISCUSSION
where
Kinetic investigations were carried out by several
series of singleꢀfactor experiments, with only one
parameter being changed in each series. The series
were as follows: (1) the influence of the catalyst conꢀ
centration on the reaction rate at constant concentraꢀ
α = (1 + K2[ROOH]0
(3)
2
+
+
K3[ROOH]0 )/k0K1[cat] ⋅ [OL])
β = (K1 – K2 – 2K3[ROOH]0
K4[ROOH]0 )/k0K1[cat] ⋅ [OL])
(4)
(5)
tions [HPMB]0 and [OL]0 and a temperature of
45 (Table 1); (2) the influence of the initial olefin
concentration [OL]0 at constant [HPMB]o and cataꢀ
lyst [cat]0 concentrations and a temperature of
45 (Table 2); (3) two series with varying initial conꢀ
centration [HPMB]о at different olefin concentraꢀ
Т =
°С
γ = (K3 – K4)/(k0K1[cat] ⋅ [OL])).
Т
=
We used this description of the process as a working
hypothesis for revealing the following problems:
°С
(i) formulation of the mathematical description of tions: [OL]0 = 7.2 and 4 mol/l at a constant catalyst
the hydroperoxide consumption and formation of concentration of [cat]0 = 2
10–3 mol/l and a temperꢀ
OMB and suggestion of the more probable mechanism ature of = 45 (Table 3); and (4) the influence of the
of the process; temperature on the behavior of the hydroperoxide
×
Т
°С
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KINETICS OF 2ꢀMETHYLBUTENEꢀ2 EPOXIDATION
383
Table 1. Effect of the catalyst concentration on the time variaꢀ
tion of the hydroperoxide concentration (mol/l) at [HPMB]0 =
1.6 mol/l, [OL]0 = 7.2 mol/l, and the temperature T = 45°C
a singleꢀfactor experimental series concerning the
effect of the catalyst concentration should give the
same curve in the [HPMB] vs. [cat]t coordinates. For
the convenience of the treatment of all of the experiꢀ
mental series, we plotted the diagrams for the time
variation of the current HPMB concentrations in the
[cat], mol/l
Time, min
1
×
10–3
2
×
10–3
3.0
10–3
×
[HPMB] vs. [cat]/[cat]0
nates, where = [cat]/[cat]0, [cat] is the catalyst conꢀ
t
or [HPMB] vs.
λ
t coordiꢀ
0
5
1.6
1.6
1.6
1.1
0.9
0.7
0.6
–
λ
1.4
1.25
1.1
centration in a given run, and [cat]0 = 0.002 mol/l is
the catalyst concentration at which all other experiꢀ
mental series were carried out.
Superimposing all kinetic curves of the series conꢀ
cerning the influence of the catalyst (Table 1) in the
10
15
20
25
35
1.25
1.15
1.05
0.97
0.85
0.92
0.8
0.72
–
same diagram in the [HPMB]–
the leftꢀhand part of Eq. 7 to be proportional to
λ
t coordinates shows
–
λ
,
indicating that the reaction is firstꢀorder in the catalyst
(Fig. 1) [11].
It may be supposed that similar to the catalyst conꢀ
centration, the olefin concentration is involved in the
rate equation as a factor and is timeꢀinvariant providꢀ
concentration with time at constant [HPMB]0 and
[OL]0 concentrations and [cat]0 = 2
(Table 4).
×
10–3 mol/l
First, we processed the rate curves of the experiꢀ ing that [HPMB]0
ꢀ [OL]0. However, the aboveꢀ
ments on the influence of the catalyst concentration described treatment of rate curves for the series of
on the epoxidation rate. Based on the assumption that experiments specified in Table 2 did not give positive
the catalyst concentration is involved as a factor in the results. The data points plotted in the [HPMB]–
rate equation and is not a function of time (the catalyst [OL]0
t coordinates did not fall on the same line. The
is stable during the reaction), i.e., the rate equation has reaction slowed down with progress—the lower the
the form of Eq. (6):
excess of olefin over HPMB, the stronger the decelerꢀ
ation. On the other hand, the initial reaction rates
–d[HPMB]/dt = [cat] ⋅ f([HPMB]),
(6)
(
W0) in this experimental series (Table 2) were proporꢀ
tional to the initial olefin concentration. The followꢀ
ing linear dependence (8) was observed over the entire
range of [OL]0 examined.
the following equation can be derived in the integral
form after the separation of the variables:
[HPMB]
W0 = (0.014 0.001)
×
[OL]0, mol l–1 min–1
.
(8)
d[HPMB]/f([HPMB]) = [cat] ⋅ t,
(7)
∫
The first order of the reaction with respect to the
olefin is also confirmed by the results of the treatment
of the rate curves of OL consumption, determined as a
difference between the current and initial HPMB conꢀ
centrations, in semilogarithmic coordinates (at
[HPMB]0
where [HPMB]0 and [HPMB] are the initial and curꢀ
rent concentrations of HPMB, and
time.
t is the reaction
Equation (7) shows that at the constant initial conꢀ [HPMB]0 ꢁ [OL]0). The rate constant of the pseudoꢀ
centration of hydroperoxide ([HPMB]0), i.e., at the firstꢀorder olefin consumption is (0.015 0.001) min–1
equality of the left parts of Eq. (7), all kinetic curves in in this case, which coincides with the value deterꢀ
Table 2. Effect of the initial concentration of olefin (OL) on the time variation of the HPMB concentration ([HPMB]0 =
1.5 mol/l, [cat]0 = 2 × 10–3, T = 45°C
Initial concentration
е
OL, mol/l
2.0
Time, min
0.1
0.3
0.5
1.0
3.0
5.0
0
10
20
30
40
50
1.5
1.5
1.5
1.5
1.5
1.3
1.5
1.5
1.49
1.48
1.47
1.46
1.45
1.44
1.43
1.42
1.41
1.41
1.43
1.39
1.35
1.32
1.3
1.4
1.3
1.16
0.91
0.81
0.74
1.3
1.18
1.07
0.96
0.9
1.25
1.2
1.1
1.03
1.02
1.18
0.9
PETROLEUM CHEMISTRY Vol. 50
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384
PETUKHOVA et al.
Table 3. Effect of the initial concentration of hydroperoxide on the time variations of its concentration at [OL]0 = 4 and
7.2 mol/l, [cat]0 = 2 × 10–3 mol/l at 45°C
[OL] = 4 mol/l
[OL] = 7.2 mol/l
Time, min
[HPMB], mol/l
0
5
0.95
0.8
1.5
1.3
1.16
1.1
1
1.7
0.5
0.83
0.63
0.48
0.4
1.2
1.6
1.5
0.35
0.3
0.97
0.76
0.65
0.58
0.53
1.25
1.1
10
15
20
25
30
0.72
0.65
0.6
1.35
1.3
0.25
0.22
0.2
0.95
0.85
0.76
1.22
1.18
1.16
0.38
0.35
0.57
0.55
0.98
0.96
mined by the method of initial rates. The comparison
of these results allows us to conclude that the olefin
interacts with the products formed during the reacꢀ
tion, causing a change in the performance of the cataꢀ
lyst. Mathematically, this means that the olefin conꢀ
centration ([OL]) is involved not only as a factor in the
The statistical treatment of the arrays of data for the
experimental series dealing with the effect of the initial
concentration of HPMB on the reaction (Table 3)
showed that the coefficient at the third term
γ
in
Eq. (9) is insignificant. On one hand, this result conꢀ
firmed our assumption that the soꢀcalled quadratic
and crossed inhibition did not manifest themselves at
hydroperoxide conversions below 50%. On the other
hand, data processing becomes much simpler, since
the quadratic term in the denominator in Eqs. (1) and
(2) disappears. In principle, the appearance of the
function
role of olefin in this process, it is necessary to express
the function ([HPMB]) in the explicit form. For this
f([HPMB]) in Eqs. (6) and (7). To clarify the
f
purpose, we treated the experimental series on the
effect of the initial HPMB concentrations given in
Tables 2 and 3.
insignificant factor
equilibrium constants К3 and К4 (see the functional
dependence of in Eq. (5)). However, a more concrete
answer can be given from the analysis of the depenꢀ
dences for and
γ
might indicate the equality of the
The integral form of Eq. (2), Eq. (9), can easily be
analyzed by a linear regression method:
γ
α
β.
ln([HPMB]0/[HPMB])
Further, we treated the data by linearization, which
is a more illustrative statistical method. With allowꢀ
αꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
t
ance for the insignificance of , Eq. (2) is reduced to
γ
([HPMB]0 – [HPMB])
Eq. (10) (notations [ROOH] and [HPMB] are the
same):
+
βꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
(9)
t
2
2
–
d
[
HPMB]/dt = [HPMB]/(
where
* = (1 + K2
* = (K1
α
* +
β
*
⋅
[
HPMB]),(10)
([HPMB]0 – [HPMB] )
+
γꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ = 1 ,
t
α
[
HPMB]0)/(k0
⋅
K1
⋅
[cat] ⋅ [OL])
where the functional values of
above (Eqs. (3)–(5)).
α
,
β
, and
γ
are given
β
–
K
2)/(k0 K1 [cat]
⋅
⋅
⋅
[OL])
and, after integration, it can be presented in a more
convenient form (Eq. (10a)) for data processing by
regression analysis:
Table 4. Effect of the temperature on the time variation of hyꢀ
droperoxide at [HPMB]0 = 1.7 mol/l, [OL]0 = 7.2 mol/l, and
[cat]0 = 2 × 10–3 mol/l
Y
= 1/β
* + (–
α
*/β
*)
⋅
X,
(10a)
where
X and Y are the variables
Temperature, °C
Time, min
Y = ([HPMB]0 – [HPMB])/t,
X = ln([HPMB]0/[HPMB])/t.
30
35
40
0
5
1.7
1.7
1.7
1.57
1.51
1.40
1.30
1.20
1.50
1.40
1.20
1.00
0.88
1.48
1.33
1.05
0.80
0.68
Indeed, processing the experimental data from Table 3
in coordinates yields a set of linear dependences
(Fig. 2, curves ). All of these straight lines cross at
Y ~ X
10
20
30
40
1–4
the same point on the ordinate axis, and the slope linꢀ
early depends on [HPMB]0. These findings indicate
the following:
PETROLEUM CHEMISTRY Vol. 50
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KINETICS OF 2ꢀMETHYLBUTENEꢀ2 EPOXIDATION
385
[HPMB], mol/l
1.8
Y
0.08
0.07
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
1
0.06
0.05
0.04
0.03
0.02
0.01
0
2
5
3
4
–0.01
–0.02
0
5
10 15 20 25 30 35 40
λ ×
, min
t
0
0.1
0.2
0.3
0.4 0.5
(1 + С3)X
Fig. 1. Experimental data points and calculated rate curves
for the experimental series: effect of the hydroperoxide iniꢀ
tial concentration (data from Table 3, ) and the effect of
᭿
Fig. 2. Results of the treatment of the experimental series
on the effect of the hydroperoxide initial concentration
(Table 3). The designation of the diagram axes is given in
the catalyst concentration (data from Table 1,
dimensionless value (see text).
᭡
).
λ
is a
the text. (
1
)
⎯
(
4
) corresponds to the experiments with
[HPMB] ) = 1.6, 1.2, 0.85, and 0.5 mol/l at
C
= 0; (5)
0
3
—the crossing of the straight lines at one point on
the ordinate axis shows that the constant does not
involves all experiments of this series at
C = 5.4.
3
β*
depend on the initial substrate concentration
[HPMB]0; i.e., there are no terms with constants К3
and К4, and
A similar treatment of the data of the experimental
series on the influence of [HPMB]0 at another olefin
concentration (Table 3) gave identical results
(Table 5). The confidence level of the approximation
was also high (R2 = 0.975).
—the linear relation of the slope to [HPMB]0 conꢀ
firms the reaction scheme involving only equilibriums
(I), (II), and (III) and the absence of the influence of
the quadratic and crossed inhibition.
From the comparison of the values of С1, С2, and
С3 and the functional dependences of the
α*
and *
β
In order to more precisely determine the constants
for Eq. (10a), we processed the whole array of data of
this experimental series (Table 2) in somewhat altered
coordinates:
parameters of Eq. (10), the values of the effective rate
constant and equilibrium constants were calculated
for 45 С (Table 5). The rate constant k0 and the conꢀ
°
stant K1 for the equilibrium formation of the catalyst
complex with hydroperoxide were the same in both
cases, whereas the equilibrium constant for the formaꢀ
Y
= C1 + C2(1 + C3[HPMB]0)
Х,
(11)
tion of the catalyst complex with alcohol (K2
depended on the olefin concentration in the reaction
mixture.
In order to more precisely investigate the depenꢀ
dence of K2 on the olefin concentration, we analyzed
the experimental data obtained at [OL]0 = 3 and
5 mol/l (Table 2). For this purpose, we minimized the
)
where С1, С2, and С3 are the constants for this experiꢀ
mental series.
One can see that there is a unique dependence
between the coefficients С1, С2, and С3 and the
parameters
α*
and * Eq. (10). From the fitting proꢀ
β
cedure, we estimated the coefficient С3 and obtained a
single linear dependence, which comprised all data of
the experimental series (Fig. 2, 5). In the range 5.2 <
function
F(K2), which was derived by integrating difꢀ
ferential equation (10):
С3 < 5.6, the confidence of approximation (R2 of the
linear regression determined by a standard Excel 93ꢀ
2003 program) was maximum R2 = 0.98. Within this
approximation for the confidence level (R2 = 0.98),
the numerical values of С1, С2, and С3 of linear
Eq. (11) were estimated (Table 5). It is noteworthy that
the values of these coefficients did not change after the
introduction of the data on the effect of the catalyst
concentration to the analysis.
F(K2) = (1 + K2 ⋅ [HPMB]0) ⋅ X
(K1 – K2) ⋅ Y – (k0 ⋅ K1 ⋅ [cat] ⋅ [OL]) = 0,
(12)
+
where
X and Y are the variables defined above
(Eq. 10a).
The optimization was carried out by the leastꢀ
squares method in parameter К2 at constant values of
PETROLEUM CHEMISTRY Vol. 50
No. 5
2010

386
PETUKHOVA et al.
Table 5. Constants C1, C2, and C3 of Eq. (11) and kinetic constants of Eq. (10)
[OL],
mol/l
T
,
°
C
C1
C2
C3
k
0, min–1
K
1, l mol–1
K
2, l mol–1
45
45
45
45
7.2
5.0
–0.020 0.001
0.2 0.01
5.3 0.2
25
25
25
25
H0
10000 500
1
0.3 0.03
0.3
5.4 0.2
6.0 0.5
7.0 0.2
8.0 0.8
4.0
–0.009 0.0005
0.15 0.01
7.0 0.5
1
0.27 0.03
0.3
3.0
30–45
0–7.2
Δ
=
Δ
H1
=
Δ
H2
=
1000 300
4000 50
k0 and K1 obtained earlier. The results are listed in
Table 5.
F(ΔH0, ΔH1, ΔH2) = (1 + K2[HPMB]0) ⋅ X
(13)
+
(K1 – K2) ⋅ Y – (k0K1[cat] ⋅ [OL]),
Thus, we found that the inhibition of the process by
virtue of the equilibrium formation of the catalyst
complex with the reaction products weakens with an
increase in the methylbutene concentration in the
solution. Without going into the reasons behind this
phenomenon, it may be stated that it is due to the
enhanced stability of molybdenum compounds in the
presence of olefins [12]. Furthermore, it has been
found [13, 14] that catalyst activation does not occur
unless the system simultaneously contains both hydroꢀ
peroxide and olefin.
where
Н1
X
and
and are the variables defined above and
Y
Δ
Н0
,
Δ
,
ΔН2 are the temperature coefficients of the
exponential dependence of the constants k0
K2, respectively.
The function
the leastꢀsquares technique with
ting parameters at fixed values of the rate constants
and equilibrium constants determined earlier for a
temperature of 45
, K1, and
F(ΔН0,
ΔН1,
Δ
Н2) was optimized by
Δ
Н0 Н1 Н2 as fitꢀ
,
Δ
,
Δ
°С [k0(318 K), K1(318 K), and
K2(318 K)
:
k0 = exp{lnk0(318 K) + ΔH0(1/318 – 1/T)}.
K1 = exp{lnK1(318 K) + ΔH1(1/318 – 1/T)}.
K2 = exp{lnK2(318K ) + ΔH2(1/318 – 1/T)}.
To determine the temperature dependence of the
kinetic constants, we analyzed the experimental data
obtained at different temperatures (Table 4) and minꢀ
imized the function
F(ΔН0,
ΔН1,
ΔН2), which was
The calculated data are listed in Table 5. The adequacy
of the mathematical description of the process under
study was confirmed as follows:
obtained by the integration of differential Eq. (10):
—the curves calculated with the use of Eq. (10)
and the kinetic constants k0, K1, and K2 fit well with the
[HPMB] , mol/l
calc
1.8
1.6
1.4
experimental data for all of the experimental series
under consideration and
—the confidence level of approximation (R2) for
the correlation of all experimental (Tables 1–3) and
calculated values of [OMB] is R2 = 0.99 (Fig. 3).
y
= 0.998x
2
1.2
1.0
0.8
0.6
0.4
0.2
R = 0.992
The analysis of the rate curves for the reaction of
HPMB with OL showed that this reaction follows the
general trends characteristic of the hydroperoxide
epoxidation of olefins. The rapidly formed catalytic
complex of HPMB with the catalyst interacts with OL
to give OMB and the corresponding alcohol. The alcoꢀ
hol also forms a complex with the catalyst, inhibiting
the entire epoxidation process. The distinctive feature
of this process is the fact that the latter equilibrium
resulting in the simple inhibition of the reaction by the
products shifts to the left with an increase in the olefin
concentration in the solution. As a result, the reaction
rate changes out of proportion to the olefin concentraꢀ
tion, although the first order of the reaction in the oleꢀ
fin is clearly observed in the initial portion of the rate
curves. The phenomenon of the unusual effect of the
0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
[HPMB] , mol/l
exp
Fig. 3. Correlation of calculated [HPMB]
and experiꢀ
calc
mental [HPMB] values of the current concentration of
exp
HPMB for all experimental series under study.
PETROLEUM CHEMISTRY Vol. 50
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2010

KINETICS OF 2ꢀMETHYLBUTENEꢀ2 EPOXIDATION
5. V. N. Sapunov, J. Mol. Catal.
387
7, 149 (1980).
olefin accounts for the enhanced stability of the
molybdenum compounds in the presence of olefins
[12] and, in some cases, the catalyst activation [13,
14]. This phenomenon is likely due to the soꢀcalled
steric factor, because the reactants possess bulky subꢀ
stituents, and is not observed for simple olefins. The
revealed features of the process and its mathematical
description make it possible to more competently
design a reactor unit for the commercial production of
isoprene according to the developed scheme.
6. V. Karnozhitskii, Organic Peroxides (Inostrannaya Litꢀ
eratura, Moscow, 1961) [in Russian].
7. Novel Petrochemical Processes and Petroleum Chemistry
Prospects: A Survey of the Proceeding of VII World Conꢀ
gress in Mexico, Ed. by I. V. Kalechits (Khimiya, Mosꢀ
cow, 1970) [in Russian].
8. R. B. Svitych, A. L. Buchachenko, O. P. Yablonskii,
et al., Kinet. Katal. 17, 73 (1976).
9. R. B. Svitych, A. L. Buchachenko, O. P. Yablonskii,
et al., Kinet. Katal. 15, 1300 (1974).
10. R. B. Svitych, N. N. Rzhevskaya, O. P. Yablonskii,
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2010