ARTICLE pubs.acs.org/IECR
Dicumyl Peroxide Thermal Decomposition in Cumene: Development of a Kinetic Model Ilaria Di Somma,*,† Raffaele Marotta,‡ Roberto Andreozzi,‡ and Vincenzo Caprio‡ † ‡
Istituto di Ricerche sulla Combustione (CNR), P.le V. Tecchio, 80, 80125, Napoli, Italy Dipartimento di Ingegneria Chimica, Facolta di Ingegneria, Universita di Napoli Federico II, P.le V. Tecchio 80, 80125 Napoli, Italy ABSTRACT: A kinetic model is developed to simulate the thermal decomposition of dicumyl peroxide (DCP) in cumene with and without oxygen in the reacting system, based on a reaction network that is comprised of a set of 51 reactions. An optimization procedure is adopted to obtain the best estimates for most of the related kinetic parameters, few of which are available in the literature. The model is successfully validated by simulating the concentration profiles of all the species participating in the decomposition of DCP in cumene, under varying initial conditions, using previously best-estimated values of the kinetic parameters.
1. INTRODUCTION Many incidents, often due to runaway phenomena, have been reported in the industrial sites in which organic peroxides are used, resulting in damage to people and plants.1 This undoubtedly indicates the dangerous nature of these species and raises many concerns about their widespread use in the chemical and process industry. In-depth characterization of the thermal decomposition of organic peroxides, from the chemical and kinetic point of view, is thus useful both for industrial applications and safety considerations. Dicumyl peroxide (DCP) is one of the most widely used peroxides in the polymer industry as a crosslinking agent for polyethylene and with ethylene vinyl acetate copolymers, and it has been used as a curing agent for unsaturated polystyrene.2 It has been reported that its thermal decomposition, due to temperature control failure and/or process disturbances, is likely to lead to the occurrence of runaway phenomena.1,3 Although many reports have focused on the effect of acid catalysts upon DCP thermal stability, it is amply recognized that, even in the absence of such catalysts, this peroxide undergoes thermal decomposition when heated in solutions of cumene.4 Moreover, we previously proved5 that DCP appears as a reaction intermediate during the thermal decomposition of cumene hydroperoxide (CHP) solutions in cumene, whose kinetic characterization is of great interest from an industrial point of view. In this context, we considered that the simulation of the thermal behavior of DCP in cumene was the first step to achieving detailed modeling of the more-complex thermal decomposition of the CHP/cumene system, which holds more interest for industrial applications. In a previous investigation,6 we studied the thermal decomposition of DCP in cumene in the temperature range of 393433 K (which is approximately the same range used to investigate CHP thermal decomposition) in kinetic and chemical terms, with and without the presence of oxygen. The results indicated that, if oxygen is present, the decomposition process is regulated by simple autocatalytic kinetics, whereas after oxygen purging, good results are obtained by modeling the substrate decay using a pseudo-first-order kinetic equation. Chemical investigations indicate that the decomposition of DCP results mainly in the r 2011 American Chemical Society
formation of acetophenone and dimethylphenylcarbinol, with minor a occurrence of 2,3-dimethyl-2,3-diphenylbutane and the presence of cumene hydroperoxide as a reaction intermediate. As reported above, different global kinetic models are necessary to account for DCP thermal decomposition when the reaction conditions change (solvent, presence of oxygen, etc). The present work is strictly associated with the results of the previous investigation and has the objective of developing and validating a single detailed kinetic model capable of predicting the concentration profiles of the reagent, intermediates, and products when a solution of DCP in cumene undergoes thermal decomposition under various starting conditions (temperature, substrate concentration, solvent, presence of oxygen in the system, etc.).
2. MODEL DEVELOPMENT According to the information collected during the previous investigation, we built a network through which the thermal decomposition of DCP in cumene develops.5 This network is depicted in Scheme 1. However, to better complete the reaction network, additional reactions are necessary. Therefore, a complete list of the reactions included in the model is presented in Table 1. A list of abbreviations used in Table 1 is given in Table 2. On the basis of this list, the material balance for each of the species participating in the process is expressed as an ordinary differential equation (ODE), which represents the sum of the rates of the reactions of consumption and generation in which the species participates: dCh ¼ ( dt
∑r kr
Y m
Cm
ð1:1Þ
Special Issue: Russo Issue Received: July 29, 2011 Accepted: September 20, 2011 Revised: September 15, 2011 Published: September 20, 2011 7493
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Scheme 1. Proposed Reaction Network for Thermal Decomposition of DCP
where
kr ¼ Ar exp
Er RT
The subscript h indicates the hth species, whereas the subscript m denotes the mth species participating in reaction r, including the possibility that h = m. Since oxygen, when admitted in the reacting system, participates in the process, its transfer from the gas phase to the liquid solution must be taken into account. In the present work, this transfer is considered under the hypothesis that the reactions with oxygen occur substantially in the liquid bulk (and only negligibly in the liquid film), where the concentration of the species that is being transferred (oxygen) is higher than zero but lower than the saturation value. An approach in which the oxygen concentration was considered at the saturation value in the liquid bulk did not give good results. dnO2 ¼ Vliq KL aðC CO2 Þ dt dCO2 ¼ KL aðC CO2 Þ dt
ð1:2Þ n
∑ ki Ci CO i¼1 "
C ¼
ð1:3Þ
2
ðn0 nO2 ÞRT 1 PO2 ¼ γPO2 ¼ γ O2 H Vgas
# ð1.4Þ
Vliq was 1.5 104 L and was kept constant during each run. The reciprocal of the Henry’s constant for oxygen (γ) was fixed at 2.5 102 mol L1 atm1 and considered to be independent of the temperature in the investigated range.7 Therefore, the model consists of a set of 31 ODEs that must be solved according to proper initial conditions. In order to test the kinetic model developed, the concentration profiles of each species was calculated upon varying the reaction time and compared with those recorded during experimental runs. To make this calculation successfully, we must know the correct
values of all the kinetic parameters in the model. In this regard, all the reactions reported in Table 1 can be divided into three groups. The first group includes few of those for which reliable values of kinetic parameters were found in the literature and that were consequently adopted in the model. Note that, for some specific reactions belonging to this group, more than one single value was reported for its parameters (see, for example, the decomposition of CHP to generate cumyloxy and OH radicals), and the determination of reliable values was achieved as a result of an optimization procedure. A second group of reactions is represented by those for which no specific data for the parameters were found in the literature, although approximate values could be derived by analogy, based on molecular similarities (see, for example, t-BuO and radical R1). In this case, the values taken from the literature were used as initial data for the optimization procedure. In the third group, all the reactions were considered for which no data at all were available from previous studies. In this case, the initial values of the parameters were fixed based on general considerations on molecularity, heat of reaction, and energy of broken bonds. For the overall mass-transfer coefficient KLa, a best-estimated value was also determined.
3. EXPERIMENTAL SECTION For the experiments in the presence of oxygen, 1.5 104 L of DCP solutions in cumene with a concentration of 0.6 mol/L was poured into a series of sealed, magnetically stirred, glass tubes with a total volume of 1.45 102 L, initially containing air at a pressure of 1 atm. For runs performed in the absence of oxygen, the mixtures in the glass tubes were previously purged with a nitrogen stream. In both cases (with and without oxygen), the tubes were placed into an oil bath, at a desired temperature in the range of 403433 K, and then were withdrawn from it after the desired reaction time and rapidly cooled. The samples were recovered with acetone, diluted with acetonitrile, and subjected to high-performance liquid chromatography (HPLC) analyses. These were performed by means of a HewlettPackard Model HP 1100 HPLC equipped with a Synergi 4 μ Fusion RP-80 7494
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Table 1. Complete List of Reactions Included in the Proposed Model, Along with the Initial and Best Estimates of the Parameters, as Well as Literature Referencesa r
reaction
1
CHP f R1 þ R5
2 3
2CHP f R1 þ R4 þ W DCP f 2R1
4
R1 f ACP þ R3
12.4 ( 0.6
R3 þ CUM f MET þ R2 R1 þ CUM f DC þ R2 R2 þ OX f R4 2R2 f DB R4 þ CUM f CHP þ R2 R4 þ R2 f DCP 2R3 f ET R5 þ CUM f W þ R2 2R5 f WX R5 þ R2 f DC R2 þ R3 f M R4 þ DCP f CHP þ R6 R6 f AMS þ R4 AMS þ CHP f R7 þ R1 R7 þ CUM f AL þ R2 R1 þ DCP f DC þ R6 R1 þ CHP f DC þ R8 R8 f AMS þ R11 R4 þ DC f CHP þ R9 R9 f AMS þ R5 R3 þ DCP f MET þ R6 AMS þ CHP f DCP R4 þ CHP f CHP þ R8 R3 þ OX f R10 R10 þ DCP f B þ R6 R10 þ CHP f B þ R8 R3 þ DC f MET þ R9 R1 þ DC f DC þ R9 R3 þ CHP f MET þ R8 WX f 2R5 R4 þ R3 f F 2R4 f DCP þ OX 2R10 f G þ OX R5 þ CHP f W þ R8 R11 þ CHP f WX þ R8 R1 þ CHP f DC þ R4 R3 þ CHP f MET þ R4 R5 þ CHP f W þ R4 R10 þ CHP f B þ R4 R7 f R12 R12 þ CUM f AL þ R2 R12 þ DCP f AL þ R6 R12 þ CHP f AL þ R8 R5 þ AMS f R7 R4 f AMS þ R11 2R11 f WX þ OX R10 þ AMS f R12 þ FO
12.5 8.40 ( 0.5 8.40 ( 0.5 7.60 8.00 8.40 ( 0.5 8.00 8.00 8.40 ( 0.5 8.00 8.00 8.00 9.20 ( 0.5 9.00 9.00 8.00 9.00 ( 0.5 9.00 ( 0.5 8.00 9.20 ( 0.5 8.00 9.00 ( 0.5 7.00 9.20 ( 0.5 7.60 9.20 ( 0.5 9.20 ( 0.5 9.00 ( 0.5 9.00 ( 0.5 9.00 ( 0.5 14.6 8.00 8.00 8.00 9.00 9.00 7.00 7.00 7.00 7.00 8.00 9.00 8.00 8.00 8.00 5.00 8.00 8.00
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
log10(kI) 12.4 10.2 7.70 14.7
Ea,I (kJ/mol)
real/analogb
optimized?
reference
log10(kopt)
Ea,opt (kJ/mol)
127.2 103.8 108.8 144.4 ( 2.1
R R R R
yes
ref 8 ref 9 ref 10 ref 4
12.3 ( 0.1
139.4 ( 0.8
7.70 14.7
108.8 144.4 ( 2.1
15.48 ( 0.8
R
yes
46.05 35.58 ( 4.2 18.42 ( 2.9 0.000 4.186 53.16 ( 4.2 4.186 4.186 51.49 ( 4.2 4.186 4.186 4.186 74.09 ( 4.2 62.79 62.79 83.72 33.07 ( 4.2 33.07 ( 4.2 83.72 74.09 ( 4.2 83.72 55.22 ( 4.2 83.72 74.09 ( 4.2 0.000 74.09 ( 4.2 74.09 ( 4.2 55.25 ( 4.2 33.07 ( 4.2 55.25 ( 4.2 127.25 4.186 4.186 4.186 62.79 62.79 41.86 41.86 41.86 41.86 83.72 83.72 83.72 62.79 41.86 4.186 4.186 4.186
R R A A A A A A A A A A A n.a.c n.a.c n.a.c A A n.a.c A n.a.c R n.a.c A A A A R A R A A A A n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c n.a.c
no no
no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes no yes yes yes yes yes no yes no yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
ref 11 ref 9 ref 12 ref 12 ref 8 ref 7 ref 12 ref 7 ref 7 ref 12 ref 7 ref 7 ref 7 ref 12
ref 12 ref 12 ref 12 ref 12 ref 12 ref 8 ref 12 ref 12 ref 12 ref 12 ref 12 ref 4 ref 7 ref 7 ref 7
9.80 ( 0.1
20.51 ( 0.4
8.40 ( 0.5 8.40 ( 0.4 7.20 ( 0.3 7.00 ( 0.3 7.20 ( 0.2 8.20 ( 0.3 9.40 ( 0.1 8.50 ( 0.1 8.40 ( 0.5 8.70 ( 0.1 9.10 ( 0.2 9.20 ( 0.3 8.20 ( 0.4 8.20 ( 0.3 8.40 ( 0.1 9.00 ( 0.6 9.30 ( 0.2 6.60 ( 0.1 9.30 ( 0.1 8.20 ( 0.3 9.00 ( 0.5 5.10 ( 0.1 7.20 ( 0.2 5.90 ( 0.3 8.20 ( 0.3 8.40 ( 0.7 9.00 ( 0.5 9.30 ( 0.2 9.00 ( 0.5 13.4 ( 0.2 9.20 ( 0.2 8.40 ( 0.1 9.20 ( 0.3 9.10 ( 0.2 7.30 ( 0.2 8.40 ( 0.2 8.50 ( 0.3 8.60 ( 0.5 8.10 ( 0.5 8.20 ( 0.3 8.20 ( 0.5 7.20 ( 0.3 8.20 ( 0.3 8.20 ( 0.4 3.20 ( 0.1 8.30 ( 0.6 9.00 ( 0.6
35.58 ( 4.2 15.91 ( 0.8 0.000 12.56 ( 0.4 50.65 ( 2.1 15.07 ( 0.7 4.605 ( 0.1 60.70 ( 2.1 2.093 ( 0.1 3.767 ( 0.2 2.093 ( 0.1 74.09 ( 2.9 63.63 ( 4.2 90.00 ( 4.2 96.28 ( 4.6 36.00 ( 3.8 47.72 ( 1.7 76.18 ( 8.4 72.42 ( 6.3 94.18 ( 2.1 55.25 ( 4.2 92.09 ( 1.7 65.30 ( 5.0 0.000 51.49 ( 3.7 37.25 ( 0.8 55.25 ( 4.2 20.09 ( 0.8 55.25 ( 4.2 100.5 ( 6.3 27.63 ( 0.8 20.51 ( 2.5 4.186 ( 0.1 59.44 ( 0.8 68.65 ( 4.2 15.49 ( 1.2 28.88 ( 2.1 60.28 ( 5.0 15.07 ( 0.8 96.28 ( 8.4 67.81 ( 2.9 89.58 ( 2.5 71.16 ( 1.7 46.46 ( 2.1 19.67 ( 1.2 8.372 ( 0.3 33.49 ( 1.7
a Legend of abbreviations: kI, initial pre-exponential factor adopted for optimization; Ea,I, initial activation energy adopted for optimization; kopt, best estimated pre-exponential factor; and Ea,opt the best-estimated activation energy. See Table 2 for an explanation of the chemical compound abbreviations used in this table. b R denotes a real value; A denotes a value adopted by analogy. c The abbreviation “n.a.” indicates that no value was available in the literature.
column and a diode array detector. The mobile phase was 65% (v/v) acetonitrile and 35% (v/v) a buffer solution (5% CH3OH,
0.4% H3PO4, and 94.6% H2O), with a flow of 1.0 103 L min1. The signals at wavelengths of 210 and 240 nm were 7495
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Table 2. Acronyms Used in Table 1 Chemical Compounds species
Radicals
Abb
species •
Abb
[C6H5C(CH3)2]2
DB
C6H5CO (CH3)2
R1
C6H5C(O)CH3
ACP
C6H5C•(CH3)2
R2
CH3OOH
B
CH3•
R3
CH3CH3
ET
C6H5COO•(CH3)2
R4
H2O
W
HO•
R5
CH3OOCH3
G
C6H5(CH3)2(CO)2(CH3)-
R6
(CH2•)C6H5 O2 H2O2
OX WX
C6H5C•(CH3)(CH2OH) C6H5(CH3)(CH2•)COOH
C6H5C(CH3)3
M
C6H5(CH3)(CH2•)COH
R9
CH4
MET
CH3OO•
R10
C6H5C(CH3)2OH
DC
HO2•
R11
C6H5C(CH3)2OOH
CHP
C6H5(CH3)(CH2O•)CH
R12
[C6H5C(CH3)2O]2
DCP
C6H5C(CH3)2H
CUM
C6H5C(CH3)dCH2 C6H5C(CH3)2OOCH3
AMS F
C6H5CH(CH3)CH2OH
AL
CH2dO
FO
R7 R8
Figure 2. Thermal decomposition of DCP at T = 403 K in the presence of oxygen; a comparison of experimental (symbols) and calculated data (continuous lines) is shown ((a) total carbinol (DC), dicumylperoxide (DCP), acetophenone (ACP), and cumene (CUM) and (b) cumylhydroperoxide (CHP), 2,3-dimethyl-2,3-diphenylbutane (DB), and αmethylstyrene (AMS)). (“Total carbinol” indicates the sum of the concentration of dimethylphenylcarbinol and 2-phenyl-1-propanol.)
used for quantitative analyses. The oven temperature was set at 305 K. Gas analysis was performed by a HewlettPackard Model HP 5890 gas chromatograph equipped with a flame ionization detection (FID) device and a PPU column (30 m 0.53 mm) with an oven temperature of 313 K and a helium flow of 7.0 mL/min. All the reagents were purchased from SigmaAldrich and were used as received. Note that, in most runs, a nonzero concentration value for CHP is observed at the beginning of the experiment, which can be ascribed to an oxidation of cumene by atmospheric oxygen during transportation and storage of the bottle containing it.
4. RESULTS AND DISCUSSION During the present investigation, 13 runs on DCP thermal decomposition were carried out, starting from different initial conditions. For each run, ∼10 concentration data features (on 7 species) were recorded. The results of a set of 10 runs performed during the present work were simultaneously used in a single optimization procedure to estimate the unknown kinetic parameters (activation energy and pre-exponential factor) and overall mass-transfer coefficient, based on the minimization of an objective function, expressed as Figure 1. Thermal decomposition of DCP at T = 403 K in the absence of oxygen; a comparison of experimental (symbols) and calculated data (continuous lines) is shown ((a) total carbinol (DC), dicumylperoxide (DCP), acetophenone (ACP), and cumene (CUM), and (b) cumylhydroperoxide (CHP), 2,3-dimethyl-2,3-diphenylbutane (DB), and αmethylstyrene (AMS)). (“Total carbinol” indicates the sum of the concentration of dimethylphenylcarbinol and 2-phenyl-1-propanol.)
j¼
f
k
a
ðyi, j, l ci, j, l Þ2 ∑ ∑ ∑ l¼1 j¼1 i¼1
ð1:5Þ
in which y and c are the calculated and experimental concentrations, respectively, and n, k, and f are the number of experimental data recorded in each experiment, the number of substances, and 7496
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Figure 3. Distribution of intermediates and products during CHP thermal decomposition at T = 403 K with the addition of α-methylstyrene. Cumylhydroperoxide (CHP), total carbinol (DC), acetophenone (ACP), and cumene (CUM). (“Total carbinol” indicates the sum of the concentration of dimethylphenylcarbinol and 2-phenyl-1-propanol.)
Figure 5. Thermal decomposition of DCP at T = 433 K in the presence of oxygen; a comparison of experimental (symbols) and calculated data (continuous lines) is shown ((a) total carbinol (DC), dicumylperoxide (DCP), acetophenone (ACP), and cumene (CUM) and (b) cumylhydroperoxide (CHP), 2,3-dimethyl-2,3-diphenylbutane (DB), and αmethylstyrene (AMS). (“Total carbinol” indicates the sum of the concentration of dimethylphenylcarbinol and 2-phenyl-1-propanol.)
NP ¼ ½ðnumber of reactions with unknown parametersÞ ðnumber of parameters per reactionÞ þ ðnumber of overall mass-transfer coefficientsÞ ¼ ½45 2 þ 1 ¼ 90 þ 1 ¼ 91
Figure 4. Thermal decomposition of DCP at T = 433 K in the absence of oxygen; a comparison of experimental (symbols) and calculated data (continuous lines) is shown ((a) total carbinol (DC), dicumylperoxide (DCP), acetophenone (ACP), and cumene (CUM), and (b) cumylhydroperoxide (CHP), 2,3-dimethyl-2,3-diphenylbutane (DB), and αmethylstyrene (AMS). (“Total carbinol” indicates the sum of the concentration of dimethylphenylcarbinol and 2-phenyl-1-propanol.)
the number of experiments used in the optimization procedure, respectively. It can be expected13 that a set of 700 total experimental data points (denoted as NQ), NQ ¼ ðconcentration data featuresÞ ðnumber of speciesÞ ðnumber of runsÞ ¼ 10 7 10 ¼ 700 will be sufficient to estimate a number of parameters (NP) equal to 91:13
Figures 1 and 2 show examples of some comparisons of calculated and experimental data for a single run. As a result of the application of this procedure, the kinetic parameters shown in Table 1 and a KLa value of 1.0 ( 0.03 min1 were estimated. Initially, the proposed model seems capable of simulating the system behavior. However, for a quantitative analysis of the results of the optimization procedure, an examination of the uncertainties on the parameters (Table 1) and the overall percentage standard deviations (given in the figure) is necessary. Careful analysis of these data indicates that: (1) the overall percentage standard deviations, in all cases, are comparable with those associated with determination of the single components; (2) The uncertainties associated with the estimates of single parameters are very small for all parameters; (3) For hydrogen abstraction reactions via a single radical, the activation energy data obtained agree with the order expected on the basis of the chemical structures involved. In fact, lower energy values were observed for benzylic hydrogen abstraction, with respect to those belonging to a methyl group. For example, for hydrogen abstraction by the cumylperoxy radical, a value of 12.1 kcal/mol was 7497
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in the “total carbinol” concentration in the run starting from CHP in cumene with the addition of α-methylstyrene. It has thus been proposed that radical R7 gives rise to the formation of radical R12: ðreaction 44 in Table 1Þ
R7 f R12
which may abstract an H atom from other molecules, for example, CHP itself: R12 þ CHP f AL þ R8
ðreaction 47 in Table 1Þ
or DCP. (It can be supposed that the same reactions occur during the thermal decomposition of DCP.) The model was also successfully validated—to confirm its reliability—using the results of the runs that were not included in the pool adopted for the optimization procedure. In this case, the model was used just to simulate the concentration profiles of the species of interest without any further adjustment of previously estimated kinetic parameters. Comparison of the calculated and experimental results is shown in Figures 4 6. Good agreement is observed in all cases between the calculated and experimental data, thus confirming the reliability of the proposed model.
Figure 6. Thermal decomposition of DCP at T = 403 K in the presence of oxygen with the addition of α-methylstyrene; a comparison of experimental (symbols) and calculated data (continuous lines) is shown ((a) total carbinol (DC), dicumylperoxide (DCP), acetophenone (ACP), and cumene (CUM) and (b) cumylhydroperoxide (CHP), 2,3-dimethyl-2,3-diphenylbutane (DB), and α-methylstyrene (AMS). (“Total carbinol” indicates the sum of the concentration of dimethylphenylcarbinol and 2-phenyl-1-propanol.)
found in the case of cumene (reaction 9 in Table 1) whereas 17.7, 17.3, and 15.6 kcal/mol were found in the case of DCP (reaction 16 in Table 1), DC (reaction 23 in Table 1), and CHP (reaction 27 in Table 1), respectively. Similar results were observed when comparing the activation energy for hydrogen abstraction by the cumyloxy radical from cumene (reaction 6 in Table 1) and CHP (reaction 21 in Table 1). On the other hand, the results obtained for reactions 12, 38, and 42 in Table 1, with an activation energy value that is not dependent on the structure of the hydrogen donor, agree well with the known unselective nature of hydroxyl radical species.14 Inclusion in the model of reaction 44 in Table 1 requires some explanation. The possibility that the radical R7 in Scheme 1 contributes to “total carbinol” relies on its ability to abstract an H atom from some molecules present in the reacting medium. Cumene is undoubtedly one of the molecules that may favorably donate an H atom to species R7. However, during the present investigation, it was observed that the addition of α-methylstyrene to a solution of CHP in cumene caused immediate consumption of the olefin and a parallel increase in the concentration of “total carbinol”, which could not be sustained by a hydrogen-donating action by cumene (it is clear from Figure 3 that, in the same time interval, the consumption of cumene is substantially lower than the increase in the concentration of “total carbinol”). Therefore, it has been concluded that other species among those present in the reacting solutions had to sustain the increase
5. CONCLUSIONS A kinetic model was developed to simulate the thermal decomposition of dicumyl peroxide (DCP) in cumene with and without oxygen in the reacting system. It consisted of a set of differential equations, each representing the material balance of species participating in the process. Only for a few reactions was it possible to derive from the literature the values of the kinetic parameters. For most such parameters, the adoption of a proper optimization procedure was necessary. The use of this model to analyze the data of 10 runs for the decomposition of DCP allowed best estimates to be obtained for unknown parameters. The model was also successfully validated by using it to simulate—without any further adjustment of the parameters—the concentration profile of all the species identified during the decomposition of DCP in cumene starting from initial conditions different from those adopted for the 10 decomposition runs considered in the optimization. ’ AUTHOR INFORMATION Corresponding Author
*Tel.: +39 081 7682225. Fax: +39 081 5936936. E-mail: idisomma@ unina.it.
’ NOMENCLATURE Ar = pre-exponential factor (s1 or l mol1 s1) Er = activation energy (kJ mol1) C°i = initial concentration of the ith species (mol L1) C* = oxygen concentration at liquid/gas interface (mol L1) Ci = concentration of the ith species (mol L1) T = temperature (K) R = universal constant of gas (J mol1 K1) kr = kinetic constant for the nth reaction (s1 or L mol1 s1) nO2 = moles of oxygen in gas phase (mol L1) 0 = initial moles of oxygen in gas phase (mol L1) nO 2 t = time (min) PO2 = partial pressure of oxygen (atm) KLa = overall mass-transfer coefficient (min1) H = Henry constant (atm L mol1) 7498
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Vliq = liquid-phase volume (L) Vgas = gas-phase volume (L) yi = calculated concentration of the ith species (mol L1) Greek Symbols
σt = total percentage standard deviation (dimensionless) γ = reciprocal of Henry constant (mol atm1 L1) ϕ = objective function ((mol L1)2)
’ REFERENCES (1) Wu, S. H.; Wang, Y.; Wu, T. C.; Hu, W. N.; Shu, C. M. Evaluation of thermal hazards for dicumyl peroxide by DSC and VSP2. J. Therm. Anal. Calorim. 2008, 93, 189. (2) Lu, K. T.; Chu, Y.; Chen, T; Hu, K. Investigation of the decomposition reaction and dust explosion characteristics of crystalline dicumyl peroxide. Process. Saf. Environ. Protect. 2010, 88, 356. (3) Wu, S.; Shyu, M.; Chi, Y. I; Shu, J. C. Evaluation of runaway reaction for dicumyl peroxide in a batch reactor by DSC and VSP2. J. Loss Prev. Process. Indust. 2009, 22, 721. (4) Bailey, H. C.; Godin, G. W. The thermal decomposition of dibenzoyl and di-α-cumyl peroxides in cumene. Trans. Faraday Soc. 1956, 52, 68. (5) Di Somma, I; Andreozzi, R.; Canterino, M.; Caprio, V.; Sanchirico, R. Thermal decomposition of cumene hydroperoxide: Chemical and kinetic characterization. AIChE J. 2008, 54, 1579. (6) Di Somma, I.; Marotta, R.; Andreozzi, R.; Caprio, V. Kinetic and chemical characterization of thermal decomposition of dicumyl peroxide in cumene. J. Hazard. Mater. 2011, 187, 157. (7) Denisov, E. T.; Mitskevich, N. I.; Agabekov, V. E. Liquid-Phase Oxidation of Oxygen-Containing Compounds; Consultants Bureau: New York, 1977. (8) Emanuel, N. M.; Denisov, E. T.; Maizus, Z. K. Liquid Phase Oxidation of Hydrocarbons. Plenum Press: New York, 1967. (9) Bhattacharya, A. Kinetic modeling of liquid phase autoxidation of cumene. Chem. Eng. J. 2008, 137, 308. (10) Swern, D. Organic Peroxides, Vol. I; WileyInterscience: New York, 1970. (11) Baignee, A.; Howard, J. A.; Scaiano, J. C.; Stewart, L. C. Absolute rate constants for reactions of cumyloxy in solution. J. Am. Chem. Soc. 1983, 105, 6120. (12) Hendry, D. G.; Mill, T.; Piszkiewicz, L.; Howard, J. A.; Eigenmann, H. K. A Critical Review of H-Atom Transfer in the Liquid Phase: Chlorine Atom, Alkyl, Trichloromethyl, Alkoxy, and Alkylperoxy Radicals. J. Phys. Chem. Ref. Data. 1974, 3 (4), 937. (13) Johnson, M. L; Faunt, L. M. Parameter estimation by leastsquares methods. Method. Enzymol. 1992, 210, 1–37. (14) Beltran, F. J.; Gonzalez, M.; Rivas, F. J.; Acedo, B. Determination of Kinetic Parameters of Ozone during Oxidations of Alachlor in Water. Water Environ. Res. 2000, 72, 689.
’ NOTE ADDED AFTER ASAP PUBLICATION The version of this paper that was published on October 13, 2011 was published with errors in Table 1. The corrected version was reposted to the Web February 8, 2012.
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dx.doi.org/10.1021/ie201659a |Ind. Eng. Chem. Res. 2012, 51, 7493–7499
