Comprehensive Kinetic Model for Adiabatic Decomposition of Di-tert

The purpose of the present investigation is to provide a comprehensive kinetic model on the adiabatic thermal decomposition of di-tert-butyl peroxide ...
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Ind. Eng. Chem. Res. 2003, 42, 2987-2995

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Comprehensive Kinetic Model for Adiabatic Decomposition of Di-tert-butyl Peroxide Using BatchCAD Y. Iizuka and M. Surianarayanan* Safety Engineering and Environmental Integrity Laboratory, Science and Technology Research Center, Mitsubishi Chemical Corporation, 1000 Kamoshida-cho, Aoba-ku, Yokohama 227-8502, Japan

This is the first comprehensive study on the kinetic modeling of adiabatic decomposition of ditert-butyl peroxide (DTBP) and its solvent mixtures. The adiabatic thermal decomposition of DTBP and its solvent mixtures was examined using an accelerating rate calorimeter under varying thermal inertia. The decomposition products were characterized using gas chromatography-total inorganic carbon analysis and gas chromatography-mass spectroscopy to elucidate the mechanistic pathways for decomposition under adiabatic conditions. Reaction models (overall stoichiometric equations) for the decomposition of neat DTBP and its mixture in various solvents have been proposed for the first time. A comprehensive kinetic analysis based on simultaneous treatment of mass and energy balances has been done using a software called BatchCAD. The activation energies for the decomposition of DTBP and its mixtures in various solvents were quite consistent. This comprehensive study has answered to many ambiguities and questions on the mechanism of DTBP decomposition and its kinetics. Introduction Predicting reaction pathways under pure adiabatic conditions ensures close matching of the runaway behavior in industrial reactors. However, there always exists a complexity in predicting adiabatic decompositions.1 In adiabatic experiments, it is difficult to carry out in situ analysis of the reaction products because of possible loss of adiabaticity. Reactions of practical interest often involve complexity with difficulty in characterization. With the secondary and complex explosive reactions toward the end, any analysis of the reaction products fails to suggest the mechanistic aspects. Such reactions invariably lead to wrong conclusions and a complex reaction mechanism.2 Kinetic estimation for reaction hazard assessment is intended for the simulation of runaway potential, design, and safe operation of hazardous reaction plants and therefore demands robust and reliable procedures.3 Kinetic analysis without understanding the underlying physical and chemical transformations does not really represent the actual process. Townsend and Tou4 have derived the adiabatic decomposition kinetics. These methods were employed in different reaction systems5-7 in the past. However, the kinetic parameters obtained from each method for the same decomposition process varied significantly from each method of estimation. The reasons for such variations in the kinetic estimates have been attributed to the simplicity of the model, which assumed the mechanism to be single-stage zero order.5,6 The interpretation of the kinetic parameters in terms of the mechanism of decomposition5 has also been found to be difficult. It is due to changes in the reaction mechanism as the decomposition proceeds. It is emphasized that kinetic estimates of decomposition reactions have physical * To whom correspondence should be addressed. Permanent address: Cell for Industrial Safety and Risk Analysis, Chemical Engineering Department, Central Leather Research Institute, Adyar, Chennai 600020, India. Tel.: 91-44-24916706. Fax: 91-44-24911589. E-mail: [email protected].

significance only when the kinetic parameters capture the essence of the exceedingly complex reaction set in a tractable mathematical way. Only a few such detailed kinetic studies have been done in the past.2 Recently, many commercial software programs have been written for kinetic treatment of calorimetric data of exothermic reaction systems.8,9 This software employs complete reaction modeling approaches by way of rigorous mathematical treatment of data to derive kinetic constants, thus making the estimation easy and highly reliable. The purpose of the present investigation is to provide a comprehensive kinetic model on the adiabatic thermal decomposition of di-tert-butyl peroxide (DTBP) using a commercially available kinetic estimation software called BatchCAD (BC). BC employs a powerful kinetic fitting system coupled with regression and integration methods as well as a sophisticated reaction modeling. DTBP is an industrially important organic peroxide widely used as an initiator for radical polymerization, a source for alkoxyl radicals, a hardener, a linking agent, and a fuel combustion additive and used in reforming operations. DTBP in a toluene mixture is also recommended as a standard sample for estimating the performance of several calorimeters.10 Because of its range of application, the thermal decomposition and its kinetics under both isothermal and adiabatic conditions have been intensively researched in the past.11-29 In most of the studies, kinetics have been reported11-14,16,18 either by measuring the rates of a few decomposition products (without considering the exothermic heat release) or by subjecting the heat rate curve to classical kinetic treatment7,11,17,19 (without considering the underlying physical processes). In a recent study, Oxley et al.22 briefly reviewed the previous studies on DTBP and compiled a table of reported kinetic parameters. The reported activation energies varied quite significantly (138-167 kJ/mol), and several decomposition routes were found possible with and without the presence of oxygen. The kinetics of adiabatic decomposition of DTBP need comprehensive study, i.e., taking into account the

10.1021/ie020687r CCC: $25.00 © 2003 American Chemical Society Published on Web 05/14/2003

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Table 1. Summary of DTBP ARC and Kinetic Data Arrhenius parameters no.

sample

wt, g

Φ

T0, °C

Tf, °C

∆Tad, °C

∆Tab, °C

∆Hr, kcal/mol

Ea, kJ/mol

A, min-1

1 2

DTBP DTBP

0.37 1.03

6.77 3.28

115.8 105.6

184.03 213.6

68.2 108.4

461.7 355.6

-33.71 -25.96

150.4 153.4

1.194 × 1016 4.528 × 1016

Table 2. Summary of ARC and Kinetic Data of 7.5-17.5% DTBP in Toluene Arrhenius parameters no.

DTBP concn in toluene, %

1 2 3 4 5 6

7.5 10 10 10 15 17.5

wt, g

Φ for solution

Φ for DTBP

T0, °C

Tf, °C

∆Tad, °C

∆Tab, °C

∆Hr, kcal/mol

Ea, kJ/mol

A, min-1

5.94 5.91 2.8 1.2 5.89 5.94

1.36 1.35 1.72 2.69 1.35 1.17

18.1 13.5 17.2 26.9 9.00 7.7

121.4 116.4 120.5 120.5 116.5 116.6

155.1 162.6 152.3 141.5 184.0 197.0

33.7 46.2 31.8 20.95 67.5 75.5

610.0 623.7 547.1 563.6 607.0 581.3

-44.53 -45.53 -47.92 -49.37 -44.31 -42.44

164.1 154.8 158.9 158.9 162.0 158.1

4.508 × 1018 2.802 × 1017 9.851 × 1017 9.303 × 1017 2.467 × 1018 7.247 × 1017

Table 3. Thermokinetic Data of Thermal Decomposition of 20% DTBP in Toluene Arrhenius parameters no.

DTBP concn in toluene, %

1 2 3 4 5 6

20 20 20 2020 20 (isothermal at 110 °C)

wt, g

Φ for solution

Φ for DTBP

T0, °C

Tf, °C

∆Tad, °C

5.92 4.0 2.8 1.2 6.03 6.17

1.36 1.54 1.72 1.85 1.30 1.36

6.8 7.7 8.6 13.5 6.62 6.8

111.4 110.6 115.8 120.6 115.3 111.4

197.5 188.4 184.8 160.4 194.8 193.3

86.1 77.8 69.0 39.8 79.5 82.27

∆Tab, °C

∆Hr, kcal/mol

Ea, kJ/mol

A, min-1

585.5 599.1 593.7 537.2 526.3 559.4

-42.74 -43.73 -43.34 -39.21 -38.42 -40.84

164.8 161.3 161.9 165.2 165.6 158.4

6.035 × 1018 2.232 × 1018 2.525 × 1018 6.189 × 1018 5.830 × 1018 6.893 × 1017

Table 4. Thermokinetic Data of Thermal Decomposition of 10% DTBP in Various Concentrations of Benzene (benz), Benzene/Biphenyl (benz/biph), and Biphenyl (biph) Arrhenius parameters

no.

DTBP concn, % (solvent)

1 2 3 4 5

10 (benz) 10 (benz/biph, 50:50) 10 (benz/biph, 1:2) 10 (benz/biph, 1:2) 10 (biph)

wt, g

Φ for solution

Φ for 100% DTBP

T0, °C

Tf, °C

∆Tad, °C

∆Tab, °C

∆Hr, kcal/mol

Ea, kJ/mol

A, min-1

5.94 5.96 5.97 5.73 6.0641

1.35 1.35 1.35 1.35 1.39

12.5 12.25 12.16 12.16 9.704

115.7 115.5 115.5 115.4 120.9

160.5 161.6 163.8 172.8 162.8

44.8 46.1 48.3 57.4 41.9

560.8 564.9 588.1 698.2 406.1

-40.94 -41.23 -42.93 -50.97 -35.58

152.4 154.3 146.4 154.7 155.2

1.542 × 1017 2.585 × 1017 2.366 × 1016 2.585 × 1017 2.585 × 1017

chemical and physical transformations simultaneously. This investigation is the first attempt at studying the kinetics of adiabatic decomposition of DTBP in a comprehensive way without the existing ambiguities. Experimental Section Accelerating Rate Calorimeter (ARC) Experiments. The ARC used in this study was an ARC 1000 supplied by CSI of Austin, TX. The working principle, design description, and operational details of ARC can be found in the literature.4 ARC measurements were made using a titanium sample vessel under both isothermal and heat-wait-search modes.4 Before loading of the sample, the bomb was inerted with nitrogen gas and precautions were taken not to allow air to enter during the sample loading as well as during attachment of the sample vessel to the instrument. After connection of the sample vessel, it was pressurized to 2500 psi nitrogen gas to ensure that there was no leak and also to replace the air in the feed through tubing of the assembly. The instrument was switched to the step mode at an initial temperature of 80 °C, and a wait time of 15 min was set prior to entering the search mode. DTBP (98% purity) and the solvents benzene, toluene, and biphenyl (all analytical-grade reagents) were obtained from Kishida Chemicals Co., Ltd., Osaka, Japan. All the chemicals were used as obtained, without

subjecting them to further purification. DTBP and DTBP-solvent mixtures at different concentrations and at varying Φ values, as given in Tables 1-4, were subjected to ARC tests. After the ARC returned to the safe mode, decomposed gaseous and liquid samples were collected as per the procedure given elsewhere2 for gas chromatographic-mass spectroscopic (GC-MS) and GC-total inorganic carbon (TIC) analysis to elucidate the decomposition reaction mechanism. GC-MS Analysis. GC analysis of the gas samples of DTBP adiabatic decomposition collected from ARC was performed using a Shimadzu GC analyzer, model GC-14 A, fitted with a stainless steel column packed with molecular sieves. The initial column, injector, and detector temperatures were set to 60, 80, and 80 °C, respectively. The column temperature was raised from 60 to 120 °C at a heating rate of 30 °C/min, after a holdup period of 14 min at 60 °C. Gas samples were fed to the injection port using the automatic gas-sampling accessory available in the equipment. Similarly, the liquid residue was analyzed using the quadrapole MS supplied by Shimadzu, model GC-MS QP-1000 A, equipped with a Porapack glass GC column of 1 m in length. The initial column, injector, and detector temperatures were 110, 110, and 150 °C, respectively. The column temperature was raised from 110 to 230 °C at a heating rate of 10 °C/min. The identities of the species were made by comparison of the chromatograph reten-

Ind. Eng. Chem. Res., Vol. 42, No. 13, 2003 2989 Scheme 1. Mechanistic Pathway for Adiabatic Decomposition of Neat DTBP

tion time and mass spectrum to the authentic samples when possible and otherwise by analysis of the fragmentation pattern as well as matching of the mass spectra with that of the standard spectrum available in the MS library. Generating calibration curves by injecting known concentrations and integrating the area of the particular peak allowed quantitative estimation of some of the known reaction products. Kinetic Analysis of DTBP Decomposition Using BC. BC is a software developed by BatchCAD Ltd., a subsidiary of GSE Systems USA. BC for windows version of 7.2 has been used for kinetic fitting of DTBP and DTBP-solvent ARC data. (a) Background of Kinetic Modeling in BC.30 For a reaction A f B, the isothermal rate expression is

d[A] ) -k1[A] dt

(1)

The previous expression is, in fact, a mass balance on a well-stirred batch reactor, and the term k1[A] is the kinetic rate expression. In general, for m chemical species, involved in q reactions with n feed streams and p streams leaving the system, the system equation becomes m

V

d[i]

∑ i)1 dt

) m

(

n

∑ ∑ i)1 j)1

p

Fj[i]Fj -

∑ k)1

q

Fk[i]Fj +

)

dV

Rl - [i] ∑ dT l)1

(2)

where i is the concentration, F, flow rate, R, reaction rate, and V, volume. Similarly, the energy balance for the system can be written as

VCpF

dTr

)

dt q

n

∑ j)1

FjCpFjFFj(Tj - Tr) + UA(Tw - Tr) +

∆HlRl ∑ l)1

(3)

where Cp is the specific heat and F is the density. The

reaction enthalpy is ∆H. T is the temperature, and the subscripts r and w denote the reaction mass and the vessel wall, respectively. The expression ∑Rl is the kinetic expression for all of the reactions in which species i takes part and occurs in these more general equations. Thus, if the mass and energy balances could be solved either separately or simultaneously, the kinetic terms of single or multiple reactions could be determined from a variety of data measurements, including concentrations. In doing so, two problems are addressed. First, there are terms in the equations, in addition to concentrations, that have to be measured experimentally such as feed rates, volume changes, and temperature and reaction heat. Secondly, unlike the case of a simple reaction in a batch reactor, the general mass and energy balance differential equations cannot be solved numerically and so mathematical solutions combined with appropriate fitting algorithms are used to calculate the kinetic parameters. The details of the computation methods employed in the software are outlined below. (b) Computation Methods. In the kinetic fitting environment, the model is the set of differential and algebraic equations (mass and energy balances) representing the process chemistry under the conditions of measurement of the data. A fourth-order Runga-Kutta integrator with a fixed step size and a simplex algorithm fitting method has been used to solve the model equations.29,30 (c) Procedure. In BC, kinetic modeling for adiabatic decomposition of DTBP involves the following steps. (a) Physical and thermodynamic properties of the components: At first, the basic properties of the reactants and products are keyed in the software. Then, using the built-in fluid package database, the thermodynamic activity model and estimation methods for temperature-dependent properties are identified for simulation requirements. In the case of DTBP kinetic simulation, the Wilson ideal activity model30-32 (property package) was chosen for estimating the temperature-dependent properties required for simulation. (b) Specification of the reaction chemistry: Reaction models (Schemes 1-3) elucidated for DTBP and DTBP-

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Scheme 2. Mechanistic Pathway for Adiabatic Decomposition of DTBP in Toluene

Scheme 3. Mechanistic Pathway for Adiabatic Decomposition of DTBP in Benzene and Benzene/ Biphenyl Solvents

reliable results (over several curve-fitting methods) while providing the best fit to the experimental data through rigorous mathematical treatment. The model takes into consideration the physical phenomena and underlying chemical processes. Results and Discussion

solvent decomposition processes, from the GC-MS studies, are entered along with their respective heat of reaction (∆Hr) and thermal inertia factor (Φ) values (Tables 1-4), which are calculated using the conventional equations.4. (c) Data input: For kinetic modeling of ARC data, time-temperature [adiabatic temperature rise (ATR)] data are the objective function. For each of the modeling exercises, corresponding ATR data of DTBP are loaded in the data editor program of the software. (d) Simulation setup: The initial conditions, viz., sample mass, onset temperature, and pressure, are entered at the simulation setup dialogue box. (e) Fitting: The integrator and method for computation is selected for fitting the experimental data. Once the fitting is done, the corresponding plots can be viewed and manipulated through the plot options menu of the software. The fitted data can also be downloaded to other Microsoft utilities for further processing. Kinetic fitting using BC yields superior and

Thermal Stability of DTBP and DTBP-Solvent Systems. The ARC results of DTBP and DTBP in three different solvents are summarized in Tables 1-4. Selfheat rate plots of neat DTBP and DTBP in toluene, benzene, and biphenyl solvent mixtures (Figures 1-3 and 7-9) show a similar trend in general. From these figures, it can also be seen that the maximum heat rate and the final temperature of decomposition were dependent on the concentration of DTBP; i.e., with increasing concentration, the observed heat rates and the final temperatures were higher. The onset temperature for decomposition processes was slightly higher for the experiments with greater thermal inertia (Tables 1-4). An early onset of the exothermic process has been noted for neat DTBP as compared to the corresponding Φ data of the DTBP-solvent system, and this can be attributed to the diluent effect of solvents. The slight variation in onset and final temperatures among the respective group experiments is generally attributed to the effect of thermal inertia. Further, it can also be seen that the rates of decomposition of neat DTBP and DTBP in the presence of toluene, benzene, and biphenyl are comparable as long as the Φ factor remains the same. This shows that the solvent has only a minimal effect on the rates of DTBP decomposition. Incidentally, 20% DTBPtoluene is recommended as a calorimetric standard,10 and the data obtained in this study (Figures 3 and 6) match well with the reported data10,28 and thereby confirm the excellent performance of our equipment. Thus, the ARC data presented in this study and thermal stability characteristics of DTBP-toluene compare well with those in the previous studies.7,10,28 Role of Thermal Inertia and Its Relevance in Kinetic Analysis. In ARC experiments, thermal inertia is an important parameter in determining the rate and

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Figure 3. Self-heat rate plots for the decomposition of 20% DTBP in toluene. Figure 1. Self-heat rate plots for DTBP decomposition at various Φ values.

Figure 4. GC-TIC chromatogram of gas-phase product analysis of the adiabatic decomposition of DTBP.

Figure 2. Self-heat rate plot for the decomposition of 7.5% DTBP in toluene.

ATR.4 Accordingly, Φ corrections have been recommended4,28 to determine the true decomposition parameters, i.e., under pure adiabatic conditions, to ensure close approximation of the runaway in a commercial reactor. A close examination of Tables 1-4 reveals that, even after carrying out the Φ corrections, the ATRs were not uniform. Similar problems can be found with the previously reported studies4,7,10,28 but have not been

stated explicitly. One of the main reasons for this deviation can be the assumption that Cv or Cp is constant throughout the course of the reaction. This assumption turns erroneous, and the difficulty is that it is impossible to determine the changes in Cv or Cp during the adiabatic experiment unless the mechanistic aspects of the process are known. Therefore, it appears that thermal inertia is not the only factor that needs to be corrected, but there are some additional parameters that have to be accounted for to get the true decomposition parameters. Though Φ correction is sensible for accounting for the heat loss of the container, often heat can also be lost through several other physical and complex chemical transformations, for example, vaporization of solvent or reagents or gaseous products or from competing endothermic processes. Vaporization effects can be larger with increasing Φ factors as a result of increasing void space at higher decomposition temperatures. Consequently, the calculated molar heat of reaction carries an error in its value. Also, using the data for kinetic estimation will lead to unrealistic and meaningless results. Further, using these results in runaway simulation and design will definitely lead to

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Figure 5. GC-MS spectrum of liquid-phase product analysis of the adiabatic decomposition of DTBP. Table 5. GC-TIC and GC-MS Analysis: Decomposition Products of Adiabatic Decomposition of DTBP species

minor

ethane propane isobutane carbon dioxide water acetone isobutylene oxide tert-butyl alcohol methyl ethyl ketone

major x

x x x

x x x x x

failure at a critical juncture. On the other hand, it can also be appreciated that there exists a difficulty in comparing the experimentally determined and theoretically calculated decomposition energies as a result of unknown reaction products. Once the enthalpies of formation of the substance and of the decomposition products are known, the decomposition energies can be calculated. Up to now, products of adiabatic exothermic decomposition of substances have rarely been determined. In a few cases, where the decomposition products have been analyzed, a variety of products have been found, rendering it difficult to calculate the decomposition energies. Oversimplification of all of the above complications in the kinetic estimation methods appears to have caused deviation from the experimental observation in earlier studies.5-7 Therefore, the only possible solution to overcome the above problem is to create a mathematical model of the reaction comprised of the

variation in physical and chemical transformations during the decomposition process. The numerical simulation of the process will then offer sensible results. This is one of the main ideas of this work, and attention is paid to the adiabatic decomposition of DTBP as an example system. Mechanism for DTBP and DTBP-Solvent Adiabatic Decompositions. The GC-TIC and GC-MS spectra for DTBP decomposition products are given in Figures 4 and 5. The results for DTBP-solvent systems are summarized in Table 6 and Schemes 1-3. The liquid phase of the decomposed product of neat DTBP showed the presence of acetone, tert-butyl alcohol, and isobutylene oxide as the principle decomposition products, while the gaseous phase product analysis indicated the presence of methane and ethane (Table 5). In the case of a DTBP-toluene system, a quantitative measurement (Table 6) of the major reaction products, i.e., acetone and tert-butyl alcohol, indicated that, for 1 mol of DTBP, 1 mol of acetone and 1 mol of tert-butyl alcohol have been formed. On the basis of the product profiles, quantitative information on specific products, reaction mechanisms, and overall stoichometric equations have been proposed for the decomposition of neat DTBP as well as DTBP in different solvent systems. The results are given in Schemes 1-3. In all of the proposed reaction pathways, the first step in the decomposition process is the well-accepted homolysis of the peroxy bond. The product formation was dependent on hydrogen abstraction and β-scission capabilities. Though GCMS analysis indicated several products in trace quantities, they were not always detected in duplicate runs and were in low concentrations (0.001-0.01 mol %). Furthermore, the products identified in minor quantities may not contribute to the significant quantity of heat liberation and hence were ignored while formulating the reaction mechanisms. The proposed reaction mechanisms for DTBP and DTBP-solvent systems (Schemes 1-3) under adiabatic conditions proceed by similar mechanistic pathways as suggested by previous researchers.15,21,22,24,26 This is for the first time a complete reaction model for adiabatic decomposition of DTBP and DTBP-solvent mixtures has been proposed. The respective reaction models have been used for kinetic fitting of the ATR data in the following section. Kinetic Modeling Using BC The kinetic analysis results for various concentrations of DTBP and DTBP-solvent systems are given in Figures 6-9, and the corresponding Arrhenius parameters obtained are summarized in Tables 1-4. The Arrhenius parameters for first-order fitting were quite

Table 6. Results of Quantitative GC-MS Analysis of the Adiabatic Decomposition Products of the DTBP-Toluene System Φ factor

DTBP concn

decomposition products

DTBP concn, wt %

total wt, g

solution

100% DTBP

g

mmol

acetone, mmol

tert-butyl alcohol, mmol

final temp, °C

final pressure at Tf, psia

20 586 417 278.1 17.5 15.0 10 258.9 140.7 7.5

5.9 4.0 2.8 1.2 5.9 5.9 5.9 2.8 1.2 5.94

1.36 1.54 1.72 1.85 1.17 1.35 1.35 1.72 2.66 1.36

6.8 7.7 8.6 13.5 7.7 9.0 13.5 17.2 26.6 18.1

1.18 0.8 0.56 0.24 0.61 0.85 0.59 0.28 0.12 0.44

8.1 5.48 3.84 1.64 4.17 6.06 4.04 1.92 0.82 3.03

8.1 5.48 3.84 1.64 4.17 6.06 4.04 1.92 0.82 3.03

8.1 5.48 3.84 1.64 4.17 6.06 4.04 1.92 0.82 3.03

197.5 193.5 184.8 160.4 197.0 184.0 162.6 157.4 141.7 155.0

586 417 278.1 143.7 554.1 424.8 258.9 140.7 81.4 195.4

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Figure 6. Comparison of experimental and modeled ATR curves of 20% DTBP in toluene at varying Φ values.

Figure 8. Comparison of experimental and calculated self-heat rate curves of 15 and 17.5% DTBP in toluene.

Figure 7. Comparison of experimental and calculated self-heat rate curves of 10% DTBP in toluene.

consistent, and the recorded activation energy is within the same range irrespective of the nature of the solvent. Comparable values of the activation energy for DTBP and DTBP-solvent systems indicate that, in the decomposition process, the breakage of the peroxy bond is the rate-determining step, a finding that corroborates the reported studies.15 Validation of the kinetic model

Figure 9. Comparison of experimental and calculated self-heat rate curves of 10% DTBP in benzene and benzene/biphenyl solvents.

is done further by matching the calculated (first-order derivative of the fitted ATR data) and experimentally determined heat rates. The results for 10-17.5% DTBP

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ated in these modeling approaches match well with the majority of the previous studies, the superiority of this study is the reliability of the results, i.e., consistent values for Ea and A, the excellent match between the experimental and modeled curves, and an insight knowledge into the physical and chemical transformations taking place in the reactor. The demerits of the present modeling approaches are that the real-time simulation calculations have been done behind the screen in the software and the final results are only accessible by the users. Conclusions

Figure 10. Linear relationship between the model fitted values of Ea and A.

in toluene and 10% DTBP in benzene/biphenyl systems are shown in Figures 7-9. It can be seen that there is an excellent match between the calculated and experimental curves. A close examination of the Ea and A values in Tables 1-4 indicates that there is a slight deviation in their values between some experimental runs, though they are within the acceptable limits. However, to ascertain the consistency of the kinetic parameters, a plot was drawn to show the relationship between Ea and A (Figure 10). The linear relationship between Ea and A reflects the distribution in reactivity and the ability of the model to fit almost any reactivity distribution for a single Ea value. This fact has been verified by fixing either A (2.585 × 1017 min-1) or Ea to a constant value (154.7 kJ/mol), and it has been found that the set of values remains the same, giving similar fitting patterns. On the basis of this analysis, an Ea value of 154.7 kJ/ mol and an A value of 2.585 × 1017 have been assigned to the adiabatic decomposition of DTBP and DTBPsolvent systems as the best values throughout this study. Merits and Demerits of the Present Modeling Approaches This detailed study not only has confirmed the findings of previous researchers but also has cleared up the ambiguities in the kinetic estimation studies of DTBP and DTBP-solvent decomposition. The perfect matching of the predicted and experimental curves has given a higher level of confidence and reliability of the kinetic parameters. Though the Arrhenius parameters gener-

Adiabatic decompositions are complex and their kinetic modeling approaches have to be comprehensive, as has been dealt within this work, to obtain reliable Arrhenius parameters. There are several commercially available softwares that can be used to obtain the kinetics of decomposition reactions with sufficient knowledge of the reaction products. BC is one of those such tools that can be used for kinetic modeling of complex decomposition reactions. In this particular study, BC has been employed successfully to model the adiabatic decomposition of DTBP and DTBP-solvent systems. This comprehensive approach yielded reliable first-order kinetic parameters for DTBP and DTBP-solvent decomposition, and the values agree with the reported values. Though DTBP yielded different products in different solvents, a consistent and single value of the activation energy indicated that the rate-determining step in the decomposition process was the breakage of the peroxy bond. Subsequent reactions were determined based on hydrogen abstraction and β-scission capabilities. Stoichiometric reactions for the heat liberation in decomposition of DTBP and DTBP-solvent systems have been elucidated for the first time in this study. Acknowledgment The authors are grateful to K. Takahashi for her technical assistance during the experimentation. The authors are also thankful to K. Murayama for useful discussions. Literature Cited (1) Kossoy, A.; Belochvostov, V.; Gustin, J. L. Methodological aspects of the application of adiabatic calorimetry for thermal safety investigation. J. Loss Prev. Process Ind. 1994, 7, 397. (2) Surianarayanan, M.; Iizuka, Y.; Miyake, A.; Itoh, A.; Ogawa, T. Modeling of adiabatic decomposition of ammonium nitrate under pressure using BatchCAD. First International Symposium on Energetic Materials, Tokyo, May 15-17, 2002. (3) Kossoy, A.; Misharev, P.; Belochvostov, V. Peculiarities of calorimetric data processing for kinetics evaluation in reaction hazard assessment. 53rd Annual Calorimetric Conference, Midland, MI, Aug 9-14, 1998. (4) Townsend, D. I.; Tou, J. C. Thermal hazard evaluation by an Accelerating Rate Calorimeter. Thermochim. Acta 1980, 37, 1. (5) Lee, P. P.; Back, M. H. Kinetic studies of the thermal decomposition of tetryl using accelerating rate calorimetry. Part 1. Derivation of activation energy for decomposition. Thermochim. Acta 1986, 107, 1. (6) Lee, P. P.; Back, M. H. Kinetic studies of the thermal decomposition of nitro guanidine using accelerating rate calorimetry. Thermochim. Acta 1988, 127, 89. (7) Tou, J. C.; Whiting, L. F. The thermo kinetic performance of an accelerating rate calorimeter. Thermochim. Acta 1981, 48, 21. (8) Kossoy, A.; Podlevskikh, N.; Sheinman, I. From calorimetric data via kinetic modeling to runaway simulation and reactor

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Received for review September 3, 2002 Revised manuscript received April 2, 2003 Accepted April 8, 2003 IE020687R