Kinetics of the Gas-Phase Noncatalytic Oxidation ... - ACS Publications

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Kinetics of the Gas-Phase Noncatalytic Oxidation of Hexafluoropropene David Lokhat, Deresh Ramjugernath, and Maciej Starzak* Reactor Technology Research Group, School of Engineering, University of KwaZulu-Natal, Durban, 4041, South Africa ABSTRACT: The kinetics of the high-temperature gas-phase oxidation of hexafluoropropene with molecular oxygen was investigated in an isothermal tubular reactor operating under laminar flow. Measurements were conducted at a total pressure of 450 kPa and over the temperature range from 463 to 493 K. A reaction scheme involving eight reactions was proposed to model the oxidation process. The initial steps are addition of oxygen to hexafluoropropene to yield hexafluoropropene oxide and some acid fluorides followed by thermal decomposition of the epoxide, radical recombination, and secondary oxidation reactions, giving three major products, viz. hexafluoropropene oxide, carbonyl fluoride, and trifluoroacetyl fluoride, as well as polyoxadifluoromethylene oligomers. Rate parameters for each of the reactions were determined through weighted nonlinear data regression. A plug flow approximation was used for modeling the reactor, as all radial concentration profiles in the long and narrow coiled reactor tube were found to be practically uniform. The proposed kinetic model of hexafluoropropene oxidation is in satisfactory agreement with the experimental observations, including carbon and oxygen element balances as well as thermochemical constraints.

1. INTRODUCTION Commercial production of 2,2,3-trifluoro-3-(trifluoromethyl)oxirane (commonly known as hexafluoropropene oxide, HFPO), a valuable fluoro-chemical intermediate that can be converted to various high-performance materials, is often carried out via the liquid-phase oxidation of hexafluoropropene (HFP) under high pressures and in the presence of chemical oxidizers and solvents.1,2 Due to concerns regarding process safety, scale-up, and environmental impact through generation of solvent waste, gas-phase epoxidation of HFP with molecular oxygen was recently investigated by the authors as a possible alternative to the existing industrial methods.3,4 Preparation of HFPO via the gas-phase process was successfully demonstrated in that study using a flow reactor. Optimal operating conditions for the best combination of yield and selectivity toward the epoxide (40% and 56%, respectively) were also identified. The literature is practically devoid of kinetic data on the thermallyinitiated, gas-phase oxidation of HFP, information which is crucial for proper reactor design, optimization, and scale-up. The purpose of the present investigation was to formulate and identify a kinetic model of the noncatalytic oxidation reaction based on experimental data obtained from a tubular flow reactor.

Most of the product stream components were analyzed by an online gas chromatograph (Shimadzu G.C. 2010), operated at 303 K, using an Agilent GS-GasPro PLOT column (30 m × 0.32 mm i.d.), helium as carrier gas and a flame ionization detector. Analysis of unreacted oxygen and acid fluorides was carried out by transferring samples of gaseous products to a second gas chromatograph (Shimadzu G.C. 2014) operating at 368 K with a 3 m long Hayesep D packed column and a thermal conductivity detector. Both instruments were calibrated and optimized for rapid analysis. Apparatus details can be found elsewhere.3,4 2.2. Hybridized Factorial Design of Experiments for Kinetic Data Generation. In the literature, various optimal strategies of experimental design for kinetic parameter assessment are given.5−8 One of the more popular methods involves minimization of the confidence volume of the current parameters to determine the next set of experimental conditions to be employed.5 Unfortunately this experimental design procedure led to a set of experimental conditions which was not attainable with our apparatus. An alternative experimental design was adopted for kinetic data generation. Measurements were made at three temperatures, viz. 463, 478, and 493 K. A regular grid of experimental points was established on the molar feed ratio-space time plane for each of the three temperatures, resulting in an expanded hybridized factorial design (cf. Figure 1). For each reaction temperature there were a total of 56 experimental runs, incorporating different reactant feed ratios and reactor residence times.

2. EXPERIMENTAL SECTION 2.1. Materials and Equipment. Hexafluoropropene (99.8%) was supplied by the South African Nuclear Energy Corporation (NECSA). Oxygen (99.5%) was obtained from Afrox (Linde Group). The noncatalytic, gas-phase oxidation reaction was carried out in an isothermal tubular reactor at a total pressure of 450 kPa. The helically coiled reactor was fabricated from 1/8 in. nominal size copper refrigeration tubing (i.d. = 1.5 mm) and 114.3 m long. Flow rates of the feed gases were controlled using thermal mass flow controllers. Product gas flow rates were measured using a drum-type wet-test meter. © 2012 American Chemical Society

Received: Revised: Accepted: Published: 13961

June 5, 2012 September 25, 2012 October 8, 2012 October 8, 2012 dx.doi.org/10.1021/ie301466t | Ind. Eng. Chem. Res. 2012, 51, 13961−13972

Industrial & Engineering Chemistry Research

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Figure 1. Generation of hybridized factorial design points for kinetic data collection.

Table 1. Reaction Model for the Thermally-Initiated, Gas-Phase Oxidation of HFP with O2a no.

reaction

rate expression

log10 A

n

1fb

C3F6 + 0.5O2 → C3F6O

r1f = k1fCC3F6CO2

1rb

C3F6O → C3F6 + 0.5O2

r1r = k1rCC3F6O

2

C3F6 + O2 → CF3COF + COF2

r2 = k2CC3F6CO2

3

C3F6O → CF3COF + CF2·

r3 = k3CC3F6O

4

CF2· + CF2· → C2F4

r4 = k4C2CF2

9.39

0.5

5

C2F4 + CF2· → c-C3F6

r5 = k5CCF2CC2F4

7.94

0.5

14.19

6b

C2F4 + 0.5O2 → COF2 + CF2·

r6 = k6CC2F4CO2

7

CF3COF + 0.5O2 → 2COF2

r7 = k7CCF3COFCO2

8

n(C3F6) + (3n/2)O2 → (CF2O)3n

r8 = k8CC3F6CO2

0

Ea

ref

162.01

12

1.66

19

26.61

19

a

Temperature dependence of the rate coefficient is given in the form of the modified Arrhenius expression, k = ATn exp(−Ea/RT). Units for A, cm3·mol−1·s−1 or s−1, as appropriate. Units for Ea, kJ·mol−1. bf and r refer to forward and reverse rate constants, respectively.

3. RESULTS

and yields were substantially lower. Variation in the space time and HFP/O2 molar feed ratio had a less significant effect on the selectivity and yield of HFPO. Molar amounts of the acid fluoride byproducts obtained were comparable to that of the epoxide. The yield of COF2 was consistently greater than CF3COF, and at 463 K practically no CF3COF was formed. Traces of C2F4 and c-C3F6 were obtained as well.

3.1. Kinetic Model. 3.1.1. Reaction Mechanism. The gasphase reaction gave HFPO, carbonyl fluoride (COF2), trifluoroacetyl fluoride (CF3COF), tetrafluoroethene (C2F4), and perfluorocyclopropane (c-C3F6) as products. Over the investigated temperature range, conversion of HFP was observed to increase from approximately 10% to almost 100%. However, at higher temperature HFPO selectivities 13962

dx.doi.org/10.1021/ie301466t | Ind. Eng. Chem. Res. 2012, 51, 13961−13972


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which is followed by a reaction of C2F4 with residual CF2· giving rise to c-C3F6

Table 2. Logarithm of the Calculated Concentration-Based Equilibrium Constants for the Reactions

C2F4 + CF2 · → c ‐C3F6

log10 Kc no.

reaction

463 K

478 K

493 K

1 2 3 4 5 6b 7

C3F6 + 0.5O2 → C3F6O C3F6 + O2 → CF3COF + COF2 C3F6O → CF3COF + CF2· CF2· + CF2· → C2F4 C2F4 + CF2· → c-C3F6 C2F4 + 0.5O2 → COF2 + CF2· CF3COF + 0.5O2 → 2COF2

0.05 124.47 28.36 51.02 16.17 45.05 60.55

−0.34 120.61 28.26 48.67 14.95 44.02 58.96

−0.71 116.98 28.16 46.47 13.80 43.06 57.47

Under our thermal reaction conditions oxidation of C2F4 should be included. Oxidation most likely proceeds through a radical mechanism involving a number of transient species.14 A simple representation of this mechanism at very high temperatures (>1200 K) is14−16

C2F4 + O2 → 2COF2

However, Matula found that for temperatures between 423 and 573 K the above stoichiometry was not obeyed and the following chemistry was proposed C2F4 + 0.5O2 → COF2 + CF2·

CF3COF + 0.5O2 → 2COF2

At the temperatures of this work, HFPO decomposes to give difluorocarbene (CF2·) and CF3COF11,12 The CF2· produced has a singlet spin multiplicity recombines to generate C2F4 CF2 · + CF2 · → C2F4

(3) 13

(7)

In addition to the gas-phase oxidation products, highly viscous oligomeric products were found deposited on the inner walls of the reactor tube. It is believed that such oligomers underwent chain extension via various radical units evolving from the interaction of HFP and molecular oxygen. Initially, oligomer formation was not included in the modeling of the HFP oxidation kinetics.3 However, since substantial deficiencies in carbon, oxygen, and fluorine element balances had experimentally been observed, it became clear that reactions 1 and 2 could not completely account for consumption of HFP and oxygen. Moreover, the rates of reactions 1 and 2, in a scheme that ignored formation of oligomers, appeared to be overpredicted at higher reaction temperatures and resulted in

(2)

C3F6O → CF3COF + CF2·

(6b)

The singlet difluorocarbene species is expected to be recycled through reactions 4 and 5. For all experimental runs the molar amount of COF2 was greater than CF3COF. Therefore, it is proposed that CF3COF decomposes in the presence of oxygen to give COF2 according to4

(1)

C3F6 + O2 → CF3COF + COF2

(6a)

17

It is generally accepted that the thermally initiated gas-phase oxidation of HFP proceeds through a complex mechanism.9 In our work we combined these steps to provide a simple kinetic scheme that can be used to model the oxidation process. The primary steps are addition of oxygen to the double bond of HFP to yield the epoxide as well as acid fluorides as byproducts. This and the biradical mechanism observed for interaction of oxygen atoms with fluoroethenes10 accounts for formation of the major products observed in this work: HFPO, COF2, and CF3COF. Accordingly, the following two reactions are proposed C3F6 + 0.5O2 ↔ C3F6O brb phone

(5)

and (4)

Figure 2. Parity and residual plots for exit molar flow rates of major species at 463 K. 13963



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Figure 3. Parity and residual plots for exit molar flow rates of minor species at 463 K.

Figure 4. Parity and residual plots for exit molar flow rates of major species at 478 K.

unrealistically high activation energies. Kartsov et al.18 showed that the oligomeric products formed during the high-temperature gas-phase oxidation of HFP had polyoxadifluoromethylene molecular structures with terminal acetyl fluoride, fluoroformate, and trifluoromethyl groups. In this study, for the sake of simplicity, the following stoichiometric expression was used to model formation of the oligomeric products n(C3F6) + (3n/2)O2 → (CF2O)3n

parameters which were not subjected to data regression and were obtained independently from the literature. 3.1.2. Thermochemistry. For each of the gas-phase reactions introduced in the preceding section the rate constants for the forward, kj, and reverse, k−j, steps are related through the equilibrium constant, Kj. The concentration-based equilibrium constant is related to the activity-based equilibrium constant through the following equation20

(8)

kj

The full kinetic model is given in Table 1, together with individual reaction rates and numerical values for those kinetic

k −j 13964

= K cj = K aj ×

⎛ P◦ ⎞Σνij ⎜ ⎟ ⎝ RT ⎠

(9)



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Figure 6. Parity and residual plots for exit molar flow rates of major species at 493 K.

where Po is the reference pressure (1 bar) and ∑vij is the sum of the stoichiometric coefficients for reaction j. The values of the concentration-based equilibrium constants predicted using thermochemical data were used to gauge the reversibility of each of the reactions involved. The temperature dependence of the activity-based equilibrium constant can be readily calculated using the standard enthalpy of reaction and standard Gibbs energy change of reaction at a reference temperature (298.15 K) as well as heat capacity data for each species involved.21 The standard enthalpy of reaction and standard Gibbs energy change of reaction may be calculated based on the enthalpies and entropies of formation at standard conditions. Reliable

thermochemical data were therefore required for each of the eight gas-phase species that were involved in the HFP oxidation process in order to assess the reversibility of individual reaction steps. Data for HFP, COF2, C2F4, CF2, and O2 were taken from the compilation of Burcat and Ruscic.22 For HFPO, CF3COF, and c-C3F6, however, no data were available. Quantum chemical calculations were used to estimate the thermochemical properties of these components. The standard enthalpy of formation of CF3COF was calculated using the Gaussian-4 composite method.23 For relatively large molecules such as HFPO and c-C3F6 the standard enthalpy of formation was 13965



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Figure 8. Arrhenius plot for the forward step of reaction 1.

Figure 9. Arrhenius plot for the reverse step of reaction 1.

predicted using the semitheoretical T1 recipe of Ohlinger et al.24 built into the Spartan 10 molecular simulation program. Standard entropies of formation and heat capacities for all three components were computed using B3LYP density functional theory at the B-3LYP/6-31G(2df,p) level with vibrational frequencies scaled by a factor of 0.9854 as recommended by Curtiss and Raghavachari.25 Details of these computations can be found elsewhere.3 Activity-based equilibrium constants can be converted to concentration-based equilibrium constants using eq 9, valid for ideal gases with a compressibility factor close to 1. It was essential to demonstrate that the reaction gas mixture in this study was also close to ideal. Pure component compressibility

factors for HFP, O2, HFPO, and COF2 were estimated using the Pitzer correlation, with parameters obtained from the Lee/ Kesler generalized correlation tables, based on the calculated reduced properties.21 Of all the components, HFP showed the greatest departure from ideality at the lowest experimental temperature used, with a compressibility of 0.9806. Compressibilities of HFP and HFPO were also calculated at 450 kPa from experimental vapor densities reported by Coquelet et al.26 and Dicko et al.,27 respectively. At 362.9 K, the highest measurement temperature reported by Coquelet et al., 26 the compressibility of HFP was estimated to be 0.946 while that of HFPO was estimated to be 0.942, based on the density data of Dicko et al.27 at 357.92 K. Both may be regarded as 13966



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Figure 10. Arrhenius plot for reaction 2.


Figure 11. Arrhenius plot for reaction 6b.


Table 3. Final Kinetic Parameter Estimates and 95% Confidence Intervals

conservative estimates. It is expected that within the considerably higher temperature range of 463−493 K the pure component compressibilities of these two species would be much closer to the ideal value of 1. A rigorous treatment of the gas mixture compressibility was considered unnecessary since the pure components were found to be nearly ideal. Since the reaction was carried out at a pressure of 450 kPa, the effect of pressure on the equilibrium constants had to be considered as well. At a given temperature, the standard free energies of formation of reactants and products are defined at a fixed pressure (1 bar) and the system temperature. Consequently, the activity-based equilibrium constant

reaction

units

1 (forward) 1 (reverse) 2 6b 7 8

m3·mol−1·s−1 s−1 m3·mol−1·s−1 m3·mol−1·s−1 m3·mol−1·s−1 m3·mol−1·s−1

pre-exponential factor (3.275 (2.334 (6.955 (4.828 (1.348 (3.033

± ± ± ± ± ±

◦ ⎛ ΔGrxn (T ) ⎞ K a(T ) = exp⎜ − ⎟= ⎝ RT ⎠

13967

0.358) 0.249) 1.187) 0.826) 0.327) 0.557)

× × × × × ×

1024 1028 1029 109 1010 1021

activation energy/ kJ·mol−1 259.13 294.63 309.69 104.49 127.51 235.07

± ± ± ± ± ±

7.21 13.08 11.91 7.43 3.52 9.08

∏ aν

i

i

(10)



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Figure 14. Parity and residual plots for exit molar flow rates of major species at all temperatures.

Figure 15. Parity and residual plots for exit molar flow rates of minor species at all temperatures.

becomes pressure independent.28,29 It can be shown, however, that in the general case the pressure dependence of the concentration-based equilibrium constant is given by29 ⎛ V̅ ⎛ ∂ ln Kc ⎞ 1⎞ ⎜ ⎟ = −∑ vi⎜ i − ⎟ ⎝ ∂P ⎠T ⎝ RT P⎠

are given in Table 2 at each of the three temperatures that was investigated. Data analysis shows that only reaction 1 exhibits significant reversibility within 463−493 K. The rate constant for the reverse step of reaction 1 was accepted as an additional fitting parameter when undertaking reaction model identification. 3.2. Reactor Model. On the basis of calculated values of the Reynolds number for the experimental reactor (long and narrow coiled tube) the regime of flow was determined to be laminar. However, preliminary simulations carried out using a rigorous laminar model incorporating radial molecular diffusion

(11)

where V̅ i is the partial molar volume of species i. For an ideal gas mixture, all individual terms of the RHS of eq 11 reduce to zero and no correction for pressure change is necessary either. The concentration-based equilibrium constants, calculated from the activity-based equilibrium constants according to eq 9, 13968



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Figure 16. Effect of HFP/O2 molar feed ratio on the exit concentration of HFP (black inverted triangle, experimental; black dashed line, simulation), O2 (purple triangles, experimental; purple dashed line, simulation), HFPO (red circle, experimental; red dashed line, simulation), CF3COF (blue diamond, experimental; blue dashed line, simulation), and COF2 (green square, experimental; green dashed line, simulation) at a fixed space time of 120 s and 463 K.

Figure 18. Effect of HFP/O2 molar feed ratio on the exit concentration of HFP (black inverted triangles, experimental; black dashed line, simulation), O2 (purple triangles, experimental; purple dashed line, simulation), HFPO (red circles, experimental; red dashed line, simulation), CF3COF (blue diamonds, experimental; blue dashed line, simulation), and COF2 (green squares, experimental; green dashed line, simulation) at a fixed space time of 120 s and 478 K.

Figure 17. Effect of HFP/O2 molar feed ratio on the exit concentration of C2F4 (red circles, experimental; red dashed line, simulation) and c-C3F6 (blue diamonds, experimental; blue dashed line, simulation) at a fixed space time of 120 s and 463 K.


showed that the reactor behavior was dramatically different from that of a conventional laminar flow reactor (LFR). The parabolic concentration profile characteristic of LFR appeared to be mitigated by radial molecular diffusion to the extent that the reactor performance approached plug flow.30 In addition, the effect of molecular diffusion was enhanced by secondary

flow induced by centrifugal forces present in the coiled tube.31−34 The additional advantage of the plug flow model was its ability to explicitly account for the overall nonequimolarity of the oxidation process. 3.3. Kinetic Parameter Identification. The temperature dependence of the estimated rate constants was given by the 13969



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fit of the experimental data to the reaction model. The objective function was defined as nE

S(b ) =

nD

∑ ∑ [wik(yik i=1 k=1

− gik (x i , b))]2

(12)

where wik is the weighting factor of the kth dependent variable in the ith experiment, yik is the measured value of the kth dependent variable in the ith experiment, and gik is the kth dependent variable in the ith experiment predicted by the model, based on the vector of independent variables xi and the parameter estimates b. There are a total of nE experiments and nD dependent variables. In the current context, the dependent variables were the exit molar flow rates of all species and the independent variables were the reaction temperature, pressure, and inlet molar flow rates. All computational procedures were programmed using MATLAB. The ordinary differential equations describing the plug flow reactor model turned out to be nonstiff, and conventional methods of numerical integration were found to be sufficient. A subspace trust region approach based on the interior-reflective Newton method described by Coleman and Li 35 was selected as the minimization algorithm. The best normalizing factor for weighted nonlinear leastsquares problems is 1/σik, where σ2ik is the variance of the kth dependent variable in the ith experiment, provided that there are replicate measurements available.33 However, due to the difficult nature of the experiments, replicate data could not be generated and the use of other normalizing factors had to be explored. The arithmetic mean of the experimental and predicted values was found to be an acceptable normalizing factor, providing a satisfactory neutral weighting between large and small measurement values.36 Initial estimates for the unidentified kinetic parameters were obtained through a series of isothermal fits, estimating the value of kj at each fixed temperature. For the isothermal fitting, a multistart technique was employed, providing a random set of initial estimates in each instance and selecting from among these the best output solution. Figures 2−7 show parity and residual plots for all species, based on the estimated rate constants, at each of the three temperatures investigated. For each reaction, the fitted rate constants and corresponding temperatures were used to form Arrhenius plots of ln k versus 1/T (cf. Figures 8−13). The gradients and intercepts of these plots yielded initial values for the activation energies and preexponential factors, respectively, required for a general nonlinear least-squares fitting of the consolidated experimental data set. Ultimate kinetic parameter estimates were obtained by repeating the nonlinear regression according to a temperaturecentering scaling method.37 The results are presented in Table 3. Figures 14 and 15 show parity and residual plots for all species at all three temperatures. Numerical simulations using the proposed oxidation mechanism were undertaken for various HFP/O2 feed ratios to test the performance of the model. A comparison between the numerical analysis and the experimental observations are given in Figures 16−21. Experimental data were generally in good agreement with the proposed kinetic model. For all temperatures, there was a satisfactory fit of the measured data and a random distribution of residuals for HFP, O2, HFPO, CF3COF, and COF2. Less satisfactory fits were obtained for C2F4 and c-C3F6 at 493 K. The temperature dependence of all the rate constants was found to be physically meaningful.

Figure 20. Effect of HFP/O2 molar feed ratio on the exit concentration of HFP (black inverted traingles, experimental; black dashed line, simulation), O2 (purple triangles, experimental; purple dashed line, simulation), HFPO (red circles, experimental; red dashed line, simulation), CF3COF (blue diamonds, experimental; blue dashed line, simulation), and COF2 (green squares, experimental; green dashed line, simulation) at a fixed space time of 120 s and 493 K.


general Arrhenius expression. Pre-exponential factors and activation energies for reactions 3, 4, and 5 were taken from the literature (cf. Table 1). Kinetic parameters for reactions 1, 2, 6b, 7, and 8 were obtained through a weighted least-squares 13970



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4. DISCUSSION Kinetic measurements of the thermally initiated, noncatalytic, gas-phase oxidation of HFP were carried out using a tubular flow reactor. The experiments were conducted over a relatively narrow temperature range within which the optimum yield and selectivity toward HFPO had previously been obtained.3,4 Experimental data were fitted to a simplified HFP oxidation scheme. Unfortunately, no kinetic data pertaining to the gasphase oxidation of HFP obtained under the conditions used in the present study are available in the literature to allow for a comparison. Among the fitted parameters, the activation energy for formation of the acid fluorides (reaction 2) was found to be 50.56 kJ·mol−1 higher than that for formation of HFPO (reaction 1), which indicates that a higher reaction temperature favors total oxidation of HFP. The difference between the activation energies for the forward and reverse steps of reaction 1 was found to be −35.5 kJ·mol−1. The standard enthalpy of reaction 1 estimated by quantum chemical calculations to be −49.24 kJ·mol−1 results in a discrepancy of 13.74 kJ·mol−1. This difference can be justified by the large confidence intervals for Ea of the forward and reverse steps of reaction 1, presented in Table 3. None of the 95% confidence intervals obtained from the fitting algorithm included a close-to-zero value for any of the parameters that were identified, indicating that all reactions were necessary for the full description of the noncatalytic oxidation process. The proposed kinetic model accounted satisfactorily for consumption of HFP and O2 as well as formation of the major products HFPO, COF2, and CF3COF at each of the reaction temperatures investigated. The model was able to provide reasonable agreement with the experimental data for the minor products C2F4 and c-C3F6 at 463 and 478 K but deviated at 493 K. For the latter, the inability to reproduce the experimental trend was most prevalent when the feed gas contained a greater proportion of HFP (cf. Figure 21). This suggests that a direct route toward the minor products, from HFP, may be possible. It is known, for example, that the process of HFP pyrolysis gives both C2F4 and c-C3F6 as end products but only at temperatures exceeding 600 K.38 The interaction of HFP with oxygen at such a low temperature as 493 K, inducing catalytic dissociation of the fluoro-olefin molecule rather than oxidation, seems a promising reaction to be studied. The rate of formation of oligomeric products varies between 0.5 and 5 g·h−1 depending on the feed composition and reaction temperature. This is consistent with the amounts obtained from the experimental runs.

temperature gas-phase oxidation of HFP, thus enabling a full description of the process for reactor modeling and optimization.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +2731 260 3117; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the South African Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation.

■

NOMENCLATURE

Latin Capital and Lowercase

a = chemical activity b = vector of parameter estimates gik = predicted value of the kth dependent variable in the ith experiment ΔGrxn ° = standard molar free energy of reaction, kJ·mol−1 kj = rate constant for reaction j Kj = equilibrium constant for reaction j nD = number of parameters nE = number of experiments P = pressure, kPa S = objective function T = temperature, K vi = stoichiometric coefficient V̅ i = molar volume of species i, m3·mol−1 wik = weighting factor of the kth dependent variable in the ith experiment xi = vector of independent variables yik = measured value of the kth dependent variable in the ith experiment Greek Symbols

■

σ2ik = variance of the kth dependent variable in the ith experiment

REFERENCES

(1) Millauer, H.; Schwertfeger, W.; Siegemund, G. Hexafluoropropene oxide - a key compound in organofluorine chemistry. Angew. Chem., Int. Ed. Engl. 1985, 24, 161. (2) Furin, G. G. Synthesis of 2,3-epoxyperfluoroalkanes by means of oxidation of fluorine containing olefins. Chem. Sustainable Dev. 2006, 14, 97. (3) Lokhat, D. Ph.D. Thesis, University of KwaZulu-Natal, 2012. (4) Lokhat, D.; Ramjugernath, D.; Starzak, M. Gas-phase noncatalytic epoxidation of hexafluoropropene in a tubular reactor: optimal reaction conditions. Ind. Eng. Chem. Res., submitted for publication. (5) Box, G. E. P.; Lucas, H. L. Design of experiments in nonlinear situations. Biometrica 1959, 46, 77. (6) Kitrell, J. R.; Hunter, W. G.; Watson, C. C. Obtaining precise parameter estimates for nonlinear catalytic rate models. AIChE J. 1966, 12, 5. (7) Froment, G. Model discrimination and parameter estimation in heterogeneous catalysis. AIChE J. 1975, 21, 1041. (8) Buzzi-Ferraris, G.; Manenti, F. Kinetic model analysis. Chem. Eng. Sci. 2009, 64, 1061. (9) dos Santos Afonso, M.; Romano, R. M.; Della Védova, C. O.; Czarnowski, J. Kinetics and mechanism of the thermal gas-phase

5. CONCLUSIONS The kinetics of the thermally-initiated gas-phase oxidation of HFP with molecular oxygen was experimentally studied between 463 and 493 K and at a total pressure of 450 kPa. Gas-phase products of the oxidation reaction include HFPO, COF2, CF3COF, C2F4, and c-C3F6. Polyoxadifluoromethylene oligomers are also produced. A simplified kinetic model is proposed for the principal reactions of HFP oxidation. Kinetic parameters of the proposed model were obtained through a least-squares minimization procedure. The kinetic model predicts most of the experimental data with the best prediction at 478 K, coinciding with the highest yield of HFPO ranging from 35% to 40%. In the literature, only the kinetics of HFPO decomposition and difluorocarbene recombination are given. The present work provides new kinetic data on the high13971



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