Identification of the Kinetic Parameters and Autocatalytic Behavior in

Article pubs.acs.org/OPRD

Identification of the Kinetic Parameters and Autocatalytic Behavior in Esterification via Isoperibolic Reaction Calorimetry Hong-Yuan Wei,† Zi-Chao Guo,† Lin Hao,* Wen-Shuai Bai, Rui Wang, and Shuai Li School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P.R. China ABSTRACT: In the fine chemical and pharmaceutical industries, the operation of highly exothermic reactions with the autocatalytic features may lead to safety issues. From the safety point of view, identification of the autocatalytic features and the corresponding kinetics for a given reaction are of significant importance. In this work the simultaneous kinetic and thermodynamic analysis of a case reaction of esterification between acetic anhydride and methanol is first carried out under isoperibolic conditions using a reaction calorimeter. Two kinetic models, that is, autocatalytic kinetic model and second order kinetic model, are used to fit the temperature profile. The results show that the calculated reaction enthalpy (ΔH, 67.88 kJ/mol) by the autocatalytic kinetic model is much closer to the experimental value (63.22 kJ/mol) than that by second order model (100.06 kJ/mol), indicating that the autocatalytic kinetic model is more appropriate to the reaction. With the case study, we also demonstrate that an insight into the reaction mechanism and the proper selection of the kinetic model to fit the experimental data is crucial otherwise the improper selection of kinetic model could lead to misleading kinetic or thermodynamic parameters and then result in an incorrect estimation of the risk level of a given reaction.

1. INTRODUCTION In the fine chemical and pharmaceutical industries, the choice of the safe operating conditions represents the first line of defense to prevent incidents and runaways in batch and semibatch reactors, especially when highly exothermic reactions or thermally unstable compounds are involved.1 In the past decades, much work has been dedicated to this issue.2−8 Nevertheless, most works are based on the knowledge of the thermodynamics and kinetics of the reactions.1 Regretfully, detailed reaction kinetics is hardly studied in practice due to the costly and time-consuming limitations.2−4 As a compromising alternative, development of an apparent kinetic and thermal model to depict the dynamic behavior of a given reaction is preferable.2 The esterification reactions between an anhydride and an alcohol are classic solvent-free reactions, that is to say, reagents are used alone without any other inert solvent. However, due to the influence of the reaction mixture composition on the activity coefficients of the reagents and products, the detailed kinetic model for this kind of reaction is difficult to determine.2 Therefore, developing an apparent kinetic model possessing the ability to describe the dynamic behavior of these reactions is preferable. Traditionally, the esterification between acetic anhydride and alcohol is assumed to obey second order kinetics or pseudo first order kinetics when acetic anhydride is in “sufficient” excess. Ubrich et al.7,9 employed second order kinetics to investigate the dynamic behavior of esterification of propionic anhydride and 2-butanol. Friedel et al.,10 Wright et al.,11 Duh et al.,13 and Casson et al.14 modeled the methanol/acetic anhydride reaction using a second order kinetic to calculate the kinetic parameters. Richner and co-workers 12 investigated the esterification of acetic anhydride by n-butanol using second order kinetics by nonisothermal calorimetry. Actually, Balland and co-workers2 experimentally and theoretically demonstrated that the esterification of acetic © XXXX American Chemical Society

anhydride by methanol is autocatalyzed by the product acetic acid. Moreover, Widell et al.15 carried out a series of isothermal experiments and proved the autocatalytic behavior in esterification between anhydride and alcohols. However, they conducted the experiments with the acetic anhydride in “sufficient” excess, meaning the kinetic order with respect to alcohol could be assumed to be pseudo-first.15 In this paper, a stoichiometric mole ratio 1:1 of acetic anhydride to alcohol is used to investigate the kinetic and thermal parameters by a series of isoperibolic semibatch experiments. The isoperibolic temperature means only the jacket temperature is controlled and maintained constant, leaving the reaction medium temperature following its temperature course as a result of the heat balance between the heat across the wall and heat release rate due to the reaction. Meanwhile, with the comparison of the simulated temperature profiles calculated by second order kinetics and autocatalytic kinetics respectively, these isoperibolic experiments undoubtedly demonstrate the autocatalytic behavior in the reaction progress As a widely accepted tool for kinetic and thermal analysis,13,16 reaction calorimetry is applied to estimate the kinetics and thermodynamics of the esterification of anhydride and methanol in this paper. The strength of the reaction calorimetry compared to the traditional methods is the ability to simultaneously determine the kinetic and thermodynamic parameters. The main purpose of this paper is to calculate the autocatalytic kinetic parameters of esterification of anhydride by methanol in a stoichiometric mole ratio 1:1 and demonstrate the autocatalytic behavior along with the reaction progress. A second goal is to present the importance of the proper selection Received: November 29, 2015

A

DOI: 10.1021/acs.oprd.5b00395 Org. Process Res. Dev. XXXX, XXX, XXX−XXX

Organic Process Research & Development

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Figure 1. Thermal power profile with 0.056 g sulfuric acid to determine ΔH under isothermal condition 50 °C. Heat flow (solid line), temperature (dash line), and dosing mass (dot line).

Figure 2. Thermal power profile for measurement of the mixing heat of acetic anhydride and methanol. Heat flow (solid line), temperature (dash line), and dosing mass (dot line).

of the kinetic model to fit the kinetic and thermodynamic parameters

analysis, indicating that the reaction mechanism is more complex. Water is produced from the esterification of the produced acetic acid by methanol. The produced water can then hydrolyze the acetic anhydride. Accordingly, the following reaction path is proposed:

2. EXPERIMENTAL SECTION 2.1. Reaction. The esterification of acetic anhydride with methanol has been chosen as a model reaction. Normally, this reaction is treated as a single acetic anhydride esterification by methanol: A+B→C+D

(3)

A + C → D + H 2O

(4)

B + H 2O → 2C

(5)

(1)

where A is methanol, B is acetic anhydride, C is acetic acid, and D is methyl acetate. The reaction rate r of eq 1 can be expressed by a simple law of the second order

r = k1cAc B

A+B→C+D

Obviously, the product of acetic acid in eq 3 could react with the reactants, namely acetic anhydride and methanol, in eqs 4 and 5, indicating the esterification is catalyzed by the produced acetic acid. For simplification, eqs 4 and 5 can be merged to one equation as followed

(2)

However, Balland et al.2 have demonstrated the presence of water in the mixture after the reaction with gas chromatography

A + B + C → 2C + D B

(6) DOI: 10.1021/acs.oprd.5b00395 Org. Process Res. Dev. XXXX, XXX, XXX−XXX


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To model this reaction pathway, the Benito-Perez model17 is employed to describe this esterification. r = k 2cAc B + k 3cAc BcC

Table 1. Experiment Conditions for Esterification of Acetic Anhydride by Methanol

(7) run1 run2 run3 run4 run5 run6 run7 run8

where k2 represents the reaction rate constant in eq 3 and k3 is reaction rate constant in eq 6. 2.2. Equipment. A reaction calorimeter (RC1) from the company of Mettler Toledo composed of a 0.5 L glass-made reactor is used to study the reaction. The reactor is equipped with a glass temperature sensor, a glass calibration heater, and a glass four pitched-blade stirrer. The calibration heater allows measuring the heat transfer coefficient (U) and the heat capacity of the reaction mixture through carrying out a calibration procedure. A dosing pump is used to introduce the methanol into the reactor. The heating−cooling system using a single heat transfer fluid (silicone oil) works within a temperature range of −50 to 200 °C. 2.3. Experiments. 2.3.1. Molar Reaction Enthalpy (ΔH) and Mixing Heat (Qmix). Run 1: To measure the molar reaction enthalpy, an isothermal experiment with addition of 0.056 g sulfuric acid to ensure the complete conversion of methanol is carried out. First after a mixture of 216.3 g acetic anhydride (purchased from Kewei Chemical Co. Ltd., Tianjin, China) and 0.056 g sulfuric acid is loaded to the reactor, the temperature of the mixture is set at 50 °C with agitation speed of 400 rpm. Once the steady state has been reached, a calibration procedure is performed to measure the product of the overall heat transfer coefficient and the heat exchange area (US). Then 67.8 g methanol (purchased from Kewei Chemical Co. Ltd., Tianjin, China) is introduced into the reactor at a constant rate of 2 g/ min at atmospheric temperature. After the reaction comes to the end point, a second calibration procedure is carried out. Run 2: The measurement procedure of determination of mixing heat is similar to that of run 1. The differences between run 1 and run 2 are that there is no addition of sulfuric acid and that reaction temperature is set at 23.5 °C for run 2. Figures 1 and 2 show the thermal power profile of run 1 and run 2, respectively. Integration of experimental thermal power profile (Figure 1) gives total heat released by reaction, 133.44 kJ. The thermal power profile in Figure 2 indicates that the endothermic mixing heat of acetic anhydride and methanol is −4.52 kJ. 2.3.2. Isoperibolic Experiments. Runs 3−5: To investigate the kinetic parameters and illustrate the different prediction results of temperature profiles by autocatalytic kinetic model and second order kinetic model, three isoperibolic experiments (runs 3, 4, and 5) with jacket temperature fixed at 50, 55, and 58 °C, respectively are carried out. Two calibration procedures are performed to measure US before and after each run. The specific experimental conditions are listed in Table 1. 2.3.3. Isothermal Experiments. Run 6: To directly verify the autocatalytic behavior of the esterification reaction, an isothermal experiment is conducted. First 216.3 g acetic anhydride is loaded in the reactor and the reaction temperature is set at 53 °C with agitation speed of 400 rpm. After the calibration procedure, 16.95 g preheated methanol with the same temperature to reaction temperature is added batchwise into the reactor. Another calibration procedure is performed after the reaction ending. Runs 7−8: To verify the validation of the kinetic and thermal parameters calculated from above isoperibolic experiment, two more isothermal experiments (runs 7 and 8) are carried out in

mode

TrorTj (°C)

v (cm3/s)

Td (°C)

R (rpm)

isothermal isothermal isoperibolic isoperibolic isoperibolic isothermal isothermal isothermal

50 23.5 49.8 54.8 57.8 53 55 58

0.042 0.042 0.042 0.042 0.042

24 25 25.6 25.6 30 53 25.6 25.5

400 400 400 400 400 400 400 400

0.042 0.042

semibatch mode. The mole ratio of two reaction components, that is, acetic anhydride and methanol is 1:1 and methanol is added dropwise into acetic anhydride. The validation is realized by comparing the experimental thermal power profiles with the simulated thermal power profiles.

3. MATHEMATIC MODELS Before developing the mathematical model for eqs 3 and 6, some assumptions should be made as follows: (1) The volumes are additive. (2) The product of the heat-transfer area and overall heattransfer coefficient, UA, is linearly increasing with the liquid volume in the reactor. (3) There is only reaction enthalpy, no mixing heat. (4) All components involved in the reaction are perfectly mixed, indicating the temperature and concentration of all the components are uniformly dispersed in the reactor. (5) The reaction volume variation during the reaction is negligible and the increase in the reaction volume is only because of the addition of methanol. 3.1. Mass and Heat Balance Equations for Isoperibolic Experiments. The partial mass balance of acetic anhydride during the dosing period can be written as dnB = −r(V0 + vt ) (8) dt where nB is the molar number of acetic anhydride in the reactor. The bulk concentrations of acetic anhydride, methanol, and acetic acid in the reactor during the dosing period respectively are C B = N0(1 − X )/(V0 + vt )

(9)

CA = N0(t /td − X )/(V0 + vt )

(10)

CC = N0X /(V0 + vt )

(11)

Substituting eqs 2, 9, 10, and 11 into eq 8 gives the following mass balance equation for second order model: dX = A1exp(−E1/RT )N0(1 − X )(t /td − X )/(V0 + vt ) dt (12)

The mass balance equation for autocatalytic kinetics model can be obtained by substituting eqs 7, 9, 10, and 11 into eq 8: dX = A 2exp(− E2 /RT )N0(1 − X )(t /td − X )/(V0 + vt ) dt + A3exp(− E3/RT )N0 2X(1 − X )(t /td − X )/(V0 + vt )2 C

(13)



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the experimental temperature curves and simulated temperature curves for runs 3−5 is taken as the objective function as followed.

After the dosing period, the reaction is automatically converted to batch operation. The reaction volume is constant. Therefore, the mass balance equations for second order model and autocatalytic kinetics model after the dosing period are dX = A1exp(−E1/RT )N0(1 − X )2 /(V0 + vtd) dt

5

min A ,E

(14)

dX = A 2 exp(−E2 /RT )N0(1 − X )2 /(V0 + vtd) dt + A3exp(−E3/RT )N0 2X (1 − X )2 /(V0 + vtd)2 (15)

for autocatalytic kinetics model. For semibatch reactors, a general heat balance can be formulated as followed:11 dt

= N0( −ΔH )

(16)

This balance contains four basic terms: the heat accumulation term at the left of eq 16, heat generation rate due to the reaction progress, the cooling rate due to circulation of the cooling liquid in the reactor jacket, and the cooling (heating) rate due to dosing of a reactant. When the dosing is completed, the cooling (heating) term disappears. With the assumptions that US increases linearly with the dosing mass and that the volumes and heat capacities are additive, eq 16 can be transformed to

ΔH =

⎡ dT 1 dX ⎢N0( −ΔH ) = (Vρc p)0 + vt(ρc p)d ⎢⎣ dt dt ⎛ ⎞ t − ⎜(UA)0 + Δ(US)⎟(T − Tj) − v(ρc p)d td ⎝ ⎠ ⎤ (T − Td)⎥ ⎥⎦

(17)

⎡ dT 1 dX = ⎢N0( −ΔH ) dt (Vρc p)0 + vtd(ρc p)d ⎣ dt (18)

3.2. Mass Balance Equations and Heat Generation Rate Equations for Isothermal Experiments. The mass balance equations for isothermal experiments have the same forms as those for isoperibolic experiments. The heat generation rate qr due to reaction progress for isothermal experiments can be expressed as follows

qr = N0( −ΔH )

dX dt

(20)

−∫ qrdt N0

(21)

The reaction enthalpy is calculated and equal to −63.23 kJ/ mol. To measure the mixing heat, an isothermal run is carried out at 23.5 °C with 1:1 mol ratio of acetic anhydride to methanol. The result is displayed in Figure 2. Obviously, the mixing of acetic anhydride and methanol is an endothermic process. The integration result of the heat signal in Figure 2 gives the total endothermic heat ∼4.52 kJ, which could be neglected as regards to reaction enthalpy. However, this endothermic heat has an obvious effect on the temperature profile especially at the initial dosing stage. As shown in Figures 3, 4, and 5, the experimental temperature curves at the initial stage are always slightly lower than those of the modeled temperature curves, which results from the significant endothermic heat effect of mixing and the negligible reaction heat at the initial dosing stage. 4.2. Experimental Determination of the Values of US. The values of US must be measured to calculate the kinetics and thermodynamics using the mathematic model in Section 3. With regards to the values of US during the semibatch processes, Westerterp et al.3,4 assumed that the values of US were proportional to the liquid volume in the reactor. However, the experiment results in this study demonstrate that this assumption is incorrect. Actually, the rate of increase of the values of US is slower than that of the values of the liquid volume, as indicated in Table 2. Hence, the values of US need to be measured before and after the esterification to calculate the values of US within the dosing period. In addition, assumptions that the values of US increase linearly within the dosing period and remain constant after the dosing period must

where Δ(US) is the difference between the initial (US)0 and the final (US)f. After the dosing period, the heat balance equation is

⎤ − (US)f (T − Tj)⎥ ⎦

run = 3 N = i

4. RESULTS AND DISCUSSION 4.1. Experimental Determination of Reaction Enthalpy ΔH and Mixing Heat Qmix. To compare the accuracy of the autocatalytic kinetic and second order kinetic models, the calculated ΔH need be compared to the experimental value of ΔH. To determine the experimental value of ΔH, run 1 was carried out in isothermal mode with addition of 0.056 g sulfuric acid to make sure that all reactants were consumed completely. The thermal power profile for run 1 is shown in Figure 1. The integration result of the total heat is 133.44 kJ. The reaction enthalpy could be calculated as

dX − (US)(T − Tj) dt

− v(ρc p)d (T − Td)

∑ ∑ {[T(t i)exp − T(t i)sim ]2 }

It is worth noting that all three isoperibolic runs are involved into the objective function eq 20. The pre-exponential factors (A1, A2, A3), activation energy (E1, E2, E3), and reaction enthalpy (ΔH) are the variables. The procedure of programming solve (PS) built into the EXCEL software is used to solve this optimization problem. A set of initial values are valuated before the optimization initiation. This simultaneous estimation method can give the kinetic and thermodynamic parameters simultaneously.

for second order kinetic model and

d(ρc pVT )

n

(19)

3.3. Simultaneous Estimation Method for Kinetic and Thermodynamic Parameters from Isoperibolic Experiments. Actually, the calculation of kinetic and thermodynamic parameters is an optimization problem. The deviation between D



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Figure 3. Tempareture profile for run 3 performed at 49.8 °C in isoperibolic mode.


Table 2. Values of US Before and After the Esterification run3 run4 run5

(US)0a, W/K

(US)fb, W/K

V0c, cm3

Vfc, cm3

2.675 2.689 2.695

3.406 3.465 3.478

200 200 200

285.6 285.6 285.6

a

0 represents initial value of US. bf represents the value of US after the esterification. cV represents the volume of the reaction mixture.

To simultaneously determine the kinetic and thermodynamic parameters, the correlated temperature points are selected from 0 to 5400 s, with the step size of 3 s for numerical calculation. As shown in Figures 3−5, the experimental temperature profiles and simulated temperature profiles for runs 3−5 are illustrated, respectively. The corresponding kinetic and thermodynamic parameters of the autocatalytic model and second order model for runs 3−5 are listed in Table 3. A comparison of the frequency factor, activation energy for second order kinetic model, is made between different experiments and summarized in Table 4.


Table 3. Kinetic and Thermodynamic Parameters of Autocatalytic Model and Two Order Model for Runs 3, 4, and 5

be made. Two calibration procedures are carried out before and after each run. The mechanism of this calibration procedure can be found in refs 18 and 19. The results of US for runs 3, 4, and 5 are listed in Table 2, which obviously indicate that the effect of reactive mixture temperature on US is weak, for example, the initial values of the (US)0 only increase from 2.675 W/K to 2.695 W/K with the temperature increasing from 50 to 58 °C. 4.3. Autocatalytic Behavior in the Esterification. 4.3.1. Estimation of the Kinetic and Thermodynamic Parameters. When kinetic and thermodynamic parameters are simultaneously determined by reaction calorimetry, a proper choice of the kinetic model for the reactions is essential, because an improper choice of the kinetic model could bring misleading results. With regards to the esterification described in this paper, the autocatalytic model and second order model were selected to fit the experiment results and were compared. In all cases, the endothermic mixing heat of acetic anhydride and methanol is neglected.

pre-exponential factors, A autocatalytic model

A2 = 1.70 × 1012 cm3/mol·s A3 = 1.37 × 103 cm6/mol2·s

two order model

A1 = 1.55 × 1010 cm3/mol·s

activation energy, E

reaction enthalpy

E2 = 88.07 ΔH = 67.88 kJ/mol kJ/mol E3 = 14.56 kJ/mol E1 = 75.71 ΔH = kJ/mol 100.06 kJ/mol

4.3.2. Demonstration of the Autocatalytic Behavior. To directly demonstrate the autocatalytic behavior, the isothermal experiment, that is, run 6 was conducted in batch mode. The corresponding result is shown in Figure 6. It is obvious that the reaction temperature is much closer to the set point (53 °C) over the reaction period, therefore the reaction temperature could be considered constant. With respect to the heat generation rate, we can see that the power profile increases E



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methanol and acetic anhydride, which has been confirmed in Figure 2. 4.3.3. Verification of the Kinetic and Thermodynamic Parameters. To verify the kinetic and thermodynamic parameters calculated by isoperibolic experiments, two isothermal experiments at 55 and 58 °C (runs 7 and 8) are carried out. The simulated thermal power profiles are compared to the experimental thermal power profiles, which are shown in Figures 7 and 8. Obviously, the simulated thermal power profiles of autocatalytic model fit better with the experimental thermal power profiles than that of the second order model.

Table 4. Comparison of the Frequency Factor, Activation Energy for Second Order Kinetic Model, Between Different Experiments experiment

A(cm3/mol·s)

E(kJ/mol)

this work reference13 reference10 reference11

1.55 × 1010 3.6 × 1010 8.97 × 1010 1.05 × 1010

75.7 72.6 73.8 73.2

Figure 6. Thermal power profile and reaction temperature profile for run 6.

with the reaction progressing during the first 2000 s, then it gradually decreases to zero after reaction extent for about 14500 s. This kind of thermal power profile demonstrates the autocatalytic behavior. As shown in Figures 4 and 5, the simulated temperature curves for autocatalytic kinetic and second order kinetic models both fit well with the experimental temperature curves, however, the simulated temperature curve of second order kinetic model at 50 °C (Figure 3) presents poor accordance with the experimental temperature curve, which can be ascribed to the stronger autocatalytic feature at lower temperature. From a mathematic point of view, the lower temperature is the bigger value of the ratio of the autocatalytic term k3cAcBcC to normal term k2cAcB. It is interesting to note that the calculated reaction enthalpy from the autocatalytic kinetic model (67.88 kJ/mol) is much closer to the experimental reaction enthalpy (63.22 kJ/mol) than that for second order kinetic model (100.06 kJ/mol). This proves the autocatalytic model is more appropriate for determination of the kinetic and thermodynamic parameters of the esterification. Also this demonstrates the existence of the autocatalytic behavior for this reaction demonstrated in this article. Based on the above results, ΔH can be considered as an indicator for the accuracy of the selected kinetic model with regards to thermodynamic and kinetic analysis. In a practical thermodynamic and kinetic analysis, it is usually difficult to decide whether the calculated kinetic parameters reflect the real values, whereas ΔH is feasible to measure via reaction calorimetry. Another interesting feature in Figures 3−5 is that at the initial dosing stage, the experimental temperatures are always smaller than those of the simulated temperatures. This can be explained by the endothermic heat effect of the mixing of

Figure 7. Thermal power profile in isothermal condition (55 °C) for verification of the thermodynamic and kinetic parameters from isoperibolic runs.

Figure 8. Thermal power profile in isothermal condition (58 °C) for verification of the thermodynamic and kinetic parameters from isoperibolic runs.

To further show the improper selection of the second order kinetic model, another individual estimation method is carried out to fit temperature profiles of runs 4 and 5. The difference between individual estimation method and the simultaneous estimation method is that for individual estimation method, ΔH is fixed and equivalent to the experimental value 63.22 kJ/ mol and only the kinetic parameters for second order kinetic model is calculated. The calculated results of temperature profiles for run 4 and run 5 are illustrated in Figures 9 and 10. F



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carefully investigate the reaction mechanism and select the proper kinetic model to fit the experimental data. Fitting the experimental results with an improper kinetic model will give misleading kinetic or thermodynamic parameters. Such misleading parameters could result in an incorrect estimation of the risk level for a given reaction, especially for reactions that possess an autocatalytic feature or a complex reaction mechanism, for example, the calculated enthalpy value 100.06 kJ/mol by second order model overestimates the risk level of the esterification in this article.

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AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]; Phone: +86 (0)22 27405754; Fax: +86 (0)22 27400287. Author Contributions †

H.-Y.W. and Z.-C.G.contributed equally.

Notes

The authors declare no competing financial interest.

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Figure 9. Comparison of the temperature profiles of individual method and simultaneous method for kinetic analysis at 55 °C.

ACKNOWLEDGMENTS The authors would like to give thanks for the assistance of Mr. David Haywood from AstraZeneca. This study is supported financially by Tianjin University Innovation Foundation.

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Figure 10. Comparison of the temperature profiles of individual method and simultaneous method for kinetic analysis at 58 °C.

NOMENCLATURE AND UNITS A =pre-exponential Arrhenius factor, s−1 c =concentration, mol/cm3 cp =specific heat capacity of the reacting mixture, J·g−1·K−1 d =dosing E =activation energy, kJ/mol N =number of moles, mol qr =heat generation rate, J/s t =time, s U =the over heat transfer coefficient for the system considered, W·m−2·K−1 v =volumetric dosing rate, cm3/s V0 =initial volume of the reaction mixture in reactor, cm3 X =conversion (%) S =heat transfer surface area, m2 s =stirrer

Greek letters

ΔH = reaction enthalpy, kJ/mol ρ = density of the reactants, g/cm3

The temperature profiles obtained by the simultaneous estimation method fit better with the experimental temperature profiles than those obtained by the individual estimation method. Moreover, it can be seen that the individual estimation method underestimates the maximum temperature obtained during the whole reaction processes, which may give a misleading prediction of the kinetics and underestimate the risk level of a given reaction.

Subscripts

5. CONCLUSION In this paper, two kinetic models, the autocatalytic kinetic model and second order kinetic model, are applied to fit the experiment profiles performed under isoperibolic conditions. Kinetic and thermodynamic parameters were also determined. The results demonstrate the existence of the autocatalytic behavior of the esterification by comparing the experimental results with the calculated results. With this case study of the esterification of acetic anhydride with methanol, we experimentally show that it is vital to

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A,B,C,D = reactants j = jacket d = dosing 0 = initial s = stirrer f = final mix = mixing exp = experimental sim = simulated

REFERENCES

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Identification of the Kinetic Parameters and Autocatalytic Behavior in

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