Runaway reaction for the esterification of acetic anhydride with

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Runaway reaction for the esterification of Acetic anhydride with Methanol catalyzed by Sulfuric acid Chiara Vianello, Ernesto Salzano, Alessio Broccanello, Alessandro Manzardo, and Giuseppe Maschio Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05160 • Publication Date (Web): 01 Mar 2018 Downloaded from http://pubs.acs.org on March 3, 2018

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Industrial & Engineering Chemistry Research

Runaway reaction for the esterification of acetic anhydride with methanol catalyzed by sulfuric acid

Chiara Vianello*a, Ernesto Salzanob, Alessio Broccanelloa, Alessandro Manzardoc, Giuseppe Maschioa a

Dipartimento di Ingegneria Industriale, University of Padova, Via F. Marzolo 9, 35131 Padova (IT) Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Alma Mater Studiorum Università di Bologna, Via Terracini 28, 40131 Bologna (IT). c CESQA (Quality and Environmental Research Centre), Department of Industrial Engineering, University of Padova, Via F. Marzolo 9, 35131 Padova (IT) b

*[email protected]

Abstract This work is devoted to the prevention of runaway reactions for the esterification of acetic anhydride with methanol in the presence of sulfuric acid. To this aim, a kinetic model has been developed and validated through the comparison with experimental data obtained by means of a batch reaction calorimeter operating in isoperibolic conditions. The model, which shows a good agreement with experimental data, has been then adopted for the prediction of the thermal runaway, which may lead to thermal explosion, through the definition of runaway criteria in a batch reactor and through the definition of stability diagram for the reactive system.

1

Introduction

The uncontrolled self-heating in chemical reactors can generate the occurrence of a runaway reaction, which may lead to an increase of temperature and the consequent acceleration in rate. This phenomenon is called thermal explosion and implies the possibility of the occurrence of side decomposition reactions with the formation of volatile substances and a substantial increase of the pressure into the process reactor 1. The most common causes of runaway reactions during the initial 1 ACS Paragon Plus Environment

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phases of the process are an incorrect kinetic evaluation, an excessive feed rate of the reagents, the presence of impurities in the reactor, an inadequate mixing of chemicals (leading to the so called hot spots) or the failure of the cooling and/or the stirring system. Human error is among of the major causes of this kind of events 2. However, it is well known that many industrial incidents are caused by runaway reactions 3: developing a theory that is able to predict their occurrence is thus fundamental in order to introduce adequate measures to prevent them 4. Several mathematical models can be adopted to predict the occurrence of runaway events

4–11

. These

models have addressed the design of appropriate Early Warning Detection Systems (EWDS). An EWDS based on the divergence theory developed by Zaldívar and Strozzi7, has been extensively applied at several reacting systems characterized by a high exothermicity during the course of the EC AWARD project 12. Another useful tool when the hazard of runaway reaction in process chemistry is relevant is based on the concept of the Boundary Diagram Safety Criterion (BDSC)

5,6,10,13,14

. Given a reaction system, the

BDSC allows the identification of runaway and inherently safe regions, thus avoiding hazardous operating conditions. In this work, several criteria for prediction of the onset of runaway and Boundary Diagram Safety Criterion have been applied to the experimental and simulated data related to the esterification of acetic anhydride with methanol catalyzed by sulfuric acid. In the chemical industry, the reactivity of the acetyl group of acetic anhydride is used to synthesize end products and intermediates. The products of esterification are methyl acetate and acetic acid. Methyl acetate has important use in industries for various purposes such as solvent in the synthesis of coating materials, cellulose based materials, plasticizers, lacquers, ink resins and many other products15,16. Acetic acid is important raw material for the synthesis of pharmaceuticals, dyes, pesticides and other organic chemicals.

2

Criteria for runaway detection

Several criteria for the prediction of the onset of runaway phenomena have been published in the last 50 years. They can be classified as geometry- or sensitivity- based methodology. In the first method, the thermal explosion is described according to the geometrical features of the system variable such as dimensionless temperature or heat release rate. The Semenov criterion17 belong to this category and it is

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based on the hypothesis of negligible reactant consumption. This represents a limit in its applicability, even if this criterion is still a good approximation for a number of real systems, in particular for thermal runaway occurring at the very early stages of the process when the conversion and reactant consumption are nearly zero. In fact, when the consumption of the reagents has to be taken into account, Semenov criterion becomes over-conservative 4. Alternative geometrical-based approaches have been proposed by different authors, still basing their criteria on the geometric features of the temperature profile (vs conversion χ or vs time t). Among others, the criterion by Bowes and Thomas 1,18

states that runaway occurs when, in the dimensionless temperature (θ) vs dimensionless time (τ)

plane, the second order derivative becomes positive before the temperature absolute maximum, i.e.:

(1)

= 0 and = 0

where the two parameters τ and θ are dimensionless parameters representing respectively the time and the temperature as in the following correlation: τ = ∙ ( ) θ=

(2) (3)

∙γ

where t is the time, k(T) is the reaction rate constant, is the initial temperature of the reaction mixture, and γ is the Arrhenius number: γ=

(4)

∙

where "#$ %&# %'( is the activation energy and R is the ideal gas constant.

The criteria discussed above are classified as geometry based criteria and they can be applied only to systems where a temperature profile exists or is modeled 19. They are not able to provide indications on the intensity of the runaway, thus limiting the effectiveness of an eventual action taken to prevent a major incident caused by a thermal explosion in a practical application. For these reasons, a different set of criteria have been developed, based on the concept of parametric sensitivity. These methods take advantage of the fact that, near the boundary between the runaway and non-runaway behavior, the system becomes very sensitive, i.e., its behavior changes dramatically even if the initial values of the



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system parameters are subject to very small perturbations: identifying this parametrically sensitive region thus allows to define the critical conditions for thermal runaway. Among these, the Hub and Jones (HJ)20 and the Strozzi and Zaldívar (SZ)7–9 criteria can be applied online and so they do not need a model for the reaction. More in details, Hub and Jones 20 criterion states that runaway occurs when the first and the second derivatives of reactor temperature are simultaneously positive, i.e.:

)

> 0 and

)

(5)

> 0

As the reactor temperature is increasing, runaway occurs if the second part of Eqn. (5) is true and the boundary between stable and runaway behavior is represented by the temperature vs. time trajectory where the maximum value of (d2T/dt2) is zero while the reactor temperature is increasing. A different generalized criterion for the detection of the runaway boundary able to operate with multiple reactions is the divergence criterion by Strozzi and Zaldívar

4,21

, which is based on the chaos

theory 7. Applying this approach, a mathematical model is not required for the process, thus making this criterion suitable for on-line application in the detection of runaway reactions. For a chemical reaction occurring in a batch reactor, when →∞, the trajectory of the system in the phase space tends to a specific point (for example, that at which the temperature of the reactor is equal to the ambient/jacket temperature and the reactant conversion is complete). In other words, the trajectory of two points that, at the beginning of the reaction, are close to each other in the phase space, must finish at the same final point when the reaction is complete. However, the orbits of the two points can diverge along the path towards the final state and so, if the system parameters are near the runaway boundary, a small initial position change results in a large change in the phase space trajectories. Evaluating the divergence of the system of ordinary differential equations that describes a chemical process (mass and energy balances), thus allows to individuate the critical condition for thermal runaway. In particular, if at a certain point of the temperature vs time trajectory, a local positive divergence appears, the process operates in runaway conditions. In the approach by Strozzi and Zaldívar, the Lyapunov exponents are used to define sensitivity and the phase space volume elements are expressed in terms of temperature differences 7. This method has been validated experimentally by different studies that demonstrated its reliability for batch, semi-batch and continuous reactors operating in both isothermal (i.e. at constant temperature of the reactor) and isoperibolic (i.e. at constant environment/jacket temperature) conditions 4 ACS Paragon Plus Environment

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and with different types of reactions (chain reactions, equilibrium, parallel and competing reactions) 8,22–24

.

The criterion by Morbidelli and Varma

4,25–27

is focused on the recognition of the parametrically

sensitive region of the system. Its aim is to mark the boundary for thermal explosion by using the normalized function sensitivity Snorm (Eq. 6) for the any characteristic parameter Φi of the system, in which I is the objective function.

+,-./ =

Φ 0

∙

1θ∗ 1Φ

=

1 45 θ∗

(6)

1 45 Φ

The method considers the maximum dimensionless temperature θ∗ as objective function and is based on the fact that, close to the boundary for thermal runaway, the normalized sensitivity of the temperature reaches its maximum value. The condition of maximum sensitivity is thus considered the critical condition for thermal runaway. Only when the normalized objective function sensitivity maximum is sharp and essentially independent on the parameter choice, a potentially explosive system is occurring. Another criterion is proposed by Steensma and Westerterp

28–30

and it is based to developed safety

diagrams for heterogeneous liquid–liquid semibatch reactions. The coordinates as used in this diagram are dimensionless groups called the reactivity number (Ry) and the exothermicity number (Ex)

10,11,14

,

expressed by the following expression: 1

(7)

1 1 ∙ 2 :'

(8)

67 = ∙ 8'+ ∙ :' "

"; = ∆#8 ∙ 6 ∙

where Co called cooling number and it is define as :' =

>? @AB C

∙ D-E

(9)

The diagram indicates the boundaries between the various types of thermal behavior that will be based on the dimensionless parameters.



3

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Methodology

In this work, the application of several criteria for the prediction of the thermal runaway to the acid catalyzed esterification of acetic anhydride and methanol is presented. In particular, geometry-based criteria (Thomas and Bowes) and three sensitivity-based ones (Hub and Jones, Morbidelli and Varma, Strozzi and Zaldìvar) are compared between each other. The Thomas and Bowes criterion and the Morbidelli and Varma one require a model for the system, in order to be applied. The section 3.1 describes the development of kinetic model of reaction studied. Also, the sensitivity based criteria of Hub and Jones (HJ), Strozzi and Zaldívar (SZ) and Morbidelli and Varma (MV) have been considered31. Finally, the Boundary Diagram Safety (BDSC) for the batch reactor examined has been development. The detailed procedure to derive the reactivity number (Ry) and the exothermicity number (Ex) for batch case is shown in Appendix I.

3.1 Kinetic model The stoichiometric scheme of esterification of acetic anhydride (Ac2O, ≥99%, Sigma-Aldrich) and methanol (MeOH, 99.8%, Sigma-Aldrich, ), catalyzed by sulfuric acid (H2SO4, 98%, Sigma Aldrich) in batch reactor is shown in Eq. (10): M ?NO

(CGH :I)J O + CGH IG PQQR CGH COOCGH + CGH COOH

(10)

In order to obtain a physically consistent model for the esterification reaction, a modified Arrhenius expression has been chosen to describe the kinetics and the effect of the catalyst concentration has been taken into account considering a linear dependence of the kinetic constant value = k1 ∙ UJ ∙ VGJ WIX Y ∙ Z UH/

31,32

, as in Eq. (11): (11)

where k1, k2 and k3 are the parameters of the equation. The model has been tested with experiments carried out using a jacketed, stirred glass calorimeter, in batch isoperibolic conditions as described in previous work of the same research group in isoperibolic conditions24. The experiments have been performed with a large excess of MeOH and so a pseudo-first order kinetics with respect to Ac2O have been assumed. The contribution of the non-catalyzed reactions with 6 ACS Paragon Plus Environment

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respect to the catalyzed one has been evaluated in the work by Casson et al.24, observing that the first contribution can be neglected with respect to the second one. The esterification reaction of acetic acid with methanol has been here neglected because it is rather slow in the condition considered

33–35

.

Therefore, in this paper, only the catalyzed reaction has been taken into account in the derivation of the kinetics expression. In each test, 0.8 mol of acetic anhydride and 7.0 mol of methanol are used: the excess of methanol justifies the assumption of a pseudo-first order kinetics for the reaction. The acetic anhydride is added thereafter to methanol with a dose time of 10 sec. The start of the reaction is considered when the temperature is equal to the jacket temperature. Through several calibrations, the values of the parameters

have been calculated: \ is 22.1, the average value of product of global heat transfer coefficient and the heat transfer area (US) is 4.3 W/K and the average value of CP is 880 J/K. The mass and the isoperibolic energy balances has been integrated by using a fourth order Runge-Kutta method and using a MATLAB® script to perform a minimization of the squared errors between the model and the experimental data

31

. The experimental runs have been fitted simultaneously for temperature and

sulfuric acid concentration variations. The termination tolerance on the function value has been set to 1·10-8. These procedures has led to the following expression: = 164.68 ∙ a.bccX ∙ VGJ WIX Y ∙ Z cdHJ.e/

(12)

where VG2WI4Y is the sulfuric acid concentration expressed in mol/m3 and the temperature is expressed in Kelvin. The comparison between the model predictions and the experimental data is represented in the following figures (Figure 1, 2).



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Figure 1 Comparison between model predictions and experimental data for the experiments carried out using an approximately constant jacket temperature of 278.45 K and different sulfuric acid concentrations, i.e. 16 mol/m3 for test (A), 29 mol/m3 for test (B), 45 mol/m3 for test (C), 52 mol/m3 for test (D), 81 mol/m3 for test (E) and 100 mol/m3 for test (F). The solid lines are referred to the experimental data, while the dashed lines are the model predictions.


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Figure 2 Comparison between model predictions and experimental data for the experiments carried out using a sulfuric acid concentration of 30 mol/m3 and different jacket temperatures, i.e. 270.9 K for curve (1), 273.45 K for curve (2), 278.31 K for curve (3), 280.77 K for curve (4), 283.22 K for curve (5), 285.63 K for curve (6), 288.09 K for curve (7) and 293.02 K for curve (8). The solid lines are referred to the experimental data, while the dashed lines are the model predictions.

In Figure 1, as the concentration of H2SO4 is increased, there is a notable difference between curve (A), which shows a stable behavior, and curve (E and F), which present a shape characteristic of thermal runaway. Curve (A) has a concave shape with respect to the time axis, while a significant part of curve 9 ACS Paragon Plus Environment


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(F) is convex with respect to this axis. Curves (B), (C) and (D) are intermediate between these extremes and the critical concentration of H2SO4, marking the boundary between stable and runaway behavior would be expected to occur in this region. In Figure 2, as the jacket temperature is increased, Curve (1) shows stable behavior and curve (8) shows the thermal runaway behavior.

The figures show the formation of a temperature peak,

characteristic of the runaway, in the temperature range of 280.15-283.15 K.

4.

Results and discussion

Table 1 shows the results of the application of the HJ and SZ criteria to the experimental and model data of Figure 1, while Table 2 to the data of Figure 2. A third-order Golay-Savitzky filter has been used to smooth the temperature data for the application of HJ criteria. In both cases, the agreement between the experimental and model results may be considered satisfactory.


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Table 1. Application of the HJ and SZ criteria for thermal runaway to the data of Figure 2. Test

H2SO4 concentration [mol/m3]

A B C D E F

16 29 45 52 81 100

HJ 10c ∙Max (d2T/dt2) [K/s2] Exp. Mod. -3.6 -3.87 -3.57 -5.87 13.51 12.96 28.78 30.44 230 213.0 360 458.7

SZ 10X ∙Max (8f) Exp. Mod. -2.6 -2.3 -2.6 -4.1 16.6 17.0 40.4 49.3 885 798 1822 2582

Table 2. Application of the HJ and SZ criteria for thermal runaway to the data of Figure 3. Test

1 2 3 4 5 6 7 8

Jacket Temperature [K] 270.9 273.45 278.31 280.77 283.22 285.63 288.09 293.02

HJ 10 ∙Max (d2T/dt2) [K/s2] Exp. Mod. -5.05 -4.88 -4.88 -7.13 -2.52 -4.26 14.39 1.83 18.26 15.44 59.31 39.14 120.0 84.4 480.0 310.0 c

X

10 Exp. -2.4 -3.3 -3.0 15.3 21.9 119 334 2887

SZ ∙Max (8f) Mod. -1.6 -2.4 -2.8 2.9 18.7 70 215 1456

The HJ and SZ criteria indicate that the critical sulfuric acid concentration should be around 40 mol/m3, while the critical jacket temperature should be 278-280 K. The transformations → h and → i are linear and the BT criterion would therefore be expected to give results similar to the HJ criterion. The maximum values of (d2 h /d i 2) for the profiles obtained at different sulfuric acid concentration are given in Table 3, while the maximum values of (d2 h /d i 2) for the ones obtained at different jacket temperature are given in Table 4.



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Table 3. Application of the BT criterion to the data obtained at different sulfuric acid concentration. Test A B C D E F G

H2SO4 concentration [mol/m3] 16 29 45 52 81 100 100

Exp. -17.3 -5.04 7.36 12.26 39.73 38.97 38.97

Max (d2θ/dτ2) [-] Mod. -17.7 -8.63 7.03 13.21 36.43 49.25 49.25

Table 4. Application of the BT criterion to the data obtained at different jacket temperature. Test 1 2 3 4 5 6 7 8

Jacket Temperature [K] 270.9 273.45 278.31 280.77 283.22 285.63 288.09 293.02

Exp. -11.29 -7.58 -1.71 6.49 4.88 11.65 16.31 26.75

Max (d2θ/dτ2) [-] Mod. -10.91 -10.97 -2.90 0.78 4.27 7.80 11.57 17.03

The MV criterion has been applied to both the experimental and the model data, calculating both the local and the normalized sensitivities with respect to the jacket temperature and to the sulfuric acid concentration. Figures 3 and 4 represent the local and normalized sensitivities profiles related to the experimental data and model results obtained at different jacket temperature and at different sulfuric acid concentrations, respectively.


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Figure 3. Local sensitivity (Left) and Normalized sensitivity (Right) of the experimental data (□) and models results (○) of the maximum temperature with respect to the jacket temperature.

Figure 4. Local sensitivity (Left) and Normalized sensitivity (Right) of the experimental data (□) and models results (○) of the maximum temperature with respect to the sulfuric acid concentration.

The normalized sensitivity is always positive: that means that the maximum temperature increases either if the jacket temperature increases or the sulfuric acid concentration increases. According to the MV criterion, the thermal runaway occurs when the normalized sensitivity is at its maximum. Therefore, in this case, the method states that the boundary between stable and unstable behavior of the system is around a jacket temperature of 282-284 K and the model can provide a good prediction of the experimental results. On the contrary, the experimental boundary between stable and unstable behavior of the system is around a sulfuric acid concentration of 55 mol/m3 and the modeled boundary is around concentration of 45 mol/m3. This discrepancy could be addressed to the limits of the Morbidelli and Varma criterion for reactions characterized by a low Arrhenius number 4. 13 ACS Paragon Plus Environment


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Based on equations 11 and 12, the boundary safety diagrams for the esterification of Ac2O with MeOH and 30 mol/m3 of H2SO4 is shows in Figure 5. The calculated Cooling number is 0.0489.

Figure 5. Safety Boundary Diagram for a batch reactor (Co = 0.0489). The SBD for a batch reactor identified two regions: no ignition region (below the marginal ignition conditions – black line) and the runaway region below the black line. In this case, the behavior of the reaction in a semi-batch reactor should be evaluated. Indeed, these reactors allow the slow addition of reagents to control the release of heat and thus the temperature in the reactor. Table 5 shows the warning data in which one passes from a stable reaction to a runaway reaction identified by the criteria applied to this study. Table 5 Summary of Warning data Runaway Criteria Parameter Variation

Warning value 3

HJ, SZ, BT MV

H2SO4 concentration [mol/m ]

29 - 45

Jacket Temperature [K]

278 - 280

H2SO4 concentration [mol/m3]

45 - 55

Jacket Temperature [K]

282 - 284


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4


Conclusions

In this paper, geometric and sensitivity based criteria have been used and compared to study the boundaries of runaway behavior for the acid catalyzed esterification of acetic anhydride with methanol. Because of the modest reaction enthalpy and low activation energy, the data provide a severe test to the runaway criteria with respect to highly reactive systems. The runaway criteria were applied to both experimental and model data, in order to compare the obtained results. The model appeared to be in good accord with the experimental data, showing that the boundary between stable and unstable zone, in the considered conditions, appears to be around a sulfuric acid concentration of 40 mol/m3 and a jacket temperature of 278 – 280 K. The HJ and SZ on-line criteria account reasonably well for the thermal runaway in the considered reaction. The BT and HJ criteria are shown to be closely related and the BT criterion also performs reasonably well. The MV criterion is shown to work well with respect to the jacket temperature, whereas the results obtained for the sulfuric acid concentration shows poor performance. That can be possibly addressed to the low Arrhenius number in the considered reaction system. Concerning the considered system, it has been shown that basically every runaway criteria applied in this work is able to detect the boundary between stable and unstable behavior and that the construction of a model of the system is the major problem in the correct application of many of these methods, often leading to huge errors (especially close to the boundary between the stable and the unstable zones). Besides of that, the need of a model implies a knowledge of the process and a calculation speed that is usually not available in real industrial systems. Therefore, runaway criteria that do not require models (such as the Hub and Jones and the Strozzi and Zaldívar criteria) are the most suitable for the application in real industrial systems subject to a possible runaway.

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Page 20 of 22

Appendix I

Based on the mathematical modeling proposed by the references

10,14

, mass and energy balanced (Eqs

A1; A2) can be written as follows: j ) )

(A1)

= k# ∙ l ∙ m = ∆nD ∙

j )

−

>∙?∙( ) p@∙C∙AB q

∙ D-E

(A2) where Da is Damköhler number, l is the dimensionless reaction rate constant and f is function dependents on the kinetic regime. (A3)

k# = ∙ D-E l=

r

(A4)

rs

(A5)

m = (1 − t) Where 6 is kinetic rate constant at the reference temperature (TR) Based on Eq. A2) the enthalpic contribution is: u6 = ∆#8 ∙

dt = ∆#8 ∙ k# ∙ l ∙ m d

The power removed by the cooling system is u$''v =

w ∙ W ∙ ( − # ) ∙ 8'+ px ∙ f ∙ $y q

The derivatives of Eqs A6; A7 are computed as: 8u6 " 1 = ∆#8 ∙ k# ∙ l ∙ m ∙ ∙ 2 8 6 8u$''v w∙W = ∙ 8'+ 8 px ∙ f ∙ $y q 20 ACS Paragon Plus Environment

Page 21 of 22 1 2 3 4 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 52 53 54 55 56 57 58 59 60


The reactivity factor FR, exothermicity factor FT and cooling factor Fcool are: z6 = k# ∙ l = ∙ 8'+ z = ∆#8 ∙

" 1 ∙ 6 2

w∙W

z$''v = px∙f∙$ q ∙ 8'+ = Co y

The reactivity Ry and exothermicity Ex are then expressed by the following expressions: 67 =

z6 1 = ∙ 8'+ ∙ z$''v :'

"; =

z " 1 1 = ∆#8 ∙ ∙ 2 ∙ 6 :' z$''v



Page 22 of 22


Runaway reaction for the esterification of acetic anhydride with

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