Safety Aspects in Batch Reactors for Styrene Suspension Polymerization

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Ind. Eng. Chem. Res. 2007, 46, 5898-5906

Safety Aspects in Batch Reactors for Styrene Suspension Polymerization Robert Cherban´ ski,* Aleksandra Milewska, and Eugeniusz Molga Department of Chemical and Process Engineering, Warsaw UniVersity of Technology, ul. Waryn´ skiego 1, 00-645 Warszawa, Poland

This study deals with safety aspects of batch reactors for styrene suspension polymerization. Polymerization is known to be the most frequent cause of thermal runaway incidents in the industrial chemical processes. Two sorts of safety problems have been studied in this work. The first one is related to an influence of process parameters on the thermal behavior of the well-mixed polymerization reactor. With regard to this part of the work the modeling results have been presented in a form of the maximum reaction temperature maps, which allow for choosing the safe process conditions. The second one is related to a stirrer malfunction in the suspension polymerization reactor. As the computational fluid dynamics (CFD) simulations have shown, thermal runaway starts when the mixing problems occur even if an emergency cooling is applied. 1. Introduction From the safety point of view polymerization is known to be the most frequent cause of thermal runaway incidents in the industrial chemical processes.1,2 The causes lie in an increasing viscosity of the reacting mixture within the reaction progress by many orders of magnitude and because polymerization is an exothermic reaction with a significant heat effect (heat of reaction 60 (kJ/mol)). It is also important from this point of view that due to significant market demands the industrial production of polystyrene in suspension is on a mass scale.3 Hence, the authors of this study want to contribute to the problem of safety of the batch styrene suspension polymerization reactors by considering some practical aspects of the safe operation in these reactors. In a previous study4 a hazard characterization of the bulk and suspension methods of styrene polymerization by the microcalorimetric techniques has been studied. Additionally, the researches have calculated the reaction temperature-time profiles for one set of the employed commercial data (UA, TR,0, mM, cBPO) and different jacket temperatures for a typical commercial suspension polymerization reactor having a batch size of 4000 kg. For the considered case, because of a very efficient mixing a lack of heat transfer resistances between the phases has been assumed. Hungenberg et al.5 have compared some thermodynamic models to calculate the runaway pressure in a batch suspension polymerization reactor. They have considered two situations in which a stirrer failure happened, mainly: (A) complete phase separation and complete immiscibility of aqueous and organic phases and, additionally, (B, C) an inclusion of traces of water into the organic phase. In the recent paper, Jang at al.6 have simulated thermal behavior of styrene suspension polymerization in an ideally mixed batch reactor showing influence of some process parameters. In the current work we are focused mostly on two safety aspects which can lead to thermal runaway in the batch suspension polymerization reactors. The first one is related to a wrong combination of the process parameters while agitating of the suspension is very effective. The second one is related to a stirrer failure when the two phases (aqueous and organic) * To whom correspondence should be addressed. Tel.: +48-22-2346375. Fax: +48-22-825-1440. E-mail: [email protected].

are separated completely and problems in withdrawal of the heat generated due to the progress of the polymerization reaction arise. The solutions of the two mentioned practical problems have been proposed twofold, as (a) the maximum reaction temperature maps, showing an influence of the process parameters on the temperature in the reactor, and (b) a computational fluid dynamics (CFD) model of the reactor, which gives a predicted temperature field in the reactor, respectively. 2. Theoretical Details 2.1. Reaction Mechanism and Kinetic Equations. Styrene polymerization is described by the following classical and wellknown free radical mechanism:7

(1) Initiation: kd

I 98 2R

(1) ki

R + M 98 P1

(2)

(2) Propagation: kp

Px + M 98 Px+1

(3)

(3) Termination: (a) disproportionation ktd Px + Py 98 Dx + Dy

(4)

(b) recombination ktc

Px + Py 98 Dx+y

(5)

(4) Chain transfer: (a) to monomer kfm

Px + M 98 Dx + P1

(6)

(b) to polymer kfp

Px + Dy 98 Py + Dx

(7)

According to this mechanism and assuming the quasi-steadystate approximation for the radicals, the following balances of species can be written:

10.1021/ie070219n CCC: $37.00 © 2007 American Chemical Society Published on Web 08/01/2007

Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007 5899

(8)

1 d([R]V) ) 2fkd[I] - ki[M][R] ) 0 V dt

(9)

1 d([M]V) ) -ki[R][M] - (kp + kfm)[M][Px] V dt

(10)

1 d([Px]V) V

∞

1 d([I]V) ) -kd[I] V dt

dt

{

∞

) ki[R][M] +kfm[M]

∑[Py] y)1

}

δx,1 + kp([Px-1] -

∑

[Py] -

∞

∞

∑y[Dy] - (ktd + ktc)[Px]y)1 ∑[Py]

(11)

y)1

1 d([Dx]V) V

dt

xk[Dx] ∑ x)1

(19)

[M0] dζM 1 + ζM dt

(20)

where dζM/dt is derived from eq 16 after its differentiation. Then its final form can be shown as below, after introducing eqs 10 and 18:

dζM ) (kp + kfm)(1 - ζM)λ0 dt

∞

) kfm[Px][M] - kfpx[Dx]

(18)

Taking into account the volume variation in the reacting (styrene/polystyrene) phase, the rate of polymerization is defined as follows:

rp )

y)1

∑xk[Px] x)1 ∞

µk )

∞

[Px])[M] - kfm[Px][M] + kfpx[Dx] kfp[Px]

λk )

∑[Py] + y)1

(21)

1 x-1 [Py] + ktc [Py][Px-y] (12) 2 y)1 y)1

A general form of the zeroth living moment is obtained after the product differentiation as shown below:

Because densities of styrene and polystyrene differ significantly, the volume contraction factor, , defined as

(22)

∞

kfp[Px]

∑

∞

y[Dy] + ktd[Px]

y)1

∑

∑

) (FM - FP)/FP

(13)

has been introduced. Therefore, an actual volume of a styrene/polystyrene phase is defined as follows:

(14)

Hence, the rate of the volume change is given by

dζM dV V dζM ) V0 ) dt dt 1 + ζM dt

(15)

The monomer conversion can be defined by the following equation:

[M0]V0 - [M]V [M0]V0

)1-

[M]V [M0]V0

(16)

After substituting eq 14 into eq 16 one can obtain the following relationship for the monomer conversion:

1ζM )

[M] [M0]

[M] 1+ [M0]

After introduction of eq 15 into eq 22, the zeroth living moment can be further presented as

dζM dλ0 1 d(λ0V) ) - λ0 dt V dt 1 + ζM dt

(23)

Then, using eq 21 the zeroth living moment is derived:

V ) V0(1 + ζM)

ζM )

dλ0 1 d(λ0V) λ0 dV ) dt V dt V dt

1 - ζM 2 dλ0 1 d(λ0V) λ ) - (kp + kfm) dt V dt 1 + ζM 0 where the term

1 d(λ0V) ) 2fkd[I] - (ktd + ktc)λ02 V dt

To reduce the number of differential equations, eqs 8-12 (as the degree of polymerization is high and, thus, x is large), the method of moments is applied (generating function approach).8 The method is widespread in polymer kinetics and it is used because the moments have a clear physical meaning in the differential molecular weight distribution (MWD).8 The kth moments for the live polymers and for the dead polymers are defined, respectively:

(25)

has been obtained by applying the definition in eq 18 into eq 11 and rearranging. At high monomer conversions, termination of polymer chains becomes diffusion-controlled, which is referred to as the gel effect or the Trommsdorf effect, and therefore a correction of the termination rate constants is needed. The following correction term has been used in this work:

kt ) kt0 exp(-P2ζM - P3ζ2M - P4ζ3M) (17)

(24)

(26)

Finally, eq 25 can be rewritten as

1 d(λ0V) ) 2fkd[I] - ktλ20 V dt

(27)

For an initiator, one can obtain

(1 - ζM) d[I] 1 d([I]V) ) - (kp + kfm) λ [I] dt V dt 1 + ζM 0

(28)

where the term (1/V){d([I]V)/dt} has been shown already in eq 8.

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Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007 Table 1. Details of the Performed Experiments T ) constant

Figure 1. Schematic diagram of the experimental setup: RC1 Mettler Toledo reaction calorimeter. 1, reactor; 2, electronics and transducers; 3, basic unit; 4, personal computer; 5, cryostat.

vessel

run

TR (°C)

RC1 RC1 RC1 RC1 RC1 RC1 RC1 bottle

R1 R2 R3 R4 R5 R6 R7 B1

75 80 85 90 90 90

TJ (°C)

N (rpm)

xBPO

xPVA

ΦMO

85 90

800 800 800 800 800 800 800 0

0.0161 0.0161 0.0161 0.0161 0.0654 0.1215 0.0161 0.0161

0.00166 0.00166 0.00166 0.00166 0.00166 0.00166 0.00166 0

0.16 0.16 0.16 0.16 0.16 0.16 0.16 1

perpendicular to a boundary. The no-slip condition has been set at the reactor walls because all velocity components are equal to zero. For the impeller and shaft the rotational velocity is equal to ωr.

Energy balance: Fcp

∂TR + ∇(-λ∇TR) ) ∆HArP - Fcpu‚∇TR ∂t

(32)

Boundary conditions for the walls and the top head of the reactor are set as the heat flux condition

Q˙ wall ) UA(TR - TJ)

(33)

Figure 2. Basic dimensions of the glass reactor: H ) 0.15 m, D ) 0.115 m, di ) 0.06 m, dS ) 0.008 m, and h ) 0.015 m.

Q˙ top ) (UA)top(TR - T0)

(34)

Finally, the kinetic model is composed of four ordinary differential equations, eqs 20-22 and 28. 2.2. Reactor Model. Mass and heat balances for an ideally mixed batch styrene suspension polymerization reactor have been defined in eqs 29 and 30. Taking into account that the number of monomer molecules consumed in the propagation step (eq 3) is much higher than in the initiation step (eq 2) provided that the polymer chain is great, rp may be identified with the rate of polymerization.7

respectively. The interior boundary condition is set as the continuity condition, that is,

Mass balance: -

[M0] dζM d[M] ) rp ) dt 1 + ζM dt

(29)

Heat balance: dTR 1 [∆HArpV - UA(TR - TJ) ) dt (mRcpR + CpI) (UA)top(TR - T0)] (30) The CFD model (Comsol Multiphysics) of the reactor, the most used in this work, takes into account the following governing equations:

Momentum balance and continuity equation: F

∂u - ∇‚[-pI + µ(∇u + (∇u)T)] + F(u‚∇)u ) F ∂t ∇‚u ) 0

(31)

To simplify and shorten the numerical computations, constant densities of each component have been assumed. However, the reacting mixture inside the reactor changes its volume with the conversion according to eq 14. The slip boundary conditions have been set at the two interphases (liquid-liquid and liquidgas). The condition states that there are no velocity components

n(Q˙ aq - Q˙ org) ) 0

(35)

Species balance: ∂ci + ∇(-Di∇ci) ) ri - u‚∇ci ∂t

(36)

Because of the complete phase separation and complete immiscibility of aqueous and organic phases, the boundary condition is set as the insulation condition at the liquid-liquid interphase. Also the walls impenetrable for mass flux are assumed. With regard to the physical and kinetic parameters the reader is referred to the appendix. 3. Experimental Section The main part of the experimental work has been carried out in an RC1 Mettler Toledo reaction calorimeter, whereas one experimental run has been carried out in a glass bottle having a capacity of 100 mL and equipped with five thermocouples for a multipoint temperature measurement. A simplified diagram of the RC1 setup is shown in Figure 1. The jacketed glass reactor (AP01) (1), having a maximal volume of 2 dm3, is equipped with four baffles, a downward propeller stirrer, a thermometer, and a calibration heater. The electronics with transducers (2) are necessary for processing signals from the sensors. The basic unit (3) is an inseparable part of the apparatus with its valves and pumps as well as heating and cooling liquid tanks. The personal computer (4) is necessary to control the progress of the reaction and to collect experimental data. The cryostat (5) is an essential apparatus for heat withdrawal from the reacting mixture. The basic dimensions of the RC1 glass vessel are presented in Figure 2.


Figure 3. Determination of the kinetic model parameters. A comparison of the model predicted and experimental (R1-R6) profiles of the monomer concentration. r2 ) square of Pearson’s correlation coefficient. Standard deviations are shown as error bars.

The working principle of the RC1 reaction calorimeter is based on simultaneously solving the appropriate heat and mass balances. These balances are presented in a general form as follows:

ζM )

Mass balance: mR ) m 0 +

∑i mD,i

(37)

Heat balance: Q˙ R + Q˙ C + Q˙ M ) Q˙ A + Q˙ F + Q˙ D + Q˙ L

(38)

∫0t Q˙ R dt k

(39)

Because the total heat produced due to the radical polymerization is caused mainly by the propagation step which, in turn,

∫0tQ˙ R dt QT

(40)

Then, the monomer concentration can be obtained using the following equation:

[M] )

Calculation of an accurate value of the power produced due to the reaction progress, Q˙ R, is the key practical problem to be solved. In the apparatus the problem has been worked out by the exact temperature measurements, a frequent data acquisition, and the efficient calibration procedures providing the overall heat transfer coefficient and the specific heat capacity of the reacting mixture. An integration of Q˙ R with respect to time gives the total heat produced due to the reaction process, QT, according to the equation below:

QT )

is identified with the polymerization rate (see section 2.2), the monomer conversion can be calculated as

[M0] (1 - ζM) 1 + ζM

(41)

All performed experiments are detailed in Table 1. They all have been carried out in the batch operating mode but some of them have been conducted at the isothermal and the rest at the isoperibolic conditions (i.e., at a constant jacket temperature). Styrene (g99%, ReagentPlus, Sigma-Aldrich) was used as a monomer source, benzoyl peroxide (Argon, Ło´dz´) was used as an initiator, and poly(vinyl alcohol) (98-99% hydrolyzed, molecular weight ) 31 000-50 000, Sigma-Aldrich) was used as a suspension stabilizer. A 10% aqueous solution of sodium hydroxide made by dissolving anhydrous pellets (g98%, reagent grade, Sigma-Aldrich) in distilled water was used for purification of the supplied styrene from an inhibitor (4-tert-butylcatechol). The purification of styrene was conducted by twice rinsing with 10% sodium hydroxide aqueous solution followed by twice rinsing with distilled water.

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Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007

Figure 4. Testing of the kinetic model. A comparison of the model predicted and experimental (R7) profiles of the monomer concentration and the reaction temperature.

Figure 5. Maximum reaction temperature reached in the course of the suspension polymerization in the ideally mixed reactor as a function of TJ and UA. Initial volume fraction of styrene Φ ) 0.1.


For the runs R1-R7 the glass reactor (RC1) was initially filled with distilled water containing the appropriate quantity of poly(vinyl alcohol) (see Table 1). Then, the purified styrene containing dissolved initiator was introduced into the already thermostated reactor. The mixture was mixed vigorously, and the baffles, with which the reactor was equipped, prevented formation of a vortex. For the run B1 the isoperibolic conditions were maintained by immersion of a bottle into a thermostatic bath. This experiment was carried out as the bulk polymerization, that is, without any water addition as well as without stirring of the reaction mixture. The batch polymerization reactions performed in RC1 (R1R7) have been carried out as long as the power generated as a result of the reaction progress, Q˙ R, was measurable in the apparatus (approximately 1 W). Regarding the run B1, for safety reasons, the polymerization reaction was stopped when styrene started to boil.

4. Results and Discussion 4.1. Parameters of the Kinetic Model. All batch isothermal experimental runs, that is, R1-R6, have been utilized for determination of the kinetic model parameters. The parameters have been calculated by minimization of a goal function. The minimization was based on a comparison of the model predicted and experimental profiles of the monomer concentration (Figure 3). The sum of the squared residuals has been used as the goal function. For the runs R1-R4 a quite good fitting accuracy can be observed in the diagrams of Figure 3. Only for the runs R5 and R6 are pronounced discrepancies noticed. The estimated parameters of the kinetic model are P1 ) f ) 0.172, P2 ) 1.69, P3 ) 2.71, and P4 ) 0.679. The isoperibolic experimental run, R7, has been employed for testing of the kinetic model. The result of the verification has been presented in Figure 4. A very good predicting accuracy is observed for the concentration profile, while for



Figure 10. Reaction temperature field in the reactor after 990 s from the stirrer failure. TR,0 ) 348.15 K, TJ ) constant ) 348.15 K, R ) 5 (rpm), Φ ) 0.16, and xNB ) 0.0161. Streamlines represent velocity field.

Figure 8. Multipoint temperature readings during the bulk styrene polymerization experiment and the average temperature in the styrene/ polystyrene phase predicted with the CFD model.

Figure 11. Average and maximum temperatures rises in the styrene phase after the stirrer malfunction (R ) 5 rpm). Points, calculated; lines, approximations of the calculated data.

Figure 9. Comparison of the average temperature in the styrene/polystyrene phase predicted with 3D geometry of the reactor (Fluent) and its 2D representation (Comsol Multiphisics).

the temperature profile a significant discrepancy is observed. However, a character of the experimental profile is well predicted, and the differences between the model results and experimental temperatures are quite low. 4.2. Maps of the Maximum Reactor Temperature. Using the reactor mass and heat balances (eqs 29 and 30), maps of

Figure 12. Average and maximum temperatures rises in the styrene phase during the stirrer malfunction (R ) 5 rpm) and emergency cooling (TJ ) 303 K). Points, calculated; lines, approximations of the calculated data.

the maximum temperature in the ideally mixed suspension polymerization reactor have been estimated. The maximum reaction temperatures have been shown as a function of the jacket temperature, TJ, and the product of an overall heat transfer coefficient and heat exchange surface area, UA. The plots in Figures 5-7 have been prepared for different initial volume fractions of styrene.

5904


Figure 13. Maximum temperature rises in the polymerization reactor as a consequence of a stirrer malfunction for different styrene conversions. Initial reaction temperature T0 ) 363 K.


It follows from Figures 6 and 7 that the blank area on the right from the curves represents a danger zone of the operating conditions in which boiling of water starts as the maximum reaction temperature reaches 100 °C. Thus, the maps calculated using the reactor model give the possibility for prediction of the safe process conditions. The maps have been presented at one selected initiator concentration in this paper (xBPO ) 0.0161). 4.3. CFD Modeling. As mentioned in the Experimental Section one bulk polymerization run has been carried out in a bottle without mixing and water addition. Five thermocouples have screened temperature in the bottle during this experiment. A record of the multipoint temperature measurement as well as a mean temperature calculated from the thermocouple signals has been shown in Figure 8. Besides the experimental temperature reading, a profile of an average temperature computed using the CFD Comsol



package (Comsol Multiphysics) has been plotted in this figure. The assumed definition of the average temperature has been given by

〈T〉 )

∫T dVS ∫ dVS

(42)

Good prediction of the experimental results can be observed, especially in the region where a steep temperature rise appears (approximately at 700 s). Because the runaway behavior of the bulk polymerization reactor under applied conditions has been validated with the CFD model, a more complex case has been examined further.


The following scenario, closely related to safety of a batch styrene suspension polymerization reactor, has been considered. Let us consider that because of a stirrer failure or an operator mistake the stirrer revolutions are so slow that the two (organic and aqueous) phases are being completely separated. As a result the aqueous phase settles at the bottom part of the reactor, whereas the organic phase settles in the upper one. With regard to the model assumptions a constant interfacial surface area has been defined and solubility of styrene in water has been neglected. The former assumption is a very good approximation for the system if the mixer speed is very slow. The latter assumption is commonly used in the styrene suspension polymerization. In comparison to the utilized CFD model of a batch bulk styrene polymerization reactor, the current CFD model of a batch styrene suspension polymerization reactor has to take into account liquid movement caused by the stirrer revolutions. Therefore the CFD model has been redefined after taking into account the momentum balance. Expecting a weak influence of the heat convection in the total heat transfer phenomena, we considered two cases in computations: three-dimensional (3D), performed using the commercial package Fluent, for the real geometry and two-dimensional (2D), performed in Comsol Multiphisics, with the simplified axialsymmetric geometry, in which a rotating disc is applied instead of a propeller stirrer. A comparison of the results presenting the average temperature of the volume of the styrene/polystyrene phase is shown in Figure 9. Because the 2D approach gives quite reasonable results in comparison to the 3D one, the former has been favored in the following calculations as being faster and creating fewer convergence problems. The CFD simulations have been carried out for several initial temperatures within the range 343-363 K which is typical for the process. It is assumed that the initial reaction temperature is equal to the jacket temperature, which in turn is constant during the process (the isoperibolic conditions). A thermal runaway leading to boiling of the styrene has been observed for the all computed cases. A typical temperature field in the reactor for one of the calculated cases has been shown in Figure 10, at the time at which boiling of the styrene starts. The average and maximum temperatures in the styrene phase for all computed cases have been presented in Figure 11. It is clearly visible that the boiling point of styrene (bp 420 K) has been reached for all simulations but at different reaction times. However, the relationship between the initial reaction temperature and the time for which boiling of styrene starts is in accordance with the expectations. In relation to safety of a batch styrene suspension polymerization reactor another scenario has been considered. It is assumed that because of a stirrer failure, an operator or a reactor control system makes a decision about emergency cooling of the reactor. Therefore, a cooling medium is pumped into the jacket of the reactor from a basin at a high flow rate, and, thus, an approximate constant temperature is maintained in the jacket, here TJ ) 303 K. Results of these simulations have been shown in Figure 12. The results reveal that because of poor mixing the emergency cooling is an insufficient countermeasure for preventing thermal runaway at these concrete process conditions. Despite an emergency cooling, the thermal runaway occurs. Whereas the observed average temperatures in the reactor increase slower

than in the previous case, the maximum temperatures rises in the reactor assume almost the same profiles as in the previous case. The third considered scenario takes into account the conversion of styrene for which the mixing problems occurs. The simulations have been carried out up to the monomer conversion equal to 30% because, for the higher values of styrene conversions, the suspended drops of the product become so rigid and tough that their coalescence is impossible. In consequence, the system rather consists of the solid phase (styrene/polystyrene pearls) and the aqueous phase, and, hence, separation of the liquids is no more possible. For this reason another CFD model is needed and will be worked out in the future. For the case when a stirrer failure occurs, before the monomer conversion less than 30% is achieved, the following set of simulations has been carried out. The initial conditions for the current CFD model related to the concentrations and the reaction temperature have been taken from the model of an ideally mixed reactor. The model of an ideally mixed reactor has been verified successfully in section 4.1 for the suspension polymerization reactor with vigorous mixing conditions. Therefore, the verified model may be utilized up to the conversion for which the stirrer failure happened. Regarding the initial velocity field, the liquids are supposed to be motionless, and the phases are completely separated. The results of the simulations, showing lack of an influence of the reaction time for which mixing problems occur on the maximum reaction temperature profiles within the examined range of the conversions, are presented in Figures 13-16. 5. Summary and Conclusions This study copes with safety aspects of batch reactors for styrene suspension polymerization. When a suspension polymerization of styrene is carried out in a perfectly stirred tank reactor, serious safety problems, which are closely related to thermal runaway, can arise from wrong combination of the process parameters such as a jacket temperature, a cooling rate, and a volume fraction of styrene as well as an initiator concentration. In this paper, the computational results obtained for different combinations of the process parameters have been presented in the form of maximum reaction temperature maps, which allow for choosing the safe process conditions. On the other hand, when mixing problems occur and the stirrer revolutions are so low that the phases are being separated, the rate of heat generation due to the reaction progress is much larger than the cooling rate so that, because of a significant heat accumulation, the reaction temperature increases. Thermal runaway begins, and as a consequence, boiling of styrene starts. The obtained results show that even the emergency cooling is not effective in this case. Future work will be directed toward finding some countermeasures for preventing thermal runaway in batch styrene suspension polymerization reactors. Acknowledgment This study has been performed with a financial support of the Ministry of Science and Higher Education (Poland) within the frame of the scientific Grant 4 T09C 023 25. Appendix: Physical and Kinetic Parameters Used in the Simulations Initiator (BPO) decomposition rate constant9 (1/s): kd ) 1.71 × 1014 exp(-30000/RT)

5906


Propagation rate constant9 (dm3/(mol s)): kp ) 2.37 × 107 exp(-7060/RT) Transfer to monomer rate constant9 (dm3/(mol s): kfm ) 2.37 × 104 exp(-7816/RT) Termination rate constant9 (dm3/(mol s)): kt ) kt0 exp(-P2ζM - P3ζM2 - P4ζM3) where kt0 ) 4.41 × 109 exp(-2268/RT) Heat capacity10 (J/(mol K)): cpW ) 92.053 - 0.039953 × T - 0.00021103 × T2 + 5.3469 × 10-7 × T3 cpM ) 66.737 + 0.84051 × T - 0.0021615 × T2 + 2.3324 × 10-6 × T3 Specific heat6 (kJ/(kg K)): cpP ) 1.225 + 4.04 × 10-3(T - 273.15) Viscosity10 (Pa s): µW ) 0.001 × 10-10.2158+1792.5/T+0.01773×T-1.2631×10-5×T2 µM ) 0.00016 × exp(8.17 × ζM) Thermal conductivity10 (W/(m K)): λM ) 10-1.7023+1.0002×[1-T/648]2/7 λW ) -0.2758 + 0.004612 × T - 5.5391 × 10-6 × T2 Nomenclature Q˙ ) heat flux accumulated within the reactor contents (W) Q˙ C ) power produced by the calibration heater (W) Q˙ D ) power needed to heat up the added substrate (W) Q˙ F ) heat withdrawal rate due to cooling (W) Q˙ L ) heat withdrawal rate due to losses (W) Q˙ M ) power dissipated by the stirrer (W) Q˙ R ) power produced due to the reaction progress (W) ∆HA ) heat of reaction (J/mol) A ) heat exchange surface area (m2) c ) concentration (mol/m3) Cp ) heat capacity (J/K) cp ) specific heat capacity (J/(kg K)) D ) diffusivity (m2/s) Dx (Dy) ) dead polymer chain with x (y) units f ) initiator efficiency I ) initiator k ) rate constants (1/s or m3/(mol s)) m ) mass (kg) M ) monomer N ) stirrer revolutions (rpm) Px (Py) ) live polymer chain with x (y) units QT ) total heat generated due to reaction progress (J) R ) free radical R ) molar gas constant ()1.987; cal/(mol K)) rp ) rate of polymerization (mol/(m3 s)) T ) temperature (K) t ) time (s) U ) overall heat transfer coefficient (W/(m2 K)) V ) volume (m3) x ) mass fraction, degree of polymerization

Greek letters ) volume contraction factor ζ ) conversion λ ) thermal conductivity (W/(m K)) F ) density (kg/m3) Φ ) volume fraction µ ) dynamic viscosity (Pa s) λk ) kth moment of live polymers (mol/m3) µk ) kth moment of dead polymers (mol/m3) σ ) standard deviation Subscripts 0 ) initial aq ) aqueous phase BPO ) benzoyl peroxide (initiator) D ) dosing I ) inserts (e.g., thermometer, calibration heater) J ) jacket M ) monomer (styrene) max ) maximum org ) organic phase PVA ) poly(vinyl alcohol) (stabilizer) R ) reaction mixture S ) styrene-polystyrene phase top ) upper cover of the reactor W ) water Literature Cited (1) Barton, J. A.; Nolan, P. A. Incidents in the chemical industry due to thermal runaway chemical reactions. Proceedings of the Conference and Exhibition on Techniques for Assessment of Chemical Reaction Hazards; London Press Centre, London ECI, and IBC Technology Press: London, 1989; p 1. (2) Westerterp, K. R.; Molga, E. J. Safety and runaway prevention in batch and semibatch reactors - A review. Chem. Eng. Res. Des. 2006, 84 (7A), 543. (3) Brydson, J. Plastics Materials [Online], 7th Ed.; Elsevier: New York, 1999. http://www.knovel.com/knovel2/Toc.jsp?BookID)440&VerticalID)0. (4) Uchida, T.; Surianarayanan, M.; Wakakura, M.; Tomioka, H. Hazards of radical polymerizations: Thermokinetic investigation styrene polymerization methods. J. Chem. Eng. Jpn. 1998, 31 (6), 960. (5) Hungenberg, K.-D., Nieken, U.; Zo¨llner, K.; Gao, J.; Szekely, A. Modeling safety aspects of styrene polymerization processes. Ind. Eng. Chem. Res. 2005, 44 (8), 2518. (6) Jang, S.-I.; Kim, S.-M.; Wu, J.-P.; Kim, T.-O. Simulation of thermal behavior of suspension polymerization of styrene in a batch reactor. J. Chem. Eng. Jpn. 2006, 39 (3), 305. (7) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: New York, 1953; pp 110-115. (8) Ray, W. H. On the Mathematical Modeling of Polymerization Reactors. ReViews in Macromolecular Chemistry; Marcel Dekker, Inc.: New York, 1973; Vol. 9. (9) Machado, R. A. F.; Bolzan, A. Control of batch suspension polymerization reactor. Chem. Eng. J. 1998, 70 (1), 1. (10) Yaws, C. L. Chemical Properties Handbook; McGraw-Hill Professional: New York, 1999.

ReceiVed for reView February 7, 2007 ReVised manuscript receiVed May 28, 2007 Accepted June 21, 2007 IE070219N

Safety Aspects in Batch Reactors for Styrene Suspension Polymerization

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