Modeling Safety Aspects of Styrene Polymerization Processes

Transcription

1 2518 Ind. Eng. Chem. Res. 2005, 44, Modeling Safety Aspects of Styrene Polymerization Processes Klaus-Dieter Hungenberg,* Ulrich Nieken, Knut Zo1 llner, Jun Gao, and Alex Szekely BASF AG, Polymer Research, Ludwigshafen, Germany Various kinetic models for thermally initiated polymerization of styrene are compared concerning their description of isothermal batch and continuous polymerization as well as their prediction for runaway reactions. All models show good agreement for conversion in both isothermal and adiabatic situations, whereas predictions for molecular weight differ considerably. Pressure predictions according to Flory-Huggins and perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS) also show good agreement considering a system from styrene/ polystyrene only. For heterogeneous systems, such as suspension polymerization of styrene, various hazardous situations, like failure of the cooling system or cooling system and stirrer, are assumed. The pressure predictions for runaway reactions mainly depend on the assumptions for the phase behavior. Realistic predictions, which take into account the solubility of water in styrene/polystyrene, are only possible with PC-SAFT EOS. Introduction One of the most important reasons for modeling polymerization processes is to provide a tool for estimating the risks of runaway reactions. This is especially important for batch processes, such as suspension polymerization of styrene and vinyl chloride. Such models should describe the temperature rise and, in the presence of volatile substances, the pressure rise. The models must also be able to provide data for reactor design in terms of maximal temperature and pressure and, if necessary, for the layout of the pressure relief system. The detailed layout of the relief system in polymerization processes will not be discussed here, but examples are given, 1-6 where pure vapor venting as well as two-phase venting have been considered. These models consist of two parts, one describing the reaction kinetics and the other the phase behavior, i.e., the vapor-liquid equilibrium, and, in the case of heterogeneous polymerization like suspension or emulsion polymerization, the liquid-liquid equilibrium. In most cases, these models are developed under controlled, mainly isothermal conditions in a limited range of temperature, pressure, etc., so the prediction of these models for the extreme runaway conditions are generally questionable. The interest of this paper is to compare various models for the polymerization of styrene and their predictions for runaway situations, especially for heterogeneous systems, to provide an estimate on the risk when relying on published models. The general reaction scheme, which is commonly accepted by most authors, is given in Table 1. There are numerous models describing the polymerization kinetics of styrene. The various models differ mainly in their description of the spontaneous thermal initiation and in the way they take into account the Dedicated to Prof. W. H. Ray on the occasion of his 65th birthday. * To whom correspondence should be addressed. Tel.: Fax: klaus-dieter.hungenberg@basf-ag.de. Table 1. Reaction Mechanisms for Thermally Initiated Free Radical Polymerization of Styrene Initiation k thermal initiation i / nm 98 mp 1 propagation P / k p / i + M 98 P i+1 Termination combination P / i + P / k t j 98 chain transfer to monomer D i+j P / k fm / i + M98 D i + P 1 continuously changing viscosity of the reaction medium and how this influences the reactivity in the various reactions steps. For the thermal initiation, Hamielec and co-workers 7,8 discussed a second- and third-order rate law, but finally recommended the use of the third-order law according to k i / 3M 98 2P 1 Weickert and Thiele 9 used a second-order law according to k i / 2M 98 2P 1 Noronha et al. 10 succeeded in modeling the runaway reaction using a second-order rate law, whereas Leung et al. 11 proposed a first-order rate law to be sufficient for the first part of the runaway reaction. Tefera et al. 12 assumed a third-order rate law for the pure thermal initiation. More detailed descriptions of the thermal initiation take into account the Mayo mechanism Here the intermediate formation of a Diels-Alder adduct from two styrene molecules is considered, which can undergo further reactions with styrene to form the finally initiating radicals. This mechanism was considered in detail by Katzenmayer, 16 Arai, 17 and Kiparissides. 18 In batch polymerization, the viscosity of the system increases by orders of magnitude, and this has dramatic /ie CCC: $ American Chemical Society Published on Web 09/21/2004

2 Ind. Eng. Chem. Res., Vol. 44, No. 8, effects on the mobility of radicals and consequently on their reactivity. Small radicals originating from initiation reactions, either from initiator decomposition or from the reaction of the Diels-Alder product with another styrene molecule, are hindered from leaving the solvent cage, thus reducing their efficiency to initiate a growing chain. This so-called cage effect may be considered in different ways, 9,12,17,18 but there are other authors 7,8,19 who describe the styrene polymerization without taking this effect into account. The strongest effect of the increasing viscosity is on the mobility of the growing radical chains, leading to the gel effect, which was first described by Trommsdorff. 20 The decreasing mobility of the growing chains reduces the termination rates between two growing radicals, thus leading to autoacceleration of the polymerization rate. For high conversions and temperatures below the glass transition temperature, even the mobility of the small monomer molecules becomes diffusion limited. This limitation on the propagation, known as the glass effect, may cause polymerization to cease before conversion has reached 100%. Reviews on various attempts to describe the effect of increasing viscosity have already been published and will not be repeated here (for examples, see Mita 21 and Curteanu 22 ). The aim of this paper is to compare the predictive capability of different models for the description of runaway reactions. Description of Kinetic Models Three different models were chosen for comparison. Model I, by Hui and Hamielec, is one of the first quantitative models 7 for bulk polymerization of styrene, where the termination rate coefficient k t as well as the transfer rate coefficient k fm are given as purely empirical functions of conversion and temperature. The initiation is given as a third-order rate law. Model II, by Weickert et al., 9 uses a different empirical formula for k t as a function of the polymer mass fraction y P and the temperature. The thermal initiation is given as a second-order rate law, and contrary to model I, it does not consider a changing chain transfer coefficient but takes into account the decreasing initiation efficiency due to the increasing viscosity, calculated by another empirical function. Model III is based on the theory of free volume as described by Marten and Hamielec. 19 Here the overall reaction is divided into three regimes: the first below some critical values of the free volume and weightaverage molecular weight, V F,cr1 and M w,cr1, where there is no diffusion limitation; a second one, where there is diffusion limitation for the growing chains above V F,cr1 and M w,cr1 ; and a third interval above V F,cr2, where propagation becomes diffusion-controlled, which is known as the glass effect. The limits between the intervals are calculated according to the method of Bueche. 23 Values for the intrinsic rate coefficients for chemically controlled propagation, termination, chain transfer, and thermal initiation for low conversion are taken from Tefera et al. 12 For the calculation of the critical free volumes, the values from Gao 24 were used. When considering runaway reactions, which may reach temperatures over 350 C, the depropagation reaction of the living chain should in principle be taken Figure 1. Conversion in thermally initiated batch polymerization of styrene at 120, 140, and 160 C according to kinetic models I-III. Figure 2. Number- and weight-average molecular weight during thermally initiated batch polymerization of styrene at 120, 140, and 160 C according to kinetic models I-III. into account, as was done in a recent study of hightemperature polymerization of styrene. 25 However, depropagation will not be considered here, because its effect, if any, would only be perceivable for conversions over 95%. Comparison of Kinetic Models The models are implemented in the Predici simulation package (CiT GmbH, Rastede, Germany). Temperaturedependent physical properties are given in the Appendix. The first step involves comparison of the predictions from kinetic models I-III for isothermal conditions with respect to conversion, M n and M w. All three models (Figures 1 and 2) give rather similar predictions for the conversion but differ somewhat in molecular weight

3 2520 Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005 Figure 4. Experimental and simulation results for conversion and weight-average molecular weight for thermal styrene polymerization at 140 C. Figure 3. Experimental conversion and number/weight-average molecular weight for thermal styrene polymerization. 7,17 predictions. Depending on the temperature, there are differences of up to 150 kg/mol for M w between the models. Similarly, also experimental results from different sources show the same features. Figure 3 gives a summary of molecular weight data as a function of conversion, as well as conversion versus time, from two different sources, 7,17 at various temperatures. For both sources, the conversion-time curves are rather similar, but in the case of molecular weight, some scattering within the data from one author is observed. Noticeable differences up to 150 kg/mol between the two sources exist. Figure 4 compares predictions and experimental results for conversion and weight-average molecular weight at 140 C. No judgment about the quality of the models is possible, because the predictions for polymerization rates are similar and describe the experiments in good agreement, whereas for M w, there are large discrepancies in both experimental and simulation results. The next step is a comparison of the kinetic models in their predictive capabilities for a continuous process. Figure 5a gives the conversion and Figure 5b the molecular weight as a function of residence time for continuous polymerization in a homogeneous CSTR. In ref 35, some experimental results of thermal styrene polymerization in a CSTR at 140 C are given; for residence times of 3.7 and 4.6 h, conversions of 52 and 64% and M w of 345 and 340 kg/mol are reported. It is evident that the predictions for conversion from the three models are again rather similar and agree well with the experimental results, but as in the case of batch reactors, the predictions for the molecular weights differ much more. To summarize the comparison of the various isothermal cases, the different models show good Figure 5. (a) Conversion as a function of residence time for thermally initiated, continuous polymerization of styrene in a CSTR for kinetic models I-III. (T ) 140 C). (b) Number- and weight-average molecular weight as a function of residence time for thermally initiated, continuous polymerization of styrene in a CSTR for kinetic models I-III (T ) 140 C). agreement for the description of conversion-time curves, but they give rather high differences in molecular weights. The same effects are also observed when comparing experimental results from different sources, but this should not have a great effect on the predictions for runaway behavior.

4 Ind. Eng. Chem. Res., Vol. 44, No. 8, Figure 7. Temperature rise according to models I-III starting from a solution of 40% PS in styrene at 120 C. Starting molecular weight of dissolved PS is M n ) 72.5 and M w ) kg/mol. Figure 6. (a) Temperature rise for runaway styrene polymerization reaction according to kinetic models I-III starting from 80 C. (b) Temperature rise for runaway styrene polymerization reaction according to kinetic models I-III starting from 150 C. Table 2. Time Elapsed for a T ) 30 C Temperature Increase in Runaway Styrene Polymerization Reaction According to Kinetic Models I-III Starting from 80 or 150 C, Respectively model time for C increase (h:min:s) time for C increase (h:min:s) I 04:32:57 00:04:12 II 04:39:00 00:04:23 III 04:03:28 00:04:57 The next step is the comparison of the kinetic models in their predictions for the runaway of pure styrene batch polymerization with 80 and 150 C as initial temperatures (Figure 6a,b), i.e., for a homogeneous system. The models are tested until a temperature of 360 C is reached. As a measure for comparison, the time until a 30 C temperature increase has been reached is shown in Table 2. During this time range, countermeasures against runaway could be taken. It is obvious from the data in Table 2 that all three models, though very different in structure, show a fairly good agreement, even under extreme conditions; the periods until T ) 30 C differ by less than 15% between models. Figure 7 provides the behavior for a runaway starting from a steady state in a continuous reactor, where a 40/ 60% polystyrene/styrene (PS/S) mixture at 120 C as initial temperature is assumed. For this scenario, the differences between the models are not too large either (20% difference to reach T ) 30 C). Description of Thermodynamic Models Until now, only the temperature rise during runaway has been discussed, but the calculation of the runaway pressure is much more important with regard to reactor safety. Knowledge of the phase equilibrium is a prerequisite for the design and optimization of polymer production plants. Modeling the thermodynamic properties of polymer mixtures is a challenge due to the fact that experimental data are generally scarce and difficult to measure. For homogeneous bulk or solution polymerization of styrene, which is the usual process for the production of general-purpose polystyrene, only the vapor-liquid equilibrium must be considered. The liquid phase consists of polystyrene, styrene, and eventually solvents such as ethyl benzene or toluene. Hazardous situations for this case have already been considered. 4,5,10,11,26 Usually the vapor pressure of a solvent above a polymer solution (solvent activity) is calculated according to the Flory-Huggins (FH) equation, 27,28 an activity coefficient model, in which the thermodynamic quantities of the solution are derived from a simple concept of the combinatorial entropy of mixing and a reduced Gibbs energy parameter, the χ parameter. Newer methods involve equations of state like the perturbed-chain statistical associating fluid theory equation of state (PC- SAFT EOS), 29,30 which was shown to accurately describe vapor pressures, densities, and caloric properties of pure components and mixtures. Physically based equations of state, derived by applying principles of statistical mechanics, have continuously been developed and improved upon over the past three decades. Modern equations of state aim at highly nonideal systems, such as polymer mixtures or associating compounds. In the framework of PC-SAFT, polymers are assumed to be chains of freely jointed spherical segments exhibiting attractive forces among each other. The model introduces a temperature independent binary interaction parameter, k ij, to correct for the interactions of each binary system. The model development is based on perturbation theories. A detailed review is given by Sadowski. 31 For heterogeneous systems with two liquid phases, e.g. water and organic phase, the liquid-liquid equilibrium must be considered in addition to the vaporliquid equilibrium. Furthermore, for nonisothermal or adiabatic reactions the thermal properties of the phases must also be taken into account. In suspension polymerization, various hazardous situations may be considered. The first situation is when the suspension remains stable during the runaway. Possible runaway reactions and the nonisothermal behavior have already been

5 2522 Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005 Figure 8. Possible hazardous situations as a result of failures in stirring and cooling system. discussed 26,32 for various initiation rates, heat transfer coefficients, and temperatures of the cooling medium. Complete immiscibility of the organic and water phase but an efficient heat transfer between the two phases was assumed. The two phases refer to organic droplets in a continuous water phase. Such a situation may occur by some failure in the cooling system, while the stirrer is still in operation. However, this situationscooling system fails but stirrer still in operationsdoes not seem to be the most hazardous case. As long as the stirrer is running, several countermeasures, like the addition of inhibitors, addition of chilled water, etc., can be taken to prevent a runaway. A more serious situation is the simultaneous failure of the cooling system and the stirrer, e.g., caused by a failure of the electric system. Initially, the lack of stirring causes coagulation of the suspended particles. At this point, various assumptions about the behavior of the two liquid phases may be considered, which are illustrated in Figure 8. For situation A, complete phase separation and complete immiscibility of water and organic phase is assumed, i.e., the organic phase forms a bulk upper layer in the reactor, and no mass or energy exchange occurs between the water and the organic phase. Temperature and pressure are entirely determined by the styrene/ polystyrene phase. Situations B and C refer to the same as in A, but they consider the inclusion of traces of water into the coagulated upper organic phase, which floats on top of the bulk water. The difference between situations B and C is the way these traces of water in the upper phase are taken into account. In situation B, as in situation A, complete immiscibility is assumed. The overall pressure is calculated as the sum of the vapor pressure of pure water, independent of the amount of water present in the upper phase, and the pressure of the organic phase (styrene in polystyrene), which is calculated using the FH method. Each pressure is calculated at the runaway temperature. This results in a very conservative and less realistic approach. Situation C, besides taking into account the solubility of styrene in polystyrene, considers the solubility of water in styrene and in polystyrene. In both cases B and C, small amounts of water will be heated during the runaway, but in case B, it is handled as a separate phase, whereas in C, a rigorous thermodynamic model, the PC-SAFT equation of state is applied to the upper liquid phase consisting of styrene, polystyrene, and traces of water. Figure 9. Solubility of styrene in polystyrene, according to PC- SAFT, T ) 140 C. Figure 10. Pressure rise during runaway reaction over temperature calculated according to FH (χ ) 0.4) and according to PC- SAFT for runaway start temperatures of 80, 140, and 200 C. It is assumed that the lower water phase does not affect the pressure, and therefore is not taken into account in the calculations. Comparison of Thermodynamic Models To calculate the pressure on the upper liquid phase of the styrene polymerization system, bubble point calculations were carried out. This was done using Multiflash (Infochem Computer Services Ltd, London, U.K.), through routines programmed into the Predici simulation package. Figure 9 gives a comparison of the vapor pressure of styrene over styrene/polystyrene at 140 C calculated according to PC-SAFT and FH with χ ) 0.4. Literature values for χ can be found in a diverse range. 5,11 The value of χ ) 0.4 was assumed, because it was found that it gives the best agreement between the PC-SAFT and FH model. The pressure rise with temperature during runaway reaction is given in Figure 10 from various initial temperatures and calculated according to the FH model and the PC-SAFT EOS. Pure component parameters of monomers, polymers, and solvents are taken from Gross 33 for the calculation of the PC-SAFT EOS. It is shown that the calculated pressures are almost independent of the method used. The FH model proves to be sufficient as long as the upper organic phase is free of water. Up to now, only runaway in a homogeneous system was considered, i.e., for bulk styrene polymerization or for situation A in suspension polymerization, where only the runaway of the upper organic layer must be considered. Situation B refers to the failure of both the cooling system and the stirrer and assumes that water

6 Ind. Eng. Chem. Res., Vol. 44, No. 8, Figure 11. Phase diagram of water and styrene at P ) 1 bar. Calculations according to PC-SAFT; experimental data taken from Dechema Chemistry Data Series. 34 Figure 12. Solubility of water in polystyrene at P ) 1 bar, according to PC-SAFT for various binary interaction parameters (k ij). as a separate phase is included and dispersed in the reacting organic phase and takes the runaway temperature. In this case, the contribution of the styrene/ polystyrene phase was calculated according to the FH model, and the water contribution corresponds to the vapor pressure of water. Both of these pressures are added to give the pressure of the whole system. This seems to be the most hazardous situation and the most conservative assumption, as the traces of water in the upper organic phase contribute to the system pressure with their vapor pressure, but the heat capacity of the traces of water enclosed in the upper phase is not sufficient to lower the runaway temperature significantly. In situation C, the solubility of water in the organic phase is also taken into account. Figures 11 and 12 show the binary systems water/styrene and water/ polystyrene. Figure 11 shows experimental data for the system water/styrene together with PC-SAFT results. Because experimental data for the system water/ polystyrene are missing, a sensitivity study using PC- SAFT with various values of k ij has been performed, showing the solubility of water in polystyrene (Figure 12). For runaway situation C, various amounts of water were assumed to be included in the organic phase, for instance as small droplets surrounded by the organic phase, By varying this amount of water, the fact that the two phases may not be completely separated after stirrer failure can be taken into account, and the risks of various situations can be estimated. Pressure over runaway temperature was calculated starting from Figure 13. Runaway pressure over temperature and conversion for situation A (0% water in organic phase), B (water + organic phase, no solubility), and C with 2 and 5% water included in the organic phase, as well as the sensitivity of the PCS EOS for various binary interaction parameters k ij. T 0 ) 80 C. 80 C (Figure 13), taking into account the solubility of water in styrene and polystyrene. For this situation, also the various values of k ij for water/polystyrene were tested, which give different solubilities of water in polystyrene. In addition, the pressure according to situations A (no water included) and B (traces of water included, but no solubility of water in the organic phase) are included in Figure 13. It is evident that situation B gives the highest pressure, mainly determined by the vapor pressure of pure water. This simplification is imprecise, as it does not consider the limited but significant solubility of water in the organic phase (Figures 11 and 12). For low temperatures (i.e., low conversions), all curves for situations C are identical to that of situation B but start to deviate at higher temperatures. The reason behind this behavior is that with increasing temperature the traces of water are dissolved in the organic phase, and thus the contribution of water to the total pressure is reduced. Naturally, the larger the amount of water included in the organic phase, the higher the pressure. Compared to the effect of the amount of included water, the parameter sensitivity with respect to k ij is rather low. Conclusions The kinetic models studied under isothermal conditions show good agreement for the description of conversion-time curves, but they differ considerably for molecular weight averages. The same effects can be observed when comparing experimental results from various sources. Under extreme conditions, the models also show fairly good accordance with respect to runaway behavior. This is the case for runaway reactions starting from zero conversion as well as starting from a steady state in a continuous reactor. So, all three kinetic models can be used to predict the runaway behavior. Various hazardous situations for heterogeneous systems were evaluated using different assumptions for failure situations using different thermodynamic models. Here, equations of state, especially the PC-SAFT EOS, seem to allow the most realistic predictions, taking into account the vapor-liquid as well as the liquidliquid equilibrium. For the homogeneous system styrene/ polystyrene, free of water, the FH method and EOS method give the same results.

7 2524 Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005 Appendix: Physical Properties C pl ) A + BT + CT 2 + DT 3 + ET 4 [J/kmol/K] Styrene: A ) , B ) , C ) , D ) 0, E ) 0 Polystyrene: A ) , B ) , C ) 0, D ) 0, E ) 0 Water: A ) , B ) , C ) 8.125, D ) , E ) Literature Cited F l ) A/B 1+(1-T/C)D [kmol/m 3 ] Styrene: A ) , B ) , C ) 636, D ) 0.28 Water: A ) , B ) , C ) , D ) F l ) A + BT [kg/m 3 ] Polystyrene: A ) , B ) P vl ) exp(a + BT -1 + C ln(t) + DT E ) [Pa] Styrene: A ) , B ) , C ) , D ) , E ) 1 Water: A ) , B ) , C ) , D ) , E ) 3 (1) Duxbury, H. A. The Sizing of Relief Systems for Polymerization Reactors. Chem. Eng. 1980, Jan, 31. (2) Rutten, H.; Mennen, J.; van Pinxteren, M. Design of an emergency relief system for a runaway polymerization reaction. Dechema-Monogr. 1992, 127, 305. (3) Jacobs, L. J., Jr.; Krupa, F. X. Designing for Safe Reactor Vent Systems. ACS Symp. Ser. 1979, 104, 327. (4) Fauske, H. K.; Leung, J. C. 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