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4178

Ind. Eng. Chem. Res. 2006, 45, 4178-4187

Origins of Product Heterogeneity in the Spheripol High Impact Polypropylene Process Idoia Urdampilleta, Alba Gonza´ lez, Juan J. Iruin, Jose´ C. de la Cal, and Jose´ M. Asua* Institute for Polymer Materials (POLYMAT), Facultad de Ciencias Quı´micas, The UniVersity of the Basque Country, Apartado 1072, 20080 Donostia-San Sebastia´ n, Spain

In the Spheripol process (Basell), high impact polypropylene (hiPP) is produced in two stages in series. First, isotactic polypropylene (i-PP) particles are produced in liquid propylene. These particles are transferred to a gas phase fluidized bed reactor where the elastomeric phase is produced within the isotactic polypropylene. The particulate product obtained in the commercial process is heterogeneous. This heterogeneity may be deleterious for the product performance. In this work, the origins of product heterogeneity were studied combining a detailed characterization of the product sampled from the exit lines of the homopolymerization stage (i-PP particles) and the fluidized bed reactor (hiPP particles) of a commercial unit with a mathematical model of the process. It was found that the experimental results were consistent with equally accessible active sites of uniform activity, the residence time distribution of the catalyst in the different reactors playing the major role in product heterogeneity. Introduction High impact polypropylene (hiPP) is a high tech commodity polymer widely used in injection molding parts for the automotive industry. With a yearly increase of 10%, hiPP is one of the fastest growing polymers. hiPP is a complex material formed by a matrix of isotactic polypropylene (i-PP) in which a poly(ethylene-propylene) elastomeric copolymer (EPR) is finely dispersed. The copolymer phase is added to increase the impact strength of the product. hiPP is produced in two stages in series. First, the isotactic polypropylene is produced in a variety of environments (liquid or gaseous reactors). However, the copolymerization is always carried out in a gas-phase reactor to avoid dissolution of the amorphous copolymer.1,2 In the Spheripol process (Basell) (Figure 1), the prepolymerized Ziegler-Natta catalyst particles are fed into one-two loop reactors where isotactic polypropylene (i-PP) particles are formed in liquid polypropylene. Usually, two loops are used in series to narrow the residence time distribution of the catalyst particles.3 The Ziegler-Natta catalyst is a titanium based catalyst supported on magnesium chloride (MgCl2). The liquid propylene/polymer suspension from the first stage is flashed to gas/ solid conditions prior to entering the second stage. Then, the particles are transferred to a continuous gas-phase fluidized bed reactor where the elastomeric phase is produced within the isotactic polypropylene. The properties of hiPP mainly depend on particle morphology, which in turn depends on both the catalyst and the process conditions. A visual observation of the particulate product obtained in the commercial process shows that the product is heterogeneous in terms of both the particle size distribution and the appearance of the particles (Figure 2). This heterogeneity may be deleterious for the product performance. Therefore, it is of great interest to understand the reasons behind the heterogeneity of the hiPP. * To whom correspondence should be addressed. Telephone number: +34 43 01 81 81. Fax number: +34 43 01 52 70. E-mail address: [email protected].

Figure 1. Spheripol process for hiPP production.

Figure 2. Heterogeneous (opaque and translucent) hiPP particles.

This work is an attempt to gain knowledge about the polymerization process and the catalyst performance, which determine the heterogeneity of the product. This was done by combining a detailed characterization of the product and a mathematical model of the process. The product included samples taken from the exit lines of the homopolymerization stage (i-PP particles) and the fluidized bed reactor (hiPP particles) of a commercial unit (Spheripol process).

10.1021/ie0514307 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/04/2006

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Experimental Section

Table 1. Chemical Shifts for the Carbon Atoms in Spectraa

Samples of i-PP and hiPP taken from the same Spheripol process (Basell) were supplied by Repsol-YPF. The isotactic PP particles were produced in the two loop reactors and constituted the feed of the fluidized bed reactor. The hiPP particles were the product of the fluidized bed reactor. The average residence times were 124 and 100 aut (arbitrary units of time) for the first and second loop reactors and 60 aut for the fluidized bed reactor. It is worth pointing out that, for proprietary reasons, neither the characteristics of the catalyst nor the process conditions could be disclosed and some magnitudes are given in arbitrary units (au). Particle Size Distribution. Particle size distributions were determined by screening using testing sieves. Atomic Absorption Spectroscopy (AAS). The titanium (Ti) content of the polypropylene particles was determined in a GBC AVanta Σ atomic absorption spectrometer equipped with a graphite furnace atomizer, a hollow-cathode lamp for Ti, and pyrolytically coated tubes. The method used is described in Appendix I. Atomic Force Microscopy (AFM). The AFM measurements were performed with a Nanoscope IV from Digital Instruments. All scans were performed with commercial Si scanning probe microscopy (SPM) tips. Height, phase, and amplitude images were performed simultaneously in tapping mode at the fundamental resonance frequency of the Si cantilever with typical scan rates of 0.5 line/s. The free oscillating amplitude was 2.0 V, while the set point amplitude was individually chosen for each sample. Details for sample preparation are given elsewhere.4 AFM has also been used by other authors to study the morphology of hiPP.5 Differential Scanning Calorimeter (DSC). The thermograms were obtained at a heating rate of 20 °C/min. Rubber Extraction. EPR was extracted by placing the particles in a Soxhlet over 7 days in boiling n-hexane. Scanning Electron Microscopy (SEM). The whole particles as well as cryosectionated particles were coated with gold and then examined in the SE microscope. Sorption Measurements. Gravimetric sorption experiments were carried out in an electromagnetic balance IGA 2 (Hiden). The experimental results of the gained mass of propylene or ethylene in particles at a determinate pressure and temperature were modeled using the solution of the material balances for spherical geometry (eq 1).6

Mt - M0 M∞ - M0

6

)1-

π

∞

∑ 2 n)1

1 2

exp(-Kn2t)

(1)

n

where

K)

Deffπ2 r2

(2)

In these equations, M0 is the initial mass of the particles, Mt, and M∞ are the mass of the samples at time t (seconds) and under equilibrium, r is the effective diffusion length in the particles, and Deff is the effective diffusion coefficient. Mercury Intrusion Porosimetry. The pore structure was determined by mercury intrusion in an Autopore II 9220. NMR. 13C NMR spectra were measured on a 270 Bruker AVance 300 DPX. The samples were dissolved in a mixture of 1,2,4-triclorobencene and deuterated bencene. The instrumental parameters used were the following: (i) pulse angle 90°; (ii)

a

13C

NMR

carbon type

chemical shift (ppm)

SRR-CH2 SRγ-CH2 SRδ-CH2 SRβ-CH2 Tδδ-EPE-CH Tβδ-EPE-CH Sγγ-CH2 Sγδ-CH2 Sδδ-CH2 Tββ-PPP-CH Sβγ-CH2 Sβδ-CH2 Sββ-CH2

45.5 36.8 36.5 33.0 31.5 31.0 29.5 29.0 28.0 26.5 23.5

The nomenclature for the different carbon types is given in Appendix

II.

Figure 3. PSD of i-PP (solid bar) and hiPP (striped bar) particles.

temperature of analysis 100 °C; (iii) nuclear Overhauser effect (NOE) was avoided by means of an one dimensional (1D) sequence with inverse gated decoupling; (iv) at least 2000 scans were used in order to achieve a good signal-to-noise ratio. Table 1 shows the chemical shifts in the 13C NMR spectra. Results and Discussion Figure 3 presents the particle size distributions (PSDs) of the i-PP and hiPP particles. It is worth pointing out that because of the mesh of the sieves used, the size interval of each bar in Figure 3 is different. Figure 3 shows that particles grew in the fluidized bed reactor upon the formation of the elastomeric phase. In terms of weight fraction, it was observed that the hiPP distribution shifted to higher particle diameters (dp) than the i-PP distribution, but the increase in dp was lower than the value calculated considering that the particle had grown proportionally to the copolymer formed. Porosimetric measurements showed that in these products a certain percentage of copolymer filled the pores leading to a relatively modest increase of the particle size.4 Table 2. Polymer Productivity per Weight Unit of Ti and Ti Weight/Particle for i-PP and hiPP Particles with Different Diameters

i-PP d ) 0.8-1 mm i-PP d ) 2-2.36 mm i-PP d ) 2.8-3 mm hiPP d ) 0.8-1 mm hiPP d ) 2-2.36 mm hiPP d ) 2.8-3 mm

polymer/Ti (wt/wt in au)

weight of Ti/particle (au)

2.93 7.30 11.74 3.37 8.37 12.69

7.18 × 10-4 4.12 × 10-3 6.07 × 10-3 6.63 × 10-4 3.77 × 10-3 5.83 × 10-3

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Figure 4. Variation of the elastomer content with the hiPP particle size.

The PSD is the result of the combined effect of the particle size distribution of the catalyst and the residence time distribution in the reactors. In an attempt to clarify which of those factors is the main one determining the PSD of the polymer, the amount of Ti in the particles was determined by AAS. Table 2 shows that, for both i-PP and hiPP particles, the smaller the particle size, the lower the amount of Ti per particle. This simply indicates that larger catalyst particles resulted in larger polymer particles. However, simple calculations showed that the particle

volume was not proportional to the amount of titanium per particle. On the other hand, the amount of polypropylene formed per weight unit of Ti increased with the polymer particle size, namely, the productivity of the large catalyst particles seemed to be higher than that of the small ones. Figure 4 presents the elastomer weight content of polymer particles of different sizes, as measured by 13C NMR. It can be observed that the elastomer content decreased with the particle size. At first sight, this result is surprising as Table 2 shows that large polymer particles contained more catalyst per particle and that the productivity of the catalyst in the large particles was higher than in the small particles. This is analyzed below by means of a mathematical model. Visually, the hiPP particles presented different appearances: some were opaque, and some, translucent (Figure 2). To find the reason for this difference, the morphology of the hiPP particles was studied by SEM. The i-PP particles were also included in the study for comparison. Figure 5 shows the surface of the i-PP and opaque and translucent hiPP particles. It can be observed that i-PP and the opaque particles presented a porous surface, while the translucent particles presented a more compact and smoother surface. This suggests that the opaque particles

Figure 5. SEM pictures of the whole particles: (a) i-PP particles; (b) opaque hiPP particles; (c) translucent hiPP particles.

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Figure 6. Internal morphology of i-PP and hiPP particles before and after extraction with boiling hexane.

had some similarities with the i-PP particles, which may indicate that they contained less elastomer than the translucent particles. To analyze the internal morphology, i-PP and hiPP particles were cut into two pieces using a cryo-ultramicrotome at low temperature (-120 °C). One of the pieces was directly coated with gold and observed by SEM. The other half of the particle was placed in a Soxhlet with boiling hexane for 7 days to extract the elastomer (and some amount of amorphous polypropylene). Then, it was coated with gold and observed by SEM. Figure 6 shows that, before extraction, the internal morphology of the i-PP particles and, in a lesser extent, that of the opaque hiPP particles presented rather large pores, whereas no pore structure was apparent in the case of the translucent particles. In addition, the extraction did not affect the internal morphology of the i-PP particles and only slightly affected that of the opaque hiPP particles, but the internal morphology of the translucent hiPP particles was strongly affected by the extraction, as large pores were formed yielding an internal microstructure similar to that of the i-PP particles. These results show that the elastomer formed in the fluidized bed reactor filled the pores of the translucent hiPP particles, whereas the pores of the opaque particles where not filled with ethylene-propylene copolymer. It is worth pointing out that both porosimetry measurements4 and sorption measurements (see below) showed that the translucent particles still contained a significant fraction of open pores. The differences between the SEM pictures (Figure

6) and the porosimetric and sorption measurements have been attributed to an artifact caused by the blade of the ultramicrotome that could spread the elastomer onto the polypropylene surface (in a way similar to spreading butter on toast).4 The light scattered by the large difference in refractive index between the empty porous structure and the polymer matrix was the reason for the appearance of the opaque hiPP particles. The distribution of the ethylene-propylene copolymer inside the particle matrix of the opaque and translucent hiPP particles was measured using AFM. Figure 7a shows that the copolymer was hardly observable in the opaque particles. On the other hand, Figure 7b shows that, in the translucent particles, the elastomer was finely distributed within the polypropylene matrix. It has to be pointed out that the pictures corresponded to the polymer matrix, namely, that pores were avoided in the observation. The translucent particles presented a wide range of copolymer content in the matrix (from about 10% to up to 60%) showing the heterogeneity of the product. The fact that translucent particles contained a higher amount of copolymer was further checked by 13C NMR finding that the opaque particles contained about 2% of copolymer while very translucent particles contained 59.4% of copolymer. The copolymerization of ethylene and propylene in the fluidized bed led to the formation of elastomer around the catalyst fragments, yielding a composite morphology of finely dispersed elastomer in the polypropylene matrix. Figure 6 and

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Figure 8. Copolymer composition based on 13C NMR triads: (-9-) opaque particles of diameter 0.8-1; (- -b- -) translucent particles of diameter 0.8-1; (-0-) opaque particles of diameter 2.8-3; (- -O- -) translucent particles of diameter 2.8-3.

Figure 7. Phase and amplitude AFM images of microtomized opaque and translucent hiPP. Scan size ) 10 µm: (a) opaque hiPP particles; (b) translucent hiPP particles with different elastomer content. Table 3. Weight Percentage of Polymer Extracted with Boiling Hexane % extract hiPP

d ) 0.8-1 mm

opaque translucent opaque translucent

d ) 2.8-3.0 mm i-PP

2.0 26.6 1.5 14.5 0.75

Table 4. Estimated Values of the Characteristic Length for Diffusion for Propylene at 60 °C for Particles with dp ) 0.8-1 mm K (s-1)

Xc

i-PP d ) 0.8-1 mm 5.2 × 10-3 0.36 opaque hiPP 5.8 × 10-3 0.40 d ) 0.8-1 mm translucent hiPP 3.1 × 10-3 0.24 d ) 0.8-1 mm

% ethylene 0 2 17.5

Deff (cm2/s)

r (cm)

Np

2.25 × 10-7 2.0 × 10-2 11 2.0 × 10-7 2.1 × 10-2 9 2.90 × 10-7 3.0 × 10-2

4

Table 4 show that a significant amount of the elastomer was in the pores; therefore, when the amount of elastomer increased, it broke the i-PP matrix flowing through the cracks created. Likely, the cracks were oriented toward the weakest part of the material, i.e., toward the pores and, hence, some of the elastomer ended filling the pores. It is a matter of speculation if catalyst fragments encapsulated by the elastomer were brought to the pores by the flowing elastomer and, once there, they contributed

to the formation of elastomer in the pores. Figure 5 shows that the surface of the translucent polymer particles was smoother than that of the opaque and i-PP particles. This strongly suggests that a part of this elastomer found its way to the surface of the polymer particle smoothing the surface. One may propose several hypotheses for the existence of opaque and translucent hiPP particles: (1) Some particles contained catalyst sites less active in the copolymerization of ethylene and propylene, and hence, not enough copolymer was produced in the fluidized bed reactor. (2) The porous structure of some particles was such that the active sites of the catalyst contained in these particles were not accessible for the comonomer mixture. (3) The residence time of the opaque particles in the second reactor was too short, and hence, no elastomer was produced. If the activity toward copolymerization of the catalyst contained in the opaque particles was lower/different from that of the catalyst in the translucent particles, the microstructure of the copolymer in each type of particle should be different. In an attempt to analyze the copolymer microstructure, extractions with boiling hexane were carried out. A 5 g portion of sample (opaque and translucent particles of two different diameters: 0.8-1 and 2.8-3 mm) were extracted in a Soxhlet over 7 days with boiling hexane. The extracted weight fractions are presented in Table 3. This table shows that the amount of extracted polymer was much higher for translucent particles than for opaque particles. This further supports the idea that the opaque hiPP did not contain significant amounts of copolymer. The extraction method was also applied to i-PP particles to determine the amount of amorphous polypropylene extracted by the boiling hexane. Table 3 shows that this amount was very modest. It is worth pointing out that the fraction of elastomer extracted in Table 3 was smaller than that determined by 13C NMR of the whole particle, indicating that only a fraction of the copolymer was extracted. The extract was analyzed by 13C NMR. Figure 8 presents the triad distribution for the different samples. In this figure, the contribution of the amorphous polypropylene to the triads has been deducted by assuming that in all cases the same amount of amorphous PP was extracted. This amount was considered to be 0.75 wt % of the sample (the amount extracted from i-PP, Table 3). Therefore, in the opaque particles of the size 0.8-1 mm, of the 2 wt % extracted, 1.25 wt % corresponded to the copolymer and 0.75 wt % to amorphous PP. Figure 8 shows that there was not any significant difference among the triad distributions measured for the opaque and translucent hiPP particles. This means that the catalyst contained in the opaque particles was similar to that within the translucent particles. Therefore, the existence of opaque particles was not due to differences in catalyst activity. In addition, the fact that the copolymer triad distribution was not affected by

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4183 Table 5. Estimated Values of the Characteristic Length for Diffusion for Propylene at 60 °C for Particles with dp ) 2.8-3 mm K (s-1)

% Xc ethylene

i-PP d ) 2.8-3 mm 2.6 × 10-3 0.38 opaque hiPP 2.4 × 10-3 0.41 d ) 2.8-3 mm translucent hiPP 1.22 × 10-3 0.26 d ) 2.8-3 mm

0 1 12.8

Deff (cm2/s)

r (cm)

Np

2.18 × 10-7 2.9 × 10-2 124 2.19 × 10-7 3.0 × 10-2 113 2.62 × 10-7 4.6 × 10-2

31

the particle size strongly indicates that the kinetics was not affected by diffusional limitations. The second hypothesis was that the porous structure of some particles was such that the active sites of the catalyst contained in these particles were not accessible for the comonomer mixture. The accessibility of the active centers was determined from sorption experiments. These experiments allow the calculation of an apparent mass transfer rate coefficient, K (eq 2), which is related to the effective diffusion coefficient, Deff. For particles with a porous structure as that shown in Figure 6, monomer sorption involves two processes in series: first, the diffusion of the ethylene and propylene through the pores and, second, the diffusion through the amorphous fraction of the solid polymer (mesoparticles). This second process is the slower one and, therefore, the rate controlling step. The characteristic length of the solid fragments for the diffusion (r in eq 2) gives an idea about the accessibility of the active centers. This characteristic length, r, was calculated from eq 2 using the values of Deff determined as described elsewhere.4 Tables 4 and 5 present the estimated values of K, the crystallinity of the particles as determined by DSC (Xc), the weight percentage of ethylene in particles as measured by 13C NMR, the effective diffusion coefficient (Deff), the characteristic length (r), and the number of mesoparticles per particle (Np) for i-PP particles, as well as for opaque and translucent hiPP particles of two different diameters (d ) 0.8-1 and d ) 2.8-3 mm). Tables 4 and 5 show that neither the effective diffusion coefficients in the mesoparticles nor the characteristic size of the mesoparticles for opaque and translucent particles were different enough to provoke substantial differences in accessibility. Therefore, mass transfer limitations were not the reason for the heterogeneity of the hiPP particles. In this context, it is worth remembering that all mesoparticles were equally reachable for the monomers as the diffusion through the pores between mesoparticles was not rate limiting. Tables 4 and 5 provide other useful information. It can be seen that the characteristic length of the mesoparticles in i-PP and opaque hiPP particles was similar, supporting the idea that opaque particles were basically i-PP particles. On the other hand, the characteristic length of the mesoparticles for the translucent particles was larger, indicating that the copolymer blocked some pores. Comparing particles with different diameters, it can be observed that the characteristic length of the mesoparticles in small particles was smaller than in large particles, so the active centers in small particles were somehow more accessible for the monomers than those in large particles. This seems to be in conflict with the results in Table 2 that show that the productivity per weight of titanium was higher in large particles. The weight of Ti per mesoparticle may be estimated from the weight of Ti per particle (Table 2) and the number of mesoparticles per particle (Table 5). Values of 6.5 × 10-5 (au) Ti/mesoparticle and 4.9 × 10-5 (au) Ti/mesoparticle were calculated for i-PP particles of sizes 0.8-1 and 2.8-3 mm. The similarity between these two values is remarkable.

The third hypothesis was that the residence time of the opaque particles in the second reactor was too short, and hence, no elastomer was produced. This is analyzed below by means of a mathematical model for the process. At this point, it is worth summarizing some of the experimental results: (1) Both the amount of Ti per polymer particle and the amount of polymer produced by weight of Ti increased with particle size. (2) The accessibility of the monomer to the active sites in small and large particles is similar; if anything, it is slightly better in small particles. (3) The elastomer content of the hiPP particles decreased with the particle size. (4) A substantial fraction of hiPP particles (opaque particles) contained only marginal amounts of elastomer, even though no significant differences in active site activity and accessibility were found. MATHEMATICAL MODEL Multistage olefin polymerization processes have been modeled by means of population balances.7,8 However, some properties such as copolymer content as a function of the particle size distribution, which was a key measured quantity, are very difficult to obtain8 using population balances. Therefore, the commercial unit depicted in Figure 1was simulated by means of a Monte Carlo approach. The model included the following assumptions. (1) The particles could be treated as a macrofluid, namely, neither particle agglomeration nor particle breakup occurred. In addition, no particle entrainment occurred in the fluidized bed. (2) The residence time distribution of these particles in each of the three reactors (two loops and the fluidized bed reactor) was that of a perfectly mixed continuous reactor. The average residence times were 124 and 100 arbitrary units of time (aut) for the first and second loop reactor and 60 aut for the fluidized bed reactor. (3) From a kinetic point of view, the three reactors behaved as perfectly mixed continuous reactors for the fluid phase, namely, all the particles within a given reactor were exposed to the same reaction conditions (monomer concentration and temperature). The uniformity in concentration was guaranteed in the loop reactors as the polymerization was performed in liquid polypropylene. On the other hand, in the fluidized bed reactor, the conversion per pass was low and, hence, no significant changes in monomer concentration were expected. In addition, the intense mixing of the solid phase helped to make the temperature uniform. (4) The two loop reactors were run under the same conditions (monomer concentration and temperature). (5) The whole process operated under steady-state conditions. (6) The catalyst had a normal particle size distribution with an average diameter of 50 µm. The standard deviation of the distribution was considered to be an adjustable parameter of the model. (7) The concentration of titanium was the same in all catalyst particles. Therefore, the total amount of titanium (Ti) in each particle was proportional to its volume (Ti ) k1Vc). (8) Fragmentation was similar in all particles, and all active sites were equally accessible to the monomer(s). (9) The catalyst deactivated. The deactivation rate was assumed to be described for the following kinetic equation, which is often applied to deactivation of heterogeneous catalysts:9

da ) -ψ([M], T)a dt

(3)

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where a is the activity of the catalyst (a ) 1 for the fresh catalyst) and ψ([M], T) is the deactivation function that depends on process conditions ([M]: monomer concentration and T: temperature). Therefore, the deactivation function in the loop reactors, ψloop, was different from that of the fluidized bed (ψfluidized). The exit activity of a catalyst particle that stayed a time t1 in a particular reactor is

a ) ae exp[-ψ([M], T)t1]

(4)

where ae is the activity of the catalyst at the entrance of the reactor. The average activity during the time that the catalyst particle was staged in the reactor is:

aj )

ae

(1 - exp[-ψ([M], T)t1]) t1ψ([M], T)

(5)

Figure 9. PSD of i-PP particles: (checked bar) experimental data and (solid bar) model prediction.

ψloop([M], T) and ψfluidized([M], T) were considered to be adjustable parameters of the model (10) In the fluidized bed reactor, the average porosity of the particles varied from 12% for the i-PP particles to 7% for hiPP particles.4 These are average values. Considering the heterogeneity of the hiPP particles, it is expected that these particles presented a wide range of porosities. In the model, it was considered that the newly formed elastomer was first accommodated within the matrix of i-PP until a critical weight fraction of elastomer was reached. The excess of elastomer was placed in the pores. The critical weight fraction of elastomer within the i-PP matrix (wcrit) was an adjustable parameter of the model. (11) The polymerization rate in a polymer particle was

dPol ) Tiaf([M], T) kg of polymer/unit of time dt

(6)

where [M] is the concentration of monomer in the active site and T is the temperature; f([M], T) also accounts for the relationship between the amount of titanium and the total number of active sites. According to the assumptions above, the two loop reactors operated under the same conditions, and hence, the amount of i-PP produced in those reactors from a catalyst particle of volume Vc that stayed a time t1 in the first loop reactor and a time t2 in the second loop reactor was

Pol ) k1ajloopVcfloop([M], T)(t1 + t2) kg of polymer/particle (7) Similarly, the amount of copolymer formed from a catalyst particle of volume Vc that stayed in the fluidized bed reactor a time t3 was

Pol ) k1ajfluidizedVcffluidized([M], T)t3 kg of polymer/particle (8) The k1, floop([M], T), and ffluidized([M], T) terms were estimated by fitting the experimental data. Therefore, the model contained seven parameters: (i) S standard deviation of the catalyst particle size distribution; (ii) wcrit critical weight fraction of elastomer within the i-PP matrix; (iii) k1 concentration of titanium in the catalyst particles; (iv) ψloop([M], T) deactivation function in the loop reactors; (v) ψfluidized([M], T) deactivation function in the fluidized bed reactor; (vi) floop([M], T) pooled kinetic parameter in the loop reactors; (vii) ffluidized([M], T) pooled kinetic parameter in the fluidized bed reactor.

Figure 10. PSD of hiPP particles: (checked bar) experimental data and (solid bar) model prediction.

To estimate these parameters, seven independent pieces of information were available: (i) particle size distribution of i-PP; (ii) particle size distribution of hiPP; (iii) distribution of the weight of Ti per particle in i-PP; (iv) distribution of the weight of Ti per particle in hiPP; (v) polymer productivity as a function of particle size in i-PP; (vi) polymer productivity as a function of particle size in hiPP; (vii) distribution of elastomer in particles of different sizes. At least 50 000 particles were simulated in the Monte Carlo approach. The size of the catalyst particle was randomly selected from the normal particle size distribution with a mean of 50 µm and a standard deviation S. The time spent by this particle in each reactor (t1, t2, and t3) was randomly selected by considering the residence time distributions characteristic of perfectly mixed continuous reactors (E(t) ) (1/τi) exp(-t/τi)). The amount of i-PP was calculated by eq 7, and that of hiPP, by eq 8. Figures 9 and 10 present a comparison between experimental results and model predictions for the particle size distributions of i-PP and hiPP, respectively. The estimated values of the parameters were the following: S ) 16,66; wcrit ) 0.7; k1 ) 1.7 × 104 wt of Ti(au)/cm3 of cat; ψloop([M], T) ) 0.06 h-1; ψfluidized([M], T) ) 0.09 h-1; floop([M], T) ) 3.2 × 10-6 kg Pol/ wt Ti aut; ffluidized([M], T) ) 5.5 × 10-6 kg Pol/wt Ti aut. It can be seen that a fairly good agreement was achieved. The model shows that the broadness of the particle size distribution

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Figure 11. Weight of Ti/particle vs particle diameter for i-PP particles: (9) experimental data and (‚‚‚) model prediction.

Figure 12. Weight of Ti/particle vs particle diameter for hiPP particles: (9) experimental data and (‚‚‚) model prediction.

of the catalyst played a major role in determining the PSD of the polymer particles. Figures 11 and 12 compare experimental results and model predictions for the effect of particle size on the catalyst content. It can be seen that good agreement was achieved and that the model accounted for the fact that the volume of the polymer particle was not proportional to the amount of catalyst in the particle (in the figures, the catalyst content is represented versus the particle diameter and not versus the particle volume). According to the model, the reason was that large polymer particles resulted from both large catalyst particles and long residence times. Figures 13 and 14 present the effect of the particle size on the polymer productivity per weight unit of Ti. It can be seen that, in agreement with the experimental results, the model predicts that the productivity of the catalyst was higher in large particles. The model shows that this was not due to a higher intrinsic activity of the catalyst in the large particles but to the fact that large particles result from long residence times, namely, that the catalyst acted for a longer period of time. Figure 15 shows that the mathematical model accounted for the decrease in elastomer content with the particle size. It has to be pointed out that these values are average copolymer contents for a given particle size. Within each particle size, there were particles with low (opaque) and high (translucent) elastomer contents. The model showed that, on average, the amount of elastomer formed per unit of Ti was the same in small and large i-PP particles and as the amount of i-PP per Ti unit was

Figure 13. Polymer/Ti (wt/wt in au) vs particle diameter for i-PP particles: (9) experimental data and (‚‚‚) model prediction.

Figure 14. Polymer/Ti (wt/wt in au) vs particle diameter for hiPP particles: (9) experimental data and (‚‚‚) model prediction.

Figure 15. Elastomer content vs particle diameter: (9) experimental data and (‚‚‚) model prediction.

higher in the large particles, the relative gain of copolymer was higher for the small particles. In the foregoing, it has been demonstrated that the mathematical model provided a good description of the two-stage hiPP process described in Figure 1. The model was used to explore the effect of other process configurations on the product heterogeneity, paying special attention to the formation of sticky hiPP particles. These are particles containing an excess of

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Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 Table 6. Effect of Process Configuration on the Fraction of Sticky hiPP Particles process config

no. % of sticky particles

wt % of sticky particles

case 1-1 case 2-1 case 2-2 case 3-1 case 3-2

17.65 8.85 8.34 5.68 4.66

14.64 9.67 6.93 7.38 4.53

small and large particles than case 2-1 (Figure 16), the weight fraction of sticky hiPP particles decreased when the number of both loop and fluidized bed reactors increased. Conclusions

Figure 16. Effect of the process configuration on the average elastomer content of particles of different sizes.

elastomer that cannot be accommodated within the particle. The excess of elastomer flows to the surface of the particles making them sticky. A sufficiently high fraction of sticky particles may jeopardize the operation of the fluidized bed reactor. The problem is aggravated by the fact that there is great demand for hiPP grades containing higher fractions of elastomer. The effect of process configuration on the product heterogeneity was simulated for hiPP with an average elastomer content of about 38 wt %. The following process configurations were considered: (case 1-1) 1 loop reactor and 1 fluidized bed reactor; (case 2-1) 2 loop reactors and 1 fluidized bed reactor; (case 2-2) 2 loop reactors and 2 fluidized bed reactors; (case 3-1) 3 loop reactors and 1 fluidized bed reactor; (case 3-2) 3 loop reactors and 2 fluidized bed reactors. In all the simulations, the total residence time in the homopolymerization stage was 224 aut and that in the gas-phase copolymerization was 90 aut. It was considered that sticky particles contained more than 75 wt % of elastomer. Figure 16 presents the effect of the process configuration on the average content of elastomer as a function of the particle size. It can be seen that surprisingly the addition of a second fluidized bed reactor led to wider differences in elastomer content between small and large particles. The effect was smaller when three loop reactors were used. Figure 16 also shows that the homogeneity of the product substantially improved by using three loop reactors. This was because, to a large extent, the distribution of elastomer as a function of the particle size was determined by the particle size distribution of the i-PP. Similar predictions were made by Debling et al.8 using a first principles model. Interestingly, Table 6 shows that even though case 2-2 led to wider variations in the average elastomer content between

The particulate product obtained in the Spheripol process is heterogeneous. Detailed analysis of the particles sampled from the exit lines of the homopolymerization stage (i-PP particles) and the fluidized bed reactor (hiPP particles) showed that (i) a substantial fraction of hiPP particles (opaque particles) contained only marginal amounts of elastomer, even though no significant differences in active site activity and accessibility were found; (ii) the elastomer content of the hiPP particles decreased with the particle size; and (iii) both the amount of Ti per polymer particle and the amount of polymer produced by weight of Ti increased with particle size. The experimental results were justified by the mathematical model that assumed uniform activity and accessibility for the active sites. Therefore, product heterogeneity was mainly determined by the residence time distribution. The model was used to explore the effect of the process configuration on product heterogeneity. It was found that when product heterogeneity was defined in terms of the average elastomer content as a function of the particle size, product homogeneity largely depended on the narrowness of the particle size distribution of the i-PP, namely, homogeneity substantially increased as the number of loop reactors increased. On the other hand, increasing the number of fluidized bed reactors was not always beneficial for the homogeneity of the product. Nevertheless, the fraction of sticky hiPP particles decreased by increasing the number of both loop and fluidized bed reactors. Acknowledgment The financial support form the European Commission (Project POLYPROP, No. GRD2-2000-30189) and the supply of samples by Repsol-YPF are acknowledged. The help provided by Dr. Rosa Garcı´a in AAS measurements is gratefully acknowledged. Appendix I: Atomic Absorption Spectroscopy The direct analysis by atomic absorption spectrometry without preliminary decomposition of the polymer sample may lead to substantial errors, mainly because of the heterogeneity of the sample. Elimination of the polymer matrix and subsequent dissolution of the inorganic residue is a more robust approach for Ti determination.10 A 5 g portion of polymer particles was carbonized to fuming in Pt crucibles on an electric plate and then ashed in a muffle furnace at 550 °C for 40 min. HF (2 mL) with addition of one drop of concentrated H2SO4 was added to the ash and evaporated to sulfuric acid fumes. After cooling to room temperature, the residue was dissolved in HCl (1 mL HCl + 1.5 mL H2O) with heating in a covered vessel, until a clear solution was obtained. Evaporation to a dry residue was subsequently performed in the open vessel. The evaporation was repeated after further addition of HCl (1 mL HCl + 1.3 mL

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H2O). The dry residue was dissolved in HNO3 (1%, 5 mL) with weak heating, then transferred into a 10-mL volumetric flask, and diluted to prepare the reagent blank. The instrumental conditions were as follows: wavelength 364.3 nm; spectral bandwidth 0.2 nm; background correction tungsten lamp; measurement mode peak area; graphite tube new and pyrocoated (previously conditioned); sample volume 20 µL. The furnace program applied was the following: drying 1 min and 20 s at 120 °C with a 15-s ramp; drying 2 min and 10 s at 280 °C with a 7-s ramp; charring 15 s at 1200 °C with a 10-s ramp; atomization 3 s at 2650 °C with an argon flow rate of 50 mL/min and temperature-controlled maximum power heating; cleaning followed for 3 s at 2700 °C with 1-s ramp. Appendix II: Carbon Nomenclature The nomenclature and assignments of the different carbon atoms along the molecular chain adopted for the absorption bands in the NMR spectra were those of Carman and Wilkes.11 A methylene carbon was identified as S with two Greek letters indicating its distance in both directions from the nearest tertiary carbon, e.g., the letter δ indicates a methylene group which was three away from a tertiary carbon. Similarly, a methane carbon was identified as T with two Greek letters showing the positions of the nearest tertiary carbons. Literature Cited (1) Galli, P.; Simonazzi, T.; Del Duca, D. New frontiers in polymer blends: The synthesis alloys. Acta Polym. 1988, 39, 81.

(2) Mulhaupt, R. Catalytic Polymerization and Post Polymerization Catalysis Fifty Years After the Discovery Ziegler’s Catalyst. Macromol. Chem. Phys. 2003, 204, 289. (3) Simonazzi, T.; Cecchin, G.; Mazzulo, S. An outlook on progress in polypropylene-based polymer technology. Prog. Polym. Sci. 1991, 16, 303. (4) Urdampilleta, I.; Gonza´lez, A.; Iruin, J. J.; de la Cal, J. C.; Asua, J. M. Morphology of hiPP particles. Macromolecules 2005, 38, 2795. (5) Bouzid, D.; Gaboriaud, F.; McKenna, T. F. Atomic Force Microscopy as a Tool to Study the Distribution of Rubber in High Impact Poly(propylene) Particles. Macromol. Mater. Eng. 2005, 290, 565. (6) Crank J. The Mathematics of Diffusion; Clarendon Press: Oxford, 1975. (7) Zacca, J. J.; Debling, J. A.; Ray, W. H. Reactor Residence time Distribution effects on the multistage polymerisation of olefins-I. Basic principles and illustrative examples, polypropylene. Chem. Eng. Sci. 1996, 51, 4859. (8) Debling, J. A.; Zacca, J. J.; Ray, W. H. Reactor residence-time distribution effects on the multistage polymerisation of olefins-III. Multilayered products: impact polypropylene. Chem. Eng. Sci. 1997, 52, 1969. (9) Corella, J.; Asua, J. M. Kinetic equations of mechanistic type with nonseparable variables for catalyst deactivation by coke. Models and data analysis methods. Ind. Eng. Chem. Process Des. DeV. 1982, 21, 55. (10) Kalaydjieva, I. G. Electrothermal atomic-absorption determination of Ti in polypropylene in the presence of Al and Mg. Fresenius’ J. Anal. Chem. 2001, 371, 394. (11) Carman, C. J.; Wilkes, C. E. Monomer sequence distribution in ethylene propylene elastomers. I. Measurement by carbon-13 nuclear magnetic resonance spectroscopy. Rubber Chem. Technol. 1971, 44 (3), 781.

ReceiVed for reView December 22, 2005 ReVised manuscript receiVed March 27, 2006 Accepted April 6, 2006 IE0514307