Ind. Eng. Chem. Res. 2005, 44, 2443-2450
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Gas-Phase Ethylene/Hexene Copolymerization with Metallocene Catalyst in a Laboratory-Scale Reactor Bo Kou,† Kim B. McAuley,* C. C. Hsu, David W. Bacon, and K. Zhen Yao‡ Department of Chemical Engineering, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Gas-phase ethylene and hexene copolymerization using a silica-supported (n-BuCp)2ZrCl2 metallocene catalyst has been investigated in a 2 L laboratory reactor. Replicate experimental runs were conducted to confirm the reproducibility of measured responses, which included polymerization rate, reactant concentrations, and copolymer properties. Comparisons of polymerization rate profiles and catalyst activity were made using a number of designed experimental runs. The experiments revealed that triisobutyl aluminum scavenger was the most important cause of low catalyst activity, and a low initial polymerization rate that was followed by a rate increase. The effects of other influencing factors, including residence time, temperature, pressure, concentration of reactants, catalyst, and cocatalyst, were also investigated. As expected, hydrogen concentration and hexene concentration had significant effects on molecular weight and shortchain branching, respectively. In addition, hexene enhanced the polymerization rate and catalyst activity, while cocatalyst and hydrogen both led to a lower polymerization rate. The results from this study provide important quantitative information that will be used for parameter estimation in fundamental models. Introduction Polyethylene, which is the largest tonnage plastic material produced worldwide, is produced commercially using free-radical initiators, Phillips-type catalysts, Ziegler-Natta catalysts, and more recently, metallocene catalysts.1 Most industrial processes use heterogeneous Ziegler-Natta catalysts because of the very broad range of products that can be produced at low cost. The desirable properties of ethylene copolymers achieved with Ziegler-Natta catalysts can be further improved by metallocenes. Compared to Ziegler-Natta catalysts, metallocenes can produce narrower molecular weight and composition distributions. Products with tailored end-use properties can be designed using a combination of several metallocene catalysts.2 As a result, metallocenes are playing a more and more important role in the polyethylene industry. Despite the successful application of gas-phase ethylene polymerization processes, which have been used commercially for more than 30 years, only a few papers in the open literature have been published on gas-phase ethylene polymerization in bench-scale reactors.3-15 Experiments in bench-scale reactors are essential for investigating the effects of operating conditions on product properties, collecting information for mathematical models, and designing commercial reactors. Unfortunately, experimental investigations in the laboratory are impeded by problems related to addition and mixing of high-activity catalysts, maintaining low impurity levels, and controlling reactor temperature, * To whom correspondence should be addressed. Tel.: 613433-2768. Fax: 613-533-5537. E-mail: mcauleyk@ chee.queensu.ca. † Current address: Research Engineering and Business Development Center, E. I. du Pont Canada, Kingston, Ontario, Canada K7L 5A5. ‡ Current address: Institute of Polymerization Reaction Engineering, Zhejiang University, Hangzhou, China 310027.
which can lead to poor reproducibility of polymerization rate and polymer properties. In this work, gas-phase ethylene-hexene copolymerization with a silica-supported (n-BuCp)2ZrCl2 catalyst was conducted in a 2 L reactor. The effects of operating conditions on the polymerization rate and product properties were investigated. Experimental Section The catalyst employed in this work was (n-BuCp)2ZrCl2 (from Aldrich) supported on silica (0.0000192 mol Zr/g Cat). MAO cocatalyst (10 wt % in toluene) was obtained from Aldrich. Triisobutyl aluminum (25 wt % in toluene from Aldrich) was added to the reactor before polymerization to scavenge impurities. Ethylene (polymer grade) and hydrogen (ultrahigh purity) were purchased from Praxair. Trace impurities were removed by passing these gases through two moisture absorbers, one oxygen trap and one carbon dioxide trap, before reaching the reactor. 1-Hexene (g99%) was purchased from Aldrich and was added to the reactor as a liquid. In each run, 140 g of sodium chloride (g99% from Sigma) was added to the reactor to help catalyst dispersion. The salt was heated in a vacuum oven at 140 °C for at least 48 h before being added to the reactor. The salt bed was further heated at 110 °C under vacuum for at least another 12 h inside of the reactor before polymerization. Ethylene polymerization was conducted in a 2 L autoclave reactor, manufactured by Autoclave Engineers, with a combined double-helix and anchor agitator.5 Before each experiment, the salt bed, scavenger, cocatalyst, hydrogen, hexene, and some ethylene were added to the reactor. Then, to start the polymerization, catalyst particles were blown into the reactor using additional ethylene. The reactor was operated isothermally by automatically adjusting the flow of cooling water and steam to the reactor jacket. A single-stage regulator on the ethylene feed line was used to maintain constant pressure in the reactor. Additional ethylene
10.1021/ie049067b CCC: $30.25 © 2005 American Chemical Society Published on Web 02/26/2005
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Figure 2. Temperature control during replicate runs at the center point. Figure 1. Polymerization rate during last batch replicate runs at the center point.
was automatically fed to the reactor as gases were consumed by the polymerization reaction. Additional hexene and hydrogen were fed proportionately with the ethylene to maintain the desired feed concentration ratio. The following responses were measured during the experimental runs: (1) Feed rate of ethylene, measured by a thermal mass flow meter. (2) Gas composition in the reactor, analyzed using a Varian Star 3400 gas chromatograph. Up to 15 samples were collected and were analyzed at the end of each run. (3) Number-average molecular weight (Mn), weight-average molecular weight (Mw), and molecular weight distribution, measured using high-temperature gel permeation chromatography (GPC) of polymer removed from the reactor at the end of each run. The GPC analyses were performed by BP Chemicals. (4) Short-chain branching (comonomer content), analyzed by 13C nuclear magnetic resonance (NMR) of copolymer collected at the end of each run. Each sample was dissolved in o-dichlorobenzene d4 at 120 °C for at least 10 h. An Avance 400 NMR was used at 120 °C with 4000 scans and 10 s saturation time for each scan. The spectrum was processed using the collective method16-19 to calculate the number of short-chain branches. (5) Triad sequence distribution, calculated using the collective method16-19 on the basis of 13C NMR for copolymer collected at the end of each run.
Figure 3. Hydrogen fraction in the gas phase during replicate runs at the center point.
Figure 4. Hexene fraction in the gas phase during replicate runs at the center point. Table 1. Polymer Properties of Replicates at the Center Point
Reproducibility of Response Variables One of the greatest challenges in lab-scale gas-phase ethylene polymerization is to achieve good reproducibility. Before embarking on a set of designed experiments, four replicate ethylene/hexene copolymerization runs were conducted. These runs indicated that the reproducibility of the polymerization rate was initially poor.20 Poor reproducibility can arise from three major sources: impurities in the feed or in the reactor, poor temperature regulation, and irreproducible catalyst addition. To improve reproducibility, modifications were made to the gas purification system, reactor cleaning procedures, tuning of the temperature controller, design of the catalyst addition system, and reactor operating procedures.20 After these modfications, four new replicate runs were performed to check the reproducibility of the response variables. The polymerization rate, temperature, hydrogen concentration, and hexene concentration for these replicate runs are shown in Figures 1-4, respectively. Final product properties are listed in Table 1. The reproducibility was considered to be acceptable, and runs at the factorial points of the screening experiments were started.
run C1 C2 C3 C4 standard deviation
peak catalyst activity g of PE mmol-1 Zr-1 100 psi-1 h-1
Mn g/mol
Mw g/mol
PD
SCB/ 1000 C
9198 5611 9154 9658 1877
9700 7500 7700 8000 1005
27 700 22 500 23 600 25 300 2265
2.9 3.0 3.1 3.2 0.13
8.3 8.2 8.8 8.9 0.34
The experimental settings used for the replicate runs were at the center point of a Plackett-Burman design (Table 2), corresponding to the “0” column in Table 3. From the replicate runs in Figures 1-4, it appears that variability in the polymerization rate is considerably smaller during the initial stages of polymerization, when the polymerization rate is low, than at the end of the runs when the polymerization rate is higher. Good temperature control, within (1 °C was obtained in all of the runs (Figure 2). As shown in Figures 3 and 4, the hydrogen and hexene concentrations in the gas phase decreased during these replicate experiments, because the hydrogen-to-ethylene and hexene-to-ethylene feed ratio settings were not large enough to make up for the hydrogen and hexene consumed by reaction.
Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005 2445 Table 2. Experimental Design Used in Screening Experiments, Additional Runs and Sequential Experimentsa run
X1
X2
X3
screening experiments 1 1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 -1 1 -1 1 -1 -1 -1 1
X4
X5
X6
X7
X8
X9
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12
1 1 -1 -1 -1 -0.8 -1 1 1 1 -1 -1
-1 -1 1 -1 -1 1 -1 1 1 -1 1 1
-1 -1 1 1 -1 -1 1 1 -1 1 1 -1
1 -1 1 1 1 -1 1 -1 1 -1 -1 -1
-1 1 1 1 -1 -1 1 -1 -1 1 -1 1
8h 9h A1 A6 A7 A10
4 4.7 1 1 -1 0
additional and very long runs 1 -1 -1 1 0 1 -1 1 1 1 -1 -1 -1 1 1 -1 3 -1 1 1 -1 1 -1 -1 -1 -1 -1 1 7 1 -1 -1 1 1 -2.2 1
-1 1 1 -1 1 -1
-1 1 -1 -1 1 1
S1 S2 S3 S4 S6 S8 S9 S10 S11 S12 S13 S14
0 -1 -0.3 -0.3 -0.7 -0.3 -1 -1 0 -1 0 -0.3
0 0 0 0 1 1 -1 -1 -1 -1 1 0
sequential experiments 0 -1 -3 0 0 -1 -3 0 0 -1 -3 -2.5 0 0 -1 -2 -1 1 -1 -2.9 -1 1 -1 -2.6 -1 1 -1 -2.8 1 -1 -2 -2.6 1 -1 -2 -2 1 -1 -2 -2.6 -1 -1 -2 -2 0 0 -1 -1.5
0 0 0 0 2 3.6 1 1 1 3.6 1 0
0 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1.7
0 0 0 0 0 0 0 0 0 0 0 0
a Coded settings were obtained by linear interpolation or extrapolation from coded settings in Table 3.
Table 3. Coding in Experimental Design X1 X2 X3 X4 X5 X6 X7 X8 X9
residence time (h) reaction temperature (°C) reactor pressure (psig) initial hexene concentration (mol %) hexene to ethylene molar feed ratio initial H2 concentration (mol %) ethylene to hydrogen molar feed ratio catalyst fed to reactor (g) cocatalyst to catalyst mole ratio scavenger fed to reactor (g) stirring speed (rpm)
-1
0
+1
0.5 60 100 0% 0 0.4% 600 0.2 400 0.3 200
2 72.5 130 2% 0.01 0.6% 600 0.3 800 0.6 225
3.5 85 160 4% 0.02 0.8% 600 0.4 1200 0.9 250
We selected the hydrogen-to-ethylene feed ratios and hexene-to-ethylene feed ratios, using experience gained from earlier reactor-commissioning experiments, in an effort to ensure that only a small composition drift occurred during the experimental runs. For hydrogen and hexene (factors X4 and X5 in Table 3), the initial gas concentration and the feed ratio (with ethylene) settings are specified for each of the levels used in the experiments. Since gas composition measurements were obtained after each run, rather than during the run, there was no feedback control of gas composition. The feed ratio policy reduced the composition drift but did not eliminate it entirely. The cocatalyst-to-catalyst ratio (factor X7) is the molar ratio of aluminum (from the MAO) to zirconium fed to the reactor. Screening Experiments To determine the relative influence and importance of various operating conditions, the 12-run Plackett-
Burman experimental design, listed in Tables 2 and 3, was used to investigate all of the factors of interest. Of the 12 runs at the factorial points, overheating and polymer agglomeration were found in three runs (runs 6, 10, and 11) because the polymerization rate was too high for the temperature control system to remove the heat generated by the reaction. In these three runs, a large temperature spike was observed soon after the catalyst was fed to the reactor, and a large chunk of polymer (instead of the usual powder) was found when the reactor was opened at the end of the experiments. After reducing the amount of catalyst fed to the reactor (run 6, 0.4 to 0.2 g; run 10, 0.4 to 0.08 g; run 11, 0.4 to 0.05 g, respectively), these three runs were redone to get appropriate data. Unfortunately, there was still significant agglomeration when run 11 was conducted with the reduced amount of catalyst, so the result of this run was not used in the subsequent data analysis. Some runs in the screening experiments had very low polymerization rates and catalyst activities, making the standard deviations in the ethylene feed rate large compared to the low polymerization rates. To obtain better data for parameter estimation in our subsequent mathematical modeling work,20-22 two runs (runs 1 and 7) were redone with all of the settings unchanged, except for an increased catalyst amount, from 0.2 to 0.6 g for run 1 and from 0.4 to 1.0 g for run 7. As shown in Table 2, two very long runs were also conducted with 8 and 9 h of residence times, respectively, to learn about the polymerization rate profile and the polymer that is produced when the catalyst has been in the reactor for an extended period of time. The operating conditions of the 8 h run were similar to those for run 4 in the screening experiments, except for the following: the initial hydrogen concentration was increased from 0.4 to 0.8%; the ethylene to hydrogen feed ratio was changed from 600 to 400; and the amount of scavenger fed to the reactor was 0.3 g instead of 0.9 g. The operating conditions for the 9 h run were the same as in run 7, except for the longer residence time. Results of Screening Experiments The measured response variables for the screening runs, including polymerization rate, catalyst activity, Mn, Mw, PDI, and SCB, are listed in Table 4 and are discussed below. Low Catalyst Activity. The catalyst used in the current research, (n-BuCp)2ZrCl2, has been studied by many researchers13,15,23,24 and is of commercial interest in gas-phase polyethylene production.25 Karol et al.23 found that (n-BuCp)2ZrCl2 polymerized ethylene/hexene at 53 000∼82 000 g PE mmol-1 Zr 100 psi-1 h-1. However, in the current research, most runs showed catalyst activities that were significantly smaller. Two copolymerization runs showed comparable catalyst activities, 34 351 and 97 468 g PE mmol-1 Zr 100 psi-1 h-1, but the catalyst activities in all other runs were below 10 000 g PE mmol-1 Zr 100 psi-1 h-1. Some runs even showed catalyst activities at only about 1% of those obtained by Karol et al.23 Reactions with the scavenger may be a possible cause of the low catalyst activity. Low activity may also result from other factors such as hydrogen and MAO. Impurities can also lead to low catalyst activity. However, since the reproducibility of the polymerization rate is good and no very fast deactivation was observed, impurities in the reactor system or the feed gases are unlikely to be the major
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Table 4. Experimental Resultsa peak activity g of PE mmol-1 Zr 100 psi-1 h-1
run
peak rate sccm/min
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12
99 188 135 261 139 1475 63 407 1916 N/A N/A 700
1105 2102 2421 1463 1562 8268 565 4562 34365 N/A N/A 6277
8h 9h A1 A6 A7 A10
690 209 1492 925 220 2174
S1 S2 S3 S4 S6 S8 S9 S10 S11 S12 S13 S14
580 1410 286 2395 324 1200 302 45 328 64 418 1300
Mn g/mol
Mw g/mol
PDI
SCB SCB/1000 C
rate increase (Y or N)
screening experiments 6500 20 700 6100 33 900 4800 14 000 6100 17 200 4200 11 400 7200 30 800 4400 15 300 12 300 45 200 12 000 33 500 N/A N/A N/A N/A 6800 26 800
3.185 5.557 2.917 2.820 2.714 4.278 3.477 3.675 2.792 N/A N/A 3.941
17.9 0.0 0.0 19.2 18.0 0.0 0.0 0.0 10.6 N/A N/A 0.0
Y N S S S N S Y Y N/A N/A S
8250 2337 5575 10 365 789 97 481
additional and very long runs 8200 34 100 5500 16 900 10 000 27 400 12 800 44 800 5000 16 700 10 400 25 200
4.159 3.073 2.740 3.500 3.340 2.423
0.0 15.7 12.5 0.0 0.0 11.6
N Y Y N S Y
5335 12 969 15 764 66 084 116277 107 614 54 222 2545 7354 3613 14 994 23 917
sequential experiments 52 803 139 510 57 647 170 610 N/A N/A 11 480 31 726 N/A N/A 17 489 38 855 N/A N/A N/A N/A 7226 33 366 8078 23 579 N/A N/A 10 766 29 577
2.642 2.960 N/A 2.764 N/A 2.222 N/A N/A 4.617 2.919 N/A 2.747
0.0 0.0 0.0 15.1 11.6 15.8 6.5 0.0 0.0 0.0 0.0 6.8
Y S N N N N S S N S N Y
a S means the reaction time is too short to tell whether there is rate increase or not. Only experiments with at least 50 min of run time were designated with a Y or N.
contributors to the low catalyst activity. To identify and verify the cause of the low activity, further experiments were conducted and will be discussed in later sections. Rate Increase. In the four replicate runs and some of the other runs (those with “Y” in the final column of Table 4), a significant increase in polymerization rate was observed after a sustained initial period with a low rate. In the short runs (30 min runs, denoted by “S” in the final column of Table 4), it is difficult to know whether there would have been a rate increase had these runs continued for longer times. The rate profiles shown in Figure 1 are different from common kinetic curves for metallocene catalysts, which usually have a peak during the early stage of polymerization followed by a gradual decrease in polymerization rate due to the deactivation of catalyst sites. The kind of rate increase behavior observed in Figure 1 is rarely observed, and only a few reports could be found in the literature. Chu et al.26 studied ethylene/1-hexene copolymerization with homogeneous, supported, and self-supported metallocene catalysts. They found that supported catalysts have different polymerization rate curves from unsupported homogeneous metallocenes. The homogeneous metallocenes showed typical rate profiles of metallocene-catalyzed ethylene polymerization, namely, a peak at the beginning followed by gradual decrease in polymerization rate. For supported metallocenes, although there was a small peak at about the fifth minute, followed by a 5 min rate decrease, the polymerization rate continued to increase for the remaining 50 min of reaction. The self-supported metallocene had
no rate peak at all, and the polymerization rate kept increasing throughout the 60 min polymerization. It was also found that the catalyst activities with both supported and self-supported catalysts were significantly lower than for the homogeneous metallocene catalyst. The molecular weight distributions obtained from supported and self-supported catalysts were broader than for copolymers produced by the homogeneous metallocene catalyst. Chu et al.27 also studied ethylene homopolymerization with metallocene catalysts. Within the 60 min polymerization runs, no decay in catalyst activity was observed with Al/Zr ratios (Al present in MAO pretreated silica supports) smaller than 1000, although decay was seen at higher Al/Zr ratios. Xu et al.10 studied the kinetics of ethylene homopolymerization and ethylene/propylene copolymerization with supported metallocene catalysts. Although no induction period was observed in ethylene homopolymerization, induction periods up to 90 min long were observed consistently during copolymerization. However, no conclusion could be drawn concerning the cause of the induction period. Chakravarti and Ray8 studied the kinetics of metallocene-catalyzed ethylene homopolymerization and ethylene/1-hexene copolymerization in the gas phase. They found an induction period exclusively in copolymerization experiments, which was not observed in ethylene homopolymerization. However, an incremental increase in the 1-hexene concentration failed to have a significant effect on the length of induction period. Temperature had a significant effect on the length of the induction
Ind. Eng. Chem. Res., Vol. 44, No. 8, 2005 2447
Figure 5. Examination of possible causes of rate increase and low catalyst activity (center point run [; run S1, no hydrogen and no hexene 9; run S3, no hydrogen, no hexene, and no scavenger 2).
Figure 6. Effect of scavenger on polymerization rate (center point run [; run S14, 0.1 g scavenger 9; run S4, no scavenger 2).
period, which was reduced from 50 min at 62 °C to 15 min at 80 °C. No explanation was given for this phenomenon in their paper. Chakravarti et al.9 investigated both bridged and unbridged metallocene catalysts. They also found an induction period that seemed to increase with decreasing comonomer fraction in the gas phase. Since they did not mention the structure of their catalysts and how they were supported, it is difficult to compare their results with our research. Hammawa et al.15 studied the effects of aluminum alkyls on polymerization rate in a gas-phase reactor with (n-BuCp)2ZrCl2. They found lower initial activity when Al:Zr was higher than 200. A peak in the rate was observed after 200 min of polymerization. It was also found that the effectiveness of the aluminum alkyls in reducing the initial catalyst activity followed the order triethyl aluminum > triisobutyl aluminum > tri-n-octyl aluminum. Kumkaew et al.14 studied the same catalyst with molecular sieves as support. Induction periods were also observed in both gas-phase and slurry polymerization. In summary, the phenomenon of a low initial rate followed by a rate increase has been exclusively observed in ethylene polymerization with supported metallocenes. No report of rate increase or induction period has been found using unsupported metallocenes, i.e., in solution processes. As observed in the current work, the rate increase is likely to be accompanied by low catalyst activity, indicating that, for some reason, a significant portion of the catalyst sites are inhibited during the early stage of polymerization. As the polymerization goes on, the catalyst sites are activated gradually. So far, no widely accepted explanation has been given for the cause of the rate increase or induction period. Further experiments were performed to investigate potential causes. Sequential Experiments. Since the results of the screening experiments did not reveal the cause of the low catalyst activity and the rate increase, sequential experiments were conducted. Because the screening experiments showed that stirring speed had no significant effect on all responses, the stirring speed was fixed at 225 rpm in the sequential experiments, instead of being adjusted as an influencing factor. Starting with the center point of the screening experiments as a basis, a new run (run S1) was conducted, in which both hydrogen and hexene were removed from the recipe. In this run, shown in Figure 5, the rate increase still occurred, and no significant increase in catalyst activity was observed. Next, scavenger was also removed, and another run was conducted (run S3). As shown in Figure
5, during the 90 min polymerization, the catalyst activity increased significantly, and no rate increase was observed, although no apparent decay was found either. Without scavenger, the catalyst activity (∼17 000 g PE mmol-1 Zr 100 psi-1 h-1) is about 4 times that at the center point of the screening experiments (∼4000 g PE mmol-1 Zr 100 psi-1 h-1). It is also noted that the new run without scavenger is a homopolymerization run, in which the catalyst activity is expected to be lower than that for copolymerization under similar operating conditions. However, this homopolymerization run still shows great enhancement in the catalyst activity over the center point copolymerization run. Therefore, it appears that the scavenger is the most plausible cause of both the low catalyst activity and the rate increase. To confirm this conclusion, two additional runs were conducted to investigate the effect of scavenger on the polymerization rate. By keeping all operating conditions the same as the center point of the screening experiments, one run was conducted using no scavenger at all and another was conducted with 0.1 g of scavenger, rather than the 0.6 g of scavenger at the center point. The results, shown in Figure 6, clearly demonstrate the effect of scavenger on both the catalyst activity and the polymerization rate. At the center point of the screening experiments, the catalyst activity is only approximately 4000 g PE mmol-1 Zr 100 psi-1 h-1 and there is a significant induction period. With 0.1 g of scavenger, the catalyst activity increased to about 24 000 g PE mmol-1 Zr 100 psi-1 h-1, which is 5 times higher than at the center point of the screening experiments. The rate profile looks like a very typical ethylene polymerization with a metallocene catalyst, although a very small rate increase rather than a decrease may be occurring between 20 and 50 min of reaction. When no scavenger was added, the polymerization rate looks like a typical metallocene-catalyzed ethylene polymerization, namely, a large peak at the beginning followed by a gradual decay. The peak catalyst activity reached is about 44 000 g PE mmol-1 Zr 100 psi-1 h-1, which is 11 times the activity achieved for the center point runs. Therefore, these two runs confirmed that high scavenger levels were responsible for both the low catalyst activity and the rate increase observed in screening experiments. To obtain more data for kinetic modeling, several more runs without scavenger were carried out. In these runs, no rate increase was observed, and the catalyst activities were similar to the range reported by Karol et al.23 These results further confirmed the dramatic effect of scavenger on the rate profile and catalyst
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Table 5. Main Effects of Influencing Factors on Polymerization Rate and Catalyst Activity from Screening Experiments and Sequential Experiments
factors
ln(peak rate) ln(sccm/min)
ln(peak activity) ln(g of PE-1 mmol-1 Zr 100 psi-1 h-1)
run time temperature pressure hexene concn H2 concn catalyst MAO scavenger 95% conf intv
0.20 2.23 -0.46 2.96 -0.74 2.44 -1.74 -2.08 0.44
-0.17 1.80 -1.81 3.99 -0.84 0.29 -0.77 -2.94 0.44
significant effect on any response from the screening experiments, the effects of stirring speed are not reported. An ordinary linear regression model, as shown in eq 1, was used to determine the effects in Tables 5 and 6:
P ) a + BX + e
a Note: (1) Numbers in bold are statistically significant at the 95% confidence level. (2) All factors are coded as in Table 3.
Table 6. Main Effects of Influencing Factors on Polymer Properties from Screening Experiments and Sequential Experiments factors
Mn g/mol
Mw g/mol
PDI
SCB SCB/1000 C
run time temperature pressure hexene concentration H2 concentration catalyst MAO scavenger 95% conf intv
503 2634 1414 4097 -4328 2306 3101 -878 3197
-3245 10311 10519 7684 -11120 8613 6980 -6334 7208
-0.564 0.267 0.509 -0.593 0.281 0.270 -0.567 -0.536 0.410
-1.71 1.74 5.81 27.66 2.62 -0.33 1.64 1.22 1.07
a Note: (1) Numbers in bold are statistically significant at the 95% confidence level. (2) All factors are coded as in Table 3.
Table 7. Investigation of Rate Increase factors
ln[P/(1 - P)]b
run time temperature pressure hexene concn H2 concn catalyst MAO scavenger
0.07 -4.61 0.07 1.13 0.07 -2.16 1.56 4.40
a Note: (1) Numbers in bold are statistically significant at the 95% confidence level. (2) All factors are coded as in Table 3. bP is the probability of occurrence of rate increase.
activity. The operating conditions of the sequential experiments are listed in Table 2. Data Analysis: Effects of Influencing Factors. The data obtained from the screening experiments and the subsequent experiments were analyzed to investigate the relative importance of the influencing factors listed in Table 3. The main effect of each influencing factor was estimated using linear regression. Six response variables were analyzed, including polymerization rate, catalyst activity, Mn, Mw, PDI, and SCB. The main effects of each of the eight influencing factors on polymerization rate and catalyst activity are listed in Table 5. Table 6 lists the main effects of each factor on polymer properties. The influence of the various factors on whether there was a low initial rate followed by a rate increase was also investigated, and the results are listed in Table 7. Bold entries in the tables indicate that the effect was significant at the 95% confidence level. Since all experiments were conducted using high enough stirring speeds so that stirring speed did not have a
(1)
where: P is the response variable, a is the coefficient of the constant term, B is a row vector of coefficients for the independent variables and the response variable P, X is a vector of the independent variable settings, and e is the random error term. The values that are reported in Tables 5 and 6 are the B coefficients that are estimated from the data, when the independent variables (the factors) are expressed in scaled form (e.g., -1,+1 using the information in Table 3). There are three problems with using eq 1 and simple linear regression to determine the effects of the independent variables on rate increase: (1) The error terms associated with the polymerization rate are heteroskedastic, which violates the classical regression assumption that the error term does not depend on the independent variables. (2) The “rate increase” response variable is different from the other responses, because it is a logical variable that can only have two values, 1 (having a lower initial rate, followed by a rate increase after a long period of time) or 0 (having no rate increase after a long period of time). As a result, error is not normally distributed for this response. (3) Using eq 1, the model prediction of the probability of a rate increase could be greater than one or less than zero, which has no physical meaning. Therefore, logistic regression,28 as shown in eq 2, was employed for the analysis of the rate increase to address problems 2 and 3:
ln[P/(1 - P)] ) a + BX + e
(2)
The logistic distribution is an S-shaped distribution function, which constrains the estimated probabilities to lie between 0 and 1. The entries in Table 7 reveal how each factor affects the ratio of the probability of having a rate increase to having no rate increase. A positive value of an effect means that an increase in the factor is likely to cause a rate increase. During linear regression, no interaction terms were considered in the empirical models. Due to the limited number of experiments that were conducted, there may be confounding between main effects and two-factor interactions. Table 5 reveals that temperature has a strong effect on the rate profile. Values of 2.23 and 1.80, respectively, for the effects of temperature on peak polymerization rate and peak catalyst activity confirm that high temperatures are associated with large polymerization rates and high catalyst activities. The effects of hexene (2.96 and 3.99, respectively), are also very significant, which is consistent with observations of the comonomer effect by many researchers.10,23,29 The effects of scavenger on polymerization rate and catalyst activity are dramatic. High scavenger levels are associated with a low peak polymerization rate and with low catalyst activity. We speculate that these effects may be caused by fast chain transfer to scavenger and slow reinitiation after chain transfer. When the reaction starts, a large number of active sites immediately experience chain transfer to scavenger and become dormant. The reinitiation rate
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is slow, and the polymerization is therefore somewhat inhibited, leading to low catalyst activity. This is consistent with scavenger being responsible for the low catalyst activity in screening experiments, where, in retrospect, too much scavenger was added to the reactor, especially in runs conducted at high scavenger levels. The effects of MAO on polymerization rate and catalyst activity are somewhat unexpected, because MAO was found to enhance catalyst activity by some researchers.10,23,30-34 Since MAO contains a fraction of trimethyl aluminum, it is expected that excessive MAO may reduce catalyst activity due to the poisoning of the active site by trimethyl aluminum. The negative effect found herein may also result from an interaction effect with scavenger or the catalyst or other factors. Possible slow reinitiation after chain transfer to MAO may also contribute to the negative effect of MAO on catalyst activity. Shaffer and Ray29 reviewed the effect of hydrogen on catalyst activity and summarized that no consistent results were achieved by different independent researchers. Both increases and decreases in catalyst activity were observed with the addition of hydrogen. In the current research, hydrogen was found to have a negative effect on both polymerization rate and catalyst activity. Whether or not hydrogen has an effect on reaction rate is mainly determined by the ratio of the rate constant for reinitiation of active sites after chain-transfer-tohydrogen to the propagation rate constant. If reinitiation is faster than or similar to the propagation rate, hydrogen should not have significant effect on catalyst activity. However, if the reinitiation reaction is slower, hydrogen can result in lower catalyst activity. This appears to be the case in current research. For average molecular weight (Table 6), hydrogen is the most important factor, because chain transfer to hydrogen is the main reaction producing dead polymer. Metallocene catalysts are much more reactive with hydrogen than are Ziegler-Natta catalysts and may have a very small activation energy for the transfer to hydrogen reaction, helping to explain the curious positive effect of temperature on Mw. If higher temperatures increase propagation rates more than chain transfer rates, then average chain lengths will increase. The positive effect of hexene concentration on both number and weight-average molecular weight indicates that hexene (partly by the cosolvent effect) has a stronger influence on propagation rates than on overall chain transfer rates. As expected, high levels of hexene lead to high levels of comonomer incorporation or short-chain branching (SCB). Higher polymerization temperatures and pressures, as well as high levels of MAO, scavenger, and hydrogen may also be associated with more comonomer incorporation. It seems that the residence time is not a very important factor. It only affects PDI and SCB significantly, both of which decrease with increasing residence time. These effects can be explained by the drift of hydrogen and hexene concentrations inside the reactor. In most runs, notably those with high polymerization rates, the concentration of both hydrogen and hexene declined during the early stage of polymerization and then became relatively stable. For example, in run S4, the starting molar fractions of hydrogen and hexene in the gas phase were 2 and 0.6%, respectively. After 30 min of reaction, they dropped to 0.6 and 0.16%, respectively, and then stayed at those levels until the end of
the experiment. With longer residence times, more of the polymer was produced with a stable concentration of hydrogen and hexene, which reduced polydispersity. With longer residence times, more polymers were also produced at lower hexene concentration; thus, lower short-chain branching levels were also obtained. Induction periods and rate increases have been observed by several researchers,8-10,27 but no unanimous explanation concerning the cause had been given. The results in Table 7 and the experiments in Figure 6 indicate that the occurrence of a low initial rate, followed by a rate increase is related to a high level of scavenger in the reactor. This is consistent with the observations of Hammawa et al.,15,34 who showed that aluminum alkyls led to low initial catalyst activity. We speculate that the mechanism for the rate increase is related to a change in the scavenger concentration in the polymer phase over the time of the reaction. When the reaction starts, a large number of active sites experience fast chain transfer to scavenger and become dormant. During the polymerization, the number of dormant sites depends on the competing rates of reinitiation and chain transfer to scavenger. As the volume of the polymer phase increases and the concentration of scavenger in the polymer phase falls, there is a reduction in the fraction of active sites inhibited by scavenger, and the rate of polymerization increases. Temperature is another important factor affecting rate increase. The rate increase phenomenon is more likely to happen at low temperature. We contemplate that the reinitiation of active sites after chain transfer to scavenger is much slower at lower temperatures so that inhibition of catalyst sites is more serious in the early stage of low-temperature runs. Conclusion Ethylene/hexene copolymerization has been performed in a 2 L gas-phase reactor using a silicasupported (n-BuCp)2ZrCl2 metallocene catalyst. Replicate experimental runs revealed that the good reproducibility of measured responses was obtained in this reactor system after modifying the reactor system and the operating procedure. Standard deviations for the hydrogen concentration, hexene concentration, numberaverage molecular weight, weight-average molecular weight, polydispersity, and short-chain branching levels were 363 ppm, 1390 ppm, 1005 g/mol, 2265 g/mol, and 0.13 and 0.34 SCB/1000 C, respectively. The standard deviation of the polymerization rate was higher at high polymerization rates than at lower polymerization rates, and the polymerization rate was reproducible within (13%. The data obtained from a set of PlackettBurman screening experiments, additional experiments, and sequential experiments have been analyzed to investigate the relative importance of experimental factors that influence reactor operating conditions and copolymer properties. The experiments revealed that high scavenger concentrations were the cause of low catalyst activity and an increase in the polymerization rate with time during some experimental runs. The observed rate increase was more pronounced at low operating temperatures than at high temperatures. As anticipated, hydrogen concentration and hexene concentration, respectively, were the most important variables affecting molecular weight and short-chain branching. In addition, hexene enhances the polymerization rate and catalyst activity. MAO and hydrogen both had
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a negative effect on polymerization rate. The data obtained from this experimental study give clues about important reaction mechanisms in this copolymerization system and have provided useful data for mechanistic model development.20-22
(17) Carman, D. J.; Hgarrington, R. A.; Wilkes, C. E. Monomer Sequence Distribution in Ethylene-Propylene Rubber Measure by 13C NMR. 3. Use of Reaction Probability Model. Macormolecules 1977, 10, 536.
Acknowledgment
(19) Hsieh, E. T.; Randall, J. C. Monomer Sequence Distributions in Ethylene-1-Hexene Copolymers. Macromolecules 1982, 15, 1402.
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Received for review September 23, 2004 Revised manuscript received January 10, 2005 Accepted January 25, 2005 IE049067B
