Dynamic Modeling of Polyethylene Grade ... - ACS Publications

Ind. Eng. Chem. Res. 2006, 45, 993-1008

993

Dynamic Modeling of Polyethylene Grade Transitions in Fluidized Bed Reactors Employing Nickel-Diimine Catalysts Dennis P. Lo† and W. Harmon Ray* Department of Chemical Engineering, UniVersity of Wisconsin-Madison, 1415 Engineering DriVe, Madison, Wisconsin 53706-1691

Dynamic simulations of grade transitions are conducted for an industrial fluidized bed polyethylene reactor using a nickel-diimine catalyst. The reactor process model incorporates a kinetic model that predicts polymer properties for nickel-diimine ethylene polymerization. The relationships between reactor process variables and the end polymer properties are determined to be more complex than for conventional early transitionmetal catalysts. In this respect, the kinetic model is demonstrated to be an effective tool for mapping out the reactor steady-state operating regions for a range of polyethylene grades and for examining process issues specific to using these catalysts. Temperature, monomer concentration, and hydrogen composition are the primary manipulated variables for achieving grade transitions in polymer density and melt index. Transitions involving changes in temperature require continual simultaneous adjustment of hydrogen and monomer feed rates to maintain the desired gas composition. Thus, where possible, it is desirable to keep the temperature constant while only changing monomer and hydrogen concentrations when making product transitions to simplify reactor operation. Quick venting and overshoot strategies are demonstrated to aid in improving product transition times. The risk of particle melting is heightened because both temperature and monomer concentration have a large influence on the branching density and the melting point of the polymer. Introduction work,1

In earlier the development of a kinetic model for ethylene polymerization over nickel-diimine catalysts is presented. The kinetic model is able to predict the polymerization rate, molecular weight, and branching characteristics for ethylene polymerization over a wide range of temperatures and monomer concentrations and is in good agreement with experimental data reported in the literature for homogeneous and heterogeneous nickel-diimine catalysts. In this paper, the kinetic model is used to examine the important reactor design and operation issues for industrial fluidized bed reactors (FBRs) using these catalysts. The model is first used to examine the effect of reactor operating conditions on the steady-state polymer properties for heterogeneous polymerization processes. Of particular concern is the ability to operate these reactors over a broad range of temperatures and monomer concentrations such that polymer grades with a wide range of densities and molecular weight can be produced. Temperature influences the polymerization rate, the molecular weight, and the short chain branching distribution of the polymer, while monomer concentration influences the polymerization rate and the polymer branching. Both variables must be balanced to maximize productivity while generating the desired polymer properties (low- or high-molecular-weight polymer, combined with large or small amounts of branching). The exact range of molecular weights, and corresponding levels of branching arising from a range of operating conditions are determined based on kinetic parameters estimated for a particular catalyst. Polymer density and melt index are correlated to molecular weight and branching density, for comparison with existing polyethylene resins manufactured using commercial metallocene and Ziegler-Natta catalysts. A second important area of investigation is the operational strategies of polymerization reactors using nickel-diimine * To whom correspondence should be addressed. Tel.: 608 263 4732/1092. Fax: 608 262 0832. E-mail: [email protected]. † Current address: DuPont Surfaces, Tonawanda, NY 14150.

catalysts. Determining the possible polymer properties is the first step. To produce commercial resin grades, it is necessary to be able operate the reactor to control the polymer properties and to be able to transition from one grade to another efficiently. To perform reactor studies, the kinetic ethylene polymerization model is incorporated into an existing suite of process reactor models contained in POLYRED, which is a polymerization reactor engineering and simulation software package that has been designed and developed at the University of Wisconsin. The work herein focuses on product transition strategies specific to the gas-phase FBR process. For example, in gas-phase reactors, the reactor temperatures must be high enough for increased yields but also controlled to limit the production of low-melting-temperature (highly branched, low-molecularweight) polymer, which can easily foul the reactor. Fluidized Bed Reactor (FBR) Process We have chosen to focus on the gas-phase FBR process, because it is a popular industrial process for catalytic ethylene polymerization and is capable of producing a wide range of high-density polyethylene (HDPE) and linear low-density polyethylene (LLDPE) products.2-6 A process schematic for a FBR is shown in Figure 1. Solids such as catalyst and upstream polymer are fed into the reactor, where they are fluidized and mixed by recirculating gas to form the reactor bed, where polymerization occurs. The gas stream, which consists of monomer, hydrogen, and diluent, are fed at the bottom of the reactor after compression to reaction pressure. In the disengagement zone at the top of the bed, the gas velocity decreases before it is recycled, because of the increase in reactor diameter, and the solid particles drop back into the bed. Recycle gas is cooled through a condenser to remove the heat of polymerization. In condensed-mode operation,3,5,6 a portion of the recycle stream condenses after cooling and vaporizes upon re-entry into the reactor, which increases the heat removal capacity of the reactor. A fraction of the recycle gas stream is

10.1021/ie0580598 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/23/2005

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Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006

Figure 1. Simplified process schematic for a fluidized bed polyethylene reactor.

vented to purge. The bed height is controlled by periodically opening the product outlet valve to remove a portion of the bed. Gas and sorbed species that are entrained with the removed bed particles are volatilized and separated by decompression and recycled back into the reactor. The monomer injection rate is adjusted to control the reactor pressure. The feed rates of other gaseous species must be adjusted simultaneously to maintain a constant gas composition. Hydrogen, diluent, catalyst, and co-catalyst levels are controlled by adjusting their respective injection feed rates. Because polymerization is very exothermic, sufficient heat removal from growing polymer particles is crucial. Because of high heat transfer resistances across the particle-gas boundary layer, particle surface temperatures can be higher than the bulk gas temperatures, especially when particles have just been introduced into the reactor and consist of almost entirely catalyst.7-11 If particle temperatures exceed the polymer melting point, particles can overheat, resulting in softened and agglomerated polymer chunks in the reactor. In severe cases, hot spots, disruption of mixing and fluidization, massive polymer melting, and reactor shutdown can occur. Gas circulation rates must be high enough to provide enough fluidization for heat transfer but low enough to prevent entrainment of solid particles in the recycle stream. Controlling particle morphology is also necessary for uniform mixing and heat transfer. Particle morphology is affected by the catalyst particle size, particle residence times, and catalyst productivities. Because of the high gas circulation rates, the percent conversion per pass is very low. Property Ranges for Polyethylene Grades Because polyethylene products are classified by their polymer density and melt index, it is necessary to be able to predict these properties from the chain microstructure. Density and melting point are related to the polymer crystallinity and, thus, are correlated to the polymer branching density. The melt index is related to the polymer melt viscosity, which is heavily dependent on the molecular weight of the polymer. There are no published reports that the catalyst modeled here produces any significant degree of long chain branching; thus, long chain branching is not considered in this study. The creation of short-chain branches is considered in some detail. Longer short-chain branches (with a length of six carbons or greater) are reported12-15 but have a tendency to occur with a frequency of 0.94 g/cm3, and their polymer chains generally contain 1 g/10 min. Using the property correlations for nickel-diimine catalysts presented below, the required polymer chain length and branching density can be determined for different grades of polyethylene (Table 1). Density. Polyethylene density data over a wide range of branching densities for various nickel-diimine catalysts are available in industrial patents by Exxon and Phillips.22,23 In Figure 4, the data is plotted along with that for polyethylene produced using a Univation metallocene catalyst.24 These data can be fit using logarithmic functions of the branching density. The data set from the Exxon nickel catalyst compares well with that from the Univation metallocene catalyst, with slightly lower densities for a given branching frequency being obtained from the nickel catalyst. Although the branch length distribution of polyethylene from the metallocene catalyst is uniform (butyl branches from 1-hexene incorporation), the branch lengths obtained from the nickel catalyst are mainly methyl but also contain various longer branch lengths. This distribution of branch lengths may explain the slightly lower densities exhibited by the nickel-diimine polyethylene for a given number of branch density. Reported data from the Phillips nickel catalyst are widely scattered, and much higher densities are reported for a given branch length, relative to the Eastman and Univation data sets. Melt Index. Melt index versus chain length data are available for polyethylene produced using a single-site metallocene

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 995

Figure 2. Melt index (MI) versus density plots for various commerical ExxonMobil (left) and Dow Chemical (right) polyethylene grades produced using conventional Ziegler-Natta type early transition-metal catalysts. (Data obtained from refs 19 and 20.) Table 1. Polymer Property Ranges for Various Polyethylene Gradesa polyethylene (PE) grade high-density polyethylene, HDPE high MI mid MI low MI linear low-density polyethylene, LLDPE high MI mid MI low MI very low-density polyethylene, VLDPE mid MI low MI a

density (g/cm3) >0.94 >0.94 >0.94 0.915-0.935 0.915-0.935 0.915-0.935 0.88-0.91 0.88-0.91

melt index, MI (g/10 min)

branches per thousand carbons, BPTC

degree of polymerization, DPn

6-80 1-6 0.1-0.6

2)

1000 BPTC )

K+1

2 (3c)

[Pk+1] ∑ k)1

∑ [Pk]

k)1

(6a)

Ind. Eng. Chem. Res., Vol. 45, No. 3, 2006 997 Table 2. Fitted Kinetic Parameters to the Eastman Supported Catalysta ktrap k0 Ea

kinsert s-1

2.55 × mol 2.8 kcal/mol 104 L

kctHb

kctM

103 s-1

104 s-1

4.52× 2.4 kcal/mol

103 L

1.03× 8.7 kcal/mol

kw1 s-1

4.4× mol 5.4× 103 kcal/mol

kw2

109 s-1

1.51× 12.9 kcal/mol

1010 s-1

4.23× 13.3 kcal/mol

kw 7.02× 1010 s-1 12.3 kcal/mol

a Reaction conditions: gas-phase polymerization, 65-80 °C, 200-800 psi, MAO co-catalyst. Data taken from ref 1. b Chain transfer to hydrogen parameters are estimated using data from Lavoie et al.27 and Lo.29

where

[Pk] ) ψk[Pk-1]

(1 < k e K + 1)

[P1] ) ψ1kinsert

(

ψ k ) ψk

kw1

∑k [Rk]

kw2

,

(6c) kw

,

(6b)

ktrap[M] ktrap[M] ktrap[M]

)

(6d)

Polymer Branching Distribution:

BPTCk )

1000[Pk+1] (7)

K+1

2

∑ [P ] k′

Figure 7. Comparison of relationships between reactor process variables and polymer properties for ethylene polymerization using nickel-diimine catalysts and conventional early transition-metal catalysts.

k′)1

Incorporation of Kinetic Model in POLYRED After the relationship between the operating conditions and the polymer properties is known, the kinetic model can be incorporated into reactor models, so that process issues such as reactor operation and transition strategies can be investigated. The reactor analyses are performed using POLYRED,29-31 a dynamic simulation software package for reactor engineering and design of polymerization reactor systems. To incorporate the nickel-diimine ethylene polymerization kinetic model, the POLYRED Ziegler-Natta chemistry kinetics module is adapted using POLYRED built-in user functions,29 which do not require hard-coded modifications to the Fortran subroutines. By redefining the existing rate constant parameters and by introducing new user variables, POLYRED user functions can be used to calculate the rate of polymerization and molecular weight distribution, as well as the instantaneous branching distribution for ethylene polymerization over nickel-diimine catalysts. Cumulative Bulk Polymer Properties. The concentration of branches of length methyl to hexyl-and-longer in bulk chains is given by eq 8, where Bk is the concentration of branches of length k; Qf is the total mass feed rate; Qo is the total mass outflow; mbed is the mass of reactor bed; H is bed height; TC is the total methylene concentration in bulk polymer chains; BPTCk denotes the number of branches of length k per thousand carbons; and fBPTC,k is the fraction of branches of length k in the branching distribution.

Qo[Bk] 1 d[Bk] Qf[Bk,f] dH ) + ktrap[M][Pn+1] - [Bk] dt mbed mbed H dt (k ) 1, ..., 6) (8) The total concentration of methylene units in all bulk chains is given by

d[TC] dt

)

Qf[TCf] mbed

K+1

+ 2ktrap[M]

[Pk] ∑ k)1

Qo[TC]

-

mbed 1 H

[TC]

dH dt

(9)

The cumulative number and relative branching distributions are then calculated as follows:

[BPTCk] ) fBPTCk )

1000[Bk] [TC]

BPTCk 6+

(k ) 1, ..., 6) (k ) 1, ..., 6)

(10) (11)

BPTCi ∑ i)1

Here, the long-chain hypothesis is again assumed to hold, whereby polymer chains are very long and, thus, on average, have the same branching density and branch length distributions. The empirical polymer property correlations (previously discussed) based on the branching frequency and molecular weight are used to calculate the cumulative bulk polymer density, melt index, and melting temperature. Steady-State Operating Regions Because of the distinctly different polymerization chemistry, the relationship between operating conditions and polymer properties for nickel-diimine catalysts is more complex than for conventional early transition-metal catalysts as illustrated in Figure 7. With traditional, early transition-metal catalysts, four process variables are used to regulate the polymerization rate, chain branching, and chain length. The comonomer composition can be manipulated independently to control the branching density. For the case of LLDPE production with metallocene catalysts,24 the molar ratio of comonomer to ethylene in the gas phase is varied from 0.01 to 0.05 to achieve polyethylene densities in the range of 0.915-0.935. Aside from certain chromium catalysts, chain transfer rates to hydrogen are commonly high enough to be able to regulate the molecular weight with hydrogen concentration. Some metallocene catalysts exhibit extremely high rate constants for chain transfer to hydrogen; thus, only very small concentrations of hydrogen are need to produce the desired-molecular-weight polymer. By

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contrast, for most early transition-metal catalysts, rate constants for chain transfer to hydrogen are quite small; thus, a large excess of hydrogen is required to control molecular weight. Catalyst concentration and temperature can be used to control the production rate. The temperature is often chosen based on process considerations. In gas-phase FBRs, the operating temperature is chosen to avoid particle overheating and to enable operation in condensed mode. The presence of the R-olefin comonomer is also generally observed to enhance the overall polymerization rate.32-34 This is contrary to standard copolymerization kinetic theory, because R-olefins have lower reactivities than ethylene. Explanations for the “comonomer effect” are varied and include both physical reasons such as enhanced ethylene sorption and more complete catalyst particle fragmentation in the presence of copolymer, and chemical reasons such as promoting activation of additional sites. Kissin and co-workers34,35 have proposed the formation of stable β-agostic metal-C2H5 complexes, which slow ethylene polymerization but are bypassed during R-olefin polymerization. When hydrogen is present, ethylene homopolymerization rates are depressed, because the ethylene insertion rate following chain transfer to the monomer is slow. Adjustments to the monomer concentration or temperature can be made in response to the influences of hydrogen and comonomer on the rate to attain the desired overall reactor productivities. For the case of nickel-diimine catalysts, the situation is both simpler, because there are only three process variables to manipulate (no comonomer is used), and more complex, because the relationships between process variables and polymer properties are more interrelated. Temperature and monomer concentration, which significantly impact the polymerization rate, are also used to control the molecular weight and branch density. In addition, two process variables are used to regulate each polymer property: hydrogen and temperature control the molecular weight, whereas the desired branch density and polymerization rate are achieved by adjusting both temperature and pressure (monomer concentration). Moreover, control of either branch density or molecular weight in isolation is more difficult because temperature impacts both properties. Similar to its effect on ethylene polymerization with early transition-metal catalysts, hydrogen is observed to reduce the overall activity for certain nickel catalysts. Because the molecular weight, polymerization rate, and branching density for nickel catalysts are all regulated simultaneously by two process variables, it is convenient to use the kinetic model to map out the steady-state polymer property contours as a function of reactor pressure, temperature, and hydrogen concentration (see Figures 8-15). In these calculations, the bulk gas contains no diluent and consists only of ethylene and hydrogen. Stern’s correlation36 is used to estimate sorbed monomer concentrations for input into the kinetic model. These contour diagrams have practical utility, because they demonstrate how to properly manipulate the reactor operating conditions to obtain desired polymer properties. Conversely, they also show the range of possible polymer properties for a given range of operating conditions. Finally, they illustrate the possible paths available between starting and ending operating conditions when transitioning between two different product grades. The plots in Figures 8 and 9 depict contours of constant branching density, chain length, and catalyst activity per active site (turnover frequency (TOF), given in units of s-1) over a range of reactor temperatures and pressures for four different levels of hydrogen in the gas phase. In each plot, the ratio of hydrogen to ethylene is held constant so that changes in reactor

Figure 8. Gas-phase polymerization property contour map for (s) the number of branches per thousand carbons (BPTC), (- ‚ -) the degree of polymerization (DPn), (- - -) the turnover frequency (TOF, expressed in units of s-1) for no hydrogen (top), and 10 mol % hydrogen or yH2/yC2 ) 0.11 (bottom). Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickeldiimine catalyst.

pressure are caused by concomitant changes in hydrogen and monomer concentration. From the shape of the contours, it is evident that, if the reactor temperature is changed, the monomer concentration must be adjusted to restore the branching density to its original level. The converse is also true if the monomer concentration is changed. This behavior is important for reactor operation, because it means that monomer concentration and temperature must be constantly balanced either to maintain the current polymer property values, in response to process upsets, or to transition to new values. The polymerization rate also changes if the temperature or monomer concentration are adjusted; however, the overall reactor productivity can be kept constant by adjusting the catalyst feed rate, as long as catalyst residues do not become too high. Contours of constant branching density extend upward to higher monomer concentrations as temperature is increased. This is because higher monomer concentrations create higher monomer trapping rates, which balance the higher chain walking rates at higher temperatures. Conversely, constant catalyst activity contours descend to lower monomer concentrations as the temperature is increased to maintain the same rate of polymerization. For each plot, lines of constant chain length are parallel with the pressure axis, because ratios of hydrogen to ethylene are held constant, and chain transfer to monomer and hydrogen is dependent only on temperature (other chain transfer mechanisms are considered negligible). As the hydrogen level is increased (progressing from Figure 8 to Figure 9), chain transfer rates to hydrogen are increased, and the DPn contours shift horizontally to lower temperatures.


Figure 10. Constant DPn contours with temperature and yH2/yC2 for gasphase polymerization. Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

Figure 9. Gas-phase polymerization property contour map for (s) BPTC, (- ‚ -) DPn, (- - -) TOF (s-1) for 20 mol % hydrogen or yH2/yC2 ) 0.25 (top) and 30 mol % hydrogen or yH2/yC2 ) 0.43 (bottom). Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

Branching density is more sensitive to monomer concentration at low reactant pressures (PH2 + PC2 < 5 atm). Under morecommon operating conditions (PH2 + PC2 ≈ 20-30 atm), temperature has a much greater impact on the branching density, relative to monomer concentration. For example, at 323 K and 30 mol % hydrogen (yH2/yC2 ) 0.43) in the gas phase (Figure 9, bottom), the reactant pressure must be reduced from 33 atm to 15 atm to increase the branching density from 5 BPTC to 10 BPTC. An increase in temperature by ∼15 K is sufficient to bring about the same change in branching density. Polymer chain length is more easily regulated by temperature than by hydrogen concentration (assuming a maximum hydrogen composition of 30 mol % in the bulk gas). At 340 K, a change in hydrogen composition from 0 mol % to 30 mol % in the bulk gas decreases the chain length from ∼4500 to 2000. Increasing the temperature by 35 K has the same effect. This is also illustrated in Figure 10 from the shape of contours of constant chain length. Because the contours are parallel, there are interesting consequences to the influence of temperature on the chain length at different hydrogen compositions (and vice versa). For instance, a change in DPn from 5000 to 1800 requires an increase in temperature by ∼40 K, regardless of hydrogen composition. Only the initial and final temperatures vary with hydrogen composition. Any adjustments in temperature to achieve the desired polymer density will also affect the molecular weight. Provided the temperature change is not too large, hydrogen levels can be altered to compensate. Because of the limited influence of hydrogen on molecular weight, large transitions in polymer density (requiring simultaneous changes in temperature and monomer concentration) will necessitate a change in the melt

Figure 11. Gas-phase polymerization property contour map for (s) density and (- - -) melt index (MI) for no hydrogen (top) and 10 mol % hydrogen or yH2/yC2 ) 0.11 (bottom). Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

index. Manipulation of monomer concentration alone to regulate polymer density will also cause small variations in the molecular weight, because the molar ratio of hydrogen to monomer will change. However, these variations are smaller and are more easily balanced by hydrogen level adjustments. Thus, minor transitions in polymer density are more simply handled by changes in monomer concentration than by changes in temperature. Figures 11 and 13 plot the contours of density and melt index over the same range of temperatures and pressures as Figures 8 and 9, respectively. The density and melt index are calculated using the correlations presented in Figures 4 and 5. The operating regions for various grades of polyethylene, based on

1000


Figure 12. Gas-phase polymerization contour map for ∆T ) Tmelt - Tbulk for no hydrogen (top) and 10 mol % hydrogen or yH2/yC2 ) 0.11 (bottom). Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

the polymer property ranges listed in Table 1, are superimposed on both plots. Generally, this supported nickel catalyst produces a high-molecular-weight, mid-melt-index polymer. Consequently, higher-density polyethylene grades, which must be produced at relatively low temperatures to limit the branching density, have very low melt index (hereafter abbreviated as MI) values ( 30 atm; 313 K < T < 320 K) where low-MI HDPE grades can be produced (see Figure 12). Similarly, the region of operation for mid-MI LLDPE is quite restricted (P > 35 atm; 350 K < T < 357 K). However, lowMI LLDPE can be produced over a broad range of operating conditions. At lower hydrogen levels (35 atm and over a very narrow temperature range of 350-355 K. There is a fairly large operating window for manufacturing low-MI LLDPE. Mid-MI VLDPE can be produced at temperatures above ∼375 K; however, the polymer will melt under these conditions (Figure 14, bottom). Low-MI grades of VLDPE can be produced with little danger of

Figure 13. Gas-phase polymerization property contour map for (s) density and (- - -) melt index (MI) for 20 mol % hydrogen or yH2/yC2 ) 0.25 (top) and 30 mol % hydrogen or yH2/yC2 ) 0.42 (bottom). Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

overheating; however, production occurs only at low pressure and, consequently, low polymerization rates. Figure 15 shows the melt index ranges for a given molar ratio of hydrogen to ethylene concentration for the supported nickel-diimine catalyst. The contours confirm that this particular catalyst is best suited to produce low-MI polyethylene. To make polyethylene with MI g 1 at 30 mol % hydrogen, the temperature must be at least ∼358 K. Unfortunately, at these temperatures, only highly branched VLDPE can be produced, for which the high risk of melting is a problem. Figure 16 shows approximate hydrogen sensitivity levels for the different types of conventional early transition-metal catalysts. Comparison with Figure 15 reveals that the hydrogen sensitivity of the nickel catalyst is similar to that of ZieglerNatta catalysts. However, the polymer from Ziegler-Natta catalysts, which are multisite in nature, will have high polydispersity (broad molecular weight distributions). Consequently, the melt index of Ziegler-Natta polymer for a given weightaverage chain length will be much higher than that from the single-site nickel-diimine catalyst, because of the presence of low-molecular-weight chains. A modified nickel-diimine catalyst would be required to facilitate production of higher-MI polyethylene. The incorporation of less bulky ligands would not only increase rates of chain transfer to monomer, thereby reducing polymer chain lengths, but also reduce the rates of chain walking and subsequent branch formation. Such a catalyst also would enable the production of higher-density polyethylene, with lower chain lengths, at lower temperatures and pressures. The greater number of longer shortchain branches found in more highly branched polymer from


Figure 16. Melt index response to hydrogen for early transition-metal catalyst families (chromium, Ziegler-Natta, metallocene). (Data taken from ref 23.)

Figure 14. Gas-phase polymerization contour map for ∆T ) Tmelt - Tbulk for 20 mol % hydrogen or yH2/yC2 ) 0.25 (top) and 30 mol % hydrogen or yH2/yC2 ) 0.42 (bottom). Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

Figure 15. Constant melt index (MI) contours with temperature and yH2/ yC2 for gas-phase polymerization and supported nickel-diimine catalyst. Bulk gas consists only of hydrogen and ethylene. Model calculations using kinetic parameters for the supported Eastman nickel-diimine catalyst.

nickel-diimine catalysts would also increase the melt index, albeit at lower polymer densities. Polyethylene Grade Transitions Knowing the range of operating conditions required to produce a particular grade of polyethylene is the first step toward achieving “drop-in” capability for a new polymerization catalyst into existing process reactor technologies. To achieve the high productivities and efficiencies required for a commodity polymer manufacturing process, it is also necessary to be able to control and sustain the desired reactor operating conditions to minimize drift in polymer properties, and to be able to utilize effective reactor-grade transition strategies. Based on the findings in the

previous section, some basic strategies are used to perform polyethylene-grade transitions in an FBR. Product transitions are typically conducted in a manner that minimizes either the transition time or the amount of off-spec product. In gas-phase reactors, the transitions are typically limited by the large gas inventory, long residence times, and broad residence time distributions for both the polymer and the gas phase.37 Some of the basic transition strategies used in industrial practice include (i) quick venting during the initial stages of the transition to more quickly change the composition or pressure; (ii) initially overshooting the final values of the manipulated variables; and (iii) temporarily dropping the reactor bed level to reduce the solid polymer residence time. Figure 7 shows the process variables used to control polymer properties and conduct grade transitions for conventional early transition-metal catalysts and nickel-diimine catalysts. For early transition-metal catalysts, comonomer and hydrogen feed rates are manipulated to regulate the gas-phase composition and to control the polymer density and melt index. Temperature is also used to regulate the polymer melt index for certain chromium catalysts, and in cases where the hydrogen response is not enough to effect the desired change in molecular weight. Because the hydrogen consumption rates for Ziegler-Natta and chromium catalysts are low and require a large excess of hydrogen, transitions involving reductions in hydrogen concentration (decrease in melt index) are inherently very slow, being limited by the length of time it takes for the excess hydrogen to wash out. Increasing the vent flow reduces the gas-phase residence time and is one method that has been used to successfully remedy this problem. Washing out hydrogen is less of an issue with metallocene catalysts, because hydrogen concentrations are much lower and a significant fraction is consumed by reaction. Product transitions for nickel catalysts involve an additional degree of complexity, because both gas composition (monomer and hydrogen concentration) and reactor temperature are changed to regulate the polymer density and melt index. When a transition involves a change in temperature, both the density and melt index will change, unless hydrogen or monomer concentrations are changed to compensate. Similar to ZieglerNatta and chromium catalysts, hydrogen consumption rates for nickel catalysts are low. Increasing the reactor vent flow can be used to purge the gas, and to accelerate the transition times, where necessary.37 The efficiency of the transition will also be dependent on the relative response dynamics of the gas composition variables and the reactor temperature. For example, if the response in hydrogen composition is much slower than

1002


Table 3. Reactor Parameters

Table 4. Simulation Cases

reactor parameter

value

bed height bed volume disengagement volume fraction of isopentane condensed heat of polymerization catalyst half-life at 353 K injection feed temperature

10 m 49 m3 49 m3 1 -25 000 cal/mol 30 min 300 K

the response in bed temperature, there may be large fluctuations in the molecular weight before the transition is complete. Two of the strategies used in industrial practice for gas-phase polymerization reactors with early transition-metal catalysts are used here, including increased purge venting and overshooting the final values of the manipulated variables to accelerate the transition to the new steady state. Catalyst feed and diluent feed are adjusted during grade transitions to maintain the overall reactor productivity and to aid in heat removal, respectively. The scope of this work does not include developing advanced process control strategies for polyethylene reactors using nickel-diimine catalysts. Nor is the objective to develop an optimization strategy for these grade transitions, as others have done previously38,39 for polymerizations using early transitionmetal catalysts. The goal is simply to illustrate how reactor process variables can be manipulated to achieve the desired polymer properties with nickel catalysts. Simulation Conditions. The reactor parameters are shown in Table 3. These parameters remain constant for all of the simulation case studies. There is no upstream powder feed stream; only catalyst, cocatalyst, hydrogen, diluent, and ethylene are fed to the reactor. When isopentane is present, the reactor is operated in condensed mode. For simulation purposes, the entire diluent fraction in the recycle stream is condensed. It is assumed that the fraction of diluent in the reactor can be adjusted to achieve the desired rate of heat removal through diluent vaporization for reactor cooling. Bed temperature is controlled by manipulating the recycle stream temperature, and by adjusting the diluent fraction, if necessary. The ethylene and hydrogen feed rates regulate the ethylene and hydrogen concentrations, respectively. The catalyst kinetic parameters for a supported nickel-diimine catalyst are used (see Table 2). For these reactor studies, temperature-dependent catalyst deactivation is included. The polymer in the reactor bed consists of a low-MI grade of LLDPE. In performing the grade transitions, the local controllers for bed level, pressure control, feed rates, recycle stream temperature, etc. were assumed to operate perfectly. The higher level supervisory control then adjusted the set points of these controllers In conducting these simulations, the relationships between process operating variables (temperature, pressure, hydrogen composition) and polymer properties in the previous section are applied: (1) Any changes in temperature must be balanced by appropriate changes in monomer and hydrogen concentration if the polymer properties are to be conserved (and vice versa) (2) Minor transitions in density are better handled by changing the ethylene concentration rather than the temperature, because molecular weight is relatively independent of ethylene concentration but is heavily dependent on temperature. (3) Large changes in density require changes in temperature; hydrogen levels must be adjusted simultaneously to prevent a change in molecular weight. (4) Large changes in melt index require changes in temperature, because the sensitivity to hydrogen is limited (due to low

base pressure (atm) temperature (K) recycle stream temperature (K) residence time (h) vent flow (cm3/s)

35 350 320 2.8 6000

case X

case Y

case Za

31 350 320 2.7 6000

19 336 306 2.8 6000

44 338 316 2.6 6000

14.1 0.9156 2071 0.52 7.3

7.9 0.9250 2055 0.53 7.8

Polymer Properties total BPTC 14.4 14.2 density (g/cm3) 0.9154 0.9156 degree of polymerization, DPn 1576 2063 melt index, MI (g/10 min) 1.0 0.53 production (ton/h) 7.1 7.6 ethylene isopentane hydrogen catalyst co-catalyst

Injection Feed Rates (g/s) 2200 2330 0 10 5.9 3.5 0.25 0.26 1.2 1.2

2135 60 3.3 0.22 1.2

2470 50 8 0.18 1.2

ethylene isopentane hydrogen

Gas Mole Fractions 0.700 0.794 0.000 0.006 0.300 0.200

0.650 0.050 0.300

0.678 0.017 0.304

Sorbed Concentrations 0.516 0.516 0.0868 0.0506

0.295 0.0821

0.678 0.0806

ethylene (mol/L-ampol) H2/ethylene ratio a

Case X conditions are the initial conditions for case Z.

chain transfer rates of this catalyst, and low gas sorption in amorphous polymer); the monomer concentration must be adjusted simultaneously, to prevent a drift in density. (5) Polymerization at high temperature and low ethylene concentration is at high risk for particle overheating and melting, because the polymer produced will have high branching densities and low melting points. Table 4 lists the base and steady-state final reactor conditions used for the reactor transitions. The base case conditions are the initial bed and bulk gas conditions. The process residence time is chosen to maximize catalyst yield and control the metal content in the polymer. Therefore, a residence time ∼5 times greater than the catalyst half-life is used. The catalyst feed rate is adjusted up or down to maintain the desired productivity level. Figure 17 illustrates the product transitions as paths in temperature and pressure superimposed on the contour plots of constant DPn and polymer density. The contour plots are not dependent on the inert isopentane diluent in the gas phase, because it does not participate in the reaction; therefore, the plots are presented as a function of the total partial pressures of the reactive species (monomer and hydrogen) and temperature. Cases X and Y demonstrate transitions from a higherMI grade (1.0 g/10 min) to a lower-MI grade (0.5 g/10 min) of low-MI LLDPE, while maintaining a constant density. In Case X, the hydrogen concentration is the primary manipulated variable used to regulate the melt index, whereas, in Case Y, temperature is used. In both cases, hydrogen, monomer, catalyst, and diluent injection feeds are adjusted during the transition to prevent the density from changing and also to sustain the reactor cooling capacity and productivity. Case Z demonstrates a transition (X f Z) from a lower-density (0.915 g/cm3) grade to a higher-density (0.925 g/cm3) grade of low-MI LLDPE. Temperature and ethylene concentration are manipulated simultaneously to bring about the density change, whereas hydrogen feed is altered to keep the polymer melt index constant. As in transitions X and Y, the reactor pressure and the species injection feeds are also adjusted. The path shown (Y f Z) illustrates how the same transition in density as Case Z could be made by holding the temperature constant, while


Figure 18. Graphical depiction of case X, showing variation of the polymer chain length and polymer melt index): (s) instantaneous polymer and (- - -) bulk polymer.

Figure 17. Transition pathways (base f X, base f Y, X f Z Y f Z) overlaid on gas-phase polymerization contour maps for (s) density and (- - -) melt index (MI) for 20 mol % hydrogen or yH2/yC2 ) 0.25 (top) and 30 mol % hydrogen or yH2/yC2 ) 0.42 (bottom). Model calculations using kinetic parameters for the supported nickel-diimine catalyst.

increasing monomer concentration, and keeping the same ratio of hydrogen to monomer concentration. Because temperature is held constant, this transition is less complex than Case Z; for the sake of brevity, the results for this simulation are not presented here. Case X: Transition in Melt Index with Hydrogen Concentration. Case X demonstrates a grade change in melt index from 1.0 g/10 min to 0.53 g/10 min, resulting from a decrease in the hydrogen gas mole fraction from 0.3 to 0.2. Because of the low hydrogen consumptions rates, the hydrogen response is slow and limits the speed of the transition. Quick venting is used to reduce the gas-phase residence time. To illustrate the benefit of quick venting, the transition is performed for the case of constant venting at 6000 cm3/s, and for the case of a pulse increase in the vent flow from 6000 cm3/s to 60 000 cm3/s during the first 10 minutes of the transition. Figure 18 shows the resulting transitions in DPn and melt index for both venting conditions. The pulse increase in vent flow shortens the response time of the hydrogen gas composition (Figure 19); the hydrogen composition is quickly reduced, initially overshooting the final steady-state value. The grade transition is made within ∼20 000 s. When constant venting is used, the hydrogen gas mole fraction is steadily reduced to the final value but does not overshoot it. The resulting transition is much slower, taking almost twice as long (∼40 000 s). To ensure a return to the same polymer density at the end of the transition, the total reactor pressure must be decreased to maintain the same monomer concentration in the reactor (Figures 20 and 21). One consequence of the quick pulse venting is that the monomer injection feed rate must also be pulsed upward initially, to mitigate a sharp decrease in the total reactor pressure and

Figure 19. Graphical depiction of case X, showing variation in hydrogen control. The hydrogen injection rate is shown in the top panel, and the response in hydrogen gas mole fraction is shown in the bottom panel.

Figure 20. Graphical depiction of case X, showing the variation in total branch frequency and polymer density: (s) instantaneous polymer and (- - -) bulk polymer.

monomer concentration (Figure 22). This also prevents any large fluctuations in the polymer density during the transition, which could result in the production of low-melting-point polymer that is prone to agglomeration. A net increase (from the base case) in the monomer injection feed rate by ∼5% is actually required to compensate for the decrease in hydrogen feed and also the slight increase in overall productivity. Obviously, the monomer injection feed rate action could be further optimized to better offset the change in pressure from increased venting.

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Figure 21. Graphical depiction of case X, showing the variation in sorbed ethylene concentration. (Sorbed concentration calculated using Stern’s correlation.36)

Figure 23. Graphical depiction of case Y, showing the variation in temperature control soak and ramp strategy (shown in the top panel) and reactor pressure (shown in the bottom panel).

Figure 22. Graphical depiction of case X, showing the variation in pressure control. The monomer injection feed rate over the initial 10 000 s is shown in the top panel, and the reactor pressure (PC2 + PH2) is shown in the bottom panel.

Figure 24. Graphical depiction of case Y, showing the variation in monomer injection rate over the initial 25 000 s (shown in the top panel) and sorbed monomer concentration (shown in the bottom panel). (Sorbed concentration calculated using Stern’s correlation.36)

Case Y: Transition in Melt Index with Temperature and Pressure. Instead of changing the hydrogen composition, the temperature is reduced from 350 K to 336 K to perform the same transition in melt index as in Case X (Figure 23, top). A soak-ramp strategy for the recycle stream temperature, where the soak overshoots the final steady-state value, is effective in bringing about a rapid change in bed temperature. To keep the polymer density constant, the monomer concentration is simultaneously reduced by reducing the monomer injection feed rate. The hydrogen injection feed rate is also reduced to keep the hydrogen gas mole fraction at 0.3 after the reduction in

temperature. As a result, the total reactor pressure decreases from 35 atm to 19 atm (Figure 23, bottom) after the transition is complete. The vent flow is pulsed to 60 000 cm3/s over the first 1000 s to quickly purge the excess hydrogen and monomer from the reactor. The monomer injection feed rate is first reduced to 0 g/s, to quickly reduce the monomer concentration (Figure 24), and then adjusted several times during the start of the transition to compensate for the increased venting and to minimize further fluctuations in the monomer concentration and polymer density. The hydrogen injection rate is also initially reduced to 0 g/s, to


Figure 28. Graphical depiction of case Z, showing the variation in total branch frequency and polymer density: (s) instantaneous polymer and (- - -) bulk polymer.

Figure 25. Graphical depiction of case Y, showing the variation in hydrogen gas injection feed rate over the initial 50 000 s (shown in the top panel) and hydrogen gas mole fraction (shown in the bottom panel).

Figure 26. Graphical depiction of case Y, showing the variation in polymer chain length and polymer melt index: (s) instantaneous polymer and (- - -) bulk polymer.

Figure 27. Graphical depiction of case Y, showing the variation in total branch frequency and polymer density: (s) instantaneous polymer and (- - -) bulk polymer.

provide an initial reduction in the hydrogen gas mole fraction (Figure 25), which augments the decrease in polymer melt index at early times and shortens the overall transition time. The resulting changes in melt index and density may be seen in Figures 26 and 27. A feedback control scheme to control the monomer concentration and the yH2:yC2 mole ratio could be used in an industrial reactor to handle the numerous adjustments in monomer and hydrogen feed. Because hydrogen and monomer injection rates are simultaneously reduced at the start of the

Figure 29. Graphical depiction of case Z, showing the variation in temperature control (shown in the top panel) and reactor pressure (shown in the bottom panel).

transition, care must be taken to avoid a large initial reduction in the total reactor pressure. Case Z: Transition in Density with Temperature and Pressure. Case Z demonstrates a transition in density from 0.915 g/cm3 to 0.925 g/cm3, using the simulation conditions of Case X as its initial conditions. The temperature is reduced by increasing the diluent feed, and monomer concentration is increased to result in the change in density. Figures 28-32 show the changes in the manipulated process variables and the corresponding responses in the polymer properties. Total reactor pressure is increased from 30 atm to 44 atm and is accompanied by a reduction in temperature from 350 K to 338 K (Figure 29). The hydrogen gas mole fraction must be simultaneously increased from 0.2 to 0.3 to maintain a constant melt index. Monomer injection feed rate and recycle stream temperature initially overshoot and then are ramped to the final values to accelerate the transition in density. The hydrogen injection feed must be rapidly increased at the start of the transition to compensate for the initial increase in total pressure, and then gradually decreased in a series of small steps and ramps to the steady state value to hold the melt index constant as the reactor temperature changes (Figure 32). Because the transition involves increases in both monomer and hydrogen concentrations, quick venting is not needed. The large overshoots in monomer and

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Figure 30. Graphical depiction of case Z, showing the variation in polymer chain length and polymer melt index: (s) instantaneous polymer and (- - -) bulk polymer.

Figure 32. Graphical depiction of case Z, showing the variation in hydrogen control. The hydrogen injection rate over the initial 40 000 s is shown in the top panel, and the hydrogen gas mole fraction is shown in the bottom panel.

Figure 31. Graphical depiction of case Z, showing the variation in monomer injection rate over the initial 5000 s (shown in the top panel) and sorbed monomer concentration (shown in the bottom panel). (Sorbed concentration calculated using Stern’s correlation.36)

hydrogen injection feed rates generate relatively fast responses in the monomer and hydrogen concentrations. Conclusions Ideally, a polyethylene reactor that uses nickel-diimine catalysts must not only be able to operate over a wide range of temperatures and pressures, but also be able to transition between different reactor conditions with relative ease and speed. This capability is necessary for producing a broad range of polymer grades. It is also crucial for responding effectively to reactor upsets in temperature or monomer concentration to prevent large drifts in bulk polymer properties. Gas-phase reactors are accommodating in this respect, because they can operate over wide ranges of temperature and pressure, and gas pressures are also more easily manipulated than liquid-phase concentrations. Relative to early transition-metal catalysts, the control of polymer properties with nickel-diimine catalysts is simpler in some aspects and more complex in others. The comonomer is not required; however, the relationships between the manipulated variables and the polymer properties are more inter-related.

Based on dynamic simulations of fluidized bed reactor (FBR) operation, it is apparent that transitions in density and molecular weight can be performed through reasonable manipulation of process variables. The hydrogen and monomer injection feed rates control the concentrations of both species respectively, whereas the recycle stream temperature regulates the reactor bed temperature. In condensed-mode operation, the FBR temperature can also be regulated by the diluent injection feed rate; however, this also requires adjustments to the total pressure to keep the concentration of ethylene and molar ratio of hydrogen to ethylene constant. The injection feed rate of catalyst can be adjusted up or down to maintain the concentration of active catalyst sites and the overall reactor productivity, as long as nickel residues do not become too large. For the same reason, reducing the temperature and pressure significantly to achieve the desired polymer properties may not be possible if the polymerization rate is reduced too much. Quick venting and overshoot strategies used in reactors with conventional catalysts also work well for reducing the gas-phase residence time and improving transition times for nickel-diimine catalysts. Soak and ramp strategies can be used to regulate the temperature and hydrogen levels and reduce the overall transition times. The initial soak overshoots the desired final value, after which the process variable (recycle stream temperature or hydrogen injection feed rate) is ramped gradually to the final value. Precise and steady control of temperature ((1 °C) and pressure ((1 atm) are required to control the branching density and chain length sensitively enough to make grade transitions in melt index or density. Whereever possible, it is preferable to achieve the desired polymer properties by changing primarily the hydrogen levels or monomer concentration, while keeping the temperature constant. If the reactor temperature is changed, the product transition becomes much more complex, because temperature affects the polymer density and molecular weight, as well as the polymerization rate. For any property transition, the reactor pressure and injection feed rates of hydrogen, monomer, catalyst, and diluent are adjusted, in addition to the primary manipulated


variables, to achieve the desired reactor productivity, cooling capacity, and species concentrations. Regulation of the polymer chain length using hydrogen is somewhat limited, because the sensitivity to hydrogen is low (similar to Ziegler-Natta catalysts). Operation with high levels of hydrogen either requires operation at high reactor pressures or places an upper limit on the monomer concentration. Temperature can be changed for larger transitions in molecular weight; however, there will be simultaneous changes in the polymerization rate and branching density, which must be taken into account. Also, for some catalysts, the presence of hydrogen can also depress the polymerization rate. The influence of monomer concentration on the polymer chain length exists only at low monomer concentrations and when other chain transfer mechanisms (such as chain transfer to a cocatalyst) are significant. The risk of particle overheating is heightened, relative to early transition-metal catalysts, because higher particle temperatures lead to the production of a highly branched, lower-meltingtemperature polymer, thus accelerating polymer melting problems. Contours of the temperature difference between the polymer melting temperature and the bulk temperature can be plotted over the range of operating conditions and used to determine regions of operation where the risk of particle overheating is high. Nomenclature [ ] ) molar concentration (mol/L) Bk ) number of short chain branches of length k BPTC ) total branches per thousand carbons in entire polymer chain BPTCk ) total number of branches per thousand carbons of length, k C*0 ) total concentration of catalyst active sites (mol/L) D ) dead polymer DPn ) degree of polymerization fBPTCk ) fraction of branches of length, k H ) fluidized reactor bed height (m) K ) maximum length of branches tracked in model k ) active site position index (k ) 1 at chain terminus) kctH ) rate constant for chain transfer to hydrogen (L/mol/s) kctM ) rate constant for chain transfer to monomer (L/mol/s) kctX ) rate constant for chain transfer to chain transfer agent, X (L/mol/s) kinsert ) rate constant for monomer insertion (s-1) ktrap ) rate constant for monomer trapping (L/mol/s) kw ) rate constant for chain walking forward or backward from active site position k (k > 2) (s-1) kwk ) rate constant for chain walking forward or backward from active site position k (k e 2) (s-1) M ) ethylene monomer MI ) melt index (g/10 min) mbed ) mass of fluidized reactor bed (g) Pk ) active catalyst site (β-agostic complex) PH2 ) hydrogen partial pressure PC2 ) ethylene (monomer) partial pressure Q ) volumetric flow rate (L/s) Rk ) active catalyst site in the resting state (alkyl-olefin complex) Rct ) total rate of chain transfer (mol/L/s) Rp ) rate of polymerization (mol/L/s) R* p ) dimensionless rate of polymerization Tmelt ) polymer melting temperature (°C) TC ) total concentration of methylene units in polymer chains

TOF ) turnover frequency (rate of polymerization per active site) (s-1) X ) chain transfer agent yH2 ) gas mole fraction of hydrogen yC2 ) gas mole fraction of monomer Subscripts eq ) sorbed concentration in amorphous polymer phase f ) feed stream o ) outlet stream

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ReceiVed for reView June 24, 2005 ReVised manuscript receiVed November 18, 2005 Accepted November 18, 2005 IE0580598

Dynamic Modeling of Polyethylene Grade ... - ACS Publications

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