Ind. Eng. Chem. Prod. Res. Dev. 1980, 79, 372-379
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CATALYST SECTION Prediction of Molecular Weight Distributions for High-Density Polyolefins Eric J. Nagel Union Carbide Corporation, Bound Brook, New Jersey 08805
Valery A. Klrlllov Institute of Catalysis, Siberian Academy of Sciences, Novosibirsk, USSR
W. Harmon Ray* Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706
Two models are used to predict the expected molecular weight distribution for polyethylene and polypropylene formed through Ziegler-Natta catalysis. Realistic values of kinetic and physical parameters, taken from experimental studies, are used to provide quantitative results. The simple core model, which neglects catalyst particle breakup, does not allow significant MWD broadening due to diffusion effects. On the other hand, a more realistic multigrain model shows that significant MWD broadening could arise due to intraparticle monomer diffusion limitations.
Introduction The polymerization of olefins such as ethylene and propylene via Ziegler type catalysts is of enormous commercial interest and yet there remains much about the polymerization kinetics which is poorly understood. One serious area of uncertainty is the physical basis for the extremely broad molecular weight distributions (MWD) often observed in these polymerizations. Commonly reported values of polydispersity, Q
(which is the ratio of weight average to number average molecular weight) are 5-30 for polyethylene and polypropylene (Crabtree e t al., 1973; Buls and Higgins, 1970; Vandenberg and Repka, 1977). For batch polymerizations the MWD is observed to be quite broad early in the polymerization and narrows only slightly as the reaction proceeds (Taylor and Tung, 1963). The question of why this MWD should be so broad is an intriguing one and has been discussed extensively in a qualitative way in the literature. In this paper, we contribute additional information to this discussion through a detailed quantitative modelling study using actual physical and kinetic parameters for ethylene and propylene polymerization. Ziegler-Natta polymerization is carried out industrially under a number of different physical conditions. Perhaps the most prevalent polymerization system for olefins is the slurry process, the system modeled in the present paper. 0196-4321/80/1219-0372$01.OO/O
In this process, titanium trichloride catalyst is slurried in a hydrocarbon diluent along with aluminum alkyl cocatalyst a t a temperature of 60-100 "C. Ethylene or propylene gas dissolves in the diluent, diffuses to the catalyst particle, and reacts. Polymer does not dissolve and remains as a solid surrounding the catalyst. Diffusion of monomer through this constantly growing polymer phase controls the monomer concentration at the catalyst surface. Other polymerization systems include bulk polymerization of propylene (slurry polymerization without diluent), solution polymerization of ethylene (high temperature, polyethylene in solution), and the recently developed gas phase processes. Vandenberg and Repka (1977) discuss these processes in an excellent review article. The polymerization is heterogeneous and proceeds by a coordination mechanism. It is thought that growing polymer is directly attached to an active titanium atom on the catalyst surface, and propagation occurs by insertion of monomer between the metal atom and the growing chain. The reaction is widely assumed to be first order in both monomer and active sites. Hypotheses as to the origin of the broad MWD in these polyolefins fall into two basic categories. The first assumes no significant diffusion effects and relies on the notion that the catalyst is composed of a spectrum of different active sites, each with its own propagation rate constant (Wesslau, 1958; Carrick et al., 1960; Overberger and Ang, 1960; Karol and Carrick, 1961; Hoeg and Liebman, 1962). The rationale behind this hypothesis is that each titanium active site has a different chemical and physical environment, 0 1980 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 3, 1980 373
which leads to the range of activities. It is clear that this kinetic scheme can produce polymer chain lengths with a broad distribution; however, Singh and Merrill (1971) suggest that the variation in kinetic activities required to produce the experimentally observed values of Q is physically unreasonable. A second hypothesis suggests that monomer diffusion to active sites is the determinant of polyolefin MWD, and all catalytic sites are assumed to be equally active. Diffusion affects the kinetic equation by creating nonconstant monomer concentrations at the reaction sites as a function of time and/or position. Several models based on the diffusion hypothesis have been proposed. The most common and simplest type of model is based on a spherical catalyst particle with a spherical shell of polymer deposited around it. Models based on this geometry are commonly called “solid core” models. Monomer diffusion through the polymer shell to active sites on the TiC13 catalyst is the central theme of these models. Begley (1966) proposes such a model and concludes that diffusion is not a factor. The monomer gradient across the polymer shell is calculated analytically after invoking the steady-state assumption for the diffusion equation. However, the numerical value of the effective diffusion which is couched in terms of a permeacoefficient ( aeff), bility factor, appears to be chosen much too high in Begley’s work. Begley proposes a second-order catalyst deactivation scheme to account for decreasing polymerization rate as a function of reaction time. Such a dropoff in rate is noted by other investigators (Kohn et al., 1962; Brockmeier and Rogan, 1976; and Buls and Higgins, 1970), but in other works, most notably the pioneering work of Natta (1959), no deactivation is seen even after long reaction times. Crabtree et al. (1973) derive a solid core model based on first-order active site decay. Their model finds reasonably good agreement with their ethylene polymerizations. Rate does decrease with time, and the authors conclude that diffusion is important throughout the polymerization except for the first few minutes of reaction. Experimentally, exceptionally high molecular weights are found early followed by a quick leveling off. Polydispersity is predicted and found to decrease slightly with reaction time. Calculated results are based on an assumed TIeffof 10-~ cm2/s. Buls and Higgins (1970) derive two very similar statistical penetration models based on semiinfinite slab geometry. Catalyst is homogeneously dispersed in the polymer and all sites have equal activity. Monomer concentration is assumed inversely proportional to distance from the slab surface. A t any given distance into the slab the Q value is 2, because local conditions remain constant and one realizes the homogeneous polydispersity for these kinetics. Summing over distance into the slab, however, produces a broad overall MWD. Predicted values for Q fall in the 8-13 range. These models predict a rapid increase in Q initially, followed by a slow increase after that. Schmeal and Street (1971,1972) and Singh and Merrill (1971) investigate a variety of models for polymerization. One of these assumes that catalyst is homogeneously dispersed throughout the polymer particle. This model has an experimental basis in the work of Hock (1966) and others. I t is found that the initial TiC13 particle fractures in the early stages of Polymerization (supposedly due to polymerization-induced mechanical forces) to form very small crystallites. The proposed model is the limiting case of total breakup with active sites spread uniformly within the particle. Both Schmeal and Street and Singh and
Merrill calculate polydispersities for various values of Thiele modulus. The predicted results show that for reaction control narrow MWD’s are found (Q 1 2) and for diffusion control broad MWD’s prevail (Q >> 2). A further prediction of the models is that for diffusion controlled cases the polymerization rate will drop off quickly a t very short times and then decrease slowly after that. The principal conclusion of these earlier modeling efforts was that for sufficiently large values of Thiele modulus, diffusion can indeed account for broad MWD’s. However, experimentally determined physical or kinetic parameters were not used in their model predictions so that the quantitative effect of diffusion limitations was not clear. Although slurry polymerizations are assumed to be isothermal, temperature gradients could exist within the growing particles if heat transfer were sufficiently poor. We shall discuss this point in more detail below. Mass transfer in the reactor is not limited to diffusion through the polymer phase. From gaseous monomer to catalyst surface there are a series of possible mass transfer limitations. There is transfer from the gas to surface liquid to bulk liquid to polymer particle surface to catalyst. Although diffusion through the polymer appears to account for the most serious diffusion resistance, the others could be important, especially at high solids content in the slurry. Keii et al. (1972,1973)report work in which stirrer speed in slurry polymerization is changed in an attempt to separate mass transfer and kinetic effects. Based on the result that at low catalyst loading the rate of polymerization is independent of stirrer speed, the authors conclude that diffusion cannot be a factor. While this conclusion may hold for the various mass transfer steps for the transport of monomer from the gas phase to the outer surface of the polymer particle, stirring could not influence diffusion rates within the polymer particle. Brockmeier and Rogan (1976) model the entire series of diffusion resistances and evaluate their relative importance based on a solid core model. Diffusion in the polymer shell is modeled by use of an empirically determined correlation. With increasing yield, the overall resistance to polymerization increases steadily. The kinetic resistance dominates in the very early stages of the polymerization, but it is quickly overtaken by the diffusion resistance associated with mass transfer of monomer through the polymer shell. The other mass transfer resistances are found to be minimal compared to the kinetic and polymer shell resistances (in agreement with Keii et al.). The present paper reports modeling of both ethylene and propylene polymerization in which diffusion through the polymer is the controlling mass transfer resistance. Although exact values of the appropriate effective diffuare difficult to determine, appropriate bounds sivities, BDeff, may be placed on this parameter and model predictions obtained for a range of physically realistic values. The study reported here considers both the classical solid core model as well as a more realistic multigrain model. The solid core model includes both nonsteady state heat and mass transfer, while the multigrain model provides a detailed treatment of an array of catalyst grains in a large growing polymer particle. In all of the calculations, actual experimentally determined parameters are used in order to predict quantitatively the effects of diffusion on the MWD.
=
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A Simple Solid Core Model The solid core model for polyolefin polymerization is simply based on a spherical catalyst particle with a spherical shell of polymer growing around it (Figure 1).
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The material balance for the various polymeric species in this semi-batch process leads to the following equations for growing polymer BULK LIQUID Tbulk
and dead polymer
Mbulk
Although it is possible to solve these equations for P,, M,, for our purposes it is only necessary to solve equations for the moments of the MWD. For the live MWD, the kth moment is Figure 1. The simple core model.
Dissolved monomer in the liquid phase diffuses through the accumulated polymer to the catalyst surface, where it reacts. Growth of the polymer shell results directly from the rate a t which polymer is produced. The kinetics depend on both the temperature at the surface of the catalyst and the monomer concentration a t that point. Particle growth, the kinetics, and mass and heat transfer are all interrelated. The particular Ziegler-Natta polymerization we shall consider is a catalyst system of 6-TiC1, + A1(C2HJ3which has recently been studied extensively by Zakharov et al. (1976a,b,c; 1977a,b). Their work reports experimentally determined values of both propagation and chain transfer rate constants. The kinetic scheme consists of an initiation step, propagation, and chain transfer. Initiation occurs when a monomer reacts with an active site to produce a polymer composed of one monomer unit attached to the active site
while for the dead MWD, the corresponding equations are
Equations for these moments may be obtained in a straightforward way (Ray and Laurence, 1977) from eq 7 and 8. Only the first few moments are required in order to predict the degree of polymerization, DP, number average molecular weight, M,, weight average molecular weight, M,, and polydispersity, Q of the polymer (live or dead)
kP
Po + M Pi (2) The propagation reaction is the addition of a monomer unit to a growing chain
p, + M
kP
(3) p,+1 The initiation and propagation rates are assumed to be equal. A number of chemical agents, including monomer, aluminum alkyl cocatalyst, and hydrogen (purposely added to control molecular weight), affect chain transfer
P, + X --%M, + P1 (4) where P, is a growing (or “living”) polymer chain of n monomer units still attached to the titanium active site and M, is a terminated (or “dead”) polymer chain with degree of polymerization n. P1is a regenerated active site with one monomer unit. A simple expression for rate of polymerization is used
Thus the moment equations of interest are
and
where [MI, is the concentration of monomer at the catalyst surface. For convenience propagation and chain transfer rates are combined to define a probability of propagation a, which is the rate of propagation divided by the rate of propagation plus the overall rate of chain transfer. a
E
kp[Mls/(kp[Mls
dt
+ k t r , ~ [ H 2 1+~ /ktr,~i[TiI ~ +
ktr,M[Mls + Ktr,.4[A111iz)(6) In most real systems, chain transfer due to hydrogen overwhelms spontaneous transfer, transfer to monomer, and aluminum alkyl.
where m
PT= C P , n=O
Ind. Eng. Chern. Prod. Res. Dev., Vol. 19,
Table I. Parameters Used for the Model Predictions parameter
Eth/PE
Prop/PP
9.6 X lo6 (80°C)
95 000 (70°C)
cm3"/ (mol '/p)
98 (80) = C)
1.4 ( 7 0 C)
ka,H,, cm3"/ (mol '/2s)
727 ( 8 0 'C)
186 (70
k&,mon,cm3/ (mobs)
840 ( 8 0 C)
40 ( 7 0
k,, cm3/mol-s
C)
C)
I'
concentration of 2.0 x active sites, (80°C) (mol sites)/mol of Ti bulk monomer 0.3 mol/L concentration, MbuIk
effective diffusivities, as,&, cmz/s
1.0 X lo-' 5.0 x
2.3 x (70°C)
references Zakharov etal (1976b) Zakharov et a1 (1977a) Zakharov et al (1976~) Zakharov et a1 (1976~) Zakharov etal (1976a)
1-2 mol/L
< D , , ~ L
