Polymerization Reactors and Processes - ACS Publications

9 Propylene Polymerization Kinetics in Gas Phase Reactors Using Titanium Trichloride Catalyst N. F. B R O C K M E I E R

Downloaded by UNIV OF QUEENSLAND on April 26, 2016 | http://pubs.acs.org Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch009

Amoco Chemicals Corp., Naperville, I L 60540

Gas phase olefin p o l y m e r i z a t i o n s are becoming important as manufacturing processes f o r h i g h d e n s i t y p o l y e t h y l e n e (HDPE) and polypropylene (PP). An understanding o f the k i n e t i c s o f these gas-powder p o l y m e r i z a t i o n r e a c t i o n s u s i n g a h i g h l y a c t i v e TiCl3 c a t a l y s t is vital to the c a r e f u l o p e r a t i o n o f these processes. Well-proven models f o r both the hexane s l u r r y process and the bulk process have been p u b l i s h e d . This article d e s c r i b e s an extension o f these models to gas phase p o l y m e r i z a t i o n in semibatch and continuous backmix r e a c t o r s . T h i s article documents the mathematical development of these gas phase k i n e t i c models and compares the c a l c u l a t e d r e s u l t s (reaction rates, y i e l d s , operating conditions) with published r e s u l t s (1). The c o r r e l a t i o n o f these r e s u l t s is q u i t e promisi n g , enough t o i n d i c a t e that these models may be fully capable of d e s c r i b i n g gas phase PP k i n e t i c s . Most of the k i n e t i c data p r e s e n t l y a v a i l a b l e come from l a b o r a t o r y semibatch r e a c t o r s . Probably the g r e a t e s t utility o f t h i s modeling work is to p r o v i d e a r i g o r o u s method to design l a r g e - s c a l e continuous r e a c t o r s from the semibatch runs performed in a l a b o r a t o r y . The r e s u l t s should be valuable to the process designer. Mathematical Development of Models The k i n e t i c models f o r the gas phase p o l y m e r i z a t i o n o f propylene i n semibatch and continuous backmix r e a c t o r s are based on the r e s p e c t i v e proven models f o r hexane s l u r r y p o l y m e r i z a t i o n (2). They are a l s o very s i m i l a r to the models f o r bulk p o l y m e r i z a t i o n . The primary d i f f e r e n c e between them l i e s i n the s u b s t i t u t i o n o f the a p p r o p r i a t e gas phase c o r r e l a t i o n s and parameters f o r those p e r t a i n i n g to the l i q u i d phase. The k i n e t i c models a r e the same u n t i l the f i n a l stage of the s o l u t i o n of the r e a c t o r balance equations, so the d e s c r i p t i o n o f the mathematics i s combined u n t i l that p o i n t o f departure. The models provide f o r the continuous o r i n t e r m i t t e n t a d d i t i o n o f monomer to the r e a c t o r as a l i q u i d a t the r e a c t o r temperature.

0-8412-0506-x/79/47-104-201$05.00/0 © 1979 A m e r i c a n C h e m i c a l Society

Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

POLYMERIZATION REACTORS AND PROCESSES


202

The monomer vaporizes instantaneously and mixes completely w i t h the gas i n the r e a c t o r . Any mass t r a n s f e r r e s i s t a n c e to mixing i s neglected w i t h respect to other r e s i s t a n c e s . A g i t a t i o n of the r e a c t i n g powder i s assumed to be s u f f i c i e n t to i n t e r m i x i t u n i formly without e n t r a i n i n g i t i n the gas above. The gas i s assumed to c i r c u l a t e through the powder s u f f i c i e n t l y to prevent concentrat i o n gradients except w i t h i n the gas trapped i n a growing polymer particle. A porous s h e l l of polymer grows w i t h geometric s i m i l a r i t y around the c a t a l y s t p a r t i c l e , which i s assumed to be s p h e r i cal. Scanning e l e c t r o n micrographs of f i n i s h e d powder p a r t i c l e s i n d i c a t e that the o r i g i n a l c a t a l y s t p a r t i c l e d i s i n t e g r a t e s under certain conditions. The assumption i s that polymer grows concent r i c a l l y around each o f the fragments. Propylene must d i f f u s e through tortuous passages i n t h i s s h e l l c o n t a i n i n g a stagnant mixture o f i n e r t gases such as s a t u r a t e d hydrocarbons, s i n c e d i f f u s i o n of propylene through s o l i d polymer i s much too slow to cont r i b u t e to the r e a c t i o n . The propylene reaches the a c t i v e c a t a l y s t s u r f a c e , where i t r e a c t s a t c o n c e n t r a t i o n C , which i s gene r a l l y somewhat lower than Cg, the c o n c e n t r a t i o n i n the well-mixed gas phase. The heat t r a n s f e r r e s i s t a n c e between p o l y m e r i z i n g s o l i d s and gas has been neglected, so both s o l i d s and gas are at the same temperature (JL). The semibatch r e a c t o r operates w i t h monomer feed on pressure c o n t r o l w i t h no m a t e r i a l s l e a v i n g . The continuous r e a c t o r has feeds o f c a t a l y s t and monomer, and powder removal to h o l d a constant l e v e l . s

The model p o s t u l a t e s two s i g n i f i c a n t r e s i s t a n c e s i n s e r i e s : d i f f u s i o n through the growing s h e l l (Rpjp) and p o l y m e r i z a t i o n at the c a t a l y s t s u r f a c e (R^AT^ • * catalytic reaction resistance, RCAT> intended to i n c l u d e any and a l l of the e f f e c t s of the s o r p t i o n r a t e o f monomer on the s u r f a c e , s t e r i c arrangement of a c t i v e s p e c i e s , the a d d i t i o n o f the monomer to the l i v e polymer chain, and any d e s o r p t i o n needed to permit the chain to continue growing. We assume a steady s t a t e i n which every mole of propylene that polymerizes i s replaced by another mole e n t e r i n g the s h e l l from the gas, so t h a t a l l of the f l u x e s are equal to Ny gmol propylene reacted per second per l i t e r of t o t a l r e a c t o r volume. The f o l l o w i n g s e t of equations r e l a t e s the molar f l u x to each of the c o n c e n t r a t i o n d r i v i n g f o r c e s . T

i e

i s

N

V

= k A

c

(Cg - C )

D i f f u s i o n through porous s h e l l

(1)

N

v

= k A

c

• C

Catalyst surface reaction

(2)

c

s

g

s

The c a t a l y s t s u r f a c e area i s defined i n the f o l l o w i n g r e l a tionship (3): 6X A = -=3L (3) 7 7 R P

d

V


9.

BROCKMEIER

Propylene

Polymerization

Kinetics

203

Note t h a t the f l u x and the area A are based on u n i t r e a c t o r v o l ume. This permits d i r e c t comparison between r e s i s t a n c e s during the course of a r e a c t i o n because i t remains constant. Propylene c o n c e n t r a t i o n i s expressed i n gmol per l i t e r of gas, a number which i s k i n e t i c a l l y s i g n i f i c a n t . The a c t i v i t y of the propylene c o n t a c t i n g the c a t a l y s t s u r f a c e i s assumed to be p r o p o r t i o n a l to i t s c o n c e n t r a t i o n a t the s u r f a c e , C . The s e r i e s nature of the model permits c a l c u l a t i o n of the o v e r a l l r e a c t i o n r e s i s t a n c e ( R Q ) simply by summing the i n d i v i dual r e s i s t a n c e s : g

v


R

R

0V

- CAT

+

( 4 )

*DF

Equations 1 and 2 are rearranged to e l i m i n a t e C form of equation 4, i n which R = C_/N__: OV E V

g

and put i n t o

the

(5) NV

k

T

A s

^ k c

K

A c

J

c

The s o l u t i o n of equation 5 f o r f l u x N^ provides the k i n e t i c s we d e s i r e . Numerous experiments w i t h the hexane s l u r r y system have l e d to the development of an expression f o r k that i s p a r t l y based on theory and p a r t l y on an e m p i r i c a l constant i n the denominator: ,

^AB 0.0245 • d

=

c

?

W

' Y

Experience has shown that the mass t r a n s f e r r a t e decreases as the r e c i p r o c a l of Y as p o l y m e r i z a t i o n proceeds (2). We assume that t h i s i s the same f o r both s l u r r y and gas phase p o l y m e r i z a t i o n . The d i f f u s i v i t y , * estimated by a method recommended f o r gases at h i g h pressure. The method used i s d e r i v e d from equations of Mathur and Thodos ( 4 ) : t

s

D

AB

=

5.43

x 10"

T

5

• T • v • P

2

/

3

cm

(7)

' V"

'« cm The value of v i s important both i n equation 7 and f o r accurate c a l c u l a t i o n of concentrations i n other equations. For s i m p l i c i t y and accuracy, the Peng-Robinson equation o f s t a t e has been used to c a l c u l a t e v f o r the model (5). This equation expresses the P-V-T r e l a t i o n s h i p as f o l l o w s : RT v - b

_

a(T) v (v+b) + b

(v-b)


(8)


204

For equations 7 and 8, temperatures must be i n degrees Rankine. The q u a n t i t i e s a(T) and b are defined i n the l i t e r a t u r e (5). Refer again to equation 5 — the value of can now be c a l c u l a t e d from v: C

E

= x /62.43v

(9)

2

where X2 = mole f r a c t i o n propylene i n vapor and the 62.43 f a c t o r converts the u n i t s to g-mol/ml. The remaining q u a n t i t y i n equat i o n 5 i s the r a t e constant k . Much experience with s l u r r y polym e r i z a t i o n has r e s u l t e d i n the f o l l o w i n g equation to d e s c r i b e how the r a t e constant decays w i t h the age of a c a t a l y s t p a r t i c l e i n the r e a c t o r and how i t i n c r e a s e s with an i n c r e a s e i n temperature:


g

k

= 0.992 x 1 0

9

exp

(-E./RT) • k ° exp

S

A

(-t/X)

(10)

S

where the s u p e r s c r i p t on k denotes the o r i g i n a l value at 80°C. The second e x p o n e n t i a l i n equation 10, exp (-t/X), i s the same as that reported by Wisseroth f o r h i s s t u d i e s of gas phase propylene p o l y m e r i z a t i o n (1). His parameter b equals 1/X. The value of X i s s e n s i t i v e to temperature, so we assume t h a t : X = X' B exp

(-E

/RT)

(11)

A

where the prime denotes the value at 80°C. A more g e n e r a l l y u s e f u l r a t e constant i s d e f i n e d by f o l l o w i n g equation:

the

r = k, - X • C • M k m s A

(12)

A

The often-quoted instantaneous c a t a l y s t a c t i v i t y i s r * X i n g/g-hr. The value of k^ i s always p r o p o r t i o n a l to k , according to the f o l l o w i n g : S

, \

_ 6 - 3600 • " 1000 • P / d

fcs

.

( U

J

;

7

T h i s now i s the p o i n t o f departure at which the semibatch t r e a t ment f o l l o w s a d i f f e r e n t course from treatment of a continuous reactor. Semibatch Model "GASPP". The k i n e t i c s f o r a semibatch r e a c t o r are the simpler to model, i n s p i t e of the experimental challenges of o p e r a t i n g a semibatch gas phase p o l y m e r i z a t i o n . Monomer i s added continuously as needed to maintain a constant o p e r a t i n g p r e s s u r e , but nothing i s removed from the r e a c t o r . A l l c a t a l y s t p a r t i c l e s have the same age. Equations 3-11 are s o l v e d a l g e b r a i c a l l y to supply the v a r i a b l e s i n equation 5, at the des i r e d o p e r a t i n g c o n d i t i o n s . The p o l y m e r i z a t i o n f l u x , N , i s summed over three-minute i n t e r v a l s from the s t a r t u p to the d e s i r e d residence time, T, i n hours:


9.

BROCKMEIER

Propylene

Polymerization

Kinetics

205

t=T

W

p

=

/

/

(3600* 0• 05• N..V M ) V R A

(14)

to give W , the cumulative production of polymer. A l l parameters that are ^ f u n c t i o n s of time, such as k , k^, Y t , and are placed i n t h i s loop that sums the polymer production i n three-minute i n tervals. This i n t e r v a l i s s u f f i c i e n t l y small that i t behaves as an i n f i n i t e s i m a l , so the summation i n equation 14 i s equivalent to integration. The computer output normally p r i n t s the values of a l l important parameters at one hour i n t e r v a l s . The user may change t h i s f o r h i s convenience.


s

Continuous Model "C0NGAS". This model p r e d i c t s performance of an i d e a l continuous w e l l s t i r r e d p o l y r e a c t o r . The model system c o n s i s t s of a continuous backmix r e a c t o r i n which the t o t a l powder volume i s h e l d constant. There are four i n l e t streams: 1) Makeup of pure propylene, 2) C a t a l y s t feed, 3) Hydrogen feed, and 4) Recycle. The s i n g l e e f f l u e n t powder stream i s d i r e c t e d through a p e r f e c t separator that removes a l l s o l i d s and polymer and then the gases are r e c y c l e d to the r e a c t o r . The makeup propylene i s assumed to d i s p e r s e p e r f e c t l y i n the well-mixed powder. An a r b i t r a r y d e c i s i o n was made to f i x the mass of c a t a l y s t i n the r e a c t o r , rather than the feed r a t e of c a t a l y s t . The feed r a t e i s c a l c u l a t e d from the l o a d i n g and the mean residence time: X . = X / T mf m The p o l y m e r i z a t i o n

(15)

r a t e i n the r e a c t o r i n g/hr

i s calculated

from: r = 3600 ' N

y

• M

A

• V

(16)

R

The y i e l d of s o l i d polymer per g of TiC&3 i s : Y^ = r/X . t mi

(17)

The y i e l d of polymer i s assumed to be the sum of the i n s o l u b l e and s o l u b l e polypropylene. The b a s i s f o r t h i s simple formulat i o n of the y i e l d and r a t e i s grounded i n the f o l l o w i n g r e l a t i o n ship:

Y

M

t,c - A

C

* s

( t )

* *k

( t )

'

T


(18)


206

For a l l l i k e l y o p e r a t i n g c o n d i t i o n s , ( i e . , f o r T < X ) , the approp r i a t e values o f the concentration and the p o l y m e r i z a t i o n rate constant are the values c a l c u l a t e d a t t = T (2). To prove t h i s , the e x i t age d i s t r i b u t i o n f u n c t i o n f o r a backmix r e a c t o r was used to weight the functions f o r C and k^ and the product was i n t e grated over a l l e x i t ages ( 6 ) . I t i s e n l i g h t e n i n g a t t h i s p o i n t to compare equation 18 w i t h one that describes the y i e l d a t t a i n able i n a t y p i c a l l a b o r a t o r y semibatch r e a c t o r a t comparable conditions . s


Y

t,s

M

- A '

\

C

s

(

t

) k

k

The y i e l d that can be a t t a i n e d by a semibatch process i s g e n e r a l l y higher because the semibatch run s t a r t s from s c r a t c h , w i t h maximum values o f both v a r i a b l e s : C (o) = and kfc(o) = k ^ . However, the y i e l d from a continuous run i n which x equals the batch time i s governed by the product o f C (T) and k^ ( x ) , so Y t,s* P l t y i n y i e l d a t t a i n a b l e i n a continuous run c a n ^ e e l i m i n a t e d by two r o u t e s . If R = 0, C ( t ) w i l l be constant; and i f the c a t a l y s t does not d e a c t i v a t e , X-*» and k^ (t) = kk°. Because n e i t h e r o f these c o n d i t i o n s i s l i k e l y to be f u l f i l l e d completely, a continuous p o l y m e r i z a t i o n i n a backmix r e a c t o r w i l l probably always f a i l t o a t t a i n the Y a t t a i n a b l e by a semibatch r e a c t o r a t the same x. However, s e v e r a l backmix r e a c t o r s i n s e r i e s w i l l approach the behavior o f a plug flow continuous r e a c t o r , which i s e q u i v a l e n t t o a semibatch r e a c t o r . Refer to equation 5, which r e l a t e s Ny t o the parameters i n the r e a c t o r . For the continuous r e a c t o r these parameters are evaluated a t t = x. However, the s o l u t i o n to equation 5 i s comp l i c a t e d by the f a c t that Ny i s not only on the l e f t hand s i d e , but Ny a l s o appears i n the expression f o r R as a f i r s t power. Newton's method o f convergence i s used to s o l v e equation 5 f o r the continuous r e a c t o r . 0

s

s

< Y

T

h

e

e n a

D F

s

t

D F

Experimental The experimental semibatch apparatus and procedure have been d e s c r i b e d i n s e v e r a l places through the t e x t o f Wisseroth's publications 7-9) , so the d e t a i l s w i l l not be repeated here. For n e a r l y a l l o f h i s work the r e a c t o r volume was one l i t e r , temperature was 80°C, pressure was 30 atm (441 p s i a ) , and the feed was p o l y m e r i z a t i o n grade C3H6. I assume that the r e a c t o r gas composition was 99% C3Hgand 1% i n e r t s . The range o f c a t a l y s t l o a d i n g was from 11 t o 600 mg o f TiC&3 per batch. The r e a c t i o n time was v a r i e d from 0.5 to 6 hours. The weight r a t i o o f a l k y l to-TiC& i n the c a t a l y s t r e c i p e was v a r i e d from 0.5 to 32. No data are reported from a continuous gas phase r e a c t o r . 3


9.

BROCKMEIER

Propylene

Polymerization

207

Kinetics

According to Wisseroth, the a g i t a t o r design was q u i t e import a n t , and was very s i m i l a r to those shown i n r e f e r e n c e 1. The speed was a d j u s t a b l e from 0-360 rpm and a gland packing s e a l was used. For s p e c i a l o p e r a t i o n s , m e t a l l i c b a l l s were added to the r e a c t o r to improve temperature s t a b i l i t y (10).


D i s c u s s i o n of Results This s e c t i o n i s d i v i d e d i n t o three p a r t s . The f i r s t i s a comparison between the experimental data reported by Wisseroth ( 1 ) f o r semibatch p o l y m e r i z a t i o n and the c a l c u l a t i o n s of the k i n e t i c model GASPP. The comparisons are l a r g e l y g r a p h i c a l , with data shown as p o i n t symbols and model c a l c u l a t i o n s as s o l i d c u r ves. The second p a r t i s a comparison between some semibatch r e a c t o r r e s u l t s and the c a l c u l a t i o n s of the continuous model C0NGAS. F i n a l l y , the t h i r d p a r t d i s c u s s e s the e f f e c t s of c e r t a i n important process v a r i a b l e s on c a t a l y s t y i e l d s and p r o d u c t i o n r a t e s , based on the models. Semibatch S i m u l a t i o n , GASPP. The experimental r e s u l t s i n Tables 3 and 4 o f r e f e r e n c e 1 appear to f a l l i n t o three groups of d i f f e r e n t a c t i v i t y f o r the BASF TiC&3 used. F i g u r e 1 shows a group of runs w i t h the lowest c a t a l y s t a c t i v i t y , most of which had a c a t a l y s t r e c i p e w i t h an alkyl/TiC&3 ( A l k / T i ) r a t i o of 8:1 or 16:1. Figure 1 shows the course of semibatch p o l y m e r i z a t i o n of propylene a t 80°C and 441 p s i a f o r r e a c t i o n times of from 1 to 4 hours. The f a m i l y of curves shows that the t o t a l ( i n s o l u b l e p l u s s o l u b l e ) polymer formed i s d i r e c t l y p r o p o r t i o n a l to the mass of TiC&3 charged and that i t i n c r e a s e s with time at a g r a d u a l l y decaying r a t e . The slope o f a curve at any p o i n t i s the i n s t a n taneous r a t e . The data p o i n t s are q u i t e s c a t t e r e d , probably because of gas phase experimental d i f f i c u l t i e s . The f a m i l y of model curves was adjusted to the best v i s u a l f i t to the data (esp.loadings of 100 and 30 mg TiC&3) by v a r y i n g the i n i t i a l r a t e constant k ° keeping the c h a r a c t e r i s t i c l i f e t i m e , X, constant a t 11.1 h r . D i f f u s i o n r e s i s t a n c e , Rr^p, i s not very important f o r t h i s low activity catalyst. Thus, the curvature of these model curves i s n e a r l y a l l c a t a l y s t r a t e decay. Wisseroth claims that t h i s c a t a l y s t has a decay parameter, b, equal to 0.09 hr.""l ( e s s e n t i a l l y the same as 1/X) (1). s

1

W i s s e r o t h s Tables 3 and 4 a l s o i n c l u d e data f o r c a t a l y s t s of much higher a c t i v i t y . These more a c t i v e c a t a l y s t s tend to be those f o r which the A l k / T i r a t i o i s lower, i e . 2:1 or 1:1. However, there are exceptions to t h i s tendency i n a l l three groups. Figure 2 shows h i s r a t e data f o r the two groups of higher a c t i v i t y c a t a l y s t s , along w i t h s o l i d model curves f o r a l l three groups. A l l r e s u l t s are shown as y i e l d i n grams of PP per gram of TiCil3 l o a d i n g f o r ease i n comparison. The model curves were adjusted to the best v i s u a l f i t u s i n g only k ° , keeping a l l other parameters constant. The more a c t i v e c a t a l y s t s have values of k ° l a r g e r than the base a c t i v i t y by f a c t o r s of 2.2 and 8.6, respecs

s




208

Reaction time, min. Figure

2.

Gas Phase Propylene Polymerization with catalysts of various ties (batch reactor, 1 L, 80°C, 441 psia, 99% pure CH) 3

6


activi-

9.

BROCKMEIER

Propylene

Polymerization

209

t i v e l y (10). The e f f e c t s of R are d e f i n i t e l y n o t i c e a b l e with the two h i g h e r a c t i v i t y c a t a l y s t s . These two upper curves i n Figure 2 demonstrate a s i g n i f i c a n t concave downward c u r v a t i o n , showing t h a t R^p r e t a r d s the p o l y m e r i z a t i o n r a t e i n the same manner as c a t a l y s t decay. Lack of data f o r longer r e a c t i o n times at the h i g h e s t a c t i v i t y prevents a more q u a n t i t a t i v e c o n c l u s i o n about Rpp, e s t i m a t i o n i n the model. The f i t f o r the middle curve at 4+ hours looks promising. T h i s good f i t i s e s p e c i a l l y noteworthy because the e m p i r i c a l constant of 0.0245 i n equation 6 i s the same value as that used i n the s l u r r y model C0NTPP (2). The output from the semibatch model GASPP permits a d e t a i l e d look a t the way i n which p o l y m e r i z a t i o n r e s i s t a n c e s i n c r e a s e duri n g the course of a run. F i g u r e 3 shows how these r e s i s t a n c e s i n c r e a s e w i t h y i e l d f o r a run u s i n g the intermediate a c t i v i t y c a t a l y s t (k ° = 0.00638 cm/sec), w i t h 50 mg T i C £ l o a d i n g . Overa l l r e s i s t a n c e , RQV> * °^ individual resistances i n s e r i e s , R ^ A T %)F- The curve f o r R ^ A T i n c r e a s e s with an upward curvature because the c a t a l y s t a c t i v i t y decays with time. Yield i n c r e a s e s with time as i n Figure 2. The equations i n d i c a t e that f o r constant composition, R i s p r o p o r t i o n a l to y i e l d , Y , as shown by Figure 3. For 80°C, 441 p s i a , and 99% C H , the equat i o n f o r BASF c a t a l y s t i s D


Kinetics

F

s

3

s

t

n

e

s

u

m

t

n

e

+

D

F

3

R

D

F

= 3.38

x 10"

6

•

6

Y /X t

(20)

independent of c a t a l y s t k ° . A change i n k ° only s h i f t s R Q A T up or down, and of course s h i f t s R Q V For c a t a l y s t modelled i n Figure 3, R i s about h a l f of R c A T at Y = 12,000, so the p o l y m e r i z a t i o n r a t e i s l a r g e l y under k i n e t i c c o n t r o l a t h i g h yield. However, f o r the most a c t i v e c a t a l y s t , R ^ A T drops to about 1/4 o f the present value and becomes the l e s s e r c o n t r i b u t i o n to R Q . Then p o l y m e r i z a t i o n becomes d i f f u s i o n - c o n t r o l l e d at high y i e l d s . For a 30% drop i n o p e r a t i n g p r e s s u r e , the constant i n equation 20 drops 40%. A 9°C drop i n temperature, however, h a r d l y a f f e c t s the constant i n equation 20, a l l other things constant. For comparison of r e s i s t a n c e s between runs with d i f ferent c a t a l y s t l o a d i n g s , note that the product of r e s i s t a n c e and i s a constant f o r a given c a t a l y s t ( f o r i n s t a n c e , i n F i g ure 1' There are very sparse data a v a i l a b l e at the long residence times t h a t are needed to evaluate the c h a r a c t e r i s t i c l i f e t i m e (X) of the BASF TiC&3 used by Wisseroth (1). Figure 4 shows these few values of A (mean a c t i v i t y ) f o r the intermediate a c t i v i t y c a t a l y s t at 80°C, covering a range of from 1 to 6 hours. For convenience on t h i s semilog p l o t , a l l i n f o r m a t i o n has been normali z e d by d i v i d i n g i t by the o r i g i n a l value at zero run time. The constant used f o r A° i s 3710 g/g hr. The s t r a i g h t l i n e and two curves i n F i g u r e 4 were generated with model GASPP f o r comparison w i t h the data. The s o l i d curve f i t s the experimental data f o r A satisfactorily. I f there were l i t t l e or no mass t r a n s f e r l i m i s

s

t

D

F

n

e

t

V



210


oL0

1 2

I

I

I

I

I

4

6

8

10

12

Catalyst yield x 1 0 , g PP/g TiCI 3

Figure 3. tion (80°C,

Figure

4.

I

3

Resistance increase during semibatch gas phase propylene polymeriza441 psia, 50 mg TiCl loading, 99% pure C H , k ° = 0.00638 cm/sec) 3

Decay of catalytic

activity (propylene 441 psia)

3

6

s

gas phase polymerization


80°C,

9.

BROCKMEIER

Propylene

Polymerization

211

Kinetics

t a t i o n s to the k i n e t i c s , the mean a c t i v i t y would decay more slowl y than the rate constant k . T h i s i s observed with c a l c u l a t i o n s on the c a t a l y s t of lowest a c t i v i t y . However, t h i s intermediate c a t a l y s t has s u f f i c i e n t d i f f u s i o n l i m i t a t i o n to cause the decay of A to n e a r l y match the decay o f k , as shown i n F i g u r e 4. This happens because d i f f u s i o n causes r (dashed curve) to drop so r a p i d l y with time. This coincidence of the curves f o r A and k means that the experimenter might e a s i l y miss seeing any d i f f u s i o n mechanism i n o p e r a t i o n , were i t not f o r other evidence (highe r a c t i v i t y c a t a l y s t , other temperatues, o r s l u r r y systems). From the slope of the s t r a i g h t l i n e f o r k decay, X i s 9.68 h r . a t 80°C. Wisseroth r e p o r t s b equals to 0.09 h r . " , or X = 11.1 h r . at 80°C. This might be the c o n c l u s i o n from the s l o p e of a s t r a i g h t l i n e drawn through the curved data A, even though t h i s i s not a r i g o r o u s l y c o r r e c t way to evaluate b. s

g

s

g


1

The semibatch model GASPP i s c o n s i s t e n t with most of the data p u b l i s h e d by Wisseroth on gas phase propylene polymerization. The data are too s c a t t e r e d to make q u a n t i t a t i v e statements about the model d i s c r e p a n c i e s . There are e s s e n t i a l l y three c a t a l y s t s used i n h i s t e s t s . These BASF c a t a l y s t s are c h a r a c t e r i z e d by the parameters l i s t e d i n Table I. The h i g h s o l u b l e s f o r BASF are expected at 80°C and without m o d i f i e r s i n the r e c i p e . The f a c t that the BASF c a t a l y s t parameters are so s i m i l a r to those e v a l uated e a r l i e r i n s l u r r y systems lends credence to the k i n e t i c model. Continuous S i m u l a t i o n , C0NGAS. There are no p u b l i s h e d data a v a i l a b l e on propylene continuous p o l y m e r i z a t i o n s u i t a b l e to check the accuracy of the C0NGAS model. However, there i s an equation f o r y i e l d vs. time p u b l i s h e d by Wisseroth (1) f o r a completely backmixed continuous r e a c t o r : A° • Y

=

T"

—

(21)

1 + b T where T = mean residence time i n r e a c t o r , hr. I assume the r e a c t o r i s p e r f e c t l y backmixed f o r t h i s d i s c u s s i o n . The C0NGAS model develops y i e l d vs. time as an output, but there i s no simple expression such as equation 21. For comparison between C0NGAS and equation 21, the R must be s e t equal to zero. When t h i s i s done, the y i e l d s c a l c u l a t e d by C0NGAS average about 4%__ lower than the y i e l d s from equation 21 over the range 0 _< 4 £ T. This 4% discrepancy i s much l e s s than the t y p i c a l experimental v a r i a t i o n s o f 20% or more, so i t seems reasonable to assume that the C0NGAS model i s accurate enough f o r design use. I t has been developed i n the same way as the other well-proven Amoco PP k i n e t i c models. Figure 5 i s a p l o t o f the c a l c u l a t e d polymer y i e l d s from the continuous model C0NGAS vs. the y i e l d s from the semibatch model D F


212



Table I

BASF CATALYST PARAMETERS

AT REFERENCE TEMPERATURE OF 80°C

GAS PHASE PROPYLENE POLYMERIZATION

Recipe

Rate Const. k ° , cm/s

Decay Time X, h r

Characteristic Size,d Microns

8/1

0.0249

9.68

9.

2/1

0.00638

9.68

9.

67.7

2/1

0.00288

9.68

9.

30.5

s

7

Rate Constant, l i t e r / h r - g TiC£ kj^ 265.

NOTE: Recipe r e f e r s to wt. r a t i o s o f A J l ^ H s ^ / T i C ^ . For a l l c a t a l y s t : E = 14,500 cal/mole (11) and E = A A -3,735 cal/mole. Wt. Percent S o l u b l e s :

20-30.


3


9.

BROCKMEIER

Figure

5.

Propylene

Polymerization

213

Kinetics

Yield comparison between semibatch and continuous polyreactors (80°C and 441 psia, k ° = 0.00638 cm/sec, 99% pure CH) s

S

6


214

POLYMERIZATION

REACTORS AND PROCESSES

GASPP, at the same c o n d i t i o n s of 80°C, 441 p s i a , k ° = 0.00638 cm/sec, and at the same value of T. Wisseroth'S equations (1_) give the same r e s u l t . The 45° l i n e i n d i c a t e s the locus o f equal yields. Obviously, the comparison between r e a c t o r y i e l d s f o r t h i s BASF TiC&3 c a t a l y s t i n the gas phase system i s e s s e n t i a l l y the same as f o r the many_ other c a t a l y s t s t e s t e d i n s l u r r y and bulk (2). At the same T, the y i e l d f o r a continuous backmix r e a c t o r i s always l e s s than f o r a semibatch r e a c t o r . The r e l a t i v e values o f the instantaneous r a t e s are j u s t the reverse of the y i e l d s ( F i g . 6 i n r e f . 2). This y i e l d p e n a l t y arises because the c a t a l y s t a c t i v i t y decays and because R^p i s s i g n i f i c a n t . These f a c t o r s operate on the RTD i n a continuous r e a c t o r to reduce the yield. Figure 5 shows a 25% y i e l d r e d u c t i o n i n a continuous r e a c t o r at T = 6 h r , based on the model c a l c u l a t i o n s . Tests with v a r i o u s k ° values give q u a l i t a t i v e l y s i m i l a r curves u s i n g the models. I f the y i e l d p e n a l t y i s much l e s s than 25%, t h i s could i n d i c a t e that the RTD i s more c h a r a c t e r i s t i c of plug flow, that Rj)F i s very s m a l l , or that the decay r a t e i s very s m a l l . The y i e l d p e n a l t y can be reduced by s t a g i n g backmix r e a c t o r s i n series.


s

s

The C0NGAS s i m u l a t i o n was used to generate the three y i e l d vs. time p r o f i l e s i n Figure 6 u s i n g the most a c t i v e BASF c a t a l y s t at 60°, 80°, and 100°C. At 60°C, d i f f u s i o n becomes dominant only at the h i g h e r y i e l d s , whereas at 80°C and 100°C, a l l of the r e s u l t s are diffusion-dominated (R p- £ CAT^ • '^ diffusion e f f e c t s reduce the slopes of the two upper p r o f i l e s to about onehalf. From 80°C, a 20° boost i n r e a c t i o n temperature causes the y i e l d to i n c r e a s e by 16%, while a 20°C drop causes y i e l d to decrease by about 37%. R

[ie

D

Reactor V a r i a b l e Study. Assuming that the k i n e t i c models are v a l i d , we have a means to r a p i d l y explore the e f f e c t s of making c e r t a i n changes i n the c a t a l y s t or i n the o p e r a t i n g conditions. F o r t u n a t e l y , Wisseroth p u b l i s h e d the r e s u l t s f o r two runs a t 100°C and two more runs at 20 atm i n h i s Table 3 (1). The model GASPP was used to c o r r e l a t e y i e l d vs. time f o r the 20°C boost to 100°C r e a c t i o n temperature. With the f i r s t run, a value of k ° = 0.00198 cm/sec was r e q u i r e d to achieve the low y i e l d reported. His second run had a y i e l d of 13750 at 4.68 h r . Model GASPP r e q u i r e s k ° = 0.00294 cm/sec to give t h i s r e s u l t at 100°C. This r a t e constant i s only 2% g r e a t e r than the k ° reported i n Table I here f o r the lowest a c t i v i t y BASF TiC&3. On t h i s b a s i s , I w i l l assume that these k i n e t i c models c o r r e c t l y account f o r temperature changes. More data are needed to v e r i f y t h i s . The temperature e f f e c t i n GASPP i s p r a c t i c a l l y the same as that claimed by Wisseroth i n a recent l e t t e r (10). Model GASPP was a l s o used to c o r r e l a t e the r e s u l t s f o r p o l y m e r i z a t i o n a t 20 atm, a 33% r e d u c t i o n i n r e a c t o r pressure. Using the parameters f o r the most a c t i v e BASF T i C £ , the model y i e l d s were 13% and 40% h i g h e r than the experimental y i e l d s . The 13% i s s

s

s

3



9.

BROCKMEIER

Propylene

Polymerization

Kinetics

Figure 6. Simulation of a continuous backmix reactor (propylene gas phase polymerization—k ° = 0.0249 cm/sec, A = 9.68 hr. 400 psia; reactor gas composition—99% C H ,1% inerts) s

S

6



216


c e r t a i n l y w i t h i n experimental v a r i a t i o n . The a c t i v i t y of the other run at l e a s t f a l l s between the a c t i v i t i e s t a b u l a t e d f o r BASF TiC&3. The two 20 atm runs were terminated at 0.53 and 0.70 hours, r e s p e c t i v e l y . There are well-known d i f f i c u l t i e s i n a c c u r a t e l y determining the k i n e t i c s from such short runs. A l though these r e s u l t s are i n s u f f i c i e n t to draw a c o n c l u s i o n , the model response to pressure i s c o n s i s t e n t w i t h the data. Table I I summarizes the y i e l d s obtained from the C0NGAS computer output v a r i a b l e study of the gas phase p o l y m e r i z a t i o n o f propylene. The r e a c t o r i s assumed to be a p e r f e c t backmix type. The base case f o r t h i s comparison corresponds to the most a c t i v e BASF TiC&3 operated at almost the same c o n d i t i o n s used by Wisseroth, 80°C and 400 p s i g . A g i t a t i o n speed i s assumed to have no e f f e c t on y i e l d provided there i s s u f f i c i e n t mixing. The v a r i a b l e study i s d i v i d e d i n t o two p a r t s f o r d i s c u s s i o n : c a t a l y s t parameters and r e a c t o r c o n d i t i o n s . The c a t a l y s t i s c h a r a c t e r i z e d by k ° , X, and dy. Percent s o l u b l e s i s not considered because there i s p r e s e n t l y so l i t t l e k i n e t i c data to d e s c r i b e t h i s . The r e a c t o r c o n d i t i o n s chosen f o r study are those that have some s i g n i f i c a n t e f f e c t on the k i n e t i c s : temperature, p r e s s u r e , and gas composition. The base case i s l i s t e d i n the second column of Table I I , f o r l f r < 5 h r s . The i n c r e a s e i n y i e l d w i t h time i s q u i t e s i m i l a r to curves_shown i n Figure 6, i n which there i s a 50% i n c r e a s e i n y i e l d as T i s boosted from one to two hours. The y i e l d i n c r e a s e s only 25% more w i t h an a d d i t i o n a l hour o f r e a c t i o n time. Consider the e f f e c t of doubling the value o f k ° . (For a l l excep_t one case, a l l other parameters are kept constant.) The y i e l d at T = 3 h r . i s boosted by only 11%, c l e a r l y demonstrating that t h i s model of continuous p o l y m e r i z a t i o n i s s t r o n g l y d i f f u s i o n - c o n t r o l l e d at these c o n d i t i o n s with t h i s c a t a l y s t . I f a c a t a l y s t i s developed that has approximately double the l i f e t i m e , T = 18.3 h r . , the y i e l d s w i l l grow as shown i n the f o u r t h column. This change improves the base y i e l d a t 3 hr. by about 2%. Greater c a t a l y s t s t a b i l i t y at r e a c t o r c o n d i t i o n s i s o f l i t t l e b e n e f i t to t h i s process. The f i f t h column shows how to change parameters so as to keep kfc constant, reducing only the d i f f u s i o n r e s i s t a n c e , Rrjp-. The c h a r a c t e r i s t i c s i z e o f the TiC&3, d-j, i s reduced by 45%. The 3-hr. y i e l d i s thereby i n c r e a s e d by 53%, a very s i g n i f i c a n t b e n e f i t to the process. Methods to achieve t h i s k i n d of change are w e l l worth i n v e s t i g a t i o n . The l a s t three columns i n Table I I demonstrate changes i n r e a c t o r c o n d i t i o n s , using the same c a t a l y s t ^ A 9°C drop i n temperature causes an 11% drop i n y i e l d a t T = 3 hr. A 33% drop i n pressure causes only a 14% drop i n y i e l d . These s m a l l y i e l d changes are expected because the system i s d i f f u s i o n - c o n t r o l l e d . Composition changes have some i n t r i c a t e e f f e c t s on the k i n e t i c s . The propylene d i f f u s i v i t y i n the gas mixture w i l l depend on comp o s i t i o n , as the i n e r t s content i s changed. These changes are f e l t i n R D F , and the changes i n y i e l d might be s i g n i f i c a n t f o r a d i f f u s i o n - c o n t r o l l e d r e a c t i o n . Another e f f e c t i s simple d i l u t i o n g

s

0



13530

15160

3

4

5

0

11630

2

Base Case

15710

13940

11900

9450

6250

&

s

3

Composition, mole f r a c t i o n i n vapor.

C3H6 :

3

0.99,

23400

20870

17820

14020

8940

T = 80°C, P = 400 p s i g , X = 0.05 g T i C £ op ga m

7

7

16810

15020

12960

10470

7180

7

C a t a l y s t Parameters Rate Constant Size d = 0.0005 cm Lifetime, ks° X=18.3 h r . (+k °=0.01384) 0.0524 cm/sec

k = 0.0249 cm/sec. X=9.68 hr, s d = 0.0009, p = 2.26,

9290

1

NOTE 1:

6180

T i m e , T ,hr.

1

Base Case Yields

Mean Residence

Inerts:

13710

12190

10390

8190

5270

0.01

13100

11680

9980

7860

5020

13490

12060

10400

8400

5870

Operating Conditions Composition Temp., Pressure C3H6,Inerts T=71°C P=261.8 p s i g .76, .24

Y i e l d s from a Continuous Backmix Reactor, Simulated with C0NGAS

REACTOR VARIABLE STUDY

Table I I


218


of the monomer by the i n e r t s that might accumulate i n a c o n t i n u ous process w i t h r e c y c l e . The r a t e equation (No. 12) i s f i r s t order i n monomer c o n c e n t r a t i o n . The l a s t column i n Table I I shows a case w i t h about 25% lower propylene c o n c e n t r a t i o n . The y i e l d i s reduced by 11%, once again showing the modifying e f f e c t of d i f f u s i o n - c o n t r o l . The c o n c l u s i o n i s that polypropylene polyr e a c t o r s tend to be d i f f u s i o n - c o n t r o l l e d , whether the process i s s l u r r y , bulk, or gas phase. The d i f f e r e n c e i s i n the y i e l d s achieved before d i f f u s i o n begins to c o n t r o l the r e a c t i o n .


ABSTRACT Appropriate equations f o r propylene p o l y m e r i z a t i o n w i t h TiCl c a t a l y s t in a gas phase system are assembled i n t o complete mathem a t i c a l s i m u l a t i o n s f o r both a semibatch and a continuous backmix p o l y r e a c t o r . These s i m u l a t i o n s are an extension o f the w e l l -proven hexane s l u r r y k i n e t i c models w i t h the s u b s t i t u t i o n of gas phase equations f o r the liquid phase. The semibatch model (GASPP) is verified as an accurate model by t e s t i n g w i t h data p u b l i s h e d by BASF, whereas the continuous model (CØNGAS) is der i v e d from GASPP using the equations a p p r o p r i a t e to backmixing. Given the inputs of c a t a l y s t parameters such as activity, stability, and p a r t i c l e s i z e and o p e r a t i n g c o n d i t i o n s such as temperat u r e , p r e s s u r e , r e a c t i o n time, and gas composition, these models generate y i e l d and p r o d u c t i o n r a t e as outputs. The models are estimated t o have l e s s than 5% e r r o r f o r the f o l l o w i n g range o f conditions: 3

Temperature: Pressure: Reaction Time: C a t a l y s t Activity:

60° to 100°C 50 to 450 p s i a 0 to 6 hours 22 to 597 liter/hr-g T i C l

3

These models i n d i c a t e t h a t propylene gas phase p o l y m e r i z a t i o n with a h i g h l y a c t i v e T i C l c a t a l y s t s h i f t s from k i n e t i c c o n t r o l at s h o r t r e a c t i o n times to d i f f u s i o n c o n t r o l at longer times as the c a t a l y s t yield exceeds about 4000 g.PP/g.TiCl . Measures t o reduce t h i s l i m i t a t i o n would significantly b e n e f i t the process. The e f f e c t s of d i f f u s i o n and c a t a l y s t decay cause y i e l d s from a continuous backmix r e a c t o r to be 25 to 30% lower than from a semibatch r e a c t o r at the same residence time. This yield p e n a l t y can be reduced by s t a g i n g backmix r e a c t o r s in s e r i e s . 3

3

NOTATION A

Catalyst a c t i v i t y ,

g./g./hr.

A

C a t a l y s t s u r f a c e area per u n i t volume of r e a c t o r , c m / l i t e r .

2


BROCKMEIER

9.

Polymerization

B

P r o p o r t i o n a l i t y constant, 0,0025.

C

Concentration, m o l e s / l i t e r .

D


Propylene

Kinetics

2

AB

D i f f u s i v i t y o f propylene i n propane, cm /sec.

d

Diameter,

E^

A c t i v a t i o n energy

E. A k

A c t i v a t i o n energy, -3735 cal/mole.

M

Molecular weight

w

cm. f o r p o l y m e r i z a t i o n , 14,500 cal/mole

Mass t r a n s f e r c o e f f i c i e n t or r a t e constant, cm./sec. g./g-mole.

N

Propylene f l u x i n g - m o l e / s e c - l i t e r .

P

Pressure, l b . / s q . i n . a b s .

R

Mass t r a n s f e r or other r e s i s t a n c e , s e c .

r

Polymerization rate,

T

Temperature,

t

Mean age of r e a c t o r contents, h r .

V

Volume, l i t e r .

v

Mixture s p e c i f i c volume, f t / l b - m o l .

g./hr.

°K.

3

W

Cumulative polymer, g. P

X

m

Catalyst loading, g . T i C ^ .

x

Mole f r a c t i o n i n vapor.

Y

Yield,

X

C a t a l y s t c h a r a c t e r i s t i c time, h r .

p

Density, g./cm .

T

E x i t age of r e a c t o r f l u i d , h r .

g.polypropylene/g.TiC&3.

3

SUBSCRIPTS A

Propylene.

B

Propane and

inerts.




220

c

V a r i a b l e i s d e f i n e d i n terms o f c o n c e n t r a t i o n d i f f e r e n c e ,

cm

Refers to p s e u d o c r i t i c a l mixture.

CAT

Catalyst surface.

DF

D i f f u s i o n i n polymer

E

Equation o f s t a t e v a l u e .

k

Volumetric r a t e constant, l i t e r / h r . - g T i C & .

m

Mixture.

mf

Mass feed r a t e .

OV

Overall.

s

Surface of c a t a l y s t .

v

P e r u n i t volume.

7

s h e l l passages.

3

T1C&3 c a t a l y s t .

ACKNOWLEDGEMENT The author thanks Amoco Chemicals Corp. f o r permission to p u b l i s h t h i s manuscript. The p u b l i c a t i o n s o f Dr. K. Wisseroth have provided a v i t a l i n p u t to v e r i f y t h i s mathematical development. LITERATURE CITED 1. Wisseroth, K., Chemiker Zeitung, (1977), 101, 271. 2. Brockmeier, N. F. and Rogan, J . B., "Simulation of Continuous Polymerization Processes", AIChE Symp. Ser. No. 160, (1976), 72, 28. 3. S a t t e r f i e l d , C.N. and Sherwood, T. K., "The Role of D i f f u s i o n i n C a t a l y s i s " , pp. 45-47, Addison-Wesley, Reading, Mass., 1963. 4. Mathur, G. P. and Thodos, G., AIChE J . , (1965 ) , 11, 613. 5. Peng, D. Y., and Robinson, D. B., I & E. C. Fundam. , (1976), 15, 59. 6. L e v e n s p i e l , 0., "Chemical Reaction Engineering", pp. 112-116 and Ch. 9, Wiley, New York, 1962. 7. Wisseroth, K., Angew, Makromol.Chemie. (1969), 8, 41. 8. Wisseroth, K., K o l l o i d Z. and Z. Polym., (1970), 241, 943. 9. Wisseroth, K., Chemiker-Zeit.,(1973), 97, 181. 10. Wisseroth, K., personal communication, Jan. 6, 1978. 11. Natta, G. and I . Pasquon, "Advances i n C a t a l y s i s " , V o l . I I , pp. 21-23, Academic P r e s s , N.Y., 1959. RECEIVED January 15, 1979.


Polymerization Reactors and Processes - ACS Publications

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