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Modeling of Fluidized Bed Reactors for the Polymerization Reaction of Ethylene and Propylene.

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Dev. Chem. Eng. Mineral Process., 6(3/4),pp.121-134, 1998.
Modeling of Fluidized Bed Reactors for the
Polymerization Reaction of Ethylene and
Propylene
A.E. Abasaeed and S.M. Al-Zahrani *
Chemical Engineering Deptment, King Saud University,PO Box 800,
Riyadh 11421, SAUIIARABIA
Polyethylene and polypropylene are used worldwide due to their versatile physical
and chemical properties. A simplHed dynamic model is developed to describe the
polymerization reactions in a fluidized bed reactor.
The efect of two important
operating parameters, i.e. catalyst injection rate and superficial velocity, on the
performance of the unit are investigated. Qualitatively as well as quantitatively
direrent bi3rcation diagrams are obtainedfor each case. However, in both cases,
operation of the reactor is confined to the stable low monomer conversion region
due to polymer softening temperature limitation.
Keymr&: Modeling;fluidized bed reactors; polymerization; ethylene; propylene.
Introduction
In recent years, polymers have emerged as an important class of materials due to
their versatile and advantageousproperties. Amongst these polymers, polyethylene
and polypropylene collstitute a significant portion (about 30%) of the currentiy
'Author for correspondence.
121
A.E. Abasaeed and S.M. Al-Zahrani
produced polymers. The use of fluidized bed reactors for ethylene and propylene
polymerization reactions has contributed significantly to lowering the required
operational pressures (down to 20-35 am) which translatesintolargesavingsin
capital expenditure and energy consumption. Models with various degrees of
sophistication have appeared in the literature [1-6].
concentrated their &or&
Some of these investigators
on modeling the reactor behaviour [l-31 while others
modeled the growth of polymer particles [4-6].
In this paper, a simplified dynamic model describing the polymerization reaction
of either ethylene or propylene to produce polyethylene or polypropylene respectively
in a fluidized bed reactor is presented. The model incorporates all important events
that take place in the reactor. Two important operatingparameters, i.e. catalyst
injection rate and the superficial gas velocity, are used to investigatetheir effects on
the bifurcation behavior and the performance of these industrially important units.
The Model
Figure 1 shows a schematic diagram of a polymerization fluidized bed reactor, the
UNIPOL process of Union Carbide [7,8]. The major components of the process are:
(a) feed gas which is partly combined with the recycled gas before entering the
bubbling fluidized bed, the other part ofthe fresh feed gas is used to introduce the
Ziegler-Natta catalyst; (b) a catalyst feeder, (c) a product withdrawal system which is
controlled in order to maintain a constant bed height inside the reactoq (d) gas
recycling which includes a cyclone and a compreso~(e) reactor with catalyst
disengagement zone.
A simplified dynamic model is developed to describe the polymerization reaction
of ethylene and propylene in a fluidized bed reactor. The model is based on the twophase (emulsion or dense and bubble phases) theory for fluidized beds. The model
assumes: (1) complete mixing in the emulsion phase which is at incipient
fluidization and where all reactionstake place; (2) the bubble phase is devoid of solid
particles and is in the plug flow regime; (3) the bubble phase is at quasi-steady state;
(4) the catalyst injection and product withdrawalratesareadjustedinsuchaway
122
Modeling offluidized bed reactorsfor polymerization reaction
that rnainta.ins constant bed height inside the reactor, (5) mass and heat are
continuously exchangedbetween the bubble and emulsionphases; (6) negligible heat
and mass transfer resistances between the polymer and the emulsion phase gas;(7)
negligible catalyst deactivation;(8) an average bubble size at 40% of the bed height
is assumed; and (9) catalyst particles are perfect spheres. Based on these assumptions
the mass and energy balances are given as follows.
C em pressor
F i r e 1. Schematic diagram of the fluidized bed reactor for polymerization
reactions.
fi) Bubble Base
The pseudo-steady state mass balance equation for the monomer is given by:
\-a
-DJ
ub
123
A.E. Abasaeed and S.M. Al-Zahrani
The pseudo-steady state energy balance equation is given by:
fi)Emukhn Base
The mass balance equation for the monomer in the emulsionphase is given by:
The catalyst mass balance in the emulsion phase is given by:
The energy balance in the emulsion phase is given by:
By defining the following dimensionlessgroups, Equations (1-5) can be transformed
into the dimensionlessEquations (6-10) below,respectively.
124
Modeling offluidized bed reactorsfor polymerization reaction
x2 = Cca
t
t=t0
x3 =- Td
Tref
x,=-cb
co
yb =- Tb
Tref
Hbe
P = PgCpgUb
Yw =- TW
T4
Results and Discussion
In this preliminary investigation, the catalyst injection rate as well as theratio
between the superficial velocity and the minimum fluidizationvelocity are used as
bifurcation parameters for both ethylene and propylene polymerization. These two
125
A.E. Abasaeed and S.M.AI-Zahrani
operating parameters are very important. The importance of the firstparameter
(catalyst injection rate) is due to the catalyst providing the nucleus upon which the
polymer grows.
The ratio of the velocities is important in determining the
fluidization regime of the reactor, and it also affects the massandheattransfer
exchange parameters. It is important to note that the softening temperature of the
polymer poses a constraint on the upper temperatures at which the reactors can be
operated. For polyethylene, the softening temperature is about 400K &=1.33)
while for polypropylene it is about 420K (X3=1.4).
The hydrodynamic and transport property correlations used in solving the model
equations are obtained from the literature [9-141 and are listed in Table 1 (unitsin
Nomenclature). AUTO86 software was used to obtain the bifurcation diagram [14].
Table 2 contains the various physical, design and operating parameters.
Kgeth=7.6~10-5 H = 100
Cpgeth'o.44
Eapro+'OOO
Cpgpro'o.46
k,=l.1 6 ~ 1 0 ~ K g p r o ~ . l ~ l Ok =~ 1~. 5 ~ 1 0 ' ~
C,,4.456
p+9.67~10'~
P,th4.95
Tw=340
Ceqro4.426
(mR)eth=916
Pspro4.91
D,,=O.05
Eaeth=-
('mR)pr0=560
D = 250
fi) Effed of Catalyst Inj&n
Rate, Qc
The bifurcation diagram for ethylene polymerization is shown in Figure 2 for
U&Jd = 6. Figure 2 relates the dimensionless ethylene concentration(XI), the
catalyst concentration (X2). and emulsion phase temperature (xj),to the catalyst
injection rate (Q as the bifurcation parameter. This bifurcation diagram is
characterized by the presence of two Hopf bifurcation points @Ell, HB2) and two
static limit points (SLP1, SLp2) which indicates the multiplicity of steady states. It
is clear from Figure 2a that as & is increased,the ethylene concentrationdecreases
in a stable fashion until a Hopfbifhcation point (Hl31) at Qc'591.67 g/his reached.
126
Modeling offluidized bed reactorsfor polymerizarion reaction
Table 2. Correlationsfor physical and operatingparameters.
~
~~~
Parameter
Bedvoidageatminhaum
fluidization
~~
Theoretical or empirical expression
~4= 05m"."(
P2
PgdP,
)om
(%)0.021
I Ref
191
- Pgv:
supascinlveiocityat
minimum fluidization
Bubble diamctn
dBo = 0.00376(U0
Bubble risingvelocity
- ud )'
Ub = U, - U d +0.71l(g.dB)05
Fradion of bubble pbse
6=
UO
-uwf
[121
[I21
ub
~fficientfamrsstxansfkr
1
ri21
U
DO5
Kb = 4 & + 1 0 . 4 1
dB
dp5
E
DU
K;? = 6.78( mf e b)05
1-
-
4
As
&
is increased fbrther, a stable periodic branch (the maxima and minima of the
oscillations are denoted by 0 in the Figure 2a) emanatingfrom HB 1 which surrounds
an unstable static branch (dashed lines) is the only stableattractorintheregion
between HB1 (&=591.67) and SLPl (Qc=760.42). Operation on this oscillatory
attractor is hampered by the sofiening temperature of polyethylene (X3=1.33) as seen
from Figure 2c which shows that the reactor temperature reaches prohibitively high
values (X3>2.0). Multiplicity of steady states exists in the region between SLPl and
127
A.E. Abasaeed and S.M.Al-Zahrani
SW2 (&=970.69); two unstable attractors coexistwithonestableattractor. The
temperature of the stable attractor which extends from HB2 (Qc'787.45) is much
higher than the softening temperature of polyethylene as shown in Figure 2c.
Therefore, in order to operate in a stable fashion and within the safe limits of the
polymer softeningtempera-,
the polymerization reaction can only be performed at
low ethylene conversion (i.e. Qc-391.67).
1.2
1.0
0.8
0.6
0.4
0.2
0.0
3.0
f20
0
r
X
(y
1.0
X
- ......1 1
_ _ _ _ -- -- - .....
I
1
3 1.5
u-4
1.0
0.6
0
2
4
6
8
1
O
t
2
Qc (x100 glh)
Fwre 2. Bifurcation diagram for ethylene polymerization with the catalyst
injection rate as the bifurcation parameter: (a) monomer concentration,XI;(h)
catalyst concentration,X2;and (c) dense phase temperature,XJ.
The corresponding bifurcation diagram for propylene polymerization as affected
by the catalyst injection rate is shown in Figure 3. The general trend of this
bifurcation diagram is quite similar to that obtained with ethylene polymerization,
however two major differencesare observed: (1) only two HB points (no SLP points)
128
Modeling offluidized bed reactorsfor polymerization reaction
are present in Figure 3; and (2) the stable branch extends over a much higher value
of catalyst injection rate (%=1565.3 in Figure 3 compared to C&=591.67 in Figure
Due to the 'softening temperature constraint, the operation of the reactor is
limited to low propylene conversion values (Qc<lS65.3), those which are stable as
2).
shown in Figure 3a. The other stable branch w
2
9
6
6
.
7(to the right of HB2) Ealls
completely in a region where the reactor temperatures (X3>1.5) exceed the sofiening
temperature of the polypropylene (X3=1.4) as shown in Figure 3b.
11
,
a04 . . . . . , . . . . . , . . . . . , . . . . . , . . . . .
Ergue 3. Bifircation diagram for propylene polymerization with the catalyst
injection rate as the bijurcationparameter: (a) monomer concentration.XI;and (b)
dense phase temperature, X3
Comparing the results of Figure 2 (polyethylene) to those of Figure 3
@olypropylene), it is clear that: (a) due to softening temperature limitations, both
systems are limited to operation at low monomer conversion values (ethylene less
than 8.3% and propylene less than 13.5%); (b) polypropylene reactors can be
operated safely at relatively higher catalyst injection rates (1565 gh compared to
591 @hfor polyethylene) before reaching the oscillatory region.
129
A.E. Abasaeed and S.M.Al-Zahrani
1.2
I
J
9.0
25
20
2
1.5
1.0
0.5
1
0
1
2
3
1
5
6
7
8
UolUmf
F i r e 4. Bijturcation diagramfor ethylene polymerization with the velocity ratio as
the bijiwcation parameter: (a) monomer concentration, XI;and (h) dense phase
temperature,X3
(ii
Effect
) of Gas Velocity Ratio, Q, = Uo/ Umf
Figure 4 shows the effect of the ratio of superficial velocity to minimum
fluidization velocity (9)on the performance of the polyethylenereactor for &=500
gh. From Figure 4, as cp is increased a Unique stable static branch exists with high
ethylene conversion (Figure 4a) at reactor temperatuns exceeding thesoftening
temperature of the polymer (Figure 4b). Between ~ 2 . 7 7 %(SLP2)and qA.1839
(HB1 which is a degenerateHopf bifurcation point very close to a static limit point
SLPI), three static steady-state branches coexist; two unstable branchesandone
stable branch still with a high reactor temperature (Figure 4b). In the region
4.2793354.966 (HB2), a stable periodic attractor surrout~dsan unstable static
attractor.
The reactor temperature obtained with the periodic attractor as it
oscillates, exceeds the softening temperature limits. At values of p4.966 a unique
stable static attractor is present. It gives low ethylene conversion (Figure 4a)
130
Modeling offluidized bed reactorsfor polymerizarion reaction
however the reactor temperature is well within the safe limits of softening
temperature (Figure 4b).
Figure 5 is the bifurcation diagram for the Sect of cp on propylene
polymerization. It reveals the existence of two Hopf bifurcation points and two static
limit points (unlike Figure 3 which shows only two HB points). From Figure 5b, the
polymer softening temperature limitations can be seen to dictate operation at cp
>3.6424 (HB2). The conversion of propylene on the stable branch (p3.6424) is
low, as seen fkom Figure 5a. The oscillatory region (2.2462<(~<3.6424)gives
uoacceptable reactor temperatures.
1
2
3
4
5
6
7
8
Udllmf
F i r e 5. Bifurcation diagramfor propylene polymerizationwith the velocity ratio
as the bifircation parameter: (a) monomer concentration,XI;and (3) dense phase
temperature,X3
Industrial fluidized bed reactors for polymerization reactions are usually operated
in the range of 3.0-w.0 [3].
polyethylene reactor
From the above analysis it is clearthatthe
6 be operated in a
stable fashion at (p’5 with about 7.8%
conversion, while for the polypropylene reactor it is ~ 3 . 6 with
4 11.4% conversion.
131
A.E. Abasaeed and S.M. AI-Zahrani
Thedore for both systems,the model predicts reactor operation within the industrial
limits.
Other operating and design parameters such as monomer feed temperature,
cooling rate, reactor dimensions, catalyst particle diameter, etc., need to be
thoroughly investigated in order to gain a better understanding of the process, and to
find ways of improving monomer conversion (thus polymer productivity) within the
softening temperature iimitatiOn.
Also Various control strategies could be
implemented to improve monomer conversion.
Conclusions
A simplified dynamic model for ethylendpropylenepolymerization in a fluidized bed
reactor was developed and used for the investigation of the effect of catalyst injection
rate and the superficial gas velocity on the polymerization reaction. The bifurcation
diagrams obtained for the two polymers showed qualitative Werences andalso
reveaIed the interesting bifurcation behavior of the polymerization process. For both
cases and for the set of design and operating conditions used in this analysis, it has
been found that the polymer soaening temperature limitation forces operation at low
monomer conversion regions. It is quite possible that manipulation of some other
operating and design parameters and/or attempts to control the unit to operate at an
unstable static attractor could lead to significant improvements witb regard to
monomer conversion.
Nomenclature
A
cb7cd
CO
CpgC+
D
DP
De
Ea
132
cross sectionalarea of fluidized bed (cm2)
Monomer concentfation in bubble and emulsion phase &/an3)
~nitialmonomer concentration wcrn3)
Heat capacity of gas and solid respectively ( d g K)
Bed diameter (cm)
Average catalyst particle diameter (cm)
Effective diffusivity (cm2/s)
Activation energy (Caymol)
Modeling offuidized bed reactors for polymerization reaction
Bed height (cm)
Coeflicient of heat exchange between bubble and dense phase (caVcm3
s K)
Wall heat transfer coefficient (caVcm2 s K)
Frequency factor (cm3/gatalyst h)
Reaction rate constant (cm3/g~talysth.)
Mass transfer coefficient ( a d s )
Coefficient of gas intercbge between bubble and cloud-wake region
(Sl)
Volumetric product withdrawa~rate (cm3m)
Catalyst injection rate (g/h)
Total pressure (atm)
Gasconstant
Reynold's number at minimum fluidization
Bubble phase temperature (K)
Emulsion phase temperature (K)
Feed gas temperature (K)
Reference temperature (K)
Reference time (s)
Wall temperature (K)
Bubble velocity ( a d s )
Inlet gas velocity ( a d s )
Minimumfluidization velocity (cmls)
Molar volume of component i
Dimensionless monomer and catalyst concentration in dense phase
Dimensionless dense phase temperature
Dimensionless monomer concentration in bubble phase
Dimensionless bubble phase temperature
Mole fraction of componentj
Dimensionless wall temperature
parameters used to nondimensionalize the model equations
Fraction of bed consisting of bubbles
Void fraction at minimum fluidization
Viscosity (g/cm s)
Density of gas (g/cm3>
Density solids (g/cm3)
Abbreviations
SPB
SSB
UPB
USP
Stable periodic branch
Stable static branch
Unstable periodic branch
Unstable static branch
133
A.E. Abasaeed and S.M. Al-Zahrani
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Received: 14 February 1997; Accepted @er revision: 21 May 1997.
134
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