Ind. E n g . Chem. Res. 1989,28, 1644-1653
1644
Literature Cited
lihood estimation leads to the following result:
32
=
l N (In A - K
N - 1,=1
) ~
(A81
where N is, as usual, the total number of failure rates, A,, available. The resulting posterior distribution is Xk-le-(lnX--x)2/(282)e-xt
f W 0 )=
~ m ~ k - l e - ( l n X - x ) P / ( 2 z ) e - r t dA
(A9)
The denominator in eq A9 has to be evaluated numerically. Weibull Distribution. The probability density function for this case is f ( A ) = 7b(qA)b-1e-(?A)b 7, A, b > 0 (A10) The distribution parameters 7 and b of eq A10 are calculated with the maximum likelihood method, which leads to the following set of nonlinear equations which have to be solved iteratively:
N
qb
= N / C Anb
(All)
n=l
The corresponding posterior distribution is Ab-l+ke-(qX)be-At
f(A/O) = JmAb-l+ke-(?A)be-At
dx
(A12)
Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions; Dover Publications: New York, 1984. Anyakora, S. N.; Engel, G. F. H.; Lees, F. P. Some Data on the Reliability of Instruments in the Chemical Plant Environment. Chem. Eng. 1971 (Nov), 396-402. Apostolakis, G. Data Analysis in Risk Assessment. Nucl. Eng. Des. 1982, 71,375-381. Apostolakis, G.; Kaplan, S.; Garrick, B. J.; Duphily, R. J. Data Specialization for Plant Specific Risk Studies. Nucl. Eng. Des. 1980,56, 321-329. De Finetti, B. Foresight: Its Logical Laws, Ita Subjective Sources. In Subjective Probability; Kyburg, H. E., Jr., Smokler, H. E., Eds.; John Wiley & Sons: New York, 1937; English Translation, 1964. Green, A. E.; Bourne, A. J. Reliability Technology; Wiley Interscience: London, 1972. Homke, P.; Krause, H. W.; Ropers, W.; Verstegen, C.; Huren, H.; Schlenker, H. V.; Dorre, P.; Tsekouras, A. ZuverlLsigkeitakenngr6genermittlung im Kernkraftwerk Biblis B-Abschldbericht. Report GRS-A-1030/I-VI; GRS: Koln, FRG, Dec 1984. IEEE. IEEE Guide to the Collection and Presentation of Electrical. Electronic Sensing Component and Mechanical Equipment Reliability Data for Nuclear-Power Generating Stations. IEEE Std. 500, 1984 (Rev. of ANSI/IEEE Std. 500, 1977). Mann, N. R.; Schafer, R. E.; Singpurwalla, N. D. Methods for Statistical Analysis of Reliability and Life Data; John Wiley & Sons: New York, 1974. Martz, H. F.; Waller, R. A. Bayesian Reliability Analysis; John Wiley & Sons: New York, 1982. OREDA-Offshore Reliability Handbook; a/s Veritas-Huset: Hervik, Norway, 1984. Ramsey, F. P. The Foundations of Mathematics and Other Logical Essays; Routledge and Kegan Paul: London, 1931. Skala, V. Improving Instrument Service Factors. Instrum. Technol. 1974 (Nov), 27-30. Received f o r review February 23, 1989 Revised manuscript received June 15, 1989 Accepted July 5, 1989
The denominator of eq A12 has to be evaluated numerically.
Temperature Control of Continuous, Bulk Styrene Polymerization Reactors and the Influence of Viscosity: An Analytical Study Louis S. Henderson, III,* and Ricardo A. Cornejo Engineering Resins R&D Department, A R C 0 Chemical Company, 3801 West Chester Pike, Newtown Square, Pennsylvania 19073
This is an analytical study of the influence of viscosity on the temperature control of a well-mixed continuous reactor producing polystyrene via thermal polymerization of styrene monomer. Three temperature control schemes are considered: (1) heat removal by cooling coils and a cooling jacket, (2) heat removal by vaporization and reflux of styrene and the solvent (autorefrigeration), (3) heat removal by a pump-around loop with external heat exchanger. In the coil/jacket-cooled reactor, the heat-transfer coefficient drops off dramatically with conversion, leading t o a narrow operating range for controllability. This factor also reduces the potential for multiple steady states. The autorefrigerated reactor permits a broad range of temperature control with reflux of the condensed vapor and shows no potential for multiple steady states. Finally, the reactor cooled by the external pump-around loop and heat exchanger can provide the most robust temperature control with recirculation rate as an additional control parameter. I. Introduction Virtually all polymerization reactions are exothermic, as the combination of molecules to form a single-polper molecule always yields a decrease in entropy. *Author to whom all correspondence should be addressed.
Conseauentlv. reactors for Dolvmer Droduction reauire a heat-rimoval"&pability for timkratire control. Sdficient mixing is also required so that the temperature control point(s) is representative of the conditions in the reaction zone. In bulk Dolvmerization mocesses. where the reactor contains 30-9b%" polymer dikolved in its monomer (or solvent), the viscosity increases by several orders of mag-
0888-5885/89/2628-l644$01.50/00 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 11,1989 1646 r _ _ _ _ _ _ _ _ _ - _ -
I
I
100 H P OR 1 V E
FEED
TEVPERED HATER RETURN
-
CONDENSATE RECYCLE
REACTOR PRODUCT
A I TERPERATURE CONTROL V I A C O O L I N G JRCKET AND C O I L S
REACTOR PRODUCT 81 T E M P E R A T U R E C O N T R O L V I A V A P O R I Z A T I O N OF SOLVENT/VONOVER
X
REACTOR RECIRCULATION PRODUCT PURP C l TEVPERATURE CONTROL V I R FORCED C I R C U L A T I O N OF SYRUP THROUGH E X T E R N A L H E A T EXCHRNCER
Figure 1. Polymerization reactor temperature control schemes.
nitude from the feed solution to the final reactor product. This makes perfect mixing impossible to achieve without a large energy input from the agitation system. Viscosity has a significant effect on the reaction kinetics and heattransfer characteristics as well. All of these factors make the analysis of polymerization reactors quite complex. At present, no generalized criteria have been developed for the interaction of viscosity with temperature stability in continuous, bulk polymerization reactors. This paper will demonstrate the complexity of the problem by examining the well-understood styrene polymerization reaction in an industrial scale, turbine-agitated, continuous stirred tank reactor (CSTR). It can be safely stated that no single polymerization system has more published data than that of styrene to polystyrene. The results presented in this work are based on the data from published sources. Three basic mechanisms for removing the heat of reaction of industrial interest are considered, which are illustrated in Figure l. Figure 1A shows the familiar jacketed reactor where the temperature is controlled by both cooling coils and a jacket. The jacket temperature is rapidly adjusted to control the reactor mass temperature. The autorefrigerated reactor is shown in Figure lB, in which controlled vaporization of the monomer and solvent serves to remove the heat of reaction. The reactor temperature and pressure are maintained very close to the bubble point. Finally, Figure 1C shows the reactor where the contents are circulated through an external heat exchanger. The tempered water in the heat-exchanger shell is rapidly adjusted to control the reactor mass temperature. As in Figure lA, heat-transfer surfaces are used to remove heat, but the task of mixing has been isolated from heat transfer, unless very high recirculation rates are utilized. All three methods of heat removal shown in Figure 1 are utilized in commercial polystyrene production, although the exact reactor configurations themselves can vary widely, as pointed out by the numerous examples in
Gerrens' review.' I t is best to cascade the continuous reactors in a polystyrene plant in order to achieve the desired molecular weight distribution while maintaining regions of controlled viscosity, but the issues related to reactor staging will not be considered further here. 11. Problem Basis
For all the results that follow, we will consider a 5OOO-gal reactor for the production of polystyrene by thermal polymerization. The feed rate to this reactor will be maintained at approximately 20 100 lb/h, which yields a corresponding residence time of 2 h. The feed consists of 90 wt 7% styrene and 10 wt % ethylbenzene. The ethylbenzene serves as a diluent which prevents the reactor contents from going to a 100% solid mass in the event of a runaway. The patent literature also suggests the use of ethylbenzene (see, e.g., ref 2). The reactor geometry, agitator dimensions, and heat-transfer specifications for the three reactor types are listed in Table I. The reactor feed is preheated to 70 OC. Extensive laboratory measurements and correlations on the thermal polymerization of styrene were done by Hamielec and co-worker~.*~ These kinetics are part of a computer program utilized to simulate the 5oOO-galCSTR, assuming perfect mixing. Figure 2 shows the reactor solids as a function of steady-state temperature. Solid content, or polymer content, is 0.9 times the conversion accounting for the 10% diluent. The solid content goes from -2 wt % at 90 "C to almost 80 wt % at 220 "C. The computed polystyrene weight-average molecular weight (M,) is presented in Figure 3 as a function of temperature. M , drops from almost 1 X los at 90 "C to -50000 at 220 "C. The apparent discontinuity at 200 "C is because a different correlation equation for M, is utilized at >200 "C. It has been demonstrated by both Hamielec5 and KhacTiens that the molecular weight of polystyrene drops off dramatically when polymerized in excess of 200 "C, but
1646 Ind. Eng. Chem. Res., Vol. 28, No. 11, 1989 Table I. (A) Reactor Dimensions and Agitator Geometry and (B) Heat-Transfer Specifications autorefrigerated, specifications jacket/coil cooled, Figure l a Figure l b Section A vessel vol, gal 5000 8300 liquid holdup, gal 5000 5000 id., in. 97.2 turbine diam, in. turbine type 4 blades same for all three cases no. of turbines 2 10 blade width, in. drive motor horsepower 100 84 agitator speed, RPM jacket area, ft2 cooling coil surface area, ft2 overhead condenser system external heat exchanger surface area, ft2 HX tube diam, in. tube length, in. no. of tubes recirculation rate, lb/hr
Section B 325 325 helical 2-in.-diam pipe none none
externally cooled, Figure IC 5000 5000
325" none
325O none
yes none
none yes 650 1.0 8 310 40000-80000
Only used to insulate the reactor (maintain adiabatic conditions). 00
40000
-I
70 60
3
5-
50
2
40
5
30
v)
s m II:
20 10
0 , 90
0
Steady-State Reaction Temperature (Deg C ) Figure 2. Solids level as a function of steady-state temperature: prediction from Hamielec kinetics.
,
I
I
1
110 130 150 170 190 210 230
Steady.State Reaction Temperature (Deg C) Figure 4. Zero-shear viscosity vs steady-state temperature: Mendelson viscosity correlation.
it is doubtful that the step change shown is real. Reactor mixing and heat-transfer characteristics are strongly dependent on viscosity. The zero-shear viscosity at 200 "C was estimated with a correlation developed by M e n d e l ~ o nfor ~ , ~40-100% polystyrene in ethylbenzene: 70(200 "C) = 3.31 X 10-'2w,'0~7Mw3~4 (1) The viscosity can then be shifted to the temperature of interest via
1000000
900000 000000
700000
6oooool\\
2 ' 500000
400000~ 300000
200000 100000
o !
90
1
110 130 150 170 190 210
230 Steady State Reaction Temperature (Deg C )
Figure 3. Weight-average molecular weight vs steady-state temperature: prediction from Hamielec kinetics.
where Ef, the activation energy for flow, is calculated by Ef = 2300 e x p ( 2 . 4 ~ ~ ) (3) The API viscosity blending method (Technical Data Book-Petroleum Refining: American Petroleum Institute: Washington, DC, 1970; Procedure 11.43.1) was used to tie-in the region of 0-40 wt % solids, where 170
= (cxi17i"3)3 I
(4)
Ind. Eng. Chem. Res., Vol. 28, No. 11,1989 1647
looOoi I i f
8000
2
50000001 4000000
I-
E!
-
3000000J
-Es
2000000
.-5
of Polymerization Only
8 Laminar
\ Region
) I
I
90 110 130 150 170 190 210 230 Steady-State Reaction Temperature (Deg C)
Figure 7. Effect of agitator power on heat-generation curve.
temperature, an empirical correlation of the data in Boundyll was developed and utilized for Figure 7. AH,, (kcal/mol) = 24.2674 - 1800.73/(T
+ 273) - O.O0529(TR + 273) (5)
The upper curve of Figure 7 includes the shaft horsepower, and in the region of 150-170 "C, the heat generation rises rapidly. This has important implications on reactor temperature stability.
111. Temperature Control via Cooling Jacket and Coils
90 110 130 150 170 190 210 230 Steady-State Reaction Temperature (Deg C )
Figure 6. Agitator shaft horsepower vs steady-state temperature: Chemineer correlation.
Figure 4 demonstrates the dramatic change in viscosity with steady-state operating temperature as developed from eq 1-4. The solid level increase dominates the expression up to 180 "C, where a peak of 38000 CPis reached. Then the effect of temperature and the production of low molecular weight species predominate at >180 "C, bringing the viscosity to a downward trend. The Reynolds number in the 5000-gal reactor, which is inversely proportional to the viscosity, drops from several thousand to -50, as shown by Figure 5. For this type of agitator, the transition from turbulent to laminar flow occurs in the region of Re = 1000.20 One must seriously question the extent of mixing at values of Re less than 100, particularly for turbine agitation of non-Newtonian fluids, as pointed out by MetmeragStudies on the residence time distribution in this region would be particularly useful. Given the viscosity and agitator characteristics, it is then possible to calculate the shaft horsepower (SHP), which is the mechanical work put into the reaction mass. By use of a set of correlations developed by Dickeyloof Chemineer, Figure 6 was constructed. Over most of the temperature range, the SHP per turbine is approximately 15, but it jumps up to almost 30 HP/turbine at 175 "C. This has an impact on the reactor energy balance as shown in Figure 7. In Figure 7, the lower curve is the heat generated due to polymerization only for the 5000-gal reactor system. Recognizing that the heat of reaction is a function of
-
The use of jackets and coils to maintain the temperature in industrial chemical reactors, such as that shown in Figure lA, is quite common, but in bulk polymerization systems, these can have serious drawbacks. The effect of increasing the reaction mixture viscosity on mixing, and consequently heat transfer, is very deleterious. There have been many publications on the temperature stability of polymerization in jacketed reactors, such as those of Amundson and Goldstein,12Ray and c o - ~ o r k e r s , who ~~-~~ experimentally demonstrated multiple steady states in certain polymerization systems, and Choi,lGbut the viscosity effects were considered insignificant. Knorr and O'Driscolll' considered the effect of viscosity on reaction kinetics for bulk styrene polymerization and demonstrated the potential for isothermal multiple steady states. Hendersonl8 was the first to show the interaction of viscosity with the heat of agitation and heat transfer. That work will be expanded upon here. Generalized equations for heat transfer in turbine-agitated vessels with and without coils have been collected and presented in the texts of Nagata,lg Oldshue,20and Rase.21 For the reactor described in Table I, the following correlations for the inside film coefficient, hi,were utilized as in ref 18: jacket, Re > 100
jacket, Re < 100 hiT
NU = k = 0.51(RePr)'/3
(7)
1648 Ind. Eng. Chem. Res., Vol. 28, No. 11, 1989
helical coils, Re > 100
hid
N u = - - - 0.0228Reo.07Pr0.37 k helical coils, Re 100 Nu
(8)
hid k
= - = 0.O228(RePr)'l3
Figure 8 shows the overall heat-transfer coefficient, U,, as a function of steady-state reactor temperature. A value of 250 BTU/(h*ft2."F) was used for the jacket water-side film coefficient. The dramatic drop in the heat-transfer coefficient with increasing conversion is clearly shown, and the lower jacket temperatures yield lower heat-transfer coefficients. This is a result of the term qR/qW, the ratio of viscosity of the bulk solution to that at the jacket surface, decreasing as the reactor jacket is made colder. The region of 160-190 "C is where the Reynolds number is less than 100 and heat transfer by conduction dominates. By use of the heat-transfer coefficients to determine the heat removal rate, the overall system energy balance can be analyzed by constructing a van Heerden diagram as shown in Figure 9. This graphical procedure was first described by van Heerden in 1953.= The heat-generation and heat-removal curves are plotted as a function of temperatue, and the intersections represent stable or unstable operating points where the rate of heat removal equals the rate of heat generation. Figure 9 illustrates several key points. First, there are only two temperatures where the heat-removal capability is equal to the heat generated. These are 145 "C for a jacket temperature of 100 "C and 150 "C when the jacket is set at 60 "C. These steady-state points are surprisingly close for such a wide variance in jacket temperature. A jacket temperature of 140 "C does not remove sufficient heat in the range of reactor temperatures shown. In the region where the heat-generation curve has the steepest upward slope, the heat-removal curves have a negative slope. A slight increase in temperature increases the reaction rate, solids, and heat release while a t the same time reducing the heat-removal capability due to increased viscosity. This is why the potential for multiple steady states in commercial-scale bulk polymerization reactors using jacket heat transfer is almost nonexistent. ArkB defines a reactor as being unstable if the slope of the heat-generation curve is greater than the heat removal curve:
-~ >Q - G
.....\
'.,\
30 C
20
3.1
T, = 140'C
-
I I;.."'
a,
I
r
,......T , = T
10 -
0
I
I
100
120
140
160
180
200
220
Steady-State Reaction Temperature (Deg C) Figure 8. Change in heat-transfer coefficient with reactor temperature. 5000000 1
-
8
160
i i o i s 0 2 i o 2io Reaction Temperature (Deg C) Figure 9. Heat-generation and heat-removal curves for the jacketcooled reactor: van Heerden diagram. 130
where C is a constant dependent on the geometry of the agitator system. Then
~ Q R
(10) dT dT The heat-removal equation is defined as follows: dQR/dT = A[(TR - Tj) dU,/dT] + U, + mFCPp (11) When dU,,/dT is zero, the equation reduces to the familiar UJ + mFCp,which is the slope of the heat-removal curve utilized in almost all publications on jacketed reactor stability. If one examines the slope of dU,/dT in terms of viscosity change, then -dU, = - - dU, dq (12) dT dq d T If we propose a Sieder-Tate-type heat-transfer equation of the same form as eq 6-9 and state that the inside film coefficient is approximately equal to the overall heattransfer coefficient, then
100 "C
T = 60°C
(14) In eq 14,we have assumed that the viscosity at the wall is constant. This may be true in the event of a small perturbation in conversion but is not true when there is a significant change in the solid content adjacent to the reactor wall. The other portion of eq 11that is required is the change of viscosity with T, which can be determined by differentiating eq 1-3
x( T
10-12w,'0.7Mw3~4 exp[ Ef 1 -
A)]]
(15)
In eq 15, the weight fraction solids, molecular weight, and activation energy all vary with T. If we assume that the molecular weight and activation energy for flow do not
Ind. Eng. Chem. Res., Vol. 28, No. 11, 1989 1649 change significantly over some perturbation in temperature, then
5000000
-dvR- - 3.31 X
4000000
dT -~
(2)
exp(Ef/R(l/T - 1/473))10.7~>~- -
1
3000000
I .. 2000000
As shown by Figure 2, dw,/dT is always positive and can be determined explicitly by differentiating the kinetic expressions. Combining eq 14 and 16 into 10 gives 0 90
1 110 130 150 170 190 210 230
Reactor Temperature (Deg C) Figure 10. Energy balance curves for autorefrigerated reactor. No reflux of condensed monomer and solvent.
exp(Ef/R(l/T - 1/473))
w,’0.’(Ef/RT2) exp(Ef/R(l/T - 1/473))
c 5000000-
I1
(17)
’ 0
+ Sens Heat Feed) 4000000-
Equation 17 exemplifies the considerable complexity in evaluating the slope of the heat-removal curve in polymerization systems, and that it is indeed a highly nonlinear function, as was illustrated by Figure 9. These are the expressions that must be evaluated to determine the reactor stability in combination with the slope of the heatgeneration-rate curve. The heat-generation rate increases monotonically with temperature as shown in Figure 7. From a more pragmatic standpoint, a key issue with jacketlcoil-cooled polymerization reactors is that the jacket temperature must be limited to prevent fouling. When the heat-transfer surfaces are allowed to get too cold, the viscosity at the surface increases dramatically. The fluid adjacent to the coils moves very slowly and is not mixed well with the bulk reactor contents. The solid content at the surface builds, and high molecular weight species form because of the low reaction temperature (see Figure 3), yielding an even higher viscosity. A “snowballing” effect occurs, because the fouling layer builds up thicker and the reactor jacket temperature is dropped further in an attempt to control the reactor temperature. Because polystyrene has such a low thermal conductivity, even a thin layer on the coils will reduce U, significantly. In commercial reactors, it has been observed that the heattransfer coefficient can drop with operating time, to the point that it is not possible to control the reactor mass temperature. At that point, T R starts to increase due to the limited heat-transfer ability.
the reactor vessel volume to have a 40% void volume which allows for vapor disengagement from the boiling mass. The heat of vaporization of the styrene monomer and ethylbenzene is about half of the heat of reaction for this system. In the autorefrigerated reactor, heat removal occurs through vaporization of solvent and monomer, the sensible heat required to warm up the cold feed, and the sensible heat required to warm up the cold reflux. The condensate temperature is set at 50 “C, well below polymerization temperatures. Therefore, the heat-removal rate is defined as QR = FC,,(TR - TF) + wAHv + fWCp,(TR- 50) (18)
IV. Temperature Control via Evaporation: The Autorefrigerated Reactor Vaporization of solvent and/or reactants is an effective means of removing heat from an exothermic reactor. Autorefrigerated reactors are used commercially for a variety of exothermic reactions including polymerizati~n.~~ Luyben2s did a very thorough control analysis of the autorefrigerated reactor in a standard hydrocarbon process. This section will examine some of the issues in the autorefrigerated styrene polymerization reactor. The reactor described in Figure 1B and Table Ib has the same residence time and other key parameters as. the jacket/coil-cooled reactor, but it is necessary to increase
where W is the vaporization rate and f is the fraction of vapor condensed and recycled to the reactor. The reactor jacket is maintained at the reaction temperature and does not contribute to heat removal. Both the sensible heat of the feed and the sensible heat of the reflux are significant portions of the total heat removal as shown in Figures 10 and 11. Boil-up rates required to achieve a given steady-state reaction temperature are substantially higher when there is no reflux (Figure 10) as opposed to total reflux (Figure 11). The boil-up rate with total reflux, shown in Figure 12, is controlled by cascading the temperature controller into the reactor pressure controller. The maximum slope of the boil-up curve is about 330 lb/(h-”F). If one were to lump the
I
090
I
,
1
0
I
!
110 130 150 170 190 210 230
Reactor Temperature (Deg C) Figure 11. Energy balance curves for autorefrigerated reactor. Total reflux of monomer and solvent. Reflux at 50 O C .
1650 Ind. Eng. Chem. Res., Vol. 28, No. 11, 1989 6o
I
I
1
0
I
90 110 130 150 170 190 210 230 Reactor Temperature (Deg C)
Figure 12. Boil-up rate required to maintain reactor temperature. Total reflux at a temperature of 50 ' C .
0
1 90 110 130 150 170 190 210 230 Reactor Temperature (Deg C )
Figure 14. Reactor pressure at steady state. Prediction from the Flory-Huggins equation.
1.7
1.6 1.5
25% Reflux
2 0
1.3
100
k
-
a
80 70
Q
1.2
20 m
1,l
75% Reflux
,//'
60 0 5
50
-
(I)
- _......'I
I
I
I
11.0
BE
30
401
*O
1
/
l o0 90 110 130 150 170 190 210 230 Reactor Temperature (Deg C)
Figure 15. Effect of percentage reflux on reactor solids level.
flow rate of the vapor boiling from the reactor goes through a maximum at about 150 O C as shown in Figure 12. The controllability becomes questionable at this transition point, as a process disturbance could move the steady-state operating temperature to either side of the peak. A given volumetric vapor rate through the control valve will offer two steady-state temperatures. As noted above, the boil-up rates become close to the reactor throughput at high conversions. Figure 15 illustrates the effect of reflux percentage on the reactor polymer (solid) content. These curves were calculated via material balance equations. We did not consider the increase in mechanical work required when there is less than total reflux or the impact on polymerization kinetics. It is clear that the return and remixing of the condensate stream has a major effect on the operation of the reactor. Any increase in reactor solids (because of condensate holdup or poor mixing) will result in even higher viscosities, more mechanical work, and higher heat duties. This could feed upon itself until either the agitator motor overloaded and/or the reactor loses temperature control. Another issue is the reactivity of the monomer in the reactor head space and condenser system. If the monomer thermally polymerizes at its dew point in the condenser, plugging of the tubes will eventually occur. This can be mitigated by feeding a continuous stream of cold recycle monomer through the condenser. If one comonomer in a copolymerization system is significantly more reactive and
Ind. Eng. Chem. Res., Vol. 28, No. 11, 1989 1651 f
1601
0,
1504
,R = 80,000
3000000
8
2000000
E-
o_
-
I
1
I
,q+ R = 40,000 Ibslhr
!\
i
m
I
(3
1
1000000 -
60
!
1
I
1
I
I
I
1
0
90 110 130 150 170 190 210 230 Reactor Temperature (Deg C )
Figure 16. Styrene polymerizationreactor with recirculation loop. Heat-exchanger outlet temperature at various recycle rates.
I
90
1
I
where R is the recirculation rate, Tois the heat-exchanger outlet temperature, and LMTD is the log-mean temperature difference between the recirculating polymer syrup and the heat-exchanger cooling fluid. As in the autorefrigerated reactor example, the reactor jacket is held at the reaction temperature and does not contribute significantly to heat removal. This also minimizes the chance for fouling on the reactor interior surface. Figure 16 shows the heat-exchanger syrup outlet temperature required for heat removal as a function of the reactor operating temperature at circulation rates varying from 40 000 to 80 000 lb/h. The required outlet temperature increases linearly with temperature initially but then drops off in the region where the heat generation curve is steep (referring to Figure 7). It is apparent that at the 40000 lb/h recirculation rate the syrup temperature goes as low as 65 O C (when the reactor is at 170 "C)and that one syrup outlet temperature can satisfy two operating points. For example, if the syrup outlet temperature is
I
1
Reactor Temperature (Deg C) Figure 17. Viscosity at heat-exchanger outlet at various recycle rates.
also more volatile than the other comonomer, polymer buildup will occur in the reactor head space and condenser. V. Temperature Control via Forced Circulation through an External Heat Exchanger In the jacketed reactor, the heat-removal capability decreased with conversion as the Reynolds number dropped off dramatically. The agitation level and heat transfer were totally interdependent. By utilizing an external heat exchanger, like that in the system shown in Figure lC, one can eliminate the dependence of the heat-removal capability on the reactor agitation level. Such a system can handle significantly more heat duty than the jacketed reactor, even with an identical amount of heat-transfer area because the circulation rate can be varied. The disadvantages of the recycle loop system are additional capital cost and increased process complexity and associated operating costs. For this example case, a shell-and-tube external heat exchanger was selected with 310 1-in.-i.d. tubes that are 8 f t long as listed in Table I. The surface area is 650 ft2, equivalent to the jacketed reactor example. This is an unnecessary restriction, but it allows a direct comparison to the other reactors on an equivalent heattransfer-area basis. The heat-removal term for the externally cooled reactor is defined as follows:
I
110 130 150 170 190 210 230
R = 40,000 Ibs/hr
f'! I I, I
1
i
a
?? 2 0 0 4
R = 50,000
\
' \ d R = 60,000
I,?'/ : : / ..., \\:,,
10oL
,
,
.___._.
Q
90
110
,.'i
130 150 170 190
-
+... .ph;.... 1
210 230
Reactor Temperature (Deg C) Figure 18. Pressure drop across the heat exchanger: various recycle rates. controlled at 80 "C, the reactor could operate at 142 "C (35% solids) or 200 OC (70% solids). The heat-exchanger syrup outlet viscosity is shown in Figure 17 at various recirculation rates. Because the lower recirculation rates require lower heat-exchanger outlet temperatures, the viscosity at the outlet becomes extremely high in the reactor temperature region of 160-200 "C. The outlet viscosities were calculated by using eq 2. These viscosities translate directly to the pressure drop, shown in Figure 18. The pressure drop was calculated by applying the Hagen-Pousille equation for laminar flow:
An arithmetic average viscosity was used: oavg = (VR + ?HX0)/2*0
(22)
where oHXO is the viscosity at the outlet of the heat exchanger. The pressure drop across the heat exchanger is a critical parameter. The heat exchanger and piping are limited to an allowable working pressure, and there will be a relief valve or rupture disk located downstream of the recirculation pump to see that this pressure is not exceeded. It is very important to note that, in polymerization reactors with external heat exchange, the pressure drop is actually higher at lower recirculation rates. This is just
1652 Ind. Eng. Chem. Res., Vol. 28, No. 11, 1989 Table 11. Design Issues Relative to the Three Reactor Types capital and ideal operating heat-removal method cost advantages
autorefrigeration
external heat exchanger
issues
variable heat-transfer coeff-long-term fouling problematic when the monomer reacts in the vapor space relatively simple to operate foaming and entrainment can be a problem, particularly during upset conditions wide flexibility (additional degree of freedom) pressure drop constraints/ high pressure piping
can operate over a wide range
mixing and polymerization
the opposite of that which would be expected in a standard low viscosity hydrocarbon process. Generally, the pressure drop is expected to go up directly in proportion to the recirculation rate as eq 20 would indicate. But the syrup outlet viscosity dominates the pressure drop calculation. There are two concerns when using multitube heat exchangers to cool polymer melts or solutions: one is fouling of the tube interior walls and the other is flow maldistribution. Fouling of the tube surfaces is not as severe as jacket fouling because the tube surface is kept closer to the bulk temperature-lower LMTD's. Nonetheless, it can occur, and mechanical or thermal cleaning would be required. The issue of flow maldistribution has been discussed in several papers. MuellerZ7did the earliest theoretical analysis of the problem, while StreifP8 expanded the analysis to non-Newtonian flow and presented data from an actual 22-tube heat exchanger used in polymer cooling. Streiff showed that many of the tubes had polymer exiting at the cooling water temperature at very low flow rates, while a few tubes had polymer syrup which was coming out hot at high flow rates. Flow maldistribution was also studied by JoostenS and Khac-Tien,30for coolers with simultaneous styrene polymerization, adding more complexity. For this analysis, we assume the residence time in the external heat exchanger is so short that the styrene conversion is insignificant. The phenomenon of a flow maldistribution in polymer syrup cooling is easily understood in principle but difficult to predict when it will occur. If a disturbance occurs that reduces the flow in one tube, the syrup will cool relative to the other tubes. The viscosity will increase, and given a constant pressure drop across the heat exchanger, the flow will decrease further. On the other hand, if a particular tube has an increased flow rate, it will leave the heat exchanger at a higher temperature, and the average viscosity in that tube will drop. At a constant pressure drop, the flow rate will increase. This problem is most likely to occur when the inlet viscosity is high (>20000 cP) and the LMTD on the heat exchanger is large (>lo0 "C). VI. Conclusions In this paper, we have presented some of the issues involved in heat removal from bulk styrene polymerization reactors. Each reactor type has advantages and disadvantages, which are summaried in Table 11. Although the jacket-cooled reactor is the simplest to design and operate, it can be the poorest design for temperature control and long-term reliable service. The autorefrigerated polymerization reactor gives robust temperature control for polymerization systems as long as the volumetric vapor rate increases monotonically with control temperature, and there is not a problem with reaction in the head space of the reactor. The externally cooled reactor is becoming more attractive with the advances in polymer heat-exchanger and pump design. LMTDs should be kept small
exchanger requires more complex control scheme
to minimize tube plugging problems. The region of flow maldistribution in a multitube exchanger must be avoided, or effective surface area will be lost. Acknowledgment This paper was presented at the 1987 Annual Meeting of the American Institute of Chemical Engineers in New York City, NY. We express our gratitude to ARC0 Chemical for allowing the publication of this work. Nomenclature A = heat-transfer area C,, = heat capacity of the feed C, = heat capacity of the reaction mixture Cpc= heat capacity of the condensate D = agitator diameter d = cooling coil tube diameter Ef= activation energy of flow f = fraction of boil-up refluxed to reactor F = volumetric feed rate AHRXN= heat of reaction/polymerization hi = inside film heat-transfer coefficient h, = outside jacket heat-transfer coefficient k = thermal conductivity of the reaction mixture L = heat-exchanger tube length M w = weight-average molecular weight N = agitator rotational speed NT = number of tubes in the heat exchanger Nu = Nusselt number P = reactor pressure Po = vapor pressure AP = pressure drop across the heat exchanger Pr = Prandtl number r = heat-exchanger tube radius R = gas constant, 1.987 cal/(moLK), or recycle rate Re = Reynolds number T = reactor internal diameter (eq 6-9) or temperature, K (eq 15-17) TF = feed temperature T . = reactor jacket coolant temperature T'R = reactor temperature U, = overall heat-transfer coefficient U,,, = overall heat-transfer coefficient in the external heat exchanger V = volume fraction polymer = reflux/vaporization rate in the boiling reactor wp = weight fraction polymer
d
Greek Symbols x = Flory-Huggins interaction parameter qo = zero shear viscosity qR = reactor fluid viscosity qw = reactor fluid viscosity at the jacket surface pF = density of the feed pR = density of the reactor contents Registry No. Polystyrene, 9003-53-6.
Ind. Eng. Chem. R e s . 1989,28, 1653-1658
References Gerrens, H. On Selection of Polymerization Reactors. Ger. Chem. Eng. 1981,4, 1-13. U.S. Patent 4,221,883,Sept 9,1980; assigned to Dow Chemical Company. Duerksen, J. H.; Hamielec, A.; Hodgins, J. W. Polymer Reactors and Molecular Weight Distribution. AIChE J. 1967, 13, 108. Hui, A. W.; Hamielec, A. Thermal Polymerization of Styrene at High Conversions and Temperatures. An Experimental Study. J. Appl. Polym. Sci. 1972, 16, 749. Husain, A,; Hamielec, A. Thermal Polymerization of Styrene. J . Appl. Polym. Sci. 1978, 22, 1207. Khac-Tien, N.; Flaschel, E.; Renken, A. The Thermal Bulk Polymerization of Styrene in a Tubular Reactor. Polymer Reaction Engineering; Hanser Publishers: Germany, 1980. Mendelson, R. A. A Method for Viscosity Measurement of Concentrated Polymer Solutions in Volatile Solvents at Elevated Temperatures. J . Rheology 1979,23(5),545. Mendelson, R. A. Concentrated Solution Viscosity Behavior at Elevated Temperatures-Polystyrene in Ethylbenzene. J . Rheology 1980,24(6),765. Metzner, A. B.; Taylor, J. S. Flow Patterns in Agitated Vessels. AIChE J . 1960, 6(1), 109. Dickey, D. S. Program Chooses Agitator. Chem. Eng. 1984, 91(1), 73. Boundy, R. H.; Boyer, R. F. Styrene: Its Polymers, Copolymers, and Derivatives, Part I; Hafner Publishing co.: Darien, CT, 1970. Goldstein, R. P.; Amundson, N. R. An Analysis of Chemical Reactor Stability and Control-Xa. Chem. Eng. Sci. 1965,20, 195. Jaisinghani, R.; Ray, W. H. On the Dynamic Behavior of a Class of Homogeneous Continuous Stirred Tank Polymerization Reactors. Chem. Eng. Sci. 1977, 32, 811. Schmidt, A. D.; Clinch, A. B.; Ray, W. H. The Dynamic Behaviour of Continuous Polymerization Reactors-111. Chem. Eng. Sci. 1984, 39(3), 419. Schmidt, A. D.; Ray, W. H. The Dynamic Behavior of Continuous Polymerization Reactors-I. Chem. Eng. Sci. 1981,36, 1401. Choi, K. Y. Analysis of Steady State of Free Radical Solution
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Polymerization in a Continuous Stirred Tank Reactor. Polym. Eng. Sci. 1986, 26(14), 975. Knorr, R. S.; O’Driscoll, K. F. Multiple Steady States, Viscosity, and High Conversion in Continuous Free-Radical Polymerization. J. Appl. Polym. Sci. 1970, 14, 2683. Henderson, L. S. Stability Analysis of Polymerization in Continuous, Stirred-Tank Reactors. Chem. Eng. Prog. 1987,83(3), 42-50. Nagata, S. Miring Principles and Applications; Halsted Press: New York, 1975. Oldshue, J. Fluid Mixing Technology; McGraw-Hill: New York, 1983. Rase, H. F. Chemical Reactor Design for Process Plants; John Wiley: New York, 1977; Vol. 1. Van Heerden, C. Autothermic Processes, Properties and Reactor Design. Znd. Eng. Chem. 1953, 45(6), 1242. Aris, R. Introduction to the Analysis of Chemical Reactors; Prentice-Hall: Englewood Cliffs, NJ, 1965. Beckman, J. Design of Large Polymerization Reactors. Polymerization Kinetics and Technology;Advances in Chemistry Series 128; American Chemical Society: Washington, DC, 1973. Luyben, W. L. Stability of Autorefrigerated Chemical Reactors. AIChE J. 1966, 12(4), 662-668. Blanks, R. F.; Stokes, R. L. Mixing of Viscous Fluids with Turbine Agitators. Chem. Eng. World 1972, 7(3), 65-69. Mueller, A. C. Criteria for Maldistribution in Viscous Flow Coolers. Paper HE1.4, Presented at the 5th International Heat Transfer Conference, Tokyo, 1974; pp 170-174. Streiff, F. A. Statische Wiirmeubertragungsaggregate. Wiirmeubertragung bei der Kunstoffaufbereitung;VDI Verlag: Dusseldorf, BRD, 1986; pp 241-275. Joosten, G. E.; Hoogstraten, H. W.; Ouwerkerk, C. Flow Stability of Multitubular Continuous Polymerization Reactors. Ind. Eng. Chem. Process Des. Dev. 1981,20(2),177-182. Khac-Tien, N.; Streiff, F.; Flaschel, E.; Renken, A. Motionless Mixers for the Design of Multitubular Polymerization Reactors. Presented at the Annual Meeting of the American Institute of Chemical Engineers, San Francisco, 1984. Received for review October 3, 1988 Accepted June 30, 1989
Combining Infrequent and Indirect Measurements by Estimation and Control Bengt E. V. Lennartson Control Engineering Laboratory, Chalmers University of Technology, S-412 96 Gothenburg, Sweden
In the process industry, it is often difficult to measure product qualities as often as desired for control purposes. Indirect information like temperature and pressure is therefore mostly used to control the process. Sampled measurements, for example, from laboratory analysis, are, however, often available. A combination of these infrequent samples with the indirect on-line measurements in an estimator is then a natural approach. This idea is investigated for the control of a continuous stirred tank reactor (CSTR). The temperature is then given every sampling interval, but the concentration measurements are obtained a t infrequent sampling instants, after a time-consuming analysis. The results give some guidelines about the benefits of the proposed estimation procedure.
1. Introduction In a process industry, it is often difficult to measure product qualities continuously for control purposes. Quantities that are closely related to these primary product characteristics are mostly used to inform the control system about the process behavior. This type of indirect or inferential control often works satisfactorily. A typical example from chemical engineering is distillation control, where a column temperature is used as an inferential measure to the product composition. Sometimes, the correlation between the measured quantities and the product qualities is not sufficient. For
example, a process disturbance can give rise to a significant deviation from the desired product composition but only cause a small change in the measured process variable. Sampled measurements of the primary quantities are often available from laboratory analysis or instrumentation close to the process. Typical examples are gas chromatographs and mass spectrometers. Shortcomings in the inferential control are today overcome by performing manual supervisory control based on these sampled data and trends in the current inferential measurements. A natural approach is to use a Kalman filter (Anderson and Moore, 1979) to estimate the process conditions based
0888-588518912628-1653$01.50/0 0 1989 American Chemical Society
