1712
Znd. Eng. Chem. Res. 1991,30, 1712-1718
Jablonaki, G.A.; Geurts, F. W.; Sacco, A., Jr.; Lee, S.; Biederman, R. R. Filamentous and Free Carbon Morphologies in the Fe, Ni, and Co C-H-0 System. Extended Abstracts of Papers; 19th Biennial Conference on Carbon, University Park, PA; American Carbon Society: University Park, PA, 1989; p 362. Kirk-Othmer. Encyclopedia of Chemical Technology; Wiley: New York, 1978 Vols. 9 and 12. MacNab, A. J. Alloys for Ethylene Cracking Furnace Tubes. Hydrocarbon Process. 1987,66,43. Sacco, A,, Jr.; Caulmare, J. Preliminary Results in the Investigation of Growth and Initiation Mechanism of Filamentous Coke. Adounces in Chemistry Series 202; American Chemical Society: Washington, DC, 1982; pp 117-191. Tsai, C. H.; Albright, L. F. In Industrial and Laboratory Pyrolysis; Albright, L. F., Crynes, B. L., Eds.; ACS Symposium Series 32; American Chemical Society: Washington, DC, 1976; pp 274-295. Velenyi, L. J.; Metcalfe, J. E. Hydrogen or Methane Production from Dilute Synthesis Gas through the Formation of Carbon Interme-
diate. Extended Abstracts of Papers; International Carbon Conference, Bordeaux, France, 1984; p 70. Velenyi, L. J.; Metcalfe, J. E. Reactive Carbon as an Intermediate for the Industrial Production of Hydrogen or Methane. Extended Abstracts of Papers; 17th Biennial Conference on Carbon, Lexington, K Y American Carbon Society: University Park, PA, 1985; p 411. Velenyi, L. J.; Metcalfe, J. E. Reactivity and Characterization of Carbon Used in Catalytic Cyclic Process. Extended Abstracts of Papers; 4th International Carbon Conference, Baden-Baden, West Germany, 1986; p 588. Velenyi, L. J.; Song, Y.; Metcalfe, J. E. Carbon Formation during Steamless Pyrolysis of Ethane. Extended Abstracts of Papers; 19th Biennial Conference on Carbon, University Park, PA; American Carbon Society: University Park, PA, 1989; p 444. Receiued for reuiew January 31, 1991 Accepted May 6, 1991
Two-Phase Model for Continuous Final-Stage Melt Polycondensation of Poly(ethylene terephthalate). 2. Analysis of Dynamic Behavior Herv6 Castres Saint Martin and Kyu Yong Choi* Department of Chemical Engineering, University of Maryland, College Park, Maryland 20742
The transient behavior of a continuous melt polycondensation reactor is analyzed for the finishing stage of poly(ethy1ene terephthalate) synthesis by using the dynamic two-phase model. The plug flow is assumed for the bulk melt phase, and the rate of removal of volatiles from the melt to the vapor phase is expressed via the effective mass-transfer parameter. The effects of reactor operating parameters such as polymerization pressure, temperature, residence time, feed prepolymer molecular weight, and the mass-transfer parameter on the polymer molecular weight and ethylene glycol flow rate have been examined through numerical simulation of the reactor model. The sensitivity of the reactor performance to effective heat-transfer coefficient, mass-transfer parameter, and the Flory interaction parameter is also reported.
Introduction High molecular weight poly(ethy1ene terephthalate) (PET) is produced by a multistage process that consists of melt transeaterifcation, prepolymerization, and finishing polymerization stages. In the transesterification stage, bis(hydroxyethy1) terephthalate (BHET) monomer is synthesized with either dimethyl terephthalate (DMT) or terephthalic acid (TPA)as a starting material. The monomers are polymerized to relatively low molecular weight prepolymers in the presence of catalyst (e.g., Sb203)in the second stage at 260-280 O C and 10-30 mmHg. High molecular weight PET is obtained in the final stage where a much lower pressure is used to drive the reaction to high conversion. The finishing reactor usually consists of a high-vacuum horizontal cylindrical vessel with a horizontal rotating agitator shaft to which disks, cages, or shallow flight screws are attached in order to facilitate the removal of volatile condensation byproducts from the highly viscous polymer melt. In our previous report (Laubriet et al., 1991), a twophase model has been proposed and solved to examine the steady-state characteristics of the finishing reactor. A detailed functional group model was used to predict the polymer molecular weight and the concentrations of various end groups and side products such as diethylene glycol, water, and aldehyde. Although some modeling works on the final stage of PET polymerization have been reported recently in the literature (Ravindranath and Mashelkar, 1982,1984;Kumar et al., 1984a,b; Laubriet et
* To whom correspondence should be addressed.
al., 1991), they were confined to the analysis of a steadystate operation. For the design of improved reactor control systems to obtain high-quality polyesters, it is crucial to develop a quantitative understanding of the transient reactor behavior to elucidate the effect of various process variables on the reactor productivity and polymer properties such as molecular weight. It is also important to identify the process parameters that can be used as manipulative variables for polymer properties control. Unfortunately, little has been reported in the literature on the global dynamic behavior of the continuous finishing melt polycondensation reactor for PET synthesis. In this paper, a dynamic two-phase model is developed and solved to examine the transient behavior of the continuous finishing polycondensation reactor under various operating conditions. Reactor Model For the modeling of the finishing polycondensation reactor, we shall consider the main polycondensation reaction only:
~
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O
O
C
,
H
,
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The above reaction is catalyzed by polyesterification catalysts such as Sbz03,and the polycondensation reaction rate is given by
Q888-5885/91/2630-1712$Q2.50/0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1713
r = kl[E,]* - 4k,’[Z][EG] where the catalyst concentration is implicitly included in the rate constants. k and k’represent the reaction rate constants for the reactions between reactive groups. [E,] is the concentration of hydroxyl ethyl group, [Z] the diester group in PET, and [EG] the concentration of ethylene glycol. The equilibrium constant for the above reaction is very unfavorable (e.g., K = 0.5), and therefore a high vacuum is applied to enhance the removal of EG from the melt phase and to drive the reaction in the forward direction. The continuous finishing polycondensation reactor to be considered in this work is a horizontal vessel equipped with a screw type or rotating disk agitator. Such agitators continuously renew the polymer melt layers on the screw or disk surfaces. After being exposed to a bulk vapor phase for a short period of time, the polymers on the disk surfaces are mixed with a bulk polymer melt. Low molecular weight PET prepolymer (e.g., X, = 20-50) is fed to the reactor, and the condensation byproduct, ethylene glycol (EG), is removed from the reactor by applying high vacuum (e.g., 0.1-1.0 mmHg). In designing a finishing polymerization reactor, it is desired to generate as large a vapor-liquid interfacial area as possible to facilitate the removal of volatiles. It is also important to minimize the back-mixing of the reacting fluid so that a narrow molecular weight distribution can be obtained. When one designs the agitator for the finishing polycondensation reactor, effective renewal of the polymer films (surface layers on the disks or screws) and minimum back-mixing in the polymer flow must also be considered. This is why agitators of complex geometry (e.g., screws, cages, disks) are used in industrial finishing reactars as well documented in numerous patent literature. Bubbles of volatiles (ethylene glycol) also account for additional vapor-liquid interfacial area. For example, it has been reported that the specific mass-transfer interfacial area even in a stirred melt polycondensation reactor can be more than 1order of magnitude larger than the area calculated from the melt volume and reactor dimension (Rafler et al., 1987). However, it is not a trivial task to characterize the flow patterns of bulk liquid (polymer melt) and to measure the exact total vapor-liquid interfacial area because of the complexities of the agitator geometry and the behavior of viscous polymer melt in the reactor, which is often poorly understood. In many of the reported modeling works, the reaction and mass-transfer phenomena have been analyzed for a well-defined local thin polymer film formed by a surface renewal equipment (Ravindranath and Mashelkar, 1982,1984; Kumar et al., 1984a,b; Amon and Denson, 1980; Ault and Mellichamp, 1972). In the two-phase model we proposed (Laubriet et al., 1991), it is assumed that the flow of the bulk melt phase is of the plug flow and that the head vapor phase is well mixed. No distinction between the film phase on the solid agitator surface and the bulk melt phase is made. A near-plug flow pattern was confirmed through an experimental analysis of residence time distribution using viscous liquid. In this approach, the polymer melt phase in the reactor is viewed as a mixture of the bulk and the film phases. The rate of mass transfer of the condensation byproducta (Le., EG) from the melt phase to the vapor phase is represented via an effective mass-transfer coefficient (kl) and the specific interfacial area (a) per unit volume of the polymer melt phase. The two-film theory is used to describe the liquid-vapor mass transfer. I t is assumed that the mass-transfer resistance is present only
in the melt phase at the phase boundary. The interfacial concentration of ethylene glycol is estimated by using the Flory-Huggins model. A major difference between the two-phase model and the models proposed by other workers is that both the films on the disk surfaces and the bulk phase are viewed as a single reacting phase from which EG is removed to a vapor phase through a vapor-liquid interface. Ravindranath and Mashelkar (1984) employed a detailed kinetic model that includes various side reactions in their modeling of the finishing polycondensation process. They investigated the reaction and mass transfer in a thin polymer film. In industrial continuous processes, polymer films or layers on the disk or screw surfaces are continuously mixed with bulk melt phase, and fresh polymer films or layers are regenerated by the rotation of the horizontal agitator shaft. Thus, the specific interfacial contact area (a) represents the total contact area per unit volume of the melt phase which consists of the film phase and the bulk melt phase where EG bubbles may be present. If there is an increase in the vapor-liquid interfacial area due to the presence of EG bubbles, such a factor is also reflected in the overall specific contact area parameter, a. Experimental observation shows that in the mechanically stirred bulk melt phase during the prepolymerization stage, many bubbles of EG are formed at a high conversion of hydroxyl end groups (Stephenson, 1990). The value of the interfacial area in wiped film reactors required to attain a high molecular weight PET has been found to be a few orders of magnitude larger than the geometrically computed value of the actual film surface on the screw elements due to a large concentration of small bubbles of EG vapor (Kumar et al., 1984a,b). The presence of such bubbles should contribute to the total vapor-liquid interfacial contact area, Then, the dynamic reactor modeling equations take the following form:
d[EG]
aT
d[EG] +-=
az
4ki[Eg12- 4ki’[Zl[EGl - (kia)([EGI - LEG*])] (5) where r = t/O and z = x / L . 6 is the residence time, and L the reactor length. The equilibrium interfacial concentration of EG ([EG*]) is estimated by using the Flory-Huggins model with x = 0.5 (interaction parameter) (Gupta et al., 1985), which corresponds to the Flory 8 conditions. This value gives conservative estimates of X,. The sensitivity of X, to the interaction parameter value will be discussed later in this paper. The energy balance equation is expressed by dT dT-a7. az +
where T H = heating jacket temperature, AHvm = enthalpy of vaporization of EG, h = effective heat transfer coefficient, D = reactor diameter, p = melt density, and C, = specific heat of PET melt. It is assumed that the effective heat-transfer coefficient (h)decreases linearly along the reactor due to the increase in melt viscosity of the polymer (LeCorre, 1990). In deriving the above energy balance
1714 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991
equation, the viscous heating effect was assumed negligible. The heat of polymerization is much smaller than the heat of vaporization of EG, so that the heat generated by the polymerization is ignored in deriving the above energy balance equation. The concentrations of functional groups in the feed stream were calculated by solving a prepolymerization reactor model (CSTRs). The interfacial concentration of EG is calculated by using the FloryHuggins model as described in Laubriet et al. (1991) and is expressed as (7) where XEG* is the equilibrium mole fraction of EG in the bulk melt phase, P the pressure, and P E G the saturated vapor pressure of EG. y~ is the activity coefficient of EG, which is given by YEG
1
(
= -exp 1 - - + x ~ E G
kEG
)
where mEG is the ratio of molar volumes of polymer and EG. The following vapor pressure equation for EG is used: 8576.7 In P E G = 49.703 - -- 4.042 log T (9)
T POEG is in mmHg, Tin K. The total EG removal rate from the reactor per unit melt volume is
S, (kla)([EGl - [EG*l) dz 1
QEG
=
(10)
The number average degree of polymerization of the polymer is given by X" = 1 + 2[ZI/[E,l
(11)
Results and Discussion The major reactor variables that affect the performance of the finishing polymerization reactor are residence time, reaction temperature, pressure, catalyst concentration, and feed prepolymer composition or molecular weight. The rate of polymerization is affected by the rate of removal of ethylene glycol. In operating the finishing polymerization reactor, polymer's molecular weight or X, (number average degree of polymerization) is the key product property to control at its target value. Some reactor variables that can be manipulated are reaction temperature, pressure, and melt flow rate, In general, industrial melt polycondensation reactors are heated by circulating hot fluid (e.g., Dowtherm) through a reactor jacket. Feed prepolymer composition (e.g., concentrations of end groups) or molecular weight may vary depending on the operating conditions of upstream processing units (e.g., transesterification and prepolymerization reactors). As in many other polymerization processes, there are not many reactor or polymer property parameters that can be monitored on-line. Besides temperature and pressure, the total flow rate of ethylene glycol is another process variable that can be monitored on-line. Molecular weight or melt index is mostly measured off-line, and therefore a direct feedback control of the polymer molecular weight is not feasible. Instead, the reactor is operated by controlling the temperature and pressure at their target values which would give a desired polymer molecular weight. It is thus of practical interest to investigate how the polymer molecular weight (unmeasurable on-line) and the ethylene glycol flow rate (measurable on-line) are affected by the variations in
Table I. Kinetic Parameters and Physical Constants kl = 1.36 X los (wt % catalyst/O.O5)exp(-l8500/Rn L/mol min k,' = 2kl p = 1.335 g/cm3 C, = 0.481 cd/g " C M"J%= 11.2 kcal/mol (at 280 "C)" h(in1et) = 2 X lo-* kcal/cm*/h "Cb h(out1et) = 2 X kcd/cm2 h O C b "Yaws et d.,19%. bLeCorre, 1990.
some of the reactor operating parameters. As described earlier, the mass-transfer parameter @,a) accounts for the total interfacial area available for the ethylene glycol transfer from the melt phase to the vapor phase. Since there are too many variables to vary for model simulations, we have chosen the following as a standard set of reactor operating conditions: T = 280 "C, P = 0.5 mmHg, B = 120 min, catalyst (SbzOJ concentration = 0.06 w t %, T,(feed temperature) = 280 O C , [E,], = 0.5986 mol/L, [Z], = 5.9588 mol/L, [EG] = 7.88 X lo9 mol/L, X, (feed) = 20, &a) = 0.05 s-l, and D (reactor diameter) = 34.93 cm (pilot plant scale). It is assumed that the reactor is filled with the polymer melt to a level of 50%. A few words are in order concerning the mass-transfer parameter value. The klavalue in high conversion PET s-l (Ravindranath polymerization is on the order of and Mashelkar, 1982; Refler et al., 1987). According to the penetration theory, the mass transfer coefficient is given by kl = 2(Di/rt,)'I2 (12) where Di is the diffueivity of solute and t, the exposure time. The diffusivity of EG in the PET melt has been reported in the literature, but the reported values vary widely (e.g., 1.66 X lo4 cmz/s (270 "C), Pel1 and Davis, 1973; 8.2 X lo+ cm2/s (270 "C), Rafler et al., 1980). In industrial finishing reactors, polymer film exposure time is on the order of 4-120 s. With these values, the masstransfer coefficient (k,)lies in the range 3.0 X 104.-7.3 X cm/s. The specific contact area based on agitator geometry is on the order of 0.5-1.0 cm2/cm3for screw type reactor with a LID ratio of 2-3. Thus, the overall masstransfer parameter (kla) ranges from 1.5 X lo4 to 7.3 X s-l. When such a value of kla was used in our model simulations, little increase in X, from the feed X, value was observed, indicating that the actual specific surface area should be much larger than the values estimated from the reactor/agitator dimension. Again, this clearly indicates the role of EG bubbles in enlarging the total vapor-liquid contact area. The above order of magnitude estimate of the klavalue is in good agreement with the reports by other workers as mentioned earlier. The modeling equations (3)-(6) were solved by using MOLCH in IMSL MATH/LIBRARY (1989). Numerical values of kinetic parameters and physical constants are listed in Table I. With these parameters, the effects of various reactor operating conditions on X,(1) (number average chain length at reactor outlet) at steady state were examined and reported in our previous paper (Laubriet et al., 1991). In the temperature range 260-300 "C, AX,/AT increases from 0.525 to 1.0 as the reactor pressure is decreased from 4.0 to 0.1 mmHg (AX, = X,(1) - X,(O)). Effect of Pressure. The main effect of reducing the reactor pressure is to enhance the removal of EG from the bulk melt phase to the vapor phase and thereby increasing the polymer chain growth rate. Figure 1shows the variation in X,(l) and the overall EG molar flow rate (Qm) as the reactor pressure is reduced from 0.5 to 0.1 mmHg at t = 24 min. Initially, the reactor is operating at steady
Ind. Eng. Chem, Res., Vol. 30, No. 8, 1991 1715
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state. The model simulations were carried out for three different values of the mass-transfer parameter (klu):0.1, 0.05 (base case), and 0.01 s-l. First notice that the product X, value is very sensitive to the reactor pressure for the (kla)values of 0.05 and 0.1 s-l. For these cases, the step change in the pressure results in about 34% and 55% increase in X,(l ) , respectively. When the mass-transfer parameter value is very small (e.g., 0.01 s-l), the decrease in the pressure has little effect on the polymer molecular weight. As the kla value is further increased from 0.1 s-l, the increase in X,(1)becomes very small, indicating that the overall polymerization is no longer mass transfer controlled (Laubriet et al. 1991). Figure l b also shows that the total EG molar flow rate increases rapidly after the pressure change followed by a gradual decrease to a new steady-state value. For the standard case (Le., kla = 0.05 s-l) the maximum increase in EG molar flow rate is about 20% of the original steady-state value before the step change. Figure 2 shows the axial profiles of X, and EG concentration in the melt phase. Note that after the new steady state is reached, the polymer molecular weight increases almost linearly with the length of the reactor. As one may have expected, the EG concentration in the melt phase decreases sharply near the inlet of the reactor. A continuous decrease in EG concentration toward the outlet of the reactor causes a significant increase in X, as is the typical characteristic of linear condensation polymerization processes. Figure 2c illustrates the equilibrium interfacial concentration of EG ([EG*]) for P = 0.5 and 0.1 mmHg, respectively. Notice that the axial variation in [EG*] is very small; however, the interfacial EG concentration at P = 0.1 mmHg is about one-fifth of the [EG*] at P = 0.5 mmHg. Thus,more EG is removed from the bulk phase at P = 0.1 mmHg to yield a higher polymer molecular weight. Also notice from Figure 2b,c that the EG concentration difference between the melt phase and the interface (i-e., [EG] - [EG*]) is quite large in the first half of the reactor but very small near the reactor outlet. In calculating the equilibrium interfacial concentration of EG, the Flory-Huggins model was used, and the interaction parameter ( x ) was taken as 0.5 as used by other workers (Gupta et al., 1985). This value corresponds to the Flory 9 conditions and tends to give conservative es-
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timates of [EG*] and polymer molecular weight. Without actual data, the interaction parameter can be approximately estimated by using (Ravindranath and Mashelkar, 1986) x = 0.34+ ( u ~ / R T ) ( G-, (13) where 6, is the solubility parameter of the polymer and bE0 is the solubility parameter of EG. With the solubility parameter data in Brandrup and Immergut (1989), the calculated value of the solubility parameter at 280 OC can be as large as 1.3. Thus, model simulations were carried out for three different values of the interaction parameter to see the sensitivity of X, to x , and the results are shown in Figure 3. Notice that the computed polymer molecular
1716 Ind. Eng. Chem. Res., Vol. 30, No. 8,1991 105
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