2
Ind. Eng. Chem. Res. 1991,30, 2-12
KINETICS AND CATALYSIS Two-Phase Model for Continuous Final Stage Melt Polycondensation of Poly(ethy1ene terephthalate). 1. Steady-State Analysis Claude Laubriet, Brice LeCorre,' and Kyu Yong Choi* Department of Chemical Engineering, University of Maryland, College Park, Maryland 20742
A two-phase model is proposed for the analysis of a continuous poly(ethy1ene terephthalate) process in a finishing polycondensation reactor. In the proposed model, the bulk melt phase is of the plug flow type, and the vapor phase is well mixed. A residence time distribution experiment has been carried out to confirm the plug flow of the polymer melt in a screw-type reactor. The rate of mass transfer of volatiles from the melt to the vapor phase is expressed via the effective mass-transfer parameter, which represents the characteristics of the reactor geometry. A detailed kinetic model has been incorporated into the steady-state reactor model for the prediction of various functional end group concentrations and side product formations. The influence of polymerization pressure, temperature, residence time, catalyst concentration, and mass-transfer parameter on the polymer molecular weight and the concentrations of end groups and side products has been investigated. Introduction Poly(ethy1eneterephthalate) (PET) is one of the most important thermoplastic engineering polymers and is manufactured commercially by semibatch or continuous process. Although different starting materials may be used (e.g., terephthalic acid (TPA), dimethyl terephthalate (DMT)), the polymerization is conducted in a stagewise mode. For example, DMT and ethylene glycol (EG) are first reacted in the presence of catalyst to bis(hydroxyethyl) terephthalate (BHET) monomer (transesterification stage) followed by a prepolymerizhtion stage and a finishing polymerization stage. In the prepolymerization stage, the degree of polymerization (X,)is increased to about 20-50 at 260-280 "C and 10-30 mmHg. A number-average molecular weight of about 15000 is required for useful fiber and film properties. Therefore, PET prepolymer is further polymerized to higher molecular weight in a high vacuum finishing polymerization reactor. Since the degree of polymerization is dependent on the rate of removal of condensation byproduct (EG) from the bulk melt phase, the finishing polymerization reactors are designed such that the rate of mass transfer from a highly viscous polymer melt to a vapor phase can be maximized. 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. The agitator moves the viscous polymer melt slowly from the reactor inlet to the outlet. Various designs of the finishing polymerization reactors are described in many patent literature. In the PET process, the control of functional end group concentrations (e.g., j3-hydroxyethyl ester (or hydroxyl), carboxyl, and unsaturated vinyl end groups) and the formation of side products (e.g., diethylene glycol (DEG), water, and acetaldehyde) is also very important. This is
* To whom correspondence should be addressed.
Present address: Rhone-Poulenc Industrialisation, Lyon, France. 0888-5885/91/2630-0002$02.50/0
because the final polymer properties are influenced by the presence of these end groups and side products (Ravindranath and Mashelkar, 1986a; Besnoin and Choi, 1989). For example, a small amount of DEG in the PET causes decreased crystallinity, which results in reduced fiber and film strength as well as lowered melting points. The instability of the aliphatic ether group in the DEG is responsible for decreased thermal oxidative and UV light stability. A trace amount of acetaldehyde gives a flavor to PET bottles and causes coloring problem. A multitude of the polymerization pathways leading to propagation, degradation, and side reactions give rise to many challenging problems for the precise control of polymer properties. Therefore, the PET reactors must be operated so as to minimize the content of these unwanted side products. In recent years, there have been many reports on the modeling of PET polymerization kinetics and reactor systems (Secor, 1969; Ault and Mellichamp, 1972; Amon and Denson, 1980; Ravindranath and Mashelkar, 1982a, 1984a,b; Gupta et al., 1984; Kumar et al., 1982a,b, 1984; Kumar and Khanna, 1989; Choi et al. 1989; Lei and Choi, 1990). As the polymer molecular weight increases, the interfacial mass transfer of volatiles becomes a major reaction controlling factor. For the modeling of the finishing stage polycondensation,which is the subject of this paper, many of the previous works dealt with diffusion and reaction phenomena in a thin film of the polymer melt in wiped film or agitated reactors. However, there is a dearth of literature on the modeling of a finishing reactor as a whole. The geometry of many industrial finishing reactors is quite complex and varies widely from one process to another. Moreover, a flow pattern of highly viscous polymer melt in a mechanically agitated finishing reactor (e.g., rotating disk ring or screw type) is also complex, and the measurement or estimation of polymer holdup, for example, on the surface of the disk or screw element is not a trivial task. There is a continuous surface renewal and a mixing with a bulk melt phase, bubble formation, and a transport of the bulk polymer melt through the reactor. 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 3 Thus, the modeling of PET polycondensation in a thin film formed on the surface of a disk or screw is valid only locally. In this paper, we propose a new approach to the modeling of a continuous finishing polycondensation reactor. The proposed model consists of a polymer melt phase and a vapor phase and no distinction between the film phase and the bulk melt phase is made. The proposed two-phase model can be used for any reactor geometry with a single reactor parameter that characterizes the liquid-vapor interfacial mass transfer.
Reaction Model The major functional end groups present in the polymerizing melt are the hydroxyl group, carboxylic acid group, DEG group, and unsaturated vinyl group. During the course of polymerization, an extensive redistribution of these functional end groups occurs and a quantitative description of the reaction kinetics becomes quite complex. The kinetics of melt polycondensation of PET has been investigated by many workers in the past, and a recent review by Ravindranath and Mashelkar (1986a,b) provides an excellent review of transesterification and polymerization chemistry and various aspects of transport phenomena and thermodynamics associated with the PET polymerization process. When one attempts to develop a PET polymerization model, the first task is to decide what reactions should be included in the kinetic scheme. For example, only the main polycondensation can be considered for the estimation of polymer molecular weight or all possible reactions among functional end groups can be considered for the prediction of other polymer properties. Of course, such a decision would be made based on the objective of the modeling and the level of sophistication in predicting the polymer properties and the availability of kinetic data. For example, a detailed molecular species model gives a complete product composition distribution and molecular weight distributions of various polymeric species; however, computational requirement is often extensive and such a detailed model may not be suitable for the design of reactor control systems (Ravindranath and Mashelkar, 1984a; Kumar et al., 1984; Choi et al., 1989; Lei and Choi, 1990). In a functional group modeling approach, only the reactions among the reactive end groups are considered. Therefore, the overall kinetic scheme can be significantly simplified, and the results of the model simulations (e.g., concentrations of end groups and side products and the polymer molecular weight) can be confirmed easily through experimentation. For the modeling of a continuous finishing melt polycondensation reactor, we shall employ a functional group model that is similar to the one used by Ravindranath and Mashelkar (1982a, 1984b). Table I lists the reactions considered in our modeling. Here, the rate constants are for the reactions between the two reacting functional end groups, and the equal reactivity hypothesis is assumed for these end groups. The main polycondensation reaction (1)indicates that ethylene glycol must be removed from the polymer melt in order to promote the forward reaction and to produce the polymers of high molecular weight. Note that reactions 1,3,5, and 8 lead to the formation of ester linkages and reactions 2, 4, 6, and 7 do not change the polymer chain length. Reaction 9 is the main degradation reaction, which becomes important at high temperature. Although cyclic polymers can also be formed (Ha and Choun, 1979; Kumar et al., 1982a, 1984), the amount of cyclic polymers is very small. In our reactor modeling, the reactions leading to the cyclic polymers are not in-
Table I. Reactions in the Melt Polymerization of PET (i) Ester Interchange Reaction (Main Polycondensation)
4
(ii) Acetaldehyde Formation
-Ir,
+
4
(2)
CH&W
A
E.
4
(iii) Diethylene Glycol Formation
4
-~ D E G
E,
4
U
k.'
E,
E.
EDEG
(iv) Water Formation
+
- @ - C O O ,
k7
HOCzH40H
EG
-
E.
k7*
E,
E,
@ -4if+ -3-
+ HzO
W
z (v) Degradation of Diester Group
z E.
Ey
(8)
4 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 Table 11. Kinetic Parameters and Physical Constantsa kl = 1.36 X lo6 exp(-18500/RT) k , = 8.32 X 10' exp(-29800/RT) k3 = k5 = kl k d = k6 = k , k , = 2.08 X lo6 exp(-17600/RT) k8 = k7 k , = 7.2 X lo9 exp(-37800/RT) equilibrium constants K1.= 0.5, K5 = 1.0, K7 = 2.5, K8 = 1.25 physical constants = 1.108, ~ D E G= 1.118, pw = 1.0 x = 0.5, O k , - k8 in L/(mol.min), k , in min-', catalyst concentration = 0.05 wt %, pj in g/cm3. Ravindranath and Mashelkar, 1984b.
Figure 1. Experimental setup for RTD measurements.
cluded in the reaction scheme. The rate expressions for reactions 1-9 take the following form: R1 = k1[EgI2- 4k,'[Z][EG] (10) R2 = k 2 W g I
(11)
R3 = k,[E,I[Egl
(12)
R4 = 2k4[EgI tEG1
(13)
R6 = k,5[Egl[EDEGI - 4kS'[zi [DEG]
(14)
R6 = k6[Eg12
(15)
R7
= 2k,[E,I[EGl - ~,'[EgI[Wl
(16)
= k,[E,I[E,I - 2ka'[ZI[Wl
(17)
R8
= kdZ1 (18) where [a] denotes the molar concentration. The numerical values of the rate constants for Sb203catalyst and the physical parameters are listed in Table 11. The concentration of the catalyst is incorporated into each rate constant, and it is assumed that the catalyst concentration remains constant in the reactor.
,
I
0.20
-
0.10
-
./
Pe-4000 Pe=3000 Pa-2000
w
I'I
0.00
0.20
I
1
/I ~ P c - 4 0 0 0 Pe=3000 Pe-2000
m
R9
Experimental curve
0.0
50 0
100.0
Time (min)
Residence Time Distribution Analysis of a Finishing Reactor In a vertically rotating disk partially immersed in a viscous liquid, the shape and thickness of film formed on a disk are influenced by many factors. They are, for example, centrifugal, viscous, inertial, surface tension, and gravitational forces (Vijayraghvan and Gupta, 1982; Matsumoto et al., 1982). The distance between the two neighboring disks or screws can also affect the formation of liquid film on the disk or screw surface (Murakami et al., 1972). Thus, the measurement or estimation of the total volume of the film phase and its thickness is quite a difficult task. For the study of a macroscopic flow behavior of the polymer melt in a screw-type reactor, a small-scale Plexiglas reactor has been built. Figure 1 shows the schematic diagram of the experimental apparatus used for the residence time distribution (RTD) analysis. The reactor body is a cylindrical vessel with dimensions of 5 in. OD X 12 in. L with 10 screw units. The reactor is partially filled (40%, 600 mL). The RTD curve is obtained by injecting a feed solution ((carboxymethyl)cellulose, CMC, in water) containing a tracer (methylene blue, 20 g/L). Before the injection of the tracer solution, the steady-state flow profile is first established with an input flow rate of 10 mL/min. The tracer concentration at the outlet is automatically monitored with a spectrophotometer interfaced with a data acquisition computer (sampling time = 2 8 ) . The linearity of the absorbance with the tracer concentration was first verified and used f o r calibration.
Figure 2. Experimental RTD curves: (a) 20 P, (b) 200 P.
Figure 2 shows the typical response curves obtained for the CMC solution of different viscosity ((a) 20 P, (b) 200 P) when a pulse of the tracer solution was injected (pulse duration = 4 s). The rotational speed of the screw was 0.16 rpm. First note that the main peak is very sharp and followed by small tails. These tails are due to the small dead zones near the inlet and outlet of the reactor. These small dead zones can be reduced through a better design of screw end in industrial reactors. The axial dispersion model was developed for this flow test equipment and applied to the main peaks. The mean residence time was 60.5 and 58 min for cases a and b, respectively. For both cases, the Peclet number (Pe = uL/DA,DA = axial dispersion coefficient) that fits the experimental response curves is 3000, indicating that the axial dispersion is negligibly small. This suggests that the flow of viscous CMC solution in the reactor can be assumed to be of the plug flow. The results of our RTD analysis agree well with other reports in that many of the industrial finishing polycondensation reactors of a similar geometry exhibit plug flow behavior (Murakami et al., 1972; Ravindranath and Mashelkar, 1982b). Reactor Modeling 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 create polymer films on the screw or disk
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 5 surfaces, and the films, after their exposure to a bulk vapor phase, are mixed with a bulk polymer melt. Low molecular weight PET prepolymer (e.g., X, = 20-50) is fed to the reactor and various volatiles such as ethylene glycol, DEG, water, and acetaldehyde are removed from the bulk melt phase by applying high vacuum (e.g., 0.1-1.0 mmHg) and high temperature (e.g., 270-300 "C). In the reversible melt polycondensation of PET, the rate of polymerization or the polymer molecular weight is strongly dependent on the vapor-liquid interfacial area. It has been reported that the specific mass-transfer interfacial area even in stirred tank reactors is considerably enlarged due to intensive bubble formation combined with high solubility of the bubbles of condensation byproduct. For example, the specific mass-transfer interfacial area generated in a stirred reactor can be more than 1order of magnitude larger than the area calculated from the melt volume and reactor dimensions (Rafler et al., 1987). In designing a finishing polymerization reactor, one is concerned about generating as large a vapor-liquid interfacial area as possible. For the design of a finishing polycondensation reactor, one needs to understand the details of fluid mechanics, mixing, and mass-transfer characteristics as well as polycondensation kinetics. In fact, many patent literature describe various designs of the reactor agitator assembly and their effectiveness in promoting the mass transfer of volatiles. However, it is often quite difficult to characterize the flow distributions and the exact contact area because of the complexities of the agitator geometry and the behavior of viscous polymer melt in the reactor. Moreover, if the bubbling of the condensation byproduct occurs, the effective vapor-liquid interfacial area can increase considerably. The prediction of the total interfacial area for mass transfer is thus quite difficult. Due to the complexity of the flow patterns of the viscous polymer melt in the finishing reactors, most of the past modeling works have been confined to the analysis of mass-transfer and reaction phenomena in a well-defined thin polymer film formed by a surface renewal equipment. Ravindranath and Mashelkar (1982b)reported modeling of the final stage polycondensation process. Higbie's penetration theory was applied to a film phase where the mass transfer of EG is assumed to be the rate-controlling process. Assuming constant concentration of ester linkages ([Z]), they derived the following approximation for the rate of change in hydroxyl group concentration in the film: d(E,]/dt = -2ai(Dk)'/2([EG]o - [EGIi) where k = 4klZ], k'is the polycondensation rate constant, [EG], is the initial concentration of EG in the film, [EGIi is the interfacial concentration of EG, D is the diffusivity of EG. The above rate expression was then used for the reactor modeling. Both plug flow and axial dispersion models were examined. In their modeling, only the main polycondensation reaction was considered and side reactions leading to other end groups and side products were not considered. In their later paper, they extended their modeling by including various reactions; however, it was limited to the analysis of polycondensation in the thin film (Ravindranath and Mashelkar, 1984b). In what fo!lows, we shall propose a two-phase model for the continuous finishing stage melt polycondensation of PET. It is proposed that the flow pattern of the melt phase is of the plug flow type and that the vapor phase is well mixed. No distinction between the film phase and the bulk phase (bulk pool) is made. Therefore, the polymer phase in the reactor is viewed as a mixture of both the film and bulk phases. No reaction is assumed to occur in the
vapor phase. The rate of mass transfer of the condensation byproducts from the melt phase to the vapor phase is described through an effective mass-transfer coefficient (k,)and the specific interfacial contact area per unit volume of the melt (a). It is assumed that the mass-transfer resistance resides only in the melt phase. The interfacial concentration of the volatiles is determined by the vapor-liquid equilibrium relation (Le., Flory-Huggins theory). Figure 3 is a diagram illustrating the concept of the proposed two-phase reactor model. A major difference between the proposed two-phase model and the model by Ravindranath and Mashelkar (1982b) is that we view both the film and the bulk phases as a single reacting phase with mass transfer to a vapor phase through the vapor-liquid interface. Thus, the specific interfacial contact area (a [cm-'1) represents the total contact area per unit volume of the melt phase, which consists of the film phase and the bulk melt phase. In other words, this parameter (a) is a characteristic of a given reactor geometry and the melt flow distribution pattern in the reactor. If there is an increase in the vapor-liquid contact area due to the formation of bubbles of the volatiles, such a factor is also reflected in the overall specific contact area parameter, a. Experimental observation (Stephenson, 1990) shows that even in the mechanically stirred bulk melt phase, many bubbles are formed at high conversion of hydroxyl end groups. The existence of such bubbles should contribute to the total vapor-liquid interfacial contact area. The value of the interfacial surface area in wiped film reactors required to attain experimentally attained values of high molecular weight is a few orders of magnitude larger than the geometrically computed value of the actual film surface on the screw elements (Gupta et al., 1984; Kumar et al., 1984). These reports also indicate that bubbly desorption takes place in the melt polymerization reactor and is an important factor to be considered in the modeling of finishing polycondensation reactors. Then the steady-state reactor modeling equations for the melt phase take the following form: nonvolatile species
volatile species
where 0 is the mean residence time and z the dimensionless distance from the reactor inlet ( z = x / L ) . [ci*] is the interfacial concentration of the volatile species J at equi-
6 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991
/
Thus, the molar volume of the polymer is given by 1 - uv
up = -
\
CPOlY
The equilibrium interfacial concentration of the volatile species j is given by cj* =
1
1 - EXj*
)xj*
6 = EG, DEG, W)
(33)
where xj* = P+yj/Prrjis the equilibrium mole fraction of volatile species j in the bulk phase. Pt is the reactor pressure. The following vapor pressure data are used in the temperature range of our interest (T in K, P in mmHg): In PEGo = 49.703 - 8576.7/T - 4.042 In T (34a)
r
VOLATILES
I VAPOR PHASE
t -It"\ t t t t t t
PREPOLYMER
PROD1 CT
MELT PHASE
X=L
X I 0
Figure 3. Two-phase model for continuous melt polymerization.
librium. Since the vapor pressure of acetaldehyde is very high a t the polycondensation temperature, acetaldehyde is assumed to be removed instantly as soon as it is formed by reactions 2 and 3. The mole fraction of the volatile species j in the vapor phase is given by
where [A] is the acetaldehyde concentration, cj is the concentration of species j in the melt phase, and cj* is the interfacial concentration of j in the liquid phase. No mass-transfer resistance is assumed in the vapor phase. The Flory-Huggins model is used to relate the interfacial concentration and the vapor-phase concentration of species j. Under vapor-liquid equilibrium, the partial pressure of the volatile species (Le., EG, DEG, and water) in the melt phase can be represented as
pj = y.p.ox. J J J
(28)
where Pj is the partial pressure of species j. yj, P?, and xj are the activity coefficient, saturated vapor pressure, and mole fraction of component j, respectively. The activity coefficient, yj, is given by the Flory-Huggins model for very small volume fraction of volatile species j: 1
( A )
exp 1 - - +
xj
where mj is the ratio of molar volumes of polymer and species j and xj is the Flory interaction parameter. The volume of the melt phase occupied by the volatile species per volume of reaction mixture is given by Mj~j
uv =
c-Pj
(i = EG, DEG, W)
j
(30)
where Mj is the molecular weight of j, pj is the density, and cj is the molar concentration. The total concentration of polymeric species is cpoly
( '7
1 = ~ ( [ E S+] [E,] + [Ea1 + [EDECI)
(31)
4047.606 T - 33.3 4122.52 In PDEGO = 17.0326 - 122.5 In Pwo= 18.568 -
(34b) (344
The mole fraction of volate species j (yj) is computed as follows. First, the initial value of yj is assumed and eqs 29-33 are used to calculate the equilibrium interfacial concentration. Then the reactor modeling equations (19)-(26) and the steady-state vapor phase (well-mixed) mass balance equations are solved. The resulting concentrations of volatile species in the melt phase are used in eq 27 to obtain a new value of yi. The integral squared error between the new and the initial values of yj is then minimized by using the simplex method. This process is repeated until the correct value of yj is obtained. Results and Discussion The major reactor variables that affect the performance of the finishing polycondensation reactor are residence time, reaction temperature, pressure, catalyst concentration, overall mass-transfer coefficient &]a), and feed prepolymer composition. The polymer property parameters of interest are number-average chain length (X,)and concentrations of various end groups, EG, and side products such as DEG, water, and acetaldehyde. Since there are many variables to vary for model simulations, we have chosen the following reaction conditions as a standard reactor operating conditions: T = 280 O C , 6 = 2 h, P = 0.5 mmHg, catalyst (Sb20,) concentration = 0.06 wt %, (kIalj = 0.05 s-l. The kla value in high conversion PET polyms-l (Ravindranath and erization is on the order of Mashelkar, 1982a;Rafler et al., 1987). With these standard value of 82 is obtained. operating conditions, the outlet XI, Since the mass-transfer parameter represents the reactor geometry or overall surface renewal and mixing capability, one should estimate the correct value of kla for a given reactor configuration. For example, Murakami et al. (1972) proposed the following empirical correlation by using Danckwert's surface renewal model for a multidisk reactor with two agitator shafts:
kla = 0.58,1/3V-3/2 (35) where n is the rotational speed and V the liquid volume. For the disk-ring reactors, Dietze and Kuhne (1969) proposed an empirical correlation for specific interfacial area: N(1.72 - 1.87h/d) a= (36) L(0.085 + 0.955h/d) where N is the number of disk rings, h is the filling level, d is the disk diameter, and L is the distance between the
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 7 disks. Other formulas of the mass-transfer coefficient and interfacial area for foam-enhanced devolatilization equipment are also described in the literature (e.g., Biesenberger and Lee, 1986). In the following, we will show how the performance of the reactor is affected by the mass-transfer parameter. In our model simulations, the parametric analysis will be carried out by varying one parameter of interest a t a time with all other variables fixed at the standard conditions. The feed prepolymer is a product from the prepolymerization stage and contains various reactive end groups, ethylene glycol, and other side products. In order to determine the feed composition, a separate model of a prepolymerization reactor (three continuous stirred tank reactors) has been solved. Methyl ester end groups (when DMT is used as a starting material for transesterification stage) react completely in the prepolymerizationstage, and thus, they are not present in the feed to the finishing reactor. The concentrations of various species [in mol/L] in the feed stream are [E If = 5.986 X lO-l, [E,], = 8.552 x [E,], = 1.181 x idJ, [EDEc]~ = 1.973 x [z], = 5.959, [EG], = 7.388 X [W], = 4.609 X lo4, and [DEGIf = 4.868 X The number-average chain length of the prepolymer is 20. The relative concentrations of [Z], and [EGIf with respect to [E If are very similar to those used by Ravindranath and kashelkar (1984b) in their analysis of thin film polycondensation. The concentration of acid end groups in the feed depends upon many factors such as catalyst type and the reaction conditions employed in the prepolymerization stage. The feed [E,] value used in our simulations is on the same order of magnitude as reported in the literature (Zimmerman and Kim, 1980; Ravindranath and Mashelkar, 1982a). Figure 4 shows the effect of various reactor operating conditions on the number-average chain length (X,)of the polymer. X, of the polymer at a given point in the reactor is given by
120.0
x
40.0
40 0 120 0
1
1
1
gO,Ol 7 7 tI *O'O
60.0
It is also easy to show that 40
[E,] and [EDEG]decrease monotonically with the reactor length (or residence time) and [E,] increases continuously. However, as shown in Figure 10, [E,] decreases near the reactor inlet but then increases slowly with the reactor length. Thus, the increase in X, near the reactor outlet becomes small. Since the concentrations of acid group, vinyl end group, and DEG end group are much smaller than the hydroxyl group concentration, one may approximate the X, value by Xn N Cf/[Egl (38) where Cfis the total concentration of five reactive groups in the feed polymer. If this approximation is applied to the feed with the standard operating conditions, the difference between the exact X, and the approximate X, (eq 38) is about 4.5%. But at the reactor outlet, the difference between the two can be as large as 12%. This is because the mole fraction of hydroxyl end group at the reactor outlet is only about 0.9. Therefore, the use of a detailed kinetic model as used in this work is required for the accurate estimation of polymer molecular weight. Figure 4a indicates that with a residence time of 2 h and at 280 O C the X, value at the reactor outlet varies from
i1
0 00
02
04 kla
06
08
10
(rec-1)
Figure 4. Effect of reactor operating conditions on X,. (f) Effect of mass-transfer parameter on XJl).
66 to 108 for the reactor pressure varying from 1.0 to 0.1 mmHg. As the pressure is decreased to a level of 0.1 mmHg, X, increases almost linearly with the reactor length. The effects of residence time, temperature, and catalyst concentration are illustrated in Figure 4, b, d, and e, respectively. As mentioned earlier, the parameter kla represents the mass-transfer capability of the finishing reactor. Figure 4c shows the effect of kp. First note that for a small value of kla (e.g., 0.01 s-l), X, increases from 20 to only 48 and X, also increases linearly with the reactor length. As kla is increased, for example, through a better design of the agitator, higher X, is obtained. For the small value of kla, the removal of EG from the melt phase is also small, and as a result, there is higher concentration of EG in the melt phase (Figure llc). As the kla value is increased, the removal of EG becomes larger and the polymer molecular weight increases. However, the outlet X, value becomes less sensitive to the kla value above 0.1 s-l. This phenomenon is clearly illustrated in Figure 4f. We can
8 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 630
I
- .
I
i
6.00
6 10 6 00
Influence of temperoture ( C)
290 280
6 20 N -
270
6 10
0 20
6 00
0.00
1
I
-ru 6 10
0 01 0 02
6.20
4
/ 0.04
6 00 000
1
00
02
I
1
04
06
08
10
590 00
02
04
06
J
os
10
I
2
Figure 5. Concentration profiles of hydroxyl end group ([E,], mol/L) for various reactor operating conditions.
observe that a 10-fold increase in the kla value from 0.1 to 1.0 s-l (280 "C,0.5 mmHg, B = 2 h) yields only a 5% increase in the outlet value of X,. This implies that the overall polymerization is no longer mass-transfer controlled. The similar observation was reported for a wiped film reactor (Kumar et al., 1984; Gupta et al., 1984). Thus, if one wants to produce higher molecular weight polymers, it is suggested, for example, to lower the pressure further or to increase the reaction temperature. The variation of hydroxyl end group concentration in the reactor is shown in Figure 5. For kla values larger than 0.05, the hydroxyl group concentration at the outlet stream is less than 20% of the feed concentration. Figure 6 shows the concentration profiles of ester linkages ([Z]). Note that [Z] increases rapidly in 0 < z < 0.5 for kla values larger than 0.05 s-l. Near the outlet of the reactor ( z > 0.5), the rate of increase in the concentration of ester linkages becomes small. From eq 37b, it is easy to show that X, depends on the concentration of ester linkages through the following equation:
Figure 6. Concentration profiles of ester linkages ([Z], mol/L).
1 Oc-OS
1
230 280 273
(39) where Xnf is the degree of polymerization of the feed prepolymer. Equation 39 indicates that a continuous increase in Xn in the second half of the reactor is due to the decrease in various functional end group concentrations (Le., Cf - 2[Z]). The [Z] value a t the outlet is about 5% higher than the inlet value, but this increase is large enough to raise X, more than 4 times the feed value. The presence of vinyl and acid groups in the PET polymer leads to the formation of anhydride and network structure (Ravindranath and Mashelkar, 1986a). The pyrolytic decomposition of such polymers during the processing gives polyenes and carboxyl end groups. The concentration profiles of vinyl end group ([E,]) are shown
2 ce40
co
02
35
04
38
' 3
z
Figure 7. Concentration profiles of vinyl end group ([E,], mol/L).
in Figure 7 for various reactor operating conditions. The vinyl end groups are formed mostly through reaction 9. Also note that [E,] increases almost linearly with the reactor length. Figure 7 also indicates that the employment of longer residence time and higher reactor temperature tends to give a much higher concentration of E,than when using lower pressure. It is observed that the vinyl end group concentration in the final PET product is in the
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 9 0.02
k I"flYB"C0
of prerrure (Torr)
-
10 05
-
8 Oe-OS
q' 4
0 ' 35
Oe-03
u
c
t
, ,
00e+00
-
1c
-I
I
'
8 Oe-OS
-4"
4
0.00
L
oe-os
05
0 oe+00
1
d i
8 Oe-03
0.0e+00
- 8.01-03 -4"
0 oc
-g
4
Oe-OS
0 Oe-00
001
I"IIY."C,
x
I\---
00
I
.I colol"sl .Wht
c2
4 r
06
04
08
0 '0 0 08 0 :6
-0
:r
-0'
32
'0
2
Figure 10. Concentration profiles of acid end group ([E,], mol/L).
0 00 02
00
06
04
08
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Figure 8. Concentration profiles of DEG end group ([EDEG], mol/L).
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range 0.02-0.06 mol/mol of hydroxyl end group or 3.0 X 10-4-l.0 X mol/mol of ester linkage. The concentration profiles of DEG end group ([EDEo]) and free DEG ([DEG]) are shown in Figures 8 and 9, respectively. In the PET process, DEG is mostly formed
in the transesterification and the prepolynerization stages (Renwen et al., 1983). Although the DEG concentration decreases during the finishing polymerization stage, it is seen that about 50% of the DEG end group and 10% of the free DEG present in the feed prepolymer are still remaining in the final polymer. At high temperature and low pressure as used in our simulations, the DEG content decreases with reaction time (Renwen et al., 1983). The ratio of DEG end group/free DEG is about 250 in the final polymer, indicating that DEG detectable by analytical means is probably the DEG incorporated into the polymer at the chain ends. It is also observed that about 0.0016 mol of DEG is present per mole of ester linkage. Both Figures 8 and 9 also show that the DEG content decreases with a decrease in pressure and increases in temperature, residence time, and catalyst concentration. In other words, if one attempts to increase the polymerization rate or the polymer molecular weight, lower DEG content in the polymer will result. The acid end group concentration in PET determines the thermal and hydrolytic stability of PET (Zimmermann and Kim, 1980). The effect of reactor operating conditions on the acid group concentration is shown in Figure 10. Note that for all the cases studied, except for the case with k p = 0.01 s-l, the acid end group concentration decreases rapidly near the inlet of the reactor (e.g., 0 C z C 0.4) and then starts to increase slowly afterward. This is because the acid end groups react with hydroxyl groups in EG and E, (reactions 7 and 8) to produce water, but the acid groups are also produced via reactions 2, 4, 6, and 9. Near the reactor inlet, the EG concentration is high, and therefore the hydroxyl group concentration is also high. Thus, reactions 7 and 8 are predominant near the inlet of the reactor. The decrease in the acid group concentration during the initial polymerization stage followed by a gradual increase was also observed experimentally in a stirred semibatch polycondensation reactor where the initial prepolymer contained carboxylic acid end groups (Rafler et al., 1987). In general, any attempt to increase the polymerization rate or X, results in higher content of
10 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 8@e-C3
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0.4 (Figure 12a). Figure 12c displays the molar fraction of various volatile species in the vapor phase for different reactor operating conditions. One can observe that the vapor-phase composition is only weakly influenced by the variations in the reaction conditions. Figure 13a shows the equilibrium mole fraction of EG in the bulk phase. The increase in the equilibrium mole fraction of EG is due to the decrease in the molar concentration of the polymer (cwlX). The interfacial concentration of EG ([EG*]) is essentially constant along the reactor length (Figure 13b).
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PET is particularly susceptible to hydrolysis. In the processing of PET, a small amount of water in the polymer can lead to lowering of molecular weight and loss of mechanical properties. For extrusion and injection molding of PET, less than 200 ppm water is usually required. Water has also an influence on some rheological properties of the PET; in the range 0.015-0.025% H20, the decrease in viscosity is 1.3% per 0.001% increase in moisture content a t 284 O C (Besnoin and Choi, 1989). The concentration of water in the melt phase is shown in Figure 14. The amount of water present in the polymer is in the range 500-600 ppm of the polymer and is about 50% of the free DEG content. Figures 11-14 indicate that there is a lim-
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 11 4.0e-03
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itation in reducing the concentrations of EG, water, and DEG in the final polymer below certain levels unless the pressure is reduced to extremely low level, which could be quite difficult in practice. Concluding Remarks We have proposed a two-phase model for a continuous finishing polycondensation reactor. It is assumed that the reactor consists of a polymer melt phase of plug flow type and a well-mixed vapor phase. A separate residence time distribution analysis of a screw-type reactor supports that the flow of the polymer melt can be approximated by a plug flow model. In the two-phase model proposed, no distinction between the film phase and the bulk melt phase is made. Therefore, separate mass balances equations are not required for each phase. The mass-transfer resistance is also assumed to reside only in the melt phase. The rate of mass transfer of various volatiles is expressed through an effective mass-transfer parameter, which represents the mass-transfer capability of the agitated reactor. The polymer molecular weight and the concentrations of various important end groups and side products have been computed with a detailed kinetic model. The proposed model shows that the steady-state behavior of the isothermal continuous finishing polycondensation reactor can be conveniently studied even with a quite complex kinetic scheme. One of the advantages of the proposed model is that this model can be applied to any reactor geometry with a single reactor parameter that characterizes the liquid-vapor interfacial mass-transfer phenomena. It must also be noted that for the applications of the proposed model to real finishing polymerization reactors, it is required to find the Kla value that would fit the experimental or plant data of molecular weight or end group concentrations. Further work is needed to develop a rational way of estimating the mass-transfer parameter for various reactor configurations and operating conditions such as shaft
05
08
2
2
Figure 13. (a) Mole fraction of EG in polymer melt; (b) interfacial concentration of EG (mol/L).
0 4
i
Figure 14. Concentration profiles of water ([W], mol/L).
rotational speed, melt viscosity, melt holdup, agitator geometry, etc. Acknowledgment This work was supported by the National Science Foundation (CBT-85-52428) and in part by the RhonePoulenc U.S.A., for which we express our gratitude. Registry No. PET,25038-59-9; TPA,100-21-0;EG,107-21-1. Literature Cited Amon, M.; Denson, C. D. Simplified Analysis of the Performance of Wiped Film Polycondensation Reactors. Znd. Eng. Chem. Fundam. 1980,19,415-420. Ault, J. W.; Mellichamp, D. A. Complex Linear Polycondensation11. Polymerization rate enhancement in thick film reactors. Chem. Eng. Sei. 1972,27,2233-2242. Besnoin, J.-M.; Choi, K. Y. Identification and Characterization of Reaction Products in the Polymerization of Polyethylene Terephthalate. J. Macromol. Sci.-Rev. Macromol. Chem. Phys. 1989, C29 (l),55-81. Biesenberger, J. A.; Lee, S. T. A Fundamental Study of Polymer Melt Devolatilization. Part I. Some Experiments on Foam-Enhanced Devolatilization. Polym. Eng. Sei. 1986,26(14),982-988. Choi, K. Y.;Besnoin, J.-M.; Lei, G. D. Melt Transesterification of Dimethyl Terephthalate with Ethylene Glycol. AZChE J. 1989, 35 (9), 1445-1456. Dietze, M.; Kuhne, H. Development and Design of Commercial Reactors for Continuous Manufacture of Polyester. Chemiefasern 1969,3, 19. Gupta, S.K.; Ghosh, A.; Gupta, S. K.; Kumar, A. Analysis of Wiped Film Reactors Using the Orthogonal Collocation Technique. J. Appl. Polym. Sei. 1984,29,3217-3230. Ha, W. S.;Choun, Y. K. Kinetic Studies on the Formation of Cyclic Oligomers in Poly(ethy1eneTerephthalate). J. Polym. Sci.: Polym. Chem. Ed. 1979,17,2103-2118. Kumar, A.; Khanna, A. Solution of Mass Transfer in Step Growth Polymerization in Films with Bulk in Equilibrium. Polym. Eng. Sei. 1989,29(24),1774-1785. Kumar, A,; Gupta, S. K.; Gupta, B.; Kunzru, D. Modelling of Reversible Poly(ethy1ene Terephthalate) Reactors. J. Appl. Polym. Sci. 1982a,27,4421-4438.
Ind. Eng. Chem, Res. 1991, 30, 12-18
12
Kumar, A,; Gupta, S. K.; Somu, N. Molecular Weight Distribution of Polyethylene Terephthalate in Homogeneous, Continuous Flow Stirred Tank Reactors. Polym. Eng. Sci. 1982b, 22 (5), 314-323. Kumar, A.; Gupta, S. K.; Madan, S.; Shah, N. G.; Gupta, S. K. Solution of Final Stages of Polyethylene Terephthalate Reactors Using Orthogonal Collocation Technique. Polym. Eng. Sci. 1984, 24 (31, 194-204. Lei, G. D.; Choi, K. Y. A Melt Polymerization of Poly(ethy1ene terephthalate) in Semibatch Stirred Reactors. J.Appl. Polym. Sci. 1990, in press. Matsumoto, S.; Takashima, Y.; Kamiya, T.; Kayano, A.; Ohta, Y. Film Thickness of a Bingham Liquid on a Rotating Disk. Ind. Eng. Chem. Fundam. 1982,21, 198-202. Murakami, Y.; Fujimoto, K.; Kakimoto, S.; Sekino, M. On a High Viscosity Polymer Finisher Apparatus with Two Agitator Axes Having Multidisks. J. Chem. Eng. Jpn. 1972, 5 (3), 257-263. Rafler, G.; Bonatz, E.; Sparing, H. D.; Otto, B. Zur Kinetik der Polykondensation von Terephthalsaure und Ethylenglykol in dunnen Schmelzeschickten. Acta Polym. 1987, 38 (l),6-10. Ravindranath, K.; Mashelkar, R. A. Modeling of Poly (Ethylene Terephthalate) Reactors: 5. A Continuous Prepolymerization Process. Polym. Eng. Sci. 1982a, 22 (lo), 619-627. Ravindranath, K.; Mashelkar, R. A. Modeling of Poly(Ethy1ene Terephthalate) Reactors: 6. A Continuous Process for Final Stages of Polycondensation. Polym. Eng. Sci. 198213, 22 (lo), 628-636. Ravindranath, K.; Mashelkar, R. A. Modeling of Poly(Ethy1ene
Terephthalate) Reactors: 7. MWD Considerations. Polym. Eng. Scz. 1984a, 24 (l),30-41.
Ravindranath, K.; Mashelkar, R. A. Finishing Stages of P E T Synthesis: a Comprehensive Model. AIChE J. 1984b,30 (3), 415-422. Ravindranath, K.; Mashelkar, R. A. Polyethylene Terephthalate-I. Chemistry, Thermodynamics and Transport Properties. Chem. Eng. S a . 1986a, 41 (9), 2197-2214. Ravindranath, K.; Mashelkar, R. A. Polyethylene Terephthalate-11. Engineering Analysis. Chem. Eng. Sci.1986b, 41 (12), 2969-2987. Renwen, H.; Feng, Y.; Tinzheng, H.; Shiming, G. The Kinetics of Formation of Diethylene Glycol in Preparation of Polyethylene Terephthalate and its Control in Reactor Design and Operation. Angew. Makromol. Chem. 1983, 119, 159-172. Secor, R. M. The Kinetics of Condensation Polymerization. AIChE J. 1969, 15 (6), 861-865. Stephenson, S. M.S. Thesis, University of Maryland, College Park, 1990. Vijayraghvan, K.; Gupta, J. P. Thickness of the Film on a Vertically Rotating Disk Partially Immersed in a Newtonian Fluid. Ind. Eng. Chem. Fundam. 1982,21, 333-336. Zimmerman, H.; Kim, N. T. Investigation on Thermal and Hydrolytic Degradation of Polyethylene Terephthalate. Polym. Eng. S C ~1980, . 20, 680-683. Received for review April 19, 1990 Revised manuscript received June 25, 1990 Accepted July 9, 1990
Effect of Crystallite Size on the Activity and Poison Resistance of a Shape-Selective Zeolite Clinton R. Kennedy,* Rene B. LaPierre, and Carmo J. Pereirat Mobil Research and Development Corporation, Paulsboro Research Laboratory, Paulsboro, New Jersey 08066
Richard J. Mikovsky Mobil Research and Development Corporation, Central Research Laboratory, Princeton, New Jersey 08543
Using a series of constant Si02/A1203ratio ZSM-5crystallites, which varied over almost 2 orders of magnitude in size, we demonstrate the cracking of n-dodecane to be what one expects for a first-order reaction limited by diffusion within the zeolite pores. At 630 K and 35 atm of hydrogen, the intrinsic activity of the crystals is independent of crystal sizes while the observed activity is adequately described by using effectiveness factors derived from classical reaction-diffusion theory. Deactivation by coke deposition is also independent of crystallite size and is only a function of time on stream. Shape selectivity is demonstrated by poisoning with a relatively bulky nitrogen-containing compound (5,6-benzoquinoline), which diffuses more slowly than n-dodecane due to steric constraints. The poisoning is well described as a shell progressive phenomenon with an active core of zeolite and a poisoned outer shell. Thus, resistance to catalyst poisoning increases with the square of the crystallite size.
Introduction Shape-selective paraffin cracking is the basis for a number of commercial processes, e.g., Mobil Distillate Dewaxing (MDDW) (Chen et al., 1977) and Mobil Lube Dewaxing (MLDW) (Smith et al., 1980). The desired shape selectivity is accomplished by utilizing zeolite catalysts with channel dimensions approaching those of the reactant molecules (i.e., configurational diffusion). This results in large diffusivity differences between linear and nonlinear molecules and allows the catalyst to discriminate among potential reactants. Haag et al. (1982), for instance, have shown how zeolite crystallite size and molecular shape influence the observed catalytic cracking rates of Cs-C9 hydrocarbons. The subject of shape-selective catalysis is
* Author to whom correspondence should be addressed.
'Present address: W. R. Grace & Cos-Conn., Research Division, 7379 Rt. 32, Columbia, MD 21044.
0888-5885/91/2630-0012$02.50/0
Table I. Catalyst Properties catalyst SiOz/A1203 A 70 B 65-70 C D
75 60
av diameter, pm 0.12 0.35 1.1 2.7
covered in depth by Chen et al. (1989). In practice, acidic zeolite catalysts can be poisoned by basic nitrogen-containing compounds in the feed. These compounds may also have molecular dimensions similar to zeolite channel dimensions, leading to diffusion effects with respect to poisoning as well as reaction. Namba et al. (1984) have investigated some of these effects in xylene isomerization. Here we address the effects of zeolite crystallite size on the activity and stability of ZSM-5 catalysts for the cracking of a n-paraffin (n-dodecane) in the presence of a bulky nitrogen poison (5,6-benzo0 1991 American Chemical Society
