Carbon deposition in ethane pyrolysis reactors - Industrial

Kevin M. Van Geem , Inge Dhuyvetter , Serge Prokopiev , Marie-Françoise Reyniers , Dominique Viennet and Guy B. Marin. Industrial & Engineering Chemi...
2 downloads 0 Views 666KB Size
1708

Ind. Eng. Chem. Res. 1991,30,1708-1712

Carbon Deposition in Ethane Pyrolysis Reactors Louis J. Velenyi,* Yihhong Song,and John C. Fagley BP Research, Warrensville Research and Environmental Science Center, Cleveland, Ohio 44128

Carbon deposition during ethane pyrolysis in INCONEL 600 reactors exhibits a bimodal distribution along reactor walls. This indicates a shift in controlling mechanism from heterogeneous to homogeneous carbon formation. Carbon deposition rate decreases with the total pyrolysis running time until it reaches an asymptotic level. It increases with the number of pyrolysis-decoking cycles. Contrary to the INCONEL 600 reactors, a-Sic tubes produce little carbon deposition during ethane pyrolysis. T h e bell-shaped carbon distribution curve suggests the dominance of pyrolytic carbon formation mechanism in a-Sic reactors, Reactor model simulations show that both radial velocity and radial temperature distributions have significant effects on carbon deposition within the metal reactor system. This effect is not as important for the a - S i c reactor because the reactor wall is noncatalytic. Introduction The reactor coils for commercial ethane crackers are made of metal alloys that have excellent resistance against high-temperature oxidation and deformation (MacNab, 1987). An inherent problem associated with the metal alloys is their tendency of promoting carbon deposition on the tube surfaces (Albright and Marek, 1988a-c; Billaud et al., 1988). Because coke formation will eventually lead to plugging and downtime of the cracker unit, trade-offs in process conditions are made to obtain an acceptable time on stream. To reduce the amount of carbon being deposited on the tube walls, per pass conversion is limited and steam is added to the ethane feed in the commercial crackers. Although steam is effective, the addition of steam has several disadvantages. First, it lowers the hydrocarbon throughput for a given size of the reactor. Second, it reduces the energy efficiency of the reactor. Finally, it necessitates the process of separating it from hydrocarbon p r o d u d in the back end of the crackers. Our goal was to test the technical feasibility of steamless ethane cracking. As part of this assessment, a-Sic was evaluated to find out whether it is the material of choice in a steamless environment. To obtain further insight into the dynamics of carbon formation, a two-dimensional, steady-state model description of the reactor system was also developed to simulate the ethane pyrolysis experiments. Experimental Section The experimental apparatus used in this study consisted of a tubular flow reactor that was electrically heated to the desired temperatures. Two reactor types were used in the experiments: INCONEL 600 tubes (0.64 cm 0.d. X 0.46 cm i.d. X 91 cm long) and a-Sic tubes (0.80 cm 0.d. X 0.50 cm i.d. X 91 cm long). A schematic of the reactor is shown in Figure 1. In order to study the aging effects, both brand-new and used reactors that had exposed to different pyrolysis-decoking cycles were utilized. All the experimental runs were carried out in two steps. First, pure ethane was fed to the reactor and was pyrolyzed. Reacting gas temperature along the center axis of the reactor was measured by a type R thermocouple inserted into the reaction zone through the back end of the reactor. All the experiments were carried out at atmospheric pressure. After pyrolysis, the next step was the measurement of the carbon deposited on the reactor walls. Air was introduced radially through a specially designed injector to burn off the carbon section by section, starting from the back end of the reactor. A constant nitrogen flow from the front of the reactor was used to control the burn-off location. The combustion product gas from each

section was collected and analyzed for CO and COP The burn-off process continued until no more carbon oxides were detected (approximately 1h per section). The total carbon deposited was also measured by introducing air directly from the front of the reactor following a duplicate pyrolysis run. The total carbon measurements were in agreement with the sum of the sectional carbon measurements. Results and Discussion Figure 2 depicts the temperature profile and the carbon deposition rate in an INCONEL 600 reactor during ethane pyrolysis for a total running time of both 6.5 and 1h. As shown,’the carbon deposition increases with rising temperature and exhibits a bimodal distribution along the length of the reactor. In the first part of the reactor the carbon formed appears to be metal-catalyzed carbon, i.e., the type that has been well described in the literature (Baker and Harris, 1978) and also found in this laboratory previously under experimental conditions (Velenyi and Metcalfe, 1984, 1985, 1986; Velenyi et al., 1989). As the temperature gets higher, pyrolytic carbon starts to form also. It is assumed that this noncatalytic carbon covers up the catalytic sites rapidly resulting in a sharp decrease in the formation of catalytic carbon. However, when the temperature starts to decrease in the latter part of the reactor, the carbon formation increases again. This is mainly because at lower temperatures catalytic carbon formation becomes dominant again. While the pyrolytic carbon continues to deposit on the cooler reactor walls, the amount is reduced significantly at these lower temperatures. The catalytic carbon growth is mostly via a mechanism that involves filamentous carbon growth. This mechanism-well described by Sacco and co-workers (Sacco and Caulmare, 1982; Jablonski et al., 1989) among others-is less influenced by coverage of pyrolytic carbon. The two cooler zones in the reactor differ significantly as far as the gas compositions and contact times are concerned. At the beginning of the reactor the ethane concentration is high and the product levels (hydrogen, ethylene, etc.) are low. In the other cooler zone after the temperature maximum, the conversion progressed well. Therefore, the ethane concentration is low while the product levels are high. The flow of gases is also increased resulting in residence time shorter than in the first cooler zone. These changes affect carbon formation. The covering of the catalytic sites by pyrolytic carbon is much less influential in the second cooler zone than in the first one. Additionally, the carbon found in this region (beyond approximately 50 cm from the entrance of the reactor) can also come from the first part of the reactor due to the

0888-5885/91/2630-1108$02.50/0 0 1991 American Chemical Society

Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1709 REACTOR SYSTEM TEMPERATURE

A. Pyrolysis Set-up

"4'0

SILICON CARBIDE 0

2ool I

\

"\

s

100

I

8. Sectlonal Burn-off Set-up DISTANCE, cm N2

Figure 3. Axial temperature profile and distribution of carbon deposition in an a-silicon carbide reactor during ethane pyrolysis with a total pyrolysis running time of 6.5 h.

N2

b

- 4.0

f+l Fume Hood 0 I Filter

E E

P

e

(2 p)

0 = Flow Controller

- 3.0

=Onion Valve

= Check Valve (1 PSI)

w'

t

z 0

= 3 Way Valve = Pressure Regulator = Pressure Relief Valve

-2.0

Figure 1. Schematic of the reactor system: (A) setup for ethane pyrolysis experiments; (B)setup for carbon burn-off (decoking) experiments. , .-."

DISTANCE, cm

Figure 2. Temperature profile and carbon deposition rate in both new and used INCONEL 600 reactors during ethane pyrolysis with total pyrolysis running time of 6.5 and 1 h.

entrainment of carbon toward the exit of the reactor. Comparing the 6.5- and 1-h-pyrolysis runs, it is clear that in the first part of the reactor the rate of carbon formation is much faster during the first hour of pyrolysis. This is due to the availability of a greater number of catalytic sites on the reactor walls at the beginning of the experiment. The fact that the rate of carbon formation is much faster during the early stages of pyrolysis proves the catalytic nature of carbon formation in the first part of the reactor. In the second half of the reactor the carbon deposition rate does not change with running time and the total amount of carbon deposited reflects only the difference in the length of the total pyrolysis running time. Figure 3 shows the results of a 6.5-h-pyrolysisrun in an a-Sic reactor. The a-Sic tube does not catalyze carbon formation; therefore, only pyrolytic carbon is formed in

5 B

- 1.0 u .

,r

-, I H-U-M.

a

p2

I

this reactor. Carbon distribution exhibits a bell-shaped curve along the length of the a-Sic tubular reactor, indicating the dominance of only one carbon formation mechanism by which pyrolytic carbon is produced. The maximum carbon deposition coincides with the highest reaction temperature. For a side-by side comparison, the individual results of the 6.5-h-pyrolysis experiments in the INCONEL 600 and the a-Sic reactors are shown together in Figure 4. Despite the similarity of the temperature profiles for both reactors, the formation rate of catalytic carbon (in INCONEL 600 reactor) is much faster than that of pyrolytic carbon (in a-Sic reactor) under the same reaction conditions. There could be a partial explanation for the difference between the amount of carbon found in the INCONEL 600 and the a-Sic tubes. It is plausible to believe that some of the carbon precursors, coke, or carbon were not detected in the experiments with the a-Sic tube. One reason could be that these carbonaceous materials were blown out from the reactor tube due to poor adhesion to the a-Sic surface. However, we found no significant blackening in the liquid traps (see Figure 1A) or in the gas collection bag (see Figure 1B). The other reason for escaping detection could be inefficient bum-off technique. While nickel and iron in the metal reactors promote combustion of coke or carbon, there is no such catalyst present in a-Sic. Therefore, at the cooler end of the reactor some coke or carbon may not have burned off. To prevent this, the reactor was moved during the burnoff to position the end into the hotter section of the furnace.

1710 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991

2.4 2.2

-

2.0 1.8

-

1.6

-

1.4

-

1.2 1.0

-

-

0.6

-

0.4

-

0.2

-

0.8

__

0

1

2

3

4

5

8

7

8

9 1 0 1 1 1 2 1 3

PYROLYSIS AND DECOKING CYCLE

Figure 6. Effects of steam, hydrogen sulfide, and pyrolysie-decoking cycle on carbon yield in an INCONEL 600 reactor during ethane pyrolysis at an average reaction temperature of 925 "C and a contact time of 35 ma.

This provided sufficient heat to facilitate noncatalyzed combustion. The amount of total carbon deposition in INCONEL 600 tube is also influenced by the number of pyrolysis-decoking cycles. As shown in Figure 5, at an average reaction temperature of 925 "C and a contact time of 35 ms, the amount of total carbon deposition in a brand-new INCONEL 600 reactor is very similar to that found in an a-Sic reactor except for the shape of carbon deposition curves (see Figures 2 and 4). However, the carbon yield in the INCONEL 600 reactor increases significantly with the number of pyrolysis-decoking cycles. This increase in carbon deposition is attributed to the increase in surface roughness and possibly to the changes of surface composition and/or oxidation state. (Contrary to INCONEL 600, a-Sic tubes produce a constant amount of coke deposition regardless of the number of pyrolysis-decoking cycles.) Also depicted in Figure 5 is the enhancement of coke deposition in an INCONEL 600 tube when ethane is pyrolyzed in a steamless environment with 25 and 100 ppmv H a . The addition of H a in the steamlw ethane pyrolysis appears to have very significant adverse effects on carbon deposition. On new INCONEL 600 tubes, 25 ppmv H2S in feed gas does not increase carbon deposition significantly, but 100 ppmv H2S in feed increases carbon deposition by a factor of 10. As the number of pyrolysisdecoking cycle increases, carbon deposition also increases, indicating a synergistic effect of H2S and surface roughness, composition, oxidation state, etc. At a first glance, our finding appears to be in contradiction with the general industrial practices of adding sulfur compounds to reduce coke formation in commercial reactors (Kirk-Othmer, 1978). It also contradicts the results of Crynes and Albright (1969), Dunkleman and Albright (1969), Tsai and Albright (1976),and Albright and Tsai (1983) in sulfiding pyrolysis reactor walls. It has been postulated by these investigators that sulfiding to a limited extent the inner surface of a reactor that has just been decoked produces a protecting metal sulfide layer on the surface, and hence reduces the production of coke. On the other hand, other investigators suggest that, depending on reactor material and reaction conditions, there may exist some threshold levels of H2S (Froment, 1988) in suppressing coke deposition. If the H a concentration is below the threshold level, it will suppress coking on the reactor surface; however, if the H2Sconcentration is above the threshold level, it can

actually promote coke deposition because H a is inherently a coke promoter. We did not observe the threshold effects in our experiments, perhaps because our reaction temperature is generally higher than those used by the previous investigators and those used in industrial crackers. Also, in a steamless environment, the interaction between H2S and the reactor walls is perhaps somewhat different from that in which steam is present. On a-Sic tubes, 25 ppmv H2S does not change carbon deposition significantly regardless of the coking cycle. We believe that this is mainly due to the lack of catalytic surfaces, thus catalytic carbon. A question can be raised whether the large differences between the a-Sic and INCONEL tubes will hold with extended time. We used the same a-Sic tube for approximately 1 year without any significant change in carbon formation behavior. When INCONEL 600 tubes the amount of carbon deposited increased with the age of the tube. Therefore, it is expected that the differences would be maintained. Another question could be the resistance of the a-Sic tube to attack by air or steam. When air or steam was passed through the reactor, no CO or C02 was detected in the absence of carbon. Finally, when ethane is pyrolyzed in the presence of steam (0.3to 1H20 to C2Hgweight ratio), the amount of carbon deposition in the INCONEL 600 reactor is reduced to a constant level regardless of the pyrolysis-decoking cycles. This amount coincides with that produced in an a-Sic reactor regardless of the age, i.e., the number of pyrolysis-decoking cycles, and/or the use of steam.

Reactor Simulations In order to obtain further insight into the dynamics of the carbon formation, a two-dimensional, steady-state model description of the reactor system was written in cylindrical coordinates to simulate the pyrolysis process. The model was used to solve the governing momentum, mass,and energy balances in order to calculate the velocity, concentration, and temperature profiles within the system. The purpose of the modeling effort was to find how radial and longitudinal variations of velocity, composition, and temperature affect the chemistry of the system. The chemical species present were simulated by using five representative components: hydrogen, methane, ethane, ethene, and benzene. A set of three fmt-order, irreversible reactions with Arrhenius temperature dependence was used to represent steam kinetics: (1)ethane forms ethene plus hydrogen, (2) ethane plus hydrogen forms methane, and (3) ethene forms benzene plus hydrogen. Kinetic parameters were regressed from experimental data, with reaction zone temperatures between 925 and 975 "C. While this reaction set is obviously a simplification of the actual free radical reaction mechanism, it is sufficiently accurate to give a good description of temperatures and composition within the reactor. This is because the major reaction pathways are included, with reactions occurring on the proper time scale with the correct heat of reaction effects. A full description of the basis of this model is presented by Fagley (1991). He gives a detailed description of the modeling equations used and shows a comparison of model results with experimental values. The model was used to simulate several of the ethane pyrolysis experiments described earlier. The model input includes an experimentally determined wall temperature profile, inlet gas temperature, and flow rate. Figure 6 shows a plot of simulated temperatures for a run with 72% ethane conversion in a 0.5-cm-i.d. a-Sic tube. In this figure, "Tube Temp" is the experimentally determined wall temperature profile, "Gas @I Wall Temp" is the simulated gas temperature 0.006 25 cm from the wall, "Mixing Cup

Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 1711 1lOOl

gOOl

0

800

ui K

700

-B

A-

e

V

"0

B 0

4

500

0 400

n

Tube Temp, C 0 Gas @ Wall Temp, C n Mixlng Cup Temp, C V Centerllne Temp, C 0

41

gv v 10

1'5 20

25

30 35 40

4b

50 55

65

60

o;

DISTANCE, cm

Figure 6. Comparison of experimental axial temperature profde and Phoenics simulated temperature profile for a pyrolysis run with 72% ethane conversion in a 0.5-cm4.d. a-silicon carbide reactor.

/u

/

0

g

Boot

750

650

1

" ;o

13 112 11

-

-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2

800

700

-14

dY @ I

0.05

I 0.1

I 0.15

1 0.2

perature is still too low to form carbon, the reactor wall already reaches a threshold temperature for the formation of the catalytic carbon. On the contrary, in the a-Sic reactor, there is no pyrolytic carbon because the temperature at the beginning section is still too low, and there is not any catalytic carbon because the a-Sic surface does not have any catalytic effect. Referring to Figure 4, note that carbon is deposited in the INCONEL 600 reactor at a distance of 10 cm, where the measured gas temperature is only 500 "C. The simulation results of Figure 6 indicate how this is possible. The temperature measured by a thermocouple placed inside the reactor may easily be 200 "C lower than the hot, slow-moving gas near the wall. These results also suggest that superior performance in the form of lower carbon formation at a given ethane conversion can result in a turbulent flow system, where eddy mixing will decrease the severity of radial temperature and velocity gradients.

Conclusions Our experimental results have shown that, while a metal (INCONEL 600) reactor has a very significant effect on the formation of carbon, the a-Sic tube produces little carbon deposition during ethane pyrolysis. It also appears that, in an a-Sic reactor, steam is not required as a coke suppresser for ethane cracking to ethylene. A model of the reactor showed the importance of radial velocity and radial temperature profiles in the system. Slow-moving, hot gas neaer the wall is reacting very rapidly compared to the fast-moving, cold gas near the centerline. This will obviously have a significant effect on carbon deposition within the metal reactor system. This effect is not as important for the a-Sic reactor because the reactor wall is noncatalytic.

0.25

RADIUS, cm

Figure 7. Phoenics predictions of radial temperature and longitudinal velocity profiles at a distance of 27 cm from the entrance of a 0.5-cm4.d. a-silicon carbide reactor during ethane pyrolysis.

Temp" is the mixing cup or flow-averaged temperature, and "Centerline Temp" is the simulated gas temperature at the centerline of the reactor. Note that the centerline gas temperature is nearly 500 "C below the wall temperature midway through the heatup zone of the reactor. This is a result of the higher velocity in the center, low inlet gas temperature, and low thermal conductivity of the gas. Figure 7 shows radial temperature and longitudinal velocity profiles at a distance of 27 cm from the entrance of the reactor. The velocity profile shown here is very close to the parabolic profile resulting from isothermal, nonreacting laminar flow in tubes. These results show that transport of momentum and heat have a significant impact on carbon formation within the system. Near the wall in the hot zone of the reactor, the gas is relatively hot and slow moving, while near the centerline, the gas is relatively cold and fast moving. This means that a great deal of the reaction that occurs in the system will be taking place near the wall, where long residence times and elevated temperatures can contribute to carbon formation. This effect is somewhat mitigated by molecular diffusion, which carries products from the wall toward the centerline and unreacted ethane from the centerline toward the wall. Simulation results reveal that molecular diffusion occurs at a rate sufficiently fast to impact the composition within the reactor. The simulation results also help explain why carbon is formed in the metal reactor "sooner" than one might expect. In the beginning section of the metal reactor, while the average gas tem-

Acknowledgment We acknowledge Drs. Joseph E. Metcalfe, Alan A. Leff, and Mike J. Manka for their constructive comments and useful suggestions. We also express our gratitude to Messrs. Wayne R. Kliewer and Richard L. Chapman for their experimental assistance.

Literature Cited Albright, L. F.; Tsai, T. C. H. Importance of Surface Reactions in Pyrolysis Units. In Pyrolysis: Theory and Industrial Practice; Albright, L. F., Crynes, B. L., Corcoran, W. H., Eds.; Academic Press: New York, 1983; pp 233-254. Albright, L. F.; Marek, J. C. Coke Formation during Pyrolysis: Roles of Residence Time, Reactor Geometry, and Time of Operation. Znd. Eng. Chem. Res. 1988a, 27, 743. Albright, L. F.; Marek, J. C. Analysis of Coke Produced in Ethylene Furnace: Insighta on Process Improvements. Znd. Eng. Chem. Res. 1988b,27, 751. Albright, L. F.; Marek, J. C. Mechanistic Model for Formation of Coke in Pyrolysis Units Producing Ethylene. Znd. Eng. Chem. Res. 1988c, 27, 755. Baker, R. T. K.; Harris, P. S. Chemistry and Physics of Carbon; Walker, P. L., Thrower, P. A., Eds.; Marcel Dekker: New York, 1978; Vol. 14. Billaud, F.; Chaverot, P.; Berthelin, M.; Freund, E. Thermal Decomposition of Cyclohexane at Approximately 810 OC. Ind. Eng. Chem. Res. 1988,27,759. Crvnes, B. L.; Albright. - Chem. Process Des. Dev. - . L. F. Znd. Ena. issi,a, 25.. Dunkleman. J. J.: Albrieht. L. F. In Zndwtrial and Laboratory Pyrolysis; Albright, L. @.,Crynes, B. L., Eds.; ACS Symposium Series 32; American Chemical Society: Washington, DC, 1976; pp 241-260. Fagley, J. C. Simulation of Transport in Laminar, Tubular Reactore and Application to Ethane Pyrolysis. Ind. Eng. Chem. Res. 1991, in press. Froment, G. F. Private communication, 1988.

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:

~

C

O

O

C

,

H

,

2

O

C

C

+~HOC&I,OH

(1)

EG

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