Ind. Eng. Chem. Res. 1997, 36, 3513-3519
3513
Transient Experiments and Mathematical Modeling of an Industrial Twin-Screw Extruder Reactor for Nylon-6,6 Polymerization† Reinaldo Giudici,*,‡ Cla´ udio Augusto Oller do Nascimento,‡ Isabel Capocchi Beiler,‡ and Nata´ lia Scherbakoff‡,§ Department of Chemical Engineering, LSCP-Process Control and Simulation Laboratory, University of Sa˜ o Paulo-Polytechnic School, P.O. Box 61548, 05424-970 Sa˜ o Paulo, SP, Brazil, and Rhodia S. A. (Group Rhoˆ ne Poulenc), Av. dos Estados, 6144, 09210-900 Santo Andre´ , SP, Brazil
This paper describes transient experiments in an industrial twin-screw extruder reactor used for the finishing stage of nylon-6,6 polycondensation. Transient experiments were specially designed to obtain pertinent information from the industrial extruder, such as the average residence time and the degree of filling. A transient model for this process was developed. The extruder is modeled as two compartments, the partially filled degassing zone where water is removed from the polymer and the fully filled zone where the polycondensation and degradation reactions take place. The axial dispersion model is successfully applied to explain the results of the experiments done in the industrial plant. Introduction Nylon-6,6 polymer is produced from hexamethylenediamine and adipic acid monomers. Like many other step-growth polymerization processes, nylon-6,6 polycondensation is typically carried out in three stages, due to the different conditions of kinetic, mass, and heat transfer, condensate removal, and viscosity in each process stage. The design of the finishing stage reactors requires special features since they usually operate with high viscosity polymers under difficult conditions of condensate removal and heat transfer. Extruder reactors can be effective in handling these conditions, as described in reviews on reactive extrusion (Tzoganakis, 1989; Berghaus and Michaeli, 1991; Xanthos, 1992). A typical example of the use of twin-screw extruder reactors for the finishing stage of a polycondensation process was presented by Mack and Herter (1976). The kinetics and equilibrium of nylon-6,6 polymerization were studied by Ogata (1960, 1961). His data was later used by other researchers, such as Kumar et al. (1981, 1982) and Steppan et al. (1987), who proposed different kinetic expressions. Steppan et al. (1991) also presented a kinetic model for the degradation reactions in this system. Previous works on modeling of nylon-6,6 finishing reactors focused primarily on thin or wiped film reactors (Steppan et al., 1990; Choi and Lee, 1996). Jacobsen and Ray (1992a,b) presented a unified general framework for the kinetic modeling of polycondensation reactions. Later, Hipp and Ray (1996) applied this general framework in a dispersion model for tubular reactors, which is able to represent a number of different reactor types, including rotating disk reactors and twinscrew extruder reactors. One of their examples was the polymerization of nylon-6,6; however, no comparison with real data was presented for this system. Modeling works on reactive extrusion using twinscrew extruders have been reported in the literature, * To whom correspondence should be addressed. Phone: (5511) 818-5637. Fax (55-11) 813-2380. E-mail:
[email protected]. † This paper is dedicated to Professor A. E. Hamielec on the occasion of his retirement. ‡ University of Sa ˜ o Paulo-Polytechnic School. § Rhodia S. A. S0888-5885(96)00814-7 CCC: $14.00
e.g., Michaeli et al. (1995), Maier and Lambla (1995), and Jongbloed et al. (1995). Potente and co-workers (1986, 1994) have studied extensively the modeling of conventional plasticating extruders. They proposed a model to predict the residence time distribution using the product of two Weibull distributions, with four adjustable parameters (Potente and Lappe, 1986). Their model showed satisfactory results for conventional plasticating extruders. The present work deals with the mathematical model for the finishing stage of nylon-6,6 polycondensation in an industrial twin-screw extruder reactor. The phenomenological modeling of this system presents some difficulties such as the complex nature of the flow in the extruder, the condensate removal (mass-transfer limitations), and the knowledge of polycondensation kinetics under catalyzed conditions, as well as the degradation reactions. Also, the lack of internal or intermediate measurements along the industrial extruder reactor represents a limitation for a detailed model validation. Furthermore, the degree of filling varies with the operating conditions, making it difficult to characterize the average residence time in the system. In addition, polymer properties such as relative viscosity that are important in industrial practice are not directly predictable from the primary model variables (e.g., the concentration of the end groups). These problems prompted us to propose a simple realistic model, in which the aforementioned difficulties were addressed. The basis of the model for steady-state operation is presented elsewhere (Giudici et al., 1997). The extruder was conceptually divided in two regions. The first region corresponds to the partially filled degassing zone, which is operated under low pressure in order to evaporate water, the condensation product. The second region represents the fully filled zone, which was modeled as a tubular reactor where polycondensation and degradation reactions take place. One specially important point required by this model is the prediction of the average residence time under different operating conditions. The main aim of the present paper is to model and compare the transient experiments in the industrial extruder reactor, which were useful for obtaining meaningful information about the average residence time of the polymer in the extruder (and the degree of filling). © 1997 American Chemical Society
3514 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
The second region was modeled as an axially dispersed plug-flow reactor. For steady-state simulations, the effect of the axial dispersion is often small so that a simple plug-flow model can be used (Giudici et al. 1997). However, for the transient experiments, it is necessary to take the axial dispersion into account. The mass balances in the second region for each species considered can be expressed in the form
∂(uzCi)
∂Ci )∂t
∑
∂z
+ DL
Ri,jrj
∂2Ci + ∂z2 (i ) A, C, L, W, SE, SB, X) (1)
j)p,d1,d2,d3,d4
Figure 1. Scheme of the two-region model for the extruder reactor.
Also, a simple model for the flow of polymer in an extruder is used as a framework to develop a semiempirical expression for the prediction of the degree of filling. Mathematical Model The dynamic model is based on the steady-state model previously developed by us (Giudici et al., 1997). The process under consideration (finishing stage of nylon-6,6 polymerization) is carried out in a self-wiping, corotating, twin-screw extruder reactor. The extruder is fed with melt polymer. There is a vacuum vent port near the entrance of the extruder to promote water evaporation and generate the driving force for the polycondensation. This degassing zone is followed by a fully filled region, where no further evaporation occurs. The ratio between the lengths of these two zones varies with the operating conditions. The polymer that leaves the extruder goes to the spinnery pack. As already pointed out in the Introduction, the model was developed by considering that the extruder can be conceptually divided in two compartments, the partially filled zone and the fully filled zone. It was assumed that in the first zone, only mass-transfer events occur (water evaporation) and in the second zone, only reaction events take place (polycondensation and degradation reactions). In addition, based on industrial measurements, isothermal conditions in the extruder are assumed. Figure 1 shows the scheme of the model. The water content in the polymer feed is obtained assuming equilibrium of the polycondensation reaction. The amount of water evaporated in the first region is expressed by an overall mass-transfer coefficient and a driving force based on the departure from the physical equilibrium between water and polymer. The solubility of water in molten nylon-6,6 was calculated as a function of temperature and pressure from the correlation given by Ogata (1961). The effective mass-transfer coefficient (including the specific area) was estimated (0.09 s-1) by fitting the steady-state model to the industrial data (for details, see Giudici et al. (1997)).
where z represents the axial position, Ri,j is the stoichiometric coefficient of species i in reaction j, rj is the rate of reaction j, uz is the transverse, area-averaged, axial velocity, and DL is an apparent or effective axial dispersion coefficient. The species considered are the amine end group (A), carboxyl end group (C), amide linkage (L), water (W), stabilized end group (SE), Schiff base (SB), and cross-link (X). The reactions considered are polycondensation (p) and four degradation reactions (d1, d2, d3, d4) according the scheme proposed by Steppan et al. (1991). More details about the kinetic scheme are given in the Appendix. The boundary conditions for eq 1 are chosen as the well-known Danckwerts conditions (Danckwerts, 1953):
Ci ) Ci,0 -
DL ∂Ci uz ∂z
∂Ci )0 ∂z
at z ) inlet of the region (1a)
at z ) outlet of the region
(1b)
Equation 1 is written for each component of the system and solved simultaneously to predict the concentration of the species as a function of position and time. The model equations were discretized in the axial domain by using the orthogonal collocation method (Finlayson, 1980; Villadsen and Michelsen, 1978) and then solved in the time domain by an adequate marching technique (standard variable-step fourth-order Runge-Kutta-Gill method). Previous numerical tests have shown that 10 axial collocation points are enough for a fair representation of the solution for the cases of interest. To represent accurately steep axial profiles for near-plug-flow conditions (high Peclet values), orthogonal collocation in finite elements can be used instead (Finlayson, 1980). RTD Experiments in a Laboratory Extruder One way to estimate the Peclet number is from residence time distribution (RTD) experiments. These experiments are possible to perform in the industrial plant, but the costs involved may be very high. Tracer experiments were done in a laboratory-scale twin-screw extruder, which is similar to the industrial extruder reactor. The choice of the adequate tracer for nylon6,6 was previously studied and is reported elsewhere (Scherbakoff et al., 1995). The tracers employed were master batches of potassium and copper salts and titanium dioxide, components normally added to the polymer formulation. The RTD runs were carried out on a self-wiping corotating twin-screw extruder (Werner & Pfleider ZSK-
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3515
model is adequate for representing the axial mixing in a twin-screw extruder. RTD Experiments in an Industrial Plant A knowledge of the mean residence time of the polymer in the extruder is necessary for any model application. The extruder normally operates not fully filled, allowing the presence of a partially filled zone where evaporation of water takes place. The evaporation of water produces the driving force for the polycondensation in the subsequent fully filled zone. The extension of the partially filled zone may vary with the operating conditions. Because of the partial filling, the residence time is not precisely known. The knowledge of the degree of filling is very important because the extension of the partially filled zone affects the space time of the polymer, with implications for the degree of polymerization. Moreover, if the conditions are such that the extruder becomes completely filled, there will be no place for the evaporation to occur, dramatically changing the process response. Therefore, it is extremely important to predict the residence time or, alternatively, the degree of filling. The initial idea was to carry out tracer experiments in the extruder to obtain the residence time distributions. However, the use of tracers in the industrial process was not possible due to operational difficulties in carrying out such an experiment. This problem led us to perform a different kind of experiment that provides similar information. Vacuum Shutdown Experiments
Figure 2. Comparison between model predictions (;) and experimental results (0) for the tracer experiments in a laboratoryscale twin-screw extruder: (a) tracer, titanium oxide, Pe ) 39; (b) tracer, potassium salt, Pe ) 48; (c) tracer, copper salt, Pe ) 50.
30). The main characteristics of the extruder are the following: screw diameter 30.7 mm, length 870 mm, 5 heating control zones, all of them kept at 280 °C. The samples were collected every 5 s at the die exit and analyzed by UV spectrometry (titanium oxide) or atomic absorption spectrometry (potassium and copper salts). Figure 2 presents the experimental RTD curves, as well as the corresponding curves calculated from the dispersion model. The dispersion model was able to fit the data quite well. Therefore, the axial dispersion
An estimate of the average residence time was obtained through a specially designed procedure that we call the “vacuum shutdown experiment”. After setting the independent variables of the process (screw rotation speed, flow rate, temperature, pressure) and waiting for the process to reach steady state, the vacuum system was suddenly turned off. Thereafter, degassing no longer occurs so that no driving force for the polycondensation is generated. After the vacuum shutdown, the polymer that enters the extruder will not increase its degree of polymerization. When this lower viscosity polymer reaches the spinnerets at the end of the extruder, the pressure drop in the spinneret pack will decrease. The elapsed time required for the decrease in the pressure drop in the spinnery pack gives an estimate of the polymer residence time in the system. This procedure was applied to a series of 23 experiments planned according to an incomplete factorial design presented in Table 1. Runs 2-17 correspond to the original incomplete factorial design, runs 1, 18, and 23 are triplicate experiments at the central point, and runs 19-22 are complementary experiments. Due to industrial constraints on the operating variables, there are some differences between the planned and the real measurements (also reported in Table 1). A typical response of the pressure drop in the spinnery pack is shown schematically in Figure 3. This figure also illustrates the procedure used to estimate the average residence time. Only 2 out of 23 runs presented an “abnormal” operation. In theses runs, no change in the pressure drop at the spinneret pack was observed, an indication of the “flooding” of the extruder under these conditions. This circumstance corresponds to a fully filled extruder, leaving no space for water evaporation.
3516 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 1. Experimental Design for the Industrial Runs originally planned design
real measurements (coded)
run
T
Pv
Q
Ph
N
T
Pv
Q
Ph
N
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
-1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1
-1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1
-1 -1 -1 -1 -1 -1 -1 +1 +1 +1 +1 +1 +1 +1 +1 +1
-1 -1 -1 -1 +1 +1 +1 +1 -1 -1 -1 -1 +1 +1 +1 +1
+1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 +1 +1 +1 -1 -1
-0.97 1.01 -1.07 0.93 -0.92 0.97 -0.93 1.00 -0.92 1.10 -0.88 0.97 -0.89 1.03 -1.01 0.95
-1.07 -1.08 1.15 1.15 -1.07 -1.09 1.13 1.05 -1.15 -1.08 1.02 1.06 -1.14 -1.17 1.05 1.06
-1 -1 -1 -1 -1 -1 -1 +1 +1 +1 +1 +1 +1 +1 +1 +1
-0.84 -1.00 0.12 -1.00 0.44 1.00 1.04 1.04 -1.64 -1.16 -1.00 -1.00 0.76 0.84 0.92 1.04
-1.03 -0.77 2.14 0.89 1.05 0.56 -1.06 -0.71 0.37 0.36 -1.31 -1.42 -1.21 -0.76 1.69 1.04
1 18 23
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
-0.01 0.13 0.04
0.03 0.02 0.01
0 0 0
0.16 0.24 0.24
0.22 0.41 0.05
19 20 21 22
0 0 0 0
-1 +1 0 0
0 0 0 0
0 0 0 0
0 0 -1 +1
0.00 -0.05 -0.01 -0.02
-1.07 +1.15 +0.03 +0.02
0 0.12 -0.04 0 0.12 -0.20 0 -0.04 -0.90 0 -1.04 0.93
Figure 3. Typical response of the pressure drop in the spinnery pack during the vacuum shutdown experiment. Stimulus: The vacuum is shut down at time t1, resulting in a step disturbance at the extruder inlet. Response: After some time, the pressure drop in the spinnery pack (at the extruder exit) decreases as a sigmoidal-like curve. The instant t2 is chosen as indicated (i.e., the same area is left under the curve after t2 and above the curve before t2, between the two steady-state limits). The average residence time is estimated as τ ) t2 - t1.
Correlating the Average Residence Time with the Process Variables For the prediction of the average residence time as a function of the process variables, the first attempt was to use a simple surface response model. However, this empirical approach proved to be nonconservative, since it was not able to reproduce the “abnormal” flooding situations. This result prompted us to use a more theoretically based approach. A simple model for the flow in an extruder is the socalled “screw pump model” or “continuous drag flow model” (Biesenberg, 1992; Meijer and Elemans, 1988; Tadmor and Gogos, 1979; Jongbloed et al., 1995). For the fully filled zone, the flow is given by the sum of the effects of the drag flow and the pressure flow in the form
πDWH FdN cos φ + Q ) (2m - 1) 2 3
(2m - 1)
dP WH F (2) 12η dz p
(
)
where m is the number of thread starts, H is the channel depth, W is the channel width, D is the barrel diameter, φ is the pitch angle, N is the screw rotation rate, η is the melt viscosity, dP/dz is the pressure gradient in the channel direction, and Fd and Fp are shape factors for the drag and pressure flow, respectively. Since there is no axial pressure gradient in the partially filled zone, the adequate boundary conditions for eq 2 are
P ) Pv
at z ) z1
(3)
P ) Ph
at z ) L
(4)
where z1 is the length of the partially filled zone and L is the total length of the extruder. Applying eq 2 to the fully filled region and lumping the effects in adjustable parameters, one obtains
Ph - Pv Q ) K1N - K2 〈η〉(L - z1)
(5)
where K1 and K2 are adjustable parameters (incorporating the geometric parameters) and 〈η〉 is the average
Figure 4. Parity plot for the degree of filling.
melt viscosity of the polymer along the extruder. Equation 5 was then used as the basis of a semitheoretical relation in which K1 and K2 are treated as fitting parameters. The average melt viscosity can be estimated from the polymer rheology and expressed as an empirical function of the operating conditions. For the conditions studied, the following empirical relation was obtained:
〈η〉 ) 0.0042Pv-0.08Ph+0.8
(6)
The predictions of eq 5 are compared with the experimental data in Figure 4. The accuracy is within the experimental error of the measurements and is similar to that obtained by other authors using different approaches (Michaeli et al., 1995; Potente and Lappe, 1986). The practical approach used here allows one to calculate the length of the fully filled zone and then the average residence time of the polymer in the reaction zone. This prediction is especially important for optimization studies, where the residence time is not known a priori for different operating conditions. Simulation of the Vacuum Shutdown Experiments The curve of pressure drop in the spinnery pack is the only response measured on-line. Experimental
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3517 Table 2. Kinetic Parameters, after Steppan et al. (1987, 1991)
a
rate const
kj0, 1/h
Ej, kcal/mol
T0 , K
kd1 kd2 kd2c kd3 kd4 kp
0.06 0.005 0.32 0.35 10.0 see eq A.9
30 30 30 10 50 21.4
566 578 578 578 578 473
DL) was estimated in order to represent the experimental curves. Good agreement was achieved. It is noteworthy that the Peclet number values obtained from the transient vacuum shutdown experiments in the industrial extruder are similar to those for the RTD experiments in the laboratory extruder. From these results, we can conclude that the dispersion model represents reasonably the system. Concluding Remarks
b
Figure 5. Comparison between model predictions and experimental results for the transient (vacuum shutdown) experiments in the industrial plant: (9) relative viscosity RV; (b) concentration of carboxyl end groups; ([) concentration of amine end groups; (;) model predictions. (a) Run 1, Pe ) 45; (b) run 6, Pe ) 45.
values of end-group concentrations and relative viscosity were obtained from samples taken at discrete time intervals during each run. Relative viscosity (RV) is an important variable used in industrial practice to characterize the “polymer quality”. In the model, this property can be predicted from the concentration of end groups through an empirical expression (Giudici et al., 1997) or alternatively by a specially developed neural network model (Nascimento et al., 1997). In this work, we used the expression presented by Giudici et al. (1997):
2F RV ) bMn ) b CA + CC
(7)
where Mn is an estimate of the number-average molecular weight (based on carboxyl and amine end groups only) and b is an empirical constant. The comparison of the model predictions with the experimental response of the variables during the vacuum shutdown is presented in Figure 5, for two different runs. The industrial data are normalized with respect to a reference value, due to confidentiality reasons. The initial conditions used in each case correspond to the previously simulated steady state at the operating conditions before the occurrence of vacuum shutdown. The value of the Peclet number (Pe ) uzL/
The transient behavior of an industrial twin-screw extruder reactor for nylon-6,6 polymerization has been modeled. The model considers the extruder in terms of two compartments: the first one consists of the partially filled zone around the vacuum vent port and the second part represents the fully filled region as an axially dispersed plug-flow reactor. The model was successfully applied to transient experiments done in the plant, as well as to tracer experiments carried out in a similar laboratory-scale twin-screw extruder. The specially designed transient experiments described in this paper (the vacuum shutdown experiments) have provided useful information about the process, allowing measurement of the average residence time in the extruder. In addition, a semiempirical correlation based on the so-called “screw pump model” was developed to predict the degree of filling. To our knowledge, this is the first time that a mathematical model for an extruder reactor is compared to industrial data for the nylon-6,6 polycondensation process under transient conditions. Acknowledgment We express our gratitude to Rhodia S. A. (Rhoˆne Poulenc Group) for supporting this work and to Prof. Frank Quina for revising the manuscript. The partial support by FAPESP, CAPES, and CNPq is also gratefully appreciated. Nomenclature b ) empirical constant in eq 7 Ci ) concentration of component i (kmol/m3) Ct ) total concentration, defined in eq A.7 (kmol/m3) D ) barrel diameter (m) DL ) effective axial dispersion coefficient (m2/s) Ej ) activation energy of reaction j (kJ/kmol) fc, fd ) correction factors for the kinetics of the polycondensation and degradation reactions, respectively Fd,, Fp ) shape factors for the drag and pressure flow, respectively H ) channel depth (m) K1, K2 ) adjustable parameters kj ) rate constant of reaction j kj0 ) rate constant of reaction j at a reference temperature T0 Kp ) apparent equilibrium constant of the polycondensation reaction
3518 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
base, and X to the cross-link. The kinetic parameters are presented in Table 2:
L ) total length of the extruder (m) Mn ) number-average molecular weight (kg/kmol) m ) number of thread starts N ) screw rotation speed (s-1) P ) pressure (Pa) Pv ) pressure of the vacuum system (Pa) Ph ) pressure at the extruder head (Pa) Pe ) Peclet number ()uzL/DL) Q ) volumetric flow rate (m3/s) rj ) rate of reaction j (kmol/(m3‚s)) R ) ideal gas constant RV ) relative viscosity t ) time (s) T ) temperature (K) T0 ) reference temperature (K) uz ) transverse, area-averaged, axial velocity (m/s) W ) channel width (m) xi ) mole fraction of component i z ) axial position (m) z1 ) length of the partially filled zone (m)
xi ) Ci/Ct
(i ) A, C, L, W, SE, SB, X) (A.6)
Ct ) CA + CC + CL + CW + CSE + CSB + CX (A.7) kj ) kj0 exp
[ (
)]
-Ej 1 1 R T T0 (j ) d1, d2, d2c, d3, d4, p) (A.8)
The strongly nonideal behavior of the species causes both the polycondensation rate constant and the equilibrium constant to vary with composition, as shown by Steppan et al. (1987)
kp0 ) exp{2.55 - 0.45 tanh[25(xw - 0.55)]} + 8.58{tanh[50(xw - 0.10)] - 1}(1 - 30.05xc) (A.9)
Greek Letters Ri,j ) stoichiometric coefficient of the species i in reaction j φ ) pitch angle η ) melt viscosity (Pa‚s) 〈η〉 ) average melt viscosity of the polymer along the extruder (Pa‚s) ∆Hp ) apparent heat of polycondensation reaction (kJ/ kmol) F ) polymer density (kg/m3)
[
)]
(
Kp ) K0 exp -
∆Hp 1 1 R T 473
{[
(
K0 ) exp 1 - 0.47 exp -
)]
}
xw1/2 (8.45 - 4.2xw) 0.2 (A.11)
∆Hp
Subscripts
R
A ) amine end group C ) carboxyl end group L ) amide linkage W ) water SE ) stabilized end group SB ) Schiff base X ) cross-link p ) polycondensation reaction d1, d2, d2c, d3, d4 ) degradation reactions
7650 tanh[6.5(xw - 0.52)] + 6500 exp -
(A.1)
degradation reactions:
L f SE + A
rdl ) Ctkd1xc
)
xw - 800 0.065
In our previous work (Giudici et al., 1997), it was shown that the effect of the catalyst present in the industrial process can be accounted for by multiplying the above reaction rates by correction factors. By fitting the model to the industrial data, the values fp ) 15 and fd ) 3.7 were found.
polycondensation:
C f SE + W
(
(A.12)
The kinetic scheme used in the model for the extruder reactor was based on the work of Steppan et al. (1987, 1991), along with correction factors estimated by Giudici et al. (1997) that take into account the effect of the industrial catalyst. The reactions and the respective rate equations are as follows:
rp ) Ctkp(xAxC - xLxW/Kp)
)
1.987
Appendix: Kinetic Model
A+CSL+W
(A.10)
(A.2)
rd2 ) CtxL(kd2 + kd2,cxA) (A.3)
SE f SB + CO2
rd3 ) Ctkd3xAxSE0.1
(A.4)
SB + 2A f X + 2NH3
rd4 ) Ctkd4xAxSB0.3
(A.5)
where A refers to the amine end group, C to the carboxyl end group, L to the amide linkage, W to water, SE to the stabilized (or cyclized) end group, SB to the Schiff
Literature Cited Berghaus, U.; Michaeli, W. Current status of the development of reactive extrusion. Kunststoffe, 1991, 81 (6), 479-485. Biesenberger, J. A. Principles of Reaction Engineering. In Reactive Extrusion, Principles and Practice; Xanthos, M., Ed.; Hansen: Munich, 1992. Choi, B. R.; Lee, H. H. Transient and steady-state behavior of wiped-film reactors for reversible condensation polymerization. Ind. Eng. Chem. Res. 1996, 35 (5), 1550-1555. Danckwerts, P. V. Continuous flow systems. Chem. Eng. Sci. 1953, 2, 1. Finlayson, B. A. Nonlinear Analysis in Chemical Engineering; McGraw-Hill: New York, 1980. Giudici, R.; Nascimento, C. A. O.; Beiler, I. C.; Scherbakoff, N. Modeling of industrial nylon-6,6 polycondensation Part I: Phenomenological model and parameter adjusting. Submitted for publication in J. Appl. Polym. Sci. 1997. Hipp, A. K.; Ray, W. H. A dynamic model for condensation polymerization in tubular reactors. Chem. Eng. Sci. 1996, 51 (2), 281-294. Jacobsen, L.; Ray, W. H. Analysis and design of melt and solution polycondensation process. AIChE J. 1992a, 38, 911-925. Jacobsen, L.; Ray, W. H. Unified modeling for polycondensation kinetics. J. Macromol. Sci.-Rev. Macromol. Chem. Phys. 1992b, C32 (3&4), 407. Jongbloed, H. A.; Kiewiet, J. A.; Van Dijk, J. H.; Janssen, L. P. B. M. The self-wiping corotating twin-screw extruder as a polymerization reactor for methacrylates. Polym. Eng. Sci. 1995, 35 (19), 1569-1579.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3519 Kumar, A.; Kuruville, S.; Raman, A. R.; Gupta, S. K. Simulation of reversible nylon-6,6 polymerization. Polymer 1981, 22, 387390. Kumar, A.; Agarwal, R. K.; Gupta, S. K. Simulation of reversible nylon-66 polymerization in homogeneous continuous-flow stirred tank reactors. J. Appl. Polym. Sci. 1982, 27, 1759-1769. Mack, W. A.; Herter, R. Extruder reactors for polymer production. Chem. Eng. Progress. 1976, Jan ,64-70. Maier, C.; Lambla, M. Esterification in reactive extrusion. Polym. Eng. Sci. 1995, 35 (15), 1197-1205. Meijer, H. E. H.; Elemans, P. H. M. Modeling of continuous mixers. Part I: The corotating twin-screw extruder. Polym. Eng. Sci. 1988, 28 (5), 275-290. Michaeli, W.; Berghaus, U.; Grefenstein, A. Twin-screw extruders for reactive extrusion. Polym. Eng. Sci. 1995, 35 (19), 14851504. Nascimento, C. A. O.; Giudici, R.; Scherbakoff, N. Modeling of industrial nylon-6,6 polycondensation. Part II: Neural networks and hybrid models. Submitted for publication in J. Appl. Polym. Sci. 1997. Ogata, N. Studies on polycondensation reactions of nylon salt. I. The equilibrium in the system of polyhexamethylene adipamide and water. Makromol. Chem. 1960, 42, 52-67. Ogata, N. Studies on polycondensation reactions of nylon salt. II. The rate of polycondensation reaction of nylon 66 salt in the presence of water. Makromol. Chem. 1961, 43, 117-131. Potente, H.; Lappe, H. Analysis of the residence time distribution in conventional plasticating extruders. Plast. Rubb. Proces. Appl. 1986, 6, 135-140. Potente, H.; Ansahl, J.; Klarholz, B. Design of tightly intermeshing corotating twin screw extruders. Int. Polym. Process. 1994, 9, 11-25.
Scherbakoff, N.; Shimizu, R. A.; Giudici, R. Residence time distribution of nylon-6,6 in a twin screw extruder (in Portuguese). Proceedings of the 3rd Brazilian Polymer Conference, Rio de Janeiro, Oct 30-Nov 2, 1995, Vol. 1, pp 14-17. Steppan, D. D.; Doherty, M. F.; Malone, M. F. A kinetic and equilibrium model for nylon-6,6 polymerization. J. Appl. Polym. Sci. 1987, 33, 2333-2344. Steppan, D. D.; Doherty, M. F.; Malone, M. F. Wiped film reactor model for nylon-6,6 polymerization. Ind. Eng. Chem. Res. 1990, 29, 2012. Steppan, D. D.; Doherty, M. F.; Malone, M. F. A simplified degradation model for nylon 6,6 polymerization. J. Appl. Polym. Sci. 1991, 42, 1009-1021 . Tadmor, Z.; Gogos, C. G. Principles of Polymer Processing; John Wiley & Sons: New York, 1979. Tzoganakis, C. Reactive extrusion of polymers, a review. Adv. Polym. Technol. 1989, 9, 321-330. Villadsen, J.; Michelsen, M. L. Solution of Differential Equation Models by Polynomial Approximation; Prentice-Hall: Englewood Cliffs, NJ, 1978. Xanthos, M., Ed. Reactive Extrusion: Principles and Practice; Hansen Publishers: Munich, 1992.
Received for review December 23, 1996 Revised manuscript received May 15, 1997 Accepted May 21, 1997X IE960814H
X Abstract published in Advance ACS Abstracts, August 1, 1997.
