Ind. Eng. Chem. Res. 1998, 37, 799-806
799
Hollow Shaft Reactor: A Useful Tool for Bulk Polymerizations at High Viscosities, Temperatures, and Polymerization Rates G. Weickert† Faculty of Chemical Technology, Industrial Processes and Products, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
The hollow shaft reactor (HSR) is an extruder-like reactor with internal recycling of the reaction medium. It has been designed for polymerizations at high viscosities up to a few hundred Pas. The HSR posesses the following properties: minimum dead volume, maximum recycle ratio, fast and predictable macro mixing, and both the recycle ratio and macromixing do not depend on the viscosity of the reaction mass in a wide range of viscosities. Because of the controllable shear rate, wall deposits on the surface can be avoided. The potential performance of this tool has been discussed by numerical simulations of the high-temperature bulk polymerization of methyl methacrylate with intermittent initiator injection. The high-conversion kinetic model, which has been used, takes into account the influence of monomer conversion and weight average molecular weight on the termination constant and the influence of monomer conversion on initiator efficiency and propagation constant. 1. Introduction. The Reactor The basic version of the hollow shaft reactor (HSR) is shown in Figure 1 (Thiele et al., 1979, 1986; Weickert et al., 1986a and 1986b). It consists mainly of a screwlike stirrer that rotates inside a cylindric reactor vessel. The reaction mass is forced to flow against the top lid of the reactor and circulates through the hollow shaft back to the bottom of the reactor. The screw scrapes the reactor wall. The clearance is optimum between 1 and 5 mm, depending on the size of the reactor. Thus, relatively high heat transfer rates can be achieved. The pumping capacity of the screw depends on the screwreactor configuration, which can be optimized. Compared with reactor concepts with external recirculation of highly viscous reaction masses, for example the wellknown loop-reactor technology (Lieberman 1996), the HSR shows a lower pressure drop (see eq 1) or higher recirculation rate (see eq 2) at a comparable pressure drop. The dead volume of the reactor is negligible, and wall deposits are avoided through the high shear rates. One of the most striking properties of the reactor is the flow behavior at increasing viscosity under bulk polymerization conditions: at constant stirrer speed, the recirculating mass flow remains nearly constant, while the horse power increases. This property holds over a wide range of viscosities because both the pressure drop in the hollow shaft and the “driving force” created by the rotating screw are proportional to and increasing with the reaction mass viscosity. At high viscosities (laminar flow), the pressure drop in the combined screwtube system can be expressed by
∆P ) C1
πDS2δ3 sin(φ) cos(φ) ηn
DTδ33 πDS2δ43 cos(φ) DT4 2 + sin (φ) + 128LT 12LS 12LSδ2
(1)
with C1 constant, DS screw diameter, DT diameter of † Fax: (+31) 53 489 4738. E-mail:
[email protected]. Internet: http://www.ct.utwente.nl.
Figure 1. Hollow shaft reactor.
the hollow shaft (tube diameter), LS screw length, LT tube length, n stirrer speed, δ2 land width, δ3 thread depth, δ4 clearance, φ screw angle, and η viscosity. Some fundamentals of the single-screw extruder modeling have been given by Mohr and Mallouk (1959). As one can see, the pressure drop is proportional to the viscosity and to the stirrer speed and, further, it depends strongly on geometric design parameters of the stirrer-reactor configuration. Its value is important not only for energy dissipation calculations but also to avoid local evaporization of the reaction mass, which may be the reason for reactor runaways. The pressure at any point of the reaction mass has to be higher than the vapor pressure, otherwise gas bubbles are formed and, because of the compressibility of the gas-liquid mixture, the recirculation stops. For that reason the reactor must be operated completely filled, and special pressure control equipment is required to avoid critical overpressures when using plunger pumps for feeding the reactor. The recirculation flow can be calculated using the
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800 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998
Figure 2. Recirculation time as function of the viscosity in the HSR.
following (single-screw extruder) equation:
Φ) C2
π2DS2δ3 sin(φ) cos(φ) n
2 3 32 DS LT 3 128 DS δ4 LT 2 1+ δ sin (φ) + π cos(φ) 3 D 4 LS 3 3 D 4 δ 2 LS T T (2)
with C2 constant (see also Mohr and Mallouk, 1959; Fenner, 1970, Torner, 1973). Obviously, there is no influence of the viscosity on the recirculating flow. This behavior has been investigated experimentally by conductivity measurements of methyl cellulose solutions. The conductivity measurements have been performed with NaCl injections into a 1.5-L batch HSR at constant stirrer speed of 100 rpm. The viscosity was varied between 0.1 and 90 Pas. After an injection has been carried out, one can observe a circulating concentration peak with, circulation-by-circulation, decreasing amplitude. Usually four peaks are visible, afterwards the reaction mass is (at least macro) mixed. The time between two successive peaks is called recirculation time. We found the recirculation time to be independend of the viscosity within the experimental error (Figure 2) measuring the electrical conductivity of methyl cellulose-water mixtures. Because of the segregation of fluid elements combined with a small conductivity cell used the experimental error is quite large, as shown in Figure 2. But, despite the wide range of viscosities, the mixing time shows no functional tendency and is considered to be constant. The Reynolds number can be calculated from:
Re )
FnDS2 η
(3)
with F density. The characteristic mixing time, t95, in batch mixing experiments is defined as the time when the concentration fluctuations remain below 5% of the final value, which corresponds to 95% complete mixing. The dimensionless mixing time can be calculated by multiplying the measured characteristic mixing time with the stirrer speed. Some experimental results are shown in Figure 3, based on the same experiments just described. Obviously there is nearly no impact of the viscosity on macromixing within a wide range. These experiments were carried out at constant stirrer speed (100 rpm) at changing viscosities up to 90 Pas. The characteristic
Figure 3. Dimensionless mixing time as function of the Reynolds number.
reactor dimensions are the following: volume ) 1.52 L; diameter of the hollow shaft ) 1.5 cm; reactor diameter ) 12 cm; screw angle ) 30°. The energy dissipated by the screw (horse power) can contribute to control the reactor in an integral way. The horse power at constant stirrer speed is a very complex function of the polymer concentration, the reaction temperature, and the structure of the polymer produced, and it indicates sensitively a change of these parameters during the polymerization. Within a certain range of operation conditions, the horse power can be expressed as function of the viscosity, for example, by
Q˙ stirr ) C3ηn2DS2LS
(4)
This relation becomes even more complex when the wall temperature is significantly different from the bulk temperature with the resulting nonisothermal wall layers. For a small distance between screw and reactor wall (clearance), much energy is dissipated near the reactor wall, which is to be removed additionally to the reaction heat, whereas for a high pumping capacity of the screw, a small value of δ4 is required. Therefore, an optimum design is to be found for a given problem. For illustration, eq 5 represents a possibility to describe the viscosity of the reaction mass at a given position in a polymerization reactor as function of the polymer concentration, the temperature, the molecular weight, and the shear rate:
( ) ( [ ] Mw M* w
A
YPB10C(T-T*)/(D+T-T*)
η ) η1 A Mw 1 + η1γ˘ YP 10C(T-T*)/(D+T-T*) M* w
)
E
(5)
with A-E constants to be determined experimentally, Mw is the weight average molecular weight, T is the temperature, YP is the polymer mass fraction, γ˘ is the shear rate, * relates to reference conditions, and η1 is the zero viscosity under reference conditions. The reference viscosity should be measured using a polymer with a representative and similar polymer structure compared with the polymer produced. Due to the complex behavior of polymers, it is not easy to find an adequate model (or better, a model that can be used for the polymerization reactor design) for the viscosity of the polymerizing reaction mass, which holds in a wide range of polymer concentrations (see Ferry, 1980). There is a critical point, determined by the polymer
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 801
concentration, the molecular weight, and the temperature, where the polymers interact intensively by forming entanglements between the polymer chains. Above this critical point the viscosity increases much faster with increasing polymer concentration than before. Usually, two ranges should be distinguished for modeling: the range below the entanglement point of polymer chains and the range above it. The latter one is more important for industrial reactor design. The HSR was tested first by the PRE (Polymerization Reaction Engineering) group of Thiele (see Thiele, 1986; Weickert, 1983), above all for styrene polymers, using small scale reactors of a few liters reactor volume. Later, the HSR has been successfully scaled-up to an annual production of 1500 ton per annum of styreneacrylonitrile (SAN) copolymer at the Buna-Werke, Germany. This development was stopped in 1990 because of the “break-down” of the East German chemical industry. However, the reactor principle is believed to have a high potential for industrial applications. Consequently the development of the reactor has been continued in the group Industrial Processes and Products of K. R Westerterp at the Twente University, The Netherlands.
A realistic kinetic model that is valid at high monomer conversions is a fundamental prerequisite for numerical reactor operation studies. A lot of proposals have been made in the public literature, but the selection of such a model remains a time-consuming step in engineering; a short overview can be found in Tefera et al. (1997) and Panke (1995). The following model is taken from Weickert (1997) and seems to be a good compromise between the accuracy (of conversion and molecular weight calculations) and the number of additional model parameters to be determined experimentally. The symbols used have the following meaning: M, monomer; P, polymer; and I1, initiator 1. Reaction Mechanism. The reaction mechanism used to describe the radical polymerizations of methyl methacrylate (MMA) and styrene (ST) is given below. The original model (Weickert, 1997) comprises additionally the transfer reactions to chain transfer agents and solvents, radical initiation using two initiator types, the thermal start, and the termination by an inhibitor. All of these reactions are neglected in the following study because they do not apply for the bulk polymerization of MMA as practiced herein. initiation:
R1 + M f P1
r1 ) ki,1I1
r4 ) kdPj+1
Kinetic Model. In the equations just presented, the symbols of the components used represent the concentrations of the species. The final resulting kinetic model consists of eqs 6-16. initiator 1:
RI1 ) -ki,1I1
(6)
RM ) -Pt(kpM - kd)
(7)
monomer:
instantaneous molecular weight distribution:
q2 (X j + qXCj2) exp(-jq) 1 + XC TD
(8)
instantaneous number and weight average polymerization degree:
Pdn ) Pdw )
(
1 + Xc q
Xc 2 1+ q 1 + Xc
)
(9)
dispersion index of the instantaneous molecular weight distribution:
Dd )
(
)
Xc 2 1+ 1 + Xc 1 + Xc
(10)
The terms required for the calculation of this kinetic model are defined by eqs 11-16. termination probability:
q)
kmM + ktPt kpM - kd + kmM + ktPt
(11)
transfer and disproportionation fraction of the instantaneous polymer:
kmM + ktdPt 1 kmM + ktdPt + ktcPt 2
(12)
XC ) 1 - XTD
(13)
overall initiation rate:
transfer to the monomer:
Pj + M f Mj + P1
r7 ) ktdPjPk
combination fraction of the instantaneous polymer:
depolymerization:
Pj+1 f Pj + M
Pj + Pk f Mj + Mk
XTD ) r3 ) kpMPj
r6 ) ktcPjPk
disproportionation:
r2 ) 2fi,1ki,1I1
propagation:
Pj + M f Pj+1
Pj + Pk f Mj+k
ydj )
2. Kinetic Model
I1 f 2R1
recombination:
r5 ) kmMPj
rg ) 2f1ki,1I1
(14)
802 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998
total concentration of polymer radicals: ∞
Pt )
Pi ) ∑ i)1
x
rg
(15)
kt
overall termination constant:
kt ) ktc + ktd
(16)
For example, the monomer consumption rate can be determined for given kinetic constants and given concentrations of initiator 1 and monomer after the overall initiation rate and the total concentration of polymer radicals have been calculated. The calculation of the instantaneous molecular weight distribution and its polymerizations degrees demands the probabilities for termination, disproportionation and combination. For a realistic description of all reaction rates, some corrections for diffusion control of the kinetic constants are to be made; that is, a so-called high conversion model must be included. The high conversion model from Panke (1995), modified by Weickert (1997; see also Tefera, 1997) is used in the form described by eqs 1721. overall termination constant:
(
1
kt ) kt,0
g3Mg4 w
()
g1 exp Bk
+ CkpcM
)
(17)
(18)
f1,0 + (1 - f1,0) exp(g2Xk)
( [ ] [ ])
(19)
(22)
The mass and energy balances of the nonsteady-state CSTR can be formulated as shown in eqs 23-26. mass fraction of the monomer:
dYM b z ) (YM - YM) - RP dt F
(23)
dt
b ) (YzI1 - YI1) - ki1YI1 F
(
(24)
)
dPn Pn b z Pzw - Pn Pdn - Pn ) Y + RP dt YP F P Pz Pd n
n
(25)
weight average polymerization degree:
dPw 1 b z z ) Y (P - Pw) + RP(Pdw - Pw) dt YP F P w
(
with
1 1 Bk B#
(20)
k
The “mobility” Bk is defined as free volume, but instead of 0.025, which is often used for the critical free volume, a value of 0.0125 has been found to give a better fit of experimental data in the high conversion range. mobility:
Bk ) 0.0125 +
m ˘z VR
number average polymerization degree:
kp,0 g5 g5 1 + g6 exp - exp # Bk Bk
Xk )
b)
dYI1
f1,0
propagation constant:
kp )
continuous stirred tank (CSTR) is given here and corresponds well to the HSR and to the simulations described next. With the kinetic model and the loading b, then
mass fraction of initiator 1:
initiator efficiency:
f1 )
Figure 4. Comparison between model and experiment in the AIBN-initiated bulk polymerization of MMA.
∑k νk∆k(T - Tg,k)
(21) B#k
The “mobility at initial kinetic conditions” corresponds to the kinetic constants at zero conversion (“initial kinetics”). 3. Reactor Model The kinetic model just derived is part of the reactor model and can be used to simulate ideally or nonideally mixed reactors or isothermal or nonisothermal reactors of different types. The reactor model for a well-mixed
)
(26)
The concentrations of the components are
F ck ) Yk Mk
(27)
The polymerization rate in terms of the changing polymer mass fraction per unit of time is defined as follows:
RP ) -RM
MM MM ) kp(M - M*)Pt F F
(28)
with M* as equilibrium concentration of the monomer. The energy balance can be expressed as follows:
dT 1 [H R - bcp(T - Tz) - KDa(T - TK)] (29) ) dt Fcp R M More details and a complete set of kinetic constants and all physical properties required are given by Weickert (1997). The model constants have been estimated using
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 803
Figure 5. Isothermal starting up of a CSTR for MMA bulk polymerization at low temperatures.
experimental data of Marten and Hamielec (1979) in the temperature range 50-90 °C. A comparison between some preliminary (batch reactor) model calculations and experimental data is shown in Figure 4. The “initial kinetics” without diffusioncontrol corrections at 50 °C, clearly indicating the importance of the high-conversion modeling, are also shown in Figure 4. The following example has been selected to demonstrate the potential performance of the HSR using the simplified model just described. 4. Application: The Continuous Polymerization of MMA at High Temperatures It has been shown both theoretically and experimentally that the high-temperature, bulk polymerization of MMA offers some advantages over low temperature polymerization. Because of the decreasing importance of diffusion control at high temperatures, the typical, S-shaped conversion-time curve observed in batch polymerizations of MMA becomes smoother with increasing temperature (Hoppe and Renken, 1997; Weickert, 1997). Simultaneously, the average polymerization degree and the dispersion index of the molecular weight distribution (MWD) are decreasing. Above a certain temperature, the polymerization can be executed without using chain transfer agents to control the molecular weight of the polymer produced. At the same time, the polymerization rate can be controlled by using lower initiator concentrations. Furthermore, the viscosity is much lower, which results in a better heat transfer and better mixing, both of which are of substantial interest for reactor control and operation. Is the HSR a useful tool to carry out continuous bulk polymerizations of MMA? In Figure 5, an example is given to demonstrate the difficulties of a continuous MMA polymerization process. At the beginning, the reactor is assumed to be filled with pure monomer. At zero time, the reactor is fed with a constant flow of monomer containing AIBN as initiator, and the average residence time is 1 h. Following an often used engineering rule of thumb, the reactor should be in steady state after ∼5 h. Actually, this is the case at temperatures 75 h, first slowly until nearly 30% conversion, then explosion-like. One can refer to this behavior as an “isothermal explosion”, which is caused mainly by the diffusion control of the
Figure 6. MMA bulk polymerization: Monomer conversion
