Bulk Polymerization in Tubular Reactors
`I. Experimental Observations on Fouling
`
`M. F. CUNNINGHAM and K. F. O'DRISCOLL
`
`Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3Gl
`
`and
`
`H. K. MAHABADI
`
`Xerox Research Centre of Canada, Mississauga, Ontario LSK 2Ll
`
`Conditions under which fouling (polymer deposition) occurs in tubular polymerization reactors were studied using
`bulk methyl methacrylate polymerizations at 70°C. It was demonstrated that reactor orientation and flow direction have
`a significant effect on fouling behaviour. Natural convection becomes increasingly important as concentration gradients
`in the reactor increase. Using the optimum reactor configuration determined in the first part of the study, a feasible
`operating region for the reactor was established, thereby permitting selection of conditions which will prevent reactor
`fouling.
`
`On a etudie Jes conditions d'encrassement (deposition de polymeres) dans des reacteurs de polymerisation tubulaires
`en utilisant des polymerisations en masse de methacrylate de methyl a 70°C. On a demontre que !'orientation des reac(cid:173)
`teurs et la direction de l 'ecoulement ont un effet significatif sur I' encrassement. La convection naturelle prend une impor(cid:173)
`tance croissante avec l 'augmentation des gradients de concentration dans le reacteur. En utilisant la configuration optimum
`du reacteur determinee dans la premiere partie de l 'etude, on a etabli une region de fonctionnement possible, ce qui
`a permis la selection des conditions qui empecheront l'encrassement des reacteurs.
`
`Keywords: polymerization, tubular reactor, fouling, reactor orientation.
`
`T ubular reactors offer a potentially simple and inexpen(cid:173)
`
`sive route for the polymerization of many monomers.
`However because of practical difficulties associated with their
`operation, they have not found widespread commercial appli(cid:173)
`cation. Their only current large scale use is in the produc(cid:173)
`tion of low density polyethylene (Rudin, 1982). Operating
`difficulties arise primarily from
`two sources:
`( 1)
`hydrodynamic instability, due to elongation of the velocity
`profile, and (2) thermal runaway, caused by inadequate
`removal of the heat of polymerization (Nauman, 1987). Elon(cid:173)
`gation of the velocity profile results from the rapidly
`increasing viscosity of the reaction mixture. In laminar flow
`radial concentration gradients develop since material near
`the tube core moves faster than material near the walls and
`hence has a smaller residence time. Because viscosity
`increases rapidly with polymer concentration, the material
`near the tube walls is slowed even further. The slow velocity
`near the walls forces material to flow radially inward and
`accelerate, resulting in centerline velocities that can be
`several times the average velocity (Hamer and Ray, 1984).
`At longer axial distances, the material near the centerline
`also polymerizes, thereby reducing the concentration gra(cid:173)
`dient and resulting in a gradual return to a parabolic velocity
`profile. Flow instability can occur if the velocity profile elon(cid:173)
`gation is sufficiently severe and results in the reactor
`becoming inoperable due to either channelling or plugging.
`As the tube diameter increases, convective diffusion of heat
`becomes increasingly difficult and radial temperature gra(cid:173)
`dients become increasingly significant. If these gradients
`become large enough,
`thermal instability will occur.
`Increased mass and thermal diffusion in smaller diameter
`tubes act to reduce gradients and facilitate trouble-free
`operation.
`The design and analysis of tubular polymerization reactors
`is complicated by the strong interaction between the reaction
`
`kinetics and the fluid dynamics of the system. The governing
`equations are explicitly linked through the viscosity equa(cid:173)
`tion because the termination reactions in free radical poly(cid:173)
`merization are diffusion controlled. The polymerization
`reaction results in rapid changes in the composition and hence
`physical properties of the reaction mixture. Viscosity, which
`itself is a strong function of conversion, molecular weight
`(i.e., molar mass) and temperature, can increase by several
`orders of magnitude thus leading to changes in such system
`properties as heat capacity, diffusivity, density, thermal con(cid:173)
`ductivity and even heat transfer coefficients. All of these can
`have a profound effect on the velocity field. In turn the
`velocity field, by creating a variety of residence times, will
`have a significant impact on the polymerization kinetics. A
`complex feedback situation thus exists, resulting in a non(cid:173)
`linear and often unpredictable response to disturbances.
`Although many modelling studies have examined the
`behaviour of tubular polymerization reactors, relatively few
`experimental studies have been conducted. (Hamer, 1983,
`has reviewed these investigations.) Those experimental
`studies that have been reported have usually focussed on
`reactors operating under steady-state (fouling free) condi(cid:173)
`tions. Despite the fact that the occurrence of fouling (or
`polymer deposition) is the primary reason tubular polymeri(cid:173)
`zation reactors have not been widely used, there have not
`been any studies reported that have examined the subject of
`fouling itself. For this work, fouling will be defined as the
`development, in the tubular reactor, of polymeric material
`which cannot be removed by ordinary flushing procedures.
`The material is probably not chemically bound to the tube
`wall. Given that operation of a fouled tubular polymeriza(cid:173)
`tion reactor will be subject to serious difficulties, it would
`be extremely valuable to possess a physical understanding
`of these problems. Experiments have therefore been initiated
`to study the fouling behaviour of free radical bulk methyl
`
`630
`
`THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 69, JUNE, 1991
`
`SNF Exhibit 1024, Page 1 of 9
`
`

`
`methacrylate polymerizations in a tubular reactor. Because
`of their strong "gel-effect", methyl methacrylate polymeri(cid:173)
`zations provide a good model for the coupling between fluid
`dynamics and reaction kinetics. Not all of the fouling
`problems experienced in bulk methyl methacrylate polymeri(cid:173)
`zations may appear in milder cases, such as solution poly(cid:173)
`merizations or polymerizations of monomers with weak
`gel-effects (e.g., styrene), but these results are nonetheless
`important for illustrating the operating characteristics with
`which a possible user of tubular polymerization reactors must
`be familiar.
`
`Experimental
`
`A novel tubular reactor system utilizing glass tubes as dis(cid:173)
`posable reactors was designed to permit the study of fouling
`behaviour. The reactors consist of thin-walled glass tubing
`with an inner diameter of 0.80 cm and a length of 180 cm.
`They are tapered to a diameter of 0.40 cm over a span of
`approximately 5 cm at both ends to minimize disturbances
`in the flow pattern and eliminate stagnant regions. Temper(cid:173)
`ature control is provided by encasing the reactors in an insu(cid:173)
`lated jacket through which water from a constant temperature
`bath is pumped. A thermocouple is located at the reactor
`outlet. Because of the potential effect of radial temperature
`gradients on the fouling behaviour, a small diameter was
`deliberately chosen in order to ensure conditions remained
`as close to isothermal as possible. Calculations showed that
`the maximum predicted radial temperature gradient was
`approximately 2 °C. Furthermore the measured effluent tem(cid:173)
`perature was always within 1 °C of the bath temperature.
`Flowrate is controlled by a peristaltic pump. Samples can
`be taken at the outlet through a sampling valve. Residence
`times are typically on the order of 10-30 minutes. Prior to
`use, the methyl methacrylate is washed with sodium
`hydroxide and deionized water, dried over calcium chloride
`and distilled under nitrogen. 2,2-azobisisobutyronitrile
`(AIBN) is recrystallized from methanol.
`
`PROCEDURE
`
`AIBN is dissolved in methyl methacrylate and the cooled
`solution fed into the reactor over four residence times, with
`samples being collected every one residence time. Samples
`are quenched with diphenylpicrylhydrazyl and then precipi(cid:173)
`tated with methanol. Conversions are determined gravimetri(cid:173)
`cally. Following the run, the reactor is flushed with 50 mL
`toluene (to remove residual monomer) and then 50 mL
`ethanol. The ethanol is used to form a "skin" of precipi(cid:173)
`tated polymer on the polymer remaining in the reactor,
`thereby preserving its shape and appearance. The samples
`were often glassy at the wall tapering radially to being
`extremely viscous. The viscous surface could not be washed
`away even by flushing with large volumes of toluene, which
`contrasts strongly with the relatively less viscous character
`of the reactor effluent. After the reactor is flushed, it is
`removed from the jacket, weighed and then cut into sections.
`Dimensions and descriptions of the deposited polymer were
`carefully recorded. Samples of the fouling polymer were also
`collected at various axial and radial positions. Axial distance
`between samples was usually 30 cm, while radial position
`was varied approximately 0.2 cm between samples. A sur(cid:173)
`gical blade was used to cut thin sections ( < 0.5 mm) of
`polymer (cuts were made in the axial direction). Molecular
`weight distributions of the samples were determined using
`
`TABLE 1
`Summary of Reactor Configurations and Critical Conversions
`
`Configuration Description
`
`Critical Conversion
`
`1
`2
`3
`4
`5
`
`Horizontal
`Vertical, feed up
`Vertical, feed down
`45 degrees, feed up
`45 degrees, feed down
`
`0.04
`O.Q7
`0.12
`0.04
`0.10
`
`gel permeation chromatography. A Waters Associates GPC
`was used with tetrahydrofuran as the mobile phase. Six
`Waters Ultrastyragel columns (pore sizes 106, 105, 104,
`103
`, 500 and 100 Angstroms) provided separation.
`
`Effect of reactor orientation
`
`In all previously reported studies of tubular polymeriza(cid:173)
`tion reactors, the reactors have been oriented either horizon(cid:173)
`tally or vertically with the feed flowing upward. The choice
`of orientation seems to have been dictated primarily by
`experimental convenience. Furthermore, when the fluid
`dynamics of these reactors were modelled, the two configu(cid:173)
`rations were treated as being mathematically equivalent (i.e.
`gravitational terms were not included in the model equations).
`Prior to this study, there has been no recognition of the
`opportunity to improve the performance of a tubular poly(cid:173)
`merization reactor by altering the reactor orientation and the
`flow direction. In this work a series of experiments was con(cid:173)
`ducted to investigate these possibilities. Significant qualita(cid:173)
`tive and quantitative differences were observed when the
`spatial orientation of the reactor and the flow direction were
`varied. Five reactor configurations were studied: (1)
`horizontal; (2) reactor inclined at 45 degrees, feed flowing
`upward; (3) vertical, feed flowing upward; (4) reactor
`inclined at 45 degrees, feed flowing downward, and (5) ver(cid:173)
`tical, feed flowing downward. These configurations are sum(cid:173)
`marized in Table 1. The bath temperature was 70°C and the
`initiator concentration was 0.05 kmol/m 3 AIBN for all
`runs. "Critical conversion" is defined as the minimum outlet
`conversion for which reactor fouling (polymer deposition)
`was observed. At conversions below the critical value,
`flushing the reactor following the run will remove all viscous
`polymer from the reactor. However above the critical con(cid:173)
`version where fouling occurs, deposits of either viscous or
`glassy polymer remain in the reactor following the flushing
`procedure.
`
`CONFIGURATION 1: HORIZONTAL
`
`With horizontal operation, the critical conversion is
`approximately 4 % . The fouling begins at the reactor outlet
`and grows towards the inlet. The cross-sectional profile of
`the fouling, shown in Figure 1, has a nearly flat surface.
`Figure l(b) is a photograph of deposited polymer from the
`reactor outlet from a run in which the conversion was 6 % .
`Deposited polymer, which is located at the bottom of the
`reactor, is thickest at the outlet and gradually tapers to a thin
`edge closer to the inlet.
`
`CONFIGURATION 2: 45 DEGREES, FEED FLOWING UPWARD
`
`The critical conversion is again about 4 % , but the qualita(cid:173)
`tive nature of the fouling differs significantly from configu(cid:173)
`ration 1 (see Figure 2). The polymer deposition begins at
`
`THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 69, JUNE, 1991
`
`631
`
`SNF Exhibit 1024, Page 2 of 9
`
`

`
`-
`
`Figure l(a)
`
`0
`
`t
`
`Figure I -
`(a) Horizontal reactor configuration. Arrows indicate
`direction of flow. Hatched area represents fouling. Left side of figure
`is a side view; right side is a cross sectional view. (b) Photograph
`of fouling from a horizontal run.
`
`t
`
`Figure 3(a)
`
`/
`
`0 -
`
`/
`
`Figure 2 - Reactor inclined at 45 degree angle, feed flowi ng
`upward .
`
`the reactor inlet and grows upward. The cross-sectional pro(cid:173)
`file shows mo re curvature than the horizontal case.
`
`CONFIGU RATION 3: V ERTICAL, FEED FLOWING UPWARD
`
`This configuration yields a higher critical conversion (7 % )
`than the previous cases and exhibits similar fouling behaviour
`to configuration 2 (see F igure 3a). The fouling again begins
`growing at the reactor inlet (where it is thickest) and tapers
`to a fine edge near the outlet. Interestingly, the fouling also
`remains on one side of the reactor and exhibits a bifurcation(cid:173)
`type behaviour at the growing edge in which two lo ng
`"fingers" of deposited polymer extend upwards ahead of
`the main body of polymer (Figure 3b).
`
`CONFIGURATION 4: 45 DEGREES, FEED FLOWING DOWNWARD
`
`A further improvement to 10% in the critical conversion
`is achieved when the reacto r is shifted to 45 degrees with
`the feed flowing downward. The fouling, which forms a
`nearly complete annulus, begins growing at the reactor outlet
`and propagates up towards the inlet (Figure 4).
`
`(a) Vertical reactor, feed flowing upward. (b) Photo(cid:173)
`Figure 3 -
`graph of fouling from a vertical, feed upward run showing
`bifurcation-type behaviour at the growing end .
`
`0 -
`
`Figure 4 - Reactor inclined at 45 degree angle, feed flowing
`downward.
`
`632
`
`THE CANADIAN JOURNAL OF CHEMICAL ENGINEERI NG, VOLUME 69, JUNE, 199 1
`
`SNF Exhibit 1024, Page 3 of 9
`
`

`
`l
`
`l
`
`Figure 5(a)
`
`Figure 5 -
`(a) Vertical reactor, feed flowing downward. (b) Pho(cid:173)
`tograph of fouling from a vertical, feed downward run.
`
`CONFIGURATION 5: VERTICAL, FEED FLOWING DOWNWARD
`
`An annulus of deposited polymer results when the reactor
`is operated in this configuration (Figure 5). Growth begins
`at the reactor outlet. The critical conversion (12 % ) is superior
`to any of the other configurations. The cross section shown
`in Figure 5(b) was taken from the reactor outlet from a run
`in which the conversion was 17 % . A summary of configu(cid:173)
`rations and critical conversions is given in Table I.
`If polymer deposition occurred during operation, the effec(cid:173)
`tive reactor volume decreased, as did the observed conver(cid:173)
`sion. If no fouling occurs, a steady state conversion is reached
`in 1-2 residence times . Figure 6 shows conversion versus
`time curves for four vertical feed down runs. Polymeriza(cid:173)
`tion conditions were identical for all runs (i.e. [AIBN] =
`0.05 kmol/m3, T = 70°C); only the flowrate was varied.
`In Run 29 extremely mild fouling occurred, while for the
`remaining runs the severity of fouling increased in the order
`
`0.20 . . . . - - - - - - - - - - - - - - - - - - - ,
`
`0.15
`
`z
`0
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`o R29
`o R38
`O R39
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`6.00
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`2.00
`3.00
`4.00
`5.00
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`HOLDING TIMES
`
`Figure 6 - Conversion versus dimensionless time (operating
`time/mean residence time) for four feed downward runs of varying
`flowrate in vertical reactor. Flowrates for R29, R39, R38 and R28
`were 7.93, 6.52.i 5.91 and 4.81 mL/min, respectively. [AIBN]
`= 0.05 kmol/m ; T = 70°C.
`
`Runs 39, 38, 28. For Run 28 the reactor completely plugged
`after operating for only three residence times. It is apparent
`from Figure 6 that the maximum in the conversion-time
`curves is observed at earlier times when fouling is more
`severe. This corresponds to a faster decrease in effective
`reactor volume as a result of polymer deposition. The
`observed decrease in reactor volume with operating time
`could be utilized as an indicator that reactor fouling is occur(cid:173)
`ring. The use of on-line sensors capable of monitoring con(cid:173)
`version (e.g., density meters) would therefore enable early
`detection of unstable operation.
`The magnitude of the qualitative and quantitative
`behavioural differences exhibited by the various reactor con(cid:173)
`figurations emphasizes the potential importance of gravita(cid:173)
`tional forces in determining the performance of tubular
`polymerization reactors. In all cases, polymer begins
`accumulating at the lowest elevation point in the reactor,
`regardless of the flow direction. Prior to Stevens' (1988)
`modelling study it had always been assumed that, regard(cid:173)
`less of reactor orientation, polymer accumulated in the form
`of an annulus. (Stevens' model predicted polymer deposi(cid:173)
`tion on the bottom of a horizontal reactor) . The appearance
`of the fouling for configurations 2 (reactor inclined at a 45
`degree angle, feed upward) and 3 (vertical reactor, feed
`upward) is particularly intriguing. In both situations fouling
`builds up from the reactor inlet suggesting that high conver(cid:173)
`sion material must be flowing down the tube against the feed
`direction. This also indicates that fouled polymer probably
`does not adhere to the reactor walls used in this study. In
`configuration 3, an annular layer of polymer is expected
`because of the angular symmetry of the gravitational field.
`However, it seems that flow instabilities result in the polymer
`depositing on one side of the reactor. The downward flow
`of high conversion material could be the cause of this insta(cid:173)
`bility. In configuration 5 (vertical reactor, feed downward),
`this partial flow reversal does not occur and the expected
`annular ring of polymer is formed.
`The importance of gravitational effects can be attributed
`to the increase in density that occurs during polymerization.
`
`THE CANADIAN JOURNAL OF CHEMICAL ENGINEERJNG, VOLUM E 69, JUNE, 1991
`
`633
`
`SNF Exhibit 1024, Page 4 of 9
`
`

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`~ en zo w I{)
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`0.2
`0.4
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`CONVERSION
`
`The effects of temperature gradients are likely minor in com(cid:173)
`parison. (For methyl niethacrylate the volume shrinkage upon
`complete conversion is approximately 24 % , while a 20 ° C
`temperature gradient would result in only a 2.5% increase
`in volume). The rapid increase in conversion accompanying
`the gel-effect in methyl methacrylate polymerizations is
`capable of creating significant density gradients within the
`reactor. Secondary flows arising from these density gradients
`could generate the type of behaviour observed in this study.
`Further experiments are underway to determine if a reduc(cid:173)
`tion in the magnitude of the gel-effect has an effect on the
`fouling pattern. Reducing the density gradients (e.g., by using
`a solvent) would also be expected to reduce the severity of
`the problem. However use of a solvent is not always desirable
`as it could necessitate additional downstream operations.
`The nonlinear kinetics typical of bulk methyl methacry(cid:173)
`late polymerizations also plays an important role in estab(cid:173)
`lishing secondary flow patterns. Rapid increases in density
`during the gel-effect can create sizable density gradients in
`the reactor. Consider the rate of density increase with respect
`to time as shown below.
`
`dp I dt = (dp I dx) (dx I dt) .................... (1)
`
`where
`P = Pm I (1 + € x) . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
`
`and €
`is the volume shrinkage factor. Hence
`dp/dx = - f Pmf(l + €X) 2 .•................ (3)
`
`Thus if dx I dt is known as a function of conversion, a plot
`of dp I dt versus x can be constructed. It is useful to normalize
`dp I dt in order to facilitate comparison of polymerizations
`carried out under different conditions. Therefore define
`
`Normalized rate of density increase
`= (dp/dt)J(dp/dt)0 ....................... (4)
`
`In Figure 7, the data of Balke and Hamielec (1973) were
`used to illustrate the normalized rates of density increase for
`three cases: (1) high molecular weight polymer produced (0.3
`wt% AIBN, 50°C, Mn ""' 5 X 105 Da); (2) low molecular
`weight polymer produced (0.5 wt% AIBN, 90°C, Mn ""' 5
`x 104 Da), and (3) no gel-effect (ideal kinetics assumed).
`It is apparent that the stronger gel-effect observed when
`higher molecular weight polymer is produced leads to higher
`rates of density increase and that these higher rates occur
`earlier in the polymerization. These observations can be
`explained by considering the influence of molecular weight
`on the gel-effect. As molecular weight increases the gel-effect
`begins earlier in the polymerization and is more pronounced.
`The importance of gravitational effects would thus seem to
`be strongly dependent on the severity of auto-acceleration.
`A reduction in the magnitude of the gel-effect would be
`expected to lessen secondary flows in the reactor and reduce
`the severity of fouling.
`The importance of natural convection (gravitational) forces
`can be represented by the Grashof number (Gr) which is
`traditionally written;
`
`Gr= g (3 (Tw - Tc)D 3 /v 2
`
`...••••.....•••...• (5)
`
`In this form density differences are assumed to arise from
`temperature gradients. In a polymerizing system density
`
`Figure 7 - Normalized rate of density increase for different poly(cid:173)
`merization conditions. The solid line is for high molecular weight
`(0.3 wt% AIBN, 50°C, Mn "" 5 X 105 Da), the dashed line is
`for low molecular weight (0.5 wt% AIBN, 90°C, Mn == 5 x
`104 Da) and the dotted line is for ideal kinetics (i.e., without gel(cid:173)
`effect). Kinetic data is taken from Balke and Hamielec (1973).
`
`gradients will also arise due to the existence of concentra(cid:173)
`tion gradients. Density variations due to temperature differ(cid:173)
`ences can be expressed as;
`
`p(T) = Po (1 -
`
`(3 AT) ...................... (6)
`
`while variations resulting from gradients in monomer con(cid:173)
`version can be written;
`
`p (x) = Po (1 -
`
`e Ax) ....................... (7)
`
`Accounting for density variations due to both temperature
`and conversion yields:
`
`p (x, I) = Po (1 -
`
`(3 AT) (1 - E Ax) .......... (8)
`
`It can be shown that in the bulk polymerization of methyl
`methacrylate a 10°C decrease in temperature causes the same
`density increase as an increase in conversion of0.05. Because
`large concentration gradients are expected in a tubular
`reactor, they will likely dominate gravitational forces. A
`more general form of the Grashof number which accounts
`for changes in density arising from both possible sources is;
`Gr' = g (pw - Pc)D 3 I Pc v2
`
`...•.............. (9)
`
`If it can be assumed that temperature gradients will make
`a negligible contribution, then the following form can be
`used.
`
`Gr' = g ( -f) (xw - Xc)D 3 I v2
`
`, where € < 0 .. (10)
`
`The ratio Gr/Re 2 represents the ratio of gravitational to
`inertial forces. The combined effects of free and forced con(cid:173)
`vection must be accounted for when Gr!Re 2
`""' 1. Signifi(cid:173)
`cantly reducing the effect of gravitational forces relative to
`inertial forces necessitates a long tube of very small diameter.
`This is difficult with a straight tube but can be achieved using
`a helical configuration. Under typical reaction conditions the
`estimated value of the ratio Gr/Re 2 is approximately 103
`
`634
`
`THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 69, JUNE, 1991
`
`SNF Exhibit 1024, Page 5 of 9
`
`

`
`0.40 ~--------------------,
`
`0.30
`
`z
`0
`Vi
`0::
`~ 0.20
`z
`0
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`
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`FOULING
`
`NON-FOULING
`
`0
`
`100
`1~
`~
`NUMBER AVERAGE MOLECULAR WEIGHT (Da x 10-3
`)
`
`Figure 8 - Feasible operating region for vertical reactor with
`downward feed. Solid line indicates onset of fouling; dotted line
`represents severe fouling.
`
`for a radial concentration difference of only 4 % . (The inlet
`Reynolds numbers used in this study ranged from 40 to 110,
`while the outlet Reynolds number is less than 1). The mag(cid:173)
`nitude of this value illustrates the potential importance of the
`density gradient in determining flow patterns in the reactor.
`In any tubular polymerization reactor the value of Gr/ Re2
`increases as the radial concentration gradient increases. Con(cid:173)
`sequently it is probable that at some point in the reactor,
`gravitational forces will become sufficiently large that they
`can no longer be considered negligible. A simple method
`of minimizing or eliminating detrimental secondary flow pat(cid:173)
`terns is to ensure that gravitational forces act in the same
`direction as axial convection. Operating a tubular reactor ver(cid:173)
`tically with the feed flowing downward achieves this and,
`as the experimental results confirm, yields the highest crit(cid:173)
`ical conversion.
`This study also has important implications concerning the
`mathematical modelling of tubular polymerization reactors.
`With the exception of Stevens' work (1988), investigators
`in this area have not included gravitational forces in the
`problem formulation. Thus vertical and horizontal reactors
`have been modelled using
`the same equations. The
`experimental results collected in this study clearly indicate
`that the assumption of negligible gravitational forces is not
`valid under all conditions. Modelling efforts are in progress
`to investigate this effect further.
`
`Effect of molecular weight on critical conversion
`
`The rapid formation of glassy polymer in a tubular reactor
`operating in the fouling regime underscores the importance
`of knowing the operating conditions which result in polymer
`deposition. Once polymer has been formed in a reactor it
`will be difficult if not impossible to clean the reactor, and
`in any event there will be lost production costs while the
`reactor is not operating. In view of these concerns it was
`decided to attempt to establish the boundaries within which
`the reactor could be safely operated. Therefore using aver(cid:173)
`tical reactor with downward feed, the effect of molecular
`weight on critical conversion was investigated. Molecular
`weight was controlled using the catalytic chain transfer agent
`
`cobaloxime boron fluoride (Sanayeii and O'Driscoll, 1989).
`Figure 8 shows a map of the feasible operating regions for
`this reactor as a function of outlet conversion and molecular
`weight. The solid line in Figure 8 represents the onset of
`fouling, while the dotted line indicates where fouling is severe
`(greater than 75 % of the reactor cross-section is fouled after
`four residence times). The limits for onset of fouling and
`severe fouling were determined by conducting a series of
`runs at slightly different flowrates for each different
`molecular weight. The variation in the flowrates was small
`enough that the estimated values are accurate to within 1 %
`conversion.
`It is apparent that as the molecular weight decreases it is
`possible to operate the reactor at higher conversions without
`experiencing fouling. The proximity of the lines representing
`the onset of fouling and severe fouling also suggests a high
`degree of parametric sensitivity. The reactor operates without
`fouling up to a critical conversion, after which even small
`increases in conversion lead to a rapid acceleration of the
`fouling behaviour. The sensitivity seems to be more acute
`at higher molecular weights, which is not unexpected given
`the strong gel-effect of methyl methacrylate.
`Runs were conducted for periods of 10 and 20 residence
`times at conversions slightly below (1-2 % ) the critical values
`shown in Figure 8. In both cases the reactor was free of
`fouling following the flushing procedure. The absence of
`fouling over such an operating period confirms the validity
`of the criterion used to denote non-fouling behaviour (i.e.
`no fouling over an operating period of four residence times).
`Additional experiments conducted at different polymeriza(cid:173)
`tion rates confirmed that critical conversion is not a func(cid:173)
`tion of the reaction rate. It therefore seems reasonable to
`conclude that fouling appears to follow an "on-off" type of
`behaviour. For purposes of commercially operating a tubular
`polymerization reactor it is extremely important to know
`where this behavioural switch occurs under different sets of
`operating conditions.
`A physical explanation for this parametric sensitivity lies
`in the nonlinear behaviour of the system. It can be hypothe(cid:173)
`sized that viscosity gradients (axial, radial and if applicable,
`angular) will play a major role in determining flow patterns
`within the reactor. It is known (Porter and Johnson, 1966)
`that zero-shear viscosity 710 obeys the following relationships
`to polymer molecular weight (M);
`
`7/o cc M .................................. (11)
`
`for dilute solutions and
`
`710 cc M 3.4
`
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 12)
`
`for concentrated solutions. The relationship between viscosity
`and polymer concentration is generally accepted as (Porter
`and Johnson, 1966):
`
`7/o cc c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (13)
`
`for dilute solutions and
`
`7/o cc c5-6 ................................. (14)
`
`for concentrated solutions. The range of viscosities present
`in the reactor would likely encompass both regions. The
`dependence of polymerization rate and molecular weight on
`conversion in bulk methyl methacrylate polymerizations is
`also highly nonlinear. Rapid increases in both conversion
`
`THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 69, JUNE. 1991
`
`635
`
`SNF Exhibit 1024, Page 6 of 9
`
`

`
`w
`(/)
`z
`0
`a..
`w
`
`(/)
`
`(1".
`
`(1".
`0
`t(cid:173)
`u
`w
`t(cid:173)
`w
`D
`
`MOLECULAR WE I GHT ( Oa )
`
`MOLECULAR WEIGHT <Oa)
`
`Figure 9 - Molecular weight distribution of fouled polymer sample
`from a vertical reactor, feed downward run. Q = 5.91 mL/min;
`x = 17%; [AIBN] = 0.05 kmol/m 3
`; T = 70°C.
`
`and weight average molecular weight occur at the onset of
`the gel-effect. Consider a streamline close to the reactor
`walls. At the inlet its viscosity will be low and approximately
`equal to that of its neighbouring stream-lines. As axial posi(cid:173)
`tion increases the viscosity will increase according to the rela(cid:173)
`tionship 770 oc (cM). During this time the polymer weight
`fraction c will increase in a roughly linear manner, while
`the molecular weight M will remain essentially constant. Thus
`the increase in viscosity will be initially linear and radial gra(cid:173)
`dients will be small. However a conversion will eventually
`be reached when nonlinear behaviours will occur. There will
`be a rapid increase in the polymerization rate and the
`molecular weight as the gel-effect becomes important and
`there will be a change (if it has not already occurred) in the
`dependence of 770 on c and M. Consider now the response
`of the viscosity to these changes. Significant increases in both
`c and Mare coupled with an increase in their order of depen(cid:173)
`dence in the viscosity equation. The development of large
`radial, axial and possibly angular gradients in viscosity (and
`density) can be expected. If this behaviour is permitted to
`occur in a tubular polymerization reactor a buildup of
`polymer is inevitable. The accumulation of polymer in the
`reactor will probably be self-propagating due in part to the
`large exotherm accompanying its formation (which will
`accelerate the polymerization reaction in the vicinity) and
`t