Experimental and Correlational Studies of a Vickers-Zimmer Style

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Ind. Eng. Chem. Res. 2008, 47, 3364-3371

Experimental and Correlational Studies of a Vickers-Zimmer Style Polyester Finisher W. Roy Penney* and Anurag Singh Ralph E. Martin Department of Chemical Engineering, UniVersity of Arkansas, 3202 Bell Engineering Center, FayetteVille, Arkansas 72701

An 8-in. (0.203 m)-diameter Vickers-Zimmer disk style polyester finisher was tested using carboxymethylcellulose and corn syrup solutions. The processor consisted of a spoked-disk style agitator, with 20, 5-spoke disks, in a horizontal cylindrical vessel. To prevent the liquid batch from rotating with the disks, stationary breaker bars, between each of five adjacent disks, and 210° baffle plates, between every fifth disk, were installed. Fractional liquid holdup, agitator power, angles of batch rise and depression at the vessel walls, fractional liquid film coverage of the spoked disk cutouts, and mass-transfer coefficients were all determined experimentally. Dimensionless correlations were developed for (1) fractional liquid disk holdup, (2) agitator power requirements, (3) angles of rise and depression at the vessel wall, (4) factional film coverage of the spoked wheel cutouts, and (5) mass-transfer coefficient. Introduction In a polycondensation process, such as the final condensation of poly(ethylene terephthalate) (PET), the reaction equilibrium, reaction rate, and product molecular weight are determined by the effective removal of reaction byproductsi.e., ethylene glycol for PET. At higher viscosities, the mass transfer of ethylene glycol controls the reaction rate. Thus, the finishing reactor must provide effective mixing and a high specific surface area to volume ratio. Melt viscosities are high requiring special types of close-clearance agitators, such as ribbons, screws, or disks, which typically operate at low rotational speeds. Engineering correlations for power consumption, blending times, heattransfer coefficients, interfacial area, mass-transfer coefficient, liquid holdup within the rotor assembly, and free surface profiles are needed for the design of such reactors. This study focused on providing correlations for several of these important parameters for the Vickers-Zimmer style polyester finisher. This study was funded by a grant from Eastman Chemical, which is the “the global leader in polyethylene terephthalate (PET)”.1 Eastman funded the study to develop models for predicting performance of their specific geometry of VickersZimmer polyester finishers. A polymerization reaction is often followed by a devolatization step where any residual monomer exiting the final polymerization reactor is removed. The design of devolatilization equipment also requires the same design methods as those required for reactors. Literature Review Ravindranath and Mashelkar2 reviewed PET processing; they included a review of Vickers-Zimmer style disk-ring processors in their paper. Dietze and Kuhne,3 in a “marketing related” paper, have covered the qualitative operating characteristics of disk-ring reactors; they discussed film forming, axial mixing, free liquid surface depression, and mean batch residence time. Murakami et al.4 studied a “DuPont” style twin rotor disk unit; correlations were developed for batch holdup, agitator * To whom correspondence should be addressed; Telephone: 479575-5681. Fax: 479-575-7926. E-mail: [email protected].

power requirement, mixing time, equivalent number of wellmixed stages, and the ratio of dead volume to batch volume.

Vh/D2L ) 0.6(µND/σ)1/7

holdup correlation

Np ) 42.1Re-1Fr-0.13(S/D)-1 Ntm ) 47(S/D)0.12

(1)

power correlation (2)

mixing time correlation

(3)

Ns ) 4.52(ReL/Re)1/4(L/S) ) 4.52(L/NDτ)1/4(L/S) number of perfectly mixed stages (4) Vd/V ) 1 - 1/[2.15(ReL/Re)1/10] ) 1 - 1/[2.15(L/NDτ)1/10] ratio: dead volume/batch volume (5) They4 also conducted mass-transfer experiments and determined that the Danckwerts surface renewal model fitted their mass-transfer data. Vijayraghavan and Gupta5 measured the local film thickness on vertical rotating disks drawing liquid from a pool. They correlated local film thickness as

[ ] [ ] [ ] [ ] /[ ] [ ] δ2Fg µΩr

1/2

)8

µΩr σ

2.93

σ3 F3gν4

0.05

2h D

5.23

µΩD 2σ

3.09

Ω2D - sin Θ 2g

×

0.024

(6)

Murakami et al.,4 Yamane and Yoshida,6 Ravetkar and Kale,7 Suga and Boongorsrang,8 and Yoon and Park10 have all investigated mass transfer in rotating disk processors. All investigators found that the Dankwerts surface renewal model (also called the penetration theory) fitted experimental data well, provided the interfacial area for mass transfer was known or predictable. Ravetkar and Kale7 present the dimensionless mass transfer correlation from the surface renewal model.

Sh ) 1.59(ND2/ξ) ) 1.59(Re)1/2(Sc)1/2

(7)

Experimental Apparatus For the experimental apparatus, refer to Figure 1-8. The entire experimental effort is covered in detail in the thesis by

10.1021/ie061656p CCC: $40.75 © 2008 American Chemical Society Published on Web 04/18/2008

Ind. Eng. Chem. Res., Vol. 47, No. 10, 2008 3365

Figure 1. Flow schematic of the experimental apparatus.

Singh.10 The experimental apparatus consisted of the following components: (1) 9 in. inside diameter cylindrical processor vessel, (2) rotating disk assembly, (3) motor and speed controller and planetary gear reducer, (4) tachometer, (5) test liquid feed

Figure 2. Horizontal Vickers-Zimmer style rotating disk processor.

pump, (6) electronic scale for test liquid feed reservoir, (7) N2 and CO2 cylinders, (8) CO2 inlet rotometers, and (9) soap film CO2 outlet gas flowmeter, Figure 1 presents a process flow schematic. Photographs of the processor and the processor and drive motor are presented as Figures 2 and 3, respectively. The processor shell (9 in. (0.229 m) inside diameter by 17 in. (43.2 cm) long) consists of a split acrylic tube with both halves mated to horizontal aluminum bars at the cylinder equator. Processor inlet and outlet ports were located as follows: top and bottom at either end, for gas and liquid inlets and outlets, respectively, and four bottom sample ports. The rotating disk assembly, Figure 4, was driven by a 1-hp variable-speed electric motor, coupled to the agitator shaft through a 6:1 planetary gear reducer. The electric motor/gear reducer assembly was cradle mounted on low friction bearings such that motor torque could be measured by a sliding weight along a horizontal lever arm, which was attached to the motor equator in a horizontal plane. The rotor-disk assembly consists of the following: (1) Twenty 0.0625-in.-thick, spoked disks, alternating between the disk shown in Figure 5 and the disk shown in Figure 6. Disk spacing, center-to-center 5 disks, 4 spaces at 1/2 in., 1 space at 3/4 in.; 5 disks, 4 spaces at 1/2 in., 1 space at 3/4 in.; 5 disks, 4 spaces at 1/2 in., 1 space at 3/4 in.; 5 disks, 4 spaces at 1/ in.. Total rotor length 0.0625 in. + 16(1/ in.) + 3(3/ in.) ) 2 2 4 10.31 in.. (2) Breaker bars, Figure 7, between all disks spaced 1/2 in. apart. Rotation was counterclockwise relative to the breaker bar of Figure 7. (3) Baffle plates, Figure 8, between all disks spaced 3/4 in. apart and at rotor ends. Rotation was counterclockwise relative to breaker bar in Figure 8.

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Ind. Eng. Chem. Res., Vol. 47, No. 10, 2008

Figure 3. Cradle-mounted electric motor drive and rotating spoked disk processor.

Figure 4. Assembly drawing of the rotating disk agitator assembly. Table 1. Data and Data Reduction for Run Number 4-5-2113a fractional fillage (%)

impeller speed (rpm)

viscosity (cP)

Re

Fr

Fr/Re

rotor volume (mL)

rotor free volume (cm3)

liquid volume holdup (cm3)

Fholdup

31

32.06

2253

12.1

0.006

0.000 49

10 800

7452

2645

0.35

a

Reference 10, page 102.

(4) The end compartments were each (17 in. - 10.31 in.)/2 ) 3.34 in. long. Carboxymethyl cellulose and household corn syrup were used to prepare the test fluids. Thymol was used as an antibacterial agent. Anhydrous Na2CO3 and NaHCO3 were the chemicals used to slowly react away the absorbed CO2. Experimental Procedures (1) The processor was filled with a buffered (with Na2CO3 and NaHCO3) CMC or corn syrup solution, by a variable-speed gear pump, from a 5-gallon reservoir, which rested on a 12-kg

electronic scale, to static fractional fillages of 15, 20, 25, 31, or 40%. The alkaline buffer solution method, including all chemical reactions, for measuring CO2 absorption rates is fully documented by Kolthoff et al.11 and the methods and procedures used for this investigation are fully documented by Abdul12 and Singh.10 (2) The rotor was set to the desired speed, and test fluid was pumped into the processor to bring the end compartment levels back to the original static level. The mass of required fluid, to bring the end compartment levels back to the original static level, is the fluid held within the rotor, against gravity drainage from the rotor.


Figure 7. Breaker bar.

Figure 5. Spoked disk-shaft flat perpendicular to midplane between spokes.

Figure 8. Baffle plate.

(8) Immediately after stopping the CO2 flow, the processor was purged with N2 to remove the CO2 from the gas space. (9) Samples were taken from the processor lower sample ports. Correlation of Data

Figure 6. Spoked disk-shaft flat perpendicular to spoke centerline.

(3) The shaft speed and motor torque were measured. (4) The angle of depression and rise, relative to the static position, were measured by scale readings along a flexible ruled tape wrapped around the processor. (5) A video camera was used to record the sheeting action within the spokes cutouts within the disks. Stills from the video were used to determine the fractional liquid coverage of the spokes cutouts. (6) The rotor was stopped momentarily and the processor was purged rapidly with 3 volumes of CO2 as the soap film flowmeter was bypassed. (7) The CO2 flow was decreased to ∼5-10% above the absorption rate. The CO2 flow into the processor was measured with a rotometer, and the CO2 flow from the processor was measured with the soap film flowmeter. Steady state was reached quickly, at which time CO2 flow was stopped.

The literature survey covers correlational work from previous studies. None of the earlier correlational methods were used here; more appropriate methods were developed to correlate the current data. Also, the rotor and stator geometry of all previous studies were sufficiently different from those of the current study, so correlations from previous work could not be compared quantitatively with current correlations. Fractional Liquid Holdup. Fractional liquid holdup (Fholdup), which is defined as the free fraction of the rotor volumesabove the end compartment levelssoccupied by liquid, is a rather unfamiliar concept; consequently, Table 1 is included to explain the data reduction procedure for one experimental run from Singh.10 The weight of corn syrup solution required to completely fill the rotor is (π/4)D2LF ) (π/4)(0.2292(0.262)1240 ) 13.38 kg. Thus, the weight of liquid required to completely fill the rotor free space is 13.38(1 - 0.31) ) 9.23 kg. Experimentally, for this run, The weight of liquid added to bring the end compartment levels to their original static condition was 3.28 kg. Thus, Fholdup was 3.28/9.23 ) 0.36. This is one of the experimental data points in Figure 9. Figure 9 is a plot of Fholdup versus Re/Fr for the fractional holdup data, including all fractional end compartment fillagess 15, 20, 25, 31, and 40%. All the data are well correlated over the range of the data. The curve is extrapolated down to Fholdup ) 0.1 and Fr/Re ) 0.000 01 because the detectable level of

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Figure 9. Fractional liquid holdup correlation.

Figure 12. Angle of depression correlation, 25% fillage.

Figure 13. Angle of depression correlation, 31% fillage. Figure 10. Angle of depression correlation, 15% fillage.

Figure 14. Angle of depression correlation, 40% fillage. Figure 11. Angle of depression correlation, 20% fillage.

end compartment lowering, estimated at about F ) 0.01, occurred at about Fr/Re ) 0.000 01. Angle of Batch Depression and Rise. The angle of depression is an important parameter from an operational standpoint, because it is possible to rotate the batch so far that it is impossible to gravity flow from the vessel through a bottom drain. For example, note from Figure 15, that the angle of depression for 40% end compartment fillage and Fr/Re ) 0.002 is 180°. At this condition, a bottom drain would not be covered with liquid. The angle of rise is not nearly so crucial from a design standpoint; however, that parameter could be important to measure and use as a performance parameter. The angle of depression was measured circumferentially around the processor from the static liquid surface in the direction of disk periphery motion. The angle of rise was similarly measured on the opposite side of the processor from

the angle of depression measurement in the direction of periphery motion. The angle of depression is correlated versus Fr/Re in Figures 10-14 for fractional end compartment fillages of 15, 20, 25, 31, and 40%, respectively. The angle of rise is correlated versus Fr/Re in Figure 15 for 40% fillage. The angle of rise was only correlated for 40% fillage because it is less than the angle of depression, and unlike the angle of depression, it is not important in making determination about vessel draining. Impeller Power. The impeller power number was defined as Np ) P/FN3D.4 For this investigation, L/D ) 10.31/8 ) 1.29; thus, one must be careful in using these correlations to take account of the fact that this rotor had 20 disks located along the shaft as follows: 5 at 1/2 in., 1 at 3/4 in., 5 at 1/2 in., 1 at 3/4 in., 5 at 1/2 in., 1 at 3/4 in., and 5 at 1/2 in. Consequently, the power correlations are only strictly applicable for a geometrically similar rotor. However, the power would be directly proportional


Figure 15. Angle of rise correlation, 40% fillage. Figure 18. Impeller power correlation, 25% fillage.

Figure 16. Impeller power correlation, 15% fillage.




to the rotor L/D and likely would be almost directly proportional to the number of disks, provided the breaker plates and baffle plates were of similar geometry with similar clearances between plates and the disks. Impeller power correlations are presented as Np versus Re in Figures 16-20 for fractional end compartment fillages of 15, 20, 25, 31, and 40%, respectively. Mass Transfer. To extract a mass-transfer coefficient from the batch CO2 absoprtion data requires a determination of interfacial area for mass transfer. Early in the investigation, video evidence clearly showed that the cutouts in the spoked disks were not always fully covered with a liquid film. To determine the surface area exposed to the gas phase, it was essential to predict the fractional film coverage of the cutouts. From the videos, the correlation of Figure 21, of fractional cutout coverage versus Fr/Re, was developed. This correlation was used to determine the total interfacial area exposed to the gas phase as

(1) exposed area on the disks and cutouts plus (2) the pool surface area, neglecting any interfacial area increase because the free surface is not flat. The mass-transfer correlation for 25% fillage is presented in Figures 22 and 23, for CMC and corn syrup data, respectively. The correlations for 31 and 40% fillage, from corn syrup data, are presented in Figures 24 and 25, respectively. All the data are conservatively fitted by the penetration theory, eq 7. Discussion of Results As shown by Figure 9, the fractional disk holdup, as defined here, is not a function of the fractional end compartment fillage. Thus, the definition of fractional fillage as liquid holdup above the static level ratioed to the maximum, i.e., 100% fillages above the static liquid levelsholdup, was a wise choice, which

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Figure 21. Fractional liquid coverage correlation for the spoke wheel cutouts.

Figure 24. Mass Transfer Correlation - 31% Fillage - Corn Syrup Data.

Figure 25. Mass-transfer correlation, 40% fillage, corn syrup data. Figure 22. Mass-transfer correlation, 25% fillage, CMC data.

Figure 23. Mass-transfer correlation, 25% fillage, corn syrup data.

allowed one correlation to be used to predict rotor holdup for all end compartment fillages. The angle of depression correlates very well with Re/Fr, which indicates that viscous and gravity forces dominate; however, interfacial tension was not varied in this investigation, so there is a possibility that changes in interfacial tension could affect bath depression and rise. Inertial forces, over the range of this investigation, do no affect the angle of depression or rise. The impeller power correlates very well with Re with no apparent effect of Fr. This is somewhat surprising because the fractional rotor fillage and the angle of depression and rise are affected by Fr. The highest ratio of Fr/Re investigated was ∼0.002; thus, below this threshold, Fr does not affect rotor power draw.

As several other investigators have found, the penetration theory correlates the mass-transfer data. Thus, the mass-transfer coefficient can be relatively well predicted. Unfortunately, the interfacial area cannot be so well predicted, especially below the rotor speed where full sheeting occurs on the disks and the disk cutouts are bridged with a liquid film. It is almost certain that the interfacial tension would affect the sheeting action on the disk cutouts. The correlation in Figure 21 indicated that Fr/ Re > 0.000 35 is needed to ensure full liquid coverage of the disk cutouts. For a different system, with different dimensions and different interfacial tension, this may not apply. Thus, one should use the disk coverage correlation very cautiously and perhaps test fluids with different interfacial tension to determine its effect on the interfacial area. Conclusions (1) The rotor liquid holdup is only a function of Fr/Re. (2) The definition of fractional fillage as the ratio of liquid holdup above the static level to the maximum 100% fillage holdup above the static liquid level was a very wise choice, which allowed one simple correlation of holdup versus Fr/Re to be used to predict rotor holdup for all end compartment fillages. (3) The angle of depression and rise is a function of fractional fillage and Fr/Re. (4) The rotor power requirement, for Fr/Re < 0.002, is only a function of fractional fillage and Re. (5) The mass-transfer data are well correlated by the penetration theory. (6) The fractional film coverage of the disk cutouts was correlated here with Fr/Re. The fluid interfacial tension was not varied in this investigation; thus, one must use this finding carefully and cautiously.


(7) The absoption of CO2 on a transient batch basis was used successfully to measure the mass-transfer coefficient. Recomendations (1) Testing with fluids of different interfacial tension is needed to be absolutely sure of correlational validity, and (2) testing a different size processor would also establish correlational validity. Nomenclature D ) disk diameter, m h ) depth of disk immersed in liquid batch, m kL ) mass-transfer coefficient, m/s L ) processor length, m N ) agitator speed, revolutions/s R ) processor radius, m S ) spacing between disks, m t ) time, s tm ) mixing time, s T ) tank diameter, m V ) volume, m3 Vb ) batch volume, m3 Vd ) volume of dead space within processor, m3 Vh ) holdup volume, m3 Dimensionless Numbers Fr ) Froude number, ND2/g J ) Sh/Sc1/2 Np ) power number, P/FN3D4 Re ) Reynolds number, ND2F/µ ReL ) Reynolds number based on vessel length and residence time, DLF/µτ Sc ) Schmidt number, ν/ξ Sh ) Sherwood number, kD/ξ; also identified as ShNum in Figures 22-25. Greek Letters R ) dimensionless disk holdup δ ) film thickness on disk, m ∆d ) angle of free surface depression from static liquid surface. ∆r ) angle of free surface rise from static liquid surface θ ) angle around a disk, measured from the pool entering location µ ) absolute viscosity, kg/m s ν ) kinematic viscosity, (µ/F), m2/s ξ ) diffusivity, m2/s

F ) liquid density, kg/m3 σ ) interfacial tension, N/m τ ) residence time within a processor, s ψ ) angle of depression, degrees Ω ) rotor speed, radians/s Acknowledgment We are grateful to Tennessee Eastman for providing a grant to fund this work, and for their patience while three different graduate students, one after the other, were assigned to the project. We thank Dr. Larry C. Windes, our contact at Tennessee Eastman, for assisting to plan and to execute the research program. Literature Cited (1) Eastman, P. E. T. to grow more. ICIS Chem. Business Am. 2007, (April 30-May 6), 22. (2) Ravindranath, K.; Mashelkar, R. A. Polyethylene Terepthalate-II. Engineering Analysis. Chem. Eng. Sci. 1986, 12, 2969-2987. (3) Dietze, M.; Kuhne, H. Development and Design of Large-Scale Reactors for the Continuous Production of Polyester Melts. Chemiefasern 1969, 3, 19-28 (English translation). (4) Murakami, Y., Fujimoto Kakimoto, K. S.; Sekino, M. Studies On a High Viscosity Polymer Finisher Apparatus with Two Agitator Axes Having Multidisks. J. Chem. Eng. Jpn., 1972, 5 (3), 257-263. (5) Vijayraghavan, K.; Gupta, J. P. Thickness of the Film Formed on a Vertically Rotating Disk Partially Immersed in a Newtonian Liquid. Ind. Eng. Chem. Fundam. 1982, 21 (4), 333-336. (6) Yamane, T.; Yoshida, F. Absorption in a Rotating-Disk Gas-Liquid Contactor. J. Chem. Eng. Jpn. 1972, 5 (4), 381-385. (7) Ravetkar, D. D.; Kale, D. D. Gas Absorption into Non-Newtonian Fluids in Rotating Disk Contactors. Chem. Eng. Sci. 1981, 36, 399-403. (8) Suga, K.; Boongorsrang, A. A New Model of Mass Transfer in a Rotating Disc Contactor. Chem. Eng. Sci. 1984, 39 (4), 767-773. (9) Yoon, K. H.; Park, O. O. Analysis of a Reactor with Surface Renewal for Poly(Ethylene Terephthalate) Synthesis. Polym. Eng. Sci., 1994, 34 (3), 190-200. (10) Singh, A. Experimental and Correlational Model Studies of a Vickers-Zimmer Style Polyester Finisher. M.S. Thesis, University of Arkansas. Fayetteville, AR, 2002. (11) Kolthoff, I. M.; Sandell, E. B.; Meehan, E. J.; Bruckenstein, S. QuatitatiVe Chemical Analysis, 4th ed.; The Macmillan Co.: New York, 1962. (12) Abdul, M. Dynamics of a Horizontal Partially Filled Multi-Stage Rotating Disc-Blade Processor for Viscous Systems. M.S. Thesis, University of Arkansas. Fayetteville, AR, 1996.

ReceiVed for reView December 21, 2006 ReVised manuscript receiVed March 20, 2008 Accepted March 24, 2008 IE061656P

Experimental and Correlational Studies of a Vickers-Zimmer Style

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