A Fundamental Model for the Prediction of Distillation Sieve Tray

average deviation, except MIBK stripping (%). -1.27. 8.36 mean absolute deviation (%). 13.28. 18.22 a % deviation )100.0 (EOG calculated - EOG experim...
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Ind. Eng. Chem. Res. 2000, 39, 1818-1825

A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 2. Model Development and Validation J. Antonio Garcia* and James R. Fair Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712

A mechanistic model has been developed for the prediction of sieve tray point efficiency for both aqueous and hydrocarbon systems. A forerunner of the model was developed from fundamental relationships by Prado and Fair in 1990 and was based on gas-liquid transfer in systems of predominantly air and water. The earlier model has now been modified and extended. Contacting on a sieve tray is considered analogous to gas-liquid contacting in a mechanically agitated vessel, and supporting research has been adapted to the tray-contacting case. Studies in bubble columns have provided information on bubble size distribution and bubble stability at high pressure; these studies coupled with isotropic flow theory have formed the basis for correlating bubble size distribution as well as the fraction of small bubbles in the sieve tray froth. New tray efficiency data taken on a semi-industrial scale have been combined with published data as well as new data released by Fractionation Research, Inc. to form a large database suitable for model testing. The development of the database is described in part 1 of this series. In part 2, details of the new model are presented along with a comparison of predicted and measured efficiencies. Predicted efficiencies were found to be within (25% of the measured (or deduced) values of the same efficiency. Comparisons are included, showing the fit of the same data bank to the model of Chan and Fair published in 1984. Introduction In part 1 of this paper1 emphasis was placed on the need and interpretation of experimental data for sieve tray efficiency model development. To satisfy this perceived need, new data were presented on the basis of distillation tests conducted by the authors in industrialscale equipment. In addition, data from a number of other sources were gathered and checked for consistency before being placed in a database. Emphasis was given to larger scale results, for a broad range of the test mixtures from which the data were derived. The final base of 233 points was described and all sources were given. A detailed background on the database development may be found in the dissertation by Garcia.2 In this part of the paper we shall develop a new, mechanistic model for predicting sieve tray distillation efficiencies and demonstrate how the model checks the database entries. Model Structure The modeling approach of Prado and Fair3 has been retained. In this approach an operating tray is divided into a number of zones, as indicated in Figure 1. At any instant, the zones are characterized by the type of vapor dispersion: jetting, large bubbling, and small bubbling. The relative sizes of these zones varies according to the loading of vapor and liquid on the tray; for example, at very high vapor rates, most holes show jetting, with the remainder predominantly producing larger bubbles. The jets break up into a distribution of bubble sizes. There is inherent instability of the larger bubbles, and they result in a range of sizes according to the hydraulic * To whom correspondence should be addressed. Dr. Garcia is with Koch-Glitsch, Inc., 4900 Singleton Blvd., Dallas, TX 75212. E-mail: [email protected].

Figure 1. Hydraulic model of the dispersion above a sieve tray (ref 3).

conditions in the contacting zone. Accordingly, an important facet of the model is to determine the relative sizes and contributions to mass transfer of these different zones. Each zone makes a contribution to the overall efficiency of the tray. As shown in Figure 2, the zone contributions can be recognized as the number of transfer units achieved within each zone. For example,

10.1021/ie0000966 CCC: $19.00 © 2000 American Chemical Society Published on Web 05/12/2000

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Figure 2. Mass-transfer model of the dispersion above a sieve tray (ref 3).

in zone 1, which includes the formation of jets, the efficiency is determined by

NG1 ) kG1RTa1′tG1 ) kG1′a1′tG1

(1)

kG1 ) DG/RTzG1

(2)

NL1 ) kL1a1*tL1

(3)

kL1 ) DL1/zL1

(4)

In these equations, the two-film model is employed, but other consistent mass-transfer models could be used. The comprehensive set of equations leading to the total point efficiency of the tray is indicated in Figure 2 and is presented in detail in the above-cited reference3 or in the dissertation of Prado.4

Because most commercial sieve trays operate in the froth regime (see part 1), the efficiency model has been designed to represent this regime; conditions under which there can be significant liquid entrainment or liquid flow through the holes (weeping/dumping) are not included in the analysis. Also, the model is based on full operation of all holes; Prado et al.5 showed that “inactive” holes (neither weeping nor passing vapor) could be disregarded under normal operating conditions. Further, the spray zone indicated in Figure 1 was found to make very little contributions to mass transfer under normal conditions. The thrust of the present work is to modify the various parameters in the efficiency equations, to account for the properties of systems other than those of air-water. The basic approach of Prado and Fair is retained, however. The evaluation of the parameters follows.

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Table 1. Results of the Sensitivity Analysis Applied to φ and K φ

κ

errorGa (%)

errorLa (%)

1 5 10 2.466b

1 5 10 3.138b

8.64 2.87 4.94 1.99b

15.24 8.81 15.26 4.79b

a

Table 2. Range of Applicability of the Φ Factor weir height (hW)

hW g 0.0254 hW,CBS ) 1 0 < hW < 0.0254 hW,CBS ) 8.3[hW(m)]0.7 hw ) 0 hW,CBS ) 8.3[hCL(m)]0.7

liquid viscosity (µL)

AJ ) constant ) 0.5372. b Values used by Prado (1986).

air/water system µL,CBS ) 1 other systems with µL > 0.6 mPa‚s µL,CBS ) 4.13[µL(Pa‚s)]1.5

New Model Parameters Diffusion Coefficients. The previous model called for slight adjustments to the molecular diffusion coefficients that might be correlated or predicted by standard procedures. A sensitivity analysis of the original Prado/Fair data showed that the correction factors φ (liquid phase) and κ (vapor phase) could be assigned values of unity with very little impact on the final efficiency determinations. This would permit use of straightforward methods for predicting the diffusion coefficients. Results are presented in Table 1. Jet Height. For zone 1, the height of jet h1 and jet diameter D1 are key parameters. Data published by Lockett et al.6 have been re-correlated to predict the jet height as a function of hole Reynolds number (ReH) and hole diameter 0.46 h1 ) 1.1 × 10-3D0.20 H ReH

DBSS ) Φ × 0.66

0.18 D0.84 H UH

Q0.07 LW

0.85 D0.84 H UH

Q0.08 LW

(6)

(7)

where

Φ ) (hW,CBS) × (µL,CBS) × (σCBS)

(8)

Consequently, the impact of liquid viscosity, surface tension, and weir height is considered in the correction factor Φ, as expressed in eqs 6 and 7. The effect of the geometric parameter, weir height, was included to avoid overprediction for weirs lower than 25.4 mm. Table 2 shows the range of applicability of factor Φ. Rise Velocity for Small Bubbles. For zones 2, 4, and 5, the residence times of bubbles must be determined. Ashley and Haselden11 determined that the small bubbles rise at velocities equal to their terminal velocities. Prado used the method proposed by Clift et al.12 to calculate the velocity of small air bubbles rising through water. We have calculated the rise velocity of

(8b)

(8c) (8d) (8e) (8f)

small bubbles for other systems using the correlation of Grace et al.13

Clift et al.: UT )

x

[2.14σ + 0.505FLgdb2] FLdb

(9)

Grace et al.: UT )

(5)

with the jet diameter calculated with the equation proposed by Hai.7 Sauter Mean Bubble Diameter at Formation. For zone 3 it is necessary to determine the distribution of bubble sizes (which includes the small bubble sizes for zone 5). The rate of liquid cross-flow influences bubble size, and this effect was not considered in the Prado model. However, the effect has been assessed by several researchers (Tsuge et al.,8 Ponter and Tsay,9 and Marshall et al.10). The effect is particularly important for high liquid-flow situations, for example, in highpressure distillations. The original Prado data have been re-evaluated in the light of refs 8-10, with the resulting flow-influenced relationships,

DBLS ) Φ × 0.605

for σ . 5.0 mN/m σCBS ) 1 for σ e 5.0 mN/m σCBS ) 3[σ(N/m)]0.6

surface tension (σ)

(8a)

µL -0.149 M (J - 0.857) FL d b

J ) 0.94H0.757

(10a)

(2 < H e 59.3)

(10b)

(H > 59.3)

(10c)

( )

(10d)

J ) 3.42H0.441

µL 4 H ) EoM-0.149 3 µW

-0.14

J ) ReM0.149 + 0.857

(10e)

The dimensionless groups are Eotvos (Eo), Morton (M), and Reynolds (Re). Bubble Size Distribution. This distribution must be predicted to determine the maximum stable bubble size in the froth. A bimodal bubble size distribution for air-water has been observed by many researchers (e.g., Hofer,14 Kaltenbacher,15 and Lockett16) and was included in the original Prado model. However, Jiang et al.17 observed that under higher pressures the bubble size distribution is much narrower and approaches the maximum stable bubble size. The use of an analogy between bioreactors and an operating sieve tray was used to determine the maximum stable bubble size. In gas-liquid contactors operating under turbulent conditions, the bubble breakup can be modeled using isotropic turbulence theory. Walter and Blanch,18 using this theory with experimental results, developed a correlation to predict the maximum stable bubble size:

dM ) 1.12

σ0.6 P 0.4 0.2 FL V

()

() µL µV

0.1

(11)

The power per unit volume for a tray, as proposed by Calderbank and Moo-Young19 and determined for stirred contactors, is

(VP)

SIEVE-TRAY

) USAFLg

(12)

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Thus, for the prediction of the maximum stable bubble size for a sieve tray, eq 11 becomes

DBSJ )

3.34 σ 0.6 µL (USAg)0.4 FL µV

()()

(13)

0.1

The factor of 3.34 was obtained considering the small bubble size distribution observed (5 mm) in the air/ water system. Wilkinson20 demonstrated that the bubble stability depends strongly on three physical properties: surface tension, liquid viscosity, and vapor density. We assumed a linear effect of these properties on the bubble size distribution. A linear regression was conducted using the two extreme cases: air/water at atmospheric conditions and the i-butane/n-butane system at high pressure (Yanagi and Sakata21). The following relationship resulted:

{ ( ) }]

[

DBLJ ) DBSJ 0.83 + 41.5 σ0.6

µL FV

0.1

(14)

Fraction of Small Bubbles in the Froth (AJ). As is evident from Figures 1 and 2, a ratio between the number of smaller and larger bubbles is needed. Prado assigned the value AJ ) 0.532 for air-water at atmospheric pressure, on the basis of a linear regression analysis. Chen22 correlated this parameter as a function of surface tension using the methanol/water and acetic acid/water systems under distillation conditions. Separate studies on bubble stability demonstrated an influence of liquid viscosity and surface tension for small bubbles (Dodd et al.23) as well as for large bubbles (Walter and Blanch18). Also, the influence of gas density on bubble breakup was proven by Wilkinson et al.24 Consequently, the fraction of small bubbles appears to be a distinct function of physical properties of the twophase system on the operating tray. At high pressures this fraction will be higher than that for systems under atmospheric conditions.

AJ ) 1 - Γ[SPRATIO] SPRATIO )

( )( σ σW

0.6

0.1

FW FL

0.6

FAIR FV

0.1

(16)

The term Γ was obtained from an analysis of the bubble stability between air/water at atmospheric conditions and i-butane/n-butane at the highest pressure, 2758 kPa, to merge most of the data. It is dimensionless and has a value of 0.463. For high-viscosity liquids, the fraction of small bubbles must be smaller because of the resistance to elongation. Therefore, the above relation was corrected for systems with higher liquid viscosities, and the correction must be applied when the liquid viscosity is higher than 0.6 mPa‚s (0.6 cp) and the surface tension is lower than 50 mN/m. The range for the liquid viscosity correction is based on the work of Mahiout and Vogelpohl.25 Finally, the expression for systems with liquid physical properties within the range noted above becomes

[ ( )]

AJµ ) AJ 0.5

µL µW

Figure 4. Comparison of measured and predicted total reflux point efficiencies for the cyclohexane/n-heptane system at 414 kPa.

(15)

)( )( )

µL µAIR µW µV

Figure 3. Comparison of measured and predicted total reflux point efficiencies for the cyclohexane/n-heptane system at 165 kPa.

0.1

(17)

Figure 5. Comparison of measured and predicted total reflux point efficiencies for the isobutane/n-butane system at 2758 kPa.

A similar correction was found by Walter and Blanch18 for the estimation of bubble size in fermentation broths which frequently exhibit pseudoplastic or elastic behavior. Equations 5-17 have been incorporated into the basic model. Model Testing The revised model was tested against the database described in part 1 of this paper. In all cases, the local, or point, efficiency was used for comparisons of predic-

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Table 3. Legend for Figures 3-11 figure

system

column diameter (m)

pressure (kPa)

open area % active

hole diameter (mm)

weir height (mm)

reference

3 4 5 6 7 8 9 10 11

cyclohexane/n-heptane cyclohexane/n-heptane i-butane/n-butane 2-propanol/water o-/p-xylenes octanol/decanol ethylene glycol/water air/ammonia/water methyl isobutyl ketone (MIBK)/water

1.22 0.43 1.22 1.22 1.22 1.22 0.43 1.22 0.46

165 414 2758 13.3 2.13 1.3 6.7 101.4 101.4

8.0 10.0 8.0 12.7 12.7 12.7 10.0 8.0 10.7

12.7 4.8 12.7 4.8 4.8 12.7 4.8 12.7 3.18

51 51 51 25 25 25 51 51 14

28 1, 2 28 29 29 29 1, 2 30 31

Figure 6. Comparison of measured and predicted total reflux point efficiencies for the 2-propanol/water system at 13.3 kPa.

Figure 8. Comparison of measured and predicted total reflux point efficiencies for the octanol/decanol system.

Figure 7. Comparison of measured and predicted total reflux point efficiencies for the o-/p-xylenes system.

Figure 9. Comparison of measured and predicted point efficiencies for the ethylene glycol/water system under stripping conditions.

tion and measurement. In all cases, the earlier model of Chan and Fair26 was also used to predict comparative efficiencies. Typical data fits for the two models are shown in Figures 3-11. The legends for these figures are given in Table 3. It is clear that the model provides a good fit for point efficiencies measured (Figures 4, 9, 11) or back-calculated from overall tray efficiency measurements. For the entire database, plots such as those in Figures 3-11 are given in the Garcia dissertation.2 The model fits of the entire database are shown in Figures 12 and 13. A summary of the fits is given in Table 4. It is clear that the new model provides a better fit than the Chan/Fair model, although it is more complicated to apply. Importantly, the new model is more fundamentally based, and a computer program (ref 2) removes the onus of difficult hand calculations. It may be noted that 84.1% of the total 233 data points fall within these limits and only 6 points fall outside

the lower limit; that is, only 6 points are in the optimistic, or nonsafe, region. If the questionable application of MIBK stripping is removed from the database, 94.6% of the 203 points fall within the (25% limits. An analysis of the model fit is shown in Table 4, and comparisons with the fit of the Chan-Fair model are included. For testing the model under nondistillation conditions, data for stripping of ammonia from water with air and stripping methyl isobutyl ketone (MIBK) from water with steam were used. Representative data plots are shown in Figures 10 and 11. The relatively high liquid rates are not completely taken into account by the model. The liquid/vapor ratio range of 3-40 is extreme in comparison with most of the data bank conditions of L/V ≈ 1.0, and some adjustment in the model may be needed in the future. In an earlier work, Fair and Harvey27 found that, for steam stripping of

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Figure 10. Comparison of the measured and predicted point efficiencies for ammonia stripping from water using air.

Figure 13. Parity plot, measured vs predicted point efficiencies, for the full database and the model of Chan and Fair. Table 4. Comparison of New Model and Chan-Fair Modela

number of data points points outside the 25% band “unsafe” points outside the lower band average deviation, all points (%) mean absolute deviation (%) average deviation, except MIBK stripping (%) mean absolute deviation (%)

new model

Chan-Fair model

233 35 6 -10.8 21.4 -1.27

233 71 34 28.7 44.1 8.36

13.28

18.22

% deviation )100.0 (EOG calculated - EOG experimental)/EOG calculated. Average deviation ) (Σ% deviation)/number of data points. Mean absolute deviation ) (Σ|% deviation|)/number of data points. a

Figure 11. Comparison of the measured and predicted point efficiencies for the stripping of methyl isobutyl ketone (MIBK) from water with steam.

into accountsin fact, Garcia has shown that the model can also be applied to certain types of valve trays.2 It should be stressed, however, that the model does not take into account the deleterious effects on efficiency of weeping and entrainment. Conclusions

Figure 12. Parity plot, measured vs predicted point efficiencies, for the full database and the new model.

toluene from water, a small correction for vapor flow effect on the liquid-phase mass-transfer coefficient was needed. Modifications to the original Prado/Fair model include the effects of bubble breakup and change in bubble size distribution and thus provide for changes in effective interfacial area for mass transfer. As is well-known, the variables affecting tray efficiency can be grouped into flow rates (loading), physical properties, and device geometry. The new model takes all these parameters

A mechanistic model for the prediction of point tray efficiency for aqueous and nonaqueous systems has been developed. Recourse has been taken to research on agitated vessels to represent turbulent conditions on an operating sieve tray. Vapor bubble breakup has been modeled using isotropic turbulence theory. Studies in bubble (sparged) vessels provided support for estimating bubble size distributions and bubble stability at higher pressures. Turbulence theory has been used to predict the fraction of small bubbles in the tray froth. The model has not been tested for conditions where there is a dominant spray (as opposed to liquid-continuous froth) on the tray under study. Also, it was not developed for extreme loads where there can be weeping or significant entrainment. Although the model has been tested against a number of chemical systems, involving a large range of physical properties, it will need further confirmation as additional data become available. Acknowledgment This work was funded by Grant 63172 from the Consejo Nacional de Ciencia y Tecnologı´a (CONACYT), Secretaria de Educacio´n Pu´blica (SEP) trough Instituto Tecnolo´gico de Durango (Mexico) and by the Separations

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Research Program at The University of Texas at Austin. The authors are grateful for these supporting contributions. Nomenclature a′ ) interfacial area per volume of gas, m2/m3 a* ) interfacial area per volume of liquid, m2/m3 AJ ) fraction of small bubbles in the bulk froth zone AJµ ) fraction of small bubbles, liquid viscosity restricted (eq 17) db ) equivalent bubble diameter, m DB ) bubble diameter, m DBLJ ) bubble diameter of large bubbles due to jets and bubble breakup, m DBLS ) Sauter mean bubble diameter of large bubbles, m DBSJ ) maximum stable bubble size, m DBSS ) Sauter mean bubble diameter of small bubbles due to jets and bubbles breakup, m DG ) molecular diffusion coefficient for gas or vapor, m2/s DH ) orifice diameter, m DL ) molecular diffusion coefficient for liquid, m2/s Eo ) Eotvos number, Eo ) g∆Fdb2/σ, dimensionless g ) gravitational constant, 9.8 m/s2 h1 ) jet height, m hCL ) clear liquid height, m (ref 32) hw ) weir height, m H ) parameter in eq 10d, dimensionless J ) parameter in eq 10b, dimensionless kG ) gas mass-transfer coefficient, mol/(s‚m2‚Pa) kG′ ) gas mass-transfer coefficient, m/s kL ) liquid mass-transfer coefficient, m/s M ) Morton number, M ) gµL4∆F/(FL2σ3), dimensionles P/V ) power input per volume, W/m3 QLW ) volumetric liquid flow rate/weir length, m3/s‚m‚weir R ) gas constant, 8.314 J/(mol K) Re ) Reynolds number, Re ) FLdbUT/µL, dimensionless ReH ) hole Reynolds number, Re ) FGDHUH/µG, dimensionless SPRATIO ) stability parameter ratio, dimensionless as defined by eq 16 tG ) mean residence time of gas in dispersion, s tL ) mean residence time of liquid in dispersion, s T ) temperature, K UH ) gas velocity through a hole, m/s Us ) superficial gas velocity, based on net area, m/s USA ) superficial gas velocity, based on active area, m/s UST ) rise velocity of small bubbles, m/s UT ) terminal rise velocity of bubbles, m/s z ) thickness of liquid film, m Greek Symbols Γ ) parameter in eq 15, dimensionless ∆F ) phase density difference, kg/m3 φ ) multiplier for liquid diffusivity, dimensionless κ ) multiplier for gas or vapor diffusivity, dimensionless µ ) viscosity, Pa‚s F ) density, kg/m3 σ ) surface tension, N/m Φ ) correction factor for bubble size, eq 8, dimensionless Subscripts G ) gas or vapor phase H ) hole L ) liquid phase V ) vapor or gas phase W ) water 1 ) zone 1 (Figure 1) CBS = corrected for bubble size

Literature Cited (1) Garcia, J. A.; Fair, J. R. A Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. 1. Database Development. Ind. Eng. Chem. Res. 2000, 39, 1809. (2) Garcia, J. A. Fundamental Model for the Prediction of Distillation Sieve Tray Efficiency. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, May 1999. (3) Prado, M.; Fair, J. R. Fundamental Model for the Prediction of Sieve Tray Efficiency. Ind. Eng. Chem. Res. 1990, 29, 1031. (4) Prado, M. The Bubble-to-Spray Transition on Sieve Trays: Mechanisms of the Phase Inversion. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, May 1986. (5) Prado, M.; Johnson, K. L.; Fair, J. R. Bubble-to-Spray Transition on Sieve Trays. Chem. Eng. Prog. 1987, 83 (3), 32. (6) Lockett, M. J.; Kirkpatrick, R. D.; Uddin, M. S. Froth Regime Point Efficiency for Gas-Film Controlled Mass Transfer on a Sieve Tray. Trans. Inst. Chem. Eng. 1979, 57, 25. (7) Hai, N. T. Hydrodynamics of Sieve Trays. Ph.D. Dissertation, The University of New South Wales, Sydney, Australia, 1980. (8) Tsuge, H.; Nakajima, Y.; Terasaka, K. Behavior of Bubbles Formed From a Submerged Orifice Under High System Pressure. Chem. Eng. Sci. 1992, 47, 3273. (9) Ponter, A. B.; Tsay, T. Sieve Plate Simulation Study: Contact Angle and Frequency of Emission of Bubbles from a Submerged Orifice with Liquid Crossflow. Chem. Eng. Res. Des. 1983, 61, 259. (10) Marshall, S. H.; Chudacek, M. W.; Bagster, D. F. A Model for Bubble Formation from an Orifice with Liquid Cross-flow. Chem. Eng. Sci. 1993, 48, 2049. (11) Ashley, M. J.; Haselden, G. G. Effectiveness of VapourLiquid Contacting on a Sieve Plate. Trans. Inst. Chem. Eng. 1972, 50, 119. (12) Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops and Particles; Academic Press: New York, 1978. (13) Grace, J. R.; Wairegi, T.; Nguyen, T. H. Shapes and Velocities of Single Drops and Bubbles Moving Freely through Immiscible Liquids. Trans. Inst. Chem. Eng. 1976, 54, 167. (14) Hofer, H. Influence of Gas-Phase Dispersion on Plate Column Efficiency. Ger. Chem. Eng. 1983, 6, 113. (15) Kaltenbacher, E. On the Effect of Bubble Size Distribution and the Gas-Phase Diffusion on the Selectivity of Sieve Trays. Chem. Eng. Fundam. 1984, 1 (1) 47. (16) Lockett, M. J. Distillation Tray Fundamentals; Cambridge University Press: Cambridge, England, 1986. (17) Jiang, P.; Lin, T.-J.; Luo, X.; Fan, L. S. Flow Visualization of High Pressure (21 Mpa) Bubble Column: Bubble Characteristics. Trans. Inst. Chem. Eng. 1995, 73 (Part A), 269. (18) Walter, J. F.; Blanch, H. W. Bubble Break-up in GasLiquid Bioreactors: Break-Up in Turbulent Flows. Chem. Eng. J. 1986, 32, B7. (19) Calderbank, P. H.; Moo-Young, M. B. The Mass Transfer Efficiency of Distillation and Gas Absorption Plate Columns. Part 2. Inst. Chem. Eng. Symp. Ser. 1960, 6, 59. (20) Wilkinson, P. M. Physical Aspects and Scale-Up of HighPressure Bubble Columns. Ph.D. Thesis, University of Groningen, The Netherlands, 1991. (21) Yanagi, T.; Sakata, M. Performance of a Commercial Scale 14% Hole Area Sieve Tray. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 712. (22) Chen, G. X. Predicting and Improving Sieve Tray Point Efficiency. Ph.D. Thesis, University of Alberta, Edmonton, Canada, 1993. (23) Dodd, P. W.; Pandit, A. B.; Davidson, J. F. Bubble Size Distribution Generated by Perforated Baffle Plates in Large Fermenters. Second International Conference of Bioreactor Fluid Dynamics, Cambridge, England, 1988; Elsevier Applied Science: London, 1988; paper G2, p 319. (24) Wilkinson, P. M.; Schayk, A. V.; Spronken, J. P.; Dierendonck, L. L. V. The Influence of Gas Density and Liquid Properties on Bubble Breakup. Chem. Eng. Sci. 1993, 48, 1213. (25) Mahiout, S.; Vogelpohl, A. Mass Transfer of Highly Viscous Media on Sieve Trays. Inst. Chem. Eng. Symp. Ser. 1987, 104, A495. (26) Chan, H.; Fair, J. R. Prediction of Point Efficiencies on Sieve Trays. 1. Binary Systems. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 814.

Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 1825 (27) Fair, J. R.; Harvey, R. Modeling of Tray-Type Steam Stripping Columns. Paper presented at AIChE Meeting, Atlanta, Spring 1994. (28) Sakata, M.; Yanagi, T. Performance of a Commercial Scale Sieve Tray. Inst. Chem. Eng. Symp. Ser. 1979, 56, 3.2/21. (29) Fractionation Research, Inc. Research Progress Reports for June and July 1966. Obtainable from Oklahoma State University Archives, Stillwater, Oklahoma. (30) Nutter, D. E. Ammonia Stripping Efficiency Studies. AIChE Symp. Ser. 1972, 124, 73.

(31) Rush, F. E.; Stirba, C. Measured Plate Efficiencies and Values Predicted from Single-Phase Studies. AIChE J. 1957, 3, 336. (32) Bennett, D. L.; Agrawal, R.; Cook, P. J. New Pressure Drop Correlation for Sieve Tray Distillation Columns. AIChE J. 1983, 29, 434.

Received for review January 21, 2000 Accepted April 3, 2000 IE0000966