Mass Transfer Performance in Karr Reciprocating Plate Extraction

Apr 17, 2008 - Highway, Port Fairy 3284, Australia. A study of the hydrodynamic and mass transfer performance for Karr reciprocating plate extraction ...
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3996

Ind. Eng. Chem. Res. 2008, 47, 3996–4007

Mass Transfer Performance in Karr Reciprocating Plate Extraction Columns Angela Stella,† Kathryn H. Mensforth,‡ Tim Bowser,§ Geoffrey W. Stevens,*,‡ and H. R. Clive Pratt† Department of Chemical and Biomolecular Engineering, The UniVersity of Melbourne, ParkVille, Victoria 3010, Australia, Particulate Fluids Processing Centre, Department of Chemical and Biomolecular Engineering, The UniVersity of Melbourne, ParkVille, Victoria 3010, Australia, and GlaxoSmithKline Australia, Princes Highway, Port Fairy 3284, Australia

A study of the hydrodynamic and mass transfer performance for Karr reciprocating plate extraction columns has been presented for a range of operating conditions and column diameters of 50, 100, and 450 mm. Although the use of Karr columns has been widespread for many years for a range of important applications, the need for more reliable methods for predicting the performance and scale-up of such columns continues to be a matter of significant importance. The present study has examined the hydrodynamic performance in terms of the dispersed phase hold up and droplet size distribution and mass transfer performance which has incorporated the effects of backmixing in the continuous phase. Work was initially carried out in a 50 mm diameter laboratory scale Karr column using the system 10 v/v% tributyl phosphate/kerosene (continuous)-phenol-water (dispersed) where hydrodynamic and mass transfer performance was analyzed for both directions of mass transfer. Using these data, models were investigated and developed to predict performance over a range of operating conditions. An alternative system consisting of an organic solvent (continuous)-phenolic alkaloid-aqueous caustic (dispersed) was also studied, using both 100 and 450 mm diameter Karr columns. These data were used to validate the hydrodynamic and mass transfer performance models developed for the phenol system in the 50 mm diameter column. Dispersed phase holdup data were found to fit the correlation presented by Kumar and Hartland [Ind. Eng. Chem. Res. 1995, 34, 3925-3940], and the drop size distribution also agreed with the relationship presented by Kumar and Hartland [Ind. Eng. Chem. Res. 1996, 35, 2682-2695] within reasonable accuracy. The mass transfer performance results indicated that the continuous phase controlled the mass transfer rate, and thus, column design was simplified by assuming that the overall mass transfer coefficient can be obtained using a standard mass transfer correlation for the continuous phase. The current mass transfer results were found to be best predicted by a refitted form of the overall mass transfer coefficient correlation developed by Harikrishnan et al. [Chem. Eng. J. 1994, 54, 7-16]. 1. Introduction Various types of solvent extraction contactors, including spray and packed columns, have been used for a range of applications in the hydrometallurgical, pharmaceutical and petrochemical industries for many years. Van Dijck4 was first to propose that the efficiency of a perforated-plate column could be improved by either applying a reciprocating motion to the plates or by pulsing the liquid in the column while keeping the plates stationary. The latter has been widely studied using the pulsed perforated plate column, while the alternative, the reciprocating plate column has also received attention since its development by Karr.5 Today, the Karr column has found application in the separation and purification of components that include aromatics, copper, phenol, penicillin, and alkaloids. The advantages of the Karr column compared to others such as the Scheibal or Ku¨hni columns include higher extraction efficiency with lower power requirement, lower axial mixing, and higher throughput.6 The optimal design of a solvent extraction column involves maximizing the performance by increasing the interfacial area for mass transfer, mass transfer coefficient and concentration driving force. As the interfacial area is dependent on the dispersed phase droplet size and holdup in the column, it is * To whom correspondence should be addressed. E-mail: gstevens@ unimelb.edu.au. † Department of Chemical and Biomolecular Engineering, The University of Melbourne. ‡ Particulate Fluids Processing Centre, The University of Melbourne. § GlaxoSmithKline Australia.

important to be able to accurately predict and optimize these hydrodynamic characteristics. With a mass transfer rate being directly related to the concentration driving force, axial dispersion must be considered as it is known to cause a reduction in the driving force, especially of the continuous phase. The present study has examined the influence of operating variables including the frequency and amplitude of agitation, as well as the solvent and aqueous phase flowrates on the dispersed phase holdup, drop size distribution, and finally mass transfer performance in columns of 50, 100, and 450 mm diameter. More importantly, the experiments have investigated the extent to which axial dispersion in the presence of solute transfer affects the performance of the unit. A model to predict axial dispersion in the continuous phase has been developed based on the work of Prvcic et al.7 and then incorporated within a mass transfer performance model. The present results, along with those of earlier studies,8–10 have been designed to aid the reliability in determining the optimal column design and operating conditions for small and large scale Karr extraction columns. 2. Background 2.1. Dispersed Phase Holdup. Introduction of a solvent into an extractor causes droplets that undergo repeated coalescence and breakage, leading to an equilibrium drop size distribution. The resulting fractional volumetric holdup, xd, is defined as the volume fraction of the active section of the column that is occupied by the dispersed phase:

10.1021/ie071623p CCC: $40.75  2008 American Chemical Society Published on Web 04/17/2008

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 3997

xd )

Vd Ve

(1)

where Vd represents the volume of the dispersed phase and Ve the total volume of the two phases for the effective length of the column. The dispersed phase holdup is a key variable in the design of solvent extraction columns as it is related to the interfacial area for mass transfer, a, as follows: 6xd a) d32

Vs ) Vj0(1 - xd)

Vd Vc + xd 1 - xd

(3)

(4)

Combination of eqs 3 and 4 resulted in the following relationship: Vd Vc ) Vj0(1 - xd) + xd (1 - xd)

(2)

Prediction of dispersed phase holdup is also important in relation to the flood point of a Karr column. On increasing flowrates, a second interface forms at some point in the column, and the column is thus characterized as flooded and any further increase in the dispersed phase flow is rejected from the column resulting in inefficient operating conditions. The dispersed phase holdup will tend to increase unstably as the flood point is approached. The importance of the dispersed phase holdup has received attention from many workers including early work by Dell and Pratt11 and Gayler et al.12 where a slip velocity, Vs, was used to relate holdup to the phase flow rates as follows: Vs )

Thornton later related Vs to a characteristic velocity, Vj0, which is a function of the system properties and drop size but independent of flow rates, as follows: 13

(5)

One of the earliest correlations for predicting dispersed phase holdup was conducted by Baird and Lane14 where holdup was found to depend on the phase flowrates, system physical properties, and diameter of the holes in the plates. Nemecek and Prochazka15 developed a correlation for holdup while investigating the effects of longitudinal mixing in a vibrating sieve plate column. Rao et al.16 have investigated holdup for a gas-liquid system and a liquid-liquid system in a reciprocating plate column for plates with a small hole size and free area, unlike previous studies that have concentrated on plates with large holes and free area. Bensalem17 undertook studies in a reciprocating plate column to investigate the effects of mass transfer on hydrodynamic performance. Correlations were presented as a function of agitation rate and phase flow rates in the absence of mass transfer and for solute transfer from

Table 1. Dispersed Phase Holdup Correlations reference 13

Thornton (1956)

Nemecek and Prochazka (1974)15

Rao, Srinivas, and Varma (1983)16

system ethylene dichloride (d)-water (c) trichloroethylene (C2HCl3) (d)-water (c)

(a) kerosene (d)-water (c) (b) MIBK (d)-water (c)

Bensalem (1985)17

toluene (d)-acetone-water (c)

Kumar and Hartland (1988)18

heptane, toluene, kerosene, Isopar M, ethyl acetate, water, aq. NaCl, kerosene + C2HCl3(d)-water, aq. NaCl, methyl isobutyl ketone, kerosene, kerosene + mineral oil (c) kerosene (d)-water (c), other solvents include butyl acetate, heptane, MIBK, and toluene.

Prvcic et al. (1990)19 with the refitted Bell and Babb model (1969)20

Kumar and Hartland (1995)1

a

heptane, toluene, kerosene, Isopar M, ethyl acetate, water, aq. NaCl, kerosene +C2HCl3(d)-water, aq. NaCl, methyl isobutyl ketone, kerosene, kerosene + mineral oil (c)

Note: Constants defined in Table 7 for Karr column.

properties

results

nozzle diameter ) 0.076 in. Vd/xd + Vc/(1 - xd) ) Vjo(1 - xd) Dc ) 50 mm dh ) 2.5-3.5 mm Fd ) 1460 kg/m3 γ ) 31-33 dyn/cm µd ) 0. 54 cP Dc ) 153 mm dh ) 3 - 8 mm Fd ) 800 kg/m3 γ ) (a) 50 (b) 9.2 dyn/cm Dc ) 76 mm dh ) 16 mm Fd ) 867 kg/m3 γ ) 34.3 mN/m µd ) 0.58 mPa s Dc ) 51-150 mm dh ) 6.35-16 mm Fd ) 686-1193 kg/m3 γ ) 6.9-53 mN/m µd ) 0.40-3.23 mPa s Dc ) 75 mm dh ) 3.2 mm Fd ) 783 kg/m3 γ ) 44 dyn/cm µd ) 1.7 cP Dc ) 51 - 150 mm dh ) 6.3-16.0 mm Fd) 686-1193 kg/m3 γ ) 6.9-53.0 mN/m µd ) 0.40-3.23 mPa s

xd ) (3 × 10-5)Vd1.5[2Af/S2/3]3.6

xd ) (3 × 10-3)We0.37Fr0.16Re0.66(Dc/dh)0.85N0.4[σc/ (σw - σd)]-0.15 where N represents the number of stages

in the absence of mass transfer xd ) 0.154(Af + Vc)0.30Vd0.606 for the direction of c f d mass transfer xd ) 0.091(Af + Vc)0.91Vd0.87 for the direction of d f c mass transfer xd ) 0.089(Af + Vc)0.437Vd0.807 xd ) [k1 + k2(Af)3.0]Vd0.81(Vd + Vc)0.32∆F-0.98 no mass transfer: k1 ) 3.87 × 103, k2 ) 3.71 × 107 c f d transfer: k1 ) 3.25 × 103, k2 ) 7.54 × 107 d f c transfer: k1 ) 2.14 × 103, k2 ) 1.65 × 107 plates wetted by the dispersed phase: k1 ) 7.91 × 103, k2 ) 3.23 × 106 xd ) Vd[C1 + (C2 + C3Vc)(Af - C4)2] where constants C1-C4 are 23.5, 3.66 × 103, 1.09 × 107, and 1.64 × 10-2, respectively.

xd ) ΠΦΨΓ Π ) CΠ + [(ψ/g)(Fc/gγ)1/4]n1 Φ ) [Vd(Fc/gγ)1/4]n2 exp[n3Vc(Fc/gγ)1/4] Ψ ) Cψ(∆F/Fc)n4(µd/µw)n5 Γ ) CΓen6[hc(Fcg/γ)1/2]n7 a

3998 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 Table 2. Drop Size Correlations for Karr Reciprocating Plate Columns reference Baird and Lane (1973)

system 14

Boyadzhiev and Spassov (1982)31

Rao, Srinivas, and Varma (1983)16

Pietzsch and Pilhofer (1984)30

Bensalem (1985)17

Kumar and Hartland (1996)2

Joseph and Varma (1998)23

a

kerosene, kerosene + mineral oil, methyl isobutyl ketone (c)-(d) water, aq. NaCl

kerosene, carbon tetrachloride (CCl4) (d)-(c) water

(a) kerosene (d)-water (c) (b) MIBK (d)-water (c)

sources include Miyauchi and Oya (1965), Khemangkorn (1977), Baird and Lane (1973),14 and Hafez (1979)

toluene (d)-water solute-acetone (c)

water, methyl isobutyl ketone, kerosene (c)-toluene, kerosene, water (d)

1. kerosene (d)-water solute benzoic acid, n-butyric acid (c) 2. toluene (d)-water solute benzoic acid, n-butyric acid, acetone (c)

properties

results

Dc ) 50.8 mm

d32 ) Kγ /[(Ψ + Ψ*)0.4Fj0.2]

dh ) 12.7 mm Fc ) 1000-1193 kg/m3 γ ) 8.7-31.0 mN/m µc ) 0.08-0.32 mPa s Dc ) 50.0 mm

where K is 0.356 and Ψ* ) g(Fm - Fd)(Vd + xdVc/(1 - xd))

dh ) 2.0 mm Fd ) 1180 kg/m3 γ ) 34.0 mN/m Dc ) 153 mm dh ) 3 - 8 mm Fd ) 800 kg/m3 γ ) (a) 50 (b) 9.2 dyn/cm Dc ) 15-50.8 mm

dh ) 2.0-12.7 mm Fd ) 818-1590 kg/m3 γ ) 8.7-45.0 mN/m µc ) 0.6-1.2 mPa s Dc ) 76 mm dh ) 16 mm Fd ) 867 kg/m3 γ ) 34.3 mN/m µd ) 0.58 mPa s Dc ) 51-76 mm dh )12.7-16.0 mm Fd ) 801-1000 kg/m3 Fc ) 805-1000 kg/m3 γ ) 8.7-34.3 mN/m µd ) 0.57-1.72 mPa s µc ) 0.82-1.07 mPa s Dc ) 153 mm

0.6

d32 ) (0.57 ( 0.11)(γ/Fc)3/5[S4/5dh2/5/ (2Af)6/5]

d32 ) Kγ0.6/Ψ0.4Fc0.2 where K is 0.287 and mechanical energy, Ψ, is Ψ ) 115Fc(Af)3 d32 ) [6γ/λ1 + 9λ22/64] - (3/8)λ2

λ1 ) ∆Fg + bFd λ2 ) CDwp2Fc/λ1; CD ) 4Ar/3Re∞2 b ) wp2/[0.9065(dh2/S)]; wp ) 2Af/0.6S + V∞ in the absence of mass transfer d32 ) 0.560(Af)-0.59Vc-0.164 for the direction of c f d mass transfer d32 ) 0.41(Af)-0.59 for the direction of d f c mass transfer d32 ) 0.757(Af)-0.400Vc-0.232Vd0.414 a d32 ) Cψ(S)n/ {1/[CΩ(γ/∆Fg)0.5]2} + 1/[CΠψ-0.4(γ/Fc)0.6]2} b

d32 ) 0.14(σ/Fc)0.5S0.6Z-1hc0.4d0.1

dh ) 3.0-12.0 mm Fd ) 805-867 kg/m3 γ ) 34.3-44 mN/m

cgs units.b Constants defined in Table 8 for Karr column.

continuous to dispersed phase and vice versa. Kumar and Hartland18 considered a large bank of experimental data to develop a single correlation to predict holdup from physical properties and operating variables. Both directions of mass transfer were considered as well as the situation where the plates were wetted by the dispersed phase. Prvcic et al.19 used a correlation developed by Bell and Babb20 to predict dispersed phase holdup in a pulsed perforated plate column by refitting the constants to incorporate the emulsion and mixer settler regions of operation. Finally Kumar and Hartland1 have further investigated holdup using published experimental results for eight different extraction columns including the Karr column. This study found that holdup can be expressed in terms of the mechanical power dissipation, phase flow rates, physical properties and column geometry. The correlations that have been developed in these studies for dispersed phase holdup have been summarized in Table 1. 2.2. Drop Size Distribution. The equilibrium droplet size distribution in a solvent extraction column is usually represented

as the ratio of the average drop volume to surface area, known as the Sauter-mean drop diameter, d32, defined by: d32 )

∑nd ∑nd

3

i i 2

(6)

i i

where ni is the number of drops of diameter di. Measurement of the drop size is typically carried out photographically, with a transparent sided square “box” around the outside of the column wall to avoid distortion. An alternate method is to draw out droplets using capillaries, of which a photograph is taken of the drops passing in the capillary.21 The Sauter-mean diameter is a key variable in extractor column design due to its influence on both throughput and specific mass transfer rate. As seen from eq 2, the drop size distribution is related to the specific interfacial area available for mass transfer and it also influences the mass transfer coefficient, the dispersed phase holdup, and flooding conditions

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 3999 Table 3. Mass Transfer Correlations for Karr Reciprocating Plate Columns reference

system

Shen, Rao, and Baird (1985)

25

properties

kerosene (d)-water (c); solute n-butyric acid

results

Dc ) 50.8 mm dh ) 13.5 mm Fd ) 805 kg/m3

Bensalem (1985)17

toluene (d)-water (c); solute acetone

Baird et al. (1994)10

kerosene (d)-water (c); solutes n-butyric acid, benzoic acid, phenol

Harikrishnan, Prabhavathy, and Varma (1994)3

kerosene (d)-water (c); solutes benzoic acid, n-butyric acid

γ ) 16.0-24.0 mN/m µd ) 0.8-1.7 mPa s Dc ) 76 mm dh ) 16 mm Fd ) 867 kg/m3 γ ) 34.3 mN/m µd ) 0.58 mPa s Dc ) 50.0 mm dh ) 0.61 or 0.99 mm Fd ) 805 kg/m3 γ ) 16.0-44.3 mN/m µd ) 0.8-1.7 mPa s Dc ) 153 mm

µd ) 1.07 cP

Aravamundan and Baird (1999)26

Isopar M (d)-water (c); solute i-propanol

Kumar and Hartland (1999)24

toluene (d)-water (c); solute acetone

kox ) 0.46d320.98(1 xd)-2.0Vc-0.68Vd0.39f0.40

where (c/) denotes the overall driving force Hox ) Hc/Nox; kox ) Vcd32/6xdHox ko/ko|z)0 ) 1 + 0.035ψ0.4(Vc/Vd)0.1 where ko|z)0 ) 1.8 × 10-3Vd0.21 benzoic acid, d f c ko|z)0 ) 3.8 × 10-3Vd0.21 n-butyric acid, d f c ko|z)0 ) 3.0 × 10-3Vd0.21 n-butyric acid, c f d and ψ ) 2π2/3 [(1 - S2)/ hcCo2S2]Fm(Af)3 with Co ) 0.7 and Fm ) xdFd + (1 xd)Fc koxa ) K5(Af)0.84dh-0.21S-0.44hc-0.41Vd0.91 where K5 ) 0.43 ko|z)0a ) K6dh-0.21S-0.44hc-0.41Vd0.91 where K6 ) 1 × 10-2

dh ) 5.0-12.0 mm

γ ) 48.6 mN/m

kerosene (d)-water (c); solutes benzoic acid, n-butyric acid

2

Nox ) ∫cc21 c1/(c - c/) dc for plug flow behavior

Fd ) 805 kg/m3

Joseph and Varma (1998)23

Ex d cx/dz +Vx dcx/dz -koxa(cx - cx/) )0 Ey d2cy/dz2 + Vy dcy/dz - koxa(cx - cx/) )0 solution of kox was then used to calculate true height of a transfer unit, Hox 2

Dc ) 43.0 mm dh )2.0-8.0 mm Fd ) 805 kg/m3 γ ) 48.6 mN/m µd ) 1.07 mPa s Dc ) 50.8 mm

Nox ) ln (cxo/cxi)

dh ) 13.7 mm Fd ) 785.3 kg/m3 γ ) 24.8-50.0 mN/m µd ) 2.4 mPa s Dc ) 76 mm

kox ) NoxVxd32/6xdHc

[Shc/(1 - xd) - Shc,rigid]/[Shc,∞ - Shc/(1 - xd)] ) (5.26 × 10-2)Re(1/3 + 6.59 × 10-2Re1/4) × Scc1/3(Vslipµc/γ)1/3 1/(1 + κ1.1)[1 + 2.44{ψ/g(Fc/gγ)1/4}1/3]

Shd ) [17.7 + 3.19 × 10-3( ReScd1/ 1.7 3) ]/[1 + 1.43 × 10-2(ReScd1/ 0.7 3) ](Fd/Fc)2/3[1/(1 + κ2/3)][1 + 2.44{ψ/g(Fc/gγ)1/4}1/3] Shc,rigid ) 2.43 + 0.775Re1/2Scc1/3 + 0.0103ReScc1/3 Shc,∞ ) 50 + 2π(Pec)1/2

dh ) 16 mm

Fd ) 867 kg/m3 γ ) 34.3 mN/m µd ) 0.58 mPa s Table 4. Column Specifications column feature column diameter effective column height effective column volume number of plates plate thickness perforation diameter hole pitch (triangular) plate spacing plate free area

symbol column 1 Dc Hc Ve N e dh p hc S

50 mm 1.4 m 2725 cm3 27 3 mm 12.7 mm 17 mm 50 mm 0.452

column 2

column 3

100 mm 5m 39270 cm3 80 5 mm 12.7 mm 17 mm 50 mm 0.6

450 mm 5m 795216 cm3 80 5 mm 12.7 mm 17 mm 50 mm 0.6

of the column. Due to the importance of d32 on extractor performance, numerous studies have been performed to develop

ways to predict the drop size distribution. Most equations have been developed for columns which are supplied with mechanical energy, such as the Karr column, have been based on the theory of isotropic turbulence. However, it has been shown that most of these equations are only valid for the system, geometry, and operating conditions for which the model was developed. Jealous and Johnson22 derived an expression for energy dissipation and mechanically agitated columns with high agitation rates as follows: ψ)

2π2 (1 - S2) (Af)3Fm 3 h C 2S2 c o

(7)

4000 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 Table 5. Physical Properties of the Continuous and Dispersed Phases for the Different Systems Studied properties (SI units) @ 25 °C

phases continuous

dispersed

µc (mPa s)

µd (mPa s)

Fc (kg/m3)

Fd (kg/m3)

γ (mN/m)

water kerosene + 10% TBP kerosene + 10% TBP organic solvent

kerosene water 3% v/v NaOH NaOH solution

1 1.76 1.8 1.76

1.67 1 1 1.0

998 809 809 843

800 998 1045 1045

44 12 8.0 7.8

system no. and desc 1 2 3 4

(no mass transfer) (phenol d f c) (phenol c f d) (alkaloid c f d)

Table 6. Operating Variable Ranges variable ranges

symbol, units

frequency amplitude pulsation rate dispersed phase velocity continuous phase velocity phase flow ratio

f, 1/s A, cm Af, cm/s Vd, cm/s Vc, cm/s R ) Vc/Vd

values

CΠ CΨ CΓ n1 n2 n3 n4 n5 n6 n7

0.13 1.0 (c f d), 0.52 (d f c) 6.87 1.0 0.84 3.74 -0.92 0 0 -0.48

column 2

column 3

2.0 and 3.0 0.5 and 1.2 1.0-3.6 0.1-0.7 0.1-0.7 0-5.0

2.0, 3.0, 3.5, and 4.0 1.0 2.0-4.0 0.1-0.7 0.1-0.7 0.8-31.7

3.5 and 3.6 1.0 and 1.2 3.5-4.3 0.1-0.7 0.1-0.7 6.0-14.0

reciprocating speed but was independent of phase flow rates which was in agreement with previous studies by Baird and Lane.14 Nemecek and Prochazka15 and Pietzsch and Pilhofer30 developed a method for calculating of drop sizes in a pulsed sieve-plate column that can also be applied to the reciprocating

Table 7. Values of Constants and Indexes in the Kumar and Hartland1 Dispersed Phase Holdup Correlation parameter

column 1

Table 8. Values of Parameters Used in the Kumar and Hartland2 Correlation for the Prediction of Drop-Size Distribution Cψ column

cfd

dfc

CΩ

CΠ

n

Karr

0.95

1.48

1.30

0.67

0.50

Baird and Lane14 used this study for a 50 mm diameter Karr column and developed an expression for drop sizes. Rao et al.16 presented a correlation for experimental data obtained in a 50 mm diameter reciprocating plate column with plates of small hole size and free area. They confirmed that d32 depends on the

Figure 2. Sample of the experimental holdup data as a function of agitation rate for mass transfer from the continuous to dispersed phase for all three columns studied.

Figure 1. Dispersed phase holdup as a function of the pulsation rate for the extraction of phenol from the dispersed to continuous phase for the 50 mm diameter column.

Figure 3. Comparison of the experimental dispersed phase holdup data with the Kumar and Hartland1 values in the 50 mm diameter column.

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 4001

Figure 4. Experimental drop size data for mass transfer from dispersed to continuous phase (d f c) and vice versa (c f d) vs the dispersed phase velocity in the 50 mm diameter column using the phenol system.

plate column. Their investigation attempted to cover the whole range of possible operating parameters by simplifying the flow conditions in the column. Bensalem17 developed a correlation that incorporated the effects of varying directions of mass transfer on drop size. It was found due to the change of interfacial tension with mass transfer (Marangoni effect) larger drop sizes resulted for mass transfer from the dispersed phase to the continuous phase. Kumar and Hartland2 have presented a unified correlation for predicting drop size for a range of liquid-liquid extraction columns including the Karr column. The correlation developed for mechanically agitated columns consisted of a two-term additive model involving the ratio of the interfacial tension to buoyancy forces at low agitation and the theory of isotropic turbulence at high agitation. The compartment height and gravitational constant were also incorporated to allow for the effect of various variables on drop size. More recently Joseph and Varma23 have presented a correlation for d32 in a reciprocating plate column as a function of plate geometry, agitation rate and physical properties of the system. The correlations discussed for drop size distribution have been summarized in Table 2. 2.3. Mass Transfer. The rate of mass transfer depends on the interfacial area of the droplet, the effective driving force, and the overall mass transfer coefficient as shown by eq 8: rate of mass transfer ) k0xa∆c

(8)

Several correlations have been proposed for the mass transfer coefficient of a single drop in motion in the continuous phase. These models have been based on either a stagnant, circulating, or oscillating drop falling or rising in the continuous phase with mass transfer occurring into or out of the drops. Similarly numerous investigations have been carried out to study the mass transfer coefficient in the continuous phase around the drops. These correlations take into account both molecular diffusion and natural and forced convection of the continuous phase as well as whether the droplet is stagnant, circulating or oscillating. Numerous correlations have been discussed and summarized by Kumar and Hartland.24 Although there are many correlations available for the individual mass transfer coefficients in the literature, they generally are not accurate for extraction columns due to the complex nature of the droplet interactions in swarms and effects

Figure 5. Drop-size distribution during mass transfer of phenol in the direction of c f d (50 mm diameter column).

such as plate agitation.24 Axial mixing also leads to a reduction in mass transfer performance due to its effect of reducing the concentration driving force for mass transfer. Other factors such as throughput, contact area and distributor geometry also affect mass transfer performance in extraction columns. Shen et al.25 investigated mass transfer for both continuous to dispersed phases (c f d) and vice versa (d f c) in a 50 mm diameter reciprocating plate column, with a stainless steel plate stack preferentially wetted by water (continuous phase). The results were corrected for axial mixing and, although the equilibrium data were nonlinear, an approximation was used to determine the concentrations at equilibrium such that the continuous and dispersed phase axial dispersion coefficients were equal. This study highlighted the mass transfer-induced coalescence effects responsible for the larger drop size, lower holdup, and reduced performance for dispersed to continuous phase solute transfer. Harikrishnan et al.3 later studied mass transfer in a reciprocating plate column for the kerosene (dispersed)-water (continuous) system. The solutes investigated included benzoic acid and n-butyric acid. This study attempted to provide an alternative prediction of mass transfer coefficients for a range of phase flow rates, agitation rates, perforation diameter, plate free area and mass transfer direction. Correlations for both volumetric and mass transfer coefficients were presented in terms of power dissipation rate, phase flow rates and physical properties of the system with results compared to various rigid- and circulatingdrop models. Recent studies for the prediction of mass transfer in single and multidrop systems have been presented by Jospeh and Varma,23 Aravamudan and Baird,26 and Kumar and Hartland.24 Table 3 provides a summary of published mass transfer correlations for reciprocating plate extraction columns. 3. Scope of Present Work This study presents results for the hydrodynamic and mass transfer performance in Karr reciprocating plate extraction columns. A 50 mm diameter laboratory scale column with nylon internals was initially studied with a system of 10 v/v% tributyl phosphate/kerosene (c)-phenol-water (d). The dispersed phase holdup, drop size distribution, backmixing coefficients, and mass transfer coefficients were measured as a function of a full range

4002 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008

Figure 6. Comparison of the experimental drop-size distribution data with the correlation by Kumar and Hartland2 in the 50 mm diameter column. Table 9. Values of Nonlinear Parameters in Equation 11 (Equilibrium Relationship) phenol system

alkaloid system

parameter

cfd

dfc

cfd

A B n

0.155 55.5 2.0

0.001 0.015 1.5

0.135 143.15 3.1

of column variables including plate frequency and amplitude of reciprocation and phase flowrates. These data were compared with existing correlations and models presented in the previous section for the prediction of the relevant hydrodynamic and mass transfer parameters. In turn, this led to the development of suitable models for predicting performance over the range of conditions considered. Further studies were then based on the extraction of a phenolic-type alkaloid in larger scale Karr columns including a 100 mm diameter pilot column and a pair of production scale Karr columns each with a column diameter of 450 mm, all using high-density polyethylene internals. Dispersed phase holdup and mass transfer performance were measured over a range of

Figure 8. Variation in mass transfer coefficient with dispersed phase velocity for the phenol system in the 50 mm diameter column.

comparable operating conditions to the 50 mm column. The models thus developed for the 50 mm diameter column were used to predict the performance of the larger sized Karr columns. 4. Experimental Details

Figure 7. Variation in mass transfer coefficient with continuous phase velocity for the phenol system in the 50 mm diameter column.

4.1. Equipment and Systems. Three Karr columns with diameters of 50, 100, and 450 mm have been investigated with the main features of each summarized in Table 4. The perforated plates provided up to 60% open area, all with a hole size of 12.7 mm and plate spacing of 50 mm. Each column retained constant plate spacing and perforation diameter, as suggested by the previous work of Karr5 for scaling up reciprocating plate extraction columns. The reciprocating motion was driven by a variable speed motor at the top of the column, and an adjustable yoke was coupled to this motor to enable the amplitude of reciprocation to be varied. Materials used in the experiments and the corresponding physical properties of the systems are presented in Table 5. 4.2. Procedures. The amplitude and frequency of reciprocation were first set to desired values. For the 50 mm diameter

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 4003

Figure 9. Variation in mass transfer coefficient with agitation rate with the dispersed phase velocity maintained at 20 L/h for the 100 mm diameter column.

Figure 11. Variation of experimental and predicted mass transfer coefficients for varying columns diameters based on the refitted model developed by Harikrishnan et al.3 Table 10. Summary of the Mass Transfer Performance for the 100 mm Diameter Column Vc/Vd

f (Hz)

xd (%)

a (1/m)

Rc

kox (µm/s)

31.2

2.0 3.0 3.5 4.0 2.0 3.0 3.5 4.0 2.0 3.0 3.5 4.0 2.0 3.0 3.5 4.0

1.9 5.3 8.1 11.7 3.5 9.9 15.2 22.0 4.7 13.2 20.3 29.3 7.1 19.9 30.5 43.9

140.9 220.3 305.7 494.2 236.5 369.7 513.0 829.3 300.3 469.5 651.5 1053.2 421.9 659.7 915.3 1480.0

0.01 0.05 0.07 0.10 0.01 0.05 0.07 0.10 0.01 0.05 0.07 0.10 0.01 0.05 0.07 0.10

47.8 44.0 32.1 16.1 32.0 32.2 24.2 13.0 31.9 29.7 22.7 13.6 28.5 28.4 21.2 11.4

16.7

12.5

8.3 Figure 10. Variation in the optimum operating conditions of the amplitude-frequency product with varying column diameters.

column, flowrates of both phases were controlled via rotameters and were fed to the column via totally enclosed March centrifugal pumps driven by flameproof 0.25 hp electric motors. Flow meters and control valves were used for the larger columns. The interface was maintained at the required level below the plate stack by controlling the outlet flow of the dispersed aqueous phase. The dispersed phase holdup was determined by the drainage method12 where the aqueous and organic inlet and outlet valves were shut simultaneously and with the sudden arrest of flows the dispersion height between the initial and final interface positions was measured. Droplet sizes in the column were determined photographically using an Olympus OM-4 camera fitted with an additional 50 mm lens to enable a magnification factor of 3.0. A transparent sided box was located around the outside of the glass column and was filled with water to avoid reflectance and to eliminate the distortion effect of the round column during photography. The exterior of the box was covered with opaque paper with openings for viewing the droplets and an external light source. Once the photo had been taken, it was scanned into Corel Draw software and the dimensions of droplets obtained. This technique provided a direct measure of the Sauter-mean diameter with the use of eq 6.

Solute concentrations for mass transfer analysis were determined by UV-visible spectroscopy for phenol and high performance liquid chromatography (HPLC) for the phenolic alkaloid. Inlet and outlet samples were taken for both aqueous and organic phases once steady state conditions had been reached. Equilibrium data were obtained via shakeup tests for both systems studied. A mass transfer performance program was developed based on the generalized design equations for backmixed liquid extraction columns with nonlinear equilibria to determine the overall mass transfer coefficient from the measured concentrations and hydrodynamic data.27 The range of variables studied for the three columns is given in Table 6. 5. Results and Discussion 5.1. Dispersed Phase Holdup. Dispersed phase holdup data has been presented in Figure 1 for the 50 mm diameter column as a function of the agitation rate, Af, over a range of flowrates for the extraction of phenol from the dispersed to continuous phase. As expected, an increase in both the dispersed phase flow rate and agitation rate led to increased holdup and, finally, to flooding.

4004 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008

Figure 12. Comparison of 1/koc with the continuous phase velocity for the alkaloid system.

error of 10.4% when compared with the present experimental data for the 50 mm diameter Karr reciprocating plate column (Figure 3). 5.2. Drop Size Distribution. The Sauter-mean drop diameter was observed not to change significantly with progressive increases in the phase flow rates (refer to Figure 4). However, as expected, a higher agitation rate resulted in a lower value of d32. A broad distribution of drop sizes resulted from solute transfer from the dispersed to continuous phase, thus enhancing the effect of coalescence resulting in larger drop sizes. This is consistent with results from previous workers including Bensalem17 who also observed larger drop sizes due to changes in interfacial tension (Marangoni effects) when mass transfer occurred from the dispersed to continuous phase. By contrast, Figure 5 highlights the drop-size distribution in the reverse direction of mass transfer (c f d) with a large proportion of droplet diameters in the range of 0.9-1.2 mm for the phenol system. Kumar and Hartland2 have also presented a correlation for the prediction of drop size, given in Table 2. With the appropriate constants for the Karr column, given in Table 8, this correlation was found to best fit the current data from the 50 mm diameter column with a relative error of 14.2%. Refer to Figure 6 for a comparison of experimental and predicted values. 5.3. Mass Transfer Performance. As the present study was based on a two-phase system with nonlinear equilibrium data, the overall mass transfer coefficient based on the continuous phase was determined via solution of the governing equations for steady state countercurrent mass transfer with continuous phase backmixing. A pair of backflow equations have been used to describe the solute material balance in the extractor.27 For the continuous phase (1 + Rx)cx,n-1 - (1 + 2Rx)cx,n + Rxcx,n+1 -

koxaV (c - c/x,n) ) 0 Fx x,n (9)

and for the dispersed phase Figure 13. Comparison of 1/kod with the dispersed phase velocity for the alkaloid system.

Experimental dispersed phase holdup data has also been presented as a function of agitation rate and phase ratio for mass transfer from the continuous to dispersed phase for the 50 mm diameter column as well as the 100 and 450 mm diameter columns as shown in Figure 2. With all columns operating in the emulsion regime, it can be seen that an increase in agitation rate led to nonlinear rises in holdup as influenced by smaller drop sizes at high agitation.10 It can also be seen from Figure 2 that higher holdup values and hence longer residence times were encountered when lower continuous to dispersed phase ratios were used. This accounts for the difference in holdup for the different column diameters in Figure 2 as the 50 mm diameter column was operated at a low phase ratio of 0.6 while the 100 mm and 450 mm diameter columns were operated with phase ratios of 2.0 and 5.7, respectively. The Kumar and Hartland1 correlation for the prediction of the dispersed phase holdup in the Karr reciprocating plate column was found to be the most accurate of the correlations presented in Table 1, with the appropriate constants given for the current data in Table 7. This method for calculating the dispersed phase holdup gave an average absolute relative

Rycy,n-1 - (1 + 2Ry)cy,n + (1 + Ry)cy,n+1 +

koxaV (c - c/x,n) ) 0 Fy x,n (10)

The equilibrium data were expressed by the following nonlinear relationship, cy ) A + B(c/x )n

(11)

where the values of A, B, and n are given in Table 9 for both the phenol and alkaloid systems. The mass transfer performance was determined from the measured dispersed and continuous phase exit concentrations, together with the equilibrium data as given in eq 11 and Table 9. The continuous phase axial dispersion was predicted from the models of Stella et al.28 The solute distribution, hydrodynamic data (including xd and d32), axial dispersion coefficient, and the appropriate boundary conditions then enabled the experimental mass transfer coefficient and hence column efficiency to be determined from solution of eqs 9 and 10 using Mathematica software. The dispersed phase axial dispersion was taken to be negligible. As pointed out by Harikrishnan et al.,3 the continuous phase flow had little influence on the value of kox, and conversely, kox was significantly influenced by the dispersed phase flow. This

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 4005

was true for the 50 mm diameter column, as shown in Figures 7 and 8. The specific interfacial area, determined as a function of the dispersed phase holdup and Sauter-mean drop diameter, showed that the effect of phase flow rates however are less pronounced than agitation intensity and mass transfer direction. Data from the 100 mm diameter column showed that the overall mass transfer coefficient in the continuous phase varied with respect to the agitation frequency as shown in Figure 9. This showed that the mass transfer performance for the alkaloid system in the 100 mm diameter column reached a maximum at a frequency of 2.5-3.5 Hz, after which it decreased sharply. Experimental data from all three columns showed that at high agitation frequencies, increased entrainment and poor extraction efficiency was observed, with the production of very fine dispersed droplets. An optimum point was found to be dependent on the flow ratio of continuous to dispersed phase. By increasing the continuous to dispersed phase flow ratio in excess of 25 in the 100 mm diameter column, the mass transfer coefficient started to fall with the formation of rigid droplets. The higher phase ratios also led to a reduction in the dispersed phase holdup and hence reduced interfacial area for mass transfer, refer to eq 2, resulting in lower mass transfer coefficients and hence reduced column performance. Continuous phase backmixing also played a significant role in determining the mass transfer performance of the columns, especially in the 50 mm diameter column which operated at low continuous to dispersed phase ratios. As the 100 and 450 mm columns were operated at high phase ratios, the effects of axial mixing were reduced7 with Peclet numbers, Pec, greater than 1.0. This was a direct consequence of increasing the continuous phase velocity with respect to the dispersed phase. A higher agitation frequency was required to overcome the effect of axial mixing to improve mass transfer performance in the 50 mm diameter column as indicted by Figure 10. This suggested that an optimum point existed where the mass transfer coefficient increased initially with frequency and thereafter fell as the circulating droplets became smaller and more rigid. Results from the 50 mm diameter column show that mass transfer in the direction of the dispersed to continuous phase (d f c) led to reduced holdup and the overall mass transfer coefficient became smaller due to the induced effect of interfacial turbulence. Conversely, for mass transfer in the opposite direction (c f d), the drop size distribution was smaller resulting in an increase in both the dispersed phase holdup and interfacial area for mass transfer resulting in higher overall mass transfer coefficients. Studies on the larger alkaloid columns involved experimental work, followed by the use of the predictive methods derived for the 50 mm diameter column. The concentrations of the fresh feed and resulting extracts were measured in the large columns, although the dispersed phase holdup was determined for only some of the conditions specified; this was due to limitations imposed by continuous plant operation and the need to minimize disturbances to normal production. Backmixing in the continuous phase has been predicted for all columns using the model developed by Stella et al.28 which was based on results obtained using the 50 mm diameter column. The experimental overall mass transfer coefficient, kox, was found to best fit a correlation based on the work of Harikrishnan et al.3 as shown by eq 12. The exponent n in this equation was refitted to experimental data from this study which resulted in values of 0.24, 0.4, and 0.52 for the 50, 100, and 450 mm diameter columns, respectively.

(

())

koxa ) VcnAf 1 + 0.035ψ0.4

Vc Vd

0.1

(12)

Figure 11 shows the resulting comparison of experimental data with predicted results, using eq 12 with the refitted constants. Data have been shown for the 50 mm diameter column using the phenol system and the 100 and 450 mm diameter columns, for the alkaloid system, with an overall average error of 21%. Table 10 presents the typical values for holdup, xd, specific interfacial area, a, and continuous phase backmixing coefficient, Rc, predicted for the 100 mm diameter column as based on models developed for the 50 mm diameter column and overall mass transfer coefficient, kox. 5.4. Effect of Chemical Reaction for the Alkaloid System. Based on an early study by Murdoch and Pratt29 for uranyl nitrate extraction in a wetted wall column, the present data were used to determine the magnitude of the chemical reaction, ri, between the NaOH ions and the phenolate ion according to eq 13. 1 1 1 ) + + ric koc kc mkd

(13)

A plot of 1/koc vs 1/Vc0.6 and 1/kod vs 1/Vd0.6, as shown in Figures 12 and 13, respectively, shows that the exponent of 0.6 gave the best straight line. Extrapolation of 1/Vc0.6 to zero, i.e., to infinite koc, gave an effectively zero intercept. Hence, the values of 1/mkd and ri, the dispersed phase mass transfer coefficient and the chemical reaction rate, were both effectively infinite and the mass transfer was therefore controlled by the continuous phase alone. 6. Conclusions The main conclusions from this study are summarized below: (i) The holdup data for the phenol system were best predicted best by the Kumar and Hartland correlation,1 with a relative deviation of 10.4%. (ii) The generalized correlation for the Sauter-mean dropsize derived by Kumar and Hartland2 presented the most suitable model with an average deviation of 14.2% for the phenol system in the 50 mm diameter column. (iii) The overall mass transfer coefficient, kox, was best predicted by a refitted correlation presented by Harikrishnan et al.3 The current data were adapted to this model based on the diameter of the column with a relative deviation of 21%. (iv) The mass transfer coefficient, kox, was found to be higher for solute transfer in the direction continuous to dispersed phase (c f d) due to the smaller drop size distribution and hence larger interfacial area for mass transfer. (v) The optimum amplitude and frequency of reciprocation were found to be 1.0-1.2 cm and 3.0-4.0 Hz, respectively, for a plate spacing of 50 mm in all columns. (vi) The interfacial reaction rates of phenol, and of its alkaloid, with OH-ions in solution, were effectively instantaneous and thus had little influence on the overall mass transfer performance. Mass transfer was found to be controlled by the continuous phase. Acknowledgment The authors would like to acknowledge the funding provided by the Australian Postgraduate Award (APA) and GlaxoSmithKline, Port Fairy, for this project and would also like to thank the Particulate Fluid Processing ARC Special Research Centre (PFPC) for the resources provided for this project.

4006 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008

Nomenclature a ) specific interfacial area, m /m A ) amplitude (trough to peak plate stroke), m Ar ) Archimedes number, (∆F/Fc) (d3gFc2/µc2), dimensionless c ) concentration of the solute, kmol/m3 c/ ) concentration in equilibrium with the second phase, kmol/m3 CD ) drag coefficient Co ) orifice coefficient ) 0.60 CΠ, CΓ, CΨ, CΩ ) parameters defined in Tables 8 and 9, dimensionless c f d ) mass transfer in the direction of the continuous to dispersed phase d f c ) mass transfer in the direction of the dispersed to continuous phase d ) droplet diameter, m d32 ) Sauter-mean drop diameter, m dh ) perforation diameter, m D ) molecular diffusivity, m2/s Dc ) column diameter, m e ) plate thickness, m E ) axial dispersion coefficient, cm2/s f ) frequency, Hz F ) flowrate, m3/s Fr ) Froude number, (Af)2/gd, dimensionless g ) gravitational acceleration, m/s2 hc ) height of compartment, m Hc ) effective column height, m Hox ) overall height of a transfer unit based on x-phase k ) individual mass transfer coefficient, m/s K ) dimensionless constant ko ) overall mass transfer coefficient, m/s m ) slope of the equilibrium line or partition coefficient ni ) number of drops of diameter di N ) number of stages Nox ) number of overall transfer units based on x-phase P ) triangular pitch ri ) rate of reaction R ) flow ratio Vc/Vd Re ) Reynolds number, FcVd/µc, dimensionless S ) fractional open area of plates Scc ) Schmidt number for the continuous phase, µc/FcD, dimensionless Shc ) Sherwood number for the continuous phase, kcd/D, dimensionless t ) time, s V ) volume, m3 Vj0 ) characteristic velocity of the droplets, m/s V ) superficial phase velocity, m/s VS ) slip velocity of the droplets, m/s We ) Weber number, Vd2d∆F/γ, dimensionless xd ) fractional holdup of dispersed phase z ) distance up the column, m Z ) agitation rate, m/s Greek Symbols R ) backmixing coefficient ε ) fractional voidage of packing φ ) volume fraction holdup of the dispersed phase γ ) interfacial tension of phases, N/m κ ) viscosity ratio, µd/µc λ ) defined in Table 2 µ ) viscosity, Pa s F ) density, kg/m3 ∆F ) density difference of phases, (kg/m3) σ ) surface tension, N/m 2

3

ψ ) mechanical or gravitational power dissipation per unit volume, W/m3 Subscripts c ) continuous phase d ) dispersed phase e ) effective i ) interface ∞ ) single particle m ) mixture n ) stage number o ) initial stage rigid ) rigid drop conditions x ) x-phase (continuous phase in present case) y ) y-phase (dispersed phase in present case) w ) water

Literature Cited (1) Kumar, A.; Hartland, S. A Unified Correlation for the Prediction of Dispersed-Phase Holdup in Liquid-Liquid Extraction Columns. Ind. Eng. Chem. Res. 1995, 34, 3925–3940. (2) Kumar, A.; Hartland, S. Unified Correlations for the Prediction of Drop Size in Liquid-Liquid Extraction Columns. Ind. Eng. Chem. Res. 1996, 35, 2682–2695. (3) Harikrishnan, T. L.; Prabhavathy, N. K.; Varma, Y. B. G. LiquidLiquid mass transfer in a reciprocating-plate column. Chem. Eng. J. 1994, 54, 7–16. (4) Van Dijck, W. Tower with Internal Perforated Plate Suitable for Extracting Liquids by Treatment with other Liquids and for similar Concurrent Processes. US Patent No. 2011186, 1935. (5) Karr, A. E. Performance of a Reciprocating Plate Extraction Column. AIChE J. 1959, 5, 446–452. (6) Prabhakar, A.; Sriniketan, G.; Varma, Y. B. G. Dispersed Phase Holdup and Drop Size Distribution in Pulsed Plate Columns. Can. J. Chem. Eng. 1988, 66, 232–240. (7) Prvcic, L. M.; Pratt, H. R. C.; Stevens, G. W. Axial Dispersion in Pulsed Perforated Plate Extraction Columns. AIChE J. 1989, 35, 1845– 1855. (8) Karr, A. E. Design, Scale-up and Applications of the Reciprocating Plate Extraction Column. Sep. Sci. Technol. 1980, 15, 877–905. (9) Lo, T. C.; Baird, M. H. I.; Rao, N. V. R. The Reciprocating Plate Column - Development and Applications. Chem. Eng. Commun. 1992, 116, 67–88. (10) Baird, M. H. I.; Rao, N. V. R.; Procha´zka, J.; Sovova´, H. Reciprocating-Plate Columns: Liquid-Liquid Extraction Equipment; Wiley: Chichester, 1994. (11) Dell, F. R.; Pratt, H. R. C. Flooding Rates for Packed Columns. Trans. Inst. Chem. Eng. 1951, 29, 89–109. (12) Gayler, R.; Roberts, N. W.; Pratt, H. R. C. Liquid-Liquid Extraction: Part IV. A Further Study of Holdup in Packed Columns. Trans. Inst. Chem. Eng. 1953, 31, 57–68. (13) Thornton, J. D. Spray Liquid-Liquid Extraction Columns: Prediction of Limiting Holdup and Flooding Rates. Chem. Eng. Sci. 1956, 5, 201– 208. (14) Baird, M. H. I.; Lane, S. J. Drop Size and Holdup in a Reciprocating Column. Chem. Eng. Sci. 1973, 947–957. (15) Nemecek, M.; Prochazka, J. Longitudinal Mixing in a Vibrating Sieve-Plate Column Two-Phase. Can. J. Chem. Eng. 1974, 52, 739–749. (16) Rao, N. V. R.; Srinivas, N. S.; Varma, Y. B. G. Dispersed Phase Holdup and Drop Size Distributions in Reciprocating Plate Columns. Can. J. Chem. Eng. 1983, 61, 168–177. (17) Bensalem, A. K. Hydrodynamics and Mass Transfer in a Reciprocating-Plate Extraction Column. Ph. D. Thesis,Swiss Federal Inst. Tech. Zurich, 1985. (18) Kumar, A.; Hartland, S. Prediction of dispersed phase Holdup and Flooding Velocities in Karr Reciprocating Plate Extraction Columns. Ind. Eng. Chem. Res. 1988, 27, 131–138. (19) Prvcic, L. M.; Pratt, H. R. C.; Stevens, G. W. Dispersed Phase Holdup in Pulsed Perforated Plate Columns. SolVent Extract. Ion Exch. 1990, 8, 695–712. (20) Bell, R. L.; Babb, A. L. Holdup and Axial Distribution of Holdup in a Pulsed Sieve-Plate Solvent Extraction Column. Ind. Eng. Chem., Process Des. DeV. 1969, 8, 392.

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 4007 (21) Kentish, S. E.; Pratt, H. R. C.; Stevens, G. W. The Measurement of Droplet Rise Velocities within a Ku¨hni Extraction Column. Ind. Eng. Chem. 1997, 36, 4928–4933. (22) Jealous, A. C.; Johnson, H. F. Power Requirements for the Generation in Pulse Columns. Ind. Eng. Chem. 1955, 47, 1159–1166. (23) Joseph, S.; Varma, Y. B. G. A Correlation for Drop Size and Slip Velocity in Reciprocating Plate Column. Bioprocess Eng. 1998, 18, 367– 371. (24) Kumar, A.; Hartland, S. Correlations for Prediction of Mass Transfer Coefficients in Single Drop Systems and Liquid-Liquid Extraction Columns. Trans. Inst. Chem. Eng. 1999, 77, 372–384. (25) Shen, Z. J.; Rao, N. V. R.; Baird, M. H. I. Mass Transfer in a Reciprocating Plate Extraction Column-Effects of Mass Transfer Direction and Plate Material. Can. J. Chem. Eng. 1985, 63, 29–36. (26) Aravamundan, K.; Baird, M. H. I. Effects of Mass Transfer on the Hydrodynamic Behaviour of a Karr Reciprocating Plate Column. Ind. Eng. Chem. Res. 1999, 38, 1596–1604.

(27) Pratt, H. R. C.; Stevens, G. W. Generalised Deisgn Equations for Backmixed Liquid Extraction Column with Non-Linear Equilibria. Ind. Eng. Chem. Res. 1991, 30, 733–739. (28) Stella, A.; Pratt, H. R. C.; Mensforth, K. H.; Stevens, G. W.; Bowser, T. Backmixing in Karr Reciprocating-Plate Extraction Columns. Ind. Eng. Chem. Res. 2006, 45, 6555–6562. (29) Murdoch, R.; Pratt, H. R. C. Liquid-Liquid Extraction: Part VIII. The Extraction of Uranyl Nitrate in a Wetted Wall Column. Trans. Inst. Chem. Eng. 1953, 31, 307–322. (30) Pietzsch, W.; Pilhofer, Th. Calculation of the Drop Size in Pulsed Sieve-Plate Extraction Columns. Chem. Eng. Sci. 1984, 39, 961–965. (31) Boyadzhiev, L.; Spassov, M. On the size of drops in pulsed and vibrating plate extraction columns. Chem. Eng. Sci. 1982, 37, 337–340.

ReceiVed for reView November 28, 2007 ReVised manuscript receiVed February 18, 2008 Accepted February 26, 2008 IE071623P