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Ind. Eng. Chem. Res. 2008, 47, 8368–8375
Performance and Scale-up of Karr Reciprocating Plate Extraction Columns Kathryn H. Smith,† Tim Bowser,‡ and Geoffrey W. Stevens*,† Particulate Fluids Processing Centre, Department of Chemical and Biomolecular Engineering, The UniVersity of Melbourne, ParkVille, Victoria 3010, Australia, and GlaxoSmithKline, Princes Highway, Port Fairy, 3284, Australia
The hydrodynamic and mass transfer performance of Karr reciprocating plate extraction columns with varying column diameters has been presented in order to examine how column performance changes with scale. An ideal liquid system of kerosene/tributyl phosphate-phenol-water was initially studied using a 50 mm diameter Karr column. Correlations were developed to predict the dispersed phase holdup, drop size distribution, and overall mass transfer coefficient over a range of operating conditions. This was followed by column performance studies using a phenolic alkaloid liquid system in Karr columns with diameters of 50, 100, and 300 mm. Overall results showed that there was no significant change in either the dispersed phase holdup or the mass transfer coefficient with column diameter. It was therefore concluded that overall column performance was independent of column diameter and the traditional Karr column scale-up equations were too conservative. This study also showed that factors such as droplet and plate coalescence, contamination of liquid systems, aging of column internals, and variation in physical properties can greatly influence the column’s performance and need to be carefully considered when designing a Karr column. 1. Introduction Optimal design of a solvent extraction column involves maximizing the column performance by increasing the rate of mass transfer while achieving high throughputs. It was with these ideas in mind that Van Dijck1 proposed that the volumetric efficiency of a perforated plate column could be improved by either pulsing the liquids or reciprocating the plates. This led to the development of the Karr column2 in 1959, which has found wide application in a number of industries including the pharmaceutical, petrochemical, metallurgical, and chemical industries.3 Although the Karr column has been used effectively for a number of separation processes, there is still a need for a greater understanding into the design of the column, in particular the change in column performance with scale. Numerous studies have been performed to analyze the hydrodynamic and mass transfer performance of the Karr column. These studies have generally concentrated on developing correlations that can predict the dispersed phase holdup, drop size distribution, axial dispersion characteristics and mass transfer coefficients. However, these correlations tend to only be accurate for the systems and geometries for which they were developed. Stella et al.4 summarized the correlations available for predicting the hydrodynamic and mass transfer characteristics in a Karr column. A summary of the correlations available for predicting the backmixing coefficient of the continuous phase in a Karr column has also been presented by Stella et al.5 Limited data are available from the literature on the performance of large-scale Karr columns, and little research has been performed on the semiempirical scale-up procedure presented by Karr and Lo.6 This method involves using correlations to predict stage requirements and operating conditions as well as performing experiments to determine equilibrium data and settling characteristics. A pilot-scale column is then set up based on this initial information and data are collected over a wide * To whom correspondence should be addressed. E-mail: gstevens@ unimelb.edu.au. † The University of Melbourne. ‡ GlaxoSmithKline.
range of operating variables in order to determine the column’s optimal conditions, which has been defined as the maximum volumetric efficiency with optimal plate spacing.7 With the plate spacing, amplitude of reciprocation, and throughput per crosssectional area all kept constant, a set of scale-up equations developed by Karr and Lo6 are used to determine the large column diameter and frequency as follows:
( ) () ( )
(HETS)Dc2 (HETS)Dc1
)
Dc2 Dc1
Dc1 f2 ) f1 Dc2
0.38
(1)
0.14
(2)
where 1 relates to the pilot-scale column and 2 relates to the larger diameter column, Dc is the column diameter, f is the frequency of reciprocation, and HETS is the height equivalent to a theoretical stage for the desired separation. It should be noted that the exponent of 0.38 in eq 1 is based on a “difficult” high interfacial tension system of o-xylene-acetic acid-water. Lower interfacial tension systems have produced exponents in the range of 0.169-0.36,8 depending on which phase is dispersed and the direction of mass transfer, with an average value reported to be 0.25. It has been recommended that the value of 0.38 be used for safety purposes; however, experimental evidence has shown that this can be very conservative leading to an oversized column and an unnecessarily large capital. These equations are also limited by the fact that very little large diameter column axial dispersion data are available. Traditionally columns were designed based on simple plug flow behavior, which does not incorporate the nonideal flow effects caused by axial mixing, which results in a reduction in the concentration driving force for mass transfer and hence a reduction in extraction efficiency. Karr and Lo6 reported that the minimum HETS with respect to agitation rate increased with column diameter, with the cause believed to be axial mixing. Other factors not considered in this scale-up procedure that can influence the performance of larger scale columns include changes in flow patterns, density gradients, and contamination
10.1021/ie800581u CCC: $40.75 2008 American Chemical Society Published on Web 10/04/2008
Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8369
Figure 3. Comparison of Kumar and Hartland11 correlation with measured holdup data for the phenol system.
Figure 1. Configuration of the 50 mm diameter Karr column using the phenol system.
Figure 4. Drop size distribution as a function of agitation rate and mass transfer direction for the phenol system. Table 1. Summary of Column Specifications column column 1 specification symbol (Melb Uni)
Figure 2. Experimental dispersed phase holdup as a function of agitation rate and mass transfer direction for the phenol system (open symbols, c-d; filled symbols, d-c).
of column internals or fluids leading to changes in droplet coalescence, which are all known to reduce overall column performance. It is therefore evident that further investigation is required into the performance of large-scale Karr columns and the corresponding scale-up procedure also needs further examination to ensure that optimal design and operation can be achieved with a Karr column. 2. Scope of Study This study aims to examine how the performance of a Karr reciprocating plate extraction column changes with scale. In order to do this, the hydrodynamic performance will be investigated by measuring the dispersed phase holdup, drop size distribution, and flood point characteristics. The column’s mass transfer efficiency will also be determined using a backflow model which provides mass transfer performance parameters that incorporate the nonideal flow effects of axial mixing. In order to see how the performance changes with scale, three
column diameter effective column height effective column volume number of plates plate thickness plate material perforation diameter hole pitch (triangular) plate spacing plate free area
column 2 (GSK)
column 3 (GSK)
column 4 (GSK)
Dc Hc
50 mm 1.3 m
50 mm 1.95 m
100 mm 5m
300 mm 6.6 m
Ve
2725 cm3
3828 cm3
39 270 cm3 360 500 cm3
N E dh
27 3 mm nylon 12.7 mm
35 80 5 mm 5 mm polypropylene HDPE 12.5 mm 12.5 mm
80 5 mm HDPE 12.5 mm
P
17 mm
17 mm
17 mm
17 mm
hc S
50 mm 0.452
50 mm 0.469
50 mm 0.531
50 mm 0.531
different sized diameter columns will be studied using two liquid systems. Experimental results will be compared with correlations from the literature, and models will be developed so that the performance of each system can be accurately predicted. Finally, the hydrodynamic and mass transfer performance will be examined to see how it changes with column diameter. 3. Experimental Section Four Karr columns and two liquid systems were investigated in this study. Initially a phenol system was studied using a 50 mm diameter column. This was followed by experiments using
8370 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 Table 2. Test Systems and Associated Physical Properties system number, name, and mass transfer direction
phase continuous, c dispersed, d solute physical properties at 21 °C dispersed phase density, Fd (kg/m3) continuous phase density, Fc (kg/m3) dispersed phase viscosity, µd (Pas) continuous phase viscosity, µc (Pa s) interfacial tension, γ (mN/m)
1 (phenol extraction, d f c)
2 (phenol stripping, c f d)
3 (alkaloid system, d f c)
10% v/v tributyl phosphate/kerosene (Shellsol 2046) water phenol
10% v/v tributyl phosphate/kerosene (Shellsol 2046) 0.1 M NaOH phenol
organic solvent mixture
997 820 0.0010 0.0019 14.99
1007 820 0.0010 0.0019 11.17
1017 835 0.00114 0.00119 6.35
rich extract phenolic alkaloid
Table 3. Range of Operating Parameters Studied for Each Column column detail column diameter frequency amplitude pulsation rate dispersed phase velocity continuous phase velocity phase flow ratio, Vc/Vd
symbol Dc f A Af Vd Vc R
column 1
column 2
column 3
50 mm 50 mm 100 mm 1.0-5.0 Hz (60-300 rpm) 0.75-2.4 Hz (45-144 rpm) 0.83-1.25 1.2 cm 1.0 cm 1.0 cm 1.20-6.00 cm/s 0.75-2.40 cm/s 0.83-1.25 0.04-0.71 cm/s 0.04-0.51 cm/s 0.21-0.44 0.17-1.42 cm/s 0.17-0.66 cm/s 0.29-0.88 0-4.0 0.8-6.0 0.8-3.1
a phenolic alkaloid liquid system in Karr columns with diameters of 50, 100, and 300 mm. 3.1. Equipment. The plate spacing and geometry, including hole size, plate thickness, and free area, were kept constant in all columns regardless of diameter. All columns were made of glass, and the main body was bound by an upper T-section for the continuous phase outlet and below by an expanded glass hemispherical section which provided an area for the settling of the dispersed droplets before exiting from the bottom of the column. All columns contained a stack of plastic plates and were operated with the dispersed aqueous phase entering from a distributor at the top of the column and the continuous organic phase entering through a distributor at the bottom of the column. The interface was maintained below the plate stack in all columns to ensure that the continuous organic phase wet the plastic plates. The plates were reciprocated using a variable speed motor at the top of the column, and the amplitude of reciprocation was set via an adjustable yoke which was coupled to this motor. The general column arrangement is shown in Figure 1, and further details on each column’s specifications have been summarized in Table 1. 3.2. Liquid Systems. Two different liquid systems were investigated in this study. Using a 50 mm diameter column, the system 10% v/v tributyl phosphate/kerosene (c)-phenolwater (d) was studied for both directions of mass transfer (i.e., d f c and c f d) and in the absence of mass transfer. This phenol system was chosen to mimic that used industrially by GlaxoSmithKline, where a phenolic alkaloid is extracted from an aqueous phase into an organic solvent phase. The alkaloid system was studied using laboratory-, pilot-, and productionscale columns (all of varying diameter as described in Table 1). A summary of the physical properties of each liquid system has been provided in Table 2. 3.3. Procedures. 3.3.1. Dispersed Phase Holdup. Holdup measurements were obtained using the drainage technique developed by Gayler, Roberts, and Pratt.9 In order to use this method, the desired flow rates, amplitude, and frequency were set and the column was brought to steady state by maintaining the interface at a fixed position below the plate stack. The inlet and outlet valves were then shut simultaneously and the dispersed phase was allowed to disengage to the interface at the bottom of the column. A period of 5-10 min was allowed
column 4
300 mm Hz (50-75 rpm) 0.92-1.08 1.0 cm cm/s 0.92-1.08 cm/s 0.39-0.59 cm/s 0.20-0.28 1.5-2.5
Hz (55-65 rpm) cm/s cm/s cm/s
for the dispersed phase to settle. Holdup was then obtained by collecting and measuring the volume of dispersed phase into a measuring cylinder, via a drainage valve, until the interface was at its initial position. For the 300 mm diameter column where large volumes of solvent were present, the change in interface height between operation and after settling was measured and then converted into the corresponding volume to determine holdup. 3.3.2. Drop Size Distribution. Drop size distribution was examined using a square viewing box made of Perspex which was placed approximately halfway down the column. The box was covered with opaque paper and contained openings for a light source and for viewing the drops. The box was filled with water to prevent refraction effects caused by the curvature of the glass column wall. The drops were photographed using a Nikon Coolpix 4500 digital camera. Drop dimensions were then determined using the software package Coral Draw 8. This involved magnifying the images so that x-y coordinates and hence drop diameters could be accurately determined for each drop. For elliptical drops both the vertical and horizontal axes were measured. Drop sizes were converted to absolute dimensions by comparing measured values with plate thickness. Approximately 150 drops per photo were analyzed. Drops were then classified into size intervals, and the Sauter mean drop diameter, d32, was determined. Droplet size was only measured for the phenol system in the 50 mm diameter column due to experimental restrictions involved with the operating alkaloid plant. 3.3.3. Mass Transfer Performance. 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, physical properties, and hydrodynamic data.10 The range of operating parameters studied for each column is given in Table 3.
Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8371
Figure 5. Comparison of Kumar and Hartland12 correlation with measured drop size distribution data for the phenol system.
Figure 6. Experimental overall mass transfer coefficient, kox, as a function of continuous phase velocity and agitation rate, with ) 0.002 12 m/s for the phenol system.
Figure 7. Comparison of Stella et al.4 correlation and measured mass transfer coefficient for the phenol system.
4. Results and Discussion 4.1. Phenol System. The hydrodynamic and mass transfer performance has been studied over a wide range of operating conditions for the phenol system using a 50 mm diameter Karr column. 4.1.1. Dispersed Phase Holdup. Dispersed phase holdup was found to increase with increases in dispersed phase velocity and agitation rate, but was independent of the continuous phase velocity. Mass transfer direction was also found to play an important role in determining holdup for the phenol system.
Figure 8. Experimental holdup as a function of dispersed phase velocity and plate age for the 50 mm diameter GSK column with Vc ) 0.0040 m/s.
Figure 9. Experimental holdup as a function of agitation rate for the alkaloid system with column diameters of 50, 100, and 300 mm.
Figure 10. Comparison of the correlation developed for this study with measured mass transfer coefficient for the alkaloid system.
When phenol was transferred from the dispersed phase to the continuous phase, lower holdup was measured as compared to the opposite direction or in the absence of mass transfer. Experimental holdup results from this column are shown in Figure 2. Numerous correlations from the literature were considered for predicting holdup in this column; however, it was found that most models tended to be limited to the system and geometry for which they were developed. Correlations which did not incorporate the effects of mass transfer, especially in the direction from the dispersed phase to the continuous phase,
8372 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008
were not appropriate for predicting holdup in the current column. For the phenol system the correlation presented by Kumar and Hartland11 was found to provide the best fit, with an average deviation between the experimental and predicted values being 23% (refer to Figure 3). This empirical equation was based on the dispersed and continuous phase velocities, agitation rate, and physical properties of the system with varying constants for the differing directions of mass transfer as follows: xd ) [k1 + k2(Af)3]Vd0.81(Vc + Vd)0.32∆F-0.98
(3)
where for no mass transfer: k1 ) 3.87 × 103, k2 ) 3.71 × 107 for c f d transfer: k1 ) 3.25 × 103, k2 ) 7.54 × 107 for d f c transfer: k1 ) 2.14 × 103, k2 ) 1.65 × 107 4.1.2. Drop Size Distribution. Drop size distribution was also examined over a range of operating conditions for the phenol system, with results showing that the Sauter mean diameter decreased with an increase in agitation rate but was independent of phase flow rates. Mass transfer of phenol from the dispersed phase to the continuous phase resulted in a larger drop size distribution due to the Marangoni effect, which occurs due to changes in local interfacial tension resulting in droplet coalescence. Experimental results are shown in Figure 4. Drop size distribution results were found to be best predicted by the correlation presented by Kumar and Hartland,12 with an average deviation of 23% (refer to Figure 5). This correlation incorporated agitation rate, mass transfer direction, and the physical properties of the system, which were most important in the current study, as follows: d32 ) CΨSn
{[
1 γ CΩ ∆Fg
0.5 2
( )]
where13 ψ)
+
[
( ) ]}
1 CΠψ-0.4
γ Fc
CΨ(c-d) ) 0.95,
CΨ(d-c) ) 1.48, CΨ(No MT) ) 1.0, CΩ ) 1.30, CΠ ) 0.67,
This correlation was also used for predicting the drop size distribution in the alkaloid columns. 4.1.3. Mass Transfer Performance. Mass transfer performance has been examined using the backflow model. Stella et al.4 described the use of this model for a Karr column using a similar phenol system. In the current study dispersed phase axial mixing was assumed to be negligible, with the continuous phase backmixing coefficient predicted using the correlation presented by Stella et al.5 Mathematica software was used to solve the material balance equations along with measured physical property and equilibrium data and the correlations developed for predicting holdup, drop size, and the backmixing coefficient of the continuous phase. The main operating parameters found to affect the column’s mass transfer performance were the agitation rate and phase flow rates. In particular, increases in the continuous phase velocity and agitation rate led to higher overall mass transfer coefficients (refer to Figure 6). Improved mass transfer performance was also observed when mass transfer occurred from the continuous phase to the dispersed phase, which is in agreement with the higher holdup present under these conditions. Numerous models for predicting the overall mass transfer coefficient in a Karr column were compared to experimental data. The best fit was provided by the models presented by Harikrishnan et al.14 and Stella et al.4 Due to the similar liquid systems and column geometry, the correlation presented by Stella et al.4 was refitted to the experimental data of this study, providing an average deviation of 21% (refer to Figure 7). This correlation incorporated the effects from phase flow rates, agitation rate, and physical properties as follows:
[
-1/2
0.6 2
(4)
( )
2π2 1 - S2 ( )3 Af 3 h C 2S2 c 0
and
n ) 0.5
koxR ) Vcn(Af) 1 + 0.035ψ0.40
()] Vc Vd
0.1
(5)
with n ) 0.30 for c f d transfer and n ) 0.41 for d f c transfer in a 50 mm diameter Karr column. 4.2. Alkaloid System. Dispersed phase holdup and mass transfer performance was also studied over a wide range of operating conditions for the alkaloid system using Karr columns of diameters 50, 100, and 300 mm.
Table 4. Refitted Constants for eqs 6-11 and Corresponding AARE Values refitted constants for Kumar and Hartland15 holdup correlation
GSK column
agitation rate, Af (m/s)
AARE (%)
CΠ ) 0.13, CΨ ) 4.8, CΓ ) 6.87, n1 ) 1, n2 ) 0.84, n3 ) 3.74, n4 ) -0.92, n5 ) n6 ) 0, n7 ) -0.48
50 mm diameter (old plates)
0.010
17.2
0.015 0.020 0.024
9.3 14.1 17.1 14.3a 4.5
CΠ ) 0.13, CΨ ) 2.0, CΓ ) 6.87, n1 ) 1, n2 ) 0.84, n3 ) 3.74, n4 ) -0.92, n5 ) n6 ) 0, n7 ) -0.48
50 mm diameter (new plates)
0.008 0.010 0.015 0.018 0.020 0.024
a
Overall values.
100 mm diameter
0.011 0.013 0.014
300 mm diameter
0.009 0.011
12.5 10.2 25.7 35.6 33.3 20.3a 17.7 22.3 15.7 18.6a 12.3 21.6 19.3a
Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008 8373
4.2.1. Dispersed Phase Holdup. As with the phenol system, holdup was found to increase with increases in dispersed phase velocity and agitation rate. However, wettability of the plate surface was also found to greatly influence the dispersed phase holdup in the alkaloid columns. The 50 mm diameter column was found to contain contaminated plastic plates, which caused the dispersed aqueous phase to wet the plates. This caused the dispersed phase to pass through the column in streams clinging to the column shaft and accumulating around the plate surface, resulting in large irregularly shaped drops with long residence times. This observation was also likely to be influenced by Marangoni effects with mass transfer occurring from the dispersed phase to the continuous phase. Higher holdup and lower flooding velocities were observed under these conditions. Cleaning the plates did not change the hydrophilicity of the plastic, so new plates were installed which resulted in a more even drop distribution and lower holdup at reduced throughputs when compared to the contaminated plates (refer to Figure 8). Although the cause of contamination is unknown, it was clear that a change in the wettability of the plate material led to a change in holdup which in turn influenced the interfacial area for mass transfer and column throughput. Holdup results from the 100 and 300 mm diameter columns showed values and trends similar to those seen with the 50 mm diameter column (refer to Figure 9). This indicated that there were no significant changes in dispersed phase holdup with column diameter. None of the correlations in the literature were appropriate for predicting holdup in the alkaloid system, which was likely to be due to the change in wettability of the plastic plate surface, Marangoni effects, and physical properties which were quite different from most ideal test systems. It was decided to redevelop a correlation for predicting dispersed phase holdup in the alkaloid columns which could also be used for the phenol system. The main parameters found to influence holdup in the alkaloid columns were the dispersed phase flow rate, agitation rate, mass transfer direction, system physical properties, and wettability of the plate material. The most appropriate correlation presented in the literature that incorporated these parameters was the Kumar and Hartland15 model: xd ) ΠΦΨΓ
(6)
where Π allowed for the effect of power input per unit mass, ψ: Π ) CΠ +
[( )] ψ Fc g gγ
1/4 n1
(7)
The power input per unit mass, ψ, incorporated the effect of agitation rate and was defined using the equation presented by Hafez and Baird:13 ψ)
2π2(1 - S2)(Af)3 3hcC02S2
(8)
Φ allowed for the effect of phase flow rates, Vd and Vc:
[( )] [ ( )]
Φ ) Vd
Fc gγ
1/4 n2
exp n3Vc
Fc gγ
1/4
(9)
Ψ allowed for the effect of physical properties and included the viscosity of water as a dummy variable to correctly allow for the effect of µd on xd: Ψ ) CΨ
( )( ) ∆F Fc
n4
µd µw
n5
(10)
Γ allowed for the geometric characteristics of the column:
[( )]
Fcg 1/2 n7 (11) γ However, the values of the constants and indices given by Kumar and Hartland15 for the Karr column were not applicable to this study. In order to fit this correlation to the alkaloid columns, the constant which allowed for the variations in physical properties of the system, CΨ, was refitted to the current data. The resulting constants and corresponding errors have been summarized in Table 4. This refitted version of Kumar and Hartland’s model15 predicted the experimental holdup data within 19% for all columns. Results from Figure 10 and Table 4 showed that when plate wettability was not an issue, dispersed phase holdup did not change with scale, and it was concluded that holdup was independent of column diameter. 4.2.2. Mass Transfer Performance. The mass transfer performance was also examined in each column using the same method as described with the phenol column. As seen with the phenol system, an increase in the continuous phase velocity and agitation rate led to higher overall mass transfer coefficients in all alkaloid columns. Poor mass transfer performance was observed with the alkaloid system in the 50 mm diameter column when the plates were wetted by the dispersed aqueous phase due to a change in the wettability of the plastic surface. Overall lower mass transfer rates were observed with the alkaloid columns when compared to the phenol system. This was likely to be influenced by the low interfacial tension and tendency for contamination in the alkaloid liquid system. Due to these physical properties, the system was sensitive to operational changes, had a lower flood point, and was prone to carryover and difficult emulsions. However, overall there were no significant changes in mass transfer performance with column diameter when plate contamination was not an issue. Numerous models for predicting mass transfer performance from the literature were compared to the current data. It was found that the model developed for the volumetric mass transfer coefficient in a Karr column by Stella et al.4 showed the most promise (refer to eq 5). However, this model reported constants which varied significantly depending on the diameter of the column. Results from the current study do not agree with this observation as there were no significant changes in mass transfer performance when the column diameter was increased. Therefore, the constant n in eq 5 was refitted to the alkaloid columns. It was found that the same constant (n ) 0.30) was applicable to both the 100 and 300 mm diameter columns, when plate wettability was not an issue. However, in the 50 mm diameter alkaloid column, the mass transfer performance was affected by the change in wettability of the plate surface and hence a larger constant (n ) 0.48) was required to fit the data. These results show that, as with the dispersed phase holdup, there was no significant change in mass transfer performance with column diameter. However, plate wettability and changing physical properties do influence both holdup and mass transfer performance and must be considered when examining column performance. This mass transfer model, represented by eq 5 and the refitted values for the constant n, provided the best fit for the current data with an overall AARE of 24% (refer to Figure 10). 4.3. Recommended Scale-up Procedure. Results from this study have shown that the dispersed phase holdup, mass transfer coefficient, and specific interfacial area for mass transfer are independent of column diameter. This leads to the conclusion that the overall performance of the Karr column is independent Γ ) CΓSn6 hc
8374 Ind. Eng. Chem. Res., Vol. 47, No. 21, 2008
of column diameter and the scale-up procedure presented by Karr and Lo6 is therefore too conservative. The scale-up equations should be as follows: (Hox)Dc2 (Hox)Dc1
( ) ( ) ( ) ( ) )
Dc2 Dc1
Dc1 f2 ) f1 Dc2
0
0
*
*
Dc2 Dc1
Dc1 Dc2
0.38
(12)
0.14
(13)
where Hox is the overall height of a transfer unit which was determined by solving the backflow model equations for backmixed liquid extraction columns with nonlinear equilibria.10 The implications of the scale-up procedure recommended by this study are a reduction in the height of a transfer unit and increased agitation rates in larger columns. The equations presented by Karr would recommend a higher height of transfer unit and lower agitation rate when the diameter of the column is increased. This was not found to be the case in the current study. 5. Conclusions This study has examined the hydrodynamic and mass transfer performance in columns with diameters of 50, 100, and 300 mm using two liquid systems. The dispersed phase holdup, mass transfer coefficient, and specific interfacial area for mass transfer were found to be independent of column diameter. Therefore, the overall performance of the column was independent of column diameter and the scale-up procedure presented by Karr and Lo6 is too conservative. This study also highlighted the importance of considering coalescence effects in the design of Karr columns. This included mass transfer induced coalescence seen when solute transfer occurred from the dispersed phase to the continuous phase (Marangoni effects) as well as coalescence of the dispersed phase with the column internals due to changes in the wettability of the plate surface. Both the dispersed phase holdup and mass transfer performance were found to be greatly influenced by aging or contamination of the plastic plate surface. The cause of this contamination and how it is affecting Karr column performance is a subject for further investigation. The physical properties of the liquid system and type of column internals have also been shown to be very important when considering these coalescence effects. Finally, this study has provided valuable information on the performance of large-scale Karr columns for which there are currently limited results. It also confirms the importance of pilot testing with actual plant liquids over a period of time for accurate results in the scale-up of Karr columns. The use of correlations for predicting column performance should be applied with caution as many correlations are only accurate for the systems and geometries for which they were developed. In completing this study, it was concluded that there were no major changes in the hydrodynamic or mass transfer performance with an increase in column diameter. 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.
Nomenclature a ) interfacial mass transfer area per unit volume, m2/m3 ) m-1 A ) plate amplitude, peak to peak, m AARE ) average absolute relative error, % Af ) agitation rate, m/s CΨ, CΠ, CΩ, n ) dimensionless coefficients defined in eq 4 c f d ) mass transfer in the direction of continuous to dispersed phase C0 ) orifice coefficient ()0.7) d f c ) mass transfer in the direction of dispersed to continuous phase d32 ) Sauter mean droplet diameter, m Dc ) column diameter, m f ) frequency, s-1 g ) acceleration due to gravity, m/s2 hc ) height of compartment (i.e., plate spacing), m HETS ) height equivalent to a theoretical stage, m Hok ) height of an overall transfer unit based on phase k, m k1, k2 ) dimensionless constants defined in eq 2 kk ) mass transfer coefficient for phase k, m/s kok ) overall mass transfer coefficient based on phase k, m/s S ) free area of perforated plate, m2 Vk ) superficial velocity of phase k in column, m/s xd ) dispersed phase holdup Greek Symbols Fk ) density of phase k, kg/m3 ∆F ) absolute density difference, kg/m3 γ ) interfacial tension, N/m µk ) viscosity of phase k, Pa s ) kg/ms3 ψ ) power dissipated per unit mass, m2/s3, defined in eq 8 Π, Φ, Ψ, Γ ) dimensionless coefficients defined in eqs 7, 9, 10, and 11 Subscripts c ) continuous phase d ) dispersed phase k ) c or d phase; or x or y phase 1 ) pilot-scale column 2 ) larger column
Literature Cited (1) Van Dijck, W. Tower with Internal Perforated Plate Suitable for Extracting Liquids by Treatment with other Liquids and for similar Concurrent Processes. U.S. Patent 2,011,186, 1935. (2) Karr, A. E. Performance of a Reciprocating Plate Extraction Column. AIChE J. 1959, 5, 446–452. (3) Mohanty, S. Modeling of liquid-liquid extraction column: A review. ReV. Chem. Eng. 2000, 16 (3), 199–248. (4) Stella, A.; Mensforth, K. H.; Bowser, T.; Stevens, G. W.; Pratt, H. R. C. Mass Transfer Performance in Karr Reciprocating Plate Extraction Columns. Ind. Eng. Chem. Res. 2008, 47 (11), 3996–4007. (5) 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. (6) Karr, A. E.; Lo, T. C. Performance and scale-up of a reciprocatingplate extraction column. Proceedings International SolVent Extraction Conference; 1971; Vol. 1, pp 299-320. (7) Karr, A. E. Design, Scale-up and Applications of the Reciprocating Plate Extraction Column. Sep. Sci. Technol. 1980, 15, 877–905. (8) Lo, T. C.; Baird, M. H. I.; Rao, N. V. R. The Reciprocating Plate ColumnsDevelopment and Applications. Chem. Eng. Commun. 1992, 116, 67–88. (9) Gayle, R.; Roberts, N. W.; Pratt, H. R. C. Liquid-Liquid Extraction: Part IV. A Further Study of Holdup in Packed Columns. Trans. Instn. Chem. Engrs. 1953, 31, 57–68.
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ReceiVed for reView April 10, 2008 ReVised manuscript receiVed July 22, 2008 Accepted August 12, 2008 IE800581U
