Dispersed-Phase Holdup and Characteristic Velocity in a Pulsed and

Article pubs.acs.org/IECR

Dispersed-Phase Holdup and Characteristic Velocity in a Pulsed and Nonpulsed Disk-and-Doughnut Solvent Extraction Column Yong Wang, Kathryn A. Mumford, Kathryn H. Smith, Zheng Li, and Geoffrey W. Stevens* Particulate Fluids Processing Centre, Department of Chemical and Biomolecular Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia S Supporting Information *

ABSTRACT: The dispersed-phase holdup and characteristic velocity, which are important hydrodynamic performance parameters for solvent extraction columns, were measured and compared to literature correlations under pulsing and nonpulsing conditions using a 75 mm diameter disk-and-doughnut column. The results show that the dispersed-phase holdup increased with increasing dispersed-phase flow rate, while there was no noticeable change in holdup with the continuous-phase flow rate. With increasing pulsation intensity from zero, the dispersed-phase holdup decreased at first and then increased. A minimum holdup was found in the transition from the mixer-settler to the emulsion regime, and it increased with increasing dispersed-phase velocity. The experimental holdup and minimum holdup were correlated over a range of pulsation rates to within 13.3% and 8.8%, respectively. The characteristic velocities under different pulsation conditions were calculated from the measured holdup for the pulsing conditions. The characteristic velocities decreased with increasing pulsation intensity and were correlated to within 3.5%.

1. INTRODUCTION Liquid−liquid extraction is one of the classical methods used in separation technology. Solvent extraction columns with diskand-doughnut internals (disk-and-doughnut column, DDC) have been used in a range of different industries, including the nuclear, hydrometallurgy, and chemical sectors.1 Compared to mixer-settlers, which are frequently used in the mining industry, the DDC is attractive from both safety and economic standpoints, in particular its simplicity of design, less space consumption, higher throughput, and no internal moving parts.2 In these columns, pulsing may be introduced by compressed air (pulsed disk-and-doughnut column, PDDC).2 A significant amount of research has been conducted using laboratory-scale PDDCs to investigate column performance under different operating conditions, including the pulsation rate. To date, most studies have been conducted at relatively high pulsation intensities as low pulsation intensity and nonpulsation are thought to be of little practical importance because of poor mass transfer performance.3 As a result, very few experimental data are available on the actual column performance in this operating regime. To evaluate the true PDDC performance in an industrial setting, it is important to evaluate the performance over the full range of potential pulsation conditions. Traditional parameters used to evaluate the performance of a solvent extraction column include hydrodynamics and mass transfer. The hydrodynamic parameters, such as dispersedphase holdup (xd) and characteristic velocity (V0), are important for the design of solvent extraction columns as they are related to the interfacial area for mass transfer and the flood point of the column.4 In this study, the dispersed-phase holdup and characteristic velocity were measured and compared to literature correlations over a wide range of operating conditions, including pulsing and nonpulsing © XXXX American Chemical Society

conditions, using a 75 mm diameter DDC and a H2O− Alamine−Shellsol system.

2. BACKGROUND The dispersed-phase holdup, xd, is defined as the volume fraction of the active section of the column that is occupied by the dispersed phase: v xd = d ve (1) where vd represents the volume of the dispersed phase and ve represents the total volume of the two phases for the effective length of the column. Jeong and Kim5 studied the dispersed-phase holdup in a 4.2 cm diameter and 200 cm long PDDC. The dispersed-phase holdup data were collected under different pulsation frequencies (f = 0.67, 1.0, and 1.33 Hz) and constant amplitude (A = 20 mm). The results were correlated with the column geometry, pulsing conditions, and velocity as follows: xd = (4.2 × 105)dc−0.44Af 1.28 Vd 0.93

(2)

6,7

Jahya et al. studied the dispersed-phase holdup and characteristic velocity of a 72.5 mm diameter PDDC for different extraction systems. The experiments were conducted over the following operating conditions: A = 0.5−1.5 cm, f = 0.5−2.0 Hz. The dispersed-phase holdup was predicted using the Kumar and Hartland8 correlation shown in eq 3 and the characteristic velocity shown in eq 4.7 Equation 3 can be used in nonpulsing conditions, but the parameters are dependent on Received: June 23, 2015 Revised: November 2, 2015 Accepted: December 9, 2015

A

DOI: 10.1021/acs.iecr.5b02293 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

intensity. Three operational regions, described as the mixersettler, transition, and emulsion regions, were observed. The dispersed-phase holdup was predicted using an empirical model (eq 6; the parameters are shown in Table S2 in the see Supporting Information). However, it should be noted that eq 6 cannot be used in nonpulsing conditions.

the region of operation and vary with scale up of the column. Equation 4 was found to fit the data well, but it cannot be applied to nonpulsing conditions. xd = k1e[k 2 |Af − (Af )m |]Vd 0.86(Vc + Vd)0.28 Δρ−0.30 ρd−0.93 μd 0.77 e−0.56hp−0.56

(3)

k6 k5 k4 4 ⎡ (Af )4 ρ ⎤k 2 ⎛ V 4ρ ⎞k3⎛ Vd ⎞ ⎛ Δρ ⎞ ⎛ μd g ⎞ d c c ⎥ ⎜ ⎟ ⎟ ⎜1 + ⎟ ⎜⎜ ⎟⎟ ⎜ xd = k1⎢ ⎢⎣ gγ ⎥⎦ ⎜⎝ gγ ⎟⎠ ⎝ Vc ⎠ ⎝ ρc ⎠ ⎜⎝ ρc γ 3 ⎟⎠

where ⎛ γeΔρ0.25 ⎞0.33 ⎟ (Af )m = (9.69 × 10 )⎜⎜ 0.75 ⎟ ⎝ μd ⎠ −3

⎞k 2 ⎛ 2

⎛d A ρ g ⎞ ⎛ γ ⎞⎛ ρ γ daρ γ ⎞ V0 = k1⎜ c ⎟ ⎜⎜ c ⎟⎟ ⎜⎜ ⎟⎟⎜⎜ c 5 ⎟⎟ ⎜⎜ c ⎟⎟ ⎝ da ⎠ ⎝ γ ⎠ ⎝ μc ⎠⎝ φμc ⎠ ⎝ μc ⎠ k3

4 ⎞k4 ⎛

⎛ Δρ ⎞k 7 ⎛ μ ⎞k8 ⎜⎜ ⎟⎟ ⎜⎜ d ⎟⎟ ρ ⎝ c ⎠ ⎝ μc ⎠

(6) 11

k5

⎛ μ 4g ⎞ ⎜⎜ c ⎟⎟ ⎝ (Δρ)γ ⎠

Kumar investigated the dispersed-phase holdup in a 25 mm diameter PDDC for a HNO3−TBP−paraffinic hydrocarbon system. The experimental amplitude was between 1.04 and 4.6 cm, and the frequency was between 1 and 2 Hz. The data were predicted using eq 5 with regressed parameters. More recently, the dispersed-phase holdup was studied by Liu12 in an annular PDDC under Af from 0.003 to 0.020 m/s. The experimental data were also predicted using eq 5 with the regressed parameters. Recently, a number or PDDC columns have been operating with no pulsation. All of the data described above and all of the correlations have pulsation. This investigation is to examine which of these correlations is most appropriate and to extend it to the case of no pulsation.

k6

(4)

where φ=

π 2(1 − ε 2) (Af )3 2ε 2C0 2hc

and k1−k8 can be found in Table S1 (see the Supporting Information). Delden9 examined the hydraulic characteristics of a 40 mm diameter PDDC for the caprolactam−toluene system. The dispersed-phase holdup data were obtained in the operational range of A = 5.8−18.5 mm and f = 1.15−2.49 Hz. Results were predicted using the unified holdup correlation (eq 5), which was proposed by Kumar and Hartland4 with the new regressed parameters.

xd = ΠΦψ Γ

3. EXPERIMENTAL SECTION 3.1. Materials. The organic phase used in this study was 3 vol % Alamine 336 (tri-n-octylamine), supplied by BASF, and 1 vol % isodecanol, supplied by ExxonMobil, in Shellsoll 2046, supplied by Shell. The aqueous phase used was tap water. The physical parameters, including densities, viscosities, and interfacial tensions, for this system were analyzed and are presented in Table S3 (see the Supporting Information). 3.2. Equipment. The pilot-scale PDDC7 used in this study consists of a 1.0 m long QVF precision bore glass column with an internal diameter of 72.5 mm. A t-piece is located on top of the main column section to act as the organic phase outlet. Below the main column an expanded glass section increases the column internal diameter to 100 mm and encloses the stainless steel (SS) distributor. It is supported by an SS conical adapter which reduces the diameter to 50 mm, and is supported by the piston-type pulsing unit. The piston-type pulsing unit consists of a motor, a variable-speed unit (controls the frequency), a variable eccentric drive head (controls the stroke/amplitude), a crank arm, and a plunger equipped with a Teflon cylinder and two rubber seals in an SS cylinder. The plunger is used to provide a sinusoidal motion to the fluids in the column. In the main column section, 32 pairs of disks and doughnuts made from Teflon were arranged alternately and spaced 9.5 mm apart in the column, resulting in a 19 mm compartment height. The disks were 62.4 mm in diameter, and the doughnut apertures were 36.9 mm, resulting in open free areas of 25.9% for each. The continuous and dispersed phases were pumped into the column via distributors from their SS storage tanks using two magnetically driven March pumps with flame-proof electric motors. Two rotameters with SS floats were installed in the inlet lines in parallel for each phase to control the flow rates. All experiments were completed at room temperature, which for the pilot plant facility ranged from 16 to 21 °C. 3.3. Column Operation. To start the column, the continuous-phase pump was turned on and the continuous-

(5)

where ⎡ ⎛ ρ ⎞0.25⎤n1 ε Π = CΠ + ⎢ ⎜ c ⎟ ⎥ ⎢⎣ g ⎝ gγ ⎠ ⎥⎦ ⎡ ⎛ ρ ⎞0.25⎤n2 ⎡ ⎛ ρ ⎞0.25⎤ Φ = ⎢Vd⎜ c ⎟ ⎥ exp⎢n3Vc⎜ c ⎟ ⎥ ⎢⎣ ⎝ gγ ⎠ ⎥⎦ ⎢⎣ ⎝ gγ ⎠ ⎥⎦ ⎛ Δρ ⎞n4 ⎛ μ ⎞n5 ⎟⎟ ⎜⎜ d ⎟⎟ ψ = C ψ ⎜⎜ ⎝ ρc ⎠ ⎝ μc ⎠

⎡ ⎛ ρ g ⎞0.5⎤n7 Γ = C Γe hc⎜ c ⎟ ⎥ ⎢⎣ ⎝ γ ⎠ ⎥⎦ n6⎢

ε=

2π 2(1 − e 2) (Af )3 3hcC0 2e 2

CΠ = 2.39, CΓ = 2.39, and n1−n7 = 0.34, 0.87, 3.34, −0.58, −0.08, 0, −0.12. Mostaedi et al.10 studied the effect of the pulsation intensity (Af = 0.6−3.6 cm/s) on the dispersed-phase holdup in a 76 mm diameter PDDC. The results showed that the dispersed-phase holdup increased with increasing velocity of the dispersed phase and continuous phase. The characteristic velocity also was calculated, and it decreased with an increase of the pulsation B


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Figure 1. Effect of the phase velocity on the dispersed-phase holdup under no pulsing conditions: (a) different dispersed-phase velocities; (b) different continuous-phase velocities.

Figure 2. Effect of pulsing on the dispersed-phase holdup with different dispersed-phase velocities.

piston was placed manually at the bottom and top positions in the column. The frequency was measured by a portable noncontact and reflective-type digital tachometer, Digitech QM 1448. Holdup was measured by the drainage technique as described by Gayler and Pratt.13 Once steady-state conditions were reached and the interface was at its desired position, the aqueous and organic flows into and out of the column were stopped by closing the inlet and outlet valves simultaneously. In this study, the droplets (aqueous dispersed) were allowed to settle, and the column was drained to bring the interface back

phase velocity was set at the desired value using a rotameter. The dispersed-phase pump was then turned on, and the flow rate was gradually increased until the desired value was achieved. The height of the interface was manually controlled via a valve on the aqueous outlet. The steady-state condition was defined as when there was no change in the solute concentration in two consecutive samples. The column was operated over a range of operating conditions as shown in Table S4 (see the Supporting Information). The stroke (amplitude peak to peak) was determined by measuring the liquid−liquid interface displacement when the C


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Figure 3. Effect of pulsing on the dispersed-phase holdup with different continuous-phase velocities.

dispersed phase forms large droplets, and these large droplets tend to stay on the plates, which increases the holdup of the column. When pulsation is introduced into the system, the large droplets are driven from the plates and the residence time is decreased. Thus, the dispersed-phase holdup decreases with an increase of the pulsation intensity. The minimum holdup corresponds to the transition from the mixer-settler to the emulsion regime. From the minima, increasing the pulsation intensity increases the inertial and shear forces on the droplets, which enhances droplet breakage. As the pulsation intensity is increased above a critical value, holdup in the PDDC begins to increase significantly. This is primarily due to the reduction of the droplet diameter, leading to a longer residence time for the dispersed phase,3 and hence increased holdup. The influence of the pulsation intensity with different amplitudes but the same dispersed- and continuous-phase velocities is also shown in Figure 2. It can be seen that, with the same velocity of the two phases, the dispersed-phase holdup obtained under different amplitudes has similar trends and values in all pulsation intensity regions. This indicates that the holdup is not affected by the variation of the amplitude (A) but the product of the amplitude and frequency (Af). Figure 3 shows the effects of the pulsation intensity on the dispersed-phase holdup with different continuous-phase velocities. The results indicate that the influence of the pulsation intensity on the dispersed-phase holdup is similar to that observed in Figure 2. Unlike that observed in Figure 2, the variation of the continuous-phase velocity does not have such an obvious impact on the holdup value at the same pulsation intensity. 4.1.3. Minimum Dispersed-Phase Holdup. The relationship between the minimum dispersed-phase holdup and the

to its original height. The volume of the dispersed phase was then used to calculate the holdup, xd, using eq 1.

4. RESULTS AND DISCUSSION 4.1. Dispersed-Phase Holdup. 4.1.1. Nonpulsing Conditions. The effects of the continuous- and dispersed-phase velocity on the dispersed-phase holdup were studied under nonpulsing conditions. The dispersed-phase velocity was varied from 4.4 × 10−4 to 3.6 × 10−3 m/s, and the continuous-phase velocity was varied from 2.6 × 10−4 to 3.5 × 10−3 m/s. Figure 1a shows that the dispersed-phase holdup increased with an increase of the dispersed-phase velocity, while Figure 1b shows that there was no noticeable trend with the continuous-phase velocity. 4.1.2. Pulsing Conditions. The effect of the pulsation intensity (at the same amplitude) on the dispersed-phase holdup was studied with varying velocities of the two phases. The results are shown in Figures 2 and 3. It can be seen from Figure 2 that the dispersed-phase holdup is relatively high at nonpulsing conditions (Af = 0). Under the same pulsation intensity, a higher dispersed phase velocity results in a higher dispersed-phase holdup. With a further increase of the pulsation intensity, the dispersed-phase holdup initially decreased before increasing. The minimum holdup value is found in the position of Af = 0.008−0.012 m/s for all dispersed-phase velocity conditions, with higher dispersed-phase velocities occurring at lower Af positions of minimum holdup and vice versa. Holdup minima have also been observed in other pulsed extraction columns with low open areas.3,14 The holdup characteristics of these types of columns are often described by a two-zone model: mixer-settler and emulsion. The column performance is described as performing in the mixer-settler regime when the pulsation intensity is low. In this regime, the D


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Figure 4. Effect of the dispersed-phase velocity on the experimental minimum holdup (Vc = 6.25 × 10−4 m/s, Af = 0−0.023 m/s).

Table 1. Regressed Parameters in Eq 7 AARD (%) k1

k2

k3

k4

k5

k6

overall

no pulsing

mixer-settler

emulsion

1.577

64.11

0.2738

0.32

−0.98

0.18

13.3

17.3

7.5

14.8

Figure 5. Comparison of the experimental data with the predicted holdup using eq 7.

E


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Industrial & Engineering Chemistry Research dispersed-phase velocity is shown in Figure 4. It can be seen that the minimum dispersed-phase holdup increased with an increase in the dispersed-phase velocity, similar to what was seen with Figure 2. 4.1.4. Correlation for Dispersed-Phase Holdup. The correlation developed by Kumar8 based on the performance of a perforated-plate extraction column (eq 3), was used to predict experimental data in this study. Using eq 3 with the parameters provided by Kumar8 (k1 = 2.14 × 106, k2 = 44.53), the dispersed-phase holdup from the current study was calculated with large deviations (AARD (average absolute relative deviation) = 54%). To extend the applicable range to include nonpulsing conditions, the holdup correlation (eq 3) was revised to a dimensionless relationship as follows:

Table 2. Regressed Parameters in Eq 9 Prabhakar14 this work

k1

k2

k3

AARD (%)

0.7 0.95

0.375 1.29

0.1 0.32

8.8

⎛ V 4ρ ⎞k3⎛ V + V ⎞k4 ⎛ Δρ ⎞k5 d c d ⎟⎟ ⎜ c ⎟⎟ xd = k1 exp[k 2|Af − (Af )m |]⎜⎜ ⎟ ⎜⎜ γ g V ⎝ ⎠ ⎝ ρc ⎠ ⎝ ⎠ d ⎛ μ ⎞k 6 ⎜⎜ d ⎟⎟ ⎝ μc ⎠

(7)

where ⎛ γeΔρ0.25 ⎞0.33 ⎟ (Af )m = (9.69 × 10 )⎜⎜ 0.75 ⎟ ⎝ μd ⎠ −3

The constants required for this correlation were fitted by minimizing the AARD: AARD =

1 n

n

∑ 1

Figure 6. Comparison of the experimental data with the predicted holdup by eq 9.

|predicted value − experimental value| experimental value

minimum holdup under different dispersed-phase velocities in the PDDC can be predicted well using eq 9 with new parameters (AARD = 8.8%). 4.2. Characteristic Velocity. The characteristic velocity is identified as the mean relative velocity of the droplets extrapolated to zero flow rates. It is very useful for relating the dispersed-phase holdup and phase flow rates.15

(8)

× 100

where n is the number of data points. Using eq 7, the calculated pulsation intensity at the minimum holdup point, (Af)m, is equal to 0.01, which is similar to the value observed from the experimental data. The constants k1 to k6 in eq 7 for all experimental data were regressed, and the results are presented in Table 1. The comparison between the experimental data and the predicted results is shown in Figure 5. The holdup data from the PDDC used in this study can be predicted with an overall AARD of 13.3% for all operating conditions. The predicted AARDs for no pulsing, mixer-settler, and emulsion conditions are 17.3%, 7.5%, and 14.8%, respectively. Prabhakar14 also proposed a correlation to predict the minimum holdup, corresponding to the transition between the mixer-settler regime and the emulsion regime. This was correlated as follows for a counter current flow liquid−liquid system in a pulsed perforated-plate column: xd,min

⎛ V ⎞k 2 ⎛ hc 3gρd 2 ⎞ ⎟⎟ = k1Fr Ga = k1⎜ d ⎟ ⎜⎜ ⎝ ghc ⎠ ⎝ μd 2 ⎠ k2

Vs =

Vd Vc + = v0̅ (1 − xd) xd (1 − xd)

(10)

The slip velocity, Vs, was used to relate the dispersed-phase holdup to the phase flow rates. It can be seen as the difference in velocity between the two phases.16 Equation 10 can be rewritten as follows: Vd +

Vcxd = v0̅ xd(1 − xd) 1 − xd

(11)

The characteristic velocity can then be found by determining the slope of the plot of Vd + Vcxd/(1 − xd) against xd(1 − xd). Figure 7 shows the characteristic velocity plots for the presented data, and the resulting characteristic velocity values are given in Table 3. From Figure 7, it is apparent that the characteristic velocity method is applicable to the PDDC under pulsing conditions since linear plots through the origin point were obtained for all pulsating conditions. However, the method is not applicable to the nonpulsing conditions, as the fitted line does not pass through the origin. This is most likely because eq 10 is based on the slip velocity, which is a function of the holdup and characteristic velocity. Under the nonpulsing condition, some dispersed-phase droplets accumulate on the plates, resulting in a decrease in the slip velocity.

k3

k3

(9)

The characteristic length, hc, of the pulsed perforated-plate column in eq 9 is the plate perforation diameter. In the work presented here, the distance between the disk and doughnut was selected as the characteristic length of the PDDC. The minimum holdup in this study was also predicted using eq 9, and the regressed parameters are presented in Table 2 Figure 6 shows the comparison of the experimental minimum holdup data with the predicted holdup results. It can be seen that F


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Jahya7 proposed a correlation (eq 4) for predicting the characteristic velocity. The values of V̅ 0 are correlated with the physical properties of the systems and the column variables. The parameters in eq 4 are fitted using experimental data and are presented in Table S1. Figure 8 shows the comparison of the experimental characteristic velocity data with the predicted results. It can be seen that the experimental characteristic velocity in the PDDC can be predicted well within 2.4%.

6. CONCLUSIONS The main conclusions from this study may be summarized as follows: (i) The dispersed-phase holdup decreased with increasing pulsation intensity in the mixer-settler regime and increased with increasing pulsation intensity in the emulsion regime. The minimum holdup was found in the transition from the mixersettler regime to the emulsion regime. The dispersed-phase holdup of the PDDC can be predicted using eq 7 for both pulsation and no pulsation conditions to within a relative deviation of 14.8%. (ii) The minimum holdup increased with increasing dispersed-phase velocity and can be predicted well using the Prabhakar14 correlation with a relative deviation of 8.8% using new regressed parameters. (iii) The characteristic velocity approach is useful for pulsed conditions but not nonpulsed operations. The characteristic velocity decreased with increasing pulsation intensity (Af), and the correlation derived by Jahya7 presented the most suitable model with an average deviation of 3.5%.

Figure 7. Characteristic velocity plots under different pulsation intensities.

Table 3. Characteristic Velocities under Different Pulsation Intensities Af (m/s) V0 (m/s)

0.0095 0.0269

0.0119 0.0280

0.0143 0.0258

0.0166 0.0192

0.0190 0.0139

0.0214 0.0115

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The characteristic velocity is independent of the phase flow rates but dependent on the column geometry and physical properties of the system.17 It also can be observed from Figure 7 that the characteristic velocity is not affected by the continuous-phase velocity. Table 3 shows that the characteristic velocity decreased with increasing pulsation intensity (Af).

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02293.

Figure 8. Comparison between the experimental data and correlation for the characteristic velocity. G


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(4) Kumar, A.; Hartland, S. A unified correlation for the prediction of dispersed-phase hold-up in liquid-liquid extraction columns. Ind. Eng. Chem. Res. 1995, 34 (11), 3925−3940. (5) Jeong, G.; Kim, C. A study on the flow characteristics in a pulsed doughnut-disc type plate extraction column. Korean J. Chem. Eng. 1984, 1 (2), 111−117. (6) Jahya, A. Performance of the Pulsed Disc and Doghnut Solvent Extraction Column; University of Melbourne: Melbourne, Australia, 2002. (7) Jahya, A. B.; Stevens, G. W.; Pratt, H. R. C. Pulsed Disc-andDoughnut Column Performance. Solvent Extr. Ion Exch. 2009, 27 (1), 63−82. (8) Kumar, A.; Hartland, S. Prediction of dispersed phase hold-up in pulsed perforated-plate extraction columns. Chem. Eng. Process. 1988, 23 (1), 41−59. (9) van Delden, M. L.; Vos, G. S.; Kuipers, N. J. M.; de Haan, A. B. Extraction of Caprolactam with Toluene in a Pulsed Disc and Doughnut ColumnPart II: Experimental Evaluation of the Hydraulic Characteristics. Solvent Extr. Ion Exch. 2006, 24 (4), 519− 538. (10) Torab-Mostaedi, M.; Jalilvand, H.; Outokesh, M. Dispersed phase holdup in a pulsed disc and doughnut extraction column. Braz. J. Chem. Eng. 2011, 28, 313−323. (11) Kumar, R.; Sivakumar, D.; Kumar, S.; Mudali, U. K. Modeling of Hydrodynamics in a 25 mm ϕ Pulsed Disk and Doughnut Column. ISRN Chem. Eng. 2013, 2013, 547489. (12) Liu, J.-Q.; Li, S.-W.; Jing, S. Hydraulic Performance of an Annular Pulsed Disc-and-Doughnut Column. Solvent Extr. Ion Exch. 2015, 33, 385−406. (13) Gayler, R.; Pratt, H. R. C. Symposium on liquid-liquid extraction. Part II. Hold-up and pressure drop in packed columns. Trans. Inst. Chem. Eng. 1951, 29, 110. (14) Prabhakar, A.; Sriniketan, G.; Varma, Y. Dispersed phase holdup and drop size distribution in pulsed plate columns. Can. J. Chem. Eng. 1988, 66 (2), 232−240. (15) 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. (16) Gayler, R.; Roberts, N. W.; Pratt, H. R. C. Symposium on liquidliquid extraction. Part IV. Further study of hold-up in packed columns. Trans. Inst. Chem. Eng. 1953, 31, 57−68. (17) Christo, R.; Shen, S.; Stevens, G. W. Effect of plate material on dispersed-phase holdup in a Karr reciprocating plate column. Solvent Extr. Ion Exch. 2011, 29 (5−6), 800−822.

Tables giving the regressed parameters for eqs 4 and 6, physical properties of the aqueous and organic phases, and range of operating conditions studied (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel: +61 3 83446621. E-mail: [email protected]. Funding

We acknowledge the funding provided by the Australian Research Council through Linkage Grant LP130100305 and BHP Billiton, Olympic Dam, for this project, and also thank the Particulate Fluids Processing Centre for the resources provided for this project. Notes

The authors declare no competing financial interest.

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NOMENCLATURE A = stroke (twice the wave amplitude), m AARD = average absolute value of the relative deviation C0 = orifice coefficient (=0.6) dc = column diameter, m da = doughnut aperture diameter, m dp = plate spacing, m e = fractional free cross-sectional area [(da/dc)2], dimensionless f = frequency, Hz Fr = Froude number (Vd/ghc) g = acceleration due to gravity, m/s2 Ga = Galileo number (hc3gρd2/μd2) hc = characteristic length (PDDC, plate space; pulsed perforated-plate column, plate perforation diameter), m hp = plate spacing, m k = parameter in the equations, dimensionless n1−n7 = indexes, dimensionless vd = volume of the dispersed phase for the effective length of the column vt = total volume of the two phases for the effective length of the column V = superficial velocity, m/s xd = volume fraction holdup of the dispersed phase, dimensionless

Greek Symbols

α = fractional free area of the perforated plate ε = mechanical power dissipation per unit mass, W/kg γ = interfacial tension, N/m μ = viscosity, Pa·s ρ = density, kg/m3 Δρ = density difference between phases, kg/m3 Subscripts

c = continuous phase d = dispersed phase

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REFERENCES

(1) Marinsky, J. A.; Marcus, Y. Ion Exchange and Solvent Extraction: A Series of Advances; CRC Press: Boca Raton, FL, 1995; Vol. 12. (2) Movsowitz, R. L.; Kleinberger, L.; Buchalter, E. M. Application of Bateman pulsed columns for uranium SX: from pilot to industrial columns. In Extraction Metallurgy Africa 1997; South African Institute of Mining and Metallurgy: Johannesburg, 1997. (3) Godfrey, J. C.; Slater, J. Liquid-Liquid Extraction Equipment; Wiley: New York, 1994. H


Dispersed-Phase Holdup and Characteristic Velocity in a Pulsed and

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