Study of holdup and slip velocity in an L-shaped pulsed sieve-plate extraction column
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Abstract
High-end applications require a very tall vertical extraction column in some cases which deteriorates protection against radiation and cannot be employed for indoor applications. On the other hand, horizontal extraction columns offer higher efficiency and pretension, but lower maximum throughput. In order to address this issue, the L-shaped pulsed extraction column is a new type of extractors which were recently introduced for such applications with area constraints. The objective of this study is to evaluate the effects of operating parameters and physical properties on the variation of holdup and slip velocity in this type of extractors for three liquid systems including toluene–water, butyl acetate–water and n butanol–water without and under mass transfer condition. A comprehensive investigation on the determination of predictive ability of available correlations for the holdup and slip velocity in pulsed plate columns has been conducted. Finally, new correlations are proposed for prediction of these parameters regarding operational conditions and physical properties.
Keywords
L-shaped pulsed plate column Slip velocity Holdup Pulsation intensity Mass transferList of symbols
- A
Amplitude of pulsation, m
- Af
Pulsation intensity, m/s
- D
Column diameter, m
- d
Hole diameter, m
- f
Frequency of pulsation, Hz
- g
Acceleration due to gravity, = 9.81 m/s^{2}
- h
Plate spacing, m
- H
Column length, m
- Q
Volumetric flow rate, m^{3}/s
- \( V_{c} \)
Superficial velocity of continuous phase, m/s
- \( V_{d} \)
Superficial velocity of dispersed phase, m/s
- \( V_{s} \)
Slip velocity, m/s
Greek symbols
- \( \alpha \)
Fractional free area
- \( \varphi \)
Holdup
- \( \mu \)
Viscosity, N s/m^{2}
- \( \rho \)
Density, kg/m^{3}
- \( \Delta \rho \)
Density difference between two phases, kg/m^{3}
- \( \sigma \)
Interfacial tension between two phases, N/m
Introduction
Solvent extraction is one of the methods applied in separation industry. There are numerous types of extractors including mixer-settlers, columns, and centrifugal extractors [1]. Pulsed columns are a class of solvent extractors which offer various advantages such as high throughput, simple design, low space requirement, and with no internal moving parts [2].
- 1.
Vertical pulsed columns.
- 2.
Horizontal pulsed columns.
- 1.
Throughput of the L-shaped pulsed sieve—plate column is less than the vertical types and more than the horizontal types.
- 2.
Height for installation and requirement surface area of an L-shaped column as indoor is less than that of the vertical or horizontal columns.
- 3.
The energy consumption in the L-shaped column is somewhat between that in the horizontal columns and the vertical columns.
In this regard, various efforts have been made. Amani et al. [7] studied the effects of operating parameters on the two-phase pressure drop in an L-shaped pulsed plate column. They also examined the throughput of the column and proposed new correlations for prediction of pressure drop and flooding points. A particular approach for preventing flooding has been developed as well. Akhgar et al. [8]. investigated the flow regime transitions in an L-shaped column and determined the values of characteristic velocities in the column under different steady-state operating conditions. In this study, the transition from dispersion to emulsion regime in the horizontal section and the transitions from mixer-settler to dispersion regime in the vertical section have been correlated, characterizing the minimum and maximum operating capacity of the column. In another study, the measurement of mean drop size and drop diameter distribution has been focused by Amani et al. [9, 10]. The drop behavior in different operating regimes has been evaluated and new correlations have been proposed for prediction of mean drop size in terms of operating parameters and physical properties of the chemical systems. Moreover, the drop size distribution is found to be well correlated using the log-normal probability density function.
Regarding the well description of extraction column operation, it is essential to evaluate the variation of drop population characteristics such as holdup and drop size [11]. In fact, pulsation improves the column performance due to providing higher drop breakage and consequently increasing the interfacial area between two phases. However, because of the entrainment of small drops and thereby increasing axial mixing, the column performance might be affected by pulsation [12]. Thus, investigation of hydrodynamic parameters including holdup and slip velocity is crucial for design and scaling up of an extraction column to determine the drag coefficients, [13, 14, 15, 16] and mass transfer performance [17, 18, 19, 20].
Correlation for prediction of holdup in pulsed plate columns
References | Correlations | Comments |
---|---|---|
[31] | \( \varphi = 4.93 \times 10^{2} \psi^{0.84} V_{\text{d}}^{2/3} ,\psi \le 0.0031\,{\text{m}}^{11/12} {\text{s}}^{ - 1} \) \( \varphi = 3.42 \times 10^{6} \psi^{0.24} V_{\text{d}}^{2/3} ,\psi \ge 0.0031\,{\text{m}}^{11/12} {\text{s}}^{ - 1} \) | Vertical pulsed column \( \psi = \frac{\text{Af}}{{(\beta h)^{1/3} }}\left( {\frac{{\mu_{\text{d}}^{2} }}{\sigma \Delta \rho }} \right)^{1/4} , \) \( \beta = \frac{{\alpha^{2} }}{{(1 - \alpha )(1 - \alpha^{2} )}} \) |
[32] | \( \varphi = 3.91 \times 10^{ - 3} \left( {\frac{{A^{2} \rho_{\text{c}} g}}{\sigma }} \right)^{ - 0.26} \left( {\frac{{f^{4} \sigma }}{{\rho_{\text{c}} g^{3} }}} \right)^{ - 0.19} \left( {\frac{{V_{\text{d}}^{4} \rho_{\text{c}} }}{g\sigma }} \right)^{0.28} \left( {1 + \frac{{V_{\text{c}} }}{{V_{\text{d}} }}} \right)^{0.19} \left( {\frac{\Delta \rho }{{\rho_{\text{c}} }}} \right)^{ - 0.81} \left( {\frac{{\mu_{\text{d}}^{4} g}}{{\rho_{\text{c}} \sigma^{3} }}} \right)^{ - 0.13} \) \( \varphi = 6.91\left( {\frac{{({\text{Af}})^{3} \rho_{\text{c}}^{1/4} }}{{\beta h\sigma^{1/4} g^{5/4} }}} \right)^{0.31} \left( {\frac{{V_{\text{d}}^{4} \rho_{\text{c}} }}{g\sigma }} \right)^{0.30} \left( {1 + \frac{{V_{\text{c}} }}{{V_{\text{d}} }}} \right)^{0.14} \left( {\frac{\Delta \rho }{{\rho_{\text{c}} }}} \right)^{ - 0.79} \left( {\frac{{\mu_{\text{d}}^{4} g}}{{\rho_{\text{c}} \sigma^{3} }}} \right)^{ - 0.01} \) \( \varphi = 3.73 \times 10^{ - 3} \left( {\frac{{({\text{Af}})^{4} \rho_{\text{c}} }}{\sigma g}} \right)^{0.31} \left( {\frac{{V_{\text{d}}^{4} \rho_{\text{c}} }}{g\sigma }} \right)^{0.31} \left( {1 + \frac{{V_{\text{c}} }}{{V_{\text{d}} }}} \right)^{0.45} \left( {\frac{\Delta \rho }{{\rho_{\text{c}} }}} \right)^{ - 2.20} \left( {\frac{{\mu_{\text{d}}^{4} g}}{{\rho_{\text{c}} \sigma^{3} }}} \right)^{ - 0.29} \) | Vertical pulsed column First equation is applicable for miser-settler regime Second equation is applicable for dispersion regime: \( \left[ {\frac{{({\text{Af}})^{3} \rho_{\text{c}} }}{{\beta h\Delta \rho^{3/4} \sigma^{1/4} g^{5/4} }}} \right] \le 0.05 \) Third equation is applicable for emulsion regime: \( \left[ {\frac{{({\text{Af}})^{3} \rho_{\text{c}} }}{{\beta h\Delta \rho^{3/4} \sigma^{1/4} g^{5/4} }}} \right] \ge 0.05 \) |
[33] | \( \begin{aligned} \varphi = C\left( {\frac{\text{Af}}{{\left( {\beta h} \right)^{1/3} }}} \right)^{1.90} \left( {\frac{{\mu_{\text{d}}^{2} }}{\sigma \Delta \rho }} \right)^{0.36} V_{\text{d}}^{1.1} , \hfill \\ {\text{for}}\left( {\frac{{\rho_{\text{c}} ({\text{Af}})^{3} }}{{2\alpha^{2} }}} \right) \ge 0.06\,{\text{kg/s}}^{2} \hfill \\ \end{aligned} \) | Vertical pulsed column The parameter C is 3.98 × 10^{5} for no mass transfer and is 2.52 × 10^{5} for mass transfer d → c and c → d |
[34] | \( \varphi = K_{1} \exp \left( {K_{2} |{\text{Af}} - ({\text{Af}})_{\text{m}} |} \right)V_{\text{d}}^{0.86} (V_{\text{c}} + V_{\text{d}} )^{0.28} \Delta \rho^{ - 0.30} \rho_{\text{d}}^{ - 0.93} \mu_{\text{d}}^{0.77} \alpha^{ - 0.56} h^{ - 0.56} , \) \( ({\text{Af}})_{\text{m}} = 9.69 \times 10^{ - 3} \left( {\frac{{\sigma \Delta \rho^{1/4} \alpha }}{{\mu_{\text{d}}^{3/4} }}} \right)^{0.33} \) | Vertical pulsed column K_{1} = 2.10 × 10^{6} and K_{2} = 44.53 for no mass transfer K_{1} = 2.14 × 10^{6} and K_{2} = 44.53 for c → d mass transfer K_{1} = 1.10 × 10^{6} and K_{2} = 50.56 for d → c mass transfer |
[14] | They proposed a correlation for slip velocity (Table 2), by which holdup can be calculated using Eq. (2) | Refer to Table 2 |
[35] | \( \varphi = K_{1} \exp \left( {K_{2} |{\text{Af}} - ({\text{Af}})_{\text{m}} |} \right)V_{\text{d}}^{1.02} {\text{V}}_{\text{c}}^{0.02} \Delta \rho^{ - 0.23} \mu_{\text{d}}^{0.52} d^{ - 0.3} \alpha^{ - 0.4} h^{ - 0.4} \) | Vertical pulsed column K_{1} = 116.5 and K_{2} = 39.35 for no mass transfer K_{1} = 84.6 and K_{2} = 42.56 for c → d mass transfer K_{1} = 92.0 and K_{2} = 42.56 for d → c mass transfer |
[35] | They proposed a correlation for slip velocity (Table 2), by which holdup can be calculated using Eq. (2) | Refer to Table 2 |
[3] | \( \varphi = 0.87\left( {\frac{{A^{2} \rho_{\text{c}} g}}{\sigma }} \right)^{ - 0.26} \left( {\frac{{f^{4} \sigma }}{{\rho_{\text{c}} g}}} \right)^{ - 0.09} \left( {\frac{{V_{\text{d}} \rho_{\text{c}} }}{g\sigma }} \right)^{0.12} \left( {1 + \frac{{V_{\text{c}} }}{{V_{\text{d}} }}} \right)^{0.27} \) | Horizontal pulsed column It is applicable for dispersion regime |
[27] | They proposed a correlation for slip velocity (Table 2), by which holdup can be calculated using Eq. (2) | Refer to Table 2 |
[29] | \( \varphi = C\left( {1 + \frac{{Q_{\text{c}} }}{{Q_{\text{d}} }}} \right)^{0.124} \left( {\frac{{({\text{Af}})^{4} \rho_{\text{c}} }}{g\sigma }} \right)^{ - 0.286} \left( {\frac{{\rho_{\text{c}} }}{\Delta \rho }} \right)^{ - 0.783} \left( {\frac{{\mu_{\text{d}}^{4} g}}{{\sigma^{3} \rho_{\text{c}} }}} \right)^{ - 0.071} \left( {\frac{{({\text{Af}})^{3} Q_{\text{d}} \rho_{\text{d}}^{2} }}{{\sigma^{2} }}} \right)^{0.282} \) | Horizontal pulsed column It is applicable for dispersion regime C = 0.97 for no mass transfer C = 0.089 for mass transfer c → d C = 0.101 for mass transfer d → c |
Correlation for prediction of slip velocity in pulsed sieve-plate columns
References | Correlations | Comments |
---|---|---|
[14] | \( V_{\text{s}} = K_{1} \exp \left( {K_{2} |{\text{Af}} - ({\text{Af}})_{\text{m}} |} \right)\Delta \rho^{0.29} \rho_{\text{d}}^{0.67} \mu_{\text{d}}^{ - 0.66} \alpha^{0.44} h^{0.43} , \) \( ({\text{Af}})_{\text{m}} = 9.69 \times 10^{ - 3} \left( {\frac{{\sigma \Delta \rho^{1/4} \alpha }}{{\mu_{\text{d}}^{3/4} }}} \right)^{0.33} \) | Vertical pulsed column K_{1} = 6.14 × 10^{−6} and K_{2} = − 36.91 for no mass transfer K_{1} = 5.04 × 10^{−6} and K_{2} = − 30.79 for c → d mass transfer K_{1} = 6.43 × 10^{−6} and K_{2} = − 31.81 for d → c mass transfer |
[35] | \( V_{\text{s}} = K_{1} \exp \left( {K_{2} |{\text{Af}} - ({\text{Af}})_{\text{m}} |} \right)\Delta \rho^{0.22} \mu_{\text{d}}^{ - 0.38} \alpha^{0.32} h^{0.31} d^{0.22} , \) \( ({\text{Af}})_{\text{m}} = 9.69 \times 10^{ - 3} \left( {\frac{{\sigma \Delta \rho^{1/4} \alpha }}{{\mu_{\text{d}}^{3/4} }}} \right)^{0.33} \) | Vertical pulsed column K_{1} = 1.35 × 10^{−2} and K_{2} = − 33.3 for no mass transfer K_{1} = 1.65 × 10^{−2} and K_{2} = − 29.6 for c → d mass transfer K_{1} = 1.55 × 10^{−2} and K_{2} = − 29.6 for d → c mass transfer |
[27] | \( V_{\text{s}} = 0.088\left( {\frac{\text{Af}}{{V_{\text{d}} }}} \right)^{ - 0.568} \left( {1 + \frac{{V_{\text{c}} }}{{V_{\text{d}} }}} \right)^{0.374} \left( {\frac{{\rho_{\text{d}} }}{{\rho_{\text{c}} }}} \right)^{0.053} \left( {\frac{{\mu_{\text{d}} V_{\text{d}} }}{\sigma }} \right)^{0.06} \) | Horizontal pulsed column It is applicable for dispersion regime with no mass transfer |
However, in accordance with the available literature, there is no investigation concerning the measurement of holdup and slip velocity in an L-shaped extraction column. So, there is a lack of data on the holdup values which are highly required for the design and understanding the performance of an extraction column. Therefore, in this study, the variation of holdup and slip velocity in a novel class of pulsed columns entitled: “L-shaped pulsed sieve-plate column” as a function of operating parameters including pulsation intensity and flow rate of both phases is investigated for three liquid–liquid systems with and without mass transfer. Moreover, new correlations for prediction of the dispersed phase holdup and slip velocity of phases are presented regarding physical properties and operating parameters.
Experimental
Description of equipment
Geometrical characteristics of the column and plates
Geometrical characteristics | Active section | |
---|---|---|
Horizontal | Vertical | |
Active parts length of the column (cm) | 146 | 146 |
Active parts internal diameter of the column (cm) | 6 | 6 |
Hole pitch (mm) | 4 | 4 |
Hole diameter (mm) | 2 | 2 |
Plate thickness (mm) | 1 | 1 |
Spacing between two plates (cm) | 1^{a}, 5^{b} | 5 |
Free area fraction (–) | 0.11 | 0.22 |
Liquid–liquid system
Physical properties of chemical systems at T = 20 °C
System | \( \rho_{\text{c}} \left( {{\text{kg/m}}^{ 3} } \right) \) | \( \rho_{\text{d}} \left( {{\text{kg/m}}^{ 3} } \right) \) | \( \mu_{\text{c}} \left( {\text{mPa s}} \right) \) | \( \mu_{\text{d}} \left( {\text{mPa s}} \right) \) | \( \sigma \left( {\text{mN/m}} \right) \) |
---|---|---|---|---|---|
Toluene–water (T–W) | 998 | 864 | 0.963 | 0.586 | 35.4 |
Butyl acetate–water (BA–W) | 997.6 | 880 | 1.0274 | 0.734 | 13.5 |
n Butanol–water (B–W) | 985.6 | 846 | 1.429 | 3.36 | 1.9 |
(Toluene–acetone)-water [(T-A)-W] | 998 | 865.2 | 0.963 | 0.571 | 30.1 |
(Butyl acetate-acetone)–water [(BA–A)–W] | 997.6 | 881.4 | 1.0274 | 0.729 | 13.2 |
(n Butanol–acetone)–water [(B–A)–W] | 985.6 | 847.8 | 1.429 | 3.34 | 1.5 |
Experimental procedure
Before conducting the experiments, both phases were saturated to avoid any solubility during the experiments. Next, storage tanks were filled with saturated phases. Initially, the column was filled with the continuous phase, followed by adjusting Q_{d}, Q_{c}, and Af to the intended values. The experiments cover a range of Q_{d} and Q_{c} from 1.5 to 7 l/h and 1.75 to 9 l/h, respectively, and a range of pulsation intensity (amplitude × frequency) from 0.4 to 1.3 cm/s.
In vertical section, variation of interface height was calculated and then holdup was measured by Eq. (1).
Results and discussion
To study the influence of operating parameters on the dispersed phase holdup and slip velocity, pulsation intensity as well as flow rate of the dispersed and continuous phases are varied in the range of 0.4–1.3 cm/s, 1.5–7 l/h and 1.7–9 l/h, respectively. Moreover, by introducing 3% volumetric fraction of acetone in the dispersed phases, the effect of mass transfer from the dispersed phase to the continuous phase on holdup along with slip velocity of phases is investigated as well.
Effect of operating parameters on holdup
The behavior of the dispersed phase holdup versus Af in vertical section of the column is shown in Fig. 2b. According to Fig. 2b, it is observed that the dispersed phase holdup incipiently decreases until it reaches a minimum value and then increases with further increase of Af. The minimum values of holdup are found to be a function of operating parameters and they vary for different systems with different physical properties. It is also obtained that systems with lower interfacial tension have higher values of holdup and flow regime transition occurs at lower Af region corresponding the position of minimum holdup and vice versa.
Holdup minima can be justified by evaluation of operating regimes in the column, which here corresponds the transition from mixer-settler regime to dispersion regime. Mixer-settler regime is characterized by the separation of dispersed and continuous phases into individual distinct layers in the inter-plate spaces during the quiescent portion of the pulse cycle. This condition enhances the formation of larger drops which stay on the internals and leads to the increase of holdup. When pulsation introduces into the column, residence time declines due to higher shear forces and drop breakage and as a consequence, the holdup decreases initially. However, with further increase of Af above the critical value, the holdup begins to increase considerably. It is mainly because of frequent drop breakage which leads to the formation of smaller drops and consequently longer residence time for the dispersed phase drops.
Figure 2b also shows that the holdup varies with interfacial tension. It is observed that for system with higher interfacial tension, the formation of larger drops and lower residence time due to higher buoyancy forces leads to higher slip velocities corresponding lower values of holdup in vertical section of the column.
Based on what has been discussed above, mass transfer d → c direction leads to formation of larger drops which can be referred to the Marangoni convection induction of local differences in the acetone concentration. Thus, when mass transfer d → c occurs, the residence time of the dispersed phase drops will be longer and consequently the holdup increases in horizontal section of the column. However, because of higher buoyancy forces on larger drops, the residence time of the dispersed phase drops will decrease with mass transfer d → c in vertical section of the column, which leads to lower holdup in this section.
Effect of operating parameters on slip velocity
The effect of variation of interfacial tension of the liquid systems can be also obtained from Fig. 6. According to Fig. 6, it is observed that the enhancement of the interfacial tension leads to the reduction of slip velocity in horizontal section, while it results in higher slip velocities in vertical section of the column. It is because of the formation of smaller drops in systems with lower interfacial tension and the variation of holdup which is discussed in Sect. “Effect of operating parameters on holdup”.
The results of presence of mass transfer from the dispersed phase to the continuous phase are also depicted in Figs. 6, 7, 8. The slip velocity for mass transfer d → c direction is lower than that for cases with no mass transfer in horizontal section of the column, while an inverse trend exists in the vertical section of the column. This behavior can be referred to the interfacial tension gradient, interface motions, and consequently lower drop breakage and higher coalescence along with the variation of dispersed phase holdup with the presence of mass transfer (d → c) which is previously shown in Figs. 2, 3, 4, 5 and well discussed in previous section. According to Eq. (2), a decrease of holdup leads to the enhancement of slip velocity in the horizontal section of the column, while an inverse trend is observed in the vertical section.
Predictive correlation for holdup
The AARE of calculated holdup from previous correlations with the experimental data
References | Column section | Condition | AARE (%) |
---|---|---|---|
Miyauchi and Oya [31] | Vertical | No transfer | 55.6 |
Kumar and Hartland [32] | Vertical | No transfer | 86.2 |
Kumar and Hartland [34] | Vertical | No transfer | 91.9 |
d → c | 74.7 | ||
Tung and Luecke [33] | Vertical | No transfer | 93.1 |
d → c | 78.5 | ||
Venkatanarasaiah and Varma [35] | Vertical | No transfer | 70.5 |
d → c | 89.4 | ||
Kumar and Hartland [14]^{a} | Vertical | No transfer | 66.3 |
d → c | 41.4 | ||
Venkatanarasaiah and Varma [35]^{b} | Vertical | No transfer | 51.8 |
d → c | 29.4 | ||
Melnyk et al. [3] | Horizontal | No transfer | 196.6 |
Khajenoori et al. [27] | Horizontal | No transfer | 79.8 |
Values of constants in Eq. (9) for different mass transfer conditions
Mass transfer condition | K _{1} | K _{2} |
---|---|---|
No solute transfer | 1.12 × 10^{9} | 11.53 |
d → c direction | 9.21 × 10^{8} | 23.56 |
Predictive correlation for slip velocity
The AARE of calculated slip velocity from previous correlations with the experimental data
Consequently, new correlations are proposed as a function of operating parameters and physical properties of the liquid systems by dimensional analysis method as follows:
Application performance of an L-shaped extraction column
In order to evaluate the performance of an L-shaped extraction column over the conventional vertical and horizontal columns, Amani et al. [9] conducted a comparative study on the mean drop size in various columns. The results of Kagan et al. [36], Miyauchi and Oya [31], Kleczek et al. [37], for vertical extraction columns and the data of Khajenoori et al. [38], and Panahinia et al. [29] for horizontal extraction columns were used for this comparison. The operating conditions and column characteristics were close to each other and to the current L-shaped column used in this study. It was seen that the horizontal section of the L-shaped column provides larger droplets compared to similar horizontal columns. On the other hand, in the vertical section of the column, smaller droplets have been formed compared to the conventional vertical columns with similar structures. Furthermore, from the comparative study conducted in this study (as partly presented in Figs. 9 and 10), one can find that the values of holdup in the horizontal section is higher than that in a separate horizontal extraction equipment. Therefore, it can be concluded that the horizontal section of the column performs better than a separate horizontal column and offers higher interfacial area available for mass transfer, while the vertical section of the column operates in a comparable manner with a separate vertical column. It is worth noting that the findings also recommend the construction of a combined tower instead of employing two separate horizontal and vertical extraction equipment in cases where we suffer from area limitations.
Conclusion
In this study, the effect of operating parameters including pulsation intensity and flow rate of the continuous and dispersed phases on the dispersed phase holdup and slip velocity of phases is investigated in a new type of extraction column entitled “L-shaped pulsed sieve-plate column”. The results reveal that increasing Q_{d} and Q_{c} leads to the enhancement of holdup in the column, while holdup decreases in horizontal section and increases in the vertical section when Af increases. Moreover, with respect to the variation of holdup and superficial velocities of phases under different operating conditions, it is observed that the slip velocity increases at higher Q_{d} in each section, while increasing Q_{c} leads to higher slip velocity in horizontal section and lower slip velocity in vertical section. Pulsation intensity is found to pose two different impacts on slip velocity similar with increasing Q_{c}.
A comparison between the experimental data with those calculated by previous correlations for holdup and slip velocity is conducted. Furthermore, new correlations are proposed for prediction of these two parameters in each section of the column, with AARE from 3.49 to 15.5%. The presented correlations give a satisfactory agreement with the experiments.
Notes
References
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