13th Iranian National Chemical Engineering Congress & 1st International Regional Chemical and Petroleum Engineering Kermanshah, Iran, 25-28 October, 2010
Prediction of Slip Velocity in Pulsed Sieve Plate Extraction Columns Meisam Torab-Mostaedi*, Seyed Jaber Safdari, Ahad Ghaemi Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, Tehran, Iran E-mail:
[email protected]
Abstract In present work, slip velocity has been measured in a 50 mm diameter pulsed sieve-plate extraction column using two different liquid-liquid systems. The effects of operating variables such as pulsation intensity, dispersed and continuous phases flow rates, and interfacial tension on slip velocity have been investigated. The existance of three different regimes, namely mixersettler, transition, and emulsion regimes, was observed when input energy was changed. Empirical correlations are presented for prediction of slip velocity in terms of physical properties of liquidliquid systems and operating variables for different operating regimes. Good agreement between prediction and experiments is found for all operating conditions that were investigated. Keywords: Slip Velocity, Pulsed Sieve Plate Column, Dispersed Phase Holdup, Characteristic Velocity
Introduction Extraction columns are useful in petroleum, pharmaceutical, chemical, nuclear and hydrometallurgical processes due to their high efficiency and low cost for solvent inventory, site area and maintenance. The efficiency of liquid-liquid contactors is primarily dependent on the degree of turbulence imparted to the system and the interfacial area available for mass transfer. The rate of mass transfer can be enhanced by pulsating motion imparted to the liquids by an external mechanical or electronic device. Van Dijck [1] was first to propose that the efficiency of a perforated-plate column could be improved by pulsing the liquid in the column while keeping the plates stationary. Among the range of industrially used extraction columns, the pulsed perforated-plate column appears to be most widely used, apart from the rotating disc contactor. The pulsed columns have a clear advantage over other mechanical extractors when processing corrosive or radioactive solutions since the pulsing unit can be remote from the column. The absence of moving mechanical parts in such columns obviates repair and servicing [2, 3]. The design of liquid-liquid extraction columns requires determination of a suitable crosssectional area for flow and the height required to achieve a specified degree of mass transfer [4, 5]. Prediction of slip velocity has a fundamental importance in the design and operation of liquid-liquid extraction columns, since it is required to estimate the mass transfer and drag coefficients. The slip velocity is also the single most important parameter for the control of
Prediction of Slip Velocity in Pulsed …
mass transfer and calculation of mass transfer coefficients. For description of hydrodynamics of liquid-liquid extraction columns, the motion of drops in dispersion relative to the continuous phase, are related to the dispersed phase holdup. When two immiscible phases flow counter-currently through an extraction column without packing, the slip velocity defined as [6]: V V (1) V slip = d + c φ 1−φ in which the superficial velocities of the continuous and dispersed phases are obtained from the volumetric flow rate of each phase as follows: Q (2) V = A A wide variety of equations exist for relating Vslip with continuous phase holdup, 1-φ; those involving characteristic velocity, Vk, have been summerized by Godfrey and Slater [7]. Other approaches involve the use of drag relationships for drops and pressure drop fomulas for packed beds. All these relationships lead to implicite equations from which it is difficult to obtain dispersed phase holdup. Kumar and Hartland [8-10] show that it is possible to develop correlations for Vslip in terms of the physical properties, phase throughputs, agitation intensity, and column geometry. These equations do not include holdup, enabling the slip velocity to be explicitly calculated. The holdup itself can also easily be calculated by substituting the predicted values of slip velocity in Eq. (1). In present study, slip velocity is measured in a pulsed sieve-plate extraction column using two different liquid systems. The effects of pulsation intensity, dispersed and continuous phases flow rates, and interfacial tension on slip velocity are investigated. Empirical correlations are also derived for prediction of slip velocity in terms of physical properties and operating conditions. Experimental The main column section comprised a 1.5m long glass tube with 50mm internal diameter, enclosing a stack of sieve plates. Below the plate section was a 150mm expanded glass section enclosing a stainless-steel solvent distributor was supported on a piston-type pulsing unit, which imparted a sinusoidal motion to the fluids of column. In total, 30 SS sieve plates were arranged alternately and spaced 50mm apart in the column. They were of 2mm perforation diameter and 22.7% free area. The inlets and outlets of column were connected to four tanks each of 50 liters capacity. The flow rates of two phases were indicated by two rotameters. The column geometry is listed in Table 1. Table 1: Geometrical characteristics of the column used
Column height (cm) Column diameter (cm) Compartment height (cm) Hole diameter (mm) Hole pitch (mm) Plate thickness (cm) Fractional free area (-)
150 5 5 2 4 1.2 0.227
13th Iranian National Chemical Engineering Congress & 1st International Regional Chemical and Petroleum Engineering Kermanshah, Iran, 25-28 October, 2010
The liquid systems studied were toluene-water (high interfacial tension) and n-butyl acetatewater (medium interfacial tension). These systems are recommended as standard test systems by the European Federation of Chemical Engineering as official test systems for extraction investigations [11]. Technical grade toluene and butyl acetate, and distilled water were used in all experiments. The physical properties of the liquid–liquid systems used in these experiments are listed in Table 2 [11]. Table 2: Physical properties of liquid systems at 20oC [11]
Physical property
Toluene-water
n-Butyl acetate-water
ρ c (kg / m3 )
998.2
997.6
ρ d (kg / m3 )
865.2
880.9
µ c ( mPa .s )
0.963
1.027
µ d ( mPa .s )
0.584
0.734
σ ( mN / m)
36.0
14.1
In starting a given run, the solvent phase and water were mutually saturated. The amplitude and frequency of pulsation were then adjusted to the desired values and, after filling the column with the aqueous phase, the organic dispersed phase was introduced. The interface position was then maintained at the desired height by using an optical sensor and the system was allowed to reach steady state, which usually necessitated three or four changes of the column volume. At the end of a run, the inlet and outlet flows were stopped simultaneously, and the dispersion was allowed to coalesce at the interface, after which the holdup obtained by determining the change of interfacial height. Visual observations of the column in operation with these systems showed that three regimes, mixer-settler, transition, and emulsion occurred depending on the flow rates and the pulsation intensity. The mixer-settler regime was indicated by a stepwise movement of droplets within the column. The transition regime was characterized by non-uniform drop size distribution and no coalescence of dispersed phase drops. At higher pulsation intensities, a transition to the emulsion regime occurred as revealed by an even dispersion of solvent drops in the column. Results and Discussion Typical variations in the slip velocity with pulsation intensity are given in Figure 1. As can be seen in this figure, in both systems studied, the slip velocity firstly increases with increase in pulsation intensity towards the mixer-settler regime, until finally a maximum is reached corresponding to the transition regime. Following this, the slip velocity decreases with further increase in pulsation intensity, corresponding to the emulsion regime. This figure also shows the effect of interfacial tension on slip velocity. In mixer-settler regime, large drops are formed for higher interfacial tension system (toluenewater) and plate holes can prevent them from moving to the next plate due to low value of pulsation intensity. Whereas drop formed for system of lower interfacial tension (butyl acetate-water) are small and they can pass through the plate hole at low value of pulsation
Prediction of Slip Velocity in Pulsed …
intensity. Thus, for the system with low interfacial tension dispersed phase holdup is lower than that of the system with high interfacial tension and consequently higher slip velocity is obtained for the former system. In transition and emulsion regimes, the decrease in interfacial tension results in the decrease of the slip velocity. The effect of continuous phase velocity can also be observed in Figure 1. As shown in this figure, the slip velocity decreases with an increase in continuous phase velocity. By increasing the continuous phase velocity, the drag force between the dispersed drops and continuous phase increases, so the drop movement will be limited and the residence time will increase. Consequently, the slip velocity between drops and continuous phase will decrease. 100
90
Vslip (mm/s)
80
70
60
Vc=1.13 mm/s, Butyl acetate/Water Vc=1.695 mm/s, Butyl acetate/Water Vc=2.26 mm/s, Butyl acetate/Water Vc=1.13 mm/s, Toluene/Water Vc=1.695 mm/s, Toluene/Water Vc=2.26 mm/s, Toluene/Water
50
40 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Af (cm/s)
Figure 1: Effect of pulsation intensity on slip velocity
Figure 2 illustrates the effect of dispersed phase velocity on slip velocity. As shown in this figure, the slip velocity increases with an increase in dispersed phase velocity. When the value of dispersed phase velocity increases at constant continuous phase velocity, the dispersed phase holdup increases monotonously and the drop diameter also increases due to the decrease in residence time. But it is found that the effect of drop size is higher than that of dispersed phase holdup, so the slip velocity between two phases will increase.
13th Iranian National Chemical Engineering Congress & 1st International Regional Chemical and Petroleum Engineering Kermanshah, Iran, 25-28 October, 2010 100 V c=1.695 (m m /s) Toluene-Water
90 80 Vslip (mm/s)
70 60 50 Af= 1.5 (cm /s) Af=2.4 (cm /s) Af=3 (cm /s) Af=3.6 (cm /s) Af=4.5 (cm /s)
40 30 20 0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
V d (m m /s)
120 Vc=1.695 (m m/s) Butyl acetate-Water 100
Vslip (mm/s)
80
60
40 Af=1 (cm /s) Af=2 (cm /s) Af=2.6 (cm/s) Af=3.6 (cm/s) Af=4.2 (cm/s)
20
0 0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
V d (mm /s)
Figure 2: Effect of dispersed phase velocity on slip velocity
Predictive correlations for slip velocity One of the main objectives of this study is to derive precise correlation for prediction of slip velocity in pulsed sieve plate extraction columns. From the experimental observations it can be concluded that the slip velocity in pulsed sieve plate columns strongly depend both on physical properties of the liquid-liquid systems and the operating conditions. On this basis, empirical correlations are developed in terms of physical properties of the liquid-liquid systems and operating variables for prediction of slip velocity. The following correlations are derived by using least square method:
V slip
Af 4 ρc = 78.55 × gσ
0.025
0.1
V d4 ρc V d 1 + g σ Vc
0.22
∆ρ ρc
0.26
(mixer-settler regime)
(3)
Prediction of Slip Velocity in Pulsed …
V slip
Af 4 ρc = 477.46 × gσ
Vd 1 + Vc
0.11
∆ρ ρc
−0.12
V d4 ρc gσ
0.12
(transition and emulsion regimes)
0.83
(4)
which are based on 140 data points. The average absolute value of relative error, AARE, is used to compare the predicted results with the experimental data. This is defined as follows: AARE =
1 NDP
NDP
Predicted value-Experimental value
i =1
Experimental value
∑
in which NDP is the number of data points. These equations reproduce the experimental results with an AARE of 4.27%. The comparison of experimental data with those calculated by Eqs. (4) and (5) is illustrated in Fig. 3. This figure indicates that the suggested correlations are in very good agreement with experimental results. 120
Vslip (mm/s)(experimental)
100
80
60
40
20
0 0
20
40
60
80
100
120
V slip (m m /s)(calculated)
Figure 3: Comparision of experimental values of slip velocity with calculated ones
Conclusions This paper presented a study on slip velocity of a pulsed sieve plate extraction column. Three operational regions, described as mixer-settler, transition, and emulsion regime, were observed. Slip velocity in the mixer-settler regime increased with increase in pulsation intensity until a maximum was reached. This maximum corresponded to the transition from mixer-settler to transition regime. Beyond this maximum, the slip velocity decreased with pulsation intensity. The slip velocity decreased with increase in continuous phase velocity, while it increased with increase in dispersed phase velocity. New empirical correlations were derived for prediction of slip velocity. The results showed that the predictive correlations can reproduce the experimental data with very high accuracy.
13th Iranian National Chemical Engineering Congress & 1st International Regional Chemical and Petroleum Engineering Kermanshah, Iran, 25-28 October, 2010
References [1]. W. J. D., Van Dijck, Process and apparatus for intimately contacting fluids, U.S. Patent 2,011, 186 (1935). [2]. R. L., Yadav, A. W., Patwardhan, Design aspects of pulsed sieve plate columns, Chem. Eng. J., 138 (2008) 389-415. [3]. A. A., Hussain, T. –B., Liang, M. J., Slater, Characteristic velocity of drops in a liquidliquid extraction pulsed sieve plate column, Chem. Eng. Res. Des., 66 (1988) 541-554. [4]. R. Berger, K. Walter, Flooding in pulsed sieve plate extractors, Chem. Eng. Sci., 40 (1985) 2175-2184. [5]. M. Napeida, A. Haghighi Asl, J. Safdari, M. Torab-Mostaedi, Holdup and characterstic velocity in Hanson mixer-settler extraction column, Chem. Eng. Res. Des., 88 (2010) 703711. [6]. J. D., Thornton, Spray liquid-liquid extraction columns: Prediction of limiting holdup and flooding rates, Chem. Eng. Sci., 5 (1956) 201-208. [7]. J. C., Godfrey, M. J. Slater, Slip velocity relationships for liquid-liquid extraction columns, Chem. Eng. Res. Des., 69 (1991) 130-141. [8]. A. Kumar, S. Hartland, Prediction of drop size, dispersed phase holdup, slip velocity and limiting throughputs in packed extraction columns, Chem. Eng. Res. Des., 72 (1994) 89-104. [9]. A. Kumar, S. Hartland, Independent prediction of slip velocity and holdup in liquid-liquid extraction columns, Can. J. Chem. Eng., 67 (1989) 17-25. [10]. A. Kumar, S. Hartland, Empirical prediction of operating variables, in: J. C. Godfrey, M. J. Slater, "Liquid-liquid extraction equipment," John Wileyand Sons Ltd, New York, USA, 1994, pp. 625-735. [11]. T. Misek, R. Berger, J. Schroter, Recommended systems for liquid extraction studies, European Federeation of Chemical Engineering, Institution of Chemical Engineers, Rugby (1985).
… Prediction of Slip Velocity in Pulsed
ﭘﯿﺶﺑﯿﻨﯽ ﺳﺮﻋﺖ ﻟﻐﺰﺷﯽ در ﺳﺘﻮنﻫﺎي اﺳﺘﺨﺮاج ﺿﺮﺑﻪاي ﺳﯿﻨﯽدار ﻏﺮﺑﺎﻟﯽ ﻣﯿﺜﻢ ﺗﺮاب ﻣﺴﺘﻌﺪي ،*1ﺳﯿﺪ ﺟﺎﺑﺮ ﺻﻔﺪري ،2اﺣﺪ ﻗﺎﺋﻤﯽ
3
ﭘﮋوﻫﺸﮑﺪه ﭼﺮﺧﻪ ﺳﻮﺧﺖ ﻫﺴﺘﻪاي ،ﭘﮋوﻫﺸﮕﺎه ﻋﻠﻮم و ﻓﻨﻮن ﻫﺴﺘﻪاي ،ﺗﻬﺮان ،اﯾﺮان آدرس ﭘﺴﺖ اﻟﮑﺘﺮوﻧﯿﮏ
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ﭼﮑﯿﺪه
در اﯾﻦ ﻣﻘﺎﻟﻪ ،ﺳﺮﻋﺖ ﻟﻐﺰﺷﯽ در ﯾﮏ ﺳﺘﻮن اﺳﺘﺨﺮاج ﺿﺮﺑﻪاي ﺳﯿﻨﯽدار ﻏﺮﺑﺎﻟﯽ ﺑﺎ ﻗﻄﺮ 50ﻣﯿﻠﯽﻣﺘﺮ ﺑﺮاي دو ﺳﯿﺴﺘﻢ ﻣﺨﺘﻠﻒ اﻧﺪازهﮔﯿﺮي ﺷﺪه اﺳﺖ .اﺛﺮات ﭘﺎراﻣﺘﺮﻫﺎي ﻋﻤﻠﯿﺎﺗﯽ ﻧﻈﯿﺮ ﺷﺪت ﺿﺮﺑﻪ ،ﺳﺮﻋﺖ ﻓﺎزﻫﺎي ﭘﺮاﮐﻨﺪه و ﭘﯿﻮﺳﺘﻪ و
ﮐﺸﺶ ﺑﯿﻦ ﺳﻄﺤﯽ روي ﺳﺮﻋﺖ ﻟﻐﺰﺷﯽ ﻣﻮرد ﺑﺮرﺳﯽ ﻗﺮار ﮔﺮﻓﺘﻪ اﺳﺖ .ﻫﻤﭽﻨﯿﻦ در آزﻣﺎﯾﺶﻫﺎي اﻧﺠﺎم ﺷﺪه وﺟﻮد
ﺳﻪ رژﯾﻢ ﻋﻤﻠﯿﺎﺗﯽ ﻣﺘﻔﺎوت ﺷﺎﻣﻞ رژﯾﻢﻫﺎي ﻣﯿﮑﺴﺮ -ﺳﺘﻠﺮ ،اﻧﺘﻘﺎل و اﻣﻮﻟﺴﯿﻮن ﺑﺎ ﺗﻐﯿﯿﺮ اﻧﺮژي ورودي ﻣﺸﺎﻫﺪه ﮔﺮدﯾﺪ. دو راﺑﻄﮥ ﺗﺠﺮﺑﯽ ﺑﺮاي ﭘﯿﺶﺑﯿﻨﯽ ﺳﺮﻋﺖ ﻟﻐﺰﺷﯽ در رژﯾﻢﻫﺎي ﻋﻤﻠﯿﺎﺗﯽ ﻣﺘﻔﺎوت ﺑﺮ ﺣﺴﺐ ﺧﻮاص ﻓﯿﺰﯾﮑﯽ ﺳﯿﺴﺘﻢﻫﺎي ﻣﺎﯾﻊ -ﻣﺎﯾﻊ و ﻣﺘـﻐﯿﺮﻫﺎي ﻋﻤﻠﯿﺎﺗﯽ اراﺋـﻪ ﺷﺪه اﺳﺖ .ﻧﺘـﺎﯾﺞ ﺑﺪﺳﺖ آﻣﺪه ﻧﺸﺎن داد ﮐﻪ اﯾﻦ رواﺑـﻂ ﻗﺎدر ﺑﻪ ﭘﯿﺶﺑﯿﻨﯽ دادهﻫﺎي ﺗﺠﺮﺑﯽ ﺑﺎ دﻗﺖ ﺑﺴﯿﺎر ﻣﻨﺎﺳﺐ ﺑﺮاي ﮐﻞ ﺷﺮاﯾﻂ ﻋﻤﻠﯿﺎﺗﯽ ﺑﺮرﺳﯽ ﺷﺪه ﻣﯽﺑﺎﺷﻨﺪ.
واژهﻫﺎي ﮐﻠﯿﺪي :ﺳﺮﻋﺖ ﻟﻐﺰﺷﯽ ،ﺳﺘﻮن ﺿﺮﺑﻪاي ﺳﯿﻨﯽدار ﻏﺮﺑﺎﻟﯽ ،ﻣﻮﺟﻮدي ﻓﺎز ﭘﺮاﮐﻨﺪه ،ﺳﺮﻋﺖ ﻣﺸﺨﺼﻪ
-1دﮐﺘﺮي ﺗﺨﺼﺼﯽ ﻣﻬﻨﺪﺳﯽ ﺷﯿﻤﯽ ،اﺳﺘﺎدﯾﺎر ﮔﺮوه ﭘﮋوﻫﺸﯽ ﻓﺮآوري ﺳﻮﺧﺖ -1دﮐﺘﺮي ﺗﺨﺼﺼﯽ ﻣﻬﻨﺪﺳﯽ ﺷﯿﻤﯽ ،داﻧﺸﯿﺎر ﮔﺮوه ﭘﮋوﻫﺸﯽ ﻓﺮآوري ﺳﻮﺧﺖ
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