Ind. Eng. Chem. Process Des. Dev. 1983,22, 553-563
553
Hydrodynamics of Mixer-Settlers K. T. Hossaln,' S. Sarkar,+ C. J. Mumford,' and C. R. Phllllps't Department of C h m " Engineering and Appibd Chemisfry, University of Toronto, Toronto, Ontario, M5S 1A4. and Department of Chemical Engineering, University of Aston in Birmingham, Engknd
An experimental study was made of the hydrodynamics of a continuous mixer-settler by using model systems to obtain appropriate design information. Drop-size distributions in the fully baffled mixer were measured from photographs and found to be consistently lognormal. Above a critical agitator speed, holdup values were dependent upon phase flow rates. Settler characteristicswere investigated by observation of the variation In wedge length with system parameters. A 40-50% reduction in wedge length was achieved with a circular baffle of optimum diameter at an optimum distance from the inlet. Design criteria are provided for maximum volumetric capacity of the mixing system based upon the onset of phase inversion.
Introduction The wide variety of equipment now available for liquid-liquid extraction includes mixer-settlers, centrifugal extractors, and spray, packed, pulsed, and rotary agitated columns (Mumford, 1968). However, the simple box-type mixemettler, incorporating up to 16 separate stages, is still widely used for handling high flow ratios. One reason is that mixer-settlers can be operated at high efficiencies, more or less regardless of the properties of the phases. Scale-up on a semiempirical basis is often possible, although it does not always result in an optimum design. For any particular design of mixersettler, the limits on volumetric throughput and energy input are governed by the system properties; for example, low interfacial tension systems tend to result in smaller drops with poor settling characteristics. Surprisingly, the simple mixemettler itself has not been thoroughly investigated. Typically, a specific process, or what i8 claimed to be a novel design, has been operated to obtain data on "overall" efficiency and volumetric capacity specific to the extractor and extraction process studied. However, numerous studies have been made of mass transfer efficiency in agitated tanks (Treybal, 1963; Calderbank, 1958;Rushton et al., 1964;Nagata and Yamaguchi, 1960). Studies have also been made of the hydrodynamics of vertical or horizontal gravity settlers in the absence of mass transfer, both with and without coalescing aids (Hanson and Kay, 1964;Davies et al., 1970;Vijayan et al., 1975;Jeffreys et al., 1967;Drown and Thompson, 1977). These studies provide a fundamental understanding of the basic processes involved-such as interfacial phenomena and drop-drop interactions-but the experimental conditions are usually quite unlike those in continuous liquid-liquid mixer-settlers. Although the settler is generally the volumetric capacity limiting item in a mixer-settler train, little information is available upon which to base an optimum design; design is largely empirical or stems from pilot plant experience. The methods commonly employed (Treybal, 1963;Ryon et al., 1960)are based either on the residence time of the phases or the thickness of the dispersion (or wedge) in the settler. The classical study of scale-up procedures by Ryon and co-workers (1960),relating to uranium extraction from leach liquors, is still used as the basis for mixer-settler design. New settler designs have, however, been developed t University of Toronto.
* University of Aston.
0196-4305/83/1122-0553$01.50/0
and applied industrially by Mizrahi and Barnea (I.M.I.) (1973)and StBner and Wohler (Lurgi) (1975)for specific metallurgical processes. However, important design parameters have been ignored, for example, the geometry of the settler as related to the mixer design, coalescence characteristics inside the settler, and phase stability to ensure minimum entrainment. Industrial settlers are usually operated in a mode whereby the wedge extends across the entire length of the settler, thereby enhancing the probability of mutual phase entrainment. Industrial equipment seldom operates under steady-state conditions. Process fluctuations typically occur, and this often results in severe phase entrainment. Further, the mixers are usually overdesigned through lack of data relating to volumetric capacity. Evaluation of a design procedure for a mixer-settler unit requires knowledge of the system hydrodynamics. At present, no consistent hydrodynamic data are available on continuous operation. Most of the current work (Lewis, 1977;Barnea, 1977)tends not to deal with system hydrodynamics. A detailed experimental study was therefore carried out on the hydrodynamics of a continuous mixer-settler in a pilot-scale multistage cascade to obtain design criteria. The work included investigation of (a) dispersion characteristics in the mixer: drop-size distribution and mean drop size, (b) settler characteristics: wedge length and height, and (c) phase inversion in two-phase systems. In this context, phase inversion refers to the interchange of phases in an agitated two-phase system such that the dispersed phase becomes continuous and vice versa under conditions determined by system properties, phase ratio, and energy input. Sarkar et al. (1980)pointed out the importance of phase inversion in defining the limiting volumetric capacity of agitated columns, and some analogous effects were observed in the present study. Although a 5-stage cascade was operated, the hydrodynamic data presented were obtained from a single stage since no significant change was found in the hydrodynamics from stage to stage. The mass transfer performance of the multistage cascade is reported elsewhere (Hossain, 1976).
Experimental Section The continuous countercurrent mixer-settler incorporated five 15.2 X m high, 10.16 X m diameter cylindrical vessels with dished bottoms (Figure 1). Each mixing vessel was provided with a six-bladed turbine and vertical baffles. The speed of agitation was varied in the range 850-1250 rpm. Each agitator was provided with a 0 1983 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 I
1
1
I
03
0.4
I
I
0.5 Hold-up, x(%)-w
0.6
,
07
Figure 3. Drop size (Sauter mean drop diameter) vs. holdup. 850 rpm; (A)950 System: toluene-water (toluene dispersed): (0) rpm; (0) 1050 rpm; (X) 1150 rpm; (@) 1250 rpm. Figure 1. Flow diagram. Adiustable baffle tie-rods
+-r ,/,
Baffle
Mixed phase inlet
O . t 0.4
-
Organic phase outlet Aqueous phase outlet
\\
\ Baffle detail Stainless steel plate baffle
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I
0.3
0.4
0.5
0.6
0.7
Hold-up, x (%)+
Figure 2. Baffle mounting arrangement in settlers.
photoelectric probe connected to an electronic tachometer through a five-way switch box. Phase separation occurred in five 30.48 X m long, 10.16 X m diameter horizontal cylindrical settlers constructed of industrial glassware with stainless steel end-plates. The ratio of the mixed volume to the available settler volume was approximately 1:3. The design of the turbine agitator was dimensionally similar to that of Rushton and Oldshue (1953). The height of the impeller above the bottom of the vessel was made equal to the impeller diameter in accordance with published recommendations (Rushton and Oldshue, 1953; Holland and Chapman, 1966; Bales et al., 1963). The ratio of impeller to vessel diameter (DID,)was taken as 0.3, consistent with standard tank configurations. Each mixing vessel was provided with four baffles, the width of each being one tenth of the diameter of the vessel. A vertical disk baffle was installed opposite the inlet to each settler (Figure 2); this was preferred to a perforated disk-type baffle (Treybal, 1953) which proved inefficient owing to jetting effects. The “ideal” liquid-liquid, mutually saturated, systems kerosene-water and toluene-water were used in the investigation. In most runs,water was the continuous phase. Direct photography was used for drop-size measurement (Mumford, 1970). A Carl Zeiss particle size Analyser TG.Z.3 and S.P.R.I. particle size Analyser Type I1 were used to count and measure droplets from the photographs. At the start of each run the mixers and settlers were filled with the two liquids until the height of liquid in the mixer was equal to the mixer diameter and the interface was at the mid-position in the settler. After the agitator speed was set, feed and solvent flow rates were adjusted to give the required ratio of v,: v d . The range of v,: v d covered was 1:lO to 1O:l. Drop Size. Initially, the Sauter mean droplet diameter was determined as a function of time in order to determine the time for dispersion equilibrium. In all cases, 10 min was found to be sufficient for achievement of equilibrium, resulting in a homogeneous dispersion with a relatively small drop size distribution. The critical speed for substantially uniform dispersion was approximately 850 rpm
Figure 4. Drop size (Sauter mean drop diameter) vs. holdup. System: kerosene-water (kerosene dispersed): (0) 850 rpm; CO, 950 rpm; ( 0 )1050 rpm; (0) 1150 rpm.
I
1
I
I
0.2
0.4 dd”)
0.6
0.6
Figure 5. Drop size distribution with impeller speed. System: toluene-water (toluene dispersed): (1)1150 rpm; (2) 1050 rpm; (3) 950 rpm; v d = V, = 19.
/ / x
0.81
I
1
I
02
0.4
,
0.6
I
/
0.8
d32(m m )
Figure 6. Drop size distribution with phase ratio. System: toluene-water (toluene dispersed): (1) 1:1 = vc:vd;(2) 1:2 = vc:vd; (3) 1:3 = Vc:Vd; rpm = 1150.
for both systems. The Sauter mean drop diameter was calculated from the usual expression d32 = Cnd3/Cnd2 Results are illustrated in Figures 3-6. Settler Characteristics. Settler characteristics were studied by photographing a wedge by means of mirrors inclined at 45O above and below the settler. This procedure enabled the upper and lower surfaces of the wedge to be
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 555 a
lO.0C
-/
16-
a
9.08.0-
--E
7.0-
? 6.01
5.0-
4.03.04
6
8
10
V, x 1 04(misec) b
b
91
//
19t 17
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8 U d x l O'( m/sec)
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I
Figure 7. (a) Wedge length w. dispersed phase flow rate. System: toluene-water (toluene dispersed): (0) without baffle; (A) 2.54 X m diameter baffle; (X) 3.81 X m diameter baffle; ( 0 )5.08 m diameter baffle; (0) 6.35 X m diameter baffle; (a)7.62 x X IO-* m diameter baffle; V , = 6 X lo-' (m d); rpm = 1150. (b) Wedge length vs. dispersed phase flow rate. System: kerosene dispersed): (0) without baffle; (A) 2.35 X 10" m diameter baffle; (X) 3.81 X 1W2m diameter baffle; ( 0 )5.08 X m diameter baffle; ( 0 ) m diameter baffle; (a)7.62 X m diameter baffle; V, 6.35 X = 6 X lo-' (m s-l); rpm = 1150.
viewed and photographed. The mean axial velocity of drops within the dispersion was determined by observation of an organic-soluble, non-surface-active red dye injected into the short transfer line between the mixer and the settler. The range of axial velocity was 0.1-0.37 X 1W2m/s. m, 7.62 X 1C2 Circular baffles of 2.54 X 1W2m, 5.08 X m, and 8.89 X 1W2m diameter, respectively, were installed opposite the phase inlet. Wedge dimensions were measured and photographed over a range of phase flow rates and energy input to the mixer. Baffle positions of 2.54 X m, 5.08 X m, 7.62 X m, 10.16 X m, and 12.7 X lom2m from the phase input were used. Drop sizes in the wedge in the settler were found to be in the range 1 to 3.5 mm. Unlike in the mixer, no satellite secondary drops were detected in the settler although some must have been carried over with the continuous phase. Normally the baffle was continuous phase wetted, but as part of the investigation,the optimum sized baffle was also made preferentially wetted by the disperse phase by suitable surface treatment (Storey, 1971). The length and height of the wedge were measured over a range of phase ratios, flow rates, energy input, and baffle sizes for dispersions of both the organic and the aqueous phase. The
V,xlO*(m/sec)
Figure 8. (a) Wedge length vs. dispersed phase flow rate. System: kerosene-water (kerosene dispersed): nonwetted baffle; (X) 850 rpm; ( 0 )950 rpm; (A) 1050 rpm; V, = 6 X lo4 m s-l. (b) Wedge length vs. dispersed phase flow rate. System: toluene-water (toluene dispersed): nonwetted baffle; (X) 850 rpm; ( 0 )950 rpm; (A)1050 rpm; V, = 6 X lo-' m s-'.
effects of these parameters on wedge characteristics are illustrated in Figures 7-12. Phase Inversion. Following the procedure used in previous investigations into phase inversion in continuous differential contactors (Sarkar et al., 1976), the agitator speed and the phase flow rate were kept constant and the dispersed phase flow rate was then increased incrementally by between 2 and 5% until phase inversion occurred. A similar procedure was also used with the continuous phase flow being gradually decreased incrementally. The impeller was centrally located in the aqueous or the organic phase. The impeller position in the upper phase was 3.04 X m above the interface, that is, the same distance as from the bottom of the mixing vessel in the alternative case. Studies were carried out within an impeller speed range of 850 to 1250 rpm, since below 850 rpm dispersion was not uniform and above 1250 rpm effective separation of the phases was not obtained in the settler due to the formation of a secondary haze. A dispersion was classified as being either water or organic phase continuous by testing with the addition of an organic soluble methyl red dye. This dye was used at a concentration less than 0.0190, at which concentration it is non-surface-active and has no significant effect on interfacial tension (Hitit, 1972). Measurements were made of the change in wedge length in the settler. Conditions in the settler changed when phase inversion occurred in the mixer. Following inversion
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Ind. Eng. Cbm. Process Des. Dev., Vol. 22, No. 4, 1983
8t
a
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4
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6
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8
I
10
v, x 104( m / s e ~ ) b
Superficial Velocity x 10*(m/sec)
Figure 11. Wedge length vs. superficial velocity. System: toluene-water (toluene dispersed): (0) without baffle; (X) 2.54 X m diameter baffle; (A)5.08 X m diameter baffle; ( 0 )7.62 X m diameter baffle; rpm = 1150.
3t I
1
4
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6
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8
1
10
1
X
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I
V,x104(m/sec)
Figure 9. (a) Wedge length vs. continuous phase flow rate. System: kerosene-water (keroseme dispersed): nonwetted baffle; ( 0 )950 rpm; (A)1050 rpm;. (0) 1150 rpm; V, = 6 X lo-" m s-'. (b) Wedge length vs. continuous phase flow rate. System: toluenewater (toluene dispersed): nonwetted baffle; ( 0 )950 rpm; (A)1050 rpm; (0) 1150 rpm; V, = 6 X lo-' m s-l.
I
I
4
I
6
I
8
Vdx 1o'( m/sec)
Figure 12. Wedge height vs. dispersed phase flow rate. System: kerosene-water (kerosenedispersed): (0)without baffle; ( 0 )5.08 X m diameter baffle; (X) 7.62 X m diameter baffle; V, = 6 X lo-' m s-l; rpm = 1150.
I
10
Vdx104(m/sec)
Figure 10. Wedge length vs. dispersed phase flow rate. System: wetted baffle (5.08 X m toluenewater (toluene dispersed): (0) diameter); (A)nonwetted baffle (5.08 X m diameter); (A) 850 rpm; (B)950 rpm; (C) 1050 rpm; V, = 6 X lo-' (m s-l).
from o/w (organic dispersed/water continuous) to w/o in the mixer, the wedge length decreased. The reverse was true for inversion from w/o to o/w. The time required for the settler to regain equilibrium was found to be about 16% less for inversion from o/w to w/o than for inversion from w/o to o/w. For any one combination of parameters, observations were repeated 2 or 3 times. The results obtained were reproducible within about 2%; mean values are therefore reported. The onset of inversion was not restricted to any particular volume within the mixer. Inversion was spontaneous and, unlike in agitated columns (Sarkar, 1976), extended throughout the vessel volume. Figure 13 shows the formation of very large drops in the mixer exit line immediately following inversion. As would be expected, inversion in the mixer was not instantaneous, and it required of the order of 30-35 s. Similar time scales have been observed for phase inversion in agitated columns (Sarkar, 1976). In multistage operation, inversion occurred consecutively in each stage, with
Figure 13. Onset of phase inversion in mixer. System: toluenewater. Slugs of continuous phase and smaller dispersed phase droplets in the transfer line to the settler.
a well-defined time lag between successive stages. This time lag was found to be approximately 55-60 s due to the time taken for each downstream stage to reach the point of inversion equilibrium. Depending upon which phase inverted, 2-3 min was needed for wedge length to reach equilibrium after inversion. For a water dispersion, the time needed following inversion was approximately 2 min; for an organic dispersion, approximately 3 min. Figure 14 shows the variation of the inversion point with agitator speed for different dispersed and continuous phase
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 557
5 6
41
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1
2
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6
4
8
Vdx104(m/sec)
Figure 14. Continuous phase throughput vs. dispersed phase throughput a t phase inversion. System: toluene-water (toluene dispersed): ( X ) 850 rpm; (0) 950 rpm; (A)1050 rpm; (0)1150 rpm. 1.oc
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0.9L
I
859
950
I
1050 R.P M
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1150
1250
no difficulties in the settler because, at the energy inputs used, they were a small proportion of the dispersed phase. Drop size distributions were measured in all five stages over a range of rotor speeds and phase flow rates. However, no appreciable change in drop size was observed. Figures 5 and 6 are typical of the distribution curves obtained. The Sauter mean drop diameters were found to be log-normally distributed, consistent with the observations of Giles et al. (1971) but contrary to those of Rodger et al. (1956). However, precise comparison is difficult since drop sizes are very much dependent on the geometrical configuration of the contactor. The mean drop size varied with rotor speed, holdup, and system physical properties, as illustrated in Figures 3 and 4. At low rotor speeds the variation in drop size was greater than at the higher speeds. This arose because there was a distribution of drop residence times in the mixer, and only a proportion of the drops spent a sufficient time in the discharge region of the impeller to cause breakup. No attempt was made to measure any variation in drop size with position in the vessel since, provided the critical speed was exceeded, conditions in the relatively small vessel were homogeneous, as confirmed by the absence of any holdup profile. Figures 3 and 4 illustrate that the Sauter mean drop diameter at constant rotor speed increases linearly with holdup due to coalescence effects. As holdup increases, the probability of droplet collision followed by subsequent coalescence also increases. Experimental values of dS2were compared with the correlation of Bouyatiotis and Thornton (1967). Although that work was carried out without a settler and the ratio of impeller to tank diameter was 0.386 compared to 0.3 in the present work, the average difference in mean drop sizes was approximately 30%. The difference is probably due to the different geometric configuration of the mixing systems, and also to the presence of a settler in the present work, which creates a back pressure related to the wedge dimension; that is, the greater the hindrance, the larger the back pressure. Under steady-state conditions, momentum transfer in the mixer-settler interconnection enhances the level of turbulence in the mixer. No correlation has previously been published for drop size and holdup in the mixer of a continuous mixer-settler. Such a correlation can be derived by dimensional analysis of the physical properties of the system, operating conditions, and the impeller geometry
Figure 15. Holdup values vs. impeller speed a t inversion. Systems: toluene-water and kerosene-water: (O)(X) toluene-water; (A)@) kerosene-water.
flow rates. Figure 15 illustrates the variation of holdup at inversion with impeller speed and impeller position. In the region above the curve 1,3 (Figure 15), the impeller was in the heavier (bottom) water phase; below the curve 2,4 the impeller was in the lighter (top) organic phase. Above curves 1and 3, water was completely dispersed, and below curves 2 and 4, the organic phase was completely dispersed. The region between these two sets of curves is usually termed the ambivalent zone. Either component may remain dispersed in this zone, outside of which instability in dispersion leads to phase inversion. Discussion Drop Sizes. The range of drop sizes observed in the mixer was mainly between 0.25 and 0.7 mm, characteristic of those normally found in agitated aqueous organic systems (compared to 0.25 to 5 mm in agitated columns). In all cases some droplets were produced in the secondary dispersion size range of less than 0.2 mm, but these created
Y
D
Calculation of the exponents a,@,y,and the value of K from the experimental results yields 1.02
d32 =
D
0.43(We)””8( L, l + r
(--) pd
4x21
(3)
which describes the data with a correlation coefficient of 0.92. Figure 16 shows that the measured experimental values lies within f7% of those calculated by using eq 3. In Table I, the exponents are compared with published results for related but not identical systems. No data are available for drop size in a mixer of a mixer-settler cascade. The exponents of N and D agree with the reported work to within * E % , and that of r / ( l + T ) of 1.02 agrees with
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Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983
Table I. Exponents o n Groups Affecting Drop Size in Continuous Mixer Settlers this work, pub1 data, mouP det exponents range of values general value We N D
-0.5 8 -1.1 6 -1.74
(vDIv~)
(rlr
+ 1)
-1.0 to -1.5 -1.0 to -2.0
("D/"c)o.Z1
1.02
-0.6 -1.2 -2.0 -0.20 1.o
ref Arnold (1974) Arnold (1974) Arnold (1974) Rodgers et al. (1956) Buoyatiotis and Thornton (1967)
-
I
b
0.6
Experimental d32(m)
Figure 16. Calculated vs. experimental mean drop size. Systems: kerosene-water and toluene-water: ( 0 )kerosene-water; (0) toluene-water.
Bouyatiotis and Thornton (1967). The exponent of pd/pc agrees with the experimental correlation of Rodger et al. (1956) and is in good agreement with previous work. The differences in the exponents of D and N may be due to differences in mixer geometry, impeller size, and position in the mixing vessel (Arnold, 1974), and the presence of a settler. Equation 3 may be used in the estimation of interfacial area, provided the dispersed phase holdup is known. Some modification may, however, be necessary for its application to real mass transfer situations since drop sizes may in practice be larger, or smaller, depending on the direction of solute transfer. Settler Characteristics. For both systems studied, wedge length increases with increasing dispersed phase flow rate, increasing continuous phase flow rate and increasing agitator speed as illustrated in Figures 8 and 9. All of these parameters affect drop size and holdup in the mixer and hence coalescence and flow in the settler. When the dispersed phase throughput was increased at fixed agitator speed and continuous phase flow rate, wedge length increased linearly as illustrated in Figure 8. The increase in wedge length corresponding to an increase in the flow of the continous phase was only about one-third of that produced by the same increase in the flow of the dispersed phase (Figure 9). Similar observations were made using a stainless steel baffled settler (Thomas and Mumford, 1971). In general, an increase in throughput causes the axial velocity component of the drops to be much higher than the vertical component, thus hindering drop-interface coalescence, and resulting in an increase in wedge length (Vijayan et al., 1975). When the rotor speeds were varied at a fixed dispersed phase throughput, the wedge length increased by approximately 10% for every 100 rpm increment. A t high energy input levels, that is, at about 1250 rpm, the small drops (0.2-9.3 mm diameter) produced required a long time to coalesce (Lawson, 1967). A preliminary investigation was made of wedge characteristics in an unbaffled settler. Irregular wedge shapes were observed as shown in Figure 17. These wedges ex-
Figure 17. Wedge in settler without a baffle. System: toluenewater (for comparison with Figure 19). At a similar flow rate the wedge extends the full settler length.
tended to the end of the settler at flow rates in excess of 13.3 X lo4 m3/s. Severe phase entrainment was observed a t higher loadings. The conventional operating mode of having the wedge impact the end of the settler for enhancing coalescence (although dependent upon liquidliquid system) is not always desirable since the concentration of small drops increases at the end of the wedge. These small drops do not readily coalesce and are eventually swept away by either or both of the phases. A baffle was therefore added to enhance coalescence upstream. The optimum baffle size was found to be three-quarters of the settler diameter. As the baffle size was increased up to the optimum, the wedge length decreased. The possible explanation for this optimum is that a t small baffle areas any increase serves to improve the efficiency with which entry turbulence is damped out. However, the area of the annulus for flow in the settler is reduced so that for any given throughput the superficial velocity is increased as shown in Figure 11. Beyond the optimum size, the increase in superficial velocity, which serves both to elongate the wedge and to reduce coalescence efficiency, overrides any improvement in damping effects. However, there was some enhanced coalescence upstream of the baffle, as shown in Figure 18, a phenomenon also reported with a single layer of polypropylene steel mesh (Thomas and Mumford, 1972). Above the optimum size, the wedge changed in shape as a result of enhanced turbulence caused by reduction of the annulus area (Figures 19 and 20). Figure 18 illustrates packing of large drops formed by coalescence in front of the settler. The effect of these large drops, which were displaced continuously downstream, would be to enhance coalescence in the normal wedge. Insertion of a baffle in the settler acts not only as a turbulence damper but also serves to retard the velocity of the dispersion wedge relative to the bulk phases. The overall effect is to enhance coalescence.
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 559
Figure 18. Inter-droplet coalescence in the settler-between inlet and baffle. Reduction in droplet velocities due to impingement aids coalescence. System: toluene-water.
Figure 20. Wedge in settler under optimum conditions. System: toluenewater. (The discrete droplets adhering to the settler wall played no part in the wedge formation and did not contaminate any samples. They arose from "wall flow" due to entrainment in the continuous phase.)
rll 4
Figure 19. Wedge in settler with baffle above the optimum size. The wedge shape differs due to the reduced annulus for flow. System: toluene-water.
The optimum position of the baffle was found to be one-tenth of the settler length from the phase inlet. At close positions, wedge length was found to increase due to the creation of localized turbulent zones on both sides of the baffle, which significantly affected the rate of dropdrop coalescence. Also, for baffle positions closer than the optimum, the capacity of the settler was reduced (Figure 21). The baffles used in this study had stainless steel (high energy) surfaces which were not wetted by organics, except
b Figure 21. Wedge in settler with a baffle of optimum size incorrectly positioned. System: toluenewater. Double wedge formation has occurred with the second wedge extending the full settler length as in Figure 16.
for one baffle which was made wettable by the organic phase to examine the effect of wetting on the wedge characteristics in the settler. No significant effect was found (Figure 10). A perforated disk-type baffle (Treybal, 1963) was tested but was discarded due to the ineffectiveness of separation caused by the "jetting" effects. These effects are under-
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standable since with 19 holes of 0.3 X m diameter a throughput of 8.33 X lo4 m3/s results in a nozzle velocity of 0.15 m/s, which is above the transition velocity from drip-point to jetting from perforated plates (Alhemeri, 1973). Figure 7 shows that a reduction in wedge length of about 50% was achieved with a baffle of 7.62 X m diameter positioned one-tenth of the settler length from the inlet. This reduction in wedge length was not at the expense of wedge height; there was an overall reduction in total wedge volume. Figure 12 illustrates the variation of wedge height with dispersed phase throughput and shows that it was relatively insignificant compared with wedge length (Figure 8a). The insertion of a baffle therefore does not necessitate any increase in settler diameter or cross-sectional area. Previously Jeffreys et al. (1970) observed that the capacity of a horizontal settler was increased twofold by replacing the outlet pipe by a divergent rectangular duct. The divergent duct presumably improves settling performance by trapping any unsettled dispersed phase droplets. I.M.I. (1970) also found that the capacity of either a normal or "compact" settler could be increased by 50-100% by the use of a "low-pressure drop" packing as a coalescing aid. However, little is known of the mechanism by which the wedge length in a continuous liquid-liquid settler may be predicted in a practical situation. The only thorough investigation in this regard was carried out by Jeffreys et al. (1970), who observed a zone immediately past the settler entrance in which initial mixing and turbulence effects were damped out followed by a dispersion zone where both drop-drop and drop-interface coalescence occur simultaneously. Based on this observation, Jeffreys et al. developed a theoretical model to predict the dispersion size. The model requires coalescence rates, the average drop diameter, the drop packing efficiencies, and an a priori knowledge of the axial velocity within the dispersion zone. A recent theoretical analysis proposed by Drown and Thomson (1977) is rather inconclusive because of the limitations of the relationship between the coalescence rate and the rate of decrease of the volume of the dispersion. Theoretical analysis of the process is difficult due to the complex coalescence characteristics of a multi-drop dispersion. The following empirical correlation, however, can be deduced from the data in this work as an approximate design equation for the evaluation of wedge length in practical settlers
1
I
vd
AX
13
I 15
+
VC = A(1- X)
v,
This form of equation for holdup has previously been used for countercurrent packed, spray, and mechanical columns (Sarkar, 1976; Longsdail et al., 1957). It has also been used by Buoyatiotis and Thornton (1967) to describe cocurrent flow in a stirred tank, but in that work the slip velocity is equal to the difference-as opposed to the sum-of the terms of the left-hand side. They found that V, was approximately proportional to the square of the drop size and that drop size was proportional to holdup. For the present purpose, V, can be related to holdup by V , = KX", where k is a constant to account for the physical properties of the system and agitator speed (Longsdail et al., 1957). Equation 5 can therefore be written as vd
_ -- 3.3 x
Figure 22 shows that the experimental values lie within &9% of those predicted by eq 4. Wedge length can be seen to be more influenced by throughput than energy input. Davies and Jeffreys (1970), using the systems kerosenewater and amyl alcohol-water, found that the length of the dispersion zone was directly proportional to the droplet input rate. Phase Inversion. A Mathematical Model for Phase Inversion in a Multistage Countercurrent Extractor. Which phase is dispersed in an industrial mixer-settler is clearly of importance since: (a) Mass transfer efficiency is dependent on the direction of transfer of solute. A knowledge of the inversion point is desirable so that it is not exceeded, resulting in a decrease in the rate of solute transfer. (b) Wedge length is dependent on which phase
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I
is dispersed. Phase inversion is accompanied either by a decrease or by an increase in wedge length. Phase inversion thus affects the effective settler length. A mathematical model is therefore derived to characterize phase inversion. When two phases are in countercurrent flow in a series of stirred tanks, the velocity of the dispersed phase relative to the continuous phase may be defined in terms of a slip velocity V,
AX
(4)
I
Figure 22. Calculated vs. experimental wedge length. Systems: kerosene-water, toluene-water: ( 0 )kerosene-water; (A) toluenewater.
Lw
L.
I
5 7 9 11 Experimental L,~lO*(m)
3
+
VC = KX" A ( l - X)
At phase inversion, X reaches a maximum value. With inversion representing a stationary point, the inversion holdup may be obtained from eq 6 by imposing the necessary conditions dVd/dX = 0
(7)
dVc/dX = 0
(8)
On differentiating eq 6 with respect to X and combining with eq 7 and 8, the following equations result Vd
= AKX"" - AKnX""(1 - X)
Vc = AK(l - X)'X"(n
+ 1)
(9) (10)
Combining eq 9 and 10 gives
Based on the data of Bouyatiotis and Thornton (1967), n
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 561
0,4t
VI\
0.2-
w
\s,
q..
I
I
I
vc _ - I - - +4- + - +1vd
3x
9X2
I
-,
2 27X3
4 81X4
(12)
In the limits when V, = 0,X = 1 and v d = 0, X = 0. Hence eq 12 gives a maximum value of X of 100% when there is no continuous phase flow (V, = 0). Obviously this condition is not attainable in reality. However, dispersions of kerosene with X as high as 97% have been reported (Alhemeri, 1973) in continuous stirred vessels. Figure 23 shows the difference between predicted and experimental values of holdup at phase inversion. The model agrees reasonably well for higher holdups for both systems, being almost exact at 90% holdup and about 25% high at 60% holdup. Poorer agreement is found as the holdup decreases further. It may be concluded that the model approximately predicts holdup values at the point of inversion. The model also predicts the maximum capacity of the mixing vessel in practical situations. In this work the model was only tested for relatively narrow ranges of liquid-liquid system properties: a density difference range of 0.14 to 0.19 X kg/m3, a viscosity range of 0.40 to 0.54 X lo-’ (kg m)/s,and an interfacial tension range of 28 to 34.1 X kg/s2. Clearly, it will be necessary to test the model over other systems. If the model proves valid over a wide range of system properties, it should provide a more accurate method for determining the maximum volumetric capacity of a contactor than the conventional empirical approach of s u i mixers. Mixers are usually overdesigned through lack of data relating to volumetric capacity. Inversion Characteristics. Phase inversion in a continuous mixer-settler has not previously been characterized. Limited data are now available on the hydrodynamically different case of inversion in countercurrent extraction columns (Sarkar et al., 1976; Arnold, 1974). Figures 14 and 15 illustrate that holdup at inversion varies inversely with agitator speed. This result, which is in agreement with previous work (Quinn and Sigloh, 1963), can be explained in terms of a considerably increased rate of coalescence at high energy input overriding the tendency for smaller mean drop sizes to exist. The holdup values corresponding to the inversion point at different agitator speeds are within 15 to 25% of the values of Queen and Sigloh (1963) in batch mixing vessels. Some difference would be expected because of the different geometric configuration of the mixing vessel, different flow condi-
tions, and the presence of a downstream settler in the present work. Luhning and Sawistowski’s (1971) correlation to predict the width of ambivalence in batch operation was tested by using the experimental data, but a discrepancy of about 75% was observed. In their batch system, Luhning and Sawistowski used a double-paddle mixer instead of the single-impeller mixer used in this work and this different mixing technique may result in a substantial change in the width of the ambivalent region (Quinn and Sigloh, 1963). Furthermore, Selker and Sleicher (1965) suggested that a difference should be expected between batch and flow systems. These considerations suggest that the Luhning and Sawistowki batch correlation is probably inapplicable to most flow systems. The width of ambivalence increased with decreasing Weber number, in this case in agreement with Luhning and Sawistowski (1971). As illustrated in Figure 15, the width of the ambivalent zone for the kerosene-water system was approximately 25% greater than for toluenewater. Apart from the difference in drop size and settling rates due to the difference in physical properties, a difference in the rate of coalescence would be expected to cause a change in width. Luhning and Sawistowski (1971) have shown that the width of the ambivalent range depends mainly on the interfacial tension, which has a direct effect on the rate of coalescence. As discussed earlier, drop size increased with increasing volume of the dispersed phase, the increase being more pronounced at lower agitation speeds. Except for very dilute dispersions, drop size was found to be larger for organic dispersions than water dispersions at equal stirring speed and volume fraction, so that at phase inversion from organic dispersed/water continuous (o/w) to water dispersed/organic continuous (w/o) the mean drop size decreased. The reverse was true for inversion from water dispersed/organic continuous to organic dispersed/water continuous. A similar phenomenon was observed by Luhning and Sawistowski (1971) for batch systems. The smaller time required for phase inversion from o/w to w/o could be attributed to the fact that water in organic dispersions always coalesce more rapidly than the corresponding organic in water dispersion (Rodger et al., 1956). Figure 15 shows clearly that the maximum range of phase inversion holdup with rpm is between 50 to 90%. Arnold (1974) reported that the range of phase inversion holdup was between 60 and 80% in an Oldshue Rushton column in which the nature of inversion was cyclic. In the present work, it was steady state. This fundamental difference in the mode of inversion prevents detailed comparison with Arnold’s results. Application to Design Based on this study, some recommendations may be made for the design of industrial scale mixemettlers. The recommendations apply mainly to horizontal arrangements, but some, for example those concerned with the mixer, are equally applicable to other designs. (a) With either phase dispersed, drop size in a standard geometry mixing vessel followed by a settler may be predicted by eq 3. Effects of mass transfer are not taken into account. (b) The minimum value of the rotor speed, N , should be above the critical speed to produce a uniform dispersion in the mixer. On the basis of the present data, this critical speed corresponds to an energy input per unit volume >5910 J m-3. The maximum N should be below the value producing excessive secondary haze which prevents effective separation in the settler. The corresponding maximum energy input per unit volume is 18830 J m-3.
562
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983
Provision for a variable speed drive is preferable to ensure uniformity of dispersion and to allow for variations in d3z due to possible changes in recycled solvent properties, or feed, with time. Above the critical speed, holdup values are dependent only on phase flowrates. (c) A vertical baffle should be located centrally immediately opposite the phase inlet of the settler. The materials of construction-which determine whether or not the component parts are wetted by the dispersed phase-are of no significance. The ratio of the phase inlet port diameter to the settler diameter should not be less than 0.16 and clearly should not be so large as to reduce the mixing efficiency. The baffle should be approximately 0.75 X the diameter of the settler. The baffle position should be approximately one-tenth of the settler length from the inlet. The wedge length under such conditions may be predicted by eq 4. (d) With a baffle installed according to the above recommendations, the ratio of settler volume to mixer volume, within normal operating limits, need only be 2 to 2.5;this represents a 20-30% reduction in settler size compared with an unbaffled settler. For normal operation it is preferable for the wedge to extend only 70% along the settler to allow for process fluctuations which often lead to severe phase entrainment. For sizing settlers, the criterion of wedge volume to settler volume as a possible design parameter is impractical since the interdrop and drop-interface coalescence, which control the wedge volume, can never be predicted with any degree of accuracy. The current state of knowledge on coalescence is indeed limited (Sarkar et al., 1980). (e) With the system kerosene-water, but not to any noticeable extent with toluene-water, there wm a tendency for scum to accumulate at the interface in the settler. To obtain reproducible results on an industrial scale, therefore, it is desirable to incorporate some tapping off device for interfacial debris removal. (f) The total linear velocity of both phases in the settler m/s for efficient phase sepashould ideally be 0.8 X ration. Davies and Jeffries (1970)concluded that mean axial velocity of the phases in a horizontal gravity settler should not exceed 1.0 cm/s. Above this value, the efficiency of separation of any secondary haze would be low in practical sized equipment. If, however, a certain degree of entrainment is allowed in a specific application, the linear velocity may be as high as 6 cm/s (Orjans and Godfrey, 1977). By analogy,if a rectangular settler is used, scale-up should be on the basis of velocity in the annulus. (g) Phase flow rates should preferably be within the range V,$v, = 1:3-3:l;or if necessary, the contactor can be operated over the wider range. A range of V&vc = 1:80 can be accommodated by recycling the continuous phase. The recycle stream must be taken from the settler itself in order to avoid excessive back-mixing; allowance must be made for back-mixing within the stage on the basis of a mass balance. (h) Holdup values a t the point of inversion may be determined by means of the mathematical model developed in this work. Equation 11 may be used to predict the maximum capacity of a mixer-settler in which phase inversion occurs in the mixer prior to phase entrainment in the settler. However, the phase inversion point is very susceptible to minor fluctuations in flow rate, agitator speed, or the presence of impurities. A limitation of the present work is that it covered only two systems with a range of interfacial tension of 28-24.1 X kg/s2, of density difference 0.14to 0.19 X 103 kg/m3, and of viscosity difference 0.40 to 0.54 X lo-' (kg m)/s.
Ideally, a wide range of physical properties should be used. The interfacial tension is of particular interest because it is a major factor affecting the efficiency of inter-drop coalescence in the settler and difficulties may arise with the mixer-settler for systems with interfacial tension cr
