Znd. Eng. Chem. Res. 1995,34,2427-2435
2427
SEPARATIONS Batch Settling of Liquid-Liquid Dispersion Corinne Nadiv and Raphael Semiat* Chemical Engineering Department, Technion, Institute of Technology Haifa 32000, Israel
A liquid-liquid dispersion separation process was reviewed to enlighten a few aspects. A physical comprehensive model, followed by a mathematical model, was developed and compared to a set of experiments for the investigation of the liquid-liquid batch settler phase separation. Different parameters were checked experimentally, as initial dispersion heights, settler diameters, dispersion types, etc. Results allow the use of the experimental procedure, with the mathematical model, as a tool in monitoring the dispersion behavior in commercial units.
Introduction
A liquid-liquid two-phase flow takes place in many industrial processes. Common examples are water separation from crude oil, dispersion separation in different solvent extraction settlers, or dispersion separation a t the ends of differential direct contact mass transfer columns. Proper design of the industrial equipment is usually based on local experience gained through complicated, large scale industrial processes or on the know-how supplied by the equipment manufacturer. Many parameters influence this type of a separation flow. Among them are the physical properties of industrial fluids that are not always well-defined. Solvents accumulate impurities that tend to change the important properties, such as viscosity and surface tension. In most cases, impurities change with time, because changes in feeds to the working systems cause behavioral changes in the dispersion flow. Dispersion is made by mixing one phase with the other, using high shear, high turbulence devices. Different mixers may produce different particle size distributions from the same solutions involved. When solvents in contact are not in chemical equilibrium, mass transfer derives dynamic changes in physical properties and hence different size distribution of the drops are generated by mixing. Dependence of particle sizes on different parameters is discussed in detail in Hoffer (19721, Barnea (19721, and Kumar (1983). In this article we concentrate on a relatively small part of the problem: assuming dispersion is controllable and the settling device is well-defined, it is important to know more about the parameters affecting coalescence and separation. The preferred approach in this work is, therefore, to investigate a batch settler in order to try gaining a better understanding of the device often used in continuous solvent extraction: a dispersion band gravity settler. Gravity settling is based on density differences between the two solvents in contact. The industrial demand is the separation of both phases, a t minimum entrainment of the opposite phases at low settler volume and area. Settlers of this type are divided between empty vessels or vessels furnished with parallel plates
* To whom correspondence should be addressed. E-mail:
[email protected].
(Perry, 1984; Treybal, 19631, or the “compact settler” as suggested by Mizrahi and Barnea (1973). The last one is preferable, since it would tolerate higher fluxes than an empty settler. On the other hand, the horizontal or near horizontal surfaces are subjected to volume clogging, even when low solids concentration is present in the dispersions. Many authors have suggested t o relate batch experiments of phase separation to continuous operation in order to cut scale-up expenses. Ryon et al. (1959) suggested first a simple mathematical relation between dispersion height and volumetric flow rate; Gondo and Kussunoki (1969) suggested an empirical relation of this type for the water kerosene system. Barnea and Mizrahi (1975) arrived at the same empirical relations but through a semitheoretical approach. Different relations were found by Stonner and Wohler (1975)that suggested performing a few batch experiments in order to obtain values of constants that relate t o the total flux with the dispersion height. The most recent works, by Dalingaros et al. (1985, 1986a) and Hartland and Jeelani (1985,1987,1988), made a significant approach, taking into account most physical phenomena to model the process. Hartland (1988) reviewed many research works that include most viewpoints taken in order t o get a better understanding of this separation process. The batch settler has another use (not very common in the literature): as a tool for observing the changes in the expected settling behavior, because of changes with time, of solvents’ properties in a commercial unit. This is a first-hand tool t o monitor large plant operations. We would like to enlighten this point in this work.
Phase Separation Characteristics Assuming a two-phase liquid-liquid dispersion, generated in a mixer, is poured into a vertical tube, a characteristic dependence of the changes of dispersion height with time is shown in Figure 1. The height of the dispersion band is reduced from the initial value on the left side into the interface between the two phases a t the end of separation on the right side. Parameters that affect the separation are (Skelland and Lee, 1978, Van Heuven and Beck, 1971, Luhning and Sawistowski, 1971 and McClarey and Mansoori, 1978) the following: (1)size and size distribution of drops in the continuous phase; (2) drop motion in the disperison;
0888-5885/95/2634-2427$09.oo/o0 1995 American Chemical Society
2428 Ind. Eng. Chem. Res., Vol. 34, No. 7,1995
L
0
50
100
.
L
’
*
.
’
.
150
.
‘
.
’
.
,
200
250
Time, [SI Figure 1. Dispersion height changes with time.
(3) drop coalescence, into their own phase and binary coalescence between drops; (4) existence of different dispersion types, that is, oil in water, water in oil, or a combination of both; (5) geometry, that is, diameter of the settling tube, height of the initial dispersion band, and insertions in the separation volume; (6) existence of solid or gas phase in the dispersion. It is also important t o recognize the influence of the following operational parameters that depend on prior conditions and may influence partially the parameters listed earlier: (1) physical properties of the phases involved, that is, viscosity, density difference, surface tension, etc.; (2) mass transfer in the mixer and its influence on drop sizes and size distribution; (3)volume ratio of the two phases, or concentrations of the phases involved; (4) mixing characteristics, such as mixer geometry, mixer type, impellers, impeller relative position to interface before mixing started; (5) intensity and residence time of mixing. This list depends on the choice of solvents, as well as on the choice of equipment for the process. Assuming chemical (solvents and solutes) and mechanical systems (impeller, dimensions, housing of the mixer, etc.) are chosen, a defined dispersion is being poured into a settling tube. For simplicity, the description here assumes “oil in water” ( O W )dispersion. ‘Water in oil” (W/O) will show a similar picture, except that drop motion will be directed usually downward. The case when both can take place in the same settler will not be discussed here. As seen in Figure 1, two branches describe the height of the two boundaries of the dispersion height (Hartland and Jeelani, 1987). Since the height is described against time, the lines’ slope represents the decay velocity of the two fronts. Settling and Coalescence in Dispersion Band Region A in Figure 1 describes the beginning of the process. Dispersion just poured into the tube has drops generated in the mixer that move in all directions due t o turbulence induced during the short history of the flow from the mixer into the tube. The decay of this turbulence is shown as the change of line slope that develops from close to 0 at t = 0, as average velocity is equal t o 0. After a short time front velocities are increased to almost constant values (constant curve slope). Different mechanisms take place in the two different coalescence and sedimentation fronts. Drops that are close to their phase start to coalesce with it. This mechanism is relatively slow, so drops start to
accumulate and to “stay in line” in order to reach the coalescence position. On the other side of the dispersion band drops start to develop the “slip” velocity, while accelerating to the maximum possible drop velocity according to drop size and local drop concentration. This happens all over the dispersion band, up to the coalescence front, except that the motion inside the dispersion is almost invisible from the outside, while velocities on both ends can be seen. Region A continues until fronts on both sides reach slight changes in velocity and enter region B or C. The time scale of region A is usually short in relation to the entire coalescence process duration (depending on dispersion band height). A long A region shows basically slow turbulence decay as longer time is needed t o start accelerating into significant vertical slip velocity. Sedimentation Front (B). The curve slope increases slowly with time, as in region B in Figure 1. The maximum possible velocity in this region depends on the drop size, fluids’physical properties, and the local drop Concentration. A local change in velocity may occur in cases of local binary coalescence that might take place between usually large drops, and depends on the drop concentration in the dispersion. Sedimentation velocity varies according to size distribution. The sedimentation front can be seen sharply in cases where drops form a narrow size distribution and/or at high drop concentration. The front is difficult to be seen in cases where wide size distributions exist, as well as in cases where dispersion has a dilute drop concentration. Sedimentation continues until drops meet the coalescence zone. In most cases when the coalescence velocity is smaller than the sedimentation velocity, drops decelerate to coalescence velocity and join “the line”, waiting for coalescence to take place. This can be seen as changes in the curve slope, which usually looks like deflection point. The curve slope then reduces to the corresponding slope of the coalescence front. This explains the often found sigmoidal curves. When coalescence is faster than or closer to sedimentation, the curve has a near-parabolic shape. Coalescence Front (C). The rate of drops which coalesce with their own phase may be faster or slower than the drop velocity in the dispersion. Schematics of the coalescence front is shown as region C in Figure 1. When slower drops are waiting to coalesce, a thick layer of relatively large drops is formed. This was described earlier (Jeelani and Hartland, 1985,1986)as the “dense layer” in the settling zone. Coalescence velocity is then almost constant, and is affected by the thickness of the layer, applying pressure on the drops in front of the coalescing front. This average drop size is usually larger than the initial average drop size due to multibinary coalescence during the short history in the settler. Usually, the coalescence front has a near-constant slope. Final Stage (D). In most cases, either one or both coalescing and sedimentation fronts show a change in the slope toward the end of the separation process, as can be seen as region D in Figure 1. This is due to the existence of a tail of small drops that appears in the size distribution of the drops in the settler. Since they are small, they also move in low velocity. A portion of these drops might even move in the opposite direction, entrained with the continuous phase. This portion can be seen only after the large and moderate size drops are already coalesced. Naturally, the slope of the front tends to zero as time passes due to a small fraction of the last small drops. Usually, it is seen that the
Ind. Eng. Chem. Res., Vol. 34,No. 7,1995 2429
n
-1cm
U
t>O
t=O
A€)= E U ( € )
Two constraints exist for the flux. For a sedimentation zone, limflc) = uOc
Figure 2. Schematic presentation of the mathematical model assumptions.
dispersed phase has reached the final height, yet separation continues slowly in the continuous phase. Even though a relatively small portion of the mass is separated, it represents the entrainment of the dispersed phase in the continuous one. If it is not allowed to settle, in continuous process, this entrainment will be responsible for backmixing, which will cause performance reduction in large scale units. It is important therefore t o pay attention even t o this small portion, especially in those industrial processes which are so sensitive to entrainment or back mixing. The above description is valid for oil in water dispersion. As mentioned earlier, this also can explain the behavior of water in oil dispersions. The choice between the two types, if possible (since it depends mainly on the volumetric flow ratio of the two phases), depends on the character of the process. It is clear, however, that the type of dispersion dictates the nature of the entrainment and hence the nature of backmixing. Mathematical Model Assume a dispersed phase fraction EO at time t = 0 and an all over dispersion volume which changes into three discrete zones a t any time t , as shown in Figure 2. When the upper and lower zones have values of 0 and 1,the central dispersion zone has an average value of E . This assumes no segregation inside the dispersion zone and no entrainment of the opposite phases in the separated clear phases. Based on the analysis by Aris and Amundson (1973) for batch solids suspension precipitation, it is possible to suggest a simple model for the liquid-liquid separation as follows. Declaring f l ~ as ) dispersed phase volumetric flux, along the z axis originated at the bottom of the batch settler with horizontal cross-sectional area A, differential mass balance can be written as follows:
For a coalescence zone, lim
RE)= 0
Relation between the dispersed phase flux and the velocity U ( E ) is given for a sedimentation zone as well as for a coalescence zone by
(5)
C-cmax
where uo is a single drop sedimentation velocity in infinite medium and cmax= 1. Nondimension parameters are chosen as Z = z/ho, F = A E ) / u o Eand ~ ~ T, = uot/ho for the z axis, flux f, and time t at the sedimentation zone; ho is the initial dispersion height. For the coalescence zone, time t turns to T = u*t/ho and flux f changes to F = A E ) / u * E ~Substituting ~. the nondimensional variables yields a6 a6 - F(E)at az = 0
(6)
where F is a flux derivative with respect to E . Boundary and initial conditions are as follows:
E=O ~
at Z > 1 T > O
= atl Z < O T > O
at Z < 1 T=O
(7)
Flux conditions are therefore as follows. For the sedimentation zone, lim F(E)IE = 1
(8)
€4
R E= ) 0 at
E=
0
For the coalescence zone, lim F ( E )= 0
(9)
€-Emax
F(E)= 0 at
E
=1
Equation 6 can be solved by the characteristics method, assuming the existence of a family of characteristic curves in plane Z-T, given parametrically as Rs),Z(s), and 4 s ) . Multiplying eq 6 by dT/ds and rearranging yields the following: (10)
+
Choosing a family of c w e s so that U/ds P ( EdT/ds, ) will lead into the characteristic equation
F ( E= ) -dZ/dT Dividing by A dz and rearranging yields
(4)
€4
n
w’ok
(3)
(11)
Dispersion concentration E is constant along the characteristics as ddds = 0. Characteristics lines Z(t) intersect a t two different concentrations E . The sequence of the intersection points represents the front separating between the characteristics. In order to represent the batch separation process, it is necessary to supply an expression for front velocities to solve an actual front location with time. Mass balance on a control volume across two front sizes is given by
2430 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995
tP[2ne0u,3(1- t , 2 ( 3 a e ~ ~ , u+ *~) tJ6h;(uo - E ~ ( u * uJ)] 6h03= 0 (20) Similar expressions can be derived in the case of O N . Four unknown constants are needed for solving the system completely. For known drop sizes, the sedimentation velocity, UO,is calculable from the Stokes expression. It may also be extracted from a simple experiment as will be demonstrated later, together with the coalescence velocity, u* and the two other unknowns n and a. Since velocities are found from experiments, it is easier and more accurate to refer to the group constants nuo2 and au*2.
+
Vis the volume of drops within the control volume. dzl dt is the front velocity that can be nondimensionalized as
(13) For the sedimentation front Therefore,
€1
=
EO
and
€2
= 0.
+
(19)
Experimental Section Apparatus. The experimental work was carried out in a closed cycle system shown schematically in Figure 3. The dispersion was formed in a mixer consisting of a 5 L, cylindrical glass tank with a half-spherical bottom. The total height of the mixer was 0.3 m and its diameter was 0.2 m. It was fitted with four equally vertical W C baffles. Agitation was provided by a PVDF turbine, shown also in Figure 3. Turbine motion was controlled by an adjustable speed motor, between 1and 10 s-l. The turbine relative location in the mixer housing was controlled by an adjustable shaft. The formed dispersion was poured in a vertical glass pipe of 1.3 m height, serving as gravitational settler. The pipe could be easily replaced and two diameters, 0.065 and 0.023 m, used as settlers. The bottom of the settler was initially filled with water from a storage tank. At the end of the dispersion separation the two phases were returned to the mixer by the use of a centrifugal pump. Liquid-Liquid System. Water and 40%n-heptane in parafin oil were chosen for the two liquid phases. The physical properties of the phases at 20 "C are density and viscosity of water, 998.0 kg/m3 and 0.98 m Pps, respectively; and those of the organic phase, 799.0 kg/m3 and 4.15 m Pa-s, respectively. Interfacial tension is 58.9 mN/m. Procedure. The mixer was filled with a known volume of each phase. The impeller was placed at the required height. The motor was switched on, and the impeller speed was set by means of a tachometer. The two phases were agitated during a chosen mixing time. The formed dispersion was then poured instantaneously into the settler in which water was kept beforehand at the bottom. During the batch separation, the variations in the position of the sedimentation and coalescing interfaces with time were recorded until two clear phases were formed. The final separation time was also recorded. Ideally, the separation time is the time required for the two phases to separate completely, but in practice is defined as the time when a clear immobile area of interface appears since some drops tend to cling tenaciously to the wall or there is often some entrainment. In order to keep the phase ratio constant along the different experiments, the water that was filled at the bottom of the settler should be drained out before the return of the two phases into the mixer. This was repeated a t different dispersed phase holdup fractions, different agitator speeds, and different mixing times in the mixer, and also at different diameters and different initial dispersion heights in the settler.
Time for complete separation t f , is calculated by equating zeoa1= Zsed. A third-order polynomial is obtained in tf.
Results and Discussion Initial Dispersion Height. The influence of an initial dispersion height on a total separation time is
For the coalescence front €1 = 1,F(1)= 0, € 2 = eo, hence,
Expressions for velocities and fluxes are needed in order to integrate eqs 14 and 15. Kumar and Hartland (1985) collected many correlations for a drop relative velocity in dispersion. Based on the wide range of equations, it was decided to choose an expression that may combine some of the most important terms. Sedimentation velocity might then be written as
where n is constant. The first term takes into account the dispersion influence while the second increases the velocity slightly with time due to binary coalescence that takes place during sedimentation. This term increases with E , as collision chances increase too in high drop concentration. Coalescence velocity was chosen as
(
u, = (1- E ) 1
+ a-
u*
(17)
a is a constant.
In this velocity expression, first introduced here, the first term takes into account a reduction due to a high concentrated dispersion, while the second term introduces the influence of the hydrostatic pressure applied by the drop layer that is built with time and increases coalescence velocity. u* is the coalescence velocity of a single drop with its phase, yet to be detected. Rearranging eqs 14 and 15 together with velocity expressions 16 and 17 and returning to dimensional terms and integrating lead to two expressions for the different fronts. Sedimentation front for water in oil dispersion takes the form
While the coalescence front takes the form
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2431 VNiahle speed Motor
350
y
.--I
I
I
1so
I
‘J
t
v1
i,,l l,,E!l Settler diameter
50
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n Batch settler
P
150
$ -100
* .
Mixing time = 10 min Mixing speed = 275 rpm
300
0
20
I
,,,,
40
60
80
100
120
Initial dispersion height [cm]
Figure 6. Overall dispersion separation time versus initial dispersion height.
Retum pump Figure 3. Experimental system.
a
100
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sM
2
40
20
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Time [sec]
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explained later in this work. The upper lines in the figure demonstrate coalescence of the organic phase, while the lower lines represent sedimentation fronts. It is clear that O/W type dispersion was created in this set of experiments. The overall separation time strongly depends on the initial dispersion height. Upper fronts are almost parallel, especially for higher initial dispersion heights. This shows that coalescing velocity is independent of initial dispersion height, at least for this pair of solvents. Lower fronts is Figure 4a form the same line for at least the first 80 s but later separate to form different sedimentation fronts as dictated by the overall settling behavior. The picture is not so clear in Figure 4b. Here, due to a larger diameter, initial sedimentation fronts are not so clear and no observations of the fronts were made. Instead, straight lines were drawn from the origin to the first observed points that represent the appearance of the clear sedimentation fronts. The straight lines appear in the same vicinity and represent similar behavior at the beginning of the separation process. Comparing Figure 4a with 4b shows that, for the same initial height, a longer separation time is needed for the larger settler diameter. The settling region is relatively shorter, with respect to the overall separation time, for the larger settler diameter, but the coalescence rate is faster (higher slope) for the smaller diameter settler. Final separation times are plotted against initial dispersion heights in Figure 5. It is clear that the use of larger separation area for the same initial dispersion heights needs a longer overall coalescence time. This is explained by higher flow disturbances that may appear in the larger settler. This “turbulence” is caused mainly by the motion of the continuous phase, opposite to the direction of the settling drops, and it is affected by the wall. An attempt to correlate the data into a straight line yield an equation of the form:
300
Time [sec]
Figure 4. Effect of initial dispersion height on dispersion separation. Symbols represent different initial heights. Diameter of batch settler: (a) 2.3 cm; (b) 6.5 cm.
shown in Figure 4 for two different settler diameters, 2.3 (a)and 6.5 cm (b). Mixing speed was kept constant at 275 rpm, and mixing time was 10 min for all experiments. Solvents phase ratio was kept close to 1:l. The mixer impeller was located inside the organic phase when at rest. The importance of this location will be
here tf represents the final separation time, to represents the mentioned wall effect, HOis the initial dispersion height, and Va is an average separation velocity. Simple least squares analysis shows that V, is the same for both curves and has a value of about 0.41 c d s . Values of t o , on the other hand, change from 21 s for the narrow settler to 88.5 s for the larger diameter settler. This is a large difference that needs to be taken into account in the design of liquid-liquid settlers. It is possible to conclude that a proper design of a dispersion band settler would be improved if an attempt
2432 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Mixing time = 10 min hO = 87 + 3 em D ~ 2 . 3 c m
1
80
2 .-M
80
c
60
.-e L 0
h .n
rh
60
-
Mixing speed 1831" +2356111 -A280rpm 326rpm 385rpm 437rpm
40
40
Y
T
r
20
20
r
v -
0
50
100
150 Time
200
250
300
[SI
results. Experimental points are identical with Figure 4a.
b
-3
U D=2.3cm
t-Dn2.3cm -€ID=6.5cm D=6.5cm
*
300
100
80
60
sM
.r?
2
0.6 Y
Coaiescense
200
I
Sedimentation
$ 1
100
Time [sec]
Figure 6. Implementation of theoretical model to experimental
-
0
I
40
20
0
0 0 20
40 60 80 100 Initial dispersion height [cm]
120
Figure 7. Calculated sedimentation and coalescence velocities versus initial dispersion heights (data from Figure 6).
is made to subdivide it into parallel vertical settlers by introducing vertical or close to vertical plates. This will be similar, in a way, to the compact settler suggested by Mizrahi and Barnea (1973), who introduced nearhorizontal plates into settlers, or to the recent work of Rommel et al. (19921, who investigated the settling behavior in near-horizontal plates. It appears that the small distance between plates, horizontal as well as vertical, tends t o reduce turbulence effects. Vertical plates will accumulate less solids, if they tend to precipitate in industrial cases, than horizontal plates. More research work is needed, however, for the optimization of this finding. Figure 6 shows the results of the application of the mathematical model to the data shown in Figure 4a for the narrow batch settler (2.3 cm diameter). The lines in the figure were calculated using an optimization program written in Matlab. The program was designed to obtain the best values for uo and nuo3 from the upper sedimentation front (eq 16) and for u* and U U * ~from the lower coalescence front (eq 17). As mentioned earlier, the model ignores the entrance and end effects (A and D regions, respectively); however, the calculated lines shows a good agreement with the experimental points. Experimental and calculated final separation times match together. Based on calculations, the sedimentation and coalescence velocities were plotted in Figure 7 against initial dispersion height for the two batch settler diameters 2.3 and 6.5 cm, respectively.
100
200 Time [sec]
300
Figure 8. Effect of mixing speed on dispersion separation. Diameter of batch settler: (a) 2.3 cm.; (b) 6.5 cm.
Sedimentation velocity u g of the narrow settler is shown to be constant over the range, in the order of 0.6 c d s . This can give some idea on the average size of the drops in the dispersion. The sedimentation velocity of the larger settler is similar, except for smaller initial dispersion heights. For both settlers the coalescence velocity is lower than the sedimentation velocity and therefore controls the separation process. It is clear from Figure 7 that a narrower settler presents higher coalescence velocities than a wider settler. This may be explained by wall effects that enhance coalescence. Mixing Intensity. The influence of mixing intensity can be seen in the two settlers in Figures 8 and 9. The mixing range was chosen between 180 and 457 rpm. Mixing time before settling was 10 min. Initial dispersion height was 87 f 3 cm for the 2.3 cm diameter settling tube and 94 f 1 cm for the 6.5 cm diameter tube. The phase ratio was kept close to 1:1, and the impeller position was in the organic phase. A dispersion of type OM' was presented in the settlers. Two different zones can be seen in the figures. For low mixing intensity, say up t o 330 rpm in both settlers, the separation time increased with the mixing intensity. Further increase of the mixing intensity yields no change in the separation time and the second zone presents a plateau. As can be seen in Figure 8, again, the lower sedimentation front is clear in the small diameter settler and it is not clear in the large diameter settler. Since no clear front was seen, straight lines were drawn at the left lower front to represent the sedimentation front, up t o the region where the clear front was seen. This is probably not accurate, as can
Ind. Eng. Chem. Res., Vol. 34,No. 7, 1995 2433 a 100
Mixing time 10 min h O = 94 + 1 cm
400
e
m
80
m
m n
8
60
I
D
loo[,
, , ,
I * ,
, ,
@
,,,
,El,, 1
25
40
Settler diameter
20
23Ull
0
0
100 200 300 400 Mixing speed [rpm]
0
500
0
100
200 Time lsecl
300
Figure 9. Overall dispersion separation time versus mixing speed for the experiments in Figure 10.
be seen in Figure 8a. It is important to note that, a t low mixing intensities, the sedimentation front moves faster than that for higher mixing intensities due to larger drops being generated there. Lines of sedimentation front coalesce together in the figure, to form an apparent identical front. Drop sizes at high mixing intensities, according to the sedimentation fronts, appear insensitive to the mixing intensity. It is also clear, from the shape of the sedimentation front (also in this set of experiments), that the coalescence front is controlling the separation time. The sedimentation front moves faster a t the beginning and then slows, awaiting the coalescence t o take place. Figure 9 presents the variations of separation time, for the two settlers, at different mixing speeds. This figure summarizes the results in Figure 8. For both settlers, separation time increases with mixing intensity, affected by increasing shear and reducing drop sizes. At some mixing intensity, separation time remains constant, as can be seen. At higher mixing intensities, the larger diameter settler needs a longer separation time, while a t low mixing intensities where drops are large, the smaller diameter settler needs a longer separation time. Mixing Time. The effect of mixing time is shown in Figure 10. Experiments were conducted for mixing times between 1 and 10 min. Other parameters were kept constant. A low mixing speed of 275 rpm was chosen in order t o sharpen the influence of the mixing time that might fade out at higher shears. The initial dispersion height was kept 88 f 3 cm in the smaller diameter pipe. Phase ratio was kept close t o 1:l and the impeller position was a t the organic phase. Overall separation times are shown in Figure 11. Figure 12 shows the front velocities calculated by the mathematical model. It is clear from the results of Figures 10-12 that little influence exists a t low mixing times (up to 3 min), as overall separation time increases with mixing time. This is again attributed to the influence of the controlling mechanism which is the coalescence velocity. No influence exists for higher mixing times. At the cited conditions (chosen solvents and high intensity mixer used) the phase separation is almost independent of mixer residence time. The conclusions may change for different conditions. It is important also to note that mixing time, or mixing residence time in a continuous operation, needs to be determined by the rate of mass transfer of the solute between the phases. A proper
Mixing time
-2min -4min +Smin
-8min +%in -1Omin
6min
0
200
100
0
300
500 Mixing speed = 275 rpm
400
-
300
1
n L
P)
:.* e
*
. I
E 0
200
-
* e
. e . *
m
. m m m . H
e
ISettler diameted
100
W
0
* * * O * . a * l a . * l l l l l l l
0
2.5cm 6.3cm
.'"""."
100 200 300 400 500 600 700
Mixing time
[SI
Figure 11. Overall dispersion separation time versus mixing time.
design would minimize the volumes of the mixer and the settler in order to reduce the equipment and solvent costs. Location of Mixer Impeller. Figure 13 demonstrates an important parameter that is rarely mentioned in the literature, namely, the influence of impeller location. The impeller used in the experiments is a variation of the turbine type impeller that occupies a large portion of the mixer volume, as shown in Figure 3. The impeller locations could therefore be chosen either in the organic phase, in the aqueous phase, or in
2434 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995
,
1 ,
-1
Settler diameter D12.3cm -&D=2.3cm &D-6.5cm D=Q.Scm
-+-
0.8
+
t
0.6
0.2
0
2
4 6 8 1 0 1 2 Mixing time [min]
Figure 12. Calculated sedimentation and coalescence velocities versus mixing time (data from Figure 10). 140
-r' 200
I
1
120 100 80 c'm 6 0
-5 -r'
120 100 80 60 40
20
0
0
0
100
200
Conclusions
40
20
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300
Time [SI
Mixing time: 4 minutes Phase ratlo: 1:l Impeller position 0 aqueousphase o Interface o organic phase
100
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Time [SI
-B 5
the coalescing bed while reducing significantly the sedimentation velocity. The second curve, where the impeller was initially submerged in the aqueous phase, shows shorter separation times. The third type of curves shows a significant reduction in the overall separation time. The improvement in separation time may be attributed to the coexistence of the two types of dispersions in the same settler. As mentioned earlier, the coalescence front velocity was found to be slower than the sedimentation front. An area increase a t the coalescence front will therefore undoubtedly increase the coalescence rate. In this case, two types of dispersions coexist in the settler: two coalescence fronts on the two branches of the separation curve where the coalescing velocity on both sides is lower than sedimentation velocities, but the coalescing area is twice as much, and, therefore, the overall dispersion separation is faster. Unlike the previous sets, a difference exists between the separation times for varying mixing intensities. This interesting finding calls for a wider investigation, with the use of more sophisticated equipment than with the naked eye, to determine the real behavior of such important flows.
120
100 80 60
40 20 0
0
200 Time [SI
100
300
Figure 13. Separation curves for different impeller locations: (a) 307 rpm; (b) 367 rpm; (c) 428 rpm.
between the two phases. At this set of experiments, the phase ratio was kept P:l, mixing time was 4 min, and mixing velocity was 307,367, and 428 rpm as shown in Figure 13a, 13b, and 13c, respectively. The lower fronts were monitored, and the upper fronts were simulated by straight lines. The lower curves present the case where the impeller was initially located inside the organic phase as in the previous experiments. In the central curves the impeller was located in the aqueous phase. The other curves present the cases where the impeller was centered at the interface between the two solvents. The lower curves represent a simple separation case, where most of the dispersion in the settler behaved as oil in water. The other two curves are not so clear, and they are believed to correspond to different combinations of the two types of dispersions, O M and W/O, that coexist in the same settler. When the two fluids are equal in volume, or close to that, two different types of dispersions may be produced. Expected differences between separation times in different types of dispersions can be observed, due t o a large difference in the physical properties of the continuous phases. Viscosity, for example, changes considerably between the two phases and affects significantly the fluidity of the continuous phase throughout
A physical model was suggested to allow better understanding of the liquid-liquid separation process. A simple mathematical model was developed in order to analyze the experimental results and to calculate parametric values such as sedimentation and coalescence velocities. It was shown that, at least for the solvents used here and the turbine mixer, overall separation time is strongly dependent on the initial dispersion height, the diameter of the batch settler, and on the type of dispersion generated. Parameters as mixing intensity and mixing time have less importance. Based on the analysis, the batch settler may be used as a tool for monitoring the changes in the solvents in an industrial unit, in order to predict any expected deterioration in the overall fluid dynamic behavior.
Acknowledgment The authors would like t o acknowledge the support by the fund of the Benard L. Maas Foundation and for support by the fund for the promotion of research at Technion. Nomenclature A = settler cross-sectionalarea [m21 D, = settler diameter [ml RE)= dispersed phase flux [&SI F = dimensionless dispersed phase flux h = batch settler dispersion height [m] ho = initial dispersion height s = parameter, eq 10 t = time [SI tf = final dispersion separation time T = dimensionless time u = velocity [ d s l uo = single drop sedimentation velocity [ d s l uC = dispersion coalescence velocity [&SI us = dispersion sedimentation velocity [&SI u* = single drop coalescence velocity [ d s ] U = dimensionless front velocity V, = average separation velocity z = vertical axis [ml
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2435 zcoa1 = coalescence front location [m] Zsed
= sedimentation front location [ml
2 = dimensionless height Greek Letters e = dispersion concentration emax= maximum dispersion concentration
6 = dimensionless coalescence front location 5 = dimensionless sedimentation front location Literature Cited
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Received for review October 10, 1994 Revised manuscript received March 22, 1995 Accepted April 3, 1995* IE9405870
@
Abstract published in Advance A C S Abstracts, May 15,
1995.
