Ind. Eng. Chem. Res. 1989, 28, 1096-1101
1096
COMMUNICATIONS Partial Mass-Transfer Coefficients and Packing Performance in Liquid-Liquid Extraction As droplets pass through a contactor such as a packed tower, they experience a sequence of hydrodynamic events which include (a) free movement within the packing voids, (b) collision with the packing and subsequent distortion, (c) collision followed by breakdown into two daughter droplets, (d) passage through narrow voids accompanied by droplet elongation, and (e) coalescence with a stationary drop in the interstices of the packing followed by redispersion. Each of these events is characterized by its own rate of mass transfer, which can be expressed in terms of partial mass-transfer coefficients. The scale-displacement technique has been used to measure such coefficients, and the available data are examined in order to identify those events that promote high mass-transfer rates. Partial coefficients thus provide a valuable guide to those events that promote high mass-transfer rates and therefore to those features that are important in the design of high-efficiency packings. When systems exhibit interfacial turbulence, mass-transfer coefficients frequently decrease with time due to aging of the droplet interface. In this situation, it is important t h a t a fresh interface be maintained, and this can be brought about by packings that promote a rapid coalescence-redispersion cycle. In any liquid-extraction operation, the environment of the dispersed phase changes from point to point in the contactor as the droplets progress through the system. Thus, for example, in a mixer-settler contactor, the turbulence levels experienced by the drops vary with both radial and axial positions in the mixer and are very different from the degree of turbulence in the settling chamber. Each of these levels makes its own contribution to the overall mass-transfer process and should be properly understood if a realistic evaluation is to be made of the mass-transfer characteristics of the unit as a whole. Another very relevant situation arises in packed towers where a range of events can be experienced by the drops as they move through the column. Thus, different transfer rates will operate during drop formation at the inlet nozzles and during passage through the packing. During the latter period, drops may either move freely within the interstices of the packing or suffer deformation, rupture, and/or coalescence as they pass through the packing voids. Each situation will be characterized by a different mass-transfer rate and once again a knowledge of the respective masstransfer coefficients is essential if the behavior of the packing is to be understood and the overall coefficient computed. It has been customary to date to adopt an overall approach to mass-transfer studies of specific contactors and to express the transfer performance in terms of a single coefficient for the unit as a whole without reference to the individual mechanisms involved. It is true that the different mass-transfer rates during drop formation have been recognized for some years but transfer occurring thereafter has usually been aggregated in terms of a single coefficient. In order to examine contactor performance on a microscale and thereby achieve a better understanding of the transfer process, it is now proposed that “partial” masstransfer coefficients be adopted, each of which relates to a particular event or set of events during the life cycle of the drops as they pass through the contactor. Ultimately a knowledge of such partial coefficients is essential to the synthesis of the true overall coefficient, which reflects 0888-5885/89/2628-1096$01.50/0
events within the contactor as a whole. A related (and complicating) feature in the assessment of contactor performance lies in the characteristics of the extraction system under investigation. Many systems of commercial interest exhibit spontaneous interfacial turbulence which must be taken into consideration when selecting a contactor for a particular duty. This problem and the nature of partial coefficients are now discussed below.
Measurement of Partial Mass-Transfer Coefficients The concept of partial coefficients is best illustrated by reference to the behavior of packed towers since this is virtually the only contactor that has received any attention in this context up to the present time. After a drop has detached from the inlet nozzle, it may experience one or more events depending upon the nature of the packing (Thornton, 1964). Thus, a drop may (1) move freely within the packing voids, (2) collide with packing elements and suffer distortion, (3) collide with packing and break down into two daughter drops, (4) become elongated during its passage through narrow voids, and ( 5 ) coalesce with a stationary drop trapped in a void before being redispersed. In a real situation, a drop will experience most of these events during its passage through the tower, and in order to assess the relative contribution of each to the overall transfer process, it is necessary to establish the value of the partial mass-transfer coefficient for each possibility. This, in turn, implies using an experimental technique that will measure changes in the drop solute concentration over very small intervals of time. Such a procedure, termed the scale-displacement technique, was developed at the University of Newcastle upon Tyne in 1969 and was first described in 1976 by Thornton et al. In principle, the technique is simple and involves placing a ruled graticule behind a drop undergoing mass transfer and recording its history on high-speed cine film.The drop functions as a compound lens and produces an image of 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 1097
Figure 3. Simulation of droplet behavior in packed towers.
Figure 1. Image of graticule formed by moving droplet. GRATICULE
OBJECT
1 IMAGE I
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Figure 2. (a) Optical arrangement. (b) Ray trace (droplet refractive index greater than that of the continuous phase).
the graticule which is recorded on the film. A typical graticule image produced by a moving droplet is shown in Figure 1. When the geometry of the image is compared to that of the original graticule, the refractive index of the droplet and thus, by calibration, the solute concentration inside the droplet may be computed. Analysis of successive frames of the film provides a picture of the solute concentration as a function of time. Hence, if filming is carried out at 250 frames/s, the solute concentration during mass transfer is known at 1/250-s intervals without any need to sample and thereby disturb the system. The technique assumes that the fluid in the droplet is perfectly mixed, and this was shown to be the case with droplets in the present size range by photographically observing the internal flow patterns of suspended aluminum particles. The principle is shown in Figure 2a, which illustrates a droplet moving freely in a cell of continuous phase. A ruled graticule is placed a t a known distance behind the droplet, and it is assumed in this instance that the refractive index of the droplet is greater than that of the continuous phase so that it behaves as a converging lens. Figure 2b shows a ray trace for an assumed droplet refractive index, and by use of an iterative procedure, the correct refractive index is found when ray traces from the observed image pass through the corresponding points on the graticule. Since the variation in refractive index with solute concentration is known, the latter may be computed for each frame of the film.
By contrast, if the refractive index of the droplet is less than that of the continuous phase, the former will behave as a diverging lens and an image will be produced remote from the camera. The ray tracing procedure may be facilitated by locating the camera a considerable distance from the droplet so that the distance between the two is very much greater than the droplet diameter. This has the advantage that the image is now viewed only by rays parallel to the optical axis, and the analysis is simplified. In both situations, care must be taken to thermostat the transfer cell so that variations in refractive index occur solely as a result of solute concentration changes. Extreme accuracy is also called for in setting up the cell so that the geometry of the optics and the magnification factors are known precisely. The five events listed above can be simulated by studying transfer to or from droplets in a single-drop column (Thornton et al., 1976). If the moving droplet is allowed to impinge on various obstacles and the changes in solute concentration are recorded during the process, corresponding partial coefficients can be established for each of the events. Typical arrangements of "obstacles" for the various simulations are shown in Figure 3 for the case where the droplets are moving upward; i.e., the less dense phase is dispersed. Thus, in Figure 3, a represents the empty single-drop column where the mass-transfer rate corresponds to free movement within the packing voids and b and c depict solid baffles which simulate droplet splitting and droplet impact followed by deformation after impact, while d and e show the use of wide and narrow glass funnels to simulate droplet elongation and coalescence, respectively. In order to calculate the rate of mass transfer for a transient event, it is essential to have a measure of the actual time over which that event took place. The effects, for example, of droplet deformation after collision with a fixed obstacle such as an element of packing only persist for a very short time. Nevertheless, all the information is contained in the film record, and if the droplet oscillation frequency is measured from the rate of change of profile as recorded on the film and this is plotted versus time, the lifetime of the perturbation is shown up by the enhanced oscillation frequency, which subsequently decays to its steady-state value. Typical frequency-time curves are shown in Figure 4 for three different sizes of water droplets impacting with a solid baffle of the type shown in Figure 3c. The effective time of the perturbation in each case is indicated by At.
Typical Values of Partial Coefficients The results of mass-transfer measurements during each of these events are characteristic of the column packing, and some typical values are summarized below for different droplet sizes. These data are for aqueous droplets dispersed in toluene with diacetone alcohol as solute transferring from the toluene into the dispersed aqueous phase.
1098 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989
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A , cm2
A*2,cm2
K , cm/s
K *, cm/s
A*/A
K*/K
0.376 0.465 0.550
0.296 0.332 0.50C
0.450 0.680 0.954
0.453 0.700 1.000
0.0136 0.0207 0.0276
0.0719 0.0876 0.0853
1.01 1.03 1.05
5.29 4.23 3.09
The asterisk denotes perturbed values during the time interval At. Table IIn d./dr
At, s
A , cm2
A*, cm2
K , cm/s
K *, cm/s
A*/A
K*/K
1.00 1.06 1.10
0.421 0.500 0.540
0.954 0.954 0.954
0.973 0.957 0.951
0.0298 0.0297 0.0303
0.0570 0.0616 0.0667
1.020 1.003 0.997
1.91 2.07 2.20
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asterisk denotes perturbed values during the time interval At.
Figure 3 still shows the types of obstacles employed, but they are now inverted because the heavier phase is dispersed. Droplet Collision and Distortion. This corresponds to the experimental arrangement shown in Figure 3c and simulates a droplet colliding with an element of packing and subsequently bouncing off without breaking but with an enhanced oscillation frequency-a common occurrence when the droplet strikes the side of a horizontal packing ring. Values of interfacial areas and mass-transfer coefficients for three droplet sizes are shown below in Table I. Areas were calculated directly from the filmed droplet profiles, and the coefficients were averaged over the very small perturbation period, which was usually less than half a second. The first thing to note is the short time interval, At, during which the effect of the collision or perturbation is manifest and is in the range 0.30-0.50 s. During this time, the mean surface area and the oscillation frequency of the drop are enhanced with a consequent increase in the turbulence inside and outside the drop. This, in turn, gives rise to increased values of the instantaneous mass-transfer coefficient, and this is brought out very clearly in the last column of Table I. Typical variations in drop surface area before, during, and after impact are shown in Figure 5 for
the 0.376-cm-diameter droplet. The enhancement in the mass-transfer coefficients is most marked in the cases of the smaller droplets where the improvements in K are 5- and 4-fold, respectively. On the other hand, because the corresponding increases in interfacial area are small (less than 5701,the observed improvement in the extraction rate is a direct result of the interfacial turbulence generated by the collision process. Droplet Elongation. This situation is depicted in Figure 3d. Similar experiments carried out using glass funnels to deform the drops during their passage again indicated an increase in the partial mass-transfer coefficients (Rahman, 1977) but to a lesser degree than in the earlier case of droplet impact. Table I1 shows some data obtained for a drop of equivalent diameter 0.55 cm a t three levels of distortion obtained using three different funnel diameters. As the diameter of the constricting funnel, df, becomes smaller, the elongation of the drop becomes larger as the drop passes through the constriction. The extent of elongation is therefore represented by the ratio d,/df in Table 11. In all these runs, the area ratio is sensibly constant a t a value of unity but the ratios of the perturbed to unperturbed mass-transfer coefficients are approximately two and tend to increase with the degree of elongation.
Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 1099
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Thus, the effect of passing through a constriction such as a packing void is to increase the partial mass-transfer coefficient but not to the same extent as a collision with a static obstacle such as an element of packing. It should be noted however that, in the present instance, the area available for mass transfer decreases with increasing values of d,/d, but is compensated by the increased circulation within the drop and therefore by an increased value of K*. Droplet Splitting. When a drop collides with a narrow obstacle such as the edge of a packing element, the drop can split into two daughter droplets (Ramshaw and Thornton, 1967) and is represented by Figure 3b. The scale-displacement method has been applied to this situation, and it has been found (Bozorgzadeh, 1980) that the partial mass-transfer coefficients for the splitting process (taking into account the increased surface area arising from the formation of two daughter droplets) are generally 100-200% higher than the unperturbed values predicted by the oscillating drop film coefficient equations of Skelland and Wellek (1964) and Garner and Tayeban (1960). At first sight, an enhancement of only 100-200% seems surprising since it might be thought that the act of splitting would expose two raw liquid interfaces with imperfectly developed boundary layers. In practice, however, this is not the case, and what is commonly thought of as splitting is, in reality, only a folding of the droplet around the obstacle until the two lobes separate as two new daughter droplets (Ramshaw and Thornton, 1967). Droplet Coalescence and Redispersion. This is the situation represented by Figure 3e. Unfortunately, the scale displacement technique has not been applied to this particular case to date, so it is not possible to compare the partial coefficients with those for the other events reported above. Nevertheless, certain predictions can be made based on other findings. Three steps are involved in the transfer process. Initially a drop is stationary within a packing void, and any mass transfer will take place into or out of a stagnant drop. A second drop then enters the same void and coalesces with the stationary drop. The additional hydrostatic head thus created forces the coalesced phase to move through the void and issue as a new drop.
Mass transfer to a stagnant interface proceeds by molecular diffusion only and is a slow process. When a planar interface is disturbed by the continuous arrival of fresh drops which then coalesce, the enhancement of the transfer rate is small and is usually less than 10% (Liddell, 1963). Confirmation of this is provided by the work of Lindland and Terjesen (1956), who found that increasing the frequency of impact of the drops had no appreciable effect on the transfer rate across an interface. It must be borne in mind, however, that coalescence between two drops involves a very much smaller mass of fluid so that the kinetic energy contribution per unit mass would be that much greater. Under these conditions, it might be expected that the enhancement over and above the stagnant diffusion rate would be appreciable, and the effect of interdroplet coalescence should not be dismissed without experimental confirmation. The subsequent behavior of the new emergent drop might well then follow that for elongated drops referred to earlier so that the overall result in terms of transfer enhancement could be significant. Clearly experimental confirmation is required in this area.
Overall Packing Performance The conclusions arising from measurements of this kind are important in terms of understanding the way in which column packings operate. The conventional explanation for the improved performance of packed towers over spray columns is in terms of a stabilized, equilibrium droplet size distribution and a reduction in backmixing as a result of the baffling effect of the packing. Whilst these factors are no doubt important, it must also be realized that such effects as droplet collision, splitting, and coalescence coupled with redispersion play a key role in the observed enhanced mass-transfer rates. Measurements of partial coefficients can be of service in identifying those characteristics of the packing that most enhance the overall mass-transfer rate and, in this connection, enable packings to be designed to exploit such characteristics. The results reported above also provide an explanation for the superior performance of packed towers in relation to simple spray columns. Thus, if only free rise, collision, and droplet elongation are considered, and assuming that
1100 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989
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700
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Figure 6. Overall mass-transfer coefficient as a function of time for various initial solute concentrations.
the fraction of time spent by the drops undergoing each of these events under constant driving force conditions is the same, the ratio K * / K swill be equal to 2.7, indicating that the mass-transfer coefficient in the packed tower is 2.7 times the corresponding value for the spray column. This neglects any effects due to droplet splitting, coalescence, and redispersion and of course the reduced effects of backmixing in the packed tower, all of which will tend to increase the ratio beyond 2.7, which is in line with published performance data for spray and packed towers. In the longer term, the use of partial coefficients will be of use in predicting overall coefficients for contactors once information is available on the relative times occupied by each of the several events to which the dispersed phase is subjected.
centration when uranium is transferring from an aqueous nitric acid drop into TBP/OK. A particularly significant feature is the rate at which the coefficient decays as the interface ages, and in the example given, the coefficient can decrease by as much as 30% over the first 20 s of the life of the drop. This finding has important implications for packing design. If aging of the drop interface is to be avoided, an efficient packing must continuously promote the formation of fresh interface so that the mass-transfer coefficient will remain at a high value. One way of doing this is to ensure that the packing induces a perpetual coalescence/redispersion cycle in the column. There is scope here for the development of new packings and fixed internal devices which promote this feature.
Packing Characteristics and Interfacial Turbulence The scale-displacement technique is only applicable when interfacial turbulence or so-called Marangoni effects are negligible. When the liquid-liquid interface is disturbed by surface turbulence, it becomes very difficult to obtain a clear image of the graticule, and no reliable measurements can be obtained. Quite apart from such considerations, other problems arise which render the concept of constant and reproducible coefficients questionable. Two effects are of particular significance: (1)The magnitude of the mass-transfer coefficient depends upon the rate at which the droplet interface is renewed by interfacial turbulence. This in turn is a function of the solute concentration so that K is also concentration dependent (Thornton et al., 1985; Thornton, 1987). (2) The value of the mass-transfer coefficient is time dependent and decreases as the interface ages (Mardous and Sawistowski, 1964;Javed and Thornton, 1984; Rogers et al., 1987). Such effects can occur with both organic and inorganic solutes, many of which are of industrial importance. An interesting case is that of uranyl nitrate partitioning between aqueous nitric acid and tributyl phosphate in odorless kerosene (Rogers et al., 1987). Figure 6 shows the way in which the coefficient varies with time and con-
Conclusions The mass-transfer behavior of packed towers can be better understood by assigning partial mass-transfer coefficients to each of the hydrodynamic events experienced by the droplets. In the absence of interfacial turbulence, the scale-displacement technique enables instantaneous values of these coefficients to be determined. Droplet impact with fixed obstacles such as elements of packing can result in a 5-fold increase in the coefficient, while droplet splitting and droplet elongation resulting from passage through narrow voids can give rise to a doubling of the coefficient. It has been shown that, when interfacial effects are present, the mass-transfer coefficient decreases rapidly with time due to the aging of the droplet interface. All these factors are significant in the design of highefficiency tower packings, and it appears that frequent droplet impact and elongation are essential to high performance. When interfacial turbulence is present, high coefficients can be preserved by ensuring that the packing maintains a fresh interface through a rapid coalescenceredispersion cycle. Nomenclature A = man area of droplet, (length)2 A* = mean area of droplet during perturbation, (length)2 d, = equivalent drop diameter, length
Ind. Eng. Chem. Res 1989, 28, 1101-1103 df = diameter of funnel constriction, length K = overall mass-transfer coefficient before perturbation, length/ time K * = perturbed value of the mass transfer coefficient, length/ time K * = mean overall coefficient in a packed tower, length/time K , = overall coefficient in a spray column, length/time At = duration of perturbation, time
Literature Cited Bozorgzadeh, F. Study of Mass Transfer during Droplet Splitting using a New Optical Technique. Ph.D. Thesis, University of Newcastle upon Tyne, 1980. Garner, F. H.; Tayeban, M. The Importance of the Wake in Mass Transfer from both Continuous and Dispersed Phase Systems. An. Real SOC.ESP.Fis. Quim. Ser. B-Quim. 1960, LVl(B),479. Javed, K. H.; Thornton, J. D. Time Dependent Mass Transfer Rates in a Liquid-Liquid System exhibiting Interfacial Turbulence. Inst. Chem. Eng. Symp. Ser. 1984, 88, 203. Liddell, J. Liquid-Liquid Extraction Stuides in a Single Droplet Column. Ph.D. Thesis, University of Durham, 1963. Lindland, K. P.; Terjesen, S. G. Effect of a Surface Active Agent on Mass Transfer in Falling Drop Extraction. Chem. Eng. Sci. 1956, 5, 1. Mardous, N. G.; Sawistowski, H. Simultaneous Transfer of Two Solutes across Liquid-Liquid Interfaces. Chem. Eng. Sci. 1964, 19, 919. Rahman,M. Study of Mass Transfer into Droplets in Liquid-Liquid Systems using a new Optical Technuque. Ph.D. Thesis, University of Newcastle upon Tyne, 1977. Ramshaw, C.; Thornton, J. D. Droplet Breakdown in a Packed Extraction Column: Part 1. The Concept of Critical Droplet Size. Inst. Chem. Eng. Symp. Ser. 1967,26, 73.
1101
Rogers, D.; Thompson, P. J.; Thornton, J. D. Time Dependence of the Mass Transfer of Uranyl Nitrate between Nitric Acid and Tributyl Phosphate. Inst. Chem. Eng. Symp. Ser. 1987,103,15. Skelland, A. H. P.; Wellek, R. M. Resistance to Mass Transfer inside Droplets. AZChE J. 1964, 10, 491, 789. Thornton, J. D. Droplet Behaviour and Mass Transfer Rates in Liquid-Liquid Extraction Operations. Ind. Chem. 1963,39(12), 632; 1964, 40(1), 13. Thornton, J. D. Interfacial Phenomena and Mass Transfer in Liquid-Liquid Extraction. Chem. Ind. 1987, G(March 16), 193. Thornton, J. D.; Egbuna, D. 0.;Rahman, M. Simulation of Droplet Behaviour in Packed Liquid Extraction Columns. Proceedings of Solvent Extraction Symposium, University of Newcastle upon Tyne, 1976. Thornton, J. D.; Anderson, T. J.; Javed, K. H.; Achwal, S. K. Surface Phenomena and Mass Transfer Interactions in Liquid-Liquid Systems. AZChE J . 1985, 31(7), 1069. *Author to whom correspondence should be addressed at Battle Well, Greenhill, Evesham, Worcestershire W R l l 4NA, England.
William Batey Dounreay Nuclear Power Development Establishment UKAEA Thurso, Caithness KW14 7TZ, Scotland
John D. Thornton* Department of Chemical Engineering University of Newcastle upon Tyne Newcastle upon Tyne NE1 7RU, England Received for review October 17, 1988 Revised manuscript received March 2, 1989 Accepted March 26, 1989
Recovery of Uranium and Lanthanides from Ca(H2P04)2-Ca(N03)2-H20 and Ca(H2P04)2-CaC12-H20Systems Solutions containing Ca(H2P04)2-Ca(N03)2-H20and Ca(H2P04),-CaC12-H20 obtained by leaching phosphate rock in situ or in dumps can be treated for uranium and lanthanides recovery prior t o P205recovery as follows: In a nitrate system, uranium is first extracted by a mixture of bis(2ethylhexy1)phosphoric acid (DBEHPA) and tributyl phosphate (TBP) in hexane followed by the extraction of the lanthanides with TBP. In a chloride system, uranium is first extracted by the same mixture, DBEHPA TBP, followed by the extraction of lanthanides with D2EHPA in toluene.
+
Solutions containing Ca(H2P04)2-Ca(N03)2and Ca(H,P04)2-CaC12 are obtained when phosphate rock is leached by dilute HNO, and HC1, respectively. This is the basis of a new process proposed for leaching phosphate rock in situ or in dumps to decrease material handling problems especially when dealing with deposits like those in Central Florida, which is one of the largest phosphate rock producers in the world. The mineralogical analysis of these deposits is approximately 28% calcium phosphate, Ca3(PO4I2(Bone phosphate of lime), 36% silica sand (Si02), and 34% clay minerals. To get 1 ton of a commercial product, 4.2 tons overburden must be removed to expose 3.36 tons of ore, which is processed by physical and mechanical means to get the concentrate (1 ton), and to reject 1.4 tons of tailings and 0.95 ton of slime waste (clays). Due to the excessive material handling problems facing this technology (rejection of 7.56 tons of waste material per ton of product, plus enormous amounts of water) and the loss of about onethird of the phosphate values, the techniques known as in situ and dump leaching were pr0posed.l When using these techniques, which are applied in the uranium, gold, and copper industries,* the leach solution would be either injected in the bed containing the phosphate values or 0888-5885/ 89/ 2628- 1101$01.50/0
sprayed on the phosphate rock dumps with minimum material handling and efficient phosphate value recovery. It would be necessary in these cases to leach the rock with 10% HC1 or 20% HN03 to prevent the blocking of the beds with insoluble dicalcium phosphate. Also, H2S04, which is the cheapest acid, cannot be used because of the blocking of the bed with insoluble gypsum. Under the conditions of the proposed process, a solution of monocalcium phosphate was obtained, from which the double salts CaC1H2P04.H20or Ca(NO3)H2PO4-H20 were crystallized depending on the acid used.l The crystals were then separated and decomposed a t 200-250 "C to get dicalcium phosphate product (CaHP04). Nitric and hydrochloric acids used for this purpose, although they are expensive, have the advantage of solubilizing rapidly not only P205content of the rock but also uranium, lanthanides, and radium; hence their recovery or disposal (in the case of radium) can be c ~ n d u c t e d . ~In - ~case of H2S04 leaching in conventional plants, only uranium can be recovered because lanthanides and radium remain in the gypsum. Uranium in the rock is about 0.015%e and the lanthanides about 0.5%.' Considering the large tonnage of rock treated annually, which is about 150 X lo6 short tons, 0 1989 American Chemical Society
