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Mass-transfer effects on droplet phenomena and extraction column hydrodynamics revisited
Chemical Engineering Science, Printed in Great Brimin.
Vol. 48, No. 8. pp. lsO3-ISIS.
1993.
ooo%xoP/93 s6.00 + 0.00 0 1993 Pcrsnmon Pm Ltd
MASS-TRANSFER EFFECTS ON DROPLET PHENOMENA AND EXTRACTION COLUMN HYDRODYNAMICS REVISITED Department
C. TSOURIS and L. L. TAVLARIDES of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, U.S.A. (First receiued 28 February 1992; accepted
in revisedform 2 June 1992)
Abstract-The effect of solute mass transfer between the two liquid phases on the drop size distribution and holdup profiles. of the dispersed phase in a multistage extraction column is experimentally investigated in this article. Experimental results of the drop size distribution, dispersed-phase volume fraction (holdup), and concentration profiles are obtained for both directions of mass transfer. The drop size distribution is measured by a photomicrographic technique, the holdup profile is measured by an ultrasonic technique, and the concentration profiles are measuredby refractionindex measurements. A strong influenceof the
mass-transfer direction on drop size aad holdup has been found.The resultsare in qualitativeagreement with the observations of other investigators. Mass transfer of butyric acid from toluene (dispersed) to water (continuous) produced larger drop sizes and lower values of the dispersed-phase holdup than for the equilibrated toluene-water system. For mass transfer of butyric acid from water (continuous) to toluene (dispersed) smaller drop sixes and higher holdup values are observed than for the equilibrated toluenc-water system. This behavior significantly affects the performance of the extractor and indicates the necessity for more studies to determine the physics of the phenomenon and to model these processes appropriately.
INTRODUCTION
It has been found by many investigators who studied two-phase liquid-liquid systems that mass transfer has a significatit effect on the behavior of the dispersed-phase droplets (Lewis, 1954; Logsdail, 1957; Groothuis and Zuiderweg, 1960). For example, experiments were conducted by Groothuis and Zuiderweg (1960) for the benzene/CCl,-acetic acid-water system where they observed the behavior of two droplets attached at the tips of two capillary tubes as they approach each other. When the transfer of acetic acid occurred from the drop phase to the continuous water-phase immediate coalescence resulted, while for the transfer of acetic acid from the continuous phase to the drop phase a strong retardation of coalescence was noted. This phenomenon is qualitatively explained by the effect of the interphase mobility on the drainage rate of the liquid film between the two droplets. The interface mobility is a result of gradients in the interfacial tension caused by nonuniform mass transfer along the interface. In a liquid-liquid extraction column, the effect of mass transfer on the column hydrodynamic behavior is of great importance, and it should be taken into consideration in equipment design. The rate of drop coalescence, which is strongly affected by the direction of mass transfer, becomes a decisive factor for the determination of the drop size. Since the rising velocity of the drops is a function of their size, the drop residence time is also affected by the mass transfer. Larger drops, produced by higher coalescence rates, iAuthor to whom correspondence
should be addressed. 1503
travel faster through the extractor, and the result is lower residence times of the drops and, therefore, lower volume fraction (holdup) of the dispersed phase. Both properties, larger drop sizes and lower holdup values, lead to smaller interfacial area for mass transfer between the two phases and, hence, lower masstransfer efficiency. Under the same conditions, the maximum allowable flow rates of both phases (throughput) before the occurrence of flooding are increased substantially. Experimental studies confirming this behavior have been reported by many investigators including Logsdail et al. (1957) and Komasawa and Ingham (197&a,b). The throughput before the onset of flooding and the mass-transfer rate are the most important parameters for the design of column extractors; therefore, the effect of mass transfer on the hydrodynamic behavior of the extractor should be studied quantitatively. Fundamental studies on the mobility of the liquid film between colliding droplets and the film drainage rate have been reported by Zapryanov et al. (1983). Malhotra and Wasan (1987) studied the effects of surfactant adsorption-desorption kinetics and interfacial rheological properties on the rate of drainage of foam and emulsion films. The objective of their study was to predict the rate of drainage of surfactantstabilized/polymer-stabilized foam and emulsion films from the knowledge of bulk and interfacial properties. Results showed higher interfacial mobility when the surfactant is soluble in the droplet phase than when it is soluble in the film. Although this analysis has included the effect of mass transfer of a surfactant from either phase to the interface on the interfacial mobility, still these results are far from complete to be
C. TSOURISand L. L. TAVLARIDES
lS@4
applied for the prediction of the effect of mass transfer from one phase to the other on talk droplet behavior in extraction columns. Gourdon and Casamatta (1991), in an attempt to predict the influence of the mass transfer direction on the operation of a pulsed sieveplate pilot extraction column, suggested that, in the case of mass transfer from the drops to the continuous phase, every drop-drop collison results in coalescence. This assumption is probably true for a high mass-transfer driving force. However, as the driving force becomes smaller and smaller, experimental results obtained here indicate that the coalescence efficiency decreases. In the present paper, more experimental results of the holdup and drop size distribution profiles in the presence of mass transfer along the extractor obtained by novel techniques are presented. The holdup profile is measured by an ultrasonic technique, while the drop size distribution is measured by a photomicrographic technique. Experimental data show the effect of the mass-transfer direction on the above hydrodynamic parameters and indicate the need for a model to predict this behavior.
EXPERIMENTAL
Pilot plant An extraction pilot-plant unit, the geometry of which is described by Kirou et al. (1988), is used for the experiments. The extraction column is of 125 mm diameter and is divided by rings into seven compartments of 127 mm height each. The free area between consecutive compartments is 29% of the cross-sectional area of the column. The two immiscible liquid phases are introduced into the column countercurrently; the continuous phase flows from top to bottom, and the dispersed-phase drops move from bottom to top. Breakage and coalescence of the drops occur as they move upwards due to mixing provided by six-blade impellers of 63.5 mm diameter. The impellers are located at the center of each compartment. The two phases are separated at the top of the column where the interface is located. A level controller based on conductivity measurements is used to control the height of the interface. Mass-transfer system The chemical system used in this study is water (continuous)-butyric acid (solute)-toluene (dispersed). The column hydrodynamic behavior in terms of holdup and drop size distribution profiles is studied for both mass-transfer directions. Measurement techniques The holdup profile of the droplet phase along the extractor and the exit concentration in the continuous phase are monitored continuously by data acquisition systems during the mass-transfer experiments. The drop size distribution and the concentration profiles in both phases are measured at steady state along the extractor.
A photomicrographic technique consisting of a microscope tube with eye piece and objective lenses, a camera, and fiber-optic light guides (Kirou et al., 1988) is employed for drop size measurements. The drops are magnified 10 times, and pictures are taken near the wall of the contactor. The drop size is measured by a semiautomatic particle analyzer (MOP-34 Carl Zeiss, Inc.) interfaced with an IBM PC computer. Concentration in both phases is measured by a digital refractometer (AO, ABBE Mark II). Phase separation devices have been developed for separating and sampling in situ pure phases for concentration measurements. For the droplet phase, a coalescor is employed as described by Schmidt et al. (1989), while, for the continuous phase, a stainless-steel mesh mounted at the tip of a vertically directed l/8” diameter pipe is used. Such devices have been introduced in each compartment. Real-time concentration and holdup measurements are obtained by data acquisition systems. For concentration measurements at the exit of the aqueous phase, a conductivity cell connected with a conductance meter (Yellow Springs Instruments Co., Inc., YSI Model 32) is employed. The signal from the conductance meter is transmitted to a data acquisition system (DAS 16F, A/D converter from Metrabyte) located in an IBM-XT computer and to an analog recorder. A calibration function is used in the data acquisition algorithm to convert the voltage signal into concentration. The same computer incorporates the data acquisition for an ultrasonic technique employed for holdup measurements along the extractor. This technique provides travel-time measurements of ultrasound through liquid media and is described in detail by Bonnet and Tavlarides (1987) and Tsouris et al. (1990). The absolute error introduced in the holdup measurements by the ultrasonic technique was estimated by Bonnet and Tavlarides (1987) as iO.017. The following model is used for the calculation of the holdup, 4 (Yi and Tavlarides, 1990; Tsouris and Tavlarides, 1990):
where t* is the travel time through the liquid dispersion, tc and tp are the travel times through pure wntinuous and dispersed phases, and gs and g, are wrrection factors for the path length of sound in each phase. Analytical expressions for these correction factors are available in the above articles. Calibration of the ultrasonic technique. For the calibration of the ultrasonic technique, the travel time of ultrasound in pure phases is measured in the beginning of each experiment. The holdup calculations are essentially based on the comparison of ultrasound travel-time measurements through the liquid dispersion with measurements through the pure phases. However, during mass transfer the solute concentration in both phases varies, and, since the ultra-
Mass-transfer
effects on droplet
sonic velocity is a function of solute concentration (see Fig. l), the values of the travel time through pure phases have to be updated to account for concentration variations. For this purpose, concentration profiles in both phases have to be obtained on-line. A technique to provide such measurements from 14 different points (two per stage) along the extractor was not available for
phenomena
1505
concentrations profiles have been assumed and calculated on-line from a steady-state material balance which utilizes the on-line concentration measurements at the exit of the continuous phase. Figure 2 shows the effect of the linear-concentrationprofile approximation on the calculations of the holdup profile. The holdup .profile calculated using the assumed linear profile is compared with the holdup profile calculated using the measured concentrations of solute in both phases. The maximum relative error in this example is less than 5%. Also shown in Fig. 2 is the holdup profile calculated without any corrections related to concentration variations.
RESULTS
Equilibrium data Equilibrium data for the water-butyric acidtoluene system have been generated at 20°C. Experimental data are correlated by the following relation suggested by Treybal (1963, p. 32):
-&B __+. XBB
0.954
. 0
I 2
.
w 4
weight
Fig.
1.
.
. 6
.
96 of butyrlc
Effect of solute concentration
I 8
.
I 10
1 12
add
on sound travel time.
r
( >
Here, XC- and Xc, are the weight percent concentrations of butyric acid (C) in toluene (A) and water (B), respectively, and XAA, XgB are the weight percent concentrations of toluene in the toluene-rich solution and water in the water-rich solution. When the mutual solubility of A and B is very low, such as the water-toluene system, one can assume that
35
10
1
2
3
(2)
AA
4
5
6
7
column height (stage number) Fig. 2. Comparison of noncorrected and corrected holdup profiles by using approximated and experimental concentration data. Feed concentration: 3.8 wt% in continuous, 0 wt% in dispersed.
1506
C. TSOURIS and L. L. TAVLARIDES
X ““zlXCA and XBB z 1 - Xc,. This assumption, however, is reliable only for low concentrations of the solute. The parameters k and r of eq. (2) are determined by plots of In (X,/X,,) vs ln(XcA/XAA) as shown in Fig. 3. For the system studied here, k = 0.122 and r = 0.584.
Concentrution proJiles Concentration profiles have been measured in both phases at steady state. Figure 4 presents an example of experimental data obtained for the case of mass transfer from the continuous to the dispersed phase. The feed concentration in the continuous phase is 3.8% by weight, while the dispersed phase is pure toluene. As the continuous phase travels from the top to the bottom compartments of the extractor, butyric acid transfers from the continuous to the dispersed phase which flows in the opposite direction. The equilibrium concentration in toluene shown in Fig. 4 is calculated from concentration data in water and by using eq. (2). In the case of mass transfer from the dispersed to the continuous phase, the concentration profiles show a maximum in the first compartment and minimum in the seventh. The reason is that the toluene phase is loaded with solute and is introduced from the bottom of the column. The slope of the concentration profiles is a function of phase flow rates and feed concentrations.
Eflect of agitation
speed on exit concentration The effect of the agitation speed on the exit concentration in the dispersed phase is examined in Fig. 5,
where a maximum is obtained at 160 rpm. The maximum relative error introduced in these measurements is 15%. This behavior is a result of two competitive phenomena: (i) the area of mass transfer increases at higher agitation speeds, yielding higher mass-transfer rates, and (ii) axial mixing in both phases increases also with agitation speed, reducing in this way the driving force for mass transfer. The significance of Fig. 5 is to show that the extraction efficiency does not increase monotically with the agitation speed or the dispersed-phase holdup, but that there is value of the agitation speed which gives optimum equipment performance.
E@ct of muss transfer on hydrodynamic
parameters The effect of mass transfer on drop size, holdup, and flooding performance of the extractor is discussed below.
Holdup. In the case of mass transfer from the continuous to the dispersed phase, the holdup behavior is similar to the one observed for the mutually equilibrated water-toluene system (Kirou et al., 1988). At moderate rotational speeds, the holdup profile has a concave form with a maximum in the upper compartments of the column. As the agitation speed increases, the average holdup increases too, and the maximum shifts towards the lower stages of the column. This behavior is shown in Fig. 6. Further increase in the agitation speed leads to flooding at which the holdup profile assumes a sigmoidal form
of buyric acid in the wrtor sOlutlOn weight% of water in the water solution Fig. 3. Equilibrium data for the toluene-butyric
acid-water
system.
1
effects on droplet phenomena
Mass-transfer
1507
. .
.
.
I
:
.
.
2
1
3
4
5
-
6
7
column height (stage number) Fig. 4. Concentration
1.51 150
profiles. Feed concentration:
160
170
3.8 wt%
in continuous,
180
190
0 wt%
in dispersed.
200
Agitation speed, rpm (l/min) Fig. 5. Exit concentration
of butyric acid in toluene vs agitation speed. Feed concentration:3.8 wt% continuous, 0 wt% in dispersed.
with maximum in the first stage. Also, an increase in either the continuous- or the dispersed-phase flow rate leads to higher holdup values. A different holdup-profile behavior has been found for the case of mass transfer from the dispersed to the
in
continuous phase. The holdup profile in Fig. 7 shows two distinguishable local maximums in the second and sixth compartments. In this experiment, the concentration profiles in both phases are monotonically decreasing, indicating that mass transfer occurs in all
C. TSOURIS and L. L. TAVLARIDES
1508
”
7
.
.
1
3
;
4
5
7
6
Column height (stage number) Fig. 6. Effect of the agitation
speed on the holdup profile. Feed concentration: 0 wt% in dispersed.
20-+--t--a__
3.8 wt%
-c,
4 = I” S
,+ 5
I
I
I
2
3
4
5
6
7
Column Hek~htbage numbed
‘.
12 8
w,_l’
,K 2
-4
S
-a ‘6 s i? .P --~--~_-_~-
-Q---o---Q0
9
G
IF_-,
-----o-r__
in continuous,
OL
I
I
r __ I
I
--O---4
I
2 3 4 5 6 Column Height (stage nvnber)
7
Fig. 7. Holdup and concentration profiles for mass transfer from the dispersed to the continuous phase. Feed concentration: 0 wt% in continuous, 7.6 wt% in dispersed.
Fig. 8. Holdup and concentration profiles for mass transfer from the dispersed to the continuous phase. Feed concentration: U wt% in continuous,12.6 wt% in dispersed.
compartments. This is, in fact, a result of the large difference between the selected flow rates of the two phases. One explanation for this profile could be in terms of the variation in drop breakage and coalescence rates along the column under the experimental conditions. The f&t maximum suggests that breakage dominates in the first few stages due to Large drop sizes of the feed stream. Eventually, small enough drops are produced to increase holdup. Coalescence rates appear to increase in the middle sections due to interphase mass transfer, causing increasing drop size
and decreasing holdup. At the top of the column, the drops have been depleted of solute, and coalesance rates decrease as coalescence enhanced by mass transfer no longer occurs. Breakage again dominates and, with the resulting smaller drops, holdup increases. The second maximum occurs because of the increased escape frequency of drops at the top section due to end effects. In the experiment of Fig. 8, however, the selected flow rates are such that equilibrium occurs in the lower compartments of the extractor, as indicated by the concentration profiles. This situation yields
Mass-transfer effects on droplet phenomena large drops at the top compartments due to intense coalescence rates caused by the mass transfer. Furthermore, interfacial concentration gradients formed in the equilibrated toluene-butyric acid-water system at the lower compartments cause higher drop breakage frequencies which yield smaller drops in that region (Koshy et al., 1988). Both effects, i.e. larger drops at the top compartments due to higher coalescence rates induced by mass transfer from drops to the continuous phase and smaller drops at the bottom due to higher breakage rates occurring at equilibrium concentrations, explain the higher holdup in the lower compartments of the extractor. The experimental results shown in Figs 7 and 8 indicate that the holdup profile is affected significantly by mass transfer from the drops to the continuous phase. To illustrate another effect of the mass-transfer direction on the holdup profile, Fig. 9 displays the holdup profiles for the three cases of (i) physically equilibrated water and toluene, (ii) mass transfer from the continuous to the dispersed phase, and (iii) mass transfer from the dispersed to the continuous phase. The operating conditions are the same (Qr = Q,, = 0.54 1 min- ’ and rpm = 160), with the exception of the feed stream composition. The second case, mass transfer from the continuous to the dispersed phase, produced the highest holdup. Mass transfer from the dispersed to the continuous phase produced the lowest holdup with the exception of the first two compartments. Apparently, the reason for this holdup behavior is that mass transfer from the continuous to the dispersed phase produces smaller
-m-
~88~
-mass
1
drops than the physically equilibrated water-toluene system, and mass transfer from the drops to the continuous phase produces larger drops. Furthermore, as stated above, the equilibrated water-butyric acid-toluene system also produces smaller drops than the equilibrated water-toluene system. This conclusion is drawn by the fact that larger drops travel faster inside the extractor and, therefore, are associated with lower holdup values. When mass transfer occurs from the drop phase to the continuous phase, larger drop sizes are produced due to enhanced coalescence rates. This shift in the drop size can be balanced by increasing the agitation speed. For example, in Fig. 10, a 20 rpm change, from 160 to 180 rpm, is capable of decreasing the drop size and yielding the concave holdup profile. The magnitude of the agitation intensity required to counterbalance the coalescence effect is related to the concentration gradient or the mass-transfer driving force. For instance, in Fig. 7, where the concentration driving force is higher, at 200 rpm the holdup is still low and the holdup profile is not concave. This behavior is a result of higher coalescence efficiency at higher concentration gradients with mass transfer from the dispersed to the continuous phase. Therefore, the coalescence efficiency of colliding droplets under mass transfer from the dispersed to the continuous phase is a function of the concentration driving force, and it should be modeled accordingly. Drop size. The effect of mass transfer on the drop size is related to the holdup behavior. Figure 11 shows
transferof butyrb
acid from water@)
transfer
add
2
of butyti
3
1509
to tokmne(d)
fmm toluene(d) to water(c)
4
5
6
7
Column height (stage number) Fig. 9. Effect of the mass-transfer direction on the holdup profile. Feed concentration for mass transfer from continuous to dispersed: 3.8 wt% in continuous, 0 wt% for dispersed. Feed concentration for mass transfer for dispersed to continuous: 0 wt% in continuous, 12.6 wt% in dispersed.
C. TSOURIS and L. L. TAVLARIDES
1510
”
1
1
;
4’
j
;
;I
7
column height (stage number) Fig. 10. Effect of the agitation speed on the holdup profile. Feed concentration in the continuous phase: 0 wt%. Feed concentration in the dispersed phase: 10.9 wt% for 150 rpm, 12.6 wt% for 160 rpn, and 13 wt% for 18Orpm.
the difference in the Sauter mean diameter in the fourth compartment, at various values of the agitation speed, for the two cases of (i) mass transfer from the continuous to the dispersed phase, and (ii) physically equilibrated water-toluene system. The Sauter mean diameter is calculated by the following relation:
(3)
where R is the number of drops in the sample. Mass transfer from the continuous to the dispersed phase produces smaller drop sizes which result in a reduction of the Sauter mean diameter of the order of 30%. The drop size distribution in this case shifts to lower sizes as shown in Fig. 12 for the agitation speed of 180 rpm. In the other case of mass transfer from the dispersed to the continuous phase, the drop size increases significantly, and the photomicrographic technique is not appropriate for drop measurements. However, when the mass-transfer system reaches equilibrium, the drop size becomes smaller than in the water-toluene system due to higher breakage frequencies as explained above in the discussion of Fig. 8. This behavior is shown in Fig, 13 and is another indication that the drop size under mass-transfer conditions is a function of the concentration driving force. Photographs of the liquid dispersion in the fourth compartment taken externally reveal some visual in-
formation regarding the effect of mass transfer from the dispersed to the continuous phase on the drop size. The dispersion produced by the water-toluene system is fairly homogeneous, and the drop diameter is of order 1 mm. At the same operating conditions and for the case of mass transfer from the drops to the continuous phase, the drops become larger due to higher coalescence rates, and the holdup decreases due to lower residence times of larger drops. This behavior is shown in Fig. 14(a) and (b). Furthermore, large drops formed by mass transfer from drops to the continuous phase are accumulated above the impeller in each compartment, causing spatial inhomogeneities. The shape of these drops is clearly not spherical. Also, the size of the largest drops is comparable to the shaft diameter which is approximately 10 mm. Flooding. The effect of mass transfer also impacts on the flooding performance of the extractor. An example is presented in Fig. 15, where the flooding behavior of the extractor for the physically equilibrated system is presented by the curves at various values of the agitation speed (Kirou et al., 1988). Values of the flow rates above the curves in Fig. 15 lead to flooding. Hence, the conditions of the experiment shown by the cross sign should cause flooding. The average holdup at these conditions, however, is only 9.2%. This value is far from the holdup at flooding which is around 45% (Kirou et al., 1988). This
Mass-transfer
1511
effects on droplet phenomena
0.8 0.7 -I 150
160 Agitatation
180
170 spead,
190
rpm (llmin)
Fig. 11. Effect of the mass-transfer direction on the Sauter mean diameter; fourth compartment. concentration for mass transfer: 3.8 wt% in continuous, 0 wt% in dispersed.
Feed
Diameter (mm) Fig. 12. Effect of mass transfer on the drop size distribution; fourth stage. Feed concentration transfer: 3.8 wt% in continuous, 0 wt% in dispersed.
behavior is again due to higher coalescence rates and, hence, larger drop sizes in the case of mass transfer from the drops to the continuous phase. DlSCUS!GON
It has been shown that mass transfer has a significant effect on the drop breakage and coalescence in agitated liquid dispersions. While the objective of this
for mass
article is to experimentally describe the result of the mass-transfer effect on the drop size distribution and holdup profiles of the dispersed phase, a qualitative discussion is offered here which can help in the modeling of the process. Consider the breakage and coalescence rate functions developed by Coulaloglou and Tavlarides (1977) for isotropic turbulence:
C. TSOURIS and
1512
m
MMQ IrMQfer
of bufyllo
eold
L. L. TAVLARIDES
fmmlchmIw(clJ
lo waler(c),
n M-lranafQr(syatemwtthmllbutytiacid).~
I&
- 0.78 n-m.
-1.Olmm.
Flowrat6s:Oc-Qd-0.54Umin. 180rpm
0.1
0.3
0.5
0.7
Diameter Fig. 13. Effect of mass transfer
0.Q
1.1
1.3
1.5
1.7
1.9
(mm)
on the drop size distribution; mass transfer: 0 wt% in continuous,
fourth compartment. 7.6 wt% in dispersed.
Feed concentration
for
Fig. 14. Effect of mass transfer on the liquid dispersion, fourth compartment. (a) Equilibrated water-toluene system; (b) feed concentration 0 wt% in continuous, 12.6 wt% in dispersed. rpm = 160, Q. = Qd = 0.54 lfmin.
1513
Mass-transfereffects on droplet phenomena
+ tpm-2co.msmJtlmhrdtxlyrlc~
0.2 -
$zzz$TS@ S O.Oq 0.0
-
1 0.1
-
I 0.2
.
I 0.3
.
. 0.4
.
. 0.5
_
. 0.6
.
. 0.7
. 0.6
.
. 0.9
1.0
Qd (Vmin) Fig. 15. Effect of mass transfer
on the flooding performance of the extractor. Feed concentrationfor mass transfer:0 wt% in continuous, 7.6 wt% in dispersed.
Breakage:
Coalescence: F(d,, d,) = 9/s
-((d, ksl+$
+ dJ)2(df/3 + dj13)I12 exp
(
- $ -1
(5)
where dt, d, are drop diameters, Eis the energy dissipation per unit mass, 6 is the dispersed-phase holdup, u is the interfacial tension, F is the average coalescence time, f is the average contact time, and kl , kl, and k3 are proportionality constants. The contact time is the duration of contact between two drops after a collision and is a function of the size of the two drops and the itensity of agitation. The coalescence time is the time required to drain the continuousphase film between the two drops until a critical thickness is reached after which coalescence occurs. The coalescence time is a function of the continuousphase viscosity and density, the sixes of the colliding drops, and the intensity of agitation. A first approach for including the effect of mass transfer in either direction on the drop breakage is through the interfacial tension. It has been shown by Groothuis and Zuiderweg (1960) that, when a solute is introduced into an immiscible system, the interfacial tension decreases. The equilibrium interfacial tension is a function of the solute concentration. Equation (4) shows that, as the interfacial tension N the breakage frequency increases and, therefore, the drop size in this case is expected to be smaller. This effect is
qualitatively in the right direction as compared to the experimental results of this work. The effect of mass transfer from the dispersed phase to the continuous phase on the drop coalescence can be described by a different mechanism which has to do with the gradients of interfacial tension on the drop surface (the Marangoni effect). The pre-exponential term of eq. (5) gives the drop-drop collision frequency. This term is not expected to change with the mass-transfer direction. What changes is the exponential term which gives the coalescence efficiency or the fraction of collisions which result into coalescence. The contact time, r, is a function of the drop size and the intensity of agitation and, therefore, is not affected by mass transfer. Hence, the only quantity in the coalescence function that can vary with mass transfer is the coalescence time, which is related to the interfacial mobility. For instance, the time needed to drain the continuous-phase film is smaller for liquid drops than for solid spheres, due to the mobility of the drop surface. Introduction of surfactants (Zapryanov et al., 1983; Malhotra and Wasan, 1987) may increase the interfacial mobility. In the case of a solute transferring from the dispersed phase to the continuous phase, the solute concentration in the continuous phase at the point of collision reaches equilibrium with the drop concentration very fast. The concentration in the continuous phase at the collision point is, therefore, maximum and, hence, the interfacial tension is minimum according to the data of Groothuis and Zuidenveg (1960). as compared to other points in the neighborhood of collision. The gradient in the interfacial tension creates surface flow from low to high interfacial tension (Probstein, 1989) which accelerates the film
C. T~OURIS and L. L. TAVLARIDFB
1514
drainage between the drops and, hence, enhances coalescence. A reasonable approach to include the effect of mass transfer from drops to the continuous phase could be to express the coalescence time, T, as a function of the interfacial tension gradient. Population balance models could then be employed with breakage and coalescence functions, such as those above, modified as suggested to model the hydrodynamic behavior of extraction columns in the presence of mass transfer, regardless of mass-transfer direction.
Wi, 4) ddjl ge gd
k
ki, kz
k3
r
CONCLUSIONS
The effect of mass transfer on the hydrodynamic behavior of a multistage extraction column is discussed in this article. Experimental data have shown that mass transfer plays an important role in the drop breakage and coalescence rates which determine the drop size, holdup, and flooding performance of the column contactor. Mass transfer of solute from the dispersed phase to the continuous phase enhances drop coalescence and, therefore, the drop size increases, yielding lower holdup values. Mass transfer from the continuous phase to the dispersed phase enhances drop breakage and, hence, the drop size decreases, yielding higher holdup values. Similar behavior is observed for the equilibrated water-butyric acid-toluene system in comparison to the watertoluene system. The effect of mass transfer on holdup has analogous results on the column flooding behavior. When holdup decreases due to mass transfer, flooding occurs at higher values of the operating parameters and vice versa. While these phenomena have been observed and recorded previously, more detailed experimental data of holdup profiles, drop size distributions, and concentration profiles obtained in this work from a wellinstrumented pilot-plant extraction unit help us to understand better the role of mass transfer on the drop phenomena and on the hydrodynamic behavior of liquid-liquid extraction columns. The comparisons of the drop size distribution and the holdup profiles with the solute concentration profiles in both phases suggest that both drop breakage and coalescence rates are quantitatively related with the mass flux of solute. Additional information such as these results and the quantification of these effects in the design equations are needed for a more reliable design of extraction process equipment. Further studies are required in this direction. Acknowledgements-The authors gratefullyacknowledge the National Science Foundation for supporting the research described in this paper through Grant CTS-9017138. The assistance of Mr. Mohammed-Kamal Ahmad during the
execution ofthe experiments is also gratefully acknowledged. NOTATION
d d 32
drop diameter, m Sauter
m
mean diameter
defined by eq. (3),
tc td
t* f f Xi,
collision frequency of drops size di and d,, s-l
breakage
frequency
of drops
of size
dj, s-’ correction factor for the sound length in the continuous phase correction factor for the sound length in the dispersed phase
path path
parameter in equilibrium expression, eq. (2) constants in breakage function, eq. (4) constant in coalescence function, eq. (5) parameter in equilibrium expression, eq. (2) sound travel time through pure continuous phase, s sound travel time through pure dispersed phase, s sound travel time through the dispersion, s contact time, s coalescence time, s weight percent concentration of species i in solvent j
Greek letters E energy dissipation per unit mass, m* se3
density, kg m- 3 interfacial tension, N m- 1 dispersed-phase volume fraction up)
P
u d
(hold-
REFERENCES
Bonnet, J. C. and Tavlarides, L. L., 1990, Ultrasonic technique for dispersed-phase holdup measurements. Ind.
Engsqj Chem. Res. 29,924-927. Coulaloalou. C. A. and Tavlarides. , L. L.. 1977. Descrintion of interaciion processes in agitated liquid-liquid dispersions. Chem. Engng Sci. 32, 1289-1297. Gourdon, C. and Casamatta. G.. 1991. Influence of mass transfer direction on the operation of & pulsed sieve-plate pilot column. Chem. Eww Sci. 46, 2799-2808. Groothuis, H. and Zuiderwea, F. G.. 1960. Influence of mass transfer on coalescence oi drops. C&m. Engng Sci. 12, 288-289. Kirou, V. I., Tavlarides. L. L., Bonnet, J. C. and Tsouris, C., 1988, Floodina holdup. and drou-size measurements in a multistage &umn e&actor. A.-I.Ch.E. J. 34, 283-292. Komasawa, I. and In&am, J., 1978a, Effect of system properties on the performance of liquid-liquid extraction columns-1. Chem. Emmu Sci. 33. 341-347. Komasawa, I. and In&m, J., ld78b, Effect of system properties on the performance of liquid-liquid extraction columns-11. Gem. Engng Sci. 33,479485. Koshy, A. T., Das, T. R. and Kumar, R., 1988, Effect of surfactants on drop breakage in turbulent liquid dispersions. Chem. Engng Sci. 43, 649654. Lewis, J. B., 1954. The mechanism of mass transfer of solute across liquid-liquid interfaces. Part I. The determination of individual transfer coefficients for binary systems. Chem. Engng Sci. 3, 248-259. Logsdail, D. H., Thornton, J. D. and Pratt, H. R. C., 1957, Liquid-liquid extraction. Part XII. Flooding rates and performance data__. for _. a rotary disc eontactor. Trans. Insrn . __. _
them. Kngrs
35, 301-315.
Mass-transfer effects on droplet phenomena Malhotra, A. K. and Wasan, D. T., 1987, Effacts of surfactant adsorption-desorption kinetics and interfacial rheologieal properties on the rate of drainage of foam and emulsion films, Chem. Engng Commun. 55,95-128. Robstein, R. F., i9g9, Physicochemical Hydrodynamics: an Introduction, p. 300. Butterworth-Heinema, London. Schmidt, H., Tsouris, C., Eggert, E. and Tavlarides, L. L., 1989, Laser photomet& p&be for concentration measure+ ments in liquid dispersions. A.I.0.E. J. 35. 507-510. Treybal, R. E., 1963, Liquid Extrction, 2nd Edition. McGraw-Hill, New York. Tsouris, C. and Tavlarides, L. L., 1990, Comments on model for holdup measurements in liquid dispersions using an
MS 48:8-K
1515
ultrasonic technique. Ind. Engng Chem. Res. W, 217&2172. Tsouris, C., Tavlarides, L. L. and Bonnet, J. C., 1990, Application of the ultrasonic technique for real-time holdup monitorinn for the control of extraction columns. Chem. Engng Scir45, 30553062. Yi, I. and Tavlarides, L. L., 1990, A model for holdup measurements in liquid dispersions using the ultrasonic technique. Ind. Engng Chem. Res. 29, 475482. Zapryanov, Z., Malhotra, A. K.. Aderangi, N. and Wasan, D. T., 1983, Emulsion stability: an analysis of the effects of bulk and interfacial properties on film mobility and drainage rate. Inc. J. Multiphase Flow 9, 10.5-129.
Vol. 48, No. 8. pp. lsO3-ISIS.
1993.
ooo%xoP/93 s6.00 + 0.00 0 1993 Pcrsnmon Pm Ltd
MASS-TRANSFER EFFECTS ON DROPLET PHENOMENA AND EXTRACTION COLUMN HYDRODYNAMICS REVISITED Department
C. TSOURIS and L. L. TAVLARIDES of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, U.S.A. (First receiued 28 February 1992; accepted
in revisedform 2 June 1992)
Abstract-The effect of solute mass transfer between the two liquid phases on the drop size distribution and holdup profiles. of the dispersed phase in a multistage extraction column is experimentally investigated in this article. Experimental results of the drop size distribution, dispersed-phase volume fraction (holdup), and concentration profiles are obtained for both directions of mass transfer. The drop size distribution is measured by a photomicrographic technique, the holdup profile is measured by an ultrasonic technique, and the concentration profiles are measuredby refractionindex measurements. A strong influenceof the
mass-transfer direction on drop size aad holdup has been found.The resultsare in qualitativeagreement with the observations of other investigators. Mass transfer of butyric acid from toluene (dispersed) to water (continuous) produced larger drop sizes and lower values of the dispersed-phase holdup than for the equilibrated toluene-water system. For mass transfer of butyric acid from water (continuous) to toluene (dispersed) smaller drop sixes and higher holdup values are observed than for the equilibrated toluenc-water system. This behavior significantly affects the performance of the extractor and indicates the necessity for more studies to determine the physics of the phenomenon and to model these processes appropriately.
INTRODUCTION
It has been found by many investigators who studied two-phase liquid-liquid systems that mass transfer has a significatit effect on the behavior of the dispersed-phase droplets (Lewis, 1954; Logsdail, 1957; Groothuis and Zuiderweg, 1960). For example, experiments were conducted by Groothuis and Zuiderweg (1960) for the benzene/CCl,-acetic acid-water system where they observed the behavior of two droplets attached at the tips of two capillary tubes as they approach each other. When the transfer of acetic acid occurred from the drop phase to the continuous water-phase immediate coalescence resulted, while for the transfer of acetic acid from the continuous phase to the drop phase a strong retardation of coalescence was noted. This phenomenon is qualitatively explained by the effect of the interphase mobility on the drainage rate of the liquid film between the two droplets. The interface mobility is a result of gradients in the interfacial tension caused by nonuniform mass transfer along the interface. In a liquid-liquid extraction column, the effect of mass transfer on the column hydrodynamic behavior is of great importance, and it should be taken into consideration in equipment design. The rate of drop coalescence, which is strongly affected by the direction of mass transfer, becomes a decisive factor for the determination of the drop size. Since the rising velocity of the drops is a function of their size, the drop residence time is also affected by the mass transfer. Larger drops, produced by higher coalescence rates, iAuthor to whom correspondence
should be addressed. 1503
travel faster through the extractor, and the result is lower residence times of the drops and, therefore, lower volume fraction (holdup) of the dispersed phase. Both properties, larger drop sizes and lower holdup values, lead to smaller interfacial area for mass transfer between the two phases and, hence, lower masstransfer efficiency. Under the same conditions, the maximum allowable flow rates of both phases (throughput) before the occurrence of flooding are increased substantially. Experimental studies confirming this behavior have been reported by many investigators including Logsdail et al. (1957) and Komasawa and Ingham (197&a,b). The throughput before the onset of flooding and the mass-transfer rate are the most important parameters for the design of column extractors; therefore, the effect of mass transfer on the hydrodynamic behavior of the extractor should be studied quantitatively. Fundamental studies on the mobility of the liquid film between colliding droplets and the film drainage rate have been reported by Zapryanov et al. (1983). Malhotra and Wasan (1987) studied the effects of surfactant adsorption-desorption kinetics and interfacial rheological properties on the rate of drainage of foam and emulsion films. The objective of their study was to predict the rate of drainage of surfactantstabilized/polymer-stabilized foam and emulsion films from the knowledge of bulk and interfacial properties. Results showed higher interfacial mobility when the surfactant is soluble in the droplet phase than when it is soluble in the film. Although this analysis has included the effect of mass transfer of a surfactant from either phase to the interface on the interfacial mobility, still these results are far from complete to be
C. TSOURISand L. L. TAVLARIDES
lS@4
applied for the prediction of the effect of mass transfer from one phase to the other on talk droplet behavior in extraction columns. Gourdon and Casamatta (1991), in an attempt to predict the influence of the mass transfer direction on the operation of a pulsed sieveplate pilot extraction column, suggested that, in the case of mass transfer from the drops to the continuous phase, every drop-drop collison results in coalescence. This assumption is probably true for a high mass-transfer driving force. However, as the driving force becomes smaller and smaller, experimental results obtained here indicate that the coalescence efficiency decreases. In the present paper, more experimental results of the holdup and drop size distribution profiles in the presence of mass transfer along the extractor obtained by novel techniques are presented. The holdup profile is measured by an ultrasonic technique, while the drop size distribution is measured by a photomicrographic technique. Experimental data show the effect of the mass-transfer direction on the above hydrodynamic parameters and indicate the need for a model to predict this behavior.
EXPERIMENTAL
Pilot plant An extraction pilot-plant unit, the geometry of which is described by Kirou et al. (1988), is used for the experiments. The extraction column is of 125 mm diameter and is divided by rings into seven compartments of 127 mm height each. The free area between consecutive compartments is 29% of the cross-sectional area of the column. The two immiscible liquid phases are introduced into the column countercurrently; the continuous phase flows from top to bottom, and the dispersed-phase drops move from bottom to top. Breakage and coalescence of the drops occur as they move upwards due to mixing provided by six-blade impellers of 63.5 mm diameter. The impellers are located at the center of each compartment. The two phases are separated at the top of the column where the interface is located. A level controller based on conductivity measurements is used to control the height of the interface. Mass-transfer system The chemical system used in this study is water (continuous)-butyric acid (solute)-toluene (dispersed). The column hydrodynamic behavior in terms of holdup and drop size distribution profiles is studied for both mass-transfer directions. Measurement techniques The holdup profile of the droplet phase along the extractor and the exit concentration in the continuous phase are monitored continuously by data acquisition systems during the mass-transfer experiments. The drop size distribution and the concentration profiles in both phases are measured at steady state along the extractor.
A photomicrographic technique consisting of a microscope tube with eye piece and objective lenses, a camera, and fiber-optic light guides (Kirou et al., 1988) is employed for drop size measurements. The drops are magnified 10 times, and pictures are taken near the wall of the contactor. The drop size is measured by a semiautomatic particle analyzer (MOP-34 Carl Zeiss, Inc.) interfaced with an IBM PC computer. Concentration in both phases is measured by a digital refractometer (AO, ABBE Mark II). Phase separation devices have been developed for separating and sampling in situ pure phases for concentration measurements. For the droplet phase, a coalescor is employed as described by Schmidt et al. (1989), while, for the continuous phase, a stainless-steel mesh mounted at the tip of a vertically directed l/8” diameter pipe is used. Such devices have been introduced in each compartment. Real-time concentration and holdup measurements are obtained by data acquisition systems. For concentration measurements at the exit of the aqueous phase, a conductivity cell connected with a conductance meter (Yellow Springs Instruments Co., Inc., YSI Model 32) is employed. The signal from the conductance meter is transmitted to a data acquisition system (DAS 16F, A/D converter from Metrabyte) located in an IBM-XT computer and to an analog recorder. A calibration function is used in the data acquisition algorithm to convert the voltage signal into concentration. The same computer incorporates the data acquisition for an ultrasonic technique employed for holdup measurements along the extractor. This technique provides travel-time measurements of ultrasound through liquid media and is described in detail by Bonnet and Tavlarides (1987) and Tsouris et al. (1990). The absolute error introduced in the holdup measurements by the ultrasonic technique was estimated by Bonnet and Tavlarides (1987) as iO.017. The following model is used for the calculation of the holdup, 4 (Yi and Tavlarides, 1990; Tsouris and Tavlarides, 1990):
where t* is the travel time through the liquid dispersion, tc and tp are the travel times through pure wntinuous and dispersed phases, and gs and g, are wrrection factors for the path length of sound in each phase. Analytical expressions for these correction factors are available in the above articles. Calibration of the ultrasonic technique. For the calibration of the ultrasonic technique, the travel time of ultrasound in pure phases is measured in the beginning of each experiment. The holdup calculations are essentially based on the comparison of ultrasound travel-time measurements through the liquid dispersion with measurements through the pure phases. However, during mass transfer the solute concentration in both phases varies, and, since the ultra-
Mass-transfer
effects on droplet
sonic velocity is a function of solute concentration (see Fig. l), the values of the travel time through pure phases have to be updated to account for concentration variations. For this purpose, concentration profiles in both phases have to be obtained on-line. A technique to provide such measurements from 14 different points (two per stage) along the extractor was not available for
phenomena
1505
concentrations profiles have been assumed and calculated on-line from a steady-state material balance which utilizes the on-line concentration measurements at the exit of the continuous phase. Figure 2 shows the effect of the linear-concentrationprofile approximation on the calculations of the holdup profile. The holdup .profile calculated using the assumed linear profile is compared with the holdup profile calculated using the measured concentrations of solute in both phases. The maximum relative error in this example is less than 5%. Also shown in Fig. 2 is the holdup profile calculated without any corrections related to concentration variations.
RESULTS
Equilibrium data Equilibrium data for the water-butyric acidtoluene system have been generated at 20°C. Experimental data are correlated by the following relation suggested by Treybal (1963, p. 32):
-&B __+. XBB
0.954
. 0
I 2
.
w 4
weight
Fig.
1.
.
. 6
.
96 of butyrlc
Effect of solute concentration
I 8
.
I 10
1 12
add
on sound travel time.
r
( >
Here, XC- and Xc, are the weight percent concentrations of butyric acid (C) in toluene (A) and water (B), respectively, and XAA, XgB are the weight percent concentrations of toluene in the toluene-rich solution and water in the water-rich solution. When the mutual solubility of A and B is very low, such as the water-toluene system, one can assume that
35
10
1
2
3
(2)
AA
4
5
6
7
column height (stage number) Fig. 2. Comparison of noncorrected and corrected holdup profiles by using approximated and experimental concentration data. Feed concentration: 3.8 wt% in continuous, 0 wt% in dispersed.
1506
C. TSOURIS and L. L. TAVLARIDES
X ““zlXCA and XBB z 1 - Xc,. This assumption, however, is reliable only for low concentrations of the solute. The parameters k and r of eq. (2) are determined by plots of In (X,/X,,) vs ln(XcA/XAA) as shown in Fig. 3. For the system studied here, k = 0.122 and r = 0.584.
Concentrution proJiles Concentration profiles have been measured in both phases at steady state. Figure 4 presents an example of experimental data obtained for the case of mass transfer from the continuous to the dispersed phase. The feed concentration in the continuous phase is 3.8% by weight, while the dispersed phase is pure toluene. As the continuous phase travels from the top to the bottom compartments of the extractor, butyric acid transfers from the continuous to the dispersed phase which flows in the opposite direction. The equilibrium concentration in toluene shown in Fig. 4 is calculated from concentration data in water and by using eq. (2). In the case of mass transfer from the dispersed to the continuous phase, the concentration profiles show a maximum in the first compartment and minimum in the seventh. The reason is that the toluene phase is loaded with solute and is introduced from the bottom of the column. The slope of the concentration profiles is a function of phase flow rates and feed concentrations.
Eflect of agitation
speed on exit concentration The effect of the agitation speed on the exit concentration in the dispersed phase is examined in Fig. 5,
where a maximum is obtained at 160 rpm. The maximum relative error introduced in these measurements is 15%. This behavior is a result of two competitive phenomena: (i) the area of mass transfer increases at higher agitation speeds, yielding higher mass-transfer rates, and (ii) axial mixing in both phases increases also with agitation speed, reducing in this way the driving force for mass transfer. The significance of Fig. 5 is to show that the extraction efficiency does not increase monotically with the agitation speed or the dispersed-phase holdup, but that there is value of the agitation speed which gives optimum equipment performance.
E@ct of muss transfer on hydrodynamic
parameters The effect of mass transfer on drop size, holdup, and flooding performance of the extractor is discussed below.
Holdup. In the case of mass transfer from the continuous to the dispersed phase, the holdup behavior is similar to the one observed for the mutually equilibrated water-toluene system (Kirou et al., 1988). At moderate rotational speeds, the holdup profile has a concave form with a maximum in the upper compartments of the column. As the agitation speed increases, the average holdup increases too, and the maximum shifts towards the lower stages of the column. This behavior is shown in Fig. 6. Further increase in the agitation speed leads to flooding at which the holdup profile assumes a sigmoidal form
of buyric acid in the wrtor sOlutlOn weight% of water in the water solution Fig. 3. Equilibrium data for the toluene-butyric
acid-water
system.
1
effects on droplet phenomena
Mass-transfer
1507
. .
.
.
I
:
.
.
2
1
3
4
5
-
6
7
column height (stage number) Fig. 4. Concentration
1.51 150
profiles. Feed concentration:
160
170
3.8 wt%
in continuous,
180
190
0 wt%
in dispersed.
200
Agitation speed, rpm (l/min) Fig. 5. Exit concentration
of butyric acid in toluene vs agitation speed. Feed concentration:3.8 wt% continuous, 0 wt% in dispersed.
with maximum in the first stage. Also, an increase in either the continuous- or the dispersed-phase flow rate leads to higher holdup values. A different holdup-profile behavior has been found for the case of mass transfer from the dispersed to the
in
continuous phase. The holdup profile in Fig. 7 shows two distinguishable local maximums in the second and sixth compartments. In this experiment, the concentration profiles in both phases are monotonically decreasing, indicating that mass transfer occurs in all
C. TSOURIS and L. L. TAVLARIDES
1508
”
7
.
.
1
3
;
4
5
7
6
Column height (stage number) Fig. 6. Effect of the agitation
speed on the holdup profile. Feed concentration: 0 wt% in dispersed.
20-+--t--a__
3.8 wt%
-c,
4 = I” S
,+ 5
I
I
I
2
3
4
5
6
7
Column Hek~htbage numbed
‘.
12 8
w,_l’
,K 2
-4
S
-a ‘6 s i? .P --~--~_-_~-
-Q---o---Q0
9
G
IF_-,
-----o-r__
in continuous,
OL
I
I
r __ I
I
--O---4
I
2 3 4 5 6 Column Height (stage nvnber)
7
Fig. 7. Holdup and concentration profiles for mass transfer from the dispersed to the continuous phase. Feed concentration: 0 wt% in continuous, 7.6 wt% in dispersed.
Fig. 8. Holdup and concentration profiles for mass transfer from the dispersed to the continuous phase. Feed concentration: U wt% in continuous,12.6 wt% in dispersed.
compartments. This is, in fact, a result of the large difference between the selected flow rates of the two phases. One explanation for this profile could be in terms of the variation in drop breakage and coalescence rates along the column under the experimental conditions. The f&t maximum suggests that breakage dominates in the first few stages due to Large drop sizes of the feed stream. Eventually, small enough drops are produced to increase holdup. Coalescence rates appear to increase in the middle sections due to interphase mass transfer, causing increasing drop size
and decreasing holdup. At the top of the column, the drops have been depleted of solute, and coalesance rates decrease as coalescence enhanced by mass transfer no longer occurs. Breakage again dominates and, with the resulting smaller drops, holdup increases. The second maximum occurs because of the increased escape frequency of drops at the top section due to end effects. In the experiment of Fig. 8, however, the selected flow rates are such that equilibrium occurs in the lower compartments of the extractor, as indicated by the concentration profiles. This situation yields
Mass-transfer effects on droplet phenomena large drops at the top compartments due to intense coalescence rates caused by the mass transfer. Furthermore, interfacial concentration gradients formed in the equilibrated toluene-butyric acid-water system at the lower compartments cause higher drop breakage frequencies which yield smaller drops in that region (Koshy et al., 1988). Both effects, i.e. larger drops at the top compartments due to higher coalescence rates induced by mass transfer from drops to the continuous phase and smaller drops at the bottom due to higher breakage rates occurring at equilibrium concentrations, explain the higher holdup in the lower compartments of the extractor. The experimental results shown in Figs 7 and 8 indicate that the holdup profile is affected significantly by mass transfer from the drops to the continuous phase. To illustrate another effect of the mass-transfer direction on the holdup profile, Fig. 9 displays the holdup profiles for the three cases of (i) physically equilibrated water and toluene, (ii) mass transfer from the continuous to the dispersed phase, and (iii) mass transfer from the dispersed to the continuous phase. The operating conditions are the same (Qr = Q,, = 0.54 1 min- ’ and rpm = 160), with the exception of the feed stream composition. The second case, mass transfer from the continuous to the dispersed phase, produced the highest holdup. Mass transfer from the dispersed to the continuous phase produced the lowest holdup with the exception of the first two compartments. Apparently, the reason for this holdup behavior is that mass transfer from the continuous to the dispersed phase produces smaller
-m-
~88~
-mass
1
drops than the physically equilibrated water-toluene system, and mass transfer from the drops to the continuous phase produces larger drops. Furthermore, as stated above, the equilibrated water-butyric acid-toluene system also produces smaller drops than the equilibrated water-toluene system. This conclusion is drawn by the fact that larger drops travel faster inside the extractor and, therefore, are associated with lower holdup values. When mass transfer occurs from the drop phase to the continuous phase, larger drop sizes are produced due to enhanced coalescence rates. This shift in the drop size can be balanced by increasing the agitation speed. For example, in Fig. 10, a 20 rpm change, from 160 to 180 rpm, is capable of decreasing the drop size and yielding the concave holdup profile. The magnitude of the agitation intensity required to counterbalance the coalescence effect is related to the concentration gradient or the mass-transfer driving force. For instance, in Fig. 7, where the concentration driving force is higher, at 200 rpm the holdup is still low and the holdup profile is not concave. This behavior is a result of higher coalescence efficiency at higher concentration gradients with mass transfer from the dispersed to the continuous phase. Therefore, the coalescence efficiency of colliding droplets under mass transfer from the dispersed to the continuous phase is a function of the concentration driving force, and it should be modeled accordingly. Drop size. The effect of mass transfer on the drop size is related to the holdup behavior. Figure 11 shows
transferof butyrb
acid from water@)
transfer
add
2
of butyti
3
1509
to tokmne(d)
fmm toluene(d) to water(c)
4
5
6
7
Column height (stage number) Fig. 9. Effect of the mass-transfer direction on the holdup profile. Feed concentration for mass transfer from continuous to dispersed: 3.8 wt% in continuous, 0 wt% for dispersed. Feed concentration for mass transfer for dispersed to continuous: 0 wt% in continuous, 12.6 wt% in dispersed.
C. TSOURIS and L. L. TAVLARIDES
1510
”
1
1
;
4’
j
;
;I
7
column height (stage number) Fig. 10. Effect of the agitation speed on the holdup profile. Feed concentration in the continuous phase: 0 wt%. Feed concentration in the dispersed phase: 10.9 wt% for 150 rpm, 12.6 wt% for 160 rpn, and 13 wt% for 18Orpm.
the difference in the Sauter mean diameter in the fourth compartment, at various values of the agitation speed, for the two cases of (i) mass transfer from the continuous to the dispersed phase, and (ii) physically equilibrated water-toluene system. The Sauter mean diameter is calculated by the following relation:
(3)
where R is the number of drops in the sample. Mass transfer from the continuous to the dispersed phase produces smaller drop sizes which result in a reduction of the Sauter mean diameter of the order of 30%. The drop size distribution in this case shifts to lower sizes as shown in Fig. 12 for the agitation speed of 180 rpm. In the other case of mass transfer from the dispersed to the continuous phase, the drop size increases significantly, and the photomicrographic technique is not appropriate for drop measurements. However, when the mass-transfer system reaches equilibrium, the drop size becomes smaller than in the water-toluene system due to higher breakage frequencies as explained above in the discussion of Fig. 8. This behavior is shown in Fig, 13 and is another indication that the drop size under mass-transfer conditions is a function of the concentration driving force. Photographs of the liquid dispersion in the fourth compartment taken externally reveal some visual in-
formation regarding the effect of mass transfer from the dispersed to the continuous phase on the drop size. The dispersion produced by the water-toluene system is fairly homogeneous, and the drop diameter is of order 1 mm. At the same operating conditions and for the case of mass transfer from the drops to the continuous phase, the drops become larger due to higher coalescence rates, and the holdup decreases due to lower residence times of larger drops. This behavior is shown in Fig. 14(a) and (b). Furthermore, large drops formed by mass transfer from drops to the continuous phase are accumulated above the impeller in each compartment, causing spatial inhomogeneities. The shape of these drops is clearly not spherical. Also, the size of the largest drops is comparable to the shaft diameter which is approximately 10 mm. Flooding. The effect of mass transfer also impacts on the flooding performance of the extractor. An example is presented in Fig. 15, where the flooding behavior of the extractor for the physically equilibrated system is presented by the curves at various values of the agitation speed (Kirou et al., 1988). Values of the flow rates above the curves in Fig. 15 lead to flooding. Hence, the conditions of the experiment shown by the cross sign should cause flooding. The average holdup at these conditions, however, is only 9.2%. This value is far from the holdup at flooding which is around 45% (Kirou et al., 1988). This
Mass-transfer
1511
effects on droplet phenomena
0.8 0.7 -I 150
160 Agitatation
180
170 spead,
190
rpm (llmin)
Fig. 11. Effect of the mass-transfer direction on the Sauter mean diameter; fourth compartment. concentration for mass transfer: 3.8 wt% in continuous, 0 wt% in dispersed.
Feed
Diameter (mm) Fig. 12. Effect of mass transfer on the drop size distribution; fourth stage. Feed concentration transfer: 3.8 wt% in continuous, 0 wt% in dispersed.
behavior is again due to higher coalescence rates and, hence, larger drop sizes in the case of mass transfer from the drops to the continuous phase. DlSCUS!GON
It has been shown that mass transfer has a significant effect on the drop breakage and coalescence in agitated liquid dispersions. While the objective of this
for mass
article is to experimentally describe the result of the mass-transfer effect on the drop size distribution and holdup profiles of the dispersed phase, a qualitative discussion is offered here which can help in the modeling of the process. Consider the breakage and coalescence rate functions developed by Coulaloglou and Tavlarides (1977) for isotropic turbulence:
C. TSOURIS and
1512
m
MMQ IrMQfer
of bufyllo
eold
L. L. TAVLARIDES
fmmlchmIw(clJ
lo waler(c),
n M-lranafQr(syatemwtthmllbutytiacid).~
I&
- 0.78 n-m.
-1.Olmm.
Flowrat6s:Oc-Qd-0.54Umin. 180rpm
0.1
0.3
0.5
0.7
Diameter Fig. 13. Effect of mass transfer
0.Q
1.1
1.3
1.5
1.7
1.9
(mm)
on the drop size distribution; mass transfer: 0 wt% in continuous,
fourth compartment. 7.6 wt% in dispersed.
Feed concentration
for
Fig. 14. Effect of mass transfer on the liquid dispersion, fourth compartment. (a) Equilibrated water-toluene system; (b) feed concentration 0 wt% in continuous, 12.6 wt% in dispersed. rpm = 160, Q. = Qd = 0.54 lfmin.
1513
Mass-transfereffects on droplet phenomena
+ tpm-2co.msmJtlmhrdtxlyrlc~
0.2 -
$zzz$TS@ S O.Oq 0.0
-
1 0.1
-
I 0.2
.
I 0.3
.
. 0.4
.
. 0.5
_
. 0.6
.
. 0.7
. 0.6
.
. 0.9
1.0
Qd (Vmin) Fig. 15. Effect of mass transfer
on the flooding performance of the extractor. Feed concentrationfor mass transfer:0 wt% in continuous, 7.6 wt% in dispersed.
Breakage:
Coalescence: F(d,, d,) = 9/s
-((d, ksl+$
+ dJ)2(df/3 + dj13)I12 exp
(
- $ -1
(5)
where dt, d, are drop diameters, Eis the energy dissipation per unit mass, 6 is the dispersed-phase holdup, u is the interfacial tension, F is the average coalescence time, f is the average contact time, and kl , kl, and k3 are proportionality constants. The contact time is the duration of contact between two drops after a collision and is a function of the size of the two drops and the itensity of agitation. The coalescence time is the time required to drain the continuousphase film between the two drops until a critical thickness is reached after which coalescence occurs. The coalescence time is a function of the continuousphase viscosity and density, the sixes of the colliding drops, and the intensity of agitation. A first approach for including the effect of mass transfer in either direction on the drop breakage is through the interfacial tension. It has been shown by Groothuis and Zuiderweg (1960) that, when a solute is introduced into an immiscible system, the interfacial tension decreases. The equilibrium interfacial tension is a function of the solute concentration. Equation (4) shows that, as the interfacial tension N the breakage frequency increases and, therefore, the drop size in this case is expected to be smaller. This effect is
qualitatively in the right direction as compared to the experimental results of this work. The effect of mass transfer from the dispersed phase to the continuous phase on the drop coalescence can be described by a different mechanism which has to do with the gradients of interfacial tension on the drop surface (the Marangoni effect). The pre-exponential term of eq. (5) gives the drop-drop collision frequency. This term is not expected to change with the mass-transfer direction. What changes is the exponential term which gives the coalescence efficiency or the fraction of collisions which result into coalescence. The contact time, r, is a function of the drop size and the intensity of agitation and, therefore, is not affected by mass transfer. Hence, the only quantity in the coalescence function that can vary with mass transfer is the coalescence time, which is related to the interfacial mobility. For instance, the time needed to drain the continuous-phase film is smaller for liquid drops than for solid spheres, due to the mobility of the drop surface. Introduction of surfactants (Zapryanov et al., 1983; Malhotra and Wasan, 1987) may increase the interfacial mobility. In the case of a solute transferring from the dispersed phase to the continuous phase, the solute concentration in the continuous phase at the point of collision reaches equilibrium with the drop concentration very fast. The concentration in the continuous phase at the collision point is, therefore, maximum and, hence, the interfacial tension is minimum according to the data of Groothuis and Zuidenveg (1960). as compared to other points in the neighborhood of collision. The gradient in the interfacial tension creates surface flow from low to high interfacial tension (Probstein, 1989) which accelerates the film
C. T~OURIS and L. L. TAVLARIDFB
1514
drainage between the drops and, hence, enhances coalescence. A reasonable approach to include the effect of mass transfer from drops to the continuous phase could be to express the coalescence time, T, as a function of the interfacial tension gradient. Population balance models could then be employed with breakage and coalescence functions, such as those above, modified as suggested to model the hydrodynamic behavior of extraction columns in the presence of mass transfer, regardless of mass-transfer direction.
Wi, 4) ddjl ge gd
k
ki, kz
k3
r
CONCLUSIONS
The effect of mass transfer on the hydrodynamic behavior of a multistage extraction column is discussed in this article. Experimental data have shown that mass transfer plays an important role in the drop breakage and coalescence rates which determine the drop size, holdup, and flooding performance of the column contactor. Mass transfer of solute from the dispersed phase to the continuous phase enhances drop coalescence and, therefore, the drop size increases, yielding lower holdup values. Mass transfer from the continuous phase to the dispersed phase enhances drop breakage and, hence, the drop size decreases, yielding higher holdup values. Similar behavior is observed for the equilibrated water-butyric acid-toluene system in comparison to the watertoluene system. The effect of mass transfer on holdup has analogous results on the column flooding behavior. When holdup decreases due to mass transfer, flooding occurs at higher values of the operating parameters and vice versa. While these phenomena have been observed and recorded previously, more detailed experimental data of holdup profiles, drop size distributions, and concentration profiles obtained in this work from a wellinstrumented pilot-plant extraction unit help us to understand better the role of mass transfer on the drop phenomena and on the hydrodynamic behavior of liquid-liquid extraction columns. The comparisons of the drop size distribution and the holdup profiles with the solute concentration profiles in both phases suggest that both drop breakage and coalescence rates are quantitatively related with the mass flux of solute. Additional information such as these results and the quantification of these effects in the design equations are needed for a more reliable design of extraction process equipment. Further studies are required in this direction. Acknowledgements-The authors gratefullyacknowledge the National Science Foundation for supporting the research described in this paper through Grant CTS-9017138. The assistance of Mr. Mohammed-Kamal Ahmad during the
execution ofthe experiments is also gratefully acknowledged. NOTATION
d d 32
drop diameter, m Sauter
m
mean diameter
defined by eq. (3),
tc td
t* f f Xi,
collision frequency of drops size di and d,, s-l
breakage
frequency
of drops
of size
dj, s-’ correction factor for the sound length in the continuous phase correction factor for the sound length in the dispersed phase
path path
parameter in equilibrium expression, eq. (2) constants in breakage function, eq. (4) constant in coalescence function, eq. (5) parameter in equilibrium expression, eq. (2) sound travel time through pure continuous phase, s sound travel time through pure dispersed phase, s sound travel time through the dispersion, s contact time, s coalescence time, s weight percent concentration of species i in solvent j
Greek letters E energy dissipation per unit mass, m* se3
density, kg m- 3 interfacial tension, N m- 1 dispersed-phase volume fraction up)
P
u d
(hold-
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