130
I d . EW. Chem. PrOceSs Des. DeV. 1983, 22, 130-135
Unsteady-State LiqW-LlquM IMspershs in Agitated Ve-k Paul 0. Hong and James M. Lee” Chemical Enghwhg Depertment, Clevelend State University, Clevelend, Ohb 44 115
The changes of the average drop size and the minimum transition time required to reach steady state during the initlal perkdof iquid-liquid asperskn have been studied using a "photographic technique and a light tratwmbbn method. A spectrophotometer was converted into a light transmittance unit by employing a specialty designed fiber optic probe, which allowed the investigators to follow a wkle range of changing drop slzes. The average drop size dvfngthe hitkdperkdof mkhg was found to change exponentially from large to mi while the distribution changed less drastidy from wide to narrow. The minimum transltion time was found to depend on impeller speed and on the impellerltank diameter ratio as well as the system’s physical properties.
Introduction The transitional behavior of liquid-liquid dispersions during batch agitation is a complicated phenomenon which has only recently begun to be explored. A study of the unsteady-state drop size and its distribution during the initial period of mixing and of the minimum time required to reach steady state will provide valuable fundamental knowledge for a number of important chemical processes such as suspension polymerization and liquid-liquid extraction. In suspension polymerization, residual monomers have to be stripped from the product due to either their carcinogenic properties or economic reasons. It is known that the residual monomer stripping is easier if the properties of each polymer particle are uniform. The uniform properties are closely related to conditions of the initial period of dispersion such as the time required to reach the steady state, the change of droplet size, and droplet size distribution in the initial period. In liquid-liquid extraction, the correlation of the Sauter mean dimeter as a function of time, physical properties, impeller speed, and impeller and tank geometry will facilitate the mass transfer study in batch systems. When two immiscible liquids are brought into contact in an agitated vessel, a dispersion is formed as a result of two competing processes: the rate at which the bulk liquid of the dispersed phase breaks up to produce fine drops and the droplet coalescence rate which gives back the bulk liquid. If agitation continues over a sufficiently long time, a local dynamic equilibrium is established between breakup and coalescence. The equilibrium drop size distribution in a batch system will mainly depend on the relative magnitude of these two processes. In turn, the breakage and coalescencerates will depend on such variables as the geometry of the vessel, the energy input per unit mass, dispersed phase fraction, as well as the physical properties of the two phases. The breakage rate dominates the coalescence rate during the initial period of a batch agitation process until the equilibrium drop size distribution is established. Thus, the droplet size and its distribution in an agitated vessel are closely related to the mechanisms of drop breakup and coalescence. McCoy and Madden (1969)published a limited amount of data on the effect of stirring speed and time on drop size distribution in demonstration of the encapsulation method and drop classification procedures. Ramkrishna (1974)studied the probabilities of droplet breakup as a function of drop size using McCoy and Madden’s data and proposed a “power law” expression for the transition probability of droplet breakage. Narsimhan et al. (1980) 0 196-4305/83/ 1 122-0 130$01.5010
Table I. Systems Studied system 1
continuous dispersed
phase
5cSt DOWCorning
water
200 fluid
2
ethyl acetate
water
Table 11. Physical Properties at 23 “C interf ac density viscosity sys- tenstion, cont, disp, cont, disp, tem 1 2
N/m kg/m3 kg/m3 N-s/mz 0.0425 1000 920 0.0010 0.006 1000 894 0.0010
Ndm2 0.00460 0.00046
later measured transient drop size distributions in a stirred liquid-liquid dispersion with a low dispersed phase fraction (leas than 0.5%) and found that the transition probability function for droplet breakage shows a steeper decline as drop size decreases toward a maximum stable value. Skelland and Lee (1981,and also Lee, 1978)presented a correlation for average drop size for the initial period of mixing, but it was limited to the prediction of the Sauter-mean diameter for a specific moment they defined. There appears to have been no study on the minimum transition time required to reach steady-state drop size. The objectives of this study are, therefore, to obtain more data on the change of drop size during the initial period of dispersion and the minimum transition time required to reach steady-state drop size for future correlations and uses. Experimental Details Material and Mixing Vessels. The systems chosen for the dispersed phase were 5 cSt Dow Coming fluid and ethyl acetate. Distilled water was used for the continuous phase. The Dow Corning 200 fluids are clear dimethyl siloxanes with low vapor pressures and relatively flat viscosity-temperature curves. The physical properties of two systems are listed in Tables I and 11. The mixing vessels were two sizes (0.292and 0.387 m in dimeter) of flat-bottom glass cylinders fitted with four equally spaced, radial, vertical wall baffles. A model ELB experimental agitator kit manufactured by Bench Scale Equipment Co. was used for mixing the liquids. The impellers chosen for this study were six-bladed flat turbines, since this type showed the best dispersion performance in preliminary runs. Light Transmission Unit. The light transmittance technique is most frequently used for the determination 0 1982 Amerlcan Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 131 LAMP
h
W A K LENGTH CAM
A: CAMERA B EXT. TUBE
il
N
C FLASH D OBJECTIVE E R?OTECTIVEW
I1
w
Figure 1. Schematic diagram of light transmission unit.
of average drop sizes of liquid-liquid dispersion. It has the advantages of quick measurement and on-line operation. It consists of a light source, detector unit, and probe. The probes are usually made of mirror-treated glass rods or of internally blackened tubes, neither of which is versatile in ita uses. The construction and assembly of the whole unit also require a fair amount of knowledge of spectrophotometry. In this research, a spectrophotometer was successfully converted into a light transmission unit by using two flexible fiber optic light guides as its probe. The spectrophotometer used was Spectronic 20 manufactured by B a d and Lomb. The light guide consisted of glass fiber bundles sheathed in plastic tubing, with ground and polished ends and with metal tips, which are procured from Edmond Scientific. The optical system of modified light transmission unit is shown in Figure 1. A fiber optic light guide (3.2 mm F.O. diameter, 910 mm long) received monochromatic light through one end, which was secured at the drilled hole (4.6 mm diameter) in the occluder. The emergent light moved to a photocell through a different size of light guide (6.4 mm F.O. diameter, 910 mm long), which was fastened in a hole drilled in an opaque plate fitted in the filter holder. The probe had a 15-mm gap through which dispersion passed, as shown in Figure 1,for which the light guides were encased in stainless steel tubes. The light guides exited from the case of the spectrophotometer through two holes drilled in the upper surface, one in the lid of the sample holder and the other in the case itself 20 mm to the viewer's right of the sampling compartment. To check the reliability of the modified transmission unit, the light transmittance of a known sample in the cuvette was measured by placing it between the gap of the probe in the dark. The wavelength range tested was from 420 to 600 nm. The readings by the new unit were remarkably accurate within the error range of the equipment specification, f 2 %T. Thus, the modified spectrophotometer may have a wide range of applications for the on-line measurement of light transmittance. All the measurements in this study were made at 500 nm wavelength. Photographic Techniques. A microphotographic technique with a low magnification ratio (3.87) was employed to take clear pictures of liquid-liquid or gas-liquid dispersion during agitation. Figure 2 shows the schematic diagram of the microphotographic setup. It consisted of a camera (Nikon F-2A) with a motor drive, an extension tube, an objective (planachromatic) lens with 4X magnification, and a protective cup to eliminate the interference of dispersed drops between the objective lens and the
W
Figure 2. Schematic diagram of microphotographic setup.
object plane. The internal wall of the extension tube and the cup were painted black. An electronic flash (Sunpak Auto 322) with a fiber optic light guide (6.4 mm F.O. diameter, 910 mm long) was used to light the object plane effectively and at the same time to catch fast moving drops (Figure 2). Kodak Tri-X Pan film (ASA 400) was used with a flash duration of l/lm or l/lms depending on the impeller speed and phase fraction chosen. When the above-mentioned setup was used, the dispersions with a magnification ratio of 3.87 could be photographed at any position in the vessel by immersing the end of the microscope tube directly in liquids. Since typical droplet sizes of liquid-liquid dispersion lie between 0.1 and 1 mm, the magnification ratio of 3.87 recorded suitable numbers of drops for statistical analysis of drop sizes. No commercial microscope-camera adaptor was available which could produce this low magnification. The negatives were developed and made into slides to be projected on a piece of graph paper to estimate the dropsize spixtrum by counting about 200-300 drops. The light transmission unit was then calibrated. The quality of the pictures was significantly improved over the ones taken previously by Skelland and Lee (1981). Experimental Procedures. The continuous and dispersed phases of each system were prepared separately by presaturating each liquid with the other. The continuous phase was placed in the tank and the agitator was started. The impeller speed was always above the minimum impeller speed for 98% uniformity as defined and correlated by Skelland and Lee (1978). The light transmittant probe was placed in a desired location before the measured amount of dispersed phase was injected near the impeller shaft. In some experiments, the dispersed phase was placed in the vessel with the continuous phase before the agitator was started. The light transmittance was measured and recorded from the moment the agitator was started until no further decrease could be observed. About 20 photographs were taken at intervals of 1-60 s during each run. All runs were performed at a temperature of 23 f 1 oc. Results and Discussion Average Drop Sizes. The theory and application of light transmission devices to the measurement of interfacial area have been fully described by Roger et al. (1956) md Vermeulen et al. (1955). It was found that a plot of the extinction ratio (Io/Ior 1/T, where Io is initial intensity set to unity and I or T is transmitted intensity) against interfacial area per F i t volume of mixture (specific area, a) gave a straight line of 1/T = ml f mza (1) In theory m, is unity and m2 is a constant independent of drop-size distribution as long as all the particles are
132
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983
d'
: 0.05 0
: 0.10
3t
-
1
2
0
4
1 0 N
8
6 5 , MIN
01 I
2 3 LIGHT TRWWISSKh RATIO
I
Figure 6. The change of Sauter mean diameter during initial period of mixing (01 = 0.102 m, DT = 0.292 m,N = 216 rpm, C$d = 0.20,
4
system 1).
I/T
Figure 3. Calibration curves (system 1).
I
I
100
ed I 0
0 60 bI
0.1
0
40
1
2
3
4
5
6
7
1
8
t.MIN
Figure 6. Change of drop size with time (DI = 0.076 m, DT = 0.292 m,C$d = 0.20, system 1). 20
2
4
6
8
1 0 1 2
t ,MIN
Figure 4. Typical recorder output (DI= 0.102 m, DT = 0.292 m, N = 216 rpm, I#Id = 0.20, system 1).
spherical or nearly so. A typical plot of 1/T vs. a for the 5 cSt Dow Corning 200 fluid/water (system 1)is shown in Figure 3. Here the specific area was computed from the Sauter mean diameter observed in the photographs
Cnid:
d32
=Enid?
(2)
and the relation a = - 6#' d' d32
(3)
where $)d is the fraction of the dispersed phase. It should be noted that both steady-state and unsteady-state data were used to construct these calibration plots, and they both fitted equally well to the same lines. Figure 4 is a typical recorder output showing the percent transmittance changes with respect to time during the initial. period of liquid-liquid dispersion. Note that transmittance decreases with time until it reaches a constant steady-state value. Figure 5 shows the plot of average drop sizes measured with photographs taken during this period. The solid curve represents the calculated values from a calibration line and the recorder output (transmittance). It is apparent from these two figures that the light transmittance method offers a reliable means to measure the change of unsteady-state drop sizes as well as that of the steady state.
The power input per unit volume of vessel for this study ranged from 0.05 to 0.68 W/kg. The power input and fluid properties used in this study gave a Kolmogoroff turbulence microscale, 9 = (p3/p340*25ranging from 0.03 to 0.07 mm. Since only a small volume fraction of the dispersion occurred as drops smaller than 0.100 mm, the drop breakage process, as well as vessel hydrodynamics, could be considered to be in the inertial regime. Various investigators have already presented numerous correlations involving steady-state drop size along with the possible mechanism. Since such study is outside the scope of this paper it will not be discussed here in detail. It is sufficient to say that our steady-state data seemed to fit well with Coulaloglou and Tavlarides' (1976) correlation. Notice that both light transmittance and cfrop size appears to decrease exponentially with time (Figures 4 and 5). To test the validity of this statement one may assume that
-d32-
-1+
(4)
d32*
where d32*is a steady-state drop size, an.d is constant for a given system. Then the plots of In (d32 - d32*)/d32* vs. time should result in a straight line. One such plot shown in Figure 6 suggests that the decrease indeed follows an exponential decay rule very closely. Rims et al. (1978) stated chat the location of the sampling point is not critical. Since an average drop makes many journeys around the vessel before coalescing, the dispersion can be considered approximately statistically homogeneous. In other systems such as Sprow's strongly coalescing experiments (Sprow, 1967) where drop sizes were
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983
I v)
80
$
’
0.2
t = 0 . 2 5 min
0.1 0 0.2
-
133
J
t = 0 5 min
01
E::K-
0
I
I
t = 2 m i In
I
0
,
0
0
01
L L
c
0
z
p
o 05
“L t.60 min
0 2 01 0 20 0
2
4
6
8
I012
I4
t , MIN.
Figure 7. Effect of the probe location on light transmittance data (DI= 0.101 m, DT = 0.292 m, N = 280 rpm, @Jd = 0.10, system 1).
0
1
2
3
4
5
6
lo4, m Figure 9. Drop size distribution histograms (Dl= 0.076 m, DT = DROP DIAMETER x
0.292 m, N = 565 rpm, & = 0.05, system 1).
t=lmin Y 01 0 i L h z L -
$
0.3 r t=2min
0
I-
P c
2
E
0.3 r
o
-
0.3 r 0.2 01
-0
0
t = 3 0 min
0
2
6 8 DROP DIAMETER x 4
10
12
io4, m
Figure 8. Drop size distribution histograms (01 = 0.102 m, DT = 0.292 m, N = 216 rpm, & = 0.20, system 1).
significantly different near and away from the impeller, this obviously is not the case. We measured light transmittance a t three different locations, top, middle, and bottom, all halfway between the impeller and tank wall during the early part of this study. Figure 7 reveals that there are some differences in steady-state transmittance (and in the drop size) but not as much as Sprow’s system exhibited. Furthermore, the shapes of the curves were relatively similar, enough so that differences in minimum transition time measurements (to be discussed later) were well within the experimental error, thus justifying the choice of any convenient location for this kind of study. However, for other reasons, we have picked the middle location at the same level as the impeller to do most of our study. Drop Size Distribution. Photographs taken during the experimental runs were analyzed by measuring each drop and classifying by 0.03-mm size ranges. Figures 8 and 9 show the changes in drop size distribution at low and high energy input levels. At a low level of energy input (Figure 8),the distribution approaches a normal distribution as a steady state is achieved. On the other end at the high energy input level the distribution moves toward a skewed or log-normal distribution. Most of the drop size distribution in between displays normal distribution. Figure 10 shows the drop size distribution at low energy
2
4 6 8 1 0 1 DROP DIAMETER x lofm
2
Figure 10. Cumulative drop size distributions (01 = 0.101 m, DT = 0.292 m, N = 216 rpm, &d = 0.20, system 1).
t
5h A
I
‘
0
1
2
3
4
5
I
6
t , MIN
Figure 11. Change of drop size and drop size distribution with time during initial period of dispersion (DI= 0.102 m, DT = 0.292 m, N = 216 rpm, system 1).
input level (Figure 8)on a normal distribution graph. Note that the initial distribution (at 1min after dispersion) does not appear to be a straight line, exhibiting a characteristic of bimodal distribution, if not multi-modal. In this graph, the top three lines are reasonably straight, which indicates a normal distribution as the distribution becomes m o w e r . The narrowing of drop size distribution follows the drop size decrease very closely. Figure 11shows two different d32fson top and the corresponding drop size distributions, as measured by the standard deviation (a), on the bottom part. As can be seen, the distribution changes with drop size, but not as rapidly.
134
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983
i ', I
~
450
N I
0
2
4
6
8
1
0
1
2
1
4
i
X
lo". RPM
Figure 14. Effect of impeller speed on the m i n i u m transition time (DT= 0.292 m, system 2).
t ,MIN
Figure 12. Effect of the impeller speed on average light transmittance value and ita deviation from the average (DI = 0.076 m, D, = 0.292 m, $ J ~= 0.10, system 1).
I 51
NX
Id'. RPM
Figure 15. Effect of impeller speed on the minimum transition time (DT= 0.292 m, system 1).
0
1
2
3
4
5
A T x 100
Figure 13. Dependence of AT on standard deviation based on Sauter mean diameter.
Another interesting way to measure distribution is by using the light transmission curve. Figure 12 shows typical
recorder outputs similar to Figure 4, but at three different rpm's. The fluctuation AT or noise level for 350 rpm is higher than at 450 rpm, which in turn is higher than at 565 rpm. If the standard deviations of drop sizes are plotted against this fluctuation (AT), a linear relationship is obtained (Figure 13). This method may not be very accurate when the AT is small and difficult to read, but when AT is large (initial period) or when a photograph is not available it gives good estimations. Minimum Transition Time. Minimum transition time (t,) is the minimum time required to reach a steady-state drop size. In obtaining the minimum transition time several methods have been tried. In one method the minimumtime is arbitrarily defined as the time when light t r k d e s a stsady value and no further change in reading can be observed within a specified time period (1-3 min). The steady-state values were later c o n f i i e d by matching with the final values obtained when impeller speeds were brought down to the original speeds from substantially higher ones. Since this is a subjective method, three separate sets of reading8 by different indinduals were made and compared. In moat cases the agreement was surprisingly good, and in a few cases when differences existed, average values were taken. Another method of obtaining the minimum transition time (t,) was
by plotting In ((d32- d 3 2 * ) / d 3 2 * ) vs. time, as in Figure 6, to find the time when (&- da*)/da* equals an arbitrarily specified value (0.01-0.05). This second method was found to be less accurate since a small error in ds2* would lead to a bigger error in t, than with the first method. Since drop size and distribution depends mainly on impeller size (DI)and speed (N)in addition to the physical properties of dispersed and continuous phases and their relative amounts (&), the f i t variables investigated were D , N , and 4.J (dispersed phase fraction). Figure 14 illustratea the influence of impeller speed on minimum time for system 2 (ethyl acetate/water) using a 0.076-m flat turbine and a 0.102-m flat turbine. The steep negative slope indicates a very strong dependence of t, on impeller speed. Although the data seem somewhat scattered, there exists a definite correlation that can be expressed as
t,
a
N'
(5)
where y is approximately -6 for system 2. A similar plot for system 1@ow Coming fluid/water) is shown in Figure 15. It should be noted that the dependence of t, on impeller size is much less for system 1in comparison with system 2. The y for system 1is found to be approximately -1. The large difference in y for the two systems may be caused by the differences in their breakage and/or coalescence mechanism due to physical property differences. Figures 14 and 15 have been replotted to compare the relative effectiveness of different impeller diameter (DI) to tank diameter (DT) ratios. On an equal power input basis, the DI/DT = l/s case is superior to the DI/DT= l/q case in both systems in reducing the time required to reach a steady state. In other words, the bigger the size of impeller, the more efficient the impeller is when used for
Ind. Eng. Chem. process Des. Dev, lg83, 22, 135-143
liquid-liquid dispersion. Since equal power per unit mass results in equal drop size, this implies that a bigger impeller can be employed to produce the same final drop size faster using the same amount of energy. Conclusion 1. Unsteady-state drop size, ita distribution, and the minimum transition time required to reach steady state during the initial period of liquid-liquid dispersion have been measured by using a microphotographic technique and a light transmittance method. 2. The average drop size was found to follow the exponential decay rule. 3. The drop size distribution changes from a very wide (multi-modal) distribution to a narrower (normal) distribution to, finally, a very narrow (skewed or log-normal) distribution as drop size becomes smaller and smaller. 4. The minimum time required to reach a steady state is very strongly dependent on impeller size and speed and on tank size. At the same power input per unit mass, a larger impeller is more efficient. Acknowledgment This material is based upon work supported by the National Science Foundation under Grant CPE-8006666. Nomenclature a = interfacial area per unit volume, m-l DI = impeller diameter, m DT = tank diameter, m d = particle or droplet diameter, m ds2= Sauter mean droplet diameter defined by eq 2, m dS2* = Sauter mean droplet diameter at steady state, m I = emergent light intensity Io = incident light intensity
135
ml, m2 = constants used in eq 1 n = number of drops N = impeller stirring speed, rpm T = fractional light transmittance = I/&,, dimensionless AT = fluctuation in T readings, dimensionless t = time, min t , = minimum transition time required to reach steady-state drop size, min Greek Letters a,6 = constants used in eq 4 y = constant defined in eq 5 t = rate of energy dissipation per unit mass of fluid, W/kg p = viscosity, N.s/m2 p = density, kg/m3 9 = Kolmogoroffs length scale, m u = standard deviation based on dS2,m ‘$d = volume fraction of dispersed phase, dimensionless Literature Cited Coulakglou, C. A.; Tavlarides, L. L. AIChE J . 1976, 22, 289. Lee, J. M. Ph.D. Dlssertatlon, University of Kentucky, Lextngtm, KY, 1978. McCoy, B. J.; Madden, A. J. Chem. Eng. Sci. 1969, 24, 416. Narslmhan, G.; Ramkrishna, D.; Gupta, J. P. A I C M J . 1980. 2 6 , 991. Roger. W. A.; Trlce. V. G., Jr.; Rushton, J. H. Chem. Eng. Prog. 1956, 52, 515. Ross, S. L.; V e h f f , F. H.; Curl, R. L. Ind. Eng. Chem. Fundam. 1878, 77, 101. Ramkrishna, D. Chem. Eng. Scl. 1974, 2 9 , 987. Skelland. A. H. P.; Lee, J. M. Ind. Eng. Chem. Process D e s . Dev. 1978, 77, 473. Skelland, A. H. P.; Lee, J. M. AIChE J . 1981, 27, 99. Sprow. F. B. A I C M J . 1967, 73, 995. Vermeulen, T.; Williams, G. M.; Langlols, 0. E. Chem. Eng. Prog. 1955, 57, 85-F.
Received for review March 23, 1982 Accepted August 16, 1982
Presented at the Fall 1981Annual Meeting of AIChE, New Orleans, LA,Nov 8-12,1981,
Model Building in Complex Catalytic Reaction Systems. A Case Study: p-Xylene Manufacture Nlgel H. Orr’ and Davld L. Cresswell’ Systems Engineedng Grow, E. T.H. Zentrum, CH-8092 Z m , Switzerlend
Davld E. Edwards I.C.I. Petrochemlcels Dlvlsiim H.O., P.O.B. 90, WHton, Cleveland TS6 &I Englend €,
A strategy of model building In complex catalytic reaction systems is described based on the deployment of different types of laboratory reactors and independent measurement of pore diffusion within a single-pellet diffusion cell. The approach is applied to the kinetic modeling of simultaneous isomerlzation and disproportionation of a mixture of xylenes over a commercial silica-alumina catalyst, which Is subject to continuous W i n g and pore diffusion limltatlons. A comparison between the predictions of product distributions In an integral reactor containing commerdal-size catalyst beads, employing a reactor model in which all effects were previously identified by independent experiment, and observed values shows that the model can pvdctp-xylene “lifts” to withi 16% error and integral selectivities to within 11% error over wide ranges of temperature, pressure, and space velocity.
1. Introduction
This paper is concerned with the quantitative &scription of the yield and selectivity of p-xylene formation by isomerization with simultaneous disproportionation reacBP Chemicals, Grangemouth, Scotland. 0198-4305/83/1122-0135$01.50/0
tions and catalyat deactivationby deposition of coke. Mass transfer through the diffusion film is shown to have no important influence on the complex chemistry. However, pore diffusion is of significance and is studied experimentally (e.g., with catalyst pellets of various sizes in both reactive and nonreactive conditions) as well as mathematically, using diffusion equations. 0 1982 Amerlcan Chemical Society
