Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 473 Sell, N. J., Fischbach, F. A., Rock Prod., 79 (6),78 (1976). Siegert, L. D., Rock Prod., 77 (2), 52 (1974).
Received for review September 12, 1977 Accepted May 10, 1978
This paper is based on a study funded by General Portland, Inc., Dallas, Texas. The authors also wish to thank the University of Wisconsin-Green Bay for use of the facilities in certain aspects of this work.
Agitator Speeds in Baffled Vessels for Uniform Liquid-Liquid Dispersions A.
H. P. Skelland” and Jal Moon Lee
Chemical Engineering Department, University of Kentucky, Lexington, Kentucky 40506
This work examines the effects of impeller type, speed, size, and location, and of liquid properties on the degree of mixing of two immiscible liquids in a baffled vessel. The degree of mixing was expressed in terms of a mixing index developed by Hixson and Tenney. I t was found that Skelland and Seksaria’s correlations for the minimum impeller speeds required for complete dispersion in baffled vessels, N, could be adapted to correlate the minimum impeller speeds for nearly uniform mixing, N’, defined as the rotational speed at which the mixing index reached 98%. The correlations for N are N = C o D a ~ ~ , ” s ~ ~ - 1 ‘ s o 0 and ~3Apo~2s
where Co, cyo, C,, and a , depend upon the type of impeller and its location. The average deviations between N’and N are given as x in Table V, such that N‘ = N( 1 x ) . Values of N‘were about 8 % greater than N , on the average.
+
This paper relates to the design of liquid-liquid mixers which, in conjunction with settlers, are widely used in liquid-liquid extraction. In addition to mass transfer coefficients, drop size, and interfacial area, knowledge is also required of the minimum mixing impeller speeds for both complete dispersion and uniform dispersion of one liquid in the other. Skelland and Seksaria (1978) showed, for example, that in some cases one liquid will not be completely dispersed in the other a t impeller speeds as high as 1000 rpm. Correlations were established by Skelland and Seksaria (1978) for a variety of impellers, giving the minimum impeller speed for complete liquid-liquid dispersion in baffled vessels. The latter condition refers to the complete elimination of separate liquid layers, without regard to the uniformity of the dispersion. Data on power and degree of mixing for seven designs of agitators operating in homogeneous liquids and twophase liquid mixtures were presented by Miller and Mann (1944). However, the industrial application of their findings was limited by the restriction of their work to unbaffled vessels. Furthermore, their agitators were all different from the more commonly used types studied in the present paper. Coulaloglou and Tavlarides (1976) recently summarized the dozen correlations that are currently available for predicting drop size and hence the interfacial area existing in liquid-liquid systems in an agitated vessel. About two-thirds of the correlations are for batch systems and the remainder are for continuous-flow vessels. Clearly, however, such correlations are of major value only a t impeller speeds above those a t which dispersion first 0019-7882/78/1117-0473$01.00/0
Table I. Fluid Properties at 25 C interfacial
fluid
5 cSt Dow Corning 200 fluid 10 cst Dow Corning 200 fluid
tension dynamic with density, viscosity, water, kg/m3 Ns/mZ Nim 920 0.0046 0.0425
cSt Dow Corning 200 fluid
15
benzaldehyde
ethyl acetate water
0.0094
0.0435
948.3 0.0143
0.0437
940
1041 894 1000
0.0014 0.0145 0.00046 0.00627 0.0010 - -
becomes not merely complete, but also uniform throughout the vessel. The object of this study is therefore to correlate the minimum impeller speeds needed for nearly uniform liquid-liquid dispersion in baffled vessels and to describe the effects of impeller type, speed, size, and location, and of liquid properties on the degree of mixing. The latter quantity is expressed in terms of the mixing-index concept developed by Hixson and Tenney (1935) in their work on solid-liquid systems. Experimental Apparatus and Procedure Materials Used. The fluid properties investigated were viscosity, density, and interfacial tension using water, benzaldehyde, ethyl acetate, and three Dow Corning 200 silicone fluids of different viscosities. The Dow Corning 200 fluids are clear dimethyl siloxanes with low vapor pressures and relatively flat viscosity-temperature curves. 0 1978 American Chemical Society
474
Ind. Eng. Chem. Process Des. Dev., Vol. 17,No. 4, 1978 Shaft
T
Handle Glass Tube rn i.d.
r0.012
LT-7
Side View
@
’
E a t e n d To Vessel Bottom
E
m
T h r e a d e d Steel Rod 10.0032 rn T h i c k n e s s )
Impeller
B o t t o m View
Figure 1. Schematic diagram of the experimental apparatus.
1
L&-..-Rubber
Plunger
Table 11. Apparatus Dimensions internal diameter of vessel liquid height in vessel height of vessel diameter of shaft baffle length baffle width baffle thickness length of baffle immersed in the liquid from air-liquid interface volume fraction of organic liquid, @
0.2135 m 0.2135 m 0.2500 m 0.0140 m 0.2300 m 0.0190 m 0.0025 m 0.1930 m 0.50
Water was common to all five binary systems, which were mutually saturated before the mixing runs began. All runs were made a t 25 “ C and the fluid properties a t this temperature are reported in Table I. Apparatus. Figure 1 shows the apparatus. A 0.01-m3 cylindrical, flat-bottomed glass jar was used to permit visual observation. Four baffles, placed radially a t 90” intervals, were present to prevent vortex formation. Two conductivity electrodes made of soldering wire were placed 0.01 m apart in the liquid and connected to a conductivity monitor for continuous-phase identification. Mixing was effected by an impeller on the vertically centered shaft, rotated by a motor drive. Table I1 gives the apparatus dimensions. The shaft, impellers, and baffles were all made of 316 stainless steel. An Experimental Agitator, Model ELB, manufactured by the Bench Scale Equipment Co., was used for mixing the liquids. It was equipped with a 1/4-hpdrive motor and provided a continuously variable output speed of 0 to 20 rps. The speed-control dial was calibrated directly in rps using a stroboscope. The four types of impeller tested were three-bladed propellers, and pitched, flat, and curved-blade turbines all having six blades. Each was available in three different sizes and their characteristics are described by Skelland and Seksaria (1978). The degree of mixing was measured by taking grab samples from representative regions of the agitated vessel. This procedure had been employed by Hixson and Tenney (1934) for a liquid-solid system and by Miller and Mann (1944) for liquid-liquid systems. Figure 2 shows a sketch of the sampling tube. It consisted of a 0.012-m i.d. glass tube, 0.28 m long, fitted with two movable plungers which were 0.06 m apart and attached to a threaded rod 0.38 m in length. The upper plunger was located inside the tube. The lower plunger was a conical plug which, when seated in the end of the glass tube, effectively trapped a sample between it and the upper plunger. The thread of the rod between the two
Y Figure 2. The sampling tube.
plungers was stripped off to prevent coalescence of the dispersed phase on it. The sample volumes were approximately 6 mL. Operational Procedure. Before filling with liquids, all equipment was washed with detergent, rinsed with hot water, and air-dried. Two immiscible liquids in equal volumetric proportions were then put into the vessel to a total height equal to its diameter. Baffles were mounted as shown in Figure 1. The impeller was placed a t the desired location of H/4, H/2, or 3H/4 from the bottom of the vessel and agitation started. Speed was increased slowly in increments of 0.33 rps, starting with zero. Some time was allowed after each speed increment to enable the system to attain its new steady-state condition. This normally varied from 100 to 400 s and could be visually determined. While running the impeller at constant speed, the overall appearance of the liquids in the vessel was sketched, the fraction of the vessel contents that were mixed was measured, and samples were removed from five locations, as indicated in dashed outline in Figure 1. The sampling method was as follows. After being properly located in the vessel, the sampler was shaken to prevent coalescence of the dispersed phase on the plungers and the rod. Next, the glass tube was forced quickly down past the upper plunger and seated on the lower one, trapping a sample from the desired location. The exterior of the sampler was wiped dry upon its removal from the tank, and the sample was transferred by means of a funnel to a 10-mL graduated cylinder. The agitation speed was then increased for further sampling. These samples were allowed to separate completely with the help of a thin brass stirrer, and the volumes of each phase were read. Degree of Mixing. The degree of mixing was computed using the Hixson-Tenney (1935) mixing-index concept. The composition of each sample was calculated as “percentage mixed” by the formula percentage mixed = R x 100 (1) s/2 where R is the volume of the phase present in smaller amount in the sample and S is the total sample volume. T h e mixing index (I,) is the average of t h e
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978 io0
I
I
475
100
I
Fluid ond W a t e r 3
4
5
6
7
8
9
n(RPS)
n(RPS1
Figure 3. Comparison between the mixing index and its corrected value.
loo
"percentage-mixed'' values for all the samples taken from the different locations within the vessel for a given set of conditions. In determining the mixing index for a given run, the percentage-mixed value obtained for location 3 of Figure 1 was doubled before evaluating the mixing index. Thus the equivalent of six samples was used in evaluating the mixing index.
Results and Discussion The types of mixing patterns observed with increasing impeller speed have been described by Skelland and Seksaria (1978) for various impeller locations. For impellers at H / 2 and speeds well below N the vessel contents consisted of a two-phase, mixed layer of measurable height around the impeller, with a clear liquid layer above and/or below the mixed region. The rotational speed of the impeller that was just sufficient to eliminate separate liquid layers-without regard to uniformity-was defined by Skelland and Seksaria (1978) as N , the minimum speed for complete liquid-liquid dispersion. The minimum speed of the impeller for nearly uniform mixing (denoted by N') was here defined as the rotational speed that is just sufficient to give a mixing index of 98%. This condition corresponded to gross uniformity of the proportions of dispersed-to continuous-phase in all sampled parts of the vessel. It is not necessarily implied, however, that all droplets were either equally sized or equally spaced in this state. The reproducibility of the experimental I , (mixing index) was good, ranging from 4% in the absence of separate layers to 20% at lower speeds when separate layers were still present. This was observed with consecutive sampling during one run as well as with sampling on another run performed after a considerable lapse of time. The corrected mixing index for incomplete mixing (characterized by clear liquid layers above and/or below the mixed region) was defined as the mixing index calculated from samples of the mired region of the vessel multiplied by the fraction of the vessel contents that were mixed. The latter quantity was evaluated as the height of the mixed region divided by H. This corrected mixing index was formulated because it seemed to be a more reasonable measure of the degree of incomplete mixing than the normal mixing index. Figure 3 is typical of how the mixing index and its corrected value increased as the impeller speed increased. Although the differences between the mixing indices and their corrected values were not small (up to 25%), it was decided that the uncorrected mixing index was an adequate measure of the degree of mixing because the corrected values did not change the general slope of the curve, and because it was difficult to
2o
t
I
i
LL
O L
8
9
n(RPS1
Figure 4. Mixing index vs. impeller speed for flat-blade turbines.
loo 80
-
D:O102~z0{{//
/,
wafer 'On'
Phase
0 5 C S D o w C o r n i n g 200 Fluid AlOCS
=j/o6 ;3m
L 4 I 100 L
-Water
Conl Phase Con Phose
-,-Oil
0 Benzoldehyde A E t h y I Acetote
1
2
3
4
5
6
1
I
1
7
8
9
n(RPS)
Figure 5. Mixing index vs. impeller speed for curved-blade turbines.
estimate them objectively. The mixing index without correction was used with confidence hereafter. Figures 4 to 7 show variations in the mixing index with impeller speed. The impeller was mounted axially at the oil-water interface prior to agitation for these plots. The phase which proved to be continuous is noted in the figures; techniques for identifying continuous and disperse phases were described by Skelland and Seksaria (1978). Figure 8 shows plots of the mixing index against rotational speed for impeller locations at H/4, H / 2 , and 3H/4, respectively. Values of N' are listed in Table I11 as measures of impeller performance at H / 2 . The final column of Table
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
476
f0I
> _.Water
40
2o
___Oil
0 4
”
0 l5CS
--
2
4
6
1 /i/ 1’‘
“EO
Cont Phase
0 5 CS Dow Corning 200 Fluid A IOCS
t L
n c - a
Cont Phase
,
8 IO n(RPS)
4
16
18
I
I
I2
14
I 16
18
___
-Water
Cont Phase 011Cont Phase 0 Benzaldehvde AEthyl acetale
Dz0062m
2
14
I2
I 6
I 8
1 IO nlRPS)
L
Figure 6. Mixing index vs. impeller speed for pitched-blade turbines.
>
n
m
a
w
80
;MI 40
2o
t
i
100
a
L n(RPS)
Figure 7. Mixing index vs. impeller speed for propellers.
I11 shows that, when averaged over all conditions, the impellers exhibited increasing N‘ in the order flat-, curved-, and pitched-blade turbine, and propeller. In general, also, the N’ values for the radial flow impellers were substantially lower than for the axial flow impellers. The effect of reducing the D I T ratio from 0.47 to 0.3 was to roughly double the N’values for the flat- and curved-blade turbines and the propeller, whereas N’ increased almost fourfold for the pitched-blade turbine. The influence of physical properties on N’ was approximately in accordance with eq 2, given later. Table IV lists values of N’ to show the effect of vertical location on impeller performance. Evidently, the highest values of N’ for the propeller, pitched-, curved-, and
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
477
Effect of Impeller Location, Measured by N', the Speed Required to Produce an Zm of 98%. System: 5-cSt S.0.-H,Oa D C 0.1 m, DIT 0.47 D i 0.063 m, DIT 0.30 impeller HI4 HI2 3H/4 HI4 HI2 3H/4 C 3.58 14.5 7.33 2.92 3.92 flat-blade Table IV.
turbine curved-blade
4.58
3.40
4.25
14.8
pitched-blade
5.74
3.92
4.92
18.2
16.8
16.2b
17.5
21.7
17.2
turbine turbine
10.1
8.08
propeller a
5.91
C
Unavailable due to splashing.
Denotes a nonaqueous continuous phase.
S.O.= silicone oil.
8.75
Table V. Average Deviation between N and N
impeller
1mN'-N -E=x
ma
ml
IO0 80
3
60 a
E 40
N
flat-blade turbine
18
0.0667
curved-blade
18
0.0446
turbine pitched-blade turbine
19
0.0747
propeller overall
19 74
0.1421 0.0827
m : total values in each category; then N = N ( 1 t x).
20 0
0
2
4
6
8 IO n(RPS1 (C)
12
14
16
0
2
4
6
8
IO
12 I 4
16 18
n(RPS1 (d)
A C u r v e d - B l a d e Turbine
Figure 8. Effect of impeller location on the curves of mixing index
X
Propeller
vs. impeller speed for (a) flat-bladeturbines, (b) curved-blade turbines, (c) pitched-blade turbines, and (d)propellers. The respective impeller locations and liquids are: 0,H / 2 ; X, H/4; A, 3 H / 4 ; 5-cSt Dow Corning 200 fluid and water.
flat-blade turbines occurred when the impeller was located a t H / 2 , H / 4 , H / 4 , and H / 4 , respectively. Conversely, the lowest values of N'for these impellers occurred a t 3 H / 4 , H / 2 , H / 2 , and H / 2 , respectively. The impeller providing the lowest "for a given DIT in Table IV is the flat-blade turbine located a t H / 2 . When the two radial-flow impellers were located a t 3 H / 4 , the air-liquid interface was so violently agitated that splashing occurred when the mixing index reached about 60%. I t is noteworthy that the observations recorded above about N' from Tables I11 and IV are closely parallel to those about N in the separate but related study by Skelland and Seksaria (1978). In their paper the minimum impeller speeds for complete dispersion regardless of uniformity (N) were correlated as where Co and a0 depend upon the type of impeller and its location. Equations of the form 0.3
were also obtained from dimensional analysis. It was found in the present study that these expressions were also adaptable for correlating the minimum impeller speed for nearly uniform mixing ( N?, although N'usually had slightly larger values than N, as shown in Table V. Figure 9 shows a plot of N predicted from eq 2 vs. N'taken from Tables I11 and IV. The plot contains data for all three impeller locations and sizes and the average absolute deviation is 9.43 % . It follows from Table V that N' = N(l + x ) ; evidently "exceeds N by an average of about
Average Absolute Dewallon * 9 4 3 % Total Points = 7 2 1
I
I
2
3
1
I
4
1
1
1
1
5 6 78910 N ' Experimental l r p s l
I
20
1
30 4 0
Figure 9. Comparison between N'values for nearly uniform mixing ( I , = 98%)and corresponding N from eq 2 for complete dispersion (Le., for elimination of separate layers).
8%. The relevant aspects of scale-up were described by Skelland and Seksaria (1978). Nomenclature al, Cot C1 = constants D = impeller diameter, m g = acceleration due to gravity, m/s2 H = height of liquid in the vessel, m I , = mixing index, % n = impeller speed, rps N = minimum rotational speed of impeller for complete liquid-liquid dispersion in agitated vessels (i.e., for the elimination of separate layers, regardless of uniformity), rev/s N'= minimum rotational speed of impeller for grossly uniform liquid-liquid dispersion in agitated vessels, corresponding to an I , of 9870, rev/s R = volume of the phase present in smaller amount in the sample, m3 S = total sample volume, m3 T = vessel diameter, m n = average deviation between "and N, given in Table V
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
478 a.
= constant
Literature Cited
= viscosity, Ns/m2
Coulaloglou, C. A., Tavlarides, L. L., AIChE J., 22, 289-297 (1976). Hixson, A. W., Tenney, A. H., Trans. Am. Inst. Chem. En$, 31, 113-27 (1935). Miller, S. A,, Mann, C. A,, Trans. Am. Inst. Chem. Eng., 40, 709-745 (1944). Skelhnd, A. H. P., Seksafia, R., I d . fng. Chem. ProcessDes. Dev., 17, 56-61 (1978).
density, kg/m3 &, = positive density difference between continuous and disperse phase, kg/m3 u = interfacial tension, N/m C$= volume fraction of organic liquid, dimensionless Subscripts c = continuous d = disperse p =
Received for reuiezu September 15, 1977 Accepted June 29, 1978
This work was partially supported by National Science Foundation Grant No. ENG74-17286.
Complex First-Order Reactions in Fluidized Reactors: Application of the KL Model Octave Levenspiel" Chemical Engineering Department, Oregon State University, Corvallis, Oregon 9733 1
Nlels Baden Kemiteknik, Technical University, 2800 Lyngby, Denmark
B. D. Kulkarni National Chemical Laboratory, Poona 4 11 008, India
Conversion and product distribution equations are developed for the Denbigh reactions A - R - S
T
U
and all its special cases taking place in a bubbling bed of fine catalyst particles. The final expressions are much like the equations for fixed bed reactors except that the reaction rate constants must be suitably modified to account for the mass transfer effects in the bed.
In 1968 Kunii and Levenspiel developed a model (the KL model from now on) to account for the main features of the vigorously bubbling fluidized bed with its fast rising bubbles. They then applied this model to predict reactor behavior for first-order reactions. Since then there have been a few extensions to other first-order reactions (Kunii and Levenspiel, 1969; Kunii, 1975; Carberry, 1976). In this paper we develop the performance equations for both conversion and product distribution in fluidized bed reactors according to this model for the rather general first-order reaction scheme commonly known as the Denbigh reactions (Denbigh 1958)
U
By putting the appropriate rate constants equal to zero we can obtain at the same time the performance equations for all the following reaction schemes R
A
/ 'T
.
A -
R -
F i r s t - O r d e r Irreversible Reaction
The simple KL model assumes bubbles of one size which are fast enough (ub >> u,f) so that gas flow through the bed via cloud and emulsion is negligible compared to flow via bubbles. Figure 1then sketches the main features of the model and shows that there are five resistance steps in series-parallel arrangement for the reactant gas to contact and react on the surface of the solid. For a first-order catalytic reaction with rate given as A R, -rA = kCA,mol of A converted/s kg of cat., we find the following: for ideal plug flow
-
A - R - S
T
R
S.
A - R - S ,
\ T
0019-7882/78/1117-0478$01.00/0
W
CAO ln-=kT=kCA
UO
for the fluidized bed CAO In - = CA
KT
=
W K-
UO
where the effective rate constant K for the fluidized bed 0 1978 American Chemical Society
