monodisperse crystals. This approach is particularly useful for Class I1 systems in which the measurement of supersaturation is difficult. The analysis can be combined with that of Larson and Wolff (1971) to determine an optimal operating policy which satisfies given criteria based on a desired final crystal size distribution.
Acknowledgment The authors wish to thank R. W. Strong for assisting in the numerical computations.
Nomenclature
Dimensionless size ( X )
F i g u r e 2. Crystal size distribution for a continuously seeded, single. stage system ( b = 3).
The comments made earlier concerning the maximum growth rate allowable to avoid nucleation in the second stage of a two-stage cascade system should also hold for this case. However, there are distinct advantages in analyzing the single-stage system seeded with monodisperse crystals. With seeding, one can experimentally choose relatively large seeds so that the seeds and nuclei are discernible in size and the occurrence of nucleation can be detected in the output. Unlike the two-stage system, the size distributions here are rather sensitive to growth rate. Furthermore, as indicated in Figure 2 , the plot of In Y vs. X yields straight lines with slope proportional to -l/GT. Therefore, a reasonably accurate growth rate can be determined from the slope of this plot. Knowing the growth rate and the occurrence of nucleation, one can determine from a series of experiments the maximum ratio of suspension density to seed mass and the corresponding maximum growth rate permissible t o avoid nucleation. T h e information for this maximum growth rate is important in the design of multistage cascade crystallization systems where nucleation in the subsequent stages is undesirable.
Summary The design of a multistage continuous cascade crystallizer, operating with nucleation in the first stage only, requires a knowledge of the maximum crystal growth rate t h a t can be achieved without nucleation. This information can be obtained readily from experiments carried out using a singlestage CMSMPR crystallizer seeded continuously with
a = dimensionless parameter, L,/GT b = dimensionless parameter, M/pk,n,LS4 G = linear crystal growth rate k , = crystal volume shape factor L = linear crystal size M = crystal suspension density n = population density function n o = nuclei population density T = crystallizer mean residence time X = dimensionless variable, L/L, x = dimensionless variable, L / G I T 1 Y = dimensionless variable, n/n, Y o = dimensionless parameter, n o / n s y = dimensionless variable, n2/nIo y o = dimensionless parameter, n2O/n1' (Y = dimensionless parameter, G ~ T ~ / G ~ T I 6 = dimensionless parameter, M2/M1 p = crystal density
Subscripts 1 = first crystallizer 2 = second crystallizer s = seeds
Literature Citqd Desai, R. M., Rachow, J. W., Timm, D. C., AlChE J., 20, 43 (1974). Hulburt. H. M., Katz, S.,Chem. Eng. Sci., 19,555 (1964). Larson, M. A., Garside, J., Chem. Eng., (London), No. 274, 318 (1973). Larson. M. A.. Wolff, P. R., Chem. Eng. Prog. Symp. Ser., 67, 97 (1971). NjYlt, J., "Industrial Crystallization from Solutions," Butterworths, London, 1971 Randolph, A. D., AlChE J., 11, 424 (1965). Randolph, A. D., Larson, M. A., AlChE J.. 8,639 (1962). Randolph, A. D., Larson. M. A.. "Theory of Particulate Processes," Academic Press, New York, N.Y., 1971. Robinson, J. N., Roberts, J. E.. Can. J. Chem. Eflg., 35, 105 (1957).
Research Laboratories Eastman Kodak Company Rochester, N e w York 14650
Jong-Shinn Wey* J a m e s P. T e r w i l l i g e r
Received f o r review September 5, 1975 Accepted M a r c h 1, 1976
Mass Transfer and Power Consumption in Reciprocating Plate Extractors
Mass transfer data and power consumption in two types of reciprocating plate extractors are compared. Extractors having plates with large holes and large free area consume more energy to achieve the same performance than those having plates with small holes and small free area.
Introduction Two designs of reciprocating plate extractors, developed by Karr (1959) and Prochazka and Landau (19641, are in common use. The main difference between the two types lies
in the design and function of the plates. In the former design the plates are of open structure with large holes and large free area. The plates do not restrict the flow of the two phases but considerable agitation is required to disperse one phase in the Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
469
Table I. Comparison of Performance of Reciprocating Plate Extractors Having Plates of Different Hole Size and Free Area Large holes and free area
Small holes and free area
Karr and Lo (1971 )
Present investigation
Variable Column height, H ( m ) Column working height, h ( m ) Column diameter, D ( m ) Fractional free area, E Hole diameter, d ( m ) Number of plates, N Plate spacing, S ( m ) Amplitude, a ( m ) Frequency, f ( s - ' ) Total throughput (VC + VD (mls) Flow rate ratio (VClVD) Number of theoretical
stages, N, HETS ( m ) Power input per unit volume, P (W/m3) Amplitude, a ( m ) Frequency, f (s-' ) Total throughput (VC VD) (m/s) Flow rate ratio ( v C /VD ) Number of theoretical stages, N , HETS ( m ) Power input per unit volume, P (W/m3)
1.200 0.563
1.200 0.630
1.400 1.000
0.076 0.025 0.050 0.580 0.620 0.096 0.016 0.016 0.002 22 25 20 0.025 0.025 0.050 Methyl Isobutyl Ketone Dispersed, Water Extractant O.Gl25 0.0125 0.005-0.009 2.03-7.16 1.92-4.70 0.66-2.0 0.006-0.013 0.005-0.011 0.006-0.011
1.400 0.900 0.050
0.096 0.002 10 0.100
0.003-0.009 0.66-1.6 0.006-0.011
1.6-1.88
0.48-0.53
0.68-1.73
0.70-1.58
1.6-3.85
2.3-6.0
2.86-6.23
2.13-3.78
0.1 1-0.27
0.16-0.35 1-166
0.29-0.42 0.1-42
0.14-0.35 17-750
11-175
Methvl Isobutvl Ketone Continuous. Water Extractant - 0.01250.005-0.01 3.08-5.33 0.5-1.68 0.006-0.01 3 0.005-0.01 1
+
1.58-1.88
0.42-1.65
1.2-5.1
2.2-5.9
0.11-0.465 48-247
0.17-0.454 0.35-108
1
area with data from a column with plates of large holes and large free area. T h e average power input per unit volume is
where T is the period of reciprocation, F is the friction forces, U is the plate velocity, and u is the operating column volume. For a pulsed plate column, Thornton (1957) and Jealous and Johnson (1957) obtained the following expression
i
Figure 1. Schematic flow diagram: a, column; b, reciprocating plates: c, eccentric; d, constant head distilled water tank; e, constant pressure methyl isobutyl ketone tanks; f, acetic acid make-up; g, light and heavy phase pumps; h, valves; i, sampling valves; j, rotameters.
other. In the second design the plates have small holes and small free area. The flow is potentially restricted but one phase is easily dispersed in the other. The hydrodynamics of both designs have been investigated by several authors but little mass transfer data is available. Karr and Lo (1971) discussed the performance and scale-up of a column of the first type, while Prochazka et al. (1964,1966, 1974) studied the performance of columns of the second type with and without downcomers. This paper compares mass transfer data and power consumption for a column with plates of small holes and small free 470
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 3, 1976
where a and f are the amplitude and frequency of oscillation, respectively, e is the fractional plate free area, Co is the orifice discharge coefficient (C, = 0.61), p is the mean density of the liquids, and S is the plate spacing. This equation was used t o compare the power input of the two types of extractors for similar values of the height equivalent to a theoretical stage
HETS. Experimental Section A 0.05-m diameter, 1-m high reciprocating plate extractor, fitted with Teflon plates and similar in design to that described by Hafez and Prochazka (1974) and shown in Figure 1, was used. Two plate spacings of 0.05 m and 0.10 m were used, other geometric details being given in Table I. Experiments in the transition and emulsion regimes were performed using the water-acetic acid-methyl isobutyl ketone system. Acetic acid was transferred from the organic to the water phase and two sets of experiments were performed with methyl isobutyl ketone dispersed in the first and with water dispersed in the second. The ranges of the acetic acid concentrations used, in weight
.4
-
the variation in height equivalent to a theoretical stage HETS with the af product. The value of HETS was found to increase with increasing continuous phase flow rate and increasing plate spacing but to decrease with increasing disperse phase flow rate. Similar results were also obtained with brass plates. For power inputs greater than indicated in Figure 2 the height equivalent to a theoretical stage continues to decrease until a minimum value is reached. A still further increase in the power input causes the column operation to be unstable and ultimately to flood with a sharp increase in HETS. Table I compares the performance of 3-in. and 1-in. diameter columns used by Karr and Lo with that of the 5-cm diameter used in the present investigation. I t can be seen that for similar throughputs and similar heights equivalent to a theoretical stage, considerably smaller power inputs are required for the extractor having plates with small holes and small free area than for the extractor with large holes and large free area. Although the larger spacing of the plates with small free area tends to decrease the power input, as calculated from eq 2, it also increases the value of HETS and so must be compensated by a corresponding increase in the af product.
b
L-
w
=
.2
2
4
6
8
10
12
14
16
a If lio'
Figure 2. Variation of the height equivalent to a theoretical stage "HETS" (m) with the amplitude frequency product "af" (m/s) for: a. Constant dispersed phase flow rate U D= 12.36 X 10-6 m3/s, and plate spacings = 0.1 m; m, c', = 9.62 X m3/s; A,L', = 5.63 X m3/s. b. Constant dispersed phase flow rate UD = 12.36 X m3/s, and continuous phase flow rate U , = 5.63 X m3/s; m, S = 0.1 m; A , S = 0.05 m. c. Constant continuous phase flow rate U , = 5.63 X low6m3/s, and plate spacing S = 0.1 m; W , U D= 9.72 X m3/s; A, U D = 12.36 X m3/s. All for the case of Teflon plates, methyl
isobutyl ketone dispersed, and water extractant.
percent, were for the methyl isobutyl ketone yin = 15.6-23.3, yout = 0.95-7.5 and for the water, xin = 0, x,,t = 10.8-20.8. These were similar to the concentration ranges used by Karr and Lo which were yin = 11.4-16.8, yout = 1.4-3.8 and xin = 0.08-3.0, xout 9.1-16.2, also in weight percent. The mass balance was checked for all experiments, the maximum error being -6%, while duplicate experiments showed that the value of H E T S was reproducible to 3%. Results a n d Discussion
Conclusions Reciprocating plate extractors with small holes and small free area need less power to achieve the same performance than columns with large holes and large free area. L i t e r a t u r e Cited Baird, A. H.M., Tan, G. C., "Proceedings of the International Solvent Extraction Conference," The Hague, p 4,1971. Hafez, M., Prochazka, J., Collect. Czech. Chem. Commun., 37,3725 (1972). Hafez, M.. Prochazka, J., Chem. Eng. Sci., 29, 1755 (1974). Hafez, M., Prochazka, J., Chem. Eng. Sci., 29, 1763 (1974). Hafez, M., Nemecek, M., Prochazka, J., "Proceedings of the International Solvent Extraction Conference," Lyon, p 1671,1974. Jealous, A. C., Johnson, H. F., I d . Eng. &em., 47, 1059 (1957). Karr, E., A.l.Ch.E. J., 5,446 (1959). Karr, E., Lo, T. C., "Proceedings of the International Solvent Extraction Conference," The Hague, p 298,1971. Landau, J., Dim, A,. Shemilt, W., Can. J. Chem. Eng., 53, 9 (1975). Nemecek. M., Prochazka, J., Can. J. Chem. Eng., 52, 739 (1974). Prochazka, J., Landau, J., Souhrada, F.,Collect. Czech. Chem. Commun., 29,
3003 (1964). Prochazka, J., Landau, J., Collect. Czech. Chem. Commun., 31, 1695 (1966) Prochazka, J., Landau, J., Third Conference, CHISA, Czechoslovakia, 1969. Thornton, J. D.. Trans. lnst. Chem. Eng., 35,316 (1957).
D e p a r t m e n t of Industrial a n d Engineering Chemistry Swiss Federal I n s t i t u t e of Technology ( E T H ) Zurich. Switzerland
Equation 2 shows that for a given extractor and liquid system the power input per unit volume is proportional to the cube of the amplitude-frequency product af.Figure 2 shows
Joachim Ioannou Mahmoud Hafez Stanley Hartland*
Received for review October 28, 1975 Accepted March 25,1976
Advantage of Milling Equipment with Internal Classification
The present paper deals with theoretical consideration on milling equipment with internal classification. The result reveals some essential advantage over usual closed-circuit grinding systems.
According to the mechanism of particles flowing out of mills, we can conceptually classify mills into two types. In the first type, the materials in the mill are forced to overflow to maintain a certain bulk volume of holdup determined from
the throughput in such a manner as in conventional tube mills. In the second type, the materials are subject to a size classification effect in the mill (internal classification) and only the finer part is discharged as represented by jet mills and airInd. Eng. Chem., Process Des. Dev.. Vol. 15,No. 3, 1976
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