528
0
Ind. Eng. Chem. Process Des. Dev. 1981, 20, 528-532
I
1
I
60
120
180
240 t min
Figure 2. Aging of CaCO,, SrCO,, and BaC03 slurries: 0,0.6 M CaCO,; 0 , 0.5 M SrCO,; 0 , 0.25 M SrCO,; V, 1.0 M BaCO,; ut0.5 M BaCO,; A, 0.7 M CaCO,; A, 0.65 M CaCO,; X, 1.0 M &COS.
Nomenclature A , A', B, B', C, D,E , F = constants co = initial concentration, mol LW1 cq = equilibrium concentration, mol L-' C.C. = correlation coefficient d = particle diameter, m d = mean diameter of particle, m I$ = friction factor F b = Reynold factor f = correction factor for coagulation G = weight of cake, kg g(n) = defined by eq 9
h, = cake thickness, m h(n) = defined by eq 10 Jo = nucleation rate, s-' L-' k = Boltzmann factor k,, = nucleation rate constant M = molecular weight, kg-mol-' N = number of formed particles, L-' No = no. of particles formed at given supersaturation under the condition of instantaneous, mixing of solutions, L-' Neff=. effective number of particles n = kinetic order of nucleation n(r) = frequency distribution curve AP = pressure drop during filtration, kPa rc = specific volume filtration resistance, m-2 r = particle radius, m S = supersaturation defined by eq 22 T = temperature, K tind = induction period of precipitation, s Z = filtration area, m2 t = porosity cp = relative volume filtration resistance 7 = viscosity of liquid, g cm-' s-l T = time necessary for a thorough mixing of solutions, s $ = sphericity (surface area of sphere at volume equivalent to a given particle volume divided by its surface area) u = standard deviation p = solid phase density, kg m-3 Literature Cited Brown, G. G. "Unit operations"; Wlley: New York, 1950; p 210. "International Criticel Tables"; Mc(Law-HHI: New York, 1928: Vd. 111, p 79. Linke, W. F. "SolublHties", Van Nostrand: New York, 1958; Vol. I, pp 328, 549; Vol. 11, p 1494. Nklsen, A. E. "Kinetics of Precipitation"; Pergamon: Oxford, 1964; p 101. Nielsen, A. E. J. phys. Chem. SoW Suppl. 1987, 419. Nielsen. A. E. "Factors Influencing Reclpltatlon", 5th Symposium on Industrial Crystallization CHISA '72, Prague, 1972. Packter, A. J. Chem. Soc.A 1888, 859. S&nel, 0. Krlst. Tech. 1978, 77, 1110. Sohnel, 0.;MareEek, J. "Industrial Crystallization"; Mullin, J. W., Ed.; Plenum: New York. 1976; p 115. MareEek, J. Krist. Tech. 1978, 73, 253. Sohnel, 0.; Sohnel, 0.; Mullin, J. W. J. Cwst. Growth 1978, 44, 377.
Receiued for reuiew March 19, 1980 Accepted March 27, 1981
Entrainment from Sieve Trays Operating in the Spray Regime Henry Z. Klster,' W. Val Plnctewskl, and Chrlstopher J. D. Fell' School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Kensington, N.S.W. 2033, Australia
A correlation is developed to predict entrainment rate for the air-water system on sieve trays operating in the spray regime. The correlation utilizes liquid holdup on the tray as a correlating parameter and is successful in correlating entrainment data for a wide range of tray parameters and gas and liquid loadings. The correlation is extended to account for the effect of system physical properties and is shown to provide predictions of entrainment rate which are in encouraging agreement with the limited experimental data available for systems other than air-water. In this form the correlation is of immediate use to the tray designer in predicting entrainment rates on sieve trays operating in the spray regime.
Introduction Because of its potentially adverse effect on tray pressure drop and efficiency, entrainment from sieve tray contactors used for distillation and absorption operations has been the subject of many investigations (Hunt et al., 1955; Jones and Pyle, 1955; Friend et al., 1960; Bain and Van Winkle, C. F. Braun and Co., 1000 S. Fremont Ave., Alhambra, CA 91802. 0196-4305/81/ 1120-0528$01.25/0
1961; Lemieux and Scotti, 1969; Pinczewski et al., 1975; Lockett et al., 1976; Thomas and Ogboja, 1978; and Sakata and Yanagi, 1979, are a few). Most investigations have been conducted using air-water and a large volume of data for this system now exists. Considerably fewer data are available for systems other than air-water. Many attempts have been made to correlate the rate of entrainment data in terms of tray design parameters, gas and liquid loading, and system physical properties (Souders and Brown, 1934; Hunt et al., 1955; Fair, 1961; 0 1981 American
Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 529
Bain and Winkle, 1961; Smith and Fair, 1963). None of the proposed correlations is fully successful in satisfactorily representing the data over the full range of experimental conditions that have been used (Thomas and Ogboja, 1978; Bain and Van Winkle, 1961). It is significant that the above investigators have not considered the effect of tray flow regime in developing their correlations. Recent work (Pinczewski et al., 1975; Lockett et al., 1976; Porter and Jenkins, 1979) has demonstrated that entrainment is dependent on the type of flow regime on the tray. The two regimes most commonly encountered on industrial scale sieve trays are froth (liquid continuous) and spray (gas continuous) (Porter and Wong, 1969; Pinczewski and Fell, 1972; Loon et al., 1973) and the mechanism of entrainment generation is different in each regime. In the froth regime entrainment is produced mainly by the breakup of the liquid sheets defining emergent bubbles (Teller and Rood, 1962), whereas in the spray regime the mechanism is one of atomization of liquid a t the tray floor (Pinczewski and Fell, 1974). Because of the different mechanisms of entrainment generation in each tray flow regime it is unlikely that one correlation can apply to both regimes, or that a correlation based primarily on froth regime data will extrapolate successfully into the spray regime. When froth to spray transition criteria (Loon et al., 1973; Porter and Jenkins, 1979) are applied to industrial scale sieve trays it is found that most atmospheric and sub-atmospheric columns operate in the spray regime because of the high volumetric gas loadings now used. In contrast, most entrainment data have been collected on small scale laboratory units operated under froth regime conditions. Correlations based on such data (Hunt et al., 1955; Fair, 1961; Smith and Fair, 1963) have been shown (Pinczewski et al., 1975) to give poor predictions of entrainment on larger trays operating in the spray regime. There is a need to develop a correlation for entrainment in the spray regime, particularly as entrainment is frequently the capacity limiting factor for low to moderate pressure operations. In the present study, we have applied froth to spray transition criteria to previously unpublished data taken in our laboratory (Pinczewski, 1973; Raper, 1980) and to data already reported in the literature, to develop a set of entrainment data applying specifically to the spray regime. Utilizing these data the effect of tray design parameters on entrainment in the spray regime has been examined, and a spray regime entrainment correlation has been developed. Factors Affecting Entrainment i n t h e Spray Regime By the choice of specific spray regime entrainment data obtained at fixed liquid loading, hole diameter, tray free area, tray spacing, and weir height it is possible to illustrate the effect of these parameters on entrainment rate. All of the experimental data are for the air-water system. Effect of Tray Free Area. The effect of tray free area on entrainment rate is shown in Figure 1. The results (Pinczewski et al., 1975) are for three trays having the same hole diameter (12.7 mm) but different free area. The rate of entrainment at constant superficial gas loading shows a strong dependence on tray free area with the rate of entrainment increasing with decreasing tray free area. Effect of Hole Diameter. Figure 2 shows the dependence of rate of entrainment on hole diameter. The results (Pinczewski, 1973) are for three trays having the same nominal free area (11%) but different hole sizes (6.4, 12.7, and 19.1 mm.) The rate of entrainment increases with increasing hole diameter.
-''I
Data from Pinczewski
$
(
1975)
5 9 #/e A10 7 % 0 0
0 0011
15
16 1 %
3
2
SUPERFICIAL F-FACTOR
4 (m&kgrri'
