Ind. Eng. Chem. Process Des. Dev. 1982, 21 774-776
774
~
in the absence of SO,, which is depicted by the dot-dash line. In order that the absorption rate of NO during the simultaneous absorption for ysoZf = 2500 ppm may recover to that in the absence of SO,; that is, the interfacial concentration of SO3,- may be less than about 0.005 g-ion/L, and the dimensionless concentration of SOZ- in the bulk of liquid must be 15-20 according to Table 11. In the region of z > z2, there exists SO3,- alone, and there may occur reductions such as 2Fe"(NO)(EDTA)
+ SO3,-
-
2Fe"-EDTA 2Fe"(NO)(EDTA) 2Fe'LEDTA
+ S042-+ N 2 0 (iii)
+
+ 5So3,- + 3H20
+ 2NH(S03)22-
SO4,- + 40H- (iv)
It is deduced that the concentration of SO3,- in the bulk liquid phase is less than the saturation concentration of MgS02(s) because of existence of such reductions. Conclusion
The Mg(OH)2fine particles suspending in Fe'I-EDTA solutions apparently have no influence on the complexing reaction between dissolved NO and FeLEDTA. The absorption rate of NO into aqueous slurries of Mg(OH)2with added Fe'LEDTA first decreased, then increased, and finally approached that in the absence of SO2as the concentration of coexisting SO2increased from 0 to 2500 ppm. The absorption rate of NO during the simultaneous absorption was controlled by the concentration of SO-: at the interface. Nomenclature
A, = surface area of solid particles, cm2/cm3of slurry C = concentration in liquid phase, mol/L or mol/cm3 D = diffusivity in liquid phase, cm2/s jsoz= dimensionless absorption rate of SO2,N?02~L/DBCBs k = second-order forward rate constant of complexlng reaction, L/mol s k, = mass transfer coefficient for solid dissolution, cm/s
N = k,A,zL2/DB N A = absorption rate of NO, mol/s cm2 rI = DI/DB (I = A, E, and F) x = dimensionless distance into liquid phase from gas-liquid interface, z/zL x 2 = dimensionlessposition of secondary reaction plane, z2/zL y = gas-phase concentration, ppm YI = dimensionless concentration in liquid phase relative to that of species A at gas-liquid interface or that of species B at solid surfaces z = distance into liquid phase from gas-liquid interface, cm z2 = position of secondary reaction plane, cm zL = thickness of liquid film, cm Subscripts A = NO
B = OH-
E = SO:-
F = HS03f = feed stream i = gas-liquid interface o = effluent stream s = surface of solid particle 0 = bulk liquid phase I1 = region of 0 Iz Iz2 depicted in Figure 4 I11 = region of z 5 z 5 z L depicted in Figure 4 Literature Cited Hattori, H.; Kawai, M.; MlyaJlma, K.; Sakano, T.; Kan. F.; Saito, A.; Ishikawa, T.; Kanno, K. Kogai 1077, 12, 27. Sa&, E.; Kumazawa, H.; Kudo, I.; Kondo, T. Ind. Eng. Chem. Process D e s . D e v . 1980, 19, 377. Sada,E.; Kumazawa, H.; Kudo, I.; Kondo, T. Ind. f n g . Che" Process Des. D e v . 1981, 20, 46. SeMel, A.; Linke, W. F. "Sdubilkies of Inorganic and Metal Organic Compounds"; American Chemical Society: Washington, DC, 1965: p 524.
Department of Chemical Engineering Eizo Sada* Kyoto University Hidehiro Kumazawa Kyoto, 606, Japan Yasushi Sawada
Takashi Kondo Received for review March 30, 1981 Revised manuscript received March 8, 1982 Accepted April 29, 1982
Froth to Spray Transition on Sieve Trays A correlation is developed to predict the froth to spray transition on industrial scale sieve trays. The correlation is expressed directly in terms of tray loadings, tray geometry, and system physical properties and therefore does not require an a priati knowiedge of Quid holdup on the tray. The correlation is compared with data for the air-water system and limited data for hydrocarbon systems under actual distillation conditions which have recently become available. The correlation shows encouraging agreement with these experimental measurements.
Introduction
The two dominant flow regimes on industrial scale sieve trays are froth (liquid continuous) and spray (gas continuous). The type of regime can strongly influence the hydraulic and mass transfer performance of a tray (Pinczewski and Fell, 1977) and it is therefore important for the tray designer to have a means of determining the type of flow regime which will predominate on a given tray in terms of tray loading, tray geometry, and system physical properties. A number of studies of the froth to spray transition on sieve trays has been reported and these have been recently reviewed by Lockett (1981) and Hofhuis and Zuiderweg (1979). The most comprehensive experimental studies are those of Porter and Wong (1969), who investigated a number of gaslliquid systems on a tray with no liquid 0196-4305/82/1121-0774$01.25/0
cross-flow and Pinczewski and Fell (1972) (see also Loon et al., 1973),who examined the effect of liquid cross-flow using the air-water system. Together these data cover a wide range of tray loadings, tray geometry, and system physical properties. Both sets of data are well correlated by the equation (Hofhuis and Zuiderweg, 1979)
which shows that gas and liquid densities are the major physical properties affecting the transition with surface tension and fluid viscosities having little or no effect. This influence of system physical properties has recently been confirmed for actual distillation systems (Hofhuis and Zuiderweg, 1979; Prince et al., 1979). 0
1982 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
From the viewpoint of the tray designer, eq 1is not of immediate use since it requires an a priori knowledge of the clear liquid holdup at the transition and this in turn requires an additional correlation for clear liquid holdup in terms of tray loadings, tray geometry, and system physical properties. Although Hofhuis and Zuiderweg (1979) have recently proposed such a correlation, the work of Lockett (1981) has clearly demonstrated that their correlation for holdup is not valid in the region of the froth to spray transition and therefore cannot be used for predicting this transition. An alternative to developing a separate correlation for clear liquid holdup at the froth to spray transition is to correlate the transition in terms of gas and liquid loadings rather than clear liquid holdup. The only comprehensive measurements of the transition in terms of gas and liquid loadings are those of Pinczewski and Fell (1972) for the air-water system. Jeronimo and Sawistowski (1973) have examined these data and proposed the following correlation for the transition O.655(g(pl -
u,= Af(l + 0.000104L-0~59A~1~79)
(2)
Equation 2 correlates the experimental data with an average error of 8%. Although the correlation is based only on air/water data, the authors have introduced system physical properties by basing their analysis on the Kutateladze and Styrikovich (Kutateladze and Sorokin, 1969) correlation for deep pool bubbling. Equation 2 indicates a strong dependence of the transition on surface tension. However, this is at variance with previously reported experimental measurements (Porter and Wong, 1969; Prince et al., 1979; Hofhuis and Zuiderweg, 1979) which show little or no effect of surface tension on the transition. This suggests that eq 2 may result in significant errors if it is used to predict the transition for systems other than air/water. The purpose of the present communication is to examine the magnitude of these errors for typical distillation conditions and to present an alternative correlation for the transition in terms of tray gas and liquid loadings which is consistent with the experimentally observed effects of system physical properties. Proposed Correlation for Froth to Spray Transition On the basis of the available experimental data, we have assumed that gas and liquid densities are the only physical properties which have a significant effect on the transition. Pinczewski and Fell (1972) have shown that weir height has only a slight effect on the transition for weir heights in the range 25-75 mm. Using the groups U,v'pg and L d p l to correlate the effects of tray loadings and system physical properties (these groups have been previously used by Hofhuis and Zuiderweg (1979) in their analysis of flow regimes on sieve trays), we have found that the following simple empirical equation correlates the air/water system data of Pinczewski and Fell (1972) with a maximum error of less than 10%. = 2.75(L&)"
(3)
where n = 0.91 (&/Af). The above equation is dimensional. The equation could be rendered dimensionless by introducing the parameters g, the acceleration due to gravity, and a characteristic length term 1, representative of the jet geometry at the tray orifices. That eq 3 closely represents data for a wide range of tray geometry and loadings suggests that 1 is largely
775
Table I. Comparison between Eq 2 and 3 for the Cyclohexane-n- Heptane Data of Sakata and Yanagi (1979) pressure, k Pa vapor density, kg/m3 liquid density, kg/m3 surface tension, N/m estimated tray loadings at transition liquid loading, m3/s m superficial gas velocity, m/s predicted superficial gas velocity at transition, m/s eq 2 eq 3
34 1.1 700 0.0185
165 4.8 641 0.0135
9 2.1
7 1.3
1.3 2.1
0.54 1.0
constant, an observation that we have previously made from inspection of the location of the lower minimum in vertical dispersion profiles for trays operating in the spray regime (Pinczewski and Fell, 1974). Equations 2 and 3 result in almost identical predictions for the transition for a wide range of values of gas density (0.1-4.0 kg/m3), liquid density (200-1000 kg/m3), hole diameter (0.00633-0.01905 m), tray free area (nominal 5-15%), and liquid loading (0.001-0.020 m3/s m of weir) provided that the surface tension term in eq 2 is held constant at the value for air/water (a = 0.07 Nm-l). For other values of surface tension, eq 2 predicts transition gas velocities which are low when compared with those obtained using eq 3, by a factor of approximately (0.07/~)'/~. For distillation systems where surface tension is typically in the range 0.005-0.020 Nm-', transition gas velocities predicted by eq 2 are low by a factor of 1.5-2.5 when compared with predictions based on eq 3. To determine which of the equations should be used for the transition, we must compare their predictions under typical distillation conditions. Comparison with Distillation System Data Previous investigators of the transition on sieve trays under distillation conditions (Prince et al., 1979; Hofhuis and Zuiderweg, 1979) have not reported the liquid loading at which the transition has been measured. However, in a recent paper, Sakata and Yanagi (1979) report entrainment measurements on an industrial size sieve tray (1.2 m diameter, 0.0127 m hole diameter, 8% free area, and 0.051 m weir height) for the distillation of cyclohexanen-heptane. Porter and Jenkins (1979) have argued that the maxima in the reported entrainment curves, when vapor loading is plotted against liquid loading at constant entrainment rate, provide a reasonable estimate of the froth to spray transition. Using this criterion to estimate the froth to spray transition allows a comparison to be made between eq 2 and 3 for a distillation system. It can be seen from Figure 1and Table I that eq 3 provides the more realistic estimate of the froth to spray transition. Whereas eq 2 severely underpredicts the transition in both of the cases investigated, eq 3 is in encouraging agreement with the limited experimental data. This, together with the previously reported experimental observations which show an insignificant effect of surface tension on the transition, suggests that eq 3 provides realistic estimates of the froth to spray transition under actual distillation conditions. A more rigorous test of the validity of eq 3 will require additional measurements of the froth to spray transition in terms of tray loadings under actual distillation conditions. Such measurements are as yet unavailable. Conclusions The major factors affecting the froth to spray transition on industrial scale sieve trays are gas and liquid loading,
Ind. Eng. Chem. Process Des. Dev. 1902, 21, 776-778
Dh = hole diameter, m g = acceleration due to gravity, m/sz ht = clear liquid holdup at transition, m L = liquid load per unit length weir, m3/s m n = factor in eq 3, m U,= superficial gas velocity, m/s p1 = liquid density, kg/m3 pg = gas density, kg/m3 o = surface tension, N/m
/
Air water d a a Andrew I19691 Jeronimo and Sawistowski correlation present correlat,on Pinczewski and Fell 119 ?resent correlation .
/ ,/
I 0
--
'
Literature Cited Hydrocarbon
system data
-&present correlation - Jcronimo and - Sawstowski correlation (973)
1 2 3 OBSERVED SUPERFICIAL GAS VELOCITY ( m i s )
Figure 1. Comparison between calculated and observed superficial gm velocities at the froth-to-spray transition.
tray free area, hole diameter, and system gas and liquid densities. Surface tension would appear to have an insignificant effect on the transition. Equation 3 provides a good correlation for the air/water transition data reported by Pinczewski and Fell (1972) and is in encouraging agreement with the limited data available for hydrocarbon systems under actual distillation conditions on an industrial scale tray. Since eq 3 correlates the transition in terms of tray loadings, tray geo'metry, and system physical properties, it is of immediate use to the tray designer in determining the operating regime on sieve trays. Nomenclature Af = tray free area, fraction
Andrew, S. P. S. Inst. Chem. Eng. Symp. .. r . 1080, No. 32, 2:49. Hofhuls. P. A. M.; ZuMerweg,F. J. Inst. Chem. Eng. Symp. Ser. 1070, No. 56, 2 , 2.211. Jeronimo, M. A. da S.;Sawistowski, H. Trans. Inst. Chem. Eng. 1073, 51, 265. Kutateladze, S. S.; Sorokin, Y. L. "Problems of Heat Transfer and Hydraulics of Two-Phase Media"; Pergamon Press: Oxford, 1969; p 385. Lockett, M. J. Trans. Inst. Chem. Eng. 1081, 59, 26. Loon, R. E.; Plnczewski, W. V.; Fell, C. J. D. Trans. Inst. Chem. Eng. 1073, 51, 374. Pinczewski, W. V.; Fell, C. J. D. Trans. Inst. Chem. Eng. 1072, 50, 102. Pinczewski, W. V.; Fell, C. J. D. Trans. Inst. Chem. Eng. 1074, 52, 294. Plnczewski, W. V.; Fell, C. J. D. Chem. Eng. (London) 1077, 316, 45. Porter, K. E.; Wong. P. F. Y. Inst. Chem. Eng. Symp. Ser. 1080, No. 32, 2:22. Porter, K. E.; Jenklns. J. D. Inst. Chem. Eng. Symp. Ser. 1070, No. 56, 2, 5 -. 111 .. .. Prince, R. 0. H.; Jones, A. P.; Panlc, R. J. Inst. Chem. Eng. Symp. Ser. 1070, No. 56, 1 , 2.2127. Sakata, M.; Yanagi. T. Inst. Chem. Eng. Symp. Ser. 1070, No. 56, 2 , 3.2121.
School of Chemical Engineering & Industrial Chemistry Uniuersity of New South Wales Kensington, N.S.W . 2033 Australia
W. Val Pinczewski* Christopher J. D. Fell
Receiued for review October 29, 1981 Accepted May 17, 1982
A New Particle Size Distrlbutlon A new particle size distribution with inbuitt desirable properties has been defined. Eleven sets of data chosen from the literatwe show that the new distribution can represent a mixture of sizes of particles excellently well. Equations have veen derived to estimate the specific surface area of a powder sample where the new distribution refers to number, length, area, and volume (or weight) distribution.
Introduction The characteristic size of a powder sample can be determined when the equation for size distribution is known. Normal, log-normal, Gaudin-Schuhmann, Rosin-Rammler, Nikuyama-Tanasawa and r distribution are generally recognized to be standard distributions. In this paper, a new particle size distribution is defined and tested on available published data (Smith, 1970; Shook et al., 1973; Govindan, 1979) of a wide variety of materials. Specific surface area, which is an important property of the particulate material, is then calculated using the procedure developed by Viswanathan et al. (1982). The New Distribution Any particle size distribution is defined by ita cummulative undersize distribution, y, or ita probability density function, n,(x), where r is equal to 0, 1, 2, and 3 refer to number, length, area, and volume (or weight) distributions, respectively. 0196-4305/82/1121-0776$01.25/0
Recently, a general method was developed (Viswanathan, 1982) to determine the functional relationship between two variables which are known to vary monotonically. Since cumulative undersize varies monotonically with particle size, this method was applied and it was found that a new form of equation could explain many distributions. This idea is developed further in this paper. The new particle size distribution is defined by y = exp(-bx-")
dy/dx = n,(x) = nbx-"-l exp(-bx-")
(1)
where b and n are positive real constants. It has the following inbuilt desirable properties which can be easily verified: (I) y equals 0 and 1 at x equal to 0 and a; (2) the shape of the distribution is sigmoidal; i.e., the curve passes through an inflexion point. Hence dy/dx is a valid probability density function in the range of x equal to
0 1982 American Chemical Society
