lnd. Eng. Chem. Res. 1991,30, 2496-2503
2496 Greek Letters CY = parameter defined in eq 10 j3 = parameter defined in eq 11 r = activity coefficient
6 = binary interaction parameter 4 = fugacity coefficient A = spreading pressure (atmcm) Superscripts * = reference adsorbed state
= single-component adsorbed state = asymptotic saturation state SCF = supercritical fluid phase Ad = adsorbed phase E = experimental m
Subscripts
1 = toluene 2 = carbon dioxide i, j = component index
Registry No. MePh, 108-88-3;C, 7440-44-0;C02, 124-38-9. Literature Cited Chimowitz, E. H.; Kelley, F. D.; Munoz, F. M. Analysis of Retrograde Behavior and the Cross-Over Effect in Supercritical Fluids. Fluid Phase Equilib. 1988,44,23-52. DeFilippi, R. P.; Krukonis, V. J.; Robey, R. J.; Modell, M. Supercritical Fluid Regeneration of Activated Carbon for Adsorption of Pesticides. EPA Report; EPA: Washington, DC, 1980. Gamba, G.; Rota, R.; Storti, G.; Carra, S.; Morbidelli, M. Adsorbed Solution Theory Models for Multicomponent Adsorption Equilibria. AIChE J. 1989,35,959-966.
Kander, R. G.; Paulaitis, M. E. The Adsorption of Phenol from Dense Carbon Dioxide onto Activated Carbon. In Chemical Engineering and Supercritical Conditions; Penninger, J. M. L., Gray, R. D., Davidson, P., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983;pp 461-476. Modell, M.; Robey, R. J.; Krukonis, V. J.; DeFillippi, R. P.; Oestreich, D. Supercritical Fluid Regeneration of Activated Carbon. Presented at the AIChE Meeting, Boston, 1979. Myers, A. L.; Prausnitz, J. M. Thermodynamics of Mixed-Gas Adsorption. AIChE J. 1965,11, 121-127. Peng, D. Y.;Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976,15,59-64. Radke, C. J.; Prausnitz, J. M. Thermodynamics of Multi-Solute Adsorption from Dilute Liquid Solutions. AIChE J. 1972, 18, 761-768. Talu, 0.;Zwiebel, I. Multicomponent Adsorption Equilibria of Nonideal Mixtures. AIChE J. 1986,32,1263-1276. Tan, C. S.; Liou, D. C. Desorption of Ethyl Acetate from Activated carbon bv Supercritical Carbon Dioxide. Ind. En#. - Chem. Res. 1988,27,-988-991. Tan, C. S.; Liou, D. C. Regeneration of Activated Carbon Loaded with Toluene bv SuDercritical Carbon Dioxide. S e n Sci. Technol. 1989a,24,1111127: Tan, C. S.; Liou, D. C. Supercritical Regeneration of Activated Carbon Loaded with Benzene and Toluene. Ind. Eng. Chem. Res. 1989b,28,1222-1226. Tan, C. S.; Liou, D. C. Adsorption Equilibrium of Toluene from Supercritical Carbon Dioxide on Activated Carbon. Ind. Eng. Chem. Res. 1990a,29,1412-1415. Tan, C. S.; Liou, D. C. Loading of Toluene on Activated Carbon in Equilibrium with a Supercritical Carbon Dioxide with Toluene Concentration a t 2 mmol/l. Unpublished data, National Tsing Hua University, 1990b.
Received for review January 23, 1991 Accepted July 1, 1991
RESEARCH NOTES Particle-Liquid Mass Transfer in Mechanically Agitated Contactors Results of a study on particle-liquid mass transfer in mechanically agitated contactors are reported. The effects of particle diameter, viscosity of liquid, type of impeller, clearance, agitation speed, and vessel diameter have been studied over a wide range. A simple correlation based on critical suspension speed which satisfies present data as well as data of previous workers is proposed. A theoretical basis for this correlation emerging out of the interrelationship of speed of agitation, drag force on particles, and the resulting particle-liquid mass transfer has been suggested. Mass transfer from or to solid particles suspended in agitated liquid is relevant to many chemical processes such as adsorption, crystallization, fermentation, slurry reactions, extraction of metals, polymer processing, and wastewater treatment (Doraiswamy and Sharma, 1984). One of the main reasons for applying mechanical agitation is to ensure that all the surface area available for mass transfer is utilized. For designing mechanically agitated contactors (MAC), knowledge of mixing time, flow pattern, power consumption, and mass-transfer parameters is necessary. Interphase mass transfer is often a rate-limiting step that must be reliably predicted in the design of agitated vessels. A survey of literature related to solid-liquid mass transfer in agitated vessels shows that there is an extremely wide divergence of results, correlations, and theories. This is expected as a large number of variables affect the
transfer rates. These variables make agitated systems very complex. Variations between investigations may be partly due to dissimilar conditions used. However, the inability to derive a reliable correlation satisfying a large data bank is certainly due to poor understanding of the particle motion in turbulent liquid in agitated vessels. Table I gives details of various investigations on solidliquid mass transfer in agitated vessels, and the observed effects of various parameters or variables on mass-transfer coefficients are summarized in Table 11. Some of these investigations employing relatively large (>0.01m) particle sizes and low speeds of agitation (C16 rev/s) are likely to pertain to measurements when the particles are only partially suspended or resting on the vessel base. On the other hand, the high speeds used in some cases could have caused aeration resulting in a three-phase system rather than the two-phase system under consideration (Nienow,
0888-5885/91/2630-2496$02.50/00 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2497 Table I. Reported Work on Solid-Liquid Mass Transfer in Agitated Systemso vessel d i m , m impeller type and size, m x lo2 system x 102 no. reference 7.8-17.8; 3 propeller BA in water, benzene, and 26-61 1 Hixson and Baum (1942) ethylene glycol, rock salt in water boric acid and BA in water, 15-65 5-32.5; 6DT 2 Barker and sucrose, salt in brine Treybal (1961) BA, butyl-BA, boric acid, lead 10-51 3.75-17.5; 6DT 3 Harriott (1962) sulfate in water, dextrose; zinc in hydrochloric acid
particle diam, m x 102 0.4-0.67 0.9-14
sc 748-4.3 106
X
0.00150.03
73562OOO 325107500 770-
4 Sykes and Comezplata (1967)
Cd-coated Cu particles in iodate 13 + iodine solution, sucrose
6.32; 6DT, 6 (459 paddle, 3 propeller
0.3
5 Brian et al. (1969) 6 Nienow (1969)
pivalic acid in water
5.1, 6.3; IFBT, 3 propeller 3.6-7.3; 4DT, 6DT
0.16-0.28
10-45; 4FBT
0.39
lo00
6.3-10; GFBT, GCBT, GPTD, 3 propeller
0.0030.196
267-3.5 104
3-13; 6DT, BFBT
0.01070.285 0.02460.094 0.223
217-1410
800
0.29
300-2000
12.8-22.8 4.6-7.3; IFBT, 6PTD
0.11-0.61
lo00
12.8-22.8 4.6-7.3; IFBT, 6FBT
0.092-0.61 lo00
15
8; 6DT
14.5-25
4.0-10.0; PFBT, 2-6DT, 4 propeller
0.00250.0145 0.54-2.0
9-13.2
4.5-6.6 6DT
7 Miller (1971)
12.2
K2S04,NH,CI, alum, and salt in 12-14 water BA in water 15-69
IER in acids, bases; copper, iron 12.6-25 powder in Iz-KI, I,-KI-sucrose, stearic acid in ethanol, naphthalene in methanol 9.5-40 Sano et al. (1974) BA, &naphthol, KMnO, in water, IER in HCl IER in NaOH Kuboi et el. 10.5 (1974) sodium chloride in water Nienow and 14-28 Miles (1978) Boon-long et al. BA in water 9-63 (1978)
8 Levins and
Glastonbury (1972)
9 10 11
12
BA in water 13 Sicardi et al. (1979) 14 Conti and Sicardi BA in water, IER in NaOH (1982) 15 Yagi et al. (1984) IER in Ca(OH),, Ca(OH)2in water 16 Lal et al. (1988) BA in water, CMC, and glycol
17 Asai et al. (1988) IER in acids, bases; copper in KI + I,, lead sulfate in water-glycerin IER in NaOH, glycerol, IER in 18 Armenanteand AgN03 + NaN03 Kirwan (1989) BA in water, CMC 19 present work
5.2; 4DT 3.5-21; 6DT, IPTD, BFBT 3-21; 6DT
19
6.35; 6-blade turbine
15-57
5-19.0; 4DT, IPTU, 6PTU
correlation kSLT/D = 3.5 X 10-4(NFp/p)'.O(Sc)O"
11300
3200
0.014-0.91 405-1790
X
730
490 624-1 X 104
0.0020.096
269-
6 X lo40.0424 0.0550.368
420-1.3 X 105 800-4000
Sh=2+ 0.474(Re )0.67(sc)0." for 1 c iPe. c 800
11270
OBA = benzoic acid, DT = disk turbine, PTU = pitched-blade turbine (upflow), PTD = pitched-blade turbine (downflow), FBT = flat-blade turbine, CBT = curved-blade turbine, IER = ion-exchange resin.
1968). I t is evident from Table I that there is a wide divergence in the correlations and that a single correlation satisfying various data is not available. Table I1 also shows the variation in the dependency of the mass-transfer coefficient on each variable.
Experimental Work The experimental program included a study of the influence of all important variables which affect masstransfer rates. The system used was dissolution of benzoic acid in water and aqueous Newtonian solutions of (carboxymethy1)cellulose(CMC)(Jadhav and Pangarkar, 1988). Acrylic cylindrical vessels of diameter 0.15,0.3, and 0.57 m having flat bottoms were used. Liquid was filled to a height equal to the diameter of the vessel. Upflow
pitched-blade turbines (PTU) and a disk turbine (DT) were used in all the experiments. Loading of benzoic acid granules was restricted to 0.5% in order to avoid liquid saturation in the batch experiments. The experiments were conducted for different speeds below and above the critical suspension speed, N,. Critical suspension speed in the present case was defined as that speed at which none of the particles rest on the vessel bottom for more than 1s (Zwietering, 1958). This was measured by watching the mirror image of the bottom of the vessel. The experiment was conducted for a fixed time (240-360 s), after which a solution sample was removed, filtered and analyzed for benzoic acid by titration against 0.01 N NaOH. Some samples were also removed using a hypodermic syringe along with the usual method of bulk removal and filtration.
2498 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 Table 11. Reported Effect of Variables on Solid-Liquid Mass Transfer in Agitated Vessels no. reference particle diam viscosity diffusivity impeller speed 1 Hixson and Baum (1942) -0.5 0.56 1 2 Barker and Treybal (1961) -0.33 0.5 0.83 3 Harriott (1962) -0.7 small d, -0.06 small d, 0.6-0.8 0.3-0.5 -0.1 high d, -0.22 high d, 4 Sykes and Gomezplata (1967) -1.0 0.12 0.5 0.38 5 Brian et al. (1969) 0.33 0.67 0.67* 6 Nienow (1969) 0.27-1.22 -0.5 -0.17 0.67* 1.24 7 Miller (1971) 8 Levins and Glastonbury (1972) -0.17 -0.26 0.64 9 Nagata and Nishikawa (1972) 0.17 -0.5 0.67 0.83 10 Sano et al. (1974) 0 -0.42 0.67 11 Kuboi et al. (1974) -0.5 0 0.5* 12 Nienow and Miles (1978) 0.47-1.28 0.54 0.283 -0.25 -0.17 13 Boon-long et al. (1978) 14 Sicardi et al. (1979) 0.33 -0.67 0.67. -0.67 0.672 15 Conti and Sicardi (1982) 0.33 16 La1 et al. (1988) -0.1 and -0.67 -0.34 and 0.08 0.67 0.67 and 0.25 17 Asai et al. (1988) -0.23 -0.25 0.67 18 Armenante and Kirwan (1989) -0.32 -0.185 0.67 19 Present work -0.5 -0.53 0.53 1.16 range
-0.7-0.33
-0.67-0.12
0.5-0.8
impeller diam 1 0.67 0.2-0.33 0.78
0.174 0.83
1.12 and 0.42
0.27-1.24
0.17-1.33
Table I11 solution water O.l%CMC 0.2%CMC
density, kdm3 lo00 1004 1004
viscosity, diffusivity, kn/(ms) x IO4 m2/s x IOB Sc 8 1.0 800 19.2 0.94 1966 37.4 0.9 3996
Both these samples yielded results within 5% of each other. The syringe method was abandoned as small particles tended to choke the syringe during suction. Newtonian aqueous solutions of CMC (0.1 and 0.2% by wt) were used for studying the effect of viscosity of the liquid. Aqueous CMC solutions below a CMC concentration of 0.25% (wt) are known to exhibit Newtonian behavior. Such solutions are ideal when a variation of viscosity is desired without significant changes in other characteristics of the solution. For instance, clear visibility was an important point in this work. In our earlier investigations (Jadhav and Pangarkar, 1988,1990,1991) aqueous glucose solutions were used to vary the viscosity. However, these solutions are relatively dark and the visibility is very poor. Thus, measurement of N , by the observation method is not possible. On the other hand, the aqueous Newtonian CMC solutions used were clear and afforded measurement of N , without any difficulty. The rheological characteristics of the solutions used were measured on a Haake viscometer and were as follows: for CMC concentration 0.1 w t %, k = 0.018, n = 0.99; for CMC concentration 0.2 w t %, k = 0.035, n = 0.99. Since the value of n is nearly equal to 1, these solutions can be classified as Newtonian. Viscosity and density of the Newtonian CMC solutions were experimentally determined. Diffusivities of benzoic acid in Newtonian aqueous CMC solution have been reported by Hansford and Litt (1968), and the same were used in the data treatment. Diffusivity of benzoic acid in water has been reported by Jadhav and Pangarkar (1988), and the same was used in this work. Table I11 gives these physical properties of the various systems used. Table IV gives the summary of geometrical variations covered. Table IV vessel diam, m 0.15 0.30 0.57
type of impeller DT, PTU (4,6 bladed) DT, PTU (4 bladed), 6-bladed PTU DT, PTU (4 bladed), 6-bladed PTU
clearance 1/3 1/6-1/3 1/3
5
7
9
11
N, rev/, i correlation)
13
--+
Figure 1. Parity plot for N.. Vessel diameter = 0.15 m; impeller = six-bladed DT; particle diameter range = 550 X 10“-3680 X 10” m.
Results and Discussion Critical Suspension Speed: N,. Zwietering (1958), Nienow (1968), Baldi et al. (1978), Chapman et al. (1983), and Rao et al. (1988) are among the various investigators who have carried out investigations on the critical suspension speed. A detailed discussion on this aspect is given by Chapman et al. (1983). The available literature indicates that reliable correlations exist for predicting N , for DT, paddles, propellers (Zwietering, 1958) and downflow pitched-blade turbine, PTD (Rao et al., 1988). For PTU the data available are scanty (Rao 1987; Chapman et al., 1983) and no reliable correlation exists. In this work DT and PTU were used. N, values for all the experiments were measured on the basis of Zwietering’s criterion. These measured values of N, for DT were compared with those calculated by Zwietering’s (1958) correlation. The parity plot for N , given in Figure 1indicates that the measured values are about 10% higher than those obtained from impeller diam, m 0.05 0.1 and 0.19 0.19
particle d i m , m x 10s 550-1100 550-1100 550-1 100
sc 800
800-4000 800
NIN, 0.8-2.5 0.4-2.3 0.65-1.45
Ind. Eng. Chem. Res., Vol. 30,No. 11, 1991 2499 Table V. Operating Conditions and Symbols for Figure 2 type of impeller speed, rev/s vessel diam, m symbol DT 16 0.15 X DT 10 0.30 0 DT 12.5 0.15 A PTU 16 0.15 V
-6 10
9
a 7
Table VI. Operating Conditions and Symbols for Figure 3 particle diam, vessel type of m x 108 diam,m symbol impeller PTU 550 0.3 0 PTU 655 0.3 0 PTU 977 0.3 A DT 655 0.57 v PTU 655 0.57 e
6
--t 5 h
Ill
E
L
-1
v)
x
3
-c
2
3
4
5
6
6
7
9
101
N(rcv/s)-
Figure 3. Variation of ksL with N . d / T = C / T = 113;number of blades = 4. * indicates the values of kSL at critical suspension speed. See Table VI for other symbols.
-5 3 x 10 3x1c6
I
I
I
1
I
I
1
4
5
6
7
8
9
10''
1
dp(m)
Figure 2. Variation of ka with d,. d / T = C / T = 113; number of blades = 4. See Table V for symbols.
Zwietaring's correlation. This deviation was not considered as significant, and the measured N, values for both DT and PTU were used subsequently. Effect of d , on kSL.Figure 2 shows the effect of d, on k S L for the range of d , between 550 X 10" and 1100 X 10" m. The average dependence of ksLon d, can be described by k S L 0: d 4*s. Harriott (19621, kuboi et al. (1974),Asai et al. (1988), and Armenante and Kirwan (1989) have also obtained a negative dependence of ksL on d, for their data for approximately the same range of d,. The observed dependence of kSL in the present work agrees with that of Kuboi et al. (1974). Effect of N of kSL.From Figure 3, it is observed that kSLincreases with increase in N. Figure 3 also shows the k a values for various particle sizes at N = N,. It is evident from Figure 3 that kSL is approximately the same for various particle diameters for N = N,. This observation is in agreement with that of Nienow (19691, Nienow and Miles (1978),and Conti and Sicardi (1982). The average dependence of kSL on N which can be described as ksL W.lsagrees with that obtained by Barker and Treybal (1980) and Nienow (1969). Effect of clearance (C/T) on kSL.Figure 4 shows that k S L increases with decrease in clearance in the range of C/Tstudied. It may be noted here that a lowering of (1:
zF 1
I
I
I
I
1
01
0.2
0.3
0 .L
C1T
Figure 4. Variation of ksL with C / T . d / T = C / T = 113; number of blades = 4. See Table VI1 for symbols. Table VII. Operating Conditions and Symbols for Figure 4 type of speed, vessel diam, impeller rev/s m x 108 symbol 8.33 655 X DT 10 1100 0 DT 5.83 1100 A DT 5.83 655 0 PTU 8.33 655 V PTU
2500 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 Table VIII. Operating Conditions and Symbols for Figures 5 and 6 Vessel Diameter = 0.15 m; d / T = C / T = 113; Number of Blades = 4 type of impeller particle diam, m X lo6 symbol PTU 550 0 PTU 655 8 PTU 971 9 PTU 1100 0 A DT 550 DT 655 a 0 DT 971 DT 1100 1
lib8-
60
-
0
m
E
L-
=
3-
\
Vessel Diameter = 0.57 m; d / T = C / T = 113; Number of Blades = 4 DT DT DT DT PTU PTU GPTU
2-
,?I0.3
1
0.4
I
I
0.6
L
I
0-8
I
I
1
I
1
2
3
NINS
Figure 5. Comparison of experimental data with eq 1. See Table VI11 for symbols.
the clearance decreases N, (Zwietering, 1958; Nienow, 1968; Chapman et al., 1983). Effect of d / T Ratio on ksL. This effect was not studied in the present work since it is clearly established that larger d / T ratios yield higher kSL values (Levins and Glastonbury, 1972b; Boon-Long et al., 1978; Nienow and Miles, 1978). It is also an established fact that larger d / T results in lower N , (Zwietering, 1958) just as lowering of the clearance results in a lower N , value under otherwise identical conditions. The results described above can be summarized as follows: (1)ksL 0: dp4.5 a t constant N (2) kSL 0: N1.15at constant d,; (3) ksL increases with decreasing clearance of the impeller from the bottom in the range of C/T used; (4) ksL increases with increasing d / T ratio. These dependences are included in Table 11. The most significant conclusion from these results, however, relates to the unique relationship of kSLwith N,. Over the entire range of particle diameter, clearance, and system physical properties, kSL values are approximately same when evaluated at N,. In other words (kSL),is a unique value independent of geometrical configuration of the equipment (type of impeller, C / T , d / T , etc.) and physical properties. Conti and Sicardi (1982) have used the ratio N/N, to correlate k S b It wm felt that this approch is sound in view of the unique relationship of kSLwith N,. However, Conti and Sicardi's (1982) approach requires evaluation of (kSL)s from the power dissipation Reynolds number. This latter evaluation is based on Kolmogorroff s theory, which has been questioned by various investigators (Harriott, 1962). In view of this a simple correlation directly relating kSL to the ratio N / N , was attempted for all benzoic acid-water data (Sc = 800). The following correlation was obtained: ~ S = L
5.126 X 10-5(N/N,)1.03
(std dev =16.5%)
(1)
It can be observed from Figure 5 that eq 1describes the experimental data satisfactorily. In order to incorporate the effect of Schmidt number , data from experiments with Newtonian CMC on k s ~the
1100 655 917 550 1100 655 1100
V 0
n 0
A -
Vessel Diameter = 0.3 m; d / T = 1/3; Number of Blades = 4 type of particle diam, impeller m x lo6 clearance symbol PTU 1100 0 PTU 977 0 0 PTU 655 PTU 550 PTU 1100 PTU Q 655 PTU 1100 Q PTU 0 655 DT A 1100 DT 971 A DT 655 e DT o 550 DT 1100 0 DT e 655 DT 0 1100 X DT 655 GPTU 1100 DT 0 1100 DT e 655 PTU 0 655 DT 1100 0 * DT 655 0 PTU 1100 v PTU 655
+
solutions were included in the regression to obtain the following general correlation: kSL
= 1.72 X 10-3(N/N,)'.'6(S~)4~53
(std dev = 16.2%) (2) Equation 2 can apparently be faulted on some grounds. For instance, it is generally desirable to present a correlation in a dimensionlessform. Equation 2 is a dimensional equation with the constant on the right-hand side having the dimensions length/ time. Mass-transfer correlations available in the literature have been derived from some theoretical considerations, for instance, Kolmogoroff s theory is the basis of correlations proposed by some investigators (Table I). Unlike these correlations eq 2 has no such theoretical basis and is supported only by the observation of various workers that (kSLIsis constant regardless of system configuration. In the following an attempt has been made to give a theoretical basis to eq 2 by drawing a comparison with equations for analogy between mass and momentum transfer: Harriott and Hamilton (1985) and Kays (1975) have reported relationships between Sh and Re which can be
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2501 written as (Pandit and Joshi, 1986)
kSL/v= ~ ~ / 2 ) 0 . 5 ( ~ ~ ) 4 . 6 7
(3)
In eq 3 the dependence on Sc has been derived for the case of boundary layer flow and the same may change for other situations. Equation 3 can be written as kSL
= AV(f/2)0.5(S~)4.67
(4)
The velocity term V and the friction factor are very difficult to define in a highly turbulent system (Jadhav and Pangarkar, 1988; Joshi et al., 1990). Hughmark (1974, 1980) has suggested the following correlation based on eq 4 for particle-liquid mass transfer in MAC: kSL/
u = CY(f /2)0.5(S~)-0.67
(5)
where u is defined as the vectorial sum of the terminal settling velocity under turbulent conditions and the relative particle-liquid velocity. Both these velocities and f were obtained by Hughmark by analyzing literature data of Levins and Glastonbury (1972a) on turbulence parameters for impeller diameters between 0.05 and 0.1 m. Hughmark has, however, indicated that the lack of data on turbulence parameters for larger diameter impellers (and also different configurations encompassing different d / T , C / T , impeller shapes, etc.) precludes the use of eq 5 for scale-up purposes. Comparison of eq 2 and 4 (disregarding the different exponents for Sc) shows that AV(f/ 2)0.5= 0.172( N/ N , )
System: Pivalic acid dissolution in water. Impeller: threebladed marine propeller, N = 5 rev/s. Table X. Actual Operating Conditions for Data Points of Sicardi et al. (1979) (Symbol in Figure 6: S)" C/T d/T N , rev/s C/T d/T N , rev/s 0.33 0.3 6.0 0.5 0.24 17.5 7.5 0.33 0.24 4.0 6.7 9.9 0.33 0.38 5.4 8.3 8.1 11.8 4.75 14.6 0.22 0.24 a System = benzoic acid dissolution in water, d , = 3600 X lo* m. Impeller = flat-blade turbine.
'"9b 8 6I t
5-
(6)
It is interesting to note that most of the models for solid suspension in agitated vessels used the drag on the particle as the cause of suspension (Chapman et al., 1983). Clearly then there is a definite relationship between N , and f,. f, in turn is a function of the characteristic particle-fluid velocity at the just suspended condition, V,. It can therefore be argued that N , defines both V, and f,. Coupled with the relationship between mass transfer and drag, the above discussion can explain the relationship of N , vis il vis mass transfer. Thus, the basis for eq 2 is the relationship between particle-fluid relative motion and mass-transfer phenomena which is consolidated in the following: The friction factor for a particle in a turbulent field is given by (Bennett and Myres, 1962) vv/2)0.5 = u*
Table IX. Actual Operating Conditions for Data Points of Brian et al. (1962) (Symbol in Figure 6: R)' d,, m X lo2 '70 loading 0.165 0.0011 0.25 0.0038 0.3 0.0066 0.2 0.0019 0.28 0.0039 0.24 0.0025
(7)
Davies (1972) has shown that for pipe flow u* = u', where u'is the fluctuating velocity component normal to the wall. Similarly, Hanratty et al. (1956), Handley et al. (19661, and Lali and Joshi (1989) have indicated that for two- and three-phase fluidized beds u* N u ', where u 'is the fluctuating velocity component normal to the solid. It is likely that a similar relationship may hold for mechanically agitated contactors in which case again u* N U'.
Measurements of flow generated by propeller and paddle (Deshpande, 1988), PTD (Ranade and Joshi, 1989), and DT (Ranade and Joshi, 1990) indicate that u'is approximately proportional to N . The above arguments coupled with the observation that u' a N yield the following relationship: u* N u ' u N and hence V(f/2)0.5 a N . Therefore, Hughmarks correlation and eq 2 become equivalent. The ratio (NIN,),thus, represents the relative
4-
3-
2n 0
0
'm' %
a
xn
loZ-90 80 70 60
-
-
40 50
301 0.2
I
0.3
I
I
I
0.4 0.5 0.6
I
I
0.8
I
I
I
1
2
3
I
N/Ns
Figure 6. Comparison of experimental data with eq 2. See Tables VIII-XI for symbols.
turbulence intensity referred to the minimum suspension conditions. The minimum suspension condition as represented by N , in turn defines the system (impeller type, d / T , C / T , A p / p , p , solid loading, etc.) completely. N / N , is therefore a unique combination of factors representing the turbulence level and system characteristics. This property of NIN, is amply supported by the successful fit of the N / N , based correlation with various literature data as discussed subsequently. Figure 6 shows a parity plot of eq 2 and the data obtained in this work as well as those of other investigators. These include those of Brian et al. (1962), Harriott (1962), Miller (1971), Nienow and Miles (1978), Boon-long et al. (19781, Nienow (1979), and Sicardi et al. (1979). The N , values for the literature data were obtained by using Zwietering's (1958) of Rao et al.'s (1988) correlation de-
2502 Ind. Eng. Chem. Res., Vol. 30,No. 11, 1991 Table XI. Operating Conditions for Data Points of Other Workers d,, N, reference systema impeller m x 1Od rev/s symbol Harriot BA-water disk 130 5.0 H turbine lo00 (1962) 1.67 M Miller (1971) BA-water . flat-blade 3900 5.0 turbine 7.9 Boon-Long BA-water disk 2900 2.25 B turbine 3.5 et al. (1978) 5.67 2230 17.5 E Nienow and NaC1-water pitchedMiles (1978) 20.0 blade turbine 25.0 324 11.7 N Nienow KzS04-water disk turbine (1979) 15.0 16.7 alum-water 775 21.7 26.7 29.2 OBA = benzoic acid.
pending upon the impeller used. Together with the data from the present work, these data cover a very wide range of impeller type/size, vessel size, C/T,d / T , particle size, and density and system properties. The satisfactory correlation fit in Figure 6 clearly reflects that eq 2 can correlate data obtained from various sources covering a very wide range of variables as mentioned above. Equation 2 has the advantage that it requires only N , to be predicted and fairly reliable correlations are available for the same. Zwietering's (1958) correlation is now accepted to be a reliable method for prediction of N , for DT and paddles and propellers (Chapman et al., 1983). For PTD Rao et al.'s (1988) correlation can be used. Equation 2 yields the following relationship between kSL and D: kSL a Do.69. This dependence is close to the square-root dependence predicted by the penetration model for un-steady-state mass transfer in turbulent systems. Considerable information is available on particleliquid mass transfer in agitated vessels. However, there is no unanimity on the dependence of kSLon diffusivity. A number of investigators have concluded that ksL a (Hixson and Baum, 1942; Batker and neybal, 1962; Sykes and Gomezplata, 1967; Boon-long et al., 1978) whereas others (Brian et al., 1960; Miller, 1971; Sano et al., 1974; Sicardi et al., 1979; Conti and Sicardi, 1982; Lal et al., 1988; Armenante and Kirwan, 1989) have observed the dependence to be closer to The approximate square root dependence of ksLon D obtained in this work and by other investigators agrees with the penetration model for diffusion in turbulent systems and is thus likely to be more appropriate to the present situation dealing with a highly turbulent field.
Conclusion A systematic study of the various variables affecting particleliquid mass transfer in MAC has brought out the effect of these variables. The unique relationship between the critical suspension speed and mass-transfer coefficient indicated by previous investigators has been further consolidated. A simple yet theoretically sound mass-transfer correlation which satisfies most of the published data has been proposed. Acknowledgment We gratefully acknowledge financial support for this work and a Senior Research Fellowship (to S.V.J.) from the University Grants Commission, Government of India.
Nomenclature A = constant in eq 3 C = clearance of impeller from the bottom, m d = diameter of impeller, m d, = particle diameter, m D = diffusivity of solute in the liquid, m2/s f = friction factor g, = gravitational constant, m/s2 Ga = Galileo number (d$gc/p2) H = height of liquid in the vessel, m kgL = solid-liquid mass-transfer coefficient, m/s
N = speed of agitation, rev/s N , = critical suspension speed of the particles, rev/s P = power drawn by impeller, W ReK = Reynolds number based on Kolmogoroffs theory Sc = Schmidt number ( p / p D ) Sh = Sherwood number (ksLdp/D) T = tank diameter, m u = vectorial sum of terminal settling velocity and particleliquid velocity, m/s u' = fluctuating velocity component, m/s u* = friction velocity, m/s u, = slip velocity, m/s ut = terminal settling velocity of a particle in a quiescent fluid, m/s V = characteristic velocity, m/s Greek Symbols a = constant in eq 5 e = power dissipation per unit volume of liquid, m2/s3 p = viscosity of the liquid, kg/(m.s)
= kinematic viscosity, m2/s = density of the liquid, kg/m3 Ap = density difference between solid and liquid = shape factor of particle +DT = power number of disk turbine +imp = power number of impeller u
p
Subscript s = minimum suspension condition
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Sumant V. J a d h a v , Vishwas G. Pangarkar* Department of Chemical Technology University of Bombay, Matunga Bombay 400 019, India Received for reuiew March 12, 1990 Revised manuscript received November 26, 1990 Accepted August 15, 1991
The Chemistry and Free Energy of Formation of Silver Nitride Silver nitride, Ag3N, an extremely sensitive explosive compound, forms from ammoniacal solutions of silver oxide. This is a potential hazard to laboratory workers using Tollens reagent and silvering solutions. An excess of aqueous ammonia, 4 to 1mol, is required to dissolve Ag20to form the ammine complex. Upon loss of ammonia by evaporation, solutions of the ammine complex produce black solids consisting of Ag3N, Ag20, or mixtures. If the solution is relatively concentrated, the solids will contain much AgSN. If the solution contains less than about 5 % ammonia, the solids will be predominately Ag,O and nonexplosive. Aging of Ag,O solids in an amount of strong ammonia too small for complete solution causes conversion to Ag3N. On the basis of the chemical behavior we estimated that standard free snergy of formation of Ag3N to be 314.4 f 2.5 kJ mol-'. For more than 200 years, it has been known that the addition of aqueous ammonia to silver oxide can produce explosive solids formerly termed "fulminating silver" (Gmelin, 1971;Mellor, 1922). This explosive behavior is due to formation of silver nitride, Ag3N. Ammoniacal solutions of silver salts can produce the same explosive dark solids if a strong fixed base, such as sodium hydroxide, is added to the solution (L.A.C., 1827; Raschig, 1886). However, this potential hazard has not prevented the general use of silvering solutions, Tollen's reagent, and other ammoniacal silver solutions, and, despite the usual cautionary statements, there have been many unexpected detonations in ammoniacal silver solutions which have
accumulated dark colored solids. Earlier papers (MacWilliams and Hazard, 1977;Shanley et al., 1968)have reported the results of our studies of silver nitride formation. This report discusses the results of further studies and provides guidance for avoiding hazard. Other explosive silver species such as silver fulminate, Ag(ONC), and silver azide, AgN3, (Gmelin, 1971;Mellor, 1922;Luchs, 1966) do not form from ammoniacal preparations. Our study provides the information required to define the phase relationships in Figure 1. Various chemical species can be postulated in this system, including silver ammine ions, Ag(NHJ+ and Ag(NH3)*+;and hydroxyl ion, 0 1991 American Chemical Society
