Ind. Eng. Chem. Fundam. 1981, 20,107-108
characterizing bulk performance. Shinnar and Church (1960) made the analogous inference in developing the turbulence microscale 71 concept for a mechanically agitated vessel. The q is defined as the size of eddies at the small eddy equilibrium end of the turbulence energy spectrum in an agitated fluid medium q = 0.001674(Pe/ v)-1/4v3/4
(10)
where v is kinematic viscosity. The small eddy end of the spectrum is thought to be most important for overall mass transfer as a bulk property. The PJV term is assumed to be an order of magnitude lower in the bulk fluid as compared to the region close to the tip of the impeller. In summary, data obtained a t elevated pressure are not a t all inconsistent with our method (Miller, 1974) for calculating performance in gas-liquid contacting with
Sir: We have read Miller%letter and offer the following comments. Miller (1974) developed certain scale-up procedures based on experimental mass transfer and gas hold-up data. An effective power input was defined as the sum of part of the gas sparging and kinetic energy and the total mechanical power input pe = pg + Cl[pq + VPKl
107
mechanical agitation. With proper attention to surface aeration, our procedure gives reliable predictions and is fully adequate for the conditions studied in the Sridhar and Potter paper. The kinetic energy associated with gas sparging should be taken a t 6% of the full value for bulk correlations, although this consideration does not affect overall performance predictions appreciably. Literature Cited Abramovich, 0. N., “Theory of Turbulent Jets”, M.I.T.,Cambrkige, 1963. Caklerbank, P. H., Trans. Inst. Chem. Eng., 37, 443 (1958). Caklerbank, P. H.. Trans. Inst. Chem. Eng., 38, 1973 (1959). Lehrer, I. H., Ind. Eng. Chem. Process Des. Dev., 7, 226 (1968). Miller, D. N., AIChE J., 20, (3), 445 (1974). Srldhar, T., Potter, 0. E., Ind. Eng. Chem. Fundam., 19, 21 (1980).
Donald N. Miller
Engineering Department E. I . du Pont de Nemours & Company, Inc. Newark, Delaware 19898
I
‘I
0
O
432
(1)
The constant C1was obtained by comparing bubble sizes with and without mechanical agitation. C1is a function of vessel geometry and varied between 0.05 and 0.4. 71 was assumed to equal 0.06. Miller also used another correction factor to account for surface aeration. This came about from trial and error data fitting. Miller (1974) correlated Cz using the Strouhal number. adn NST = -
SRIDHAR 0
2
EXPERIMENTAL GAS HOLD-UP
3
8 POTTER
\ILLER 4
(x 10)
Figure 1. Comparison of equations for predicting gas holdup.
vg
y = NsT0.13/9.87
C2 = 0.348Y for Y > 2.81 Cz= 1.0 for Y < 2.81
(2)
Calderbank’s (1958) work indicates that surface aeration has negligible effect under the conditions used in our experiments. Using Cz= 1we showed (see Figure 1,Sridhar and Potter, 1980a) that Miller’s method grossly underestimated the interfacial area. If, however, we evaluate Cz using eq 2 the experimental data are consistently overpredicted. Calderbank (1958) concludes that surface aeration is negligible in the smaller vessels, whereas it becomes more important in larger vessels. Miller’s results indicate that surface aeration is important in smaller vessels. Furthermore, Miller’s estimation of power input may be subject to several sources of error. These aspects are discussed by Hassan and Robinson (1974,1977). We now focus attention on Miller’s comments (Miller, 1980) regarding our paper. Miller suggests that surface aeration causes the increase in interfacial area. Using our experimental data he extracts C2as a function of pressure. C1is taken to equal 0.1. Miller then recalculates the interfacial area and concludes that “this generalized correlation has been achieved without recourse to any empirical correction ....” “The new values of Cz, as calculated by Miller, are lower than those predicted by eq 2.” Obviously 0 1 96-43 131811 1020-0107$01 .OO/O
Czfrom mass transfer data does not agree with Czfrom interfacial area data. We should also point out that with the new correlation for Cz,Miller’s procedure will consistently overestimate Calderbank’s data by about 20%. Let us proceed to gas holdup. We have recalculated gas holdup using Miller’s equation with C1= 0.1 and Cz as given by his eq 9. The results are shown in Figure 1. Also shown, on the same graph, are the calculations using our method. It is obvious that Miller’s method overestimates gas holdup, or conversely yet another value for C2is necessary to correctly predict gas holdup. Since C1and Czcannot be independently calculated, Miller’s equations cannot be used for estimating any of the dispersion parameters. The fact that C2cannot be consistently predicted raises serious questions. Our approach shows that the same correction factor enters into all the equations. Furthermore, these correction factors are precisely defined. The essence of the argument is whether kinetic energy is negligible when considering pressure vessels. Is the larger surface area entirely due to surface aeration? We do not deny that surface aeration plays an important part, but this is largely taken care of in the correlations for impeller power input. After all, these correlations were derived using data obtained when surface aeration was present (Hassan and Robinson, 1977). Also, we are not convinced that surface aeration is so strongly dependent on pressure. 0 1981 American Chemical Society
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Ind. Eng. Chem. Fundam. 1981, 20, 108-109
Miller’s claim that less than 6% of the kinetic energy contribution is effective is difficult to test. The low values of C1 have already made the impeller power input predominant. Miller’s justification for this relies on the work of Lehrer (1968) on bubble columns. Lehrer (1980) has informed us that he is not sure that his results could be transposed to stirred vessels without being independently justified. In our experiments the gas jet interacts with the stirrer within 7 nozzle diameters, after which it does not possess an independent identity. To investigate the effects of kinetic energy it is necessary to use pressurized vessels. Such data are time-consuming and expensive to obtain. By systematically varying pressure we have shown that the effect of kinetic energy is significant. Further details are available elsewhere (Sridhar and Potter, 1980b). We are not prepared to introduce surface aeration parameters because very little
information is available. Further work on larger pressure vessels is necessary before definitive scale-up criteria can be developed. Literature Cited Hassan, I. T. M., Robinson, C. W., AIChE J., 20, 1233 (1974). Hassan, I. T. M., Robinson, C. W., AIChE J., 23,448 (1977). Lehrer, I. H., Ind. Eng. Chem. Process Des. Dev., 7, 226 (1968). Lehrer, I. H., personal communication, 1980. Miller, D. N., AIChE J., 20, 445 (1974). Miller, D. N., Ind. Eng. Chem. Fundam., preceding paper in this issue, 1980. Sridhar, T., Potter, 0. E., Ind. Eng. Chem. Fundam., 19, 21 (1980a). Sridhar, T., Potter, 0. E.,Chem. Eng. Sci., 35, 683 (1980b).
T.Sridhar* 0. E.Potter
Department of Chemical Engineering Monash University Clayton, Victoria 3168 Australia
Electrical Field Distributions and Clear Boundary Layers in Cross-Flow Electrofilters Sir: The use of electrical fields to improve the performance of filters for solid/liquid separations is attracting much attention, and in a recent article, Lee et al. (1980) describe a further possible application of the technique. The geometry of the filter tube was tubular, with the filter tube serving as one electrode and an axial wire as the other. When such a configuration is being used, much of the electrical field is dissipated in the region close to the central electrode, while the field strength near the filtering surface is considerably lower than would be expected if the total potential difference between the electrodes is simply divided by the electrode separation distance. That this is so can be verified by solving Laplace’s equation for the potential of a field between two conducting electrodes
V2@ = 0 (1) when the volume between the electrodes is filled by a solution (neglecting the presence of particles in suspension, which is reasonable for dilute slurries such as those used by Lee et al. (1980)). Considering two parallel conductors extending to infinity which are kept a t constant potentials, the solution to eq 1 is @=ux+b (2) for two flat plates, and for two coaxial cylinders the solution is @ = a’ln r + b’ (3) Although no infinitely extended conductors exist and there is fluid flow parallel to the electrodes, the field in the filter unit will be approximated by appropriate application of eq 2 or eq 3. The electric field strength between two plates is constant E=a (4) but between two cylinders it is a function the cylinder radii and the radial location between the electrodes E = a’/r (5) CP and E are plotted in Figures 1 and 2 for the filter described by Lee et al. (curve A corresponds to the polarity chosen when the particle j- potential is measured to be positive, and curve C would be used for negatively charge particles). Also drawn are @ and E for two flat plates with the same separation distance as the coaxial cylinders. 0196-4313/81/1020-0108$01.00/0
gstance frorp centre electrode
mm
Figure 1. D i s t r i b u t i o n of electrical potential.
35G1: 320,
‘
3 i!ance fro=, centre eiecxode, mm
Figure 2. D i s t r i b u t i o n of potential gradient.
It has been widely recognized (for example, Moulik (19711, Yukawa et al. (1976, 1979)) that the field strength parameter E is of major importance in this work, determining whether or not a particle will be enabled to reach the filtering surface and hence whether or not a clear 1981 American Chemical Society
