Dispersion of Liquid in a Column Packed with Screen Cylinders Bih H. Chen', Barid B. Manna', and John W. Hines' Department of Chemical Engineering, Noca Scotia Technical College, H a l i f a x , Nova Scotia, Canada Radial and axial dispersion of liquid in a single-phase flow through a column packed with open-end screen cylinders were measured as a function of liquid flow rate and packing characteristics using a point injection technique and a transient response technique, respectively. Results show that radial dispersion coefficient increases linearly with liquid flow rate. It also increases with increasing wire diameter and mesh number, but decreases with increasing packing dimension over the range of variables studied. A correlation
is presented for radial dispersion coefficients as a function of the Reynolds number, u p / d m p and the ratio, d,./d,. The experimentally obtained residence-time distribution curves were interpreted by means of a one-dimensional dispersion model. The axial dispersion coefficient was found to increase with increasing liquid flow rate and packing dimension, but it was insensitive to the change of packing mesh number from 8 to 14 meshes/in.
I t has been reported recently that on addition of openend screen cylinders t o a gas-solid fluidized column (Chen and Osberg, 1967a; Ishii and Osberg, 1965; Sutherland et al., 1963) or to a gas-liquid bubble column (Chen and Vallabh, 1970; Voyer and Miller, 1967), the growth of bubbles in the column becomes restricted. As a result, better contact between the dispersed and the continuous phases is achieved in screen-packed columns than in conventional fluidized beds or bubble columns. The screen packing has also been tested for effectiveness in reducing coalescence in a spray-type liquid extraction column. In a preliminary study, Odedra (1970) reported a significant increase in the mass transfer coefficient and dispersed phase holdup because of the addition of screen cylinders to a spray column. At very high dispersed phase flows, the continuous phase in a screen-packed bubble column or a screen-packed liquid extraction column may become completely mixed. At very low dispersed phase flows, however, the bubble or drop appears only occasionally; the flow of the continuous phase may then be regarded as approaching a single-phase flow through a bed of screen cylinders. A knowledge of both these limits is needed in understanding the mixing behavior in a packed bubble column or a spray column. The present paper is concerned with the second limit-Le., the turbulent diffusion of a liquid in a column filled with wirescreen cylinders. Injection of methylene blue solution from a continuous source into the bed was used for the determination of radial mixing. The axial mixing was measured using a transient response technique. Chen and Osberg (196713) reported data on gaseous eddy diffusivity in a screen-packed column. They found screen packing suppressed the radial mixing as compared with an unpacked column. The effect of wire screen on the flow behavior of a fluid stream in empty tubes was investigated by Schubauer
' To whom correspondence should be addressed. 'Present address, Shell Canada Ltd., P.O. Box 100, Calgary 1 2 , Alberta, Canada
(1935), Towle et al. (1939), Dryden and Schubauer (1947), and Maisel and Sherwood (1950). The work of Towle et al. indicated a marked reduction of eddy diffusivity in a region within 50 tube diameters from the screen. Dryden and Schubauer succeeded in reducing turbulence in their wind tunnel by inserting a fine mesh wire screen perpendicular to flow, and they noted that wire screens could be used either as a turbulence generator or a turbulence damper depending upon their properties. Radial mass transfer in beds of solid particles was studied by Bernard and Wilhelm (1950), Plantz and Johnstone (1955), and Fahien and Smith (1955) a t high Reynolds numbers, and by Roemer e t al. (1962) and Dorweiler and Fahien (1959) a t low Reynolds numbers. I n these cases, the Peclet number (ud,/D,) was found to be constant a t approximately 12 for fully developed turbulent flow. Numerous works dealing with axial mixing problems in packed beds have been reported. When a fluid is flowing through a packed bed of solid particles, the variation in the local velocity causes a dispersion in the direction of flow. McHenry and Wilhelm (1957), Cairns and Prausnitz (1960), and Hiby (1962) have shown that the Peclet number ( u d , l D L ) approaches 2 for fully developed turbulent flow. Experimental for Radial Mixing Studies
Figure 1A shows a schematic diagram of the experimental apparatus. The column was made from a Plexiglas tube, 6 % in. in i.d. and 5 ft long. The lower 4 in. of the column was packed with 54-in. Raschig rings to serve as the calming section. The tracer injection tube. 3/16 in. in i d . was streamlined a t the top and entered the bed through a porous plate which supported the packing. In all runs, the injection tube terminated a t a point 44. in. above the porous plate. The bed was carefully packed by dropping the cylinders, one a t a time. from the top. The packed height above the tip of the injection tube was kept a t 2212 in. for Ind. Eng. Chem. Process Des. Develop., Vol. 10, No.3, 1971
341
Thus, a plot of In (C/C,) vs. r2 gives a straight line with a slope of ( - u / 4 zD,), from which the value of D,can be evaluated. I n the present study, concentration transverses were made across two perpendicular diameters a t the same height above the injection tube. Figure 2 shows a typical smoothed concentration profile for a liquid flow rate 0.057 ftisec. Figure 3 shows the same data plotted in accordance with Equation 3. The linearity is good and D, can be determined with satisfactory accuracy.
Table I. Physical Properties of Screen Packings Meshlin
8 10 14 10 10 10 10
d,, i n x in
dw, in.
t
x 1, 12 x I, 1, x ’ 2 51 x 3 4 j 4 x 34 3 4 x 34 1x1
0.025 0.025 0.025 0.025 0.035 0.047 0.025
0.985 0.975 0.970 0.980 0.975 0.965 0.980
1,
Discussion
Experimental results are plotted as Figures 4-6 and cover the following ranges of variables: Water flow rate: Mesh number: Packing dimension: Wire diameter:
Figure 1. Flow diagram (A) radial dispersion study (6) axial dispersion study A, Water inlet; B, Tracer inlet; C, Conductivity cell; D, Drain; E, Solenoid valve; P, Packed section; R, Rotameters; 5, Sampling
all runs. The physical properties of the cylindrical packing are listed in Table I. Water was used as the main fluid and methylene blue solution as the tracer. Their flow rate was metered by calibrated rotameters. For each water flow, the tracer injection rate and the sampling rate were adjusted to equalize the velocity inside these tubes with the velocity in the column. Samples of water-dye mixture were taken from the top of the packed bed through a 3/16-in. i.d. Pitot tube. The tip of the Pitot tube terminated ?4 in. above the packing. Samples were analyzed by means of-a Fisher ac model electrophotometer coupled with a red filter. The water temperature was essentially constant a t 19”C.
2 to 10 gpm 8, 10, and 14 meshesiin. K x 1/2, 3/4 x 3/4, and 1 x 1 0.025, 0.035, and 0.047 in.
Effect of Liquid Flow Rate and Mesh Number. The effect of liquid flow on the radial mixing coefficient D , is shown in Figure 4. The corresponding data for unpacked tubes obtained in this study are also presented for comparison. In line with similar data for packed beds of solid particles, the present results show a linear relationship between Doand the interstitial velocity, u. I n addition, the presence of screen packing suppresses the diffusivity in an empty tube, in contrast to a packed bed which shows a large improvement of radial mixing over an empty tube because of solid packing. Figure 4 also shows the effect of mesh opening on eddy diffusivity; D, increases with decreasing mesh opening. Screen cylinders of close mesh are known to behave like solid-wall cylindrical rings in a flow system, while screen cylinders of wide mesh may be viewed as consisting of an assemblage of widely separate wires (Chen and Osberg, 1967b). I t may therefore-be expected that the increase
7-
6-
Procedure and Data Analysis 5-
At steady state, the diffusion-convection process of a tracer introduced continuously from a point source into the center of a liquid stream is described by
4-
. 0 U
u 3-
The solution to Equation 1 with no wall boundary and negligible axial dispersion was provided by Wilson (1904). The solution is
(m)
C ---4uR2 _ c, ZD,exp -ur2
2-
1-
which may be written as
01
I
-2
(3) 342
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
I
-1
I
0 r, in.
I
I
+I
*2
Figure 2. Typical concentration profile
in mesh number should increase the radial mixing in a screen-packed column. Effect of Wire Diameter. The effect is shown in Figure 5 for y2-in. screen packing. For a given flow rate and packing size, D,increases with increasing wire diameter. I n the present study the wire diameter was varied for 0.025 to 0.047 in. and hence the area of the packing open to flow decreased by about 14%, thereby enhancing the tendency of the packing to behave as a solid object. A result of the more solid-like behavior is to increase fluid mixing in the radial direction. 8
6
\
dm =
dn
= 0.025 = 0.5
u
= 0 . 0 5 6 5 ft./sec
dw
\e
4
@\
0
\*
2
8
\
0 U \
U
1.0
-
I n addition, wires themselves also cause flow splitting and hence contribute to the overall radial mixing. The extent of this contribution varies in proportion to the size of the wire. Effect of Packing Size. Liquid diffusivities were measured for %-in. %-in., and 1-in. screen cylinders made from 10-mesh/in. wire cloth with a uniform wire diameter of 0.025 inch. The results shown in Figure 6 indicate that the eddy diffusivity increases with decreasing packing dimension. This finding is not in line with the result for packed beds of solid packing. For example, Bernard and Wilhelm (1950) and Roemer et al. (1962) have reported that D, in a packed bed of solid particles increases with increasing particle size. Therefore, it may be concluded that the nominal dimension of a hollow porous-wall packing such
-
-
Experimental E q . ( 3 ) with
D ~ 3= . 8 4 x ft?/sec. 1.0
lo
"
-
f \.a cy.
-
8
-
T
6
O.6
-
0
0
4
1
1
1
0.8I
I
, O \ 1.6 \\
1.2 I
2.0
0.4
-
0.2
-
2
0.4
0
r2, i n 2
Figure 3. Method of plotting data
0
/
2
6
4
8
10
u x 102, ft./rec.
Figure
5. Effect of wire size on radial dispersion
1.2
1.0
1.0
Y
0.8
2 .8
-
"
-.6
: . 6
d m = 10 d w =a025
-
/O'
112 314
4A I
\ n.
*0'
dn
0
-
(Y.
x
s
0
0
-J-
0,
-
",4
0.4
0
0.2
0.2
0
I
I
I
I
2
4 ux
6
8
-
I
10
io2, ft. / r e < .
Figure 4. Effect of mesh number on radial dispersion
0
I
2
u
I
4 6 x l o 2 , ft./rec.
I
8
10
Figure 6. Effect of packing dimension on radial dispersion
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971 343
as a screen cylinder is not the proper factor characterizing its geometry with respect to transport phenomena. For a gaseous system, Chen and Osberg (196713) have presented a satisfactory correlation of eddy diffusivity as a function of N R e mand d,/d, on the assumption that packing size has no effect on D,. However, the effect of packing size could have been masked by the variation in other factors such as wire diameter or packing mesh number. Correlation of Results. Considering the results presented and the possible effect of fluid properties on flow pattern, we propose D, as DaaU'l = fi (d,,d,,d,,
~,p,p)
or
Dn = f ( N ~ e , d & / d J (41 Here, the scale of turbulence, 1, is assumed to be proportional to mesh opening of the screen, and the radial fluctuating velocity of the liquid stream, L" is assumed to be a function primarily of the mean liquid velocity, u. The Reynolds number, defined as ( u p / g d m ) is , intended to characterize the turbulence in the column. I t s use is arbitrary because p and g have not been varied. Figure 7 shows the experimental results presented as the diffusivity, D, vs. the Reynolds number, NRe for the ranges of variables indicated. A family of parallel and straight lines with the ratio d,/d, as the only parameter is obtained. The quantitative effect of d,/d, can be incorporated to give D n = a(N&,m)'(diL/dn)' (5) with CY, p, and y having the values of 0.182 x 0.97, and 1.58, respectively, Figure 8 shows the final correlation. Experimental Method for Axial Mixing Studies
Figure 1 B schematically represents the experimental apparatus. The column was made of a Plexiglas tube, 2% in. in i.d. and 7 ft long. City water was introduced to the top of the packing from a shower-type liquid distributor. A packed height of 4 % ft. was used.
0.1N KC1 solution was used as tracer. Its flow was always less than 1% of the water flow. The step change of tracer concentration was generated a t the water inlet by the instantaneous opening and closing of a solenoid valve located near the liquid distributor. An electrical conductivity cell was used in conjunction with a fast-response recording system to monitor the tracer concentration of the effluent.' The conductivity probe was identical to that used by Chen and Douglas (1969). T h e recording system consisted of a single channel carrieramplifier (HP8805A), a Honeywell strip-chart recorder and accessories. The carrier-amplifier unit received a signal from the probe and delivered it to the recorder along with a starting pip which was electronically placed on the recorder chart when the solenoid valve was turned off. This determines the point t = 0. To make a run, the instruments were turned on and allowed to warm up. The flow of water was started and the flow of tracer was adjusted to obtain full recorder output at a given attenuator setting. When steady state was reached the solenoid valve was de-energized, automatically placing a spike on the recording chart. The breakthrough curve for the purging step was thus recorded. The curve was converted to a dimensionless plot of C/C, vs. t i 0 with 0 calculated from
The dimensionless curve was then transferred to a semilogarithmic plot on which the solution of the dispersion model (Brenner, 1962) was also plotted for a number of values of u z / D L . The value of this mixing parameter that gave the best fit t o the experimental line was designated as the mixing parameter characteristic of the experimental system (Figure 9). The best fit was determined using least squares. The error involved in this procedure was believed to be less than 10%. Discussion
A typical experimental breakthrough curve is shown
r
I
dwldn
-k
0.0627
0 0.0516 0 0.05 A 0.033
+/n
1.01
/
/ 0.8
-
Y
I "2.6
-
I
's!
x
x.4
0.2
-
-
I A/-
10
2
4
6
8 100
0
I 0.1
I
0.2
I
0.3
I
0.4
NRe,m
Figure 7. Relations between radial dispersion coefficient and Reynolds number 344
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
Figure
8. Correlation of results
I
0.5
1.0
Table II. Axial Mixing Results d,:
0.8
14
W a t e r flow
Run
dn : t / 2 1 : 0.25 GPM Experimental ; Theoretical . 510%
no.
Gpm
1 2 3 4 5
0.25 0.46 1.0 2.0 3.0
6 7 8 9 10
0.25 0.46 1.0 2.0 3.0
.
Npe= 3 6
-.
0.6
Ft/sec
d, =
0 U \
U
0.4
12
0 0.7
0.9
0.8
1.0
1.1
1.2
Figure
9. Typical residence-time distribution curve
11 12 13 14 15
0.25 0.46 1.0 2.0 3.0
10
16 17 18 19 20
6 -
4-
2
--
d
-
N >
2 1.0 -
0 -
X
~
0
8
-
6 -
0.8
1.0
2
4
6
8 1 0
20
u x 1 0 2 , ft./sec.
Figure 10. Effect of packing dimension, mesh number, and liquid flow rate on axial dispersion
in Figure 9 for 10-meshiin. packing. I t is seen that the residence-time distribution curves of the experimental and the theoretical calculated from the dispersion model with the mixing parameter obtained by the procedure already outlined are in good agreement. Therefore, use of the dispersion model for data analysis in this study is justified. The axial mixing rate was expressed as an axial dispersion coefficient, DL. The values of DL are tabulated in Table I1 and also presented as Figure 10 as a function of packing size, mesh number, and liquid flow rate. Consistent with results obtained in packed beds of solid particles, the present data show a linear variation of DL with the interstitial velocity u. I t is interesting to see that the %-in. screen cylinder gives approximately the same degree of axial mixing as in a packed bed of %-in. spheres. Figure 10 also shows that DL is not sensitive to the
' 2
5, in., d, 0.014 0.0258 0.0558 0.11 0.168
0.25 0.46 1.0 2.0 3.0
320.5 173.0 79.5 40.8 26.9
0.0133 0.0246 0.0537 0.105 0.16
331.0 174.0 82.5 41.6 27.2
0.0129 0.0245 0.0517 0.102 0.156
in., d, = 8 mesheslin.,
0.0137 0.0253 0.0547 0.108 0.165
d, =
8-
ft'/sec
36 36 39 40 41
3.92 7.26 14.6 27.8 41.1
in., d, = 10 meshes/in., z = 4.25 ft 0.0138 0.0256 0.055 0.109 0.166
d, =
1.3
t/e
N,,
ft/sec
in., d,, = 14 meshes/in., z = 4.25 ft
0.014 0.0256 0.056 0.11 0.169
d, = 0.2
D I X lo',
u = z/s,
0, sec
336.6 180.0 86.0 43.1 27.7
L
39 39 38 37 42
3.51 6.65 14.5 27.8 39.6
= 4.25 ft
0.0127 0.0237 0.0496 0.098 0.154
40 42 42 41 42
3.37 6.0 12.5 25.5 39.0
= 10 meshesi in., z = 4.25 ft
335.0 187.0 86.3 44.3 27.8
0.0127 0.0229 0.0494 0.0964 0.0153
20 19 21 22 23
6.75 12.8 25.0 46.5 70.5
change of packing mesh number from 14 to 8 meshes/ in. It has already been reported that the radial mixing in a screen-packed bed is affected considerably by mesh number (Figure 4); it increases with increasing mesh number. Since in packed beds any improvement in the radial mixing should result in a corresponding reduction of axial mixing, the 14-meshiin. packing should therefore reduce the axial mixing to a greater extent than the 10- or ,%mesh/ in. packing. However, the present data do not show such a trend, probably because the present method of data analysis is not adequate to detect this reduction of axial mixing. The effect of packing dimensions on DL was also discernible from Figure 10. Much higher coefficients were obtained for %-in. than for %-in. packing. This result is obviously consistent with the data for radial mixing shown in Figure 6. Nomenclature
C C,
D, DL d, d, d, NRW
NPt!
R
r t U
z
tracer concentration, lb/ ft3 average tracer concentration, lb/ft3 radial dispersion coefficient, ft2/sec axial dispersion coefficient, ft2/sec mesh number, meshiin. packing dimension, in. x in. wire diameter, in. Reynolds number defined as up/d,p, dimensionless Peclet number u z / 4 DL, dimensionless column radius, f t radial distance, f t time, sec liquid velocity, ft/sec axial position, f t
Greek Letters p
= viscosity, lb/ft sec
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
345
= liquid density, lb/ft3 0 = average residence time, sec
p
literature Cited
Bernard, R. A., Wilhelm, R. H., Chem. Eng. Progr., 46, 233 (1950). Brenner, H., Chem. Eng. Sci., 17, 229 (1962). Cairns, E. J., Prausnitz, J. M., Chem. Eng. Sci., 12, 20 (1960). Chen, B. H., Douglas, W. J. M., Can. J . Chem. Eng., 47, 113 (1969). Chen, B. H., Osberg, G. L., ibid., 45, 46 (1967a). Chen, B. H., Osberg, G. L., ibid., 90 (1967b). Chen, B. H., Vallabh, R., Ind. Eng. Chem. Process Des. Develop., 9, 1 2 1 (1970). Donveiler, U. P., Fahien, R. W., AIChE J . , 5, 139 (1959). Dryden, H. L., Schubauer, G. B., J . Aero. Sci., 14, 221 (1947). Fahien, R. W., Smith, J. M., AIChE J., 1, 28 (1955). Hiby, J. W., Paper C71, “Symposium on the Interaction between Fluids and Particles,” London, England, June 1962.
Ishii, T., Osberg, G. L., AIChE J . , 11, 279 (1965). Maisel, D. S.,Sherwood, T. K., Chem. Eng. Progr., 46, 131 (1950). McHenry, K. W., Wilhelm, R. H., AIChE J., 3, 83 (1957). Odedra, D. A., B. Eng. Thesis, Nova Scotia Technical College, Halifax, Nova Scotia, Canada, 1970. Plantz, D. A., Johnstone, H. F., AIChE J . , 1, 193 (1955). Roemer, G., Dranoff, J. S., Smith, J. M., Ind. Eng. Chem. Fundam., 1,284 (1962). Schubauer, G. B., NASA Tech. Rept. 524, 1935. Sutherland, J. P., Vassilatos, G., Kubota, H., Osberg, G. L., AIChE J., 9, 427 (1963). Towle, W. L., Sherwood, T. K., Sedar, L. A., Ind. Eng. Chem., 31, 462 (1939). Voyer, R. D., Miller, A. I., paper presented to the 17th Canadian Chemical Engineers Conference, Niagara Falls, Ontario, Canada, Oct. 18, 1967. Wilson, H. A., Proc. Cambridge Phil. Soc., 12, 406 (1904). RECEIVED for review June 4, 1970 ACCEPTED February 19, 1971
Miniature Liquid Cyclones Effects of Fluid Properties on Performance Jan Wag nerl Arctic Health Research Center, U .S . Department of Health, Education, and Welfare, College, Alaska 99701
R. Sage Murphy Institute of Water Resources, University of Alaska, College, Alaska 99701 From experimental work on small, glass, liquid cyclones, the cyclone energy requirements and solid elimination efficiencies a t a given capacity are given by simple equations. These relationships are similar to those developed earlier for both large- and smalldiameter units. However, in addition to cyclone geometry, the equations developed in the present work include the variables of liquid viscosity and density. These fluid properties are also incorporated in cyclone Reynolds numbers which can serve as valuable comparative tools for evaluating cyclone performance and estimating design and operating variables.
Liquid cyclones continue to gain prominence in mass transfer operations. They have been used as thickeners, classifiers, washers, liquid-liquid separators, gas-liquid separators, and mass transfer promoters. Standout virtues are low capital cost and the ability to make fine separations and to deliver a gross separation at high overflow rates. The theory of cyclone design and operation appears throughout the literature as do empirical and theoretical relationships for energy requirements and solid elimination efficiencies. These relationships have accounted for cyclone geometry, operating conditions, applied energy, and physiPresent address, Institute of Water Resources, University of Alaska, College, Alaska 99701. To whom correspondence should be addressed. 346
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 3, 1971
cal properties of the fluid and solids. However, experimental basis for the effects of liquid viscosity and density on cyclone operation is meager. Many investigators have neglected these properties or have assumed the validity of Stokes’ law. Bradley (1965) points out that a liquid viscosity term does not enter into the relationship for pressure drop. The present work deals with the effects of liquid viscosity and density on the flow capacity and solid elimination efficiencies of liquid cyclones less than one inch in diameter. I n addition, empirical correlations for energy requirements and solid elimination efficiencies are derived. These relationships take into consideration cyclone geometry, operating conditions, and physical properties of the solid and liquid phases.
