Ind. Eng. Chem. Res. 1993,32, 1235-1238
1235
Natural Convection Mass Transfer at a Fixed Bed of Cylinders Gomaa H. Sedahmed,’ Rouchdy R. Zahran,t and Ibrahim Hassan Chemical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt
The free-convection mass-transfer behavior of fixed beds of randomly packed cylinders (aspect ratio = 1) has been investigated experimentally using an electrochemical technique involving the measurement of the limiting current for the cathodic deposition of copper from acidified copper sulfate solutions. Variables studied were physical properties of the solution, cylinder diameter, and bed height. The data were correlated for the ranges 0.17 X 108 < Sc X Gr < 0.23 X lolo,0.256 < d/h < 1,and 1700 < Sc < 2150 by the equation Sh = 0.31(Sc X Gr)0.32(d/h)0.12. The height effect was explained in terms of the presence of two opposing effects in the bed, namely, a concentration field and a velocity field.
Introduction In view of their high area per unit volume, fixed beds are being used in building chemical and electrochemical reactors used to conduct liquid-solid diffusion-controlled reactions. To increase the degree of conversion per pass during the continuous operation of these reactors, a low solution flow rate is used. At such low flow rates naturalconvection mass transfer contributes significally to the overall rate of mass transfer and the rate of the reaction (Tobias and Hickman, 1965). Accordingly, the rational design and operation of such reactors requires a knowledge of the natural-convection mass-transfer behavior of fixed beds. Although some work has been done on naturalconvection heat transfer in porous media (Hardee and Nilson, 1977;Rhee et al., 1978;Buretta and Berman, 1978; Busse and Joseph, 1972; Elder, 1967) in view of its importance to applications such as oil drilling, design of porous insulation for nuclear power reactor core, and storage of radioactive waste material, little has been done on the natural-convection mass-transfer behavior of porous media. Previous studies on natural-convection mass transfer at packed beds include those of Mandelbaum (1971)and Karabelas et al. (1971);in both cases onlysingle particles of the bed were active while the rest of the bed was inactive. Mandelbaum (1971) used a fixed bed of Raschig rings while Karabelas et al. (1971) used spheres. Sedahmed and Shemilt measured natural-convection mass-transfer rates at horizontal (1976) and vertical (1985) arrays of stacked screens. The authors found that the mass-transfer coefficient at horizontal beds of screens deviates by a maximum of 25 5% from that of a single screen while the mass-transfer coefficient at vertical stacks deviates by a maximum of 105% from that of a single screen. Gabitto and Bohm (1981) studied rates of naturalconvection mass transfer at a fixed bed of spheres and screens by an electrochemical technique involving the measurement of the limiting current of the cathodic reduction of potassium ferricyanide using a cell whose anode was placeddownstreamof the bed; i.e., the directions of current and flow are parallel (flow-through configuration). The authors correlated their data for the range 6.24 X 103 < Sc X Gr < 3.03 X 108 by the equation Sh = 0.228(Sc X Gr)0.32(rh/d)0.22
(1)
The hydraulic radius rt, was used as a characteristic length in calculating Sh and Gr.
* Author to whom correspondence should be addressed.
+ Present address: Chemical Engineering Department, Qatar University, Doha, Qatar.
The object of the present work is to study the freeconvection mass-transfer behavior of fixed beds built of randomly packed cylinders (aspect ratio = 1). To this end the mass-transfer coefficient was determined by measuring the limiting current of the cathodic deposition of copper on a fixed bed of copper cylinders from acidified copper sulfate solution. This system is superior to the cathodic reduction of potassium ferricyanide in studying natural convection (Selman and Tobias, 1978). A cylindrical copper anode surrounding the bed was used; i.e., the directions of current and natural convection are perpendicular (flow-byconfiguration). This c o n f i a t i o n is preferred from the industrial point of view to the flowthrough configuration (Heitz and Kreysa, 1986);the flowby configuration allows large residence times, high conversions per pass, and more uniform potential distribution if properly designed.
Experimental Technique Figure 1shows the cell and electrical circuit. The cell consisted of a 7.5-L cylindrical plastic container of 25-cm height and 20-cm diameter. The fixed bed cathode was built of randomly packed copper cylinders of aspect ratio = 1placed in a perforated plastic basket of 9.5-cm diameter and 7.5-cm height. The basket was fabricated of a plastic mesh of 0.5-cm square opening. The basket was held in position by suspending it by two plastic arms fixed to a Plexiglas cover resting on the top of the cell. The bottom of the basket was 7 cm from the cell bottom. Beds of cylinders of different diameters and heights were used cylinder diameters used were 0.7,0.95,1.43, and 1.92 cm while bed heights used ranged from 0.7 to 7.5 cm. The fixed bed cathode was surrounded by a cylindrical copper anode of 17-cm diameter. The electrical circuit consisted of a 6-V dc power supply with a voltage regulator and a multirange ammeter connected in series to the cell. Electrical current was fed to the bed through an insulated copper wire brazed to one of the packed bed cylinders. Before each run, cylinders forming the bed were treated as mentioned elsewhere (Wilke et al., 1953) and 5 L of acidified copper sulfate solution was placed in the cell. Current-potential curves from which the limiting current was obtained were constructed by increasing the current stepwise and measuring the steady-state cathode potential by means of a potentiometer; cathode potential was measured against a reference copper electrode placed in the cup of a Luggin tube containing a solution similar to the cell solution. The tip of the Luggin tube was placed in the middle of the fixed bed cathode. Four different concentrations of CuSO4
0SS8-5885/93/2632-~235$04.oo/o0 1993 American Chemical Society
1236 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 Potentiometer
Cylinder dlam.=0.7 CuSOL 200
Luggin tube w i t h
cm
Conc. > M
-
VI
\
Current feeder
6
ma 1 5 0 c
Fixed bed top
X Y
fixed bed botto
100
> 2
3
L
Bed height, cm
Figure 3. Effect of bed height on the maas-transfer coefficient. CuSOL Conc.,M 6 Volf d.c power supply with a voltage regulator
0
Figure 1. Apparatus. Cylinder
CuSO,
diameter
6ol
0.7 c m
Conc.: O.OL98
M
B e d height I cm
0.027
0
O.OL98
A
0.0966
x
0.189
X
50
'I
0;
:J A
/
50
100 Cathode potenliol, m V
(50
2 00
Figure 2. Typical polarization curves for different bed heights.
were used, namely, 0.027,0.0498,0.0966, and 0.189 mol/L. In all cases 1.5 mol/L H2S04 was used as a supporting electrolyte. All solutions were prepared from analytical reagent grade chemicals and distilledwater. Temperature was 22 f 1 OC. Each experiment was conducted twice. Preliminary experiments using plastic basketa of different opening size to accommodate the bed showed that the opening size had a negligible effect on the limiting current and the mass-transfer coefficient at the fixed bed.
Results and Discussion Figure 2 shows typical polarization curves from which the limiting current was determined and used to calculate the mass-transfer coefficient from the equation
K = IIAZFC (2) Figure 3 showsthe effect of bed height on the mass-transfer coefficient. The observed decrease in the mass-transfer coefficientwith bed height shown in Figure 3 is consistent with the finding of Sedahmed and Shemilt (19761, who studied natural-convection mass transfer at fixed beds of horizontal screens. The decrease in mass-transfer coefficient with bed height is the outcome of two opposing effects as outlined by Marsters (1972) and Smith and Wragg (19741, who studied natural-convection heat and
ISc.Gr 1
0.31
Figure 4. Sh vs (SCX Gr)o.*l.
mass transfer at vertical arrays of separated horizontal cylinders, respectively. According to these authors, as the uprising natural convection stream moves past the cylinders it loses Cu2+,i.e., becomes less dense, and consequently ita velocity increases. The increase in solution velocitywithbed height tends to increasethe mass-transfer coefficient while the decrease in Cu2+concentration has the opposite effect. It seems that in the present case the reduced Cu2+concentration dominates over the enhanced velocity thus causing a decrease in the mass-transfer coefficient with bed height. An overall mass-transfer correlation was envisaged in terms of the dimensionless groups Sh, Gr, and Sc usually used in correlating freeconvection mass-transfer data. The physical properties used in calculatingthese dimensionless groups were taken from the literature (Wilke et al., 1953; Eisenberg et al., 1956),and cylinder diameter was used as a characteristic length in calculating Sh and Gr. Figure 4 shows that the data for the conditions 1.7 X lo7 < Sc X Gr < 2.3 X los, 0.256 < d / h < 1, and 1700 < Sc < 2150 fit the equation
Sh = 0.28(Sc X Gr)Oa31 with an average deviation of 8.4%.
(3)
An improved correlation was obtained when an extra dimensionless group (dlh) was used to account for the effect of bed height. Figure 5 shows that the data fit the equation
Sh = 0.31(Sc X Gr)0*32(d/h)0.'2
Sh = 0.32(Sc X Gr)'.= (5) which is valid for the conditions 2.3 X 108 < Sc X Gr < 1.7 X loll. For natural convection at a vertical cylinder with active ends, the data can be fitted for lo7 < Sc X Gr < 10l2 by the equation (Krysa and Wragg, 1992)
+ 0.53(Sc X Gr)0.25e
0
(6)
According to previous studies on the effect of inclination on natural-convection mass transfer (Quaraishi and Fahidy, 1978; Sedahmed and Shemilt, 19821, it is expected that the mass-transfer coefficient at inclined cylinders with active ends will assume a value between that of the vertical position and the horizontal position. A comparison between eq 4 and eqs 5 and 6 shows that the mass-transfer coefficient is higher in the case of fixed beds where the flow is highly unstable compared to that at a single cylinder in different positions. The turbulent nature of the flow inside the bed may be ascribed to the enhanced velocity effect as the solution rises in the bed as mentioned before. Another way of explainingthe deviation of the bed behavior from the single cylinder behavior is to visualize the bed as a series of porous horizontal layers; in view of previous studies on free convection a t upward-facing horizontal surfaces (Sedahmed and Nirdosh, 1991; Fenech and Tobias, 1960;Wragg, 19911, it could be expected that within the present (Sc X Gr) range the flow would be turbulent at the upward-facing surface of eachlayer. This turbulent
0.027 0.&98 0.0966
-
A
60
50
-
x o * 1 8 9
(4)
with an average deviation of 6 7%. The (Sc X Gr) exponent of eq 4 is in a close agreement with the value obtained by Gabitto and Bohm, who used fixed beds of screens and spheres in their study (eq 1). Equation 4 shows that cylinder diameter has a negligible effect on the mass-transfer coefficient, which is consistent with the turbulent nature of the flow inside the bed as revealed by the (Sc X Gr) exponent of 0.32. A comparison between eq 1 and eq 4 shows that eq 1 implies that bed height has no effect on the mass-transfer coefficient. The absence of bed height effect from eq 1may be attributed to the fact that Gabitto and Bohm used relatively shallow beds (the maximum bed height used by these authors was 2.6 cm compared to 7.2 cm in the present work). Under such conditions, the effect of velocity increase with bed height on the mass-transfer coefficient is probably balanced by the decreased concentration effect. Equation 4 predicts higher mass-transfer coefficients than those obtained by eq 1. The discrepancy may be attributed to (i) the difference in the packing geometry, (Gabitto and Bohm used spheres and screens as packing material while the present work uses cylinders as packing material) or (ii) the difference in the (Sc X Gr) range (Gabitto and Bohm covered the range 6.24 X 103-3.03 X los compared to 0.17 X 10ko.22 X 1010 used in the present work). Previous studies on natural convection heat and mass transfer (Selman and Tobias, 1978) have shown that the geometry of the transfer surface and the (Sc X Gr) range affect the coefficient and the exponent of the heat- or mass-transfer equation. It would be of interest to compare eq4 with the equations obtained for asingle cylinder with active ends. For natural convection at a horizontal cylinder, Sedahmed and Nirddosh (1990) obtained the equation
Sh = Sh,
o
Lot
r' J .X
Figure 5. Overall mass-transfer correlation.
flow intensifies inside the bed as it moves upward by virtue of the enhanced velocity effects. To substantiate this explanation, mass-transfer data at a single layer of packed cylinders were correlated as shown in Figure 6. The data for the conditions 0.17 X los < Sc X Gr < 0.23 X lolo,1700 < Sc < 2150, and 0.7 cm L d L 1.92 cm fit the equation
Sh = O.O85(Sc X Gr)0*306 (7) The (Sc X Gr) exponent of 0.305 in the above equation shows that turbulent flow dominates in each layer. In the area of heat transfer Gabitto and Bohm (1981) reviewed previous experimental and analytical studies on natural-convection heat transfer in fixed beds. The data, which scatter widely, were found to lie between two asymptotes which can be represented for the range lo2 < Ra < lo6 by the equations
Nu = 0.19Ra0*69
(8)
and
Nu = 0 . 1 5 8 R ~ ~ . ~ (9) Most of the data lie closer to eq 9 than to eq 8. A comparison between eq 4 and eqs 8 and 9 shows that eqs 8 and 9 overestimate mass-transfer data. This discrepancy may be attributed to the difference in the range of Ra and the difference between the range of Sc and A. used in the present work and that used in in heat-transfer studies, respectively. Conclusions 1. The free-convectionmass-transfer behavior of packed beds of cylinders deviates considerably from single cylinder behavior. The rate of mass transfer at the fixed bed was much higher than that at a single cylinder in any position. 2. Mass-transfer rates within the bed were controlled by two opposing effects whose magnitudes depend on bed height, namely, the enhanced velocity effect and the diminishing concentration effect. 3. Under the present conditions where relatively large particles were used in building the fixed bed, mass is transferred by a turbulent flow mechanism. This advantage should be considered in designing and operating fixed bed electrochemical reactors used to conduct diffusioncontrolled reactions. In the continuous operation of such reactors, a low solution flow rate can be used to combine
1238 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993
Cylinder d l o m d c r , cm 2 1
0
0.7
X
0.95
A
1.L3
0
42
Log I S c . GrI
9
Figure 6. log Sh w)log Sc X Gr for a single layer of packed cylinders.
the high residence time and the high mass-transfer coefficient arising from turbulent flow natural convection.
Nomenclature A = bed area C, = specific heat C = bulk concentration of copper sulfate D = diffusivity of copper sulfate d = cylinder diameter F = Faraday constant g = acceleration due to gravity h = bed height I = limiting current K = mass-transfer coefficient k = thermal conductivity r,, = hydraulic radius 2 = number of electrons involved in the reaction Gr = Grashof number, gd9Aplvzp Nu = Nusselt number, hdlk A. = Prandtl number, Cpplk Ra = Rayleigh number (Gr X Pr) Sc = Schmidt number, 1.1lpD Sh = Sherwood number, KdlD 1.1 = solution viscosity Y = kinematic viscosity Ap = density difference between the bulk solution and interfacial solution p solution density
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