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Liquid-Solid Mass Transfer at a Fixed Bed of Lessing Rings, in Relation to Electrochemical Reactor Design I. Hassan, R. R. Zahran, I. S. Mansour, and G. H. Sedahmed* Chemical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt
The mass-transfer behavior of a fixed bed of Lessing rings, under single- and two-phase flow, was studied by measuring the limiting current of the cathodic reduction of the ferricyanide ion. Variables studied included ring diameter (d), solution flow rate, gas flow rate, physical properties of the solution, and the effect of drag-reducing polymers. The single-phase mass-transfer data were correlated for the conditions of 1390 < Sc < 4763 (where Sc is the Schmidt number, which represents a dimensionless kinematic viscosity/molecular diffusivity coefficient), 166 < Re < 722 (where Re is the solution Reynolds number, which represents a dimensionless flow parameter), and 1 cm < d < 1.4 cm by the equation Sh ) 1.57Sc0.33Re0.46 (where Sh is the Sherwood number, which represents a dimensionless mass-transfer coefficient). The two-phase mass-transfer data were correlated for the conditions 1390 < Sc < 4763, 144 < Re < 748, 60 < Reg < 818 (where Reg is the gas Reynolds number), and 1 cm < d < 1.4 cm by the equation Sh ) 1.93Sc0.33Re0.34Reg0.11. Polyox WSR-301 drag-reducing polymer was found to reduce the rate of mass transfer by an amount of 17.2%-32.7% for single-phase flow; for two-phase flow, the decrease in the rate of mass transfer was 27%-34%. Implication of the present results for the design and operation of electrochemical reactorssespecially those involving gas absorptions was noted. Introduction Application of electrochemical processing in fields where diffusion-controlled reactions occur in dilute solution, such as air and water pollution control, electroorganic synthesis, and the electrowinning of metals from low-grade ores has directed electrochemical engineering research toward more-efficient electrochemical reactors of high space time yield. From among the different designs that have appeared during the last few decades, the fixed-bed electrochemical reactor stands out as the most promising reactor, if properly designed. Previous studies have emphasized the use of low-porosity fixed beds that were composed of metal powder, metal felt, and metal foam, with the objective of increasing the specific area and the space time yield of the reactor. Unfortunately, such low-porosity beds suffer from several drawbacks:1 (1) They become clogged easily; in the case of metal deposition, this renders continuous operation impossible. (2) A high pressure drop and high pumping power consumption are associated with such low-porosity beds. (3) Gas bubbles, whether introduced externally or generated internally as a side reaction, are entrapped easily within the bed, with a consequent prohibitive increase in the cell resistance and electrical power consumption. To obviate these shortcomings, some work recently has been conducted on the performance of flow-by fixedbed electrochemical reactors that were composed of high-porosity packing material, such as screens, Rasching rings, and cylinders.2-4 Consistent with this trend, the objective of the present work is to examine the masstransfer behavior of a flow-by fixed-bed electrochemical * To whom correspondence should be addressed. Tel: (203) 597 1853.
reactor packed with Lessing rings. Despite the decrease in the specific area of the bed, as a result of using large particles, the high-porosity bed offers the following advantages: (1) It would be possible to conduct electrochemical reactions that are accompanied by gas absorption, such as the synthesis of hydrogen peroxide (H2O2) via the cathodic reduction of atmospheric oxygen,5 electrochemical flue gas desulfurization,6 alkene epoxidation,7 sodium dithionite production by cathodic reduction of sulfur dioxide (SO2), and hydroxylamine production via the electroreduction of nitric oxide.8 (2) Fixed-bed electrodes of high porosity would also tolerate electrochemical reactions that are accompanied by simultaneous gas evolution (H2 or O2), which is likely to occur in dilute solutions, without a high voltage penalty. (3) The high-porosity bed would allow the use of inert gas sparging as an inexpensive means of enhancing the rate of mass transfer;9,10 this would make it possible to use a low solution feed rate to increase the residence time and the degree of conversion per pass. The present work also is intended to study the effect of drag-reducing polymers on the rate of mass transfer at the fixed bed. The finding by Hanna et al.,11 that drag-reducing polymers could reduce the pressure drop across fixed beds that are comprised of relatively large particles, has made it potentially possible to use such polymers to reduce the pumping power and operating costs of fixed-bed reactors. Drag-reducing polymers work by damping the small-scale, high-frequency eddies;12 therefore, it is likely that they would adversely affect the rate of mass transfer. The extent to which the rate of mass transfer is reduced by the polymer will be revealed in this study. Lessing rings are modified Rasching rings, where the ring is internally bisected with a longitudinal baffle to
10.1021/ie040053f CCC: $30.25 © 2005 American Chemical Society Published on Web 06/25/2005
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Figure 1. Schematic diagram of the apparatus used in this work. Legend is as follows: 1, inlet section; 2, working section; 3, outlet section; 4, sintered-glass distributor; 5, perforated plastic disk; 6, anode; 7, cathode; 8, plastic screen separator; 9, plastic storage tank; 10, plastic centrifugal pump; 11, rotameter, 12, plastic valve; 13, air compressor; and 14, electrical circuit.
increase the ring area. Although Lessing rings retain all the advantages of Rasching rings, other than their specific area, they have received scant attention, in regard to the study of their gas-liquid and liquid-solid mass-transfer behavior. The present mass-transfer study was performed by measuring the limiting current of the cathodic reduction of potassium ferricyanide (FeK3(CN)6) in a large excess of sodium hydroxide (NaOH).13 Experimental Technique The apparatus (Figure 1) consisted of the fixed-bed reactor, a flow circuit, and an electrical circuit. The reactor, which consisted of a plexiglass rectangular duct with a cross section of 9 cm × 9 cm and height of 60 cm, was divided into three sections: the inlet section, the working section, and the outlet section. The bottom of the inlet section was fitted with a sintered-glass gas distributor. To avoid failure of the sintered-glass distributor, the packing of the inlet section was loaded on a perforated plastic plate that was fixed 1 cm above the sintered-glass distributor. The inlet section had a height of 25 cm and was packed with 1.6-cm-diameter glass spheres. The working section had a height of 10 cm and was packed at random with nickel-plated copper Lessing rings. Three ring sizes, with an aspect ratio of L/d ) 1, were used; the ring diameters were 1, 1.2, and 1.4 cm. The corresponding bed porosities were 0.82, 0.84, and 0.86, respectively. The working section was divided into three equal parts by two vertical perforated rigid plastic sheets. The middle portion acted as a cathode, while the other two components acted as anodes. The two anodes and the cathode were fed by electrical current through a vertical, insulated, nickel-plated copper wire. The high anode area (in comparison to the cathode area) and the use of a high ferrocyanide concentration (in comparison
to the ferricyanide concentration) allowed us to use the anode as a reference electrode to measure the limiting current. The electrical circuit consisted of a 12 V dc power supply and a multirange ammeter, whicht was connected in series with the cell. A high-impedance voltmeter was connected in parallel with the cell, to measure its voltage. Before each run, solution was circulated between the plexiglass storage tank and the reactor, using a 0.33 hp plastic centrifugal pump. The solution entered the reactor through a 1-in.-diameter inlet tube placed just above the perforated plastic bottom; a similar outlet tube was placed just below the top of the reactor. The solution flow rate was controlled by a bypass and was measured by means of a graduated cylinder and a stopwatch. In the case of two-phase flow, air was admitted to the reactor via a 1 hp compressor through the sintered glass bottom, and the superficial air flow rate was measured by a calibrated rotameter and controlled by a ball valve. Before determining the mass-transfer coefficient, the rings that formed the cathode were activated by cathodically evolving H2 on them from a NaOH solution, as mentioned elsewhere.13 The mass-transfer coefficient was determined under different conditions by measuring the limiting current of the cathodic reduction of FeK3(CN)6, using a solution that contained 0.025 M FeK3(CN)6, 0.05 M potassium ferrocyanide (FeK4(CN)6), and a large excess of NaOH as a supporting electrolyte (the NaOH concentration ranged from 1 M to 4 M). All solution were prepared using analytical-reagent (AR) grade chemicals and distilled water. Table 1 shows the physical properties of the solution used at 30 °C. Viscosity and density of the solution were measured using an Ostwald viscometer and a density bottle, respectively.14 The diffusivity of ferricyanide was taken from the literature.13,15 During each run, the temperature was measured and the physical properties of the solution were adjusted accordingly. To test the effect of drag-reducing polymers on the rate of mass transfer, Polyox WSR-301 (a product of Union Carbide) was used in the form of solid slurry, rather than in the form of a solution to minimize its shear degradation.16 The polymer powder has a density of 1.15-1.26 g/cm3, and the particle size ranged from 500 µm. The polymer was used as received, and no attempt was made to separate different sizes. Results and Discussion Figure 2 shows a typical current-voltage curve with a well-defined limiting-current plateau for single-phase flow. The limiting current obtained from these curves was used to calculate the mass-transfer coefficient K, according to the equation12
K)
I ZFAC
(1)
where Z is the number of electrons involved in the reaction, F represents the Faraday constant, and C denotes the concentration of ferricyanide. The bed area
Table 1. Physical Properties of Solutions Used at 30 ˚C solution 1 2 3
Solution Composition (M) FeK3(CN)6 FeK4(CN)6 NaOH 0.025 0.025 0.025
0.05 0.05 0.05
1 2 4
F (g/cm3)
solution viscosity, µ (x 102 g cm-1 s-1)
diffusivity, D (× 106 cm2/s)
Schmidt number, Sc
1.0544 1.0922 1.1611
1.0588 1.2636 2.053
7.197 6.031 3.712
1395 1918 4763
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Figure 2. Typical current-voltage curves at different solution velocities under single-phase flow. Conditions were d ) 1.2 cm, Sc ) 1918, and a solution velocity of (×) 2.34 cm/s, (O) 2.68 cm/s, (b) 3.15 cm/s, (*) 3.44 cm/s, (4) 4.2 cm/s, (9) 4.72 cm/s, and (y) 5.51 cm/s.
Figure 3. Effect of Re on Sh at different Sc values, for the conditions of d ) 1 cm and Sc ) (b ) 1390, (×) 1918, and (O) 4763.
(A) was obtained by multiplying the number of rings forming the cathode by the total ring area. Figure 3 shows that, for single-phase flow, the dimensionless mass-transfer coefficient (the Sherwood number, Sh) increases with the 0.46 exponent of the solution Reynolds number (Re). Figure 4 shows that the single-phase mass-transfer data for the conditions of 1390 < Sc < 4760 (where Sc is the Schmidt number, which represents a dimensionless kinematic viscosity/molecular diffusivity coefficient), 166 < Re < 722, and 1 < d < 1.4 cm (where d is the Lessing ring diameter), fit the equation
Sh ) 1.57Sc0.33Re0.46
(2)
with an average deviation of (7%. The ring diameter d was used as a characteristic length in calculating Sh and Re. The present Re exponent 0.46 agrees fairly well with the value of 0.5, which was predicted by the model
based on the concept of a series of developing boundary layers destroyed after traversing a distance equivalent to the length of a particle.17 The exponent 0.46 also agrees with the experimental value obtained by different authors, who used different packing geometries at relatively high Re values (Re > 55).18,19 From among previous studies, the present results can be compared with the data of Delaunay et al.20 and Mobarak et al.,4 in view of the experimental similarity with the present work where, in the three cases, inlet and outlet calming sections were used. Also, in the three cases, the electrochemical technique was used to measure the rate of mass transfer at an entire bed operated in the flow-by regime (the flow direction is perpendicular to the current direction). Studies using a single active particle embedded in an inert fixed bed and studies using flow through fixed beds (where the flow and current are parallel) were excluded from the comparison. Delaunay et al.,20 who used a fixed bed of spheres, correlated their
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Figure 4. Overall mass-transfer correlation, under single-phase flow, for Sc ) (b) 1.390, (O) 1918, and (4) 4763.
data for the conditions of Sc ) 1039, 10 < Re < 500, and d ) 0.4 cm, using the equation
Sh ) 1.3Sc0.33Re0.54
(3)
Mobarak et al.,4 who used a vertical array of closely packed screens, correlated their data for the conditions of 1250 < Sc < 8270, 0.6 < Re < 124, and 0.28 < dw < 1.2 mm by the equation
Sh ) 0.52Sc0.33Re0.54
(4)
The wire diameter (dw) was used as a characteristic length in calculating Sh and Re. Comparison of eq 2 with eqs 3 and 4 shows that, for a given solution velocity, the mass-transfer coefficient obtained from eq 2 is higher than that obtained from eq 4 and lower than that obtained from eq 3. The inferior performance of Lessing rings, compared to that of spheres, with regard to liquid-solid mass transfer, may be attributed to two factors: (i) unlike spheres, the effective surface area of the ring is less than the geometric surface area, because the inner surface of the rings receives less current than the outer surface, especially in the case of vertical and inclined cylinders; and (ii) the total surface of each sphere is subjected to a solution of uniform flow velocity, whereas, in the case of the rings, the flow conditions inside horizontal and inclined rings are far less energetic than the outer surface, because of the shielding effect of the outer surface. Current maldistribution inside and outside an active ring embedded in inactive bed has been confirmed experimentally by Sims et al.,21 who conducted a comparative mass-transfer study between a single hollow cylinder and a single solid cylinder, using the electrochemical technique. It should be emphasized that eq 2 can be used only for the design and operation of electrochemical reactors and should not be used in the design and operation of catalytic reactors where diffusion-controlled liquid-solid reactions occur. Current maldistribution inside and outside the rings, which is inherent to the electrochemical technique, would cause eq 2 to underestimate the rate of mass transfer in the case of catalytic reactions
where the rate of mass transfer is determined only by flow distribution inside and outside the rings. Figure 5 shows typical plots of log Sh vs log Re for different superficial gas velocities, whereas Figure 6 shows typical plots of log Sh vs log Reg (where Reg is the gas Reynolds number) for different solution velocities. The data fit the equations
Sh ) a1Re0.34
(5)
Sh ) a2Reg0.11
(6)
Figure 7 shows that the present two-phase data for the conditions of 1395 < Sc < 4763, 60 < Reg < 818, and 144 < Re < 748 fit the equation
Sh ) 1.93Sc0.33Re0.34Reg0.11
(7)
with an average deviation of (7% (many overlapping data points, which deviate slightly from the aforementioned equation, were omitted from Figure 7 for the sake of clarity). Ring diameter was used as a characteristic length in calculating Sh, Re, and Reg. Table 2 shows that, under the present range of conditions, for a given Re value, the enhancement ratio (Sh/Sh0) is in the range of 1.0451.33, depending on Re and Reg. The modest contribution of the gas phase to the enhancement of the rate of mass transfer, as shown by the Reg exponent 0.11 and the data in Table 2, may be attributed, in part, to the decrease in the gas holdup and the concentration of the turbulence-promoting bubbles, as a result of using high solution flow rates. High solution flow rates attenuate the enhancing effect of gas bubbles, such as decreasing the available solution flow area, radial momentum transfer, and diffusion layer disturbance through bubble collision with the ring surface. Delaunay et al.20 reported a higher enhancement ratio (Sh/Sh0 ) 1.13-3.33) for a fixed bed of spheres under the conditions of 0 < Reg < 30 and 15 < Re < 5000. Mobarak et al.4 also reported a higher enhancement ratio (Sh/Sh0 ) 1.05-3.1) for a vertical array of closely packed screens under the conditions of 1.4 < Reg < 77 and 1.1 < Re < 125. Besides
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Figure 5. Effect of the solution Reynolds number (Re) on Sh at different gas superficial velocities (air velocities of (b) 1.095 cm/s, (O) 2.24 cm/s, (4) 2.8 cm/s, (2) 3.4 cm/s, (0) 4.04 cm/s, (×) 4.64 cm/s, (K) 5.25 cm/s, and (9) 5.87 cm/s) for the conditions of d ) l cm and Sc ) 1918.
Figure 6. Effect of gas Reynolds number (Reg) on Sh at different solution velocities (solution velocities of (b) 2.42 cm/s, (O) 2.75 cm/s, (4) 3.29 cm/s, (2) 3.73 cm/s, (0) 4.29 cm/s, (×) 4.76 cm/s, and (K) 5.23 cm/s) for the conditions of d ) l.2 cm and Sc ) 1918.
the difference between the range of conditions used by previous studies and those of the present study, the difference in the packing geometry is also believed to be responsible for the higher enhancement ratio reported by Delauncy et al.20 and Mobarak et al.4 Although the total sphere surface used by Delaunay et al.20 and the screen surface used by Mobarak et al.4 are subjected to a uniform liquid-gas dispersion, only the outer surface of all the rings and the inner surface of the vertical rings are accessible to gas bubbles, whereas the inner surface of the horizontal and inclined rings is inaccessible to gas bubbles. The aforementioned results show that more information is needed, regarding the use of fixed beds in the rational design and operation of electrochemical and catalytic reactors. The following points deserve special attention:
(1) To asses the relative suitability of different packing geometries for building fixed-bed electrochemical reactors intended for gaseous reactants, more studies are needed on other operational aspects, such as pressure drop, gas-liquid mass transfer, axial dispersion, and electrical energy consumption. (2) To evaluate the mass-transfer behavior of Lessing rings in conducting catalytic liquid-solid reactions, another study using a different technique (such as the diffusion-controlled dissolution of copper rings in acidified dichromate25) is needed; this technique does not suffer from the effects of current distribution that accompany the electrochemical technique. Tables 3-5 show that the presence of a drag-reducing polymer reduces the rate of mass transfer in the case of both single-phase and two-phase flow. Table 3 shows that the percent decrease in the single-phase rate of
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Figure 7. Overall mass-transfer correlation, under two-phase flow, for Sc ) (O) 1390, (b) 1918, and (4) 4763. Table 2. Two-Phase Mass-Transfer Enhancement Ratio (Sh/Sh0) at Different Solution and Gas Reynolds Numbers (Re and Reg, Respectively)
Table 4. Effect of Reynolds Number (Re) on the Percent Decrease in the Mass-Transfer Coefficient K by the Drag-Reducing Polymer under Two-Phase Flowa
Sh/Sh0
a
% decrease in K
Reg
Re ) 255
Re ) 392
Re ) 542
109 223 280 340 402 462 523 585
1.18 1.205 1.228 1.256 1.274 1.292 1.317 1.333
1.07 1.1 1.127 1.146 1.172 1.172 1.2 1.228
1 1.045 1.068 1.09 1.106 1.132 1.145 1.165
For conditions of Sc ) 1395, d ) l cm.
a
Table 3. Effect of Solution Reynolds Number (Re) on the Percent Reduction of the Mass-Transfer Coefficient K at Different Concentrations of the Drag-Reducing Polymer, under Single-Phase Flowa
Re
10 ppm polyox
50 ppm polyox
100 ppm polyox
255 315 360 392 431 485 542
28.5 28.1 28.3 28.7 29.9 30.5 32.1
28.5 29.1 29.6 30.3 31.5 31.8 31.6
29.6 30.7 32 32.1 32.3 32.1 31.9
For conditions of Reg ) 109, d ) 1 cm, and Sc ) 1395.
Table 5. Effect of the Gas Reynolds Number (Reg) on the Percent Decrease in the Mass-Transfer Coefficient K by the Drag-Reducing Polymer under Two-Phase Flowa % decrease in K
% decrease in K
a
Re
10 ppm polyox
50 ppm polyox
100 ppm polyox
266 298 316 355 398 467 501 562
17.6 18.3 19.1 18 19.6 20.4 19.5 18.7
20.6 22 22.8 22.4 20.8 20.9 20.6 21.3
32.7 30.2 28.2 23.1 21.5 22.2 22.4 24
For conditions of Sc ) 1395, d ) l cm.
mass transfer ranges from 17.2% to 32.7%, whereas Tables 4 and 5 show that the polymer decreases the rate of mass transfer in two-phase flow by an amount in the range of 27.6%-34.3%, depending on the polymer concentration and the Reg value. The higher negative effect of the drag-reducing polymer on the rate of mass transfer under two-phase flow, in comparison to singlephase flow, may be attributed to the higher degree of turbulence generated at a given Re value in two-phase flow, as a result of the increase in the interstitial solution velocity caused by the presence of gas bubbles,
a
Reg
10 ppm polyox
50 ppm polyox
100 ppm polyox
109 223 280 341 402 462 523 585
32.1 30.6 31.3 31.9 31.9 32.8 33 33.4
31.6 33.2 31.8 32.2 32.5 33.2 33.4 34.1
31.9 32.3 31.9 32.5 32.6 33.4 33.5 34.3
For conditions of Re ) 542, d ) 1 cm, and Sc ) 1395.
which reduces the available solution flow area. It seems that the resulting increase in turbulence increases the proportion of the small-scale, high-frequency eddies, which are damped by the polymer molecules. Also, the increase in the solution interstitial velocity caused by gas bubbles increases the degree of stretching of the polymer molecules, with a consequent increase in the ability of these molecules to dampen the small-scale eddies.22 In view of the present findings, that dragreducing polymers adversely affect the rate of mass transfer in fixed-bed reactors, they should be used only if their benefit of reducing the pumping power and the
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operating costs of the reactor outweight the decrease in the rate of production. The interesting finding reported by Kale and co-workers23,24sthat the presence of a drag-reducing polymer increases the gas-liquid volumetric mass-transfer coefficient (Ka) in two-phase gas-liquid contactors by increasing the interfacial area (a)smay enhance the value of using drag-reducing polymers in fixed-bed reactors that involve simultaneous gas absorption and liquid-solid reaction. The benefits gained from using drag-reducing polymers would be greater if the liquid-solid reaction is partially diffusioncontrolled or chemically controlled. Conclusion (1) Study of the liquid-solid mass-transfer behavior of a flow-by fixed-bed electrochemical reactor that was composed of Lessing rings has revealed that, for a given set of conditions, the rate of mass transfer at the bed is less than that at a fixed bed of spheres and screens, because of the unfavorable current distribution and mixing conditions inside the randomly oriented rings. (2) The nonuniform current distribution inside and outside the randomly oriented rings makes the dimensionless mass-transfer correlations obtained in the work using the limiting-current technique unfit for the design and operation of catalytic reactors that are used to conduct liquid-solid diffusion-controlled chemical reactions. (3) Drag-reducing polymers decreased the rate of mass transfer in the case of single- and two-phase flow, and, for a given Reynolds number (Re), the percent decrease in the rate of mass transfer was higher in the case of two-phase flow. Before using drag-reducing polymers in fixed-bed operations, the benefits of reducing the pumping power and increasing the gas-liquid rate of mass transfer should be weighed against the adverse effect of reducing the rate of liquid-solid mass transfer. Symbols a1, a2 ) constant A ) cathode area C ) concentration of ferricyanide ion d ) Lessing ring diameter D ) diffusivity F ) Faraday’s constant I ) limiting current K ) mass-transfer coefficient L ) Lessing length V ) superficial solution velocity Vg ) superficial gas velocity Z ) number of electrons involved in the reaction Re ) solution Reynolds number; Re ) FVd/µ Reg ) gas Reynolds number; Reg ) FVgd/µ Sc ) Schmidt number; Sc ) µ/(FD) Sh ) Sherwood number; Sh ) Kd/D Sh/Sh0 ) ratio between the two-phase Sherwood number and the single-phase Sherwood number µ ) solution viscosity F ) solution density
Literature Cited (1) Walsh, F. C. A First Course in Electrochemical Engineering; The Electrochemical Consultancy: Hants, U.K., 1993. (2) Zaki, M. M.; Nirdosh, I.; Sedahmed, G. H. Liquid-Solid Mass Transfer at Horizontal Woven Screens with Upward Cocurrent Gas-Liquid Flow. Chem. Eng. Commun. 2001, 186, 43-56.
(3) Soltan, E. A.; Nosier, S. A.; Salem, A. Y.; Mansour, I. S. A.; Sedahmed, G. H. Mass Transfer Behaviour of a Flow-By Fixed Bed Electrochemical Reactor Under Different Hydrodynamic Conditions. Chem. Eng. J. 2003, 91, 33-44. (4) Mobarak, A. A.; Abdo, M. S.; Hassan, M. S.; Sedahmed, G. H. Mass Transfer Behaviour of a Flow-By Fixed Bed Electrochemical Reactor Composed of a Vertical Stack of Screens Under Single and Upward Two Phase Flow. J. Appl. Electrochem. 2000, 30, 1269-1276. (5) Oloman, C.; Watkinson, A. The Electroreduction of Oxygen to Hydrogen Peroxide on Fixed Bed Cathodes. Can. J. Chem. Eng. 1976, 54, 312-318. (6) Nassar, M.; Al-Taweel, A. M.; Mackay, G.; McMillan, A. F.; Sedahmed, G. H. An Electrochemical Technique for Production of H2 and H2SO4 from Flue Gas Desulphurization Effluents. Surf. Technol. 1983, 20, 83-90. (7) Scott, K. Status Trends and Development in Electrochemical Reactor Designs. Bull. Electrochem. 1993, 9, 170-186. (8) Storck, A.; Latifi, M. A.; Barthole, G.; Laurent, A.; Charpentier, J. C. Electrochemical Study of Liquid-Solid Mass Transfer in Packed Bed Electrodes with Upward and Downward Cocurrent Gas-Liquid Flow. J. Appl. Electrochem. 1986, 16, 947963. (9) Ibl, N.; Adam, E.; Venczel, J.; Schalch, E. Stofftransport Beider Electrolyse mit Gas Ruhrung. Chem.-Ing.-Tech. 1971, 43, 202-215. (10) Shah, Y. T. Design Parameters for Mechanically Agitated Reactors. Adv. Chem. Eng. 1992, 17, 1-206. (11) Hanna, M. R.; Kozicki, W.; Tiu, C. Flow of Drag-Reducing Fluids through Packed Beds. Chem. Eng. J. 1977, 13, 93-99. (12) Sellin, R. H.; Hoyt, J. H.; Scrivener, O. The Effect of Drag Reducing Additives on Fluid Flows and Their Industrial Applications. J. Hydraul. Res. 1982, 20, 29-67. (13) Selman, J. R.; Tobias, C. W. Mass Transfer by the Limiting Current Technique. Adv. Chem. Eng. 1978, 10, 211-318. (14) Findly, A.; Kitchener, I. K. Practical Physical Chemistry; Longman: London, 1965. (15) Bourne, J. R.; Dell’Ava, P.; Dossenbach, O.; Post, T. Densities Viscosties and Diffusivities in Aqueous Sodium Hydroxide-Potassium Ferri- and Ferrocyanide Solutions. J. Chem. Eng. Data 1985, 30, 160-163. (16) Little, R.; Shmidt, S.; Romans, J.; Dedrick, J.; Matuszko, J. S. Improved Drag Reduction by Control of Polymer Particle Size. Ind. Eng. Chem. Res. 1991, 30, 403-407. (17) Carberry, J. J. A Boundary-Layer Model of Fluid-Particle Mass Transfer in Fixed Beds. AIChE J. 1960, 6, 460-463. (18) Colquhoun-Lee, I.; Stepanek, J. Mass Transfer in Single Phase Flow in Packed Beds. Chem. Eng. 1974, 2, 108-111. (19) Seguin, D.; Montillet, A.; Brunjail, D. Commiti, LiquidSolid Mass Transfer in Packed Beds of Variously Shaped Particles at Low Reynolds Number: Experiment and Model. Chem. Eng. J. 1996, 63, 1-9. (20) Delaunay, G.; Storck, A.; Laurent, A. Charapentier, J. C. Electrochemical Study of Liquid-Solid Mass Transfer in Packed Beds with Upward Cocurrent Gas-Liquid Flow. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 514-521. (21) Sims, W. B.; Schulz, G.; Luss, D. Solid-Liquid Mass Transfer to Hollow Pellets in a Trickle Bed. Ind. Eng. Chem. Res. 1993, 32, 1895-1903. (22) White, D., Jr.; Gordon, R. J. The Influence of Polymer Conformation on Turbulent Drag Reduction. AIChE J. 1975, 21, 1027-1029. (23) Joshi, J. B.; Kale, D. D. Effect of Drag Reducing Additives on Mass Transfer Characteristics of Gas-Liquid Contactors. Chem. Eng. Commun. 1979, 3, 15-18. (24) Yadgiri, B. N.; Kale, D. D. Effect of Polymeric Additives on Mass Transfer Characteristics of Two Phase Gas-Liquid Flows in a Pipeline. Chem. Eng. Sci. 1985, 40, 679-681. (25) Sedahmed, G. H.; El-Kayar, A. M.; Farag, H. A.; Noseir, S. A. Liquid-Solid Mass Transfer in Packed Beds of Raschig Rings with Upward Two-Phase (Gas-Liquid) Flow. Chem. Eng. J. 1996, 62, 61-65.
Received for review February 12, 2004 Accepted February 16, 2005 IE040053F
