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Ind. Eng. Chem. Res. 2009, 48, 3692–3695
Natural Convection Mass Transfer Behavior of Fixed Bed of Spheres in Relation to Catalytic and Electrochemical Reactor Design Ibrahim Hassan,† Inderjit Nirdosh,* and Gomaa H. Sedahmed‡ Department of Chemical Engineering, Lakehead UniVersity, Thunder Bay, ON, Canada P7B 5E1
The free convection mass transfer behavior of a fixed bed of spheres has been studied experimentally using an electrochemical technique which involved measuring the limiting current of the cathodic deposition of copper from acidified copper sulfate solution. Variables studied were sphere diameter, bed height, and physical properties of the solution. The mass transfer coefficient was found to decrease slightly with increasing bed height and independent of sphere diameter. The data were correlated for the conditions 5 × 106 < Sc · Gr < 5.4 × 108 by the equation Sh ) 0.28(Sc · Gr)0.32. A comparison between the present and some previous data at other packing geometries shows that the rate of natural convection mass transfer at a bed of spheres is higher than that at beds of Raschig rings and at cylinders. The importance of the present results for the design and operation of catalytic and electrochemical reactors used to conduct diffusion controlled liquid-solid reactions is highlighted. Introduction In view of their advantages such as high rate of mass transfer, high area per unit volume, and low axial dispersion, fixed beds are used widely in the chemical industry to build contactors suitable for conducting diffusion controlled processes such as adsorption, ion exchange, absorption, liquid-solid catalytic reactions, and liquid-solid biochemical reactions on immobilized enzymes. With the advent of the electrochemical technique as a tool for removing heavy metals from wastewater a few decades ago, porous beds of small particles and fixed beds of large particles have been used to build high space time yield electrochemical reactors. In view of the shortcomings of the porous beds of small particles1 such as (i) the rapid clogging of the bed by the deposited metal, (ii) high pressure drop, and (iii) entrapment of side reaction gas bubbles (H2) which decrease the active electrode area and increase the cell resistance and energy consumption, fixed beds of large particles which are free of these drawbacks are gaining increased importance in building electrochemical reactors.2,3 Although much work has been done on the forced convection mass transfer behavior of high porosity fixed beds, little has been done on natural convection mass transfer behavior of these beds,4-8 despite the technical importance of the subject for the design and operation of reactors employing low feed rates to increase the residence time and the degree of conversion per pass. Under such low feed rates, free convection mass transfer either dominates the rate of mass transfer or contributes along with forced convection to the overall rate of mass transfer. The extent to which natural convection contributes to the rate of mass transfer along with forced convection under different conditions was addressed by different authors.9-16 Natural convection is induced by concentration or temperature gradients at the liquid-solid interface where a metal deposition or an exothermic reaction takes place respectively. The aim of the present work was to study the free convection mass transfer * To whom correspondence should be addressed. Tel.: (807) 343 8343. E-mail:
[email protected]. † Current Address: Faculty of Engineering, Arab Academy of Science and Technology, Alexandria, Egypt. ‡ Current Address: Department of Chemical Engineering, Alexandria University, Alexandria, Egypt.
behavior of a fixed bed of spheres in order to assist in the rational design and operations of reactors employing such beds. To this end, the rate of mass transfer at the fixed bed was measured by an electrochemical technique which involves measuring the limiting current of the cathodic deposition of copper from acidified copper sulfate solution. According to Silman and Tobias12 the Cu-CuSO4 system is superior to the ferricyanide system in natural convection studies. In a previous study, Gabitto and Bohm4 investigated the natural convection mass transfer behavior of a fixed bed of spheres by an electrochemical technique which involved measuring the limiting current of the cathodic reduction of potassium ferricyanide from an alkaline solution. The authors used a maximum bed height of three layers with a screen anode placed downstream of the bed (flow-through configuration). In the present work a flow-by configuration was used where the anode surrounds the bed and the bed height was much larger than that used by Gabitto and Bohm.4 The use of the flow-by configuration has the advantage of better current distribution.1 Gabitto and Bohm4 correlated their data by the equation: Sh ) 0.228(Sc · Gr)0.32(Rh /d)0.22
(1)
for 6.24 × 103 < Sc · Gr < 3.03 × 108. The authors used the depth of the packed bed as the characteristic length in calculating Sh and Gr; Rh is the hydraulic radius of the bed, and d is the sphere diameter. Karabelas et al.17 studied the natural convection mass transfer behavior of a single active sphere embedded in an inert bed of spheres by measuring the limiting current of the cathodic reduction of potassium ferricyanide from alkaline solution. The authors correlated their data for the condition 1.24 × 107 < Sc · Gr < 3.23 × 109 by the equation: Sh ) 0.46(Sc · Gr)0.25
(2)
The sphere diameter was used as the characteristic length in calculating Sh and Gr. Experimental Technique Figure 1 shows the cell and electrical circuit. The cell consisted of 8 L cylindrical plastic container of 26 cm height
10.1021/ie801195b CCC: $40.75 2009 American Chemical Society Published on Web 03/02/2009
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Figure 2. Typical polarization curves. Sphere diameter ) 0.95 cm. CuSO4 conc: (•) 0.027; (×) 0.0305; (2) 0.0498; (9) 0.0688; (O) 0.0813 M.
Figure 1. Apparatus (1) 6 V dc power supply, (2) perforated plastic basket containing bed of spheres, (3) current feeder, (4) electrolyte level, (5) plastic support, (6) Luggin tube with a reference electrode, (7) voltmeter, (8) cylindrical copper anode.
and 19 cm diameter. The fixed bed cathode was built of copper coated steel spheres placed in a perforated plastic basket of 6.1 cm diameter and 12.5 cm height, and the basket was made of rigid plastic mesh of 0.4 cm 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 different sphere diameters and different heights were used. Spheres of diameters 0.476, 0.953, and 1.587 cm were used, and the bed height ranged from 2 to 10 cm. The fixed bed cathode was surrounded by a cylindrical copper anode of 18.6 cm diameter and 26 cm height. The electrical circuit consisted of a 10 V dc power supply with a voltage regulator and a multirange ammeter connected in series with the cell. The electrical current was fed to the bed through an insulated copper wire brazed to one of the deep spheres in the bed. A 7 L portion of acidified copper sulfate solution was placed in the cell before each run. Current-potential curves, from which the limiting current was obtained, were constructed by increasing the current stepwise and measuring the steadystate cathode potential by means of a high impedance voltmeter; 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 packed bed cathode. Five different concentrations of copper sulfate were used, namely 0.027, 0.0305, 0.0498, 0.0688, and 0.0813 M, and in all cases, 1.5 M H2SO4 was used as a supporting electrolyte. All solutions were prepared from analytical reagent grade chemicals and distilled water. The copper sulfate concentration was checked by iodometry.18 Each experiment was conducted twice. The temperature was fixed at 22 ( 1 °C by placing the cell in a thermostatted water bath. Preliminary experiments using perforated plastic holders of different pore sizes (mesh numbers) have shown that the size of the perforation of the holding basket has no effect on the limiting current. With the relatively dilute copper sulfate solutions used in the present work, the problem of copper powder formation on the packed bed at the limiting current was not serious. After each experiment, the fine copper powder deposited during the run was removed from the spheres
Figure 3. Effect of bed height on the mass transfer coefficient. Sc: (•) 1687; (9) 1712; (2) 1754; (×) 1791; (O) 1820.
by a jet of water followed by treating the spheres with dilute nitric acid, rinsing them with distilled water and drying them. Results and Discussion Figure 2 shows typical polarization curves from which the limiting current was determined. The mass transfer coefficient was calculated from the limiting current using the equation: K ) I/AZFC
(3)
The bed area, A, was obtained by multiplying the number of spheres forming the bed by the single sphere area. Figure 3 shows the effect of bed height on mass transfer coefficient. The slight decrease in the mass transfer coefficient with increasing bed height especially at Sc > 1687 is consistent with the results previously obtained with beds of horizontal screens5 and cylinders.7 The decrease in the mass transfer coefficient with bed height cannot be attributed to an increase in the diffusion layer thickness with height because the mass transfer surface is not continuous, a diffusion layer will grow along each sphere, breakdown, and grow again on next particle. The decrease in the mass transfer coefficient with bed height is the resultant of two opposing effects as outlined by Masters19 and Smith and Wragg20 who studied natural convection heat and mass transfer at vertical arrays of separated horizontal cylinders respectively. According to these authors, as the uprising natural convection stream moves upward past the spheres it loses Cu2+ and becomes less dense; consequently,
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To throw some light on the role of particle geometry, the present data were compared with previous data obtained for a fixed bed of cylinders and a fixed bed of Raschig rings. For a fixed bed of cylinders,5 the data were correlated, for 1.7 × 107 < Sc · Gr < 2.1 × 109, by the equation: Sh ) 0.31(Sc · Gr)0.32(d/h)0.12
(5)
while for the beds of Raschig rings,6 for the range 1.06 × 107 < Sc · Gr < 2.1 × 108, the data fit the equation: Sh ) 0.15(Sc · Gr)0.32 Figure 4. Effect of sphere diameter on the mass transfer coefficient. Sc: (•) 1687; (9) 1712; (2) 1754; (O) 1791; (×) 1820.
Figure 5. Overall mass transfer correlation. Sc: (9) 1687; (2) 1712; (×) 1754; (O) 1791; (•) 1820. Table 1. Comparison between the Present Data and the Data of Gabitto and Bohm4a Sh Sc · Gr 6
10 107 108 a
Gabitto and Bohm (eq 1)
present data
13.1 27.35 57.1
23.3 48.6 101.7
Sphere diameter ) 0.975 cm; height ) 3 layers, Rh ) 0.18 cm.
its velocity increases. This increase in solution velocity with bed height tends to increase the mass transfer coefficient while the decrease in Cu2+ concentration with increasing bed height has the opposite effect. It seems that in the present case the effect of reduced Cu2+ concentration outweighs the enhanced velocity effect thus causing a decrease in the mass transfer coefficient with increasing bed height. Figure 4 shows that sphere diameter has little effect on the mass transfer coefficient, this finding may suggest that mass transfer takes place inside the bed by a turbulent flow mechanism.12 Figure 5 shows that the present data fit the overall mass transfer correlation Sh ) 0.28(Sc · Gr)0.32
(4)
with an average deviation of (9.1%. The correlation coefficient is 0.965. The physical properties used in calculating Sh, Sc, and Gr were taken from the literature,12,21,22 and sphere diameter was used as the characteristic length in Sh and Gr. The exponent 0.32 confirms the turbulent nature of the flow inside the bed.12
(6)
Calculation of the mass transfer coefficient for the three geometries using eqs 4-6 revealed that for a given set of conditions the mass transfer coefficient increases in the order Raschig rings < cylinders < spheres, i.e., spheres have the highest mass transfer coefficient among the three geometries. This is consistent with the case of forced convection mass transfer.23 Table 1 shows a comparison between the present data presented by eq 4 and the data obtained by Gabitto and Bohm4 for a fixed bed of spheres given by eq 2. The comparison was made for the maximum bed height used by the authors (3 layers), a sphere diameter of 0.975 cm and Rh ) 0.18 cm, and limited to the present range of Sc · Gr. The present data indicates higher values than those of Gabitto and Bohm.4 The discrepancy between the two sets of data may be attributed to the fact that Gabitto and Bohm4 used a small bed height (1-3 layers) which may not be sufficient to develop the flow which characterizes deep fixed beds; besides, the authors used a flow-through electrode configuration which is known to produce nonuniform current distribution on the bed. It would be of interest to compare the results of an active single sphere embedded in an inactive bed of spheres17 with the present data. Equation 3 shows that the flow at the single sphere is laminar as revealed by the Sc · Gr exponent 0.25,12 while the present flow is turbulent. The turbulent nature of the flow inside the bed may be ascribed to the enhanced velocity effect as the solution rises in the bed with the possibility of boundary layer separation and turbulent wake formation behind the spheres. Another way of explaining the difference in behavior between a single active sphere imbedded in an active bed and the present case is to visualize the present bed as a series of upward facing porous horizontal layers. Since free convection at an upward facing horizontal surface is usually turbulent,24-26 it follows that within the present range of Sc · Gr the flow at the upward facing surface of each layer would be turbulent. The turbulent flow intensifies inside the bed as the solution moves upward by virtue of the enhanced velocity effect. Conclusions 1. For a given set of conditions, fixed beds of spheres produce higher rates of natural convection mass transfer than fixed beds of Raschig rings and cylinders. The turbulent flow generated inside the bed would make it possible to operate fixed bed electrochemical reactor at low feed rates. The resulting high residence time and the high mass transfer coefficient arising from turbulent natural convection combine to increase the degree of conversion per pass in the case of heavy metal removal from waste solution. 2. Natural convection mass transfer at a single active particle imbedded in an inactive bed is different from natural convection mass transfer in active beds.
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Acknowledgment This research was funded by the Natural Sciences and Engineering Research Council of Canada. Thanks are due to Mr. Kailash Bhatia, Mechanical Engineering Technologist, Lakehead University, for fabricating the apparatus. Nomenclature A ) bed area (m2) a ) specific surface area of the bed (m2/m3) C ) bulk concentration of copper sulfate (mol/L) D ) diffusivity of Cu2+ (m2/s) d ) sphere diameter (m) F ) Faraday constant (96 500 A · s/equiv) g ) acceleration due to gravity (m/s2) h ) bed height (m) I ) limiting current (A) K ) Mass transfer coefficient (m/s) Rh ) hydraulic radius, ) ε/a, (m) Z ) number of electrons involved in the reaction Gr ) Grashoff number (gd3∆F/V2F) Sc ) Schmidt number (V/D) Sh ) Sherwood number (Kd/D) µ ) absolute viscosity (kg/m · s) V ) kinematic viscosity (m2/s) ∆F ) density difference between the bulk solution and interfacial solution (kg/m3) F ) solution density (kg/m3) ε ) bed porosity
Literature Cited (1) Walsh, F. C. A first course in electrochemical engineering; The Electrochemical Consultancy: Hants, U.K., 1993. (2) Hassan, I.; Zahran, R. R.; Mansour, I. S.; Sedahmed, G. H. Liquidsolid mass transfer at fixed bed of Lessing rings in relation to electrochemical reactor design. Ind. Eng. Chem. Res. 2005, 44, 4561. (3) Soltan, E. A.; Nosier, S. A.; Salem, A. Y.; Mansour, I. S.; Sedahmed, G. H. Mass transfer behaviour of flow-by fixed bed electrochemical reactor under different hydrodynamic conditions. Chem. Eng. J. 2003, 91, 33. (4) Gabitto, J. F.; Bohm, U. Experimental study of free convection mass transfer in porous media. Int. J. Heat Mass Transfer 1981, 24, 1675. (5) Sedahmed, G. H.; Zahran, R. R.; Hassan, I. Natural convection mass transfer at a fixed bed of cylinders. Ind. Eng. Chem. Res. 1993, 32, 1235. (6) Sedahmed, G. H.; Zatout, A. A.; Zewail, T. M. Free convection mass transfer behaviour of fixed bed of Raschig rings. Ind. Eng. Chem. Res. 1998, 37, 3481.
(7) Shemilt, L. W.; Sedahmed, G. H. Natural convection mass transfer at horizontal screens. J. Appl. Electrochem. 1976, 6, 471. (8) Sedahmed, G. H.; Shemilt, L. W. Free convection mass transfer characteristics of vertical screens. Chem. Eng. Res. DeV. 1985, 63, 378. (9) Churchill, S. W. A comprehensive correlating equation for laminar, assisting, forced and free convection. AIChE J. 1977, 23, 10. (10) Tobias, C. W.; Hickman, R. G. Ionic mass transport by combined free and forced convection. Z. Phys. Chem. 1965, 229, 145. (11) Mandelbaum, J. A.; Bohm, U. Mass transfer in packed beds at low Reynolds numbers. Chem. Eng. Sci, 1973, 28, 569. (12) Silman, J. R.; Tobias, C. W. Mass transfer measurement by the limiting current technique. AdV. Chem. Eng. 1978, 10, 211. (13) Ross, T. K.; Wragg, A. A. Electrochemical mass transfer studies in annuli. Electrochim. Acta 1965, 10, 1093. (14) Newman, J. Electrochemical Systems; Prentice Hall: Englewood Cliffs, NJ, 1973. (15) Acrivos, A. On the combined effect of forced and free convection heat transfer in laminar boundary layer flows. Chem. Eng. Sci. 1966, 21, 343. (16) Mohanta, S.; Fahidy, T. Z. Ionic mass transfer in open channel flow. Electrochim. Acta 1976, 21, 143. (17) Karabelas, A. J.; Wegner, T. H.; Hanratty, T. J. Use of asymptotic relations to correlate mass transfer data in packed beds. Chem. Eng. Sci. 1971, 26, 1581. (18) Vogel, A. A textbook of quantitatiVe inorganic analysis, 5th ed.; Longmans: London, 1989. (19) Masters, G. F. Arrays of heated horizontal cylinders in natural convection. Int. J. Heat Mass Transfer 1972, 15, 921. (20) Smith, A. F. J.; Wragg, A. A. An electrochemical study of mass transfer in free convection at vertical arrays of horizontal cylinders. J. Appl. Electrochem. 1974, 4, 219. (21) Eisenberg, M.; Tobias, C. W.; Wilke, C. R. Selected physical properties of ternary electrolytes employed in ionic mass transfer studies. J. Electrochem. Soc. 1956, 103, 413. (22) Wilke, C. R.; Eisenberg, M.; Tobias, C. W. Correlation of limiting current under free convection conditions. J. Electrochem. Soc. 1953, 100, 513. (23) Colquhoun-Lee, I.; Stepanek, J. Mass transfer in single phase flow in packed beds. Chem. Eng. 1974, 228, 108. (24) Sedahmed, G. H.; Nirdosh, I. Free convection mass transfer at an enclosure between two horizontal discs. Chem. Eng. Commun. 1991, 101, 93. (25) Fenech, E. J.; Tobias, C. W. Mass transfer by free convection at horizontal electrodes. Electrochim. Acta 1960, 2, 311. (26) Wragg, A. A. Use of Electrochemical technique to study natural convection heat and mass transfer. J. Appl. Electrochem. 1991, 21, 1047.
ReceiVed for reView August 3, 2008 ReVised manuscript receiVed December 24, 2008 Accepted February 17, 2009 IE801195B
