Ind. Eng. Chem. Res. 1998, 37, 3481-3484
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Free Convection Mass-Transfer Behavior of a Fixed Bed of Raschig Rings G. H. Sedahmed,* A. A. Zatout, and T. M. Zewail Faculty of Engineering, Chemical Engineering Department, Alexandria University, Alexandria, Egypt
Natural convection mass transfer at a fixed bed of copper Raschig ring (aspect ratio ) 1) 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 ring diameter, bed height, and physical properties of the solution. The data were correlated for the condition 1810 < Sc < 2532, 10.6 × 106 < ScGr < 21 × 107, and 0.17 < d/h < 1 by the equation Sh ) 0.15(ScGr)0.32. A comparison between the present data and previous data at other packing geometry shows that the rate of natural convection mass transfer at Raschig rings is less than that at spheres and cylinders. The importance of the results to electrochemical reactor design is highlighted. Introduction Rasching rings are used widely in the process industries to build absorption and extraction towers, and fixed-bed reactors used to conduct catalytic and heterogeneous reactions owing to their low cost, high area per unit volume, and the low-pressure drop per foot compared to other packing geometry. Although much work has been done on the gas-liquid and liquid-liquid mass-transfer behavior of fixed beds of Raschig rings, little has been done on the solid-liquid mass-transfer behavior of fixed beds of Raschig rings despite the importance of the subject in the design and operation of fixed-bed catalytic and electrochemical reactors used to conduct diffusion-controlled solid-liquid reactions.1 Recently some work has been done on the solid-liquid mass-transfer behavior of Raschig rings under singlephase flow,2 gas sparging,3 and two phase flow.4 The object of the present work is to study the natural convection mass-transfer behavior of fixed beds, of Raschig rings. Natural convection mass transfer is either dominant or contributes a great deal to the rate of mass transfer in continuos reactors operated at low solution feed rates.5-8 Free convection dominates when Gr . Re2; both free and forced convection effects become important in the range 0.01 < Gr/Re2 < 100. The overall Sh in the mixed convection region can be calculated from the forced convection and the free convection Sh using the equation5
Shoverall ) (Shforced3 + Shfree3)1/3
(1)
Natural convection arises as a result of the density difference between the interfacial solution and the bulk solution. Density difference takes place as a result of a concentration gradient or temperature gradient. Density difference due to concentration change takes place in electrochemical reactors used, for example, for the recovery of heavy metals from industrial effluents while change in density due to change in temperature takes place in the case of highly exothermic or endothermic reactions. In view of the analogy between heat and * To whom correspondence should be addressed.
mass-transfer, the present work may also be useful in calculating the natural convection heat-transfer coefficient in fixed beds of Raschig rings which can be used in the design and operation of regenerative heat exchangers employed in solar energy storage. In a previous report Sedahmed et al.9 studied the free convection mass-transfer behavior of a fixed bed of cylinders. The data were correlated for the conditions 1700 < Sc < 2150, 0.17 × 108 < ScGr < 0.23 × 1010, and 0.256 < d/h < 1 by the equation
Sh ) 0.31(ScGr)0.32(d/h)0.12
(2)
Gabitto and Bohm10 studied rates of natural convection mass transfer at fixed beds 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 placed downstream of the bed (flow-through configuration). The authors correlated their data for the range 6.24 × 103 < ScGr < 3.03 × 108 by the equation
Sh ) 0.228(ScGr)0.32 (rh/d)0.22
(3)
The hydraulic radius rh was used as a characteristic length in calculating Sc and Gr. The present study was conducted by measuring the limiting current of the cathodic deposition of copper from acidified copper sulfate solution. This system is superior to the ferricyanide-ferrocyanide system in natural convection studies as reported by Selman and Tobias.7 Experimental Technique Figure 1 shows the cell and electrical circuit. The cell consisted of a 7.5-L cylindrical plastic container of 25cm height and 20-cm diameter. The fixed bed cathode was built of randomly packed copper Raschig rings of aspect ratio ) 1 placed in a perforated plastic basket of 8.5-cm diameter and 9.5-cm height, and 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
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3482 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998
Figure 1. Apparatus.
top of the cell. The bottom of the basket was 7 cm from the cell bottom. Beds of Raschig rings of different diameters and heights were used. Rings of diameters 6, 8, 10, and 12 mm were used giving beds of porosity 0.7, 0.74, 0.77, and 0.82, respectively, the bed height ranged from 0.6 to 7.2 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 with the cell. An electrical current was fed to the bed through an insulated copper wire brazed to one of the packed rings. Before each run 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 highimpedance 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, 0.0384, 0.0498, 0.0593, and 0.0688 mol/L. 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; copper sulfate concentration was checked by iodometry.11 Each experiment was conducted twice. Temperature was 22 ( 1 °C. Preliminary experiments have shown that the size of the perforations of the holding plastic 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, the fine copper powder was removed after each run from the rings by a jet of water followed by treating the rings with dilute nitric acid, and the rings were finally rinsed in distilled water and dried. Results and Discussion Figure 2 shows typical polarization curves from which the limiting current was determined, and the mass-
Figure 2. Typical polarization curves. CuSO4 concentration, M: O, 0.27; 4, 0.038; ×, 0.069.
Figure 3. Effect of bed height on the mass-transfer coefficient. CuSO4 concentration, M: O, 0.027; 4, 0.038; ×, 0.059.
transfer coefficient was calculated from the limiting current using the equation
K)
I AZFC
(4)
The bed area A was obtained by multiplying the number of rings forming the bed by the total area of the ring which includes inner area, outer area, and area of the ring edges. Figure 3 shows the effect of bed height on the mass-transfer coefficient at different Sc; the masstransfer coefficient is insensitive to bed height. This behavior differs from that of fixed beds of cylinders where the mass-transfer coefficient decreases with increasing bed height.9 The decrease in the masstransfer coefficient with increasing bed height was explained in terms of the existence of two simultaneous opposing effects; namely, as the uprising natural convection stream moves past the cylinders, it loses copper ions and becomes less dense, and accordingly, the buoyancy force (g∆F) increases with a consequent increase in the stream velocity. The increase in the solution velocity with bed height tends to increase the mass-transfer coefficient while the decrease in copper
Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 3483
mass transfer inside the ring is given by the equation14
Sh ) 0.325(ScGr)0.28
(6)
For the outside surface, the rate can be expressed by the equation15
Sh ) 0.56(ScGr)0.25
(7)
For vertical rings the rate of natural convection masstransfer can be approximated for the inner and the outer surface by the vertical plate equation12 Figure 4. Overall mass-transfer correlation. Sc: O, 1810; ×, 2532; 0, 2298; 4, 2387; b, 2153.
Sh ) 0.67(ScGr)0.25
ion concentration has the opposite effect. It seems that, in the case of cylinder packing, the effect of reduced copper ion concentration predominates over the enhanced velocity effect, thus causing a net decrease in the mass-transfer coefficient with increasing bed height. The insensitivity of the mass-transfer coefficient to bed height in the case of Raschig rings may be attributed to the fact that owing to the high porosity of fixed beds of Raschig ring and the high solution holdup, the decrease in copper ion concentration with increasing bed height is less pronounced; the large holdup solution inside the rings replenishes the rising natural convection stream with copper ions. Figure 4 shows that the present data can be correlated for the conditions 1810 < Sc < 2532, 10.6 × 106 < ScGr < 21 × 107, and 0.17 < d/h < 1 by the equation
According to previous studies on the effect of inclination on natural convection mass transfer at cylinders,16 it is expected that the mass-transfer coefficient at an inclined ring would lie between the vertical value and the horizontal value. A comparison between the exponent of eq 5 and the exponents of eqs 6-8 shows that mass is transferred by a turbulent flow mechanism in the case of fixed beds, while at a single ring in different positions the flow is predominately laminar. A plausible explanation of the deviation of the bed behavior from the single-ring behavior is to assume that the bed is composed of a series of horizontal porous layers. According to previous studies on natural convection mass transfer at horizontal solid and porous surfaces,17-20 it could be expected that, within the present range of conditions, the flow would be turbulent at the upward facing surface of each layer.
Sh ) 0.15(ScGr)0.32
(5)
with an average deviation of (9.4%. The Raschig ring diameter was used as a characteristic length in calculating Sh and Gr. The physical properties used in calculating the dimensionless groups were taken from the literature.7,12,13 The exponent 0.32 reveals a turbulent flow mechanism and shows a little dependence of the mass-transfer coefficient on the Raschig ring diameter. It would be of interest to compare the present data with the results of previous studies on cylinders and spheres to throw some light on the role of the packing geometry. For a given set of conditions, the mass-transfer coefficient calculated from eq 5 (present data) is less than the value calculated from eqs 2 and 3. The low mass-transfer obtained at the Raschig rings compared to cylinders and spheres may be ascribed to the unfavorable position of some of the randomly oriented rings such as horizontal rings and rings with low inclination with the horizontal axis; the natural convection arising inside these rings is enclosed inside the rings and cannot contribute to enhancing the rate of mass transfer throughout the bed. Besides, local depletion of the entrapped solution in copper ions may take place with further decrease in the rate of mass transfer inside those rings. It would be instructive from the mechanistic point of view to compare the natural convection behavior of a single Raschig ring to that of the bed. Neglecting natural convection at the thin edges of the ring and neglecting interaction between the inner side natural convection of the ring and the outer side natural convection, one can consider the rate of natural convection mass transfer at the ring as the sum of the rate of mass-transfer at the inner side and the outer side. For horizontal rings, the rate of
(8)
Conclusions (1) Natural convection mass transfer inside fixed beds of Raschig rings takes place through a turbulent flow mechanism. The mass-transfer coefficient shows little dependence on the ring size and bed height. The observed strong natural convection is valuable in the design and operation of continuous fixed-bed electrochemical reactors used to conduct diffusion-controlled reactions, for example, recovery of heavy metals from industrial effluents at a low feed rate. The high natural convection mass-transfer coefficient and the high residence time arising from the low feed rate would give a high degree of conversion per pass. (2) For the present range of conditions, the rate of natural convection mass transfer at fixed beds of Raschig rings is less than that at fixed beds of spheres and cylinders. Nomenclature A ) bed area C ) bulk concentration of copper sulfate D ) diffusivity of copper sulfate d ) Raschig ring diameter F ) Faraday constant g ) acceleration due to gravity h ) bed height I ) limiting current K ) mass-transfer coefficient rh ) hydraulic radius of the bed (rh ) /φ) V ) solution velocity Z ) number of electrons involved in the reaction Gr ) Grashof number, gd3∆F/ν2F Sc ) Schmidt number, F/D Sh ) Sherwood number, Kd/D
3484 Ind. Eng. Chem. Res., Vol. 37, No. 8, 1998 Re ) Reynolds number, FVd/µ µ ) solution viscosity ν ) kinematic viscosity ∆F ) density difference between the bulk solution and interfacial solution F ) solution density ) bed porosity φ ) specific surface area of the bed
Literature Cited (1) Walsh, F. A first course in electrochemical engineering. The Electrochemical Consultancy: Romsey, U.K., 1993. (2) Noseir, S. A.; El-Kayar, A.; Farag, H. A.; Sedahmed, G. H. Forced convection solid-liquid mass transfer at a fixed bed of Raschig rings. Int. Commun. Heat Mass Transfer 1995, 22, 111. (3) Noseir, S. A.; El-Kayar, A.; Farag, H. A.; Sedahmed, G. H. Solid-liquid mass transfer at gas sparged fixed bed of Raschig rings. Int. Commun. Heat Mass Transfer, in press. (4) 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. (5) White, F. M. Heat and Mass Transfer; Addison-Wesley Publishing Co.: New York, 1988. (6) Tobias, C. W.; Hickman, R. G. Ionic mass transport by combined free and forced convection. Z. Phys. Chem. 1965, 229, 145. (7) Selman, J. R.; Tobias, C. W. Mass transfer measurement by the limiting current technique. Adv. Chem. Eng. 1978, 10, 211. (8) Mandelbaum, J. A.; Bohm, U. Mass transfer in packed beds at low Reynolds numbers. Chem. Eng. Sci. 1973, 28, 269. (9) 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.
(10) Gabitto, J. F.; Bohm, U. Experimental study of free convective mass transfer in porous media. Int. J. Heat Mass Transfer 1981, 10, 1675. (11) Vogel, A. I. A Textbook of quantitative inorganic analysis, 5th ed.; Longmans: London, 1989. (12) Wilke, C. R.; Eisenberg, M.; Tobias, C. W. Correlation of limiting currents under free convection conditions. J. Electrochem. Soc. 1953, 100, 513. (13) 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. (14) Sedahmed, G. H.; Shemilt, L. W. Natural covection mass transfer in horizontal tubes. Chem. Eng. Commun. 1983, 23, 1. (15) 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. (16) Sedahmed, G. H.; Shemilt, L. W. Natural convection mass transfer at cylinders in different positions. Chem. Eng. Sci. 1982, 37, 159. (17) Sedahmed, G. H.; Nirdosh, I. Free convection mass transfer at an enclosure between two horizontal discs. Chem. Eng. Commun. 1991, 101, 93. (18) Fenech, E. J.; Tobias, C. W. Mass transfer by free convection at horizontal electrodes. Electrochim. Acta 1960, 2, 311. (19) Wragg, A. A. Use of electrochemical techniques to study natural convection heat and mass-transfer. J. Appl. Electrochem. 1991, 21, 1047. (20) Shemilt, L. W.; Sedahmed, G. H. Natural convection masstransfer at horizontal screens. J. Appl. Electrochem. 1976, 6, 471.
Received for review September 22, 1997 Revised manuscript received January 26, 1998 Accepted January 26, 1998 IE970678W
