Mass and Heat Transfer in a Batch Bubble Column Operating with and

May 16, 2014 - *E-mail: [email protected]. ... In this work, the transfer coefficients of mass and heat (by analogy) at a vertical cylinder centered...
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Mass and Heat Transfer in a Batch Bubble Column Operating with and without Packing Mohamed Helmy Abdel-Aziz*,†,‡ †

Chemical and Materials Engineering Department, Faculty of Engineering, King Abdulaziz University, Rabigh 21911, Saudi Arabia Chemical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt

‡

ABSTRACT: In this work, the transfer coefficients of mass and heat (by analogy) at a vertical cylinder centered in a bubble column were studied experimentally in two cases: (i) freely bubbling liquid−gas and (ii) packed bubble column with plastic packing around the cylinder. The parameters studied are solution physical properties, cylinder height, packing geometry, size of packing, and gas flow rate. The presence of inert packing at the cylinder surface increased transfer rates of mass and heat (by analogy). The factor of this increase ranged from 1.46 to 2.73 times, based on the gas superficial velocity and the packing geometry. All data were correlated by dimensional analysis using the equation j = a(Re × Fr)b. The constants a and b in the dimensionless equations were determined experimentally for the unpacked column and for the packed column with different types of packing. Potential applications of the results in reactor design were discussed.

1. INTRODUCTION The proper design of most reactors requires knowledge of the transport properties of the reactor, especially for those reactors that involve diffusion controlled reactions where mass transfer of the reacting species is the controlling step. A bubble column reactor is most commonly used on a wide scale in many industrial applications involving production of organic, inorganic, or biochemical materials because of its simple construction, large interfacial area, and low energy consumption.1−3 Bubble columns are containers in which multiphase reactions occur and where there is a relative motion between a discontinuous and a continuous phase. The discontinuous phase is the gas phase, and a second continuous phase may be liquid or homogeneous slurry; the system operation mode may be batch or continuous, single stage, or multistage. Packing materials are sometimes used in bubble columns as a catalyst support and for immobilization of enzymes in biotechnology.4−6 The presence of packing in a continuous bubble column eliminates the undesirable tendency of reacted material to intermingle with unreacted material, a phenomenon known as back-mixing. This phenomenon is caused by circulation of fluids in the container, which characterizes a freely bubbling liquid−gas system and affects the degree of conversion.6,7 The current study is designed to examine the rate of transport of mass and heat (by analogy) at the outer surface of a vertical cylinder centered in a batch bubble column in relation to the superficial gas velocity. Also, the study aims to investigate the effect of the presence of packing material on the rate of transport of mass and heat at the cylinder surface. To achieve the purpose of the study, the transfer rates of mass and heat (by analogy) were measured by the limiting current (electrochemical) technique, which has been used on a wide scale to measure rates of transfer of heat and mass because it is rapid and accurate and does not involve sensors or measuring probes that may interfere with the hydrodynamics on the tested surface.8−11 Previous studies using this technique12 found that the data obtained for transfer of mass are in a good and close © 2014 American Chemical Society

agreement with the data for transfer of heat. The study was carried out with the unpacked and packed column. Three different geometries of inert plastic packing were used, namely, spheres, cylinders, and Raschig rings. Because addition or removal of heat is an essential step for the reactions occurring in bubble columns to maintain the reactor productivity, the present study would make it possible to design and operate a vertical tube cooler for a batch bubble column reactor. The present study could also provide the design of batch annular double tube electrochemical reactors

Figure 1. Apparatus.

Received: Revised: Accepted: Published: 9925

February 21, 2014 May 15, 2014 May 16, 2014 May 16, 2014 dx.doi.org/10.1021/ie500766j | Ind. Eng. Chem. Res. 2014, 53, 9925−9931

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Table 1. Physical Properties of the Solution Used at 303 K ρ (kg/m3)

μ × 103 (kg m−1 s−1)

D × 1010 (m2/s)

Sc

1004

0.988

7.5

1253

1082

1.23

6.24

1821

1116

1.54

4.99

2778

solution composition 0.01 M K3Fe(CN)6 + 0.1 M K4Fe(CN)6 + 1 M NaOH 0.01 M K3Fe(CN)6 + 0.1 M K4Fe(CN)6 + 2 M NaOH 0.01 M K3Fe(CN)6 + 0.1 M K4Fe(CN)6 + 3 M NaOH

with a packed annulus.13,14 Besides the advantage of having a uniform current distribution, the inner cylinder of the annular electrochemical reactor can be used as a working electrode and a heat exchanger facility (dual function), which lowers the capital cost of the reactor.

2. EXPERIMENTAL SECTION 2.1. Apparatus. A model of the apparatus used in conducting the experiments is shown schematically in Figure 1. The main parts of the apparatus are a cylindrical column, an electrical circuit, and a working section. The column was a vertical Plexiglas cylinder with an inner diameter of 0.2 m and a height of 0.3 m. The gas (nitrogen) entered the column from the bottom through a gas distributor. The distributor was a circular perforated Plexiglas plate with uniform pores to ensure equal distribution of the bubbles through the column. The working section (cathode) was a copper cylinder plated with nickel with a 0.025 m outside diameter. The cylinder active height was a variable, and three active heights were used, namely, 0.03, 0.09, and 0.15 m. The cell anode was a thinwalled stainless steel cylinder with its outside diameter closely fit to the column inside diameter. The anode area was large relative to the area of the cathode, enabling the anode to be used as a reference electrode instead of using an external one in identifying the limiting current. In the packed column experiments, the annular space between the two cylinders (anode and cathode) was packed with inert plastic packing, and the height of the vertical cylinder cathode was fixed at 0.15 m. Three different types of packing were used, namely, spheres, cylinders, and Raschig rings. Three different diameters of each packing were used, namely, 0.008, 0.01, and 0.012 m, with the same aspect ratio of unity. Insulated wires were used to feed current to the cell electrodes. The electrical circuit was composed of a direct current power supply of 12 V output with a built-in voltage controller. The cell current was measured by a digital ammeter connected in series with the circuit, while the cell voltage was measured by a digital voltmeter connected in parallel. 2.2. Procedure. Rates of transfer of mass at the cylinder cathode surface were obtained by identifying the limiting current of the reduction of K3Fe(CN)6 at the cathode surface using a solution composed of 0.01 M potassium ferricyanide, 0.1 M potassium ferrocyanide, and an excess of sodium hydroxide according to the reaction

Figure 2. Effect of Vg on k at different cylinder active heights.

by diffusion and convection, while migration is not participating. The limiting current was identified from the current− potential curves. The curves were plotted by changing the cell feeding current and recording the reading of the voltmeter (cathode potential) corresponding to the current. Each reading was left for sufficient time to reach a constant value. Three concentrations of sodium hydroxide (supporting electrolyte) were used, namely, 1, 2, and 3 M. All chemicals were of analytical reagent grade. The temperature was maintained at 303 ± 1 K. The physical properties and the compositions of the solutions used are found in Table 1.

Fe(CN)6−3 + e → Fe(CN)6−4

Transfer of Fe3+ to the cathode surface takes place via three mechanisms: (i) convection, (ii) diffusion, and (iii) migration of ions to the opposite electrodes. To apply the present mass transfer results in heat transfer (by analogy),8,9 electrical migration should be eliminated. Using excess NaOH confirms that the transfer of Fe3+ to the electrode surface mainly occurs 9926

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Figure 3. Overall correlation for the unpacked column.

plates,19 bubble columns,20 screens,21 and spheres,22 where a power ranging from 0.22 to 0.36 was obtained. Whitney and Tobias23 conducted a basic study to explain the mechanism by which transfer of mass occurs at gas sparged geometries. According to their study, a surface renewal mechanism caused by the gas bubbles rising inside the concentration boundary layer causes enhancement of transfer of mass. They concluded the equation

3. RESULTS AND DISCUSSION The measured limiting current values IL at various conditions enabled the calculation of the coefficient of transfer of mass (k) at the outside surface of the cylinder using the equation8,9 k=

IL ZFAC

(1)

Equation 1 was obtained on the basis of the assumption of steady state and instantaneous reaction of the ferricyanide ions at the cathode surface, which makes the interfacial concentration equal zero. 3.1. Unpacked Column Data. The effect of gas velocity on the coefficient of transfer of mass at various cylinder active heights and various Sc values is shown in Figure 2. For the studied range of Vg values (Vg < 5 cm/s), where the flow regime of the gas bubble is bubbly flow, increasing Vg leads to an increase in k. The data in Figure 2 fit the equation k ∝ Vg 0.52

k ∝ Vg 0.5

(3)

The following simplified model account outlines how mass transfer is enhanced by gas bubbles via surface renewal and may lend support to eq 2. As the bubble rises in the diffusion layer at certain locations on the cylinder surface, it induces an axial and a radial flow toward that location whose diameter is assumed to be the same as that of the bubble;15 the fresh solution stays at that location for a contact time (t). As the bubble leaves that location, the solution returns again to the mixture bulk. As the bubble rises, this process is repeated along the cylinder surface. In the contact period between the fresh solutions displaced by the gas bubbles and the outer surface of the cylinder, mass transfer to the cylinder surface occurred by a time-dependent diffusion according to Fick’s law:24

(2)

The number of rising gas bubbles increases with increasing Vg. Gas bubbles generate turbulence in the column by two mechanisms: (i) microconvection resulting from the formation of eddies and (ii) macroconvection caused by radial displacement of the solution by the rising bubbles in the container.15,16 Both types of convection enhance transfer rates of heat and mass at the surface of the cylinder. Figure 2 also shows that there is a dependency of k on the cylinder height. As the cylinder height increases, the coefficient of mass transfer decreases. This is because increasing the cylinder height causes an increase in the developed velocity boundary layer and concentration boundary thickness along the cylinder surface and an increase in the resistance to transfer of mass, which decreases k. The power of Vg in eq 2 is close to the value of 0.5 and the value of 0.55 obtained by Zarraa et al.17 and Noseir et al.,18 who studied transfer of mass between liquid and solid in gas sparged fixed beds of spheres and Raschig rings, respectively. The superficial gas velocity power (0.52) is higher than the value obtained for other geometries, for example,

dC d2C =D 2 dt dx

(4)

The frequency at which a region of thickness equal to the bubble diameter (db) receives a fresh solution as the bubble stream rises upward is the same as the number of bubbles passing per second (N) which is given by N=

Vg ° πdb3/6

The integrated form of eq 4 leads to the equation ⎛ D ⎞0.5 k = 2⎜ ⎟ ⎝ πt ⎠ 9927

(5) 25

(6)

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The time of contact (t) between the fresh solution and the cylinder surface is given by t=

πd 3 1 = b N 6Vg °

(7)

substituting for t in eq 6 gives ⎛ 6DVg ° ⎞0.5 k = 2⎜⎜ 2 3 ⎟⎟ ⎝ π db ⎠

(8)

from which k ∝ Vg . The present Vg power of 0.52 is close to the value of 0.5 that resulted from the model. All parameters were grouped in dimensionless forms as Fr, j, and Re, which are usually used to correlate the data for transfer of heat and mass in gas−liquid systems15 to obtain a dimensionless correlation from the experimental data. Figure 3 shows that the experimental data verify the equation 0.5

−0.16

j = 0.03(Re × Fr )

⎛ L ⎞−1.1 ⎜ ⎟ ⎝ de ⎠

(9)

for the operating parameters 1253 < Sc < 2778, 0.17 < Re × Fr < 6.1, and 0.17 < L/de < 0.86. The average deviation is ±8%. The use of the dimensionless group Re × Fr eliminates the need to measure the bubble diameter required for Re and Fr calculation. 3.2. Packed Column Data. Figure 4 shows the gas velocity effect on the coefficient of transfer of mass for different packing geometries and different sizes. The data show that the coefficient of mass transfer increases as the gas velocity increases and decreases as the packing size increases. The size dependency k differs for the three packings used. The size dependency is in the order spheres > cylinders > Raschig rings; this may be due to the effect of packing geometry on the hydrodynamic conditions and gas superficial velocity in the bubble column. The data shown in Figure 4 fit the equation

k ∝ Vg n

(10)

where n ranges from 0.53 to 0.63, depending on the packing geometry. An overall dimensionless correlation relating all parameters was obtained for each packing. Figure 5 shows that for spherical packing the data verify the equation j = 0.14(Re × Fr )−0.127

(11)

for the operating parameters 1253 < Sc < 2778 and 0.16 < Re × Fr < 8.7. The average deviation is 8.5%. For the column packed with Raschig rings, the data shown in Figure 6 fit the equation j = 0.133(Re × Fr )−0.155

(12)

Figure 4. Effect of Vg on k at different packing geometries and sizes.

The average deviation is 7%. Figure 7 shows that the data for the cylindrical packing fit the equation j = 0.0985(Re × Fr )−0.14

between the two transport processes of heat and mass under various flow conditions. The difference between Pr and Sc affects the values of constants in the correlations and is related to the ratio of Nu and Sh by the equation26

(13)

β Nu ⎡ Pr ⎤ =⎢ ⎥ ⎣ Sc ⎦ Sh

The average deviation is 9%. The dimensionless equations obtained in this study can be applied to heat transfer to estimate the external coefficient of heat transfer at the cylinder surface in the cases of unpacked and packed columns by exploiting the similarities between transfer of heat and mass. Previous studies using the limiting current technique8,9,12 found that there is a close agreement

(14)

where β is a constant, and its value varies between 0.33 and 0.4. Figure 8 shows the effect of (Re × Fr) on the j factor at the cylinder surface in the absence of packing and, in other cases, where the cylinder was surrounded by inert packing of different 9928

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Figure 5. Overall correlation for the packed reactor with inert spheres.

Figure 6. Overall correlation for the packed reactor with inert Raschig rings.

Figure 7. Overall correlation for the packed reactor with inert cylinders. 9929

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Figure 8. j vs (Re × Fr) for the unpacked column and packed column with different geometries.

(iii) The presence of inert packing around the cylinder enhanced the transfer of mass and heat (by analogy). The enhancement factor varies between 1.46 and 2.73, depending on the packing geometry and size.

geometries. The presence of inert packing around the cylinder increases the mass transfer rates and (by analogy) the rates of heat transfer. It is likely in the case of the packed column, where the free space available for bubble motion is limited due to the presence of packing, that frequent bubble collisions and coalescence take place in the interstices of the packing; these large bubbles penetrate the concentration boundary layer and increase the rate of transfer of mass by the surface renewal mechanism. The superior performance of spheres compared to Raschig rings and cylinders may be ascribed to the fact that the curved surface of the spheres allows the rising bubbles to rise without hindrance, while the flat bottom of the vertically oriented cylinders impedes the rising bubbles as they collide with it. The inferior position of Raschig rings compared to spheres is probably caused by the portion of vertically oriented rings; gas bubbles that enter inside the ring lose their ability to induce radial momentum to the vertical cylinder because this momentum is caught inside the Raschig rings.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +2035745962, +966540853623. Notes

The authors declare no competing financial interest.

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4. CONCLUSION (i) Gas bubbles generate microconvection and macroconvection caused by the recycling of the bubble displaced solution in the container,19 and both types of convection contribute to increasing transfer of mass and heat at the cylinder surface. The presence of packing around the cylinder deprives it of macroconvection; besides, the presence of the packing slows down microconvection by virtue of friction between eddies and the solid packing. Despite the aforementioned negative effect of the packing, mass and heat transfer rates are still high at the cylinder surface due to bubble collision and coalescence in the interstices. (ii) The dimensionless correlations obtained can be used in the design of a batch packed and unpacked bubble column that uses vertical tubes as a cooling facility. The outside coefficient of heat transfer at the cylinder surface is obtained from the correlations.25,27 Also, the correlations are useful in the scale-up and design of a gas sparged batch annular electrochemical reactor. 9930

NOMENCLATURE A = vertical cylinder outer area, m2 a = constant b = constant C = bulk concentration of ferricyanide, mol/m3 Cp = specific heat of the solution, J/kg·K D = diffusivity of ferrocyanide, m2/s d = vertical cylinder outside diameter, m db = diameter of bubble, m de = equivalent diameter (di − d), m di = column inner diameter, m dp = packing diameter, m F = Faraday’s constant (96500 C/equiv) g = acceleration due to gravity, m/s2 h = coefficient of transfer of heat, W/m2·K IL = limiting current, A k = coefficient of mass transfer, m/s k′ = thermal conductivity, W/m·K L = cylinder height, m N = number of bubbles n = constant t = contact time, s x = length of the diffusing path, m Vg = gas velocity, m/s Vg° = gas volumetric flow rate, m3/s Z = electrons transferred during the reaction dx.doi.org/10.1021/ie500766j | Ind. Eng. Chem. Res. 2014, 53, 9925−9931

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Fr = Froude number Vg2/gdb j = factor for mass or heat transfer (St × Sc0.66) Nu = Nusselt number (hdb/k′) Pr = Prandtl number (μCp/k′) Re = Reynolds number (ρVgdb/μ) Sc = Schmidt number (μ/ρD) Sh = Sherwood number (kdb/D) β = constant μ = solution viscosity, kg m−1 s−1 ρ = solution density, kg/m3

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(20) Cavatorta, O. N.; Bohm, U. Mass transfer in electrolytic cells with gas stirring. J. Appl. Electrochem. 1987, 17, 340−346. (21) Zaki, M. M.; Nirdosh, I.; Sedahmed, G. H. Liquid-solid mass transfer from horizontal woven screen packing in bubble column reactors. Can. J. Chem. Eng. 2000, 78, 1096−1101. (22) Sedahmed, G. H. Mass transfer at gas sparged spherical electrodes. J. Appl. Electrochem. 1993, 23, 167−172. (23) Whitney, G. M.; Tobias, C. W. Mass-transfer effects of bubble streams rising near vertical electrodes. AIChE J. 1988, 34, 1981−1995. (24) Higbie, R. Rate of absorption of a gas into a still liquid during short periods of exposure. Trans. AIChE 1935, 31, 365−389. (25) Kayser, R. F. Analogy among heat, mass, and momentum transfer. Ind. Eng. Chem. Res. 1953, 45, 2634−2636. (26) Mottahed, B.; Molki, M. Artificial roughness effects on turbulent transfer coefficients in the entrance region of a circular tube. Int. J. Heat Mass Transfer 1996, 39, 2515−2523. (27) Verma, A. K. Heat and Mass-Transfer Analogy in a Bubble Column. Ind. Eng. Chem. Res. 2002, 41, 882−884.

REFERENCES

(1) Degaleesan, S.; Dudukovic, M.; Pan, Y. Experimental study of gas-induced liquid-flow structures in bubble columns. AIChE J. 2001, 47, 1913−1931. (2) Shah, Y. T.; Godbole, S. P.; Deckwer, W. D. Design parameters estimations for bubble column reactors. AIChE J. 1982, 28, 353−379. (3) Prakash, A.; Margaritis, A.; Li, H. Hydrodynamics and local heat transfer measurements in a bubble column with suspension of yeast. Biochem. Eng. J. 2001, 9, 155−163. (4) Frank, M. J. W.; Kuipers, J. A. M.; Versteeg, G. F.; Van Swaaij, W. P. M. The performance of structured packings in trickle-bed reactors. Trans. Inst. Chem. Eng. 1999, 77, 567−581. (5) Urseanu, M. I.; Ellenberger, J.; Krishna, R. A structured catalytic bubble column reactor: Hydrodynamics and mixing studies. Catal. Today 2001, 69, 105−113. (6) Khamadieva, R.; Bohm, U. Mass transfer to the wall of a packed and unpacked bubble column operating with Newtonian and nonNewtonian liquids. Chem. Eng. J. 2006, 116, 105−113. (7) Therning, P.; Rasmuson, A. Liquid dispersion and gas holdup in packed bubble columns at atmospheric pressure. Chem. Eng. J. 2001, 81, 69−81. (8) Mizushina, T. The electrochemical method in transport phenomena. Adv. Heat Transfer 1971, 7, 87−161. (9) Selman, J. R.; Tobias, C. W. Mass transfer measurements by the limiting current technique. Adv. Chem. Eng. 1978, 10, 211−318. (10) Abdel-Aziz, M. H.; Nirdosh, I.; Sedahmed, G. H. Liquid−solid mass and heat transfer behavior of a concentric tube airlift reactor. Int. J. Heat Mass Transfer 2013, 58, 735−739. (11) Cavatorta, O. N.; Bohm, U. Heat and mass transfer in gas sparging systems: Empirical correlation and theoretical models. Chem. Eng. Res. Des. 1988, 66, 265−274. (12) Gay, B.; Mackley, N. V.; Jenkins, J. D. Shell-side heat transfer in baffled cylindrical shell and tube exchangersan electrochemical mass transfer modeling technique. Int. J. Heat Mass Transfer 1976, 19, 995− 1002. (13) Sedahmed, G. H.; El-Taweel, Y. A.; Konsowa, A. H.; Abdel-Aziz, M. H. Mass transfer intensification in an annular electrochemical reactor by an inert fixed bed under various hydrodynamic conditions. Chem. Eng. Process. 2011, 50, 1122−1127. (14) Sedahmed, G. H.; El-Taweel, Y. A.; Konsowa, A. H.; Abdel-Aziz, M. H. Effect of packing geometry on the rate of mass and heat transfer at a vertical tube imbedded in fixed bed under single and two phase flow. Int. Commun. Heat Mass Transfer 2013, 48, 149−154. (15) Deckwer, W. D. On the mechanism of heat transfer in bubble column reactors. Chem. Eng. Sci. 1980, 35, 1341−1346. (16) Hart, W. F. Heat transfer in bubble agitated systems: A general correlation. Ind. Eng. Chem. Process Des. Dev. 1976, 15, 109−114. (17) Zarraa, M. A.; El-Tawil, Y. A.; Farag, H. A.; El-Abd, M. Z.; Sedahmed, G. H. Effect of gas sparging on the rate of mass transfer at a single sphere. Chem. Eng. J. 1991, 47, 187−191. (18) 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 1997, 24, 733−740. (19) Sedahmed, G. H. A model for correlating mass transfer data in parallel plate gas sparged electrochemical reactors. J. Appl. Electrochem. 1984, 15, 777−780. 9931

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