MASS TRANSFER IN A LARGE BUBBLE COLUMN

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1 MASS TRANSFER IN A LARGE BUBBLE COLUMN Hiroshi KATAOKA,Hiroshi TAKEUCHI, Katsumi NAKAO, Hideharu YAGI, Teiriki TADAKI, Tsutao OTAKE, Terukatsu MIYAUCHI, Koichi WASHIMI, Kazuhiro WATANABEand Fumitake YOSHIDA Research Team on Large Scale Bubble Column* Values of the liquid-phase volumetric coefficient of mass transfer kla in a large bubble column, 550 cm in diameter and 700 cm in liquid depth, were obtained from experimental data for carbon dioxide desorption from water, on the assumptions of perfect mixing in the liquid phase and piston flow or perfect mixing in the gas phase. The liquid-phase mass transfer coefficient kl was separated from kla9 using the data10) on gas holdup and the bubble diameter obtained with the same column. Values of kla were in good agreement with a previous correlation30 based on data with small bubble columns, provided that perfect mixing was assumed for both gas and liquid phases. Values of kl ranged from 0.01 to 0.05 cm per second and were not affected appreciably by column size. The relationship between kl and bubble diameter was roughly similar to that in small columns, although bubbles in the present experiments were somewhatlarger than in small columns. Introduction The bubble column is widely used for mass transfer as well as for chemical reactions because of its simple construction and excellent performance. Although many studies have been reported on bubble columns smaller than 60 cm in diameter, information necessary for the design and operation of large bubble columns for industrial use is hardly available in the literature. Give an opportunity to use an industrial bubble column, 550cm in diameter, we obtained values of the liquid-phase volumetric mass transfer coefficient kla by desorbing carbon dioxide from water, compared them with data in the literature, and gained some basic information on mass transfer in large bubble columns. 1. Apparatus and rocedure Figure 1 shows a rough scheme of the experimental setup. The bubble column consisted of a cylindrical section, 550cm in diameter and 900cm in height, and a conical bottom section with a slope of 45. Gas was blown into the column through several nozzles, ca. 30mm in inside diameter, installed in the conical section. Liquid carbon dioxide from cylinders was vapor- Received May29, Correspondence concerning this article should be addressed to H. Kataoka, Institute of Applied Biochemistry, Univ. of Tsukuba, Ibaraki * c/o rofessor Terukatsu Miyauchi, Dept. of Chem. Eng., University of Tokyo, Tokyo 113. Details of the research team are given in a related report10). VOL. 12 NO ized in a vaporizer which was indirectly heated by steam, diluted with air to a concerntration of approximately 2 per cent, and sparged into water in the column for about 5minutes. When a sufficient amount of carbon dioxide was dissolved in water, the supply of carbon dioxide was turned off while continuing the air supply, thus staring a desorption run. Samples of water in the column were taken at fixed intervals. To prevent a time lag in sample composition, water was withdrawn continuously from the column through a sampling nozzle once a run was started. Carbon dioxide dissolved in the liquid sample was converted to methane in a reactor kept at 310 Cby the following reaction. CO2+4 H2 >CH4+2 H2O Methane was analyzed by means of a gas chromatograph with a flame ionization detector at a Fig. 1 Schematic diagram of experimental app aratus 105

2 Fig. 2 Time course of dissolved carbon dioxide concentration column temperature of 150 C. The conversion reaction was catalyzed by a nickel nitrate catalyst which was impregnated into C-22 particles of 60 to 80 mesh under vacuum, kept at 110 C for 24hours and activated at 400 C for 5hours. The conversion of the above reaction was 99% at 300 C and 100% at 310 C. Water used in the experiments was plant water supplied from Lake Imba, Chiba refecture. The temperature of water was 11 C, and that of gas supplied to the column was 6 to 13 C. 2. Calculation of Results Figure 2 shows the time-dependent change of carbon dioxide concentration C in the column water. In the figure CB indicates the blank value of C, i.e., the value of C obtained by analyzing the column water by gas chromatography after sufficient aeration. The value of CBwas higher than the concentration in equilibrium with the partial pressure of carbon dioxide in the atmosphere, probably because someorganic impurities in plant water were converted to CH4in the analytical procedure. Due to the long pipeline between the carbon dioxide vaporizer and the column, increase in carbon dioxide concentration in the column water was observed for some time even after carbon dioxide supply from the cylinders was turned off at =0. Values of C obtained after the peak of C was reached, i.e., after desorption started, were used in calculating kla. Since mixing conditions in the liquid and gas phases in large bubble columns are not yet well clarified, theoretical equations for evaluating kla were derived for the following two cases: (1) erfect mixing in both gas and liquid phases. (2) lug flow in the gas phase and perfect mixing in the liquid phase. In deriving the equations, the following assumptions were made, (a) Liquid-phase resistance controlled the rate of mass transfer, (b) Gas and liquid flowed under steady conditions, (c) Mass transfer through the free liquid surface was negligible. When the liquid phase is perfectly mixed, an instantaneous change of the dissolved carbon dioxide concentration is given by -(l -eg)dc/dt=kla(c- C*) (1) If Henry's law holds, C*, the dissolved carbon dioxide concentration in equilibrium with the average partial pressure p of carbon dioxide in the column, is given by C* =Hp (2) Case 1 erfect mixing in both gas and liquid phases The average carbon dioxide partial pressure p in the column is given by p=(pt/t) (3) A carbon dioxide balance for the entire column is given by (pt/t)gt - (pb/b)gb = ~ VL(dC/dt) (4) The carbon dioxide content in the atmosphere (ca. 0.03%) is negligible, i.e., pb=0. Furthermore, in view of the low concentration (ca. 2%) of carbon dioxide in the air supplied to the column during the absorption operation preceding a desorption run, increase of the gas rate in the column due to desorption can be neglected. Thus, Gt=G. From Eq. (4) one obtains Substituting Eqs. (2), (3), and (5) into Eq. (1), and integrating Eq. (1) with the initial conditions: f=0, C=C0 (6) one obtains where 3 klahrth klahrtvl, 1=~1^= d-eo)vo (7a) Case 2 lug flow in gas phase and perfect mixing in liquid phase From the carbon dioxide balance for a differential column volume at an arbitrary height, j^^=kla(c-hp) (8) Since the liquid phase is perfectly mixed, C is independent of z. Integration of Eq. (8) with a constant value of C gives CL / klahrt \) /m The average carbon dioxide partial pressure p in the column is defined by 106 JOURNAL OF CHEMICAL ENGINEERING OF JAAN

3 (10) From Eqs. (9) Jo and (10), 7=Apdz Substituting Eq. (ll) into Eq. (1), and integrating Eq. (1) with the initial conditions of Eq. (6), one obtains Thus, provided that the liquid phase is perfectly mixed, a semilogarithmic plot of In (C/Co) against t should give a straight line, whether perfect mixing or plug flow is assumed for the gas phase. Figure 2 shows that this is the case. From the slopes of the straight lines in Fig. 2, kla values were obtained by Eq. (7) or Eq. (12). 3. Results and Discussion Since practically no previous reports on large bubble columns are available in the literature, comparisons were madebetween the present results and data on small columns in the literature. With use of the data10) on gas holdup and bubble diameter, measured in the same column by another research group, values of the specific inter facial area a and the liquid-phase mass transfer coefficient kl were also calculated and compared with data in the literature Liquid-phase volumetric coefficient kla Akita and Yoshida1>2) proposed the following Eqs. (13), (14), and (15) for the liquid-phase volumetric mass transfer coefficient kla, the gas holdup eg, and the volume-surface mean bubble diameter dv8, respectively, based on their experiments with four bubble columns, 7.7 to 60 cm in diameter. /,. \0.5/á"T)2 ~ \0.62/nf)3 \0.31 o^o-ná") ("%å ) {Urn) (14> In comparing our experimental results with these equations, a column diameter of 60 cm was adopted for Dt, as was recommended by the original authors. According to Eq. (13) kla should increase with Dt to the 0.17 power. However, data of Akita and Yoshida1} indicated that such a trend leveled off for columns of larger diameter. The specific gas-liquid inter facial area a can be calculated from the bubble diameter, dv8 or db, and the gas holdup eg by the following known relationship. VOL. 12 NO Fig. 3 Volumetric mass transfer coefficients kla plotted against ug Fig. 4 Relationship between bubble diameter and superficial gas velocity a=6sg/dvs or a=6sg/db (16) Figure 3, in which kla is plotted against the average superficial gas velocity ug, shows that the present data of kla, obtained by assuming perfect mixing in both gas and liquid phases, agree well with the values predicted by Eqs. (13) and (14), in which Dt is taken as 60cm, and are represented by the chain line. The solid line in the figure represents kla values predicted by the following equation, using the observed values of db. ^=3.31^(^Y7<^Y/2 (17) Equation (17) was derived by Fair4) from the Frossling equation. Values of kla in the present work, obtained on the assumptions of perfect mixing in the liquid phase and plug flow in the gas phase, lie roughly midway between the values predicted by Eq. (13) and by Eq. (17) Bubble diameter db In Fig. 4 the average values of bubble diameter db, measured by Koide et al10) simultaneously with the present work, are compared with the values of db 107

4 Fig. 5 Relationship between gas holdup and superficial gas velocity Fig. 6 Relationship between specific interfacial area and superficial gas velocity Fig. 7 Comparison of liquid-phase mass transfer coefficient with previous data predicted by Eq. (15). Values ofdb are roughly three times larger than the values of dvs predicted by Eq. (15), in which Dt is taken as 60cm. Fair4) reported that for the air-water system the maximumbubble size was 2.7cm and that the majority of bubbles were between 0.16 and 1.6cm in diameter. Bubble sizes observed10) in the column we used were within this range. 3.3 GasholdupeG Two kinds of average gas holdup obtained by two different techniques, e0 and SGM,are plotted against average gas velocity ug in Fig. 5. For the details of these techniques reference should be made to the report by Koide et al.10). Figure 5 also shows the curves representing Eq. (14), in which Dt is taken as 60cm, and the correlation of Hughmark6), as well as the data points of Towell et al.u). It is seen that the present data are in good agreement with previous correlations based on data with small bubble columns Gas-liquid inter facial area a Figure 6 shows the values of the specific gasliquid inter facial area a calculated by Eq. (16) from the observed values of the gas holdup (eg and egm) and the bubble diameter db. The present data of a are roughly one-third of the values of a predicted by the correlation by Akita and Yoshida2), which is represented by the broken curve in the figure. This discrepancy is due to difference in bubble size in view offigs. 4 and Liquid phase mass transfer coefficient kl Values of the liquid-phase mass transfer coefficient kl9 obtained by dividing kla by a, are plotted against the average superficial gas velocity ug in Fig. 7. In calculating a by Eq. (16), the arithmetic mean values of eg and GMwere adopted. Two horizontal lines in the figure represent the following well-known equations for kl in dispersed systems proposed by Calderbank and Moo-Young3). for ^>0.25, ^=0.42(^)1/3(^y1/2 (18) \ L / XpL-LSL/ for ^<0.06, ^=0.3l(^f^)1/3(-^)"2/3 (19) V i ) \ldlj Akita and Yoshida2) proposed the following equation for kl. k d /ij WV/W3 \1/4/nd2n \3/8 ^7=a5UJ wrj \ ~^) (20) Figure 7 also shows two chain lines which represent the kl values precicted by Eq. (20) using two different bubble diameters, i.e., dv8 estimated by Eq. (15), in which Dt is taken as 60cm, and db observed10) and shown in Fig. 4. The figure also shows a line representing the kl values predicted by Eq. (21), which was derived by Kataoka and Miyauchi7) for gas absorption into a turbulent liquid. kl=0.5(el/vly»dy* (21) where el=ug-g (21a) Koide et al.10) measured liquid velocities ul and bubble velocities ub at various gas rates in the bubble column used in the present work. Using these velocities in the following Eq. (22), based on the Higbie model5\ a few values of kl were calculated and are shown in Fig. 7. kl-vn{t)~m db ) (22) Figure 7 also shows a few examples of kl values obtained in small bubble columns, i.e., data of Tadaki and Maeda12) for desorption of carbon di- 108 JOURNAL OF CHEMICAL ENGINEERING OF JAAN

5 oxide from water in a bubble column, 6 cm in diameter and 70 cm in liquid depth, equipped with a perforatedplate gas sparger, as well as the values of kl obtained by Towell et al.u) in a bubble column, 40.7cm in diameter. Values of kl obtained in the present work assuming perfect mixing in both gas and liquid phases are 5 to 30 per cent larger than predicted by Eq. (18) and tend to decrease with increasing gas velocity, whereas kl should be independent of gas velocity if Eqs. (18) and (19) were correct. Although the kl values are within -5 to 27 per cent of the values predicted by Eq. (21), kl should increase with gas velocity, if Eq. (21) were valid. Thus, kl seems to be affected little by turbulence in the liquid phase. Although the present kl data are 25 to 40 per cent larger than predicted by Eq. (20), the kl values obtained in the present work as well as those by Tadaki and Maeda decrease with increasing gas velocity in conformity with Eq. (20). The kl values predicted by Eq. (22) are in rough agreement with prediction by Eq. (20) and with the values obtained by Tadaki and Maeda. The present kl data, based on the assumptions of plug flow in the gas phase and perfect mixing in the liquid phase, lie between the values predicted by Eq. (19) and those by Eq. (20) but are more dependent on gas velocity. Degrees of mixing in the gas and liquid phases in the present experiments were estimated as follows. Values of the gas-phase eclet number calculated by the empirical equation of Towell et al.13). Based on their data for a bubble column, 100 cm in diameter, were 0.1 to 0.04 for gas velocities of 2.4 to 4.6cm per second, indicating almost perfect mixing in the gas phase. Values of \ul\ measured by Kojima et al.n) in the column used by us were 40 to 60cm per second, corresponding to a time for one recirculation of 13 to 20 seconds. Values of the liquidphase axial dispersion coefficient Da estimated by the correlation of Kato and Nishiwaki8) were 3.3 to 3.5X104 cm2/sec at the gas velocities used in the present experiments, indicating an extremely high degree of liquid mixing. Furthermore, in view of the fact that the ratio of liquid depth to column diameter was as small as 1.3, it could be surmised that the liquid phase was also almost perfectly mixed in the present experiments. As shown in Fig. 8, the relationship between the bubble diameter db and the kl values obtained in the present work on the assumptions of perfect mixing in both gas and liquid phases is in approximate agreement with Eq. (20), proposed by Akita and Yoshida2) from their experiments with smaller columns. Data of Towell et alu) with a bubble column, 40.7 cm in diameter, for gas velocities of 1.5 to 6.7 cm per Fig. 8 Relationship between kl and db9 dvs second and liquid velocities of 1.3 to 3.4cm per second are on the extention of the present results. Data of Kawagoe et al.9) with bubble columns, 9 to 20 cm in diameter, also agree well with Eq. (20). However, if plug flow is assumed for the gas phase, the present data would deviate greatly from Eq. (20). All these results contradict the statement of Calderbank and Moo-Young3} that kl is independent of bubble diameter dvs for the ranges of dvs<0.06 cm and dvs>0.25 cm, depending only on liquid properties. Since the degree of gas-phase mixing in the present experiments was probably between plug flow and perfect mixing, the kla values we obtained on the assumption of perfect mixing in both liquid and gas phases might be slightly greater than the real kl values. In any event, our kl values do not seem to be much different from kl values obtained with a small bubble column. The above discussion of mass transfer data in bubble columns seems to support the appropriateness of the bubble size measurements10) by the electrical resistivity probe technique conducted simultaneously with the present work. Conclusions Analysis of the data on desorption of carbon dioxide from water in a large bubble column, 550 cmin diameter and 700cm in liquid height, on the assumptions of perfect mixing in the liquid phase and perfect mixing or plug flow in the gas phase, led to the following conclusions. (1) If perfect mixing in both liquid and gas phases is assumed, values of the liquid-phase volumetric mass transfer coefficient kla obtained in the present work agree well with the correlation of Eq. (13), previously obtained1>2) from data for small bubble columns, less than 60 cm in diameter, with relatively large ratios of the column height to the diameter. (2) Values of the specific gas-liquid inter facial area obtained in the present work are roughly onethird of the values predicted by Eqs. (14) and (15), which are based on previous datalj2) with small VOL. 12 NO

6 bubble columns. This is mainly due to larger bubble size in the present experiments compared with those in small columns. (3) Values of the liquid-phase mass transfer coefficient kl are in the range of 1 to 5xlO~2cmper second, whether plug flow or perfect mixing is assumed for the gas phase, and are substantially independent of column size. (4) The relationship between kl and bubble diameter is in approximate agreement with Eq. (20), obtained1>2) from data with small bubble columns. Acknowledgments This paper reports part of the results of the group studies of a large bubble column using the gas-water system that preceded trial operation of an industrial column for hightemperature steam cracking of pertoleum asphalt at the plant of EUREKAIndustry Co., Ltd., at Sodegaura-machi, Kimitsugun, Chiba refecture. Kureha Chemical Industry Co., Ltd., gave generous financial support for organizing the research group. The authors are highly grateful to Kureha Chemical Industry Co., Ltd., EUREKA Industry Co., Ltd., and Chiyoda Chemical Engineering and Construction Co., Ltd. for their support and cooperation during the experiments and to all those who kindly assisted in the experimental work. Finally, sincere appreciation must be expressed to rof. K. Akita, School of Engineering, Tokushima University, for his helpful suggestions and advice concerning correlations of the data. Nomenclatures c* c Cpb Co Da DL DT db dvs el G G H h kl R t ub gas-liquid inter facial area per unit volume of aerated liquid [1/cm] concentration of gas dissolved in liquid [mol/cm3 ] equilibrium value of C [mol/cm3] concentration of gas dissolved in liquid [ppm] C in blank test [ppm] initial value of C [mol/cm3] axial dispersion coefficient [cm2/sec] gas diffusivity in liquid [cm2/sec] diameter of bubble column [cm ] bubble diameter measured by electrical resistivity probe volume-surface mean bubble diameter energy dissipation [cm] [cm] [cm2/sec3] [mol/sec] [mol/sec] [cm/sec2] mol/cm3à"atm] [cm] = molar gas flow rate = average molar gas flow rate =gravitational acceleration = Henry's law constant = column height liquid-phase mass transfer total pressure coefficient [cm/sec] [atm] averaged through the column [atm] partial pressure of CO2 [atm] value ofp averaged through the column[atm] gas constant [atm à" cm3/mol à" K] time [sec] velocity of gas bubble [cm/sec] ug. ul VG Vl g g gm vl ol l g Jo = superficial gas velocity at pressure of [cm/sec] = liquid velocity [cm/sec] = gas flow rate [cm3/sec] = liquid volume [cm3] = height from the bottom of bubble column [cm] = gas holdup, fraction of aerated liquid volume [-] = average gas holdup obtained from axial static pressure distribution [-] = average gas holdup measured by using the electrical resistivity probe liquid viscosity kinematic viscosity of liquid surface tension of liquid density of liquid density of gas difference between liquid and gas densities (=pl-g) [-] [g/cm - sec] [cm2/sec] [g/sec2] [g/cm3] [g/cm3 ] [g/cm3] <Subscripts> b = bottom of column G = gas L = liquid o = initial condition t = top of column Literature Cited 1) Akita, K. and F. Dev., 12, 76 (1973). Yoshida: Ind. Eng. Chem., rocess Des. 2) Akita, K. and F. Yoshida: ibid., 13, 84 (1974). 3) Calderbank, D. H. and M. B. Moo-Young: Chem. Eng. ScL, 16, 39 (1961). 4) Fair, J. R.: Chem. Eng., 67, July 3 (1967). 5) Higbie, R.: Trans. AIChE., 31, 365 (1935). 6) Hughmark, G. A.: Ind. Eng. Chem., rocess Des. Dev., 6, 218 (1973). 7) Kataoka, (1969). H. and T. Miyauchi: Kagaku Kogaku, 33, 181 8) Kato, Y. and A. Nishiwaki: ibid., 35, 912 (1971). 9) Kawagoe, M., K. Nakao and T. Otake: /. Chem. Eng. Japan, 8, 254 (1975). 10) Koide, K., S. Morooka, K. Ueyama, A. Matsuura, F. Yamashita, S. Suzuki S. Iwamoto, Y. Kato, H. Inoue, M. Shigeta, and T. Akehata: /. Chem. Eng. Japan, 12, 98 (1979). ll) Kojima, E., H. Unno, Y. Sato, T. Chida, H. Imai, K. Endo, I. Inoue, J. Kobayashi, H. Kaji, H. Nakanishi and K. Yamamoto: reprints of the 12th Autumn Meeting of The Soc. of Chem. Engrs., Japan, at Okayama, p. 17 (1978). 12) Tadaki, T. and S. Maeda: Kagaku Kogaku, 27, 803 (1963). 13) Towell, G. D., C.. Strand, and G. H. Ackerman: Chemical Reaction Engineering roc. 5th Europ. 2nd Int. Symp. on Reaction Engineering, Amsterdam, May (1972). 14) Towell, G.D., C.. Strand, and G. H. Ackerman: reprint of AIChE-Instn. June (1965). Ch. E. Joint Meeting, London, (resented at the 12th AutumnMeeting of The Soc. of Chem. Engrs, Japan, at Okayama, October 1978.) 110 JOURNAL OF CHEMICAL ENGINEERING OF JAAN