Entrance Effect and Gas-Film Mass-Transfer ... - ACS Publications

Mar 1, 2000 - School of Chemical Engineering, Ryerson Polytechnic University, Toronto, Ontario, M5B 2K3 Canada. The effects of the bed height and the ...
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Ind. Eng. Chem. Res. 2000, 39, 1039-1047

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Entrance Effect and Gas-Film Mass-Transfer Coefficient in a Large-Diameter Packed Column H. D. Doan* and M. E. Fayed† School of Chemical Engineering, Ryerson Polytechnic University, Toronto, Ontario, M5B 2K3 Canada

The effects of the bed height and the entrance section below the packing support on mass transfer in a 1.2-m diameter packed bed of 50-mm ceramic Intalox saddles were investigated under various gas flow rates from 1957 to 7828 kg‚h-1‚m-2 and liquid flow rates from 12 200 to 46 700 kg‚h-1‚m-2. The entrance effect accounted for 17% of the overall water vapor transferred from moist air to a calcium chloride solution in the tower, regardless of the packing height. For a 0.91-m high bed, the average mass-transfer coefficient was directly proportional to the gas rate and was proportional to the liquid rate to the power of 0.24. For a 1.8-m high bed, the average mass-transfer coefficient was proportional to the gas rate to the power of 0.89 and appeared to be independent of the liquid rate. The height of a transfer unit (HTU) for 50-mm ceramic Intalox saddles remained relatively constant under various gas rates used in the present study. The HTU was about 0.5 m for the short bed and 0.8 m for the tall bed. Introduction Packed columns are widely used for gas-liquid contact operations in the chemical industries. They are also becoming important in environmental protection such as in air- and water-cleaning processes.1,2 Efficient mass transfer from a gas to a liquid (and vice versa) in a column requires a maximal contact between the two phases. Packed towers are often used to achieve this objective. The packing provides a large surface area over which the gas contacts the liquid, thereby improving mass transfer as compared to, for example, a spray tower without packing. Design of industrial-scale packed towers can be difficult in many cases. This is due to uncertainty in scaling-up laboratory and pilot-plant data.3 Published data have often been obtained from investigating mass transfer in small columns (less than 0.254-m diameter) in which gas flow patterns may be different from those in a large industrial-scale column.4 Mass-transfer coefficients obtained with small columns may thus deviate from those for larger towers. In addition, other factors such as the gas entrance and the liquid distribution may also significantly affect mass transfer in packed towers. The present work was conducted to investigate the effects of some of these parameters on the overall masstransfer coefficient using a large tower of 1.2-m diameter to simulate the industrial-size tower. Numerous studies on mass transfer in a packed bed have been done. However, most reported data are for the liquid-film mass-transfer coefficient. Only a few pieces of literature for the gas-film mass-transfer coefficient are available. Some overall mass-transfer coefficients for 50-mm plastic Super Intalox were reported.5 More recently, Chiang et al. reported some masstransfer data for a packed bed of 25-mm plastic Intalox and Super Intalox saddles.6 Among various reported * To whom correspondence should be addressed at 350 Victoria Street, Toronto, Ontario, Canada, M5B 2K3. Tel.: (416) 979-5000, ext. 6341. Fax: (416) 979-5044. E-mail: [email protected] † E-mail: [email protected].

publications, only a few correlations accurately predict the liquid-film mass-transfer coefficient.7 The classical correlations of Sherwood and Holloway8 and Shulman et al.9 are the most useful and widely used for Raschig rings and Berl saddles. However, to the knowledge of the authors there is no correlation available for ceramic Intalox saddles. Potnis and Lenz reported the Sherwood number correlations for polypropylene Tripak, using humid airlithium chloride solution that is a desiccant.10 Again, the mass-transfer process was liquid-phase-controlled for this system. Gandhidasan et al. used humid aircalcium chloride solution in their studies of mass transfer in a gas-liquid contactor. They reported that the system had a significant mass-transfer resistance in the liquid phase.11,12 On the other hand, the results from the present study using the same desiccant showed that the mass-transfer resistance in the liquid phase was only substantial for a 0.91-m high bed. For a higher bed (1.8 m), the mass-transfer resistance in the liquid phase was negligible compared to that in the gas phase. Thus, this paper presents the data obtained with two bed heights (0.91 and 1.8 m) of 50-mm ceramic Intalox saddles in a 1.2-m diameter tower. The effect of gas entrance on the overall mass transfer in the tower is quantified and presented. The effect of liquid flow rate and liquid distribution on the mass-transfer rate is also reported. Experimental Method Experimental and Analytical Method for Investigating Mass Transfer in a Packed Bed. A column of 1.2-m diameter and 4.3-m height was used as an absorption tower as shown in Figure 1. To reduce the wall effect on the data obtained, a large ratio of tower diameter to packing size (>15) is recommended.13 The tower was thus filled with 50-mm ceramic Intalox saddles at varied bed heights. Humid air was brought into contact with a 35%-by-weight calcium chloride solution (brine), a desiccant, in the packed bed. Water vapor was thus transferred from the moist air to the brine solution.

10.1021/ie990604f CCC: $19.00 © 2000 American Chemical Society Published on Web 03/01/2000

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pressure of water over the brine solution at the inlet and the outlet of the tower and is expressed as

∆Plm )

[(Pai - Pbo) - (Pao - Pbi)] ln

Figure 1. Schematic diagram of the experimental setup for the mass-transfer study.

Ambient air driven by a blower was saturated with water vapor in a 0.91-m diameter humidification tower. The saturated air then entered the bottom section of the 1.2-m diameter absorption tower. From a liquidholding tank, the brine was pumped to the top of the absorption tower where it was distributed over the top of the packed bed by a ladder-type distributor. The distributor consists of a main header leading into a series of horizontal pipes with orifices drilled on their lower face. An average of 22 orifices per square meter of the cross-sectional area of the tower was used. The brine was drained back to the holding tank by gravity. Upon absorption of moisture, the temperature of the brine was raised somewhat because of the heat of condensation of water vapor. A water-cooled plate-type heat exchanger was used to cool and maintain the brine feed at a relatively constant temperature. The experiment was designed for three liquid flow rates (12 200, 24 400, and 46 700 kg‚h-1‚m-2). High liquid and gas rates were used to approximate commercial operational conditions (e.g., 46 700 kg of brine‚h-1‚m-2 and 7 828 kg of air ‚h-1‚m2-). The liquid flow rate to the tower was measured with a magnetic flowmeter (Roto Flow Sensor, Fabco, Toronto, Ontario, Canada) with an accuracy of 1%. At each liquid rate, the flow rate of air was varied from 1 957 to 7 828 kg‚h-1‚m-2. The flow rate of air was measured with a flow sensor with an accuracy of 2% (DS 300-8, Baker Instruments, Markham, Ontario, Canada). The temperature and the relative humidity of the inlet and outlet air streams were measured with type-K thermocouples and humidity sensors (HX-92C, Omega Engineering Inc., Stamford, CT). The temperature and density of the brine entering and exiting the column were also monitored. A volumetric pycnometer (Canlab, Toronto, Ontario, Canada) was used to measure the brine density. A standard equation for mass flux can be used to derive the equation for the average mass-transfer coefficient.13 The average mass-transfer coefficient, Kga, can be expressed as

Kga )

Gw H∆Plm

(1)

where Gw is the amount of water absorbed per square foot of the cross-sectional area of the tower and over the whole bed height, H, and a is the specific area of the packing. ∆Plm is the log-mean difference of the partial pressure of the water vapor in the air and the vapor

[

]

(Pai - Pbo)

(Pao - Pbi)

(2)

where Pai is the partial pressure of water vapor in the inlet air and Pao is the partial pressure of water vapor in the outlet air. Pbi is the vapor pressure of water over the brine solution at the liquid inlet and Pbo is the vapor pressure of water over the brine solution at the liquid outlet. Vapor pressure of water over the brine solution was measured with an isoteniscope using the ASTMD-2879-83 method.14 The height of a transfer unit, HTU, is defined as

HTU )

G′ KgaPT

(3)

where G′ is the molar flux of the dry air and PT is the total pressure in the tower. The average mass-transfer coefficient (Kga) and the height of a transfer unit (HTU) were determined from experimental data obtained using eqs 1-3. The Sherwood number, which is a standard dimensionless masstransfer coefficient, is used to represent the gas-phase mass-transfer coefficient in the present study. The Sherwood number is defined as

Sh )

kcDP DAB

(4)

where kc is the mass-transfer coefficient, DP is the characteristic length of the packing, and DAB is the diffusivity of water vapor in air. A published DAB value of 2.6 × 10-5m2‚s-1 for the air-water system at 25 °C was used in the present study.15 The characteristic length of the packing is the diameter of a sphere having a surface area equal to that of the packing piece. The number of pieces of 50-mm ceramic Intalox saddles in the bed was counted and found to be 9146 pieces per cubic meter of the bed. With the specific area of 118 m2‚m-3 as given in ref 13, the characteristic length of the packing was estimated at 0.032 m. For a gas-phase-controlled system, the overall masstransfer coefficient, Kg, is in the same order of magnitude of the gas-film mass-transfer coefficient, kg. Therefore, the relation of the mass- transfer coefficient, kc, and the overall mass-transfer coefficient, Kg, is written as

kc ) kgRT ) KgRT

(5)

where R is the gas constant and T is the temperature of the gas. For humid air-calcium chloride solution, the masstransfer process is expected to be gas-phase-controlled. In other words, the main resistance to mass transfer is in the gas phase at the gas-liquid interface. The overall mass-transfer coefficient (Kg) would mainly be dependent on the hydrodynamic condition of the gas phase in the bed rather than on the liquid rate. However, the overall mass-transfer rate could vary with the liquid rate because the liquid rate might have an effect on the

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Figure 2. Schematic diagram of the experimental setup for the liquid distribution study.

liquid distribution. A better liquid distribution leads to an increase in the effective area of the packing, hence, promoting more contact between the liquid and the gas in the packed bed. This results in more material transferred from the gas to the liquid. Thus, the masstransfer rate, hence, the average mass-transfer coefficient (Kga) may increase. This may be misleadingly seen as the effect of the mass-transfer resistance in the liquid phase on the mass-transfer process. Therefore, the liquid distribution in the bed was also investigated. Experimental Method for Studying Liquid Distribution in a Packed Bed. The 1.2-m diameter PVC tower was again filled with 50-mm ceramic Intalox saddles. Water was pumped to a pipe-type distributor sitting right on top of the packed bed. Water exiting the packed bed was collected in a collecting trough located beneath the packed tower as shown in Figure 2. The liquid-collecting trough consisted of 96 equal-volume cells of 0.1 × 0.1 m and 0.74 m high, which covered the whole cross-sectional area of the tower. The volume of liquid collected in each cell of the collecting trough was measured. The collecting time was also recorded. The local liquid rate to each cell was then calculated. The uniformity of the liquid distribution throughout the packed bed was evaluated using a distribution coefficient. This coefficient is defined as the root-mean square of the standard deviation from the mean of the local liquid rates to all the cells:16

MC )

x∑(xi - xj)2 nxj

(6)

where MC is a dimensionless distribution coefficient that is a variation from the distribution coefficient proposed by Hoek,17 xj is the average liquid flow rate into a cell, xi is the measured liquid rate to an individual cell, and n is the number of cells in the liquid-collecting trough. The distribution coefficient tends to zero for a perfectly ideal liquid distribution. The liquid distribution was investigated under the following conditions: (1) The height of the packed bed: 0.3, 0.6, 1.2, and 1.8 m. (2) The number of liquid-delivery points in the liquid distributor: 22 per square meter. (3) The total liquid flow rate to the packed bed: 5, 10, 20, 30, and 40 USGPM that are equivalent to 982, 1964, 3928, 5892, and 7856 kg‚h-1‚m-2. Results and Discussion Effect of Gas and Liquid Rates on the MassTransfer Coefficient. The average mass-transfer coef-

ficients, Kga, obtained under various liquid rates are plotted against the gas mass flux in Figure 3. Each data point is the average value of triplicate runs. At a given liquid rate, the average mass-transfer coefficient increased with increases in the gas mass flux or the gas rate, as expected. The thickness of the concentration boundary layer on the gas side at the gas-liquid interface becomes thinner when the gas rate is increased. This results in a higher mass-transfer coefficient because the mass-transfer coefficient is inversely proportional to the thickness of the concentration boundary layer. Under various liquid rates from 12 200 to 46 700 kg/m2‚h, the average mass-transfer coefficient appeared to be a strong function of the gas rate for both 0.91- and 1.8-m bed heights. Figure 4 shows the reciprocal of the mass-transfer coefficient versus the reciprocal of the gas mass flux for both 0.91- and 1.8-m high beds of 50-mm ceramic Intalox saddles. These curves are in fact the Wilson plots that are used to determine the dominant phase controlling the transfer process. The magnitudes of the intercepts of the plots are rather small. This indicates that the transfer process was mainly gas-phase-controlled, although the liquid rate showed some effect on the mass-transfer coefficient for the shorter bed (0.91-m high). In other words, the resistance to mass transfer in the liquid phase was negligible compared to that in the gas phase at the gas-liquid interface. The effect of the liquid rate on the average masstransfer coefficient was more obvious for the 0.91-m high bed than for the 1.8-m high bed as shown in Figure 5. For a 0.91-m high bed, increases in the liquid rate significantly improved the liquid distribution in the bed. This was observed by Doan and Fayed in an investigation of liquid distribution in a packed bed of 50-mm ceramic Intalox saddles.18 The improvement of liquid distribution was represented by smaller values of the distribution coefficient as shown in Figure 6. Good liquid distribution enhanced the contact of the gas and the liquid in the bed. The mass-transfer rate was thus increased. On the other hand, for the 1.8-m high bed, the effect of the liquid rate on the liquid distribution was marginally small. For liquid rates larger than 5000 kg‚h-1‚m-2, the curve of the distribution coefficient becomes asymptotic as shown in Figure 6, indicating an insignificant change of the liquid distribution with the liquid rate. Thus, there would be only a slight enhancement in mass transfer due to the improvement of the liquid distribution. For the 1.8-m high bed, the average mass-transfer coefficient did not show dependence on the liquid rate clearly at the gas rates from 1957 to 7828 kg‚h-1‚m-2. The mass-transfer coefficient only increased slightly with a 400% increase in the liquid rate. This reconfirmed that for the humid-air-calcium chloride solution the transfer process was controlled by the gas phase. From experimental data obtained, the Sherwood numbers were calculated using eq 4. The film theory postulates that mass transfer occurs in an “effective” film with zero velocity at the interface and the masstransfer coefficient is directly proportional to the diffusivity. However, the film theory is considered inapplicable to the gas-liquid contacting process because the contact time of the gas and the liquid may not be long enough to allow a steady concentration gradient to be developed in the film. The penetration theory of Higbie19 and the surface-renewal theory of Danckwerts20 are

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Figure 3. Overall mass-transfer coefficients at various gas mass fluxes for 0.91- and 1.8-m high beds of 50-mm ceramic Intalox saddles.

Figure 4. Wilson plots for mass transfer in 0.91- and 1.8-m high beds of 50-mm ceramic Intalox saddles with the humid air-calcium chloride solution.

often considered better alternatives for gas-liquid contacting systems. These theories predict that the mass-transfer coefficient is proportional to the diffusivity to the power of 0.5 (i.e., DAB0.5). The dependency of the mass-transfer coefficient on DAB0.5 is adopted in the present study. Therefore, to obtain the following correlation for the Sherwood number, the Sherwood number was set to be proportional to the Schmidt number (Sc) to the power of 0.5. The Sherwood numbers obtained with the 1.8-m high bed were divided by Sc0.5 and plotted against the gas Reynolds number (Re) in Figure 7 on a log-log scale. As shown in Figure 7, log(Sh/Sc0.5) varies linearly with log(Re). For the 1.8-m high bed of 50-mm ceramic Intalox saddles where the mass-transfer resistance was mainly in the gas phase, a correlation for the Sherwood number with the gas Reynolds number was obtained

by linear regression with a correlation coefficient, r2 ) 0.998:

Sh ) 0.018Re0.89Sc0.5

(7)

For the 0.91-m high bed, the mass-transfer coefficient changed slightly with the liquid rate. The average masstransfer coefficient was correlated with the gas Reynolds number and the liquid rate, L, using multiple linear regression (r2) 0.998) as

Kga ) 0.0146Re0.99L0.24

(8)

Equation 8 shows that the mass-transfer coefficient is almost directly proportional to the gas Reynolds number while it has only a slight dependence on the liquid rate, L, as indicated by the small power on the liquid rate.

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Figure 5. Variation of the mass-transfer coefficient with the liquid mass flux under various gas mass fluxes.

Figure 6. Effect of the liquid mass flux on the liquid distribution in a packed bed of 50-mm ceramic Intalox saddles under various bed heights.

The dependence of the average mass-transfer coefficient on the liquid rate to the 0.24 power falls in the reported range of 0.22-0.38.21 The average mass-transfer coefficient obtained in the present study was proportional to the gas Reynolds number to the power of 0.89 for the 1.8-m high bed and of 0.99 for the 0.91-m high bed. On the other hand, some reported studies showed that the average mass-transfer coefficient was proportional to the gas rate to the exponent of 0.80.21 This discrepancy may be due to the different gas-liquid systems used in these studies. In the literature, some of the systems might not be entirely gas-phase-controlled. The liquid phase might still affect the overall mass transfer substantially while the predominant resistance to mass transfer in the humid aircalcium chloride system used in the present study was in the gas phase. Thus, the average mass-transfer coefficient given in the literature appeared to be de-

pendent on the gas rate to a lesser extent than that in the present study. In addition, this could also be attributed to the large difference in the bed size, especially the bed diameter, which could alter the liquid and gas distribution in the bed. This results in variation of the effective specific area of the packing, hence, the average mass-transfer coefficient Kga. The gas-film mass-transfer coefficient, kg, should be theoretically independent of the bed height, as used in correlations proposed by Onda et al.,22 when the physical and hydrodynamic conditions remain the same in the two beds. The overall mass-transfer coefficient, Kg, should thus be independent of bed heights as well. However, it was noted that in the present study the Kga values for the 0.91-m high bed were substantially higher than those for the 1.8-m high bed, as shown in Figure 3. Djebbar and Narbaitz23 also reported experimental data and a correlation for the liquid-phase mass-transfer

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Figure 7. Variation of log(Sh/Sc0.5) with log(Re) for the 1.8-m high packed bed of 50-mm ceramic Intalox saddles and curve fitting of the data.

coefficient, which showed that the coefficient decreased with increases in the bed height. The concentration profile of the solute in the gas might vary nonlinearly in the packed bed. The solute concentration dropped quickly in the lower section of the bed. The mass-transfer rate in this region might thus be very high and might decrease quickly when moving upward in the bed. In the present study, a major portion of water vapor might be transferred to the brine solution in the lower 0.9 m of the bed. The upper 0.9 m of the packing might have a much lower mass-transfer rate because of a much smaller driving force for mass transfer. This was in fact the case. The measured amount of water transferred in the 1.8-m high bed was only slightly higher than that in the 0.91-m high bed. The log-mean average driving forces for the two bed heights were also very close. On the other hand, the average mass-transfer coefficient, Kga, is a volumetrically averaged coefficient that is dependent on the volume of the bed (i.e., the height of the bed), as defined in eq 1. The resultant mass-transfer coefficient, Kga, in the 1.8-m high bed was thus much lower than that in the 0.91-m high bed. The dependency of the average mass-transfer coefficient, Kga, on the bed height, as realized by many researchers, is one of the difficulties in scaling-up pilotplant and laboratory data to larger industrial-scale towers. Nevertheless, these data provide some useful quantitative estimation of the transfer coefficient for practical uses with some reservation until sufficient data have been available so that a robust model of Kga with the bed height can be obtained. Determination of the Height of a Transfer Unit (HTU). The height of a transfer unit is a simple but representative factor that shows quantitatively the potential of a given packing for promoting gas/liquid contact and mass transfer in an absorption tower. The lower the HTU, the higher the mass-transfer efficiency of the packing, because a low HTU means less packing would be required to perform a certain mass-transfer duty. The average mass-transfer coefficient, Kga, was previously shown to be dependent on the bed height.

The HTU is also expected to be influenced by the bed height as well because the HTU is inversely proportional to the Kga. For the 0.91-m high bed, the HTU was between 0.40 and 0.55 m, dependent upon the gas and liquid flow rates as shown in Figure 8. An increase in the liquid flow rate resulted in an increase in the Kga and a decrease in the HTU at a given gas flow rate. At low liquid rates, a good liquid distribution was not achieved. As the liquid flow rate was increased, the wetting of the packed bed was enhanced and the liquid distribution improved. Under this condition, the packed bed provided a higher effective contact area for the gas and the liquid; therefore, the mass-transfer rate increased. Hence, the value of Kga was higher. It is self-evident that a high mass-transfer rate contributes to a lower HTU at a fixed gas flow rate. As expected, at a given liquid flow rate, the HTU did not change significantly when the gas flow rate was increased. At a higher gas flow rate, more gas was in contact with liquid. More solute was transferred to the liquid. The value of Kga thus increased. The HTU is inversely proportional to Kga. On the other hand, the HTU is directly proportional to the gas rate. Therefore, the HTU remained relatively unchanged with increases in the gas flow rate. For the 1.8-m high bed, the average HTU was about 0.8 m with little effect of liquid flow rate, as shown in Figure 8. Figure 8 also shows a 9% increase in the HTU when the gas rate increased from 1957 to 7828 kg‚h-1‚m-2. This seems to be a nonsignificant change compared to an increase of almost 4-fold in the gas rate under the conditions of low (12 200 kg‚h-1‚m-2) or moderate liquid rates (24 400 kg‚h-1‚m-2). At a high liquid rate (46 700 kg‚h-1‚m-2), the HTU values scattered somewhat with the gas flow rate. This may be due to local flooding in the bed, which reduces the contact between the gas and liquid, leading to variation in the mass-transfer coefficient and the height of a transfer unit, HTU. Effect of Gas Entrance on the Overall Mass Transfer in a Packed Bed. To evaluate the mass

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Figure 8. Variation of HTU with the gas and liquid mass fluxes to a packed bed of 50-mm ceramic Intalox saddles. Table 1. Values of KgaH for 0.91- and 1.8-m Beds of 50-mm Ceramic Intalox Saddles and Those Due to the Effect of the Gas Entrancea

L

G

(I) KgaH (0.91-m bed) -1 (kmol‚h ‚ m-2‚atm)

12 200 12 200 12 200 24 400 24 400 46 700 46 700

1957 4892 7828 6360 7828 6360 7828

114 296 470 440 580 543 638

(II) KgaH (1.8-m bed) -1 (kmol‚h ‚ m-2‚atm)

(III) entrance -1 (kmol‚h ‚ m-2‚atm)

144 367 520 484 550b 484 662c

22.0 41.6 80.7 75.8 108.4 96.2 116.5 average: standard deviation: overall average: standard deviation:

DEV. (%) of (III) from (I) (II) 19.2 14 17.2 17.2 18.7 17.7 18.2 17.5 1.7

15.3 11.3 15.5 15.6 19.7 19.9 17.6 16.4 2.8 16.9 2.3

a L: liquid rate in kg‚h-1‚m-2. G: gas rate in kg‚h-1‚m-2. Entrance: mass transfer due to the empty section at the bottom of the tower before the packing support. DEV (%) ) (III)/(I) × 100 or (III)/(II) × 100. b Corrected for the actual gas rate of 7339 kg‚h-1‚m-2. c Corrected for the actual gas rate of 6850 kg‚h-1‚m-2.

transfer in the entrance section from the gas inlet to the packing support, which is labeled as entrance section in Figure 1, experiments with the empty bed (without packing) were carried out. The liquid distributor was set right above the packing support. The same liquid and gas rates as for previous cases with packing were used. In effect, the bottom section of the tower beneath the packing support acted as a spray tower with a significant mass transfer from the gas to the liquid. This amount of mass transfer was lumped into the overall mass transfer across the whole tower. Therefore, the data obtained with the empty tower was useful for removal of the entrance effect from the overall mass transfer. Molar fluxes of water absorbed to the liquid, obtained under various gas and liquid rates, are shown in Table 1. The quantity KgaH was used so that the amount of water transferred per unit area of the tower and over the whole bed height was obtained. This quantity is equivalent to Gw/∆Plm, in which the variation of the mass-transfer rates with different bed heights due to different mass-transfer driving forces was eliminated. The average deviation of the KgaH values was about 11.3% compared to the difference of more than 100% of

the Kga values for the two bed heights. Therefore, this quantity for the entrance section could be reasonably considered independent of the bed height and was then removed from the data for both bed heights. The amount of water absorbed to the liquid by the packing bed itself was thus obtained. A substantial amount of water was absorbed in the entrance section of the tower as shown in Table 1. On the average, this water was about 17% of the overall amount of water absorbed in the tower with a standard deviation of 2.3 when all data for both bed heights of 0.91 and 1.8 m were pooled together. Water absorbed in the entrance section was lumped into the overall water absorbed in the packed tower because the measuring points for humidity and temperature were in the air duct leading to the bottom of the tower. Thus, it is useful to correct the average masstransfer coefficient for the entrance effect so a more representative transfer coefficient for the packing itself is extracted. The molar flux of water absorbed per unit cross-sectional area of the tower was calculated from the experimental data obtained with the empty tower and subtracted from that for the tower filled with the packing. The corrected values of the mass-transfer

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coefficient for the 1.8-m high bed were then used to recalculate the Sherwood numbers and correlated as (r2 ) 0.998)

Sh ) 0.015Re0.89Sc0.5

(9)

For the 0.91-m high bed a new correlation of the corrected average mass-transfer coefficient (with a correlation coefficient r2 ) 0.998) was also obtained as shown below:

Kga ) 0.012Re0.99L0.24

(10)

The correction for the portion of mass transfer in the entrance section just caused a small decrease in the proportional constants in both eqs 9 and 10. The dependency of the Sherwood number and the average mass-transfer coefficient on the gas Reynolds number and the liquid rate remained the same.

kg ) gas-film mass-transfer coefficient (kmol‚m-2‚s-1‚atm-1) Kg ) overall mass-transfer coefficient (kmol‚m-2‚s-1‚atm-1) Kga ) average mass-transfer coefficient (kmol‚m-2‚s-1‚atm-1) L ) liquid rate to the tower (kg‚m-2‚h-1) MC ) dimensionless distribution coefficient for liquid distribution n ) number of cells in the liquid collecting trough Pai ) partial pressure of water vapor in the inlet air (atm) Pao ) partial pressure of water vapor in the outlet air (atm) Pbi ) vapor pressure of water over the inlet brine solution (atm) Pbo ) vapor pressure of water over the outlet brine solution (atm) Re ) Reynolds number for the gas phase (Re ) (DPFu)/µ) R ) gas constant (m3‚atm‚kmol-1‚K-1) Sc ) Schmidt number (Sc ) (µ)/FDAB) Sh ) Sherwood number (Sh ) (kcDP)/DAB) T ) temperature (K) u ) superficial gas velocity (m‚s-1) xi ) local liquid rate to individual cells (m3‚s-1) xj ) average liquid rate to a cell (m3‚s-1)

Conclusion

Greek Symbols

The following can be concluded from the data obtained in the present study: (1) For the system of humid air-calcium chloride solution, the resistance to mass transfer in the liquid phase was negligible as compared to that in the gas phase. (2) The average mass-transfer coefficient was proportional to the liquid rate to the power of 0.24 for the 0.91-m high bed of 50-mm ceramic Intalox saddles. On the other hand, the effect of the liquid rate on the masstransfer coefficient for the 1.8-m high bed was negligible. (3) For both 0.91- and 1.8-m high beds under liquid rates from 12 200 to 46 700 kg‚h-1‚m-2, the average mass-transfer coefficient was almost directly proportional to the gas rate. (4) For the 0.91-m high bed, the average HTU was about 0.5 m while the average HTU was about 0.8 m for the 1.8-m high bed. The HTU appeared to be unchanged with the gas rate. (5) For a gas-phase-controlled system in a bed of 50mm ceramic Intalox saddles, the entrance section of the tower contributed about 17% of the overall mass transfer over the whole tower. The corrected gas-film masstransfer coefficient can be predicted from eq 9, given that the bed is reasonably tall (1.8 m). For a shorter bed (0.91m), the corrected average mass-transfer coefficient is better represented by eq 10.

∆Plm ) log-mean pressure difference (atm) µ ) viscosity of air (kg‚m-1‚s-1) F ) density of air (kg‚m-3).

Acknowledgment Financial support during the experimentation period from Chemetics International and Ryerson Polytechnic University are gratefully appreciated. The authors also sincerely appreciate valuable comments on the experiments from Dr. Max Leva (Pittsburgh, PA). Nomenclature a ) specific area of packing (m2‚m-3) DAB ) diffusivity of water vapor in air (m2‚s-1) DP ) characteristic length of the packing (m) G′ ) molar flux of dry air (kmol‚m2-‚s-1) GW ) molar flux of water per unit cross-sectional area of the tower over the whole bed height (kmol‚m-2‚s-1) H ) packed bed height (m) HTU ) height of a transfer unit (m) kc ) mass-transfer coefficient (m‚s-1)

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Received for review August 9, 1999 Revised manuscript received December 21, 1999 Accepted January 11, 2000 IE990604F