Liquid-Side Mass-Transfer Resistance of Structured Packings

Ind. Eng. Chem. Res. 2004, 43, 7113-7120

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Liquid-Side Mass-Transfer Resistance of Structured Packings Carlos R. Murrieta,† A. Frank Seibert,‡ James R. Fair,‡ and J. Antonio Rocha-U*,§ Separations Research Program, The University of Texas at Austin, Austin, Texas 78712, and Universidad Regiomontana, Monterrey, Nuevo Leon, C.P. 64000, Me´ xico

Stripping of oxygen from water using air was performed in four different structured packings. Because the transfer of oxygen to air is easy, the resistance to mass transfer lies on the liquid side. From these experiments, the measured global volumetric mass-transfer coefficient (KLae) is equal to the individual mass-transfer coefficient of the liquid phase (kLae). The value of the interfacial area ae is estimated using a model proposed in 1992, and the individual mass-transfer coefficient of the liquid is deduced and compared to one based on the penetration theory used in the first model proposed for structured packing in distillation columns published in 1985. It was found that the correction factor CE used to equate both coefficients is close to unity. Introduction Models for predicting the mass-transfer efficiency of beds of structured packings have been based on experimental results for distillation systems. Although such systems involve transfer resistances on both vapor and liquid sides, it has usually been assumed that the vapor side dominates and thus models for the liquid side need not be very precise. The estimation of the liquid-side mass-transfer coefficient is based on the penetration theory, with the exposure time related to the residence time of flowing liquid across a single corrugation. Clearly, this represents a problem situation for distillations with a high slope of the equilibrium line, and thus a significant portion of the resistance is in the liquid phase. Also, for those cases where structured packing can be justified for absorbers or strippers, prediction of the liquid-side coefficient becomes critical. This paper provides experimental data for several structured packings under conditions of high liquid-side resistance. Background Figure 1. Experimental system.

Although structured packings were introduced in the 1970s, it was not until 1985 that Bravo et al.1 proposed the first general model for predicting their masstransfer performance. The database comprised distillation data for gauze-type packing, for which the effective interfacial area was taken as the specific packing area (i.e., complete wetting of the packing surface). The liquid-side mass-transfer coefficient was estimated from the penetration theory, and the vapor-side coefficient was then deduced using the film model and experimental values of the overall rate of mass transfer. Thus, errors in estimating the liquid-side resistance were incorporated into the models for the gas-side resistance. * To whom correspondence should be addressed. E-mail: [email protected]. † Present address: McKinsey & Co., Mexico City, Me´xico. ‡ The University of Texas at Austin. § Universidad Regiomontana.

The liquid flow velocity across the packing surface was based on falling-film relationships for laminar flow:

ULe )

( )( ) 2 3Γ FL 2FL 3µLΓ

0.333

(1)

where ULe ) effective liquid velocity through channel (m/s), Γ ) L/(PAt) [kg/s‚(m of perimeter)], At ) tower cross-sectional area (m2), and P ) available perimeter of packing (m/m2 tower cross section). The characteristic length was an average for several dimensions of the gauze packing that resulted in de ) 0.0072 m, while the width of the channel was S ) 0.009 m. Later, Bravo et al.2 generalized the model to include structured packings made from sheet metal, choosing de ) S. Effective velocities were related to liquid holdup, the packing void fraction, and the channel angle with

10.1021/ie049836r CCC: $27.50 © 2004 American Chemical Society Published on Web 09/23/2004

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Figure 2. Mass-transfer results for oxygen stripping at a constant liquid rate. Packings: Intalox 1T and 2T. Symbols: (+) measured; (0) predicted by eq 4 and/or eq 7; (b) experimental.

the horizontal. On the basis of the work of Shi and Mersmann,3 they proposed an expression to obtain the effective interfacial area:

UGe )

UGS (1 - hL) sin θ

ULS ULe ) hL sin θ ae ) FSE ap Re

29.12(WeLFrL)0.15S0.359 0.2 0.6 L

 (1 - 0.93 cos γ)(sin θ)0.3

kL ) 2xDLULe/πS (2)

(3)

(4)

The penetration model was used to provide the liquidside mass-transfer coefficient:

kL ) 2xDL/πt

as the time the liquid travels the equivalent diameter (S) at the effective velocity ULe, i.e., t ) S/ULe. Hence,

(5)

where DL ) liquid diffusion coefficient (m2/s) and t ) exposure time of liquid (s). The exposure time was taken

(6)

Combining eq 3 with eq 6:

x

kL ) 2

DLULS πShL sin θ

(7)

This relationship indicates that the mass-transfer coefficient is proportional to the liquid velocity to the 0.5 power and is a function of liquid holdup, which also depends on ULS. Apparently, the gas rate has no effect on the coefficient. We might note that the assumption is also made that the liquid flow rate is uniform throughout the packed bed. Rocha et al.4 suggested a modification for the average exposure time:

t ) S/CEULe

(8)

kL ) 2xDLCEULe/πS

(9)

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Figure 3. Mass-transfer results for oxygen stripping at a constant gas rate. Packings: Intalox 1T and 2T. Symbols: (+) measured; (0) predicted by eq 4 and/or eq 7; (b) experimental.

The correction factor CE would account for changes in the liquid rate that could affect the average residence time. A value of CE equivalent to about 1.1 has been taken empirically by some authors, e.g., Fair et al.5 Previous Work Henriques de Brito et al.6 stripped oxygen from demineralized water with air in a 0.295-m-diameter column. Beds of Mellapak 250Y and 500Y (enhanced sheet metal surfaces) of 0.42-m depth were used. Values of the volumetric coefficient kLae were measured, followed by measurement of the effective interfacial area ae using the fast pseudo-first-order reaction of CO2 with NaOH. The penetration model was used to correlate the kL values deduced:

not expect the packing with the lower surface to have higher values of the coefficient. For the exposure time, these investigators used holdup and contact length expressions suggested by Billet7 to obtain a design expression for the liquid-side coefficient that involves the liquid holdup (hL ) c3ULSc4) and the contact length (d′e)

x

kL ) 2

DLULS0.603 πd′e sin θ

(12)

The contact length d′e was measured and correlated with the results to give 0.102 m for Mellapak 500Y and 0.061 m for Mellapak M250Y. These led to the corrected expressions

k500Y ) 0.000168ULS0.39 L

(10)

) 0.000233ULS0.302 k500Y L

(13)

) 0.000429ULS0.28 k250Y L

(11)

) 0.000396ULS0.302 k250Y L

(14)

Compared with the present work, coefficient values from eqs 10 and 11 are in the same range, but one would

Weiland et al.8 absorbed CO2 and SO2 from air into a dilute caustic solution to evaluate mass transfer and

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Figure 4. Mass-transfer results for oxygen stripping at a constant gas rate. Packing: Flexipac 2. Symbols: (+) measured; (0) predicted by eq 4 and/or eq 7; (b) experimental.

liquid holdup. A 0.15-m column was used, and one structured packing, Montz A2 (a gauze packing, similar in characteristics to Sulzer BX), was included in the liquid-side mass-transfer correlations. Whether gas-side resistance contributed is questionable. The volumetric mass transfer for the liquid (kLae) was found to be about 3 times lower than that predicted by Bravo et al.1 Surprisingly, no effect of the liquid rate was found. In a second paper, Henriques de Brito et al.,9 using the same column, measured the effective mass-transfer area for Mellapak 125Y, 250Y, and 500Y. They concluded that all three sizes can provide an effective masstransfer area higher than the geometric area defined by the packing surface up to a factor of 2. The excess interfacial area was thought to result from ripples, wave detachment, and fragmentation of the film into small droplets. Because the excess interfacial area occurred at very low loadings, the results of these workers appear to be in some question. Laso et al.10 used the same equipment as the Henriques de Brito group to study Mellapak 125Y, 250Y, and 500Y sheet metal packings, with oxygen stripped from water with air. This is the same system as that used in the present work, except for a smaller column.

They correlated the volumetric mass-transfer coefficient with superficial liquid velocity (results for Mellapak 125Y were not regressed):

Mellapak 250Y:

kLae ) 0.574ULS0.62

(15)

Mellapak 500Y:

kLae ) 0.713ULS0.71

(16)

These volumetric mass-transfer coefficients make sense in that the higher surface area packing shows higher mass-transfer coefficients. No effect of the gas velocity was found. Experimental Plan Liquid-side coefficients would be measured for several structured packings at varying gas and liquid rates. The measurements would be made in a column of the same diameter as the one used by Rocha et al.4 for an extensive study of mass transfer in structured packings under distillation conditions. Guidance would be provided by the early work of Sherwood and Holloway,11 who used the oxygen/air/water system, for which there

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Figure 5. Mass-transfer results for oxygen stripping at a constant gas rate. Packing: Sulzer BX. Symbols: (+) measured; (0) predicted by eq 4 and/or eq 7; (b) experimental.

is no gas-side resistance. They measured coefficients for ceramic Raschig rings and Berl saddles. The experimental results would be given in the form of volumetric coefficients kLae. Values of kL would be deduced from ae/ap relationships as needed to compare with the reported results of others. Finally, values of the modification factor CE would be determined to enable the simple form of the penetration model to be used. Experimental Setup The experimental air stripping system is shown in Figure 1. The column inside diameter is 0.428 m and can accommodate packed heights up to 2 m. The column is connected to a 40 Hewlett-Packard air blower, and tap water is used for irrigating the packing. The liquid distributor is of the perforated pipe type, with 60 pour points (ca. 430 points/m2). Air is fed to the column through a dual-flow-type (perforated-plate) distributor, and 1.2-m height is provided between the inlet distributor and the packing support plate. For all experiments, the packed height was about 0.85 m, depending on the height of the individual packing elements.

Experimental Procedure Cylinder oxygen was bled into the feedwater, with the mixture content measured by the Winkler iodometric method (Standard Methods...12). The oxygen content of the exit water was also measured, and the amount of oxygen stripped was determined by material balance. The gas flow rate was measured and controlled by a valve that sent air to a purge. The water flow rate was measured by an orifice plate and controlled by a valve in the line. The signal outputs of both meters were linked to a Fischer Porter computer console. The use of the computer allowed flow rates to be preset, maintained, and continuously monitored during each experiment. The pressure and temperature of the air stream were monitored at the console; the values were needed to correct the air flow rate. The flow of oxygen injected into the water stream was controlled by a regulator and measured by a rotameter. The measurement was used to give an estimate of the oxygen concentration. To promote the distribution of oxygen into the water, a perforated pipe unit was used inside the flow pipe. The approximately 12 m between the point of injection and

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Figure 6. Penetration model correction factor CE for oxygen stripping. Packings: Sulzer BX and Intalox 1T. Table 1. Characteristics of Packings Used packing

ap (m2/m3)



S (m)

θ (deg)

Flexipac 2 Intalox 1T Intalox 2T Sulzer BX

233 315 213 490

0.95 0.94 0.95 0.90

0.018 0.0152 0.0221 0.009

45 45 45 60

the column was considered sufficient enough to give excellent mixing and solution of air into the water. Care was taken not to exceed the saturation value of oxygen in the water. Structured packings used were Flexipac-2, Intalox 2T, Intalox 1T, and Sulzer BX. Some tests were also conducted with 1-in. metal pall rings to establish a relationship with the early results of Sherwood and Holloway. Characteristics of the packings tested are given in Table 1. Results The basic results are given in Figures 2-5. For each figure, the experimental results for the volumetric masstransfer coefficient kLae are shown in the top panel. Calculated values of ae/ap using eq 4 are shown in the middle panel, and the deduced values of the masstransfer coefficient kL, obtained from kLae and ae, are shown in the bottom panel. Figure 2, for Intalox 1T and 2T at a constant liquid rate, shows that the gas rate has little effect on the effective area or the mass-transfer coefficient kL. This would be expected from eqs 4 and 5. This is also in agreement with the work of others. The figure also shows that for the same liquid rate the packing with the larger surface (Intalox 1T) has about 30% higher volumetric mass-transfer coefficients. Finally, the top panel shows a good agreement between measured and predicted values of the volumetric coefficient. Figure 3, for the same packings, shows the effects of the liquid rate with the gas rate held constant. Again,

the agreement between prediction and measurement (top panel) is reasonably good. Also, the volumetric coefficient for the larger surface packing (Intalox 1T) has somewhat higher volumetric coefficients. Figure 4 shows data for Flexipac 2 at two gas rates. Again, it can be concluded that the gas rate has little effect on the mass-transfer coefficient and that the measured and predicted values of the volumetric coefficient are in reasonable agreement. Figure 5 shows the effects of the gas and liquid rates on the coefficients for Sulzer BX packing. As for the Intalox packings, the gas rate has little or no effect on the mass-transfer coefficients. For varying liquid rate, the predicted volumetric coefficients are higher than the measured coefficients. The measured coefficients for Sulzer BX and Flexipac 2 (Figure 4) are about the same, but the predicted values for Sulzer BX are higher. The correction factor CE was introduced in eq 8. It is now possible to deduce this factor from the measurements, and the results are shown in Figures 6 and 7, obtained from

(kLae)exp ) 2 or

CE )

x

()

DLULeCE ae a πS ap p

[() ]

πS (kLae)exp DLULe ae 2 a ap p

2

(17)

The factor is generally greater than unity but always less than 2.0. Figure 8 shows the averaged values of CE for the packings tested, together with comparable bar charts for the packing geometric characteristics. Finally, the results of the present work are compared with those of previous investigators in Table 2.

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Figure 7. Penetration model correction factor CE for oxygen stripping. Packings: Intalox 2T and Flexipac 2. Table 2. Reported vs Measured or Predicted Mass-Transfer Parameters author(s) Henriques de Brito et

reported al.6

Henriques de Brito et al.9 Laso et al.10

this work

k500Y L k250Y L

) 0.000233ULS0.302 ) 0.000396ULS0.302 ae/ap ) 0.465ReL0.30 ) 0.465(FLULS/µLap)0.30 (kLae)M500Y ) 0.713ULS0.71 (kLae)M250Y ) 0.574ULS0.62

Conclusions On the basis of the present experimental work, which covers four different structured packings, there are several general conclusions that may be drawn. First, the gas rate has no significant effect on the liquid-side mass-transfer coefficient. Earlier work by Sherwood and Holloway11 indicates that in the loading region there can be a slight enhancement of the coefficient based on the gas rate. Our experimental work here was limited to regions below the load point. A second conclusion is that the penetration model can be used to estimate the liquid-side coefficient. The exposure time, earlier based on the residence time for

kT1 L kT2 L

) 0.0007ULS0.2 ) 0.0006ULS0.2 ae/ap ) 1.7ULS0.4 0.875 measured: kLaT1 e ) 1.596ULS 0.816 measured: kLaT2 ) 0.873U LS e 0.6 predicted: kLaT1 ) 0.392U LS e 0.6 predicted: kLaT2 e ) 0.258ULS

liquid flowing over a corrugation side, may need a small correction as given earlier in this paper. A third conclusion, more of an observation, is that very little work has been done with liquids other than water. The model proposed here takes into account liquid properties such as diffusivity, viscosity, density, and surface tension. Still, experimental verification is needed for liquids with properties significantly different from those of water. Nomenclature ae ) effective area, m2 ap ) packing area, m2

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Figure 8. Penetration model correction factor CE, corrugation width S, and specific surface area ap for the packings used in this study. Abbreviations: S-BX ) Sulzer BX; 1-IT ) Intalox 1T; 1-2T ) Intalox 2T; F2 ) Flexipac 2.

At ) tower cross-sectional area, m2 CE ) correction factor for liquid-side mass transfer de ) characteristic length of the packing, m DL ) diffusion coefficient for liquid, m2/s FrL ) Froude number for liquid (UL2/Sg) Fs ) gas flow factor (UGSFG0.5), (m/s)(kg/m3)0.5 FSE ) factor for surface enhancement hL ) liquid holdup, m3/m3 kL ) mass-transfer coefficient for the liquid phase, m/s P ) perimeter of channel packing/cross-sectional area of the channel, m/m2 ReL ) Reynolds number for liquid (ULSFL/µL) S ) side dimension of corrugation, m t ) time, s UGe ) effective gas velocity, m/s ULe ) effective liquid velocity, m/s WeL ) Weber number for liquid (UL2FLS/σgc) Greek Letters  ) void fraction of packing γ ) contact angle, deg Γ ) mass flow over the perimeter, kg/s‚(m of perimeter) F ) density, kg/m3 µ ) viscosity, kg/m‚s π ) 3.1416... θ ) angle with horizontal for the corrugation channel, deg

Literature Cited (1) Bravo, J. L.; Rocha, J. A.; Fair, J. R. Mass Transfer in Gauze Packings. Hydrocarbon Process. 1985, 64 (1), 91-95. (2) Bravo, J. L.; Rocha, J. A.; Fair, J. R. A Comprehensive Model for the Performance of Columns Containing Structured Packings, Distillation and Absorption. Inst. Chem. Eng. Symp. Ser. 1992, No. 128, 489-507.

(3) Shi, M.; Mersmann, G. Effective Interfacial Areas in Packed Columns. Ger. Chem. Eng. 1985, 8, 87-96. (4) Rocha, J. A.; Bravo, J. L.; Fair, J. R. Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 2. Mass Transfer Model. Ind. Eng. Chem. Res. 1996, 35, 1660-1667. (5) Fair, J. R.; Seibert, A. F.; Behrens, M.; Sarabar, P. P.; Olujic, Z. Structured Packing PerformancesExperimental Evaluation of Two Predictive Models. Ind. Eng. Chem. Res. 2000, 39, 1788-1796. (6) Henriques de Brito, M.; Von Stockar, U.; MenendezBangerter, A.; Bomio, P.; Laso, M. Predicting the Liquid-Phase Mass Transfer CoefficientskLsfor the Sulzer Structured Packing Mellapak, Distillation and Absorption. Inst. Chem. Eng. Symp. Ser. 1992, No. 128, 137-144. (7) Billet, R. Packed Towers in Processing and Environmental Technology; VCH: Weinheim, Germany, 1995. (8) Weiland, R. H.; Ahlgren, K. R.; Evans, M. Mass Transfer Characteristics of Some Structured Packings. Ind. Eng. Chem. Res. 1993, 32, 1411-1418. (9) Henriques de Brito, M.; Von Stockar, U.; MenendezBangerter, A.; Bomio, P.; Laso, M. Effective Mass-Transfer Area in a Pilot Plant Column Equipped with Structured Packings and with Ceramic Rings. Ind. Eng. Chem. Res. 1994, 33, 647-656. (10) Laso, M.; Henriques de Brito, M.; Bomio, P.; Von Stockar, U. Liquid-side mass transfer characteristics of a structured packing. Chem. Eng. J. 1995, 58, 251-258. (11) Sherwood, T. K.; Holloway, F. A. L. Performance of Packed TowerssLiquid Film Data for Several Packings. Trans. AIChE 1940, 36, 39-70. (12) Standard Methods for the Examination of Water and Wastewater, 18th ed.; American Public Health Association: Washington, DC, 1992; pp 4-98 and 4-99.

Received for review February 28, 2004 Revised manuscript received July 13, 2004 Accepted August 16, 2004 IE049836R