Ind. Eng. Chem. Res. 1999, 38, 4933-4937
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Mass Transfer in a Short Wetted-Wall Column. 2. Binary Systems Izak Nieuwoudt* and James C. Crause Institute for Thermal Separation Technology, Department of Chemical Engineering, University of Stellenbosch, Stellenbosch, South Africa
Mass-transfer coefficients were measured in a short wetted-wall column by evaporating binary liquid mixtures. These mass-transfer coefficients were compared with the gas-phase transfer coefficients reported in part 1 of this series. For the systems used in this study, enhanced mass transfer was observed when mixtures having large differences in pure component surface tensions were evaporated. For these systems, an increase in surface rippling was observed. This masstransfer enhancement was not exhibited in binary systems with small differences in pure component surface tensions. Introduction Although numerous studies on liquid side mass transfer have been done previously,1,4,11,14,17,22,23 most of the experimental work concentrated on the adsorption or desorption of sparingly soluble gases in water. The liquid side mass transfer in a nonrippling film can approximately be described by the penetration theory of Higbie.7,10,21 It was however found that in rippling liquid films Higby’s theory underpredicts the masstransfer coefficient by severalfold.1,4,10,12,14,16-18,23,25 It has been found experimentally that there is a negligible liquid side resistance to mass transfer for some systems in wetted-wall distillation columns.9,24 Since no data are available on the liquid side masstransfer coefficients for extractive distillation systems, it is difficult to predict what the influence of the introduction of the nonvolatile solvent will be on the ratio between the mass-transfer resistances. It is apparent that the prediction of liquid side masstransfer coefficients is still an inexact science and that factors such as liquid turbulence and surface waves can enhance mass transfer in the liquid-phase severalfold when compared to Higbie’s penetration theory. The influence of surface waves on the gas side mass-transfer coefficient is also unclear. In this study, mass-transfer coefficients were determined by the evaporation of a binary liquid mixture. These mass-transfer coefficients, together with knowledge about the pure component gas-phase mass-transfer coefficients, makes it possible to draw conclusions about the influence of nonvolatile solvents on the masstransfer process in extractive distillation.
temperatures are adjusted to the desired values. Before a run is started, the liquid is circulated through the column to heat up the liquid in the reservoir. At the start of a run the level and temperature of the liquid reservoir are noted. The liquid pump is then started, and the liquid flow rate are adjusted to the desired value. The liquid level below the wetted-wall tube is controlled to a height of approximately 5 mm below the upper part of the gas inlet piece. This ensures that there is minimal additional gas-liquid contact outside the wetted-wall tube. At the end of a run the level and temperature of the liquid reservoir are noted. To minimize the effect of the initial unsteady state at the start of a run, the duration of a run was usually 5 min or longer. Since the composition of liquid mixtures will generally change during evaporation, the experiments are stopped before 50 mL of liquid has evaporated. The total holdup of the system is about 1700 mL. The composition changes for the experiments done in this work are estimated to be less than 5%. Since the wetted-wall column is short, the composition difference between the inlet and outlet of the wetted section is very small. The largest composition change calculated over the length of the column is for the 30% acetone in ethylene glycol series (acetone percentage changed from 30% to 28%). The binary systems investigated in this study are acetone + methanol, methanol + 1-octanol, acetone + aniline, acetone + water, acetone + EG (ethylene glycol), and methanol + EG. The purities of the chemicals are reported in part 1 of this series. Data Reduction
Experimental Section The wetted-wall column used was described in detail in part 1 of this series. The wetted-wall tube is made from precision bore glass tubing, 25.4 mm diameter and 110 mm in length. Before a series of experiments is started, the wettedwall column is removed from the Perspex bath and thoroughly rinsed with acetone and dried. The wetted-wall column and reservoir are filled with liquid, and the constant-temperature bath and air * Corresponding author. Telephone: +27 21 808-4421. Fax: +27 21 808-2059. E-mail:
[email protected].
As was shown in part 1 of this series, the masstransfer coefficient for pure component evaporation is calculated by solving the following equation: h)L 1 (P - PAb) dh ∫h)0 RTPair,M Ai
n ) AikgPt
(1)
In the case of binary systems, a different driving force is defined, and an overall mass-transfer coefficient is defined which lumps the mass-transfer resistances in both the liquid and gas phases. This leads to the following expression for component A:
10.1021/ie990030e CCC: $18.00 © 1999 American Chemical Society Published on Web 10/23/1999
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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999
NA )
kog,APT∆PA RTPair,M
(2)
evaporates is
zA )
with the driving force defined as
∆PA )
(PAi - PAb)inlet - (PAi - PAb)exit ln
(
)
(PAi - PAb)inlet (PAi - PAb)exit
(3)
The interfacial pressure PAi is calculated using the NRTL equation using the bulk composition of the liquid. In the case of evaporation of a volatile component from a mixture that also contains a nonvolatile component, the rate of evaporation of the volatile component NA is equal to the total rate of evaporation. Calculation of the mass-transfer coefficient for this case is straightforward. In the case of a binary mixture consisting of two volatile components, both components are evaporated. The rate of evaporation of the individual components can be determined by analyzing the mixture before and after the experiment. This would mean having to drain the equipment completely. This is a tedious exercise that may introduce some experimental error. When the air stream is far from saturation, it can be assumed that the components do not influence the diffusion of one another in the gas phase and the mass-transfer coefficients can be calculated with an alternative method. Assuming that the liquid-phase resistance is negligible, that the transfers of the two components are independent, and that the gas-phase mass transfer can be described by the following correlation (see part 1 of this series),
Shg) 0.00283RegScg0.5Rel0.08
( )
Scg,A Shg,A ) Shg,B Scg,B
0.5
(5)
zA )
( )
NA ) zANtotal
0.5
(6)
x
kl° ) 2
( )
)R
(7)
Using a logarithmic driving force, as discussed in part 1 of this series, the following equations are obtained for the two diffusing components:
NA )
kg,APt∆PA RTPair,M
(8)
NB )
kg,BPt∆PB RTPair,M
(9)
and
The fraction of A (based on the total evaporation) that
(12)
DAB πt
(13)
The contact time t was calculated using the interfacial velocity divided by the length of the wetted-wall section. The predicted liquid- and gas-phase mass-transfer coefficients were used to predict overall gas-phase masstransfer coefficients:
(14)
with
m) 0.5
(11)
Equation 12 is then used to calculate the mass-transfer coefficient for component A. The experimental Shog values were compared with Shg values predicted by the pure component masstransfer correlation (eq 4). Comparing the experimental Shog values with the calculated Shg values for a component in a binary mixture gives an indication of the influence of the second component on the mass-transfer process. The liquid mass-transfer coefficient was calculated according to Higbie’s penetration theory:7
1 m 1 ) + kog kg kl°
and
DA kg,A ) Dg,B DB
PA,i RPi,B + Pi,A
The partial pressures were calculated using the NRTL equation and the average bulk liquid composition. Equation 11 can be used to obtain the evaporation rate of the component A from the measured total evaporation rate:
Solving for the mass-transfer coefficients yields
DB kg,A DB ) DA kg,B DA
(10)
Assuming that the free gas stream partial pressures of components A and B are zero in eq 1, eqs 7-9 can be substituted into eq 10 to give
(4)
The ratio of the mass-transfer coefficients of the two components is
NA NB + NA
( )( )
yA Mrl Fg xA Mrg Fl
(15)
This overall gas-phase mass-transfer coefficient was used to calculate the overall gas-phase Sherwood number:
Shog )
kog(d - 2δ) DAB
(16)
These Sh numbers were corrected for variations in Scg and Rel. This was done so that the data could be plotted versus Reg:
MTG )
Shog Scg0.5Rel0.08
(17)
The experimental results are presented in Figures 1-6.
Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4935
Figure 1. MTG for acetone mass transfer (92.3 mol % acetone + methanol mixture).
Figure 2. Comparison of mass transfer of acetone from a 40 mol % methanol + 1-octanol mixture with eq 4 (solid line). Broken lines denote the upper and lower limits of MTGog as calculated with eq 14.
Figure 3. Comparison of mass transfer of acetone from an acetone + aniline mixture with eq 4 (solid line). Broken lines denote the upper and lower limits of MTGog as calculated with eq 14.
The experimental data are available from the corresponding author. Discussion To verify the use of eqs 7-12, an azeotropic mixture (92.3 mol at acetone at 33 °C) of acetone and methanol was evaporated. The azeotropic composition, together with the small difference in gas-phase diffusivities (R ) 1.12), lead to small liquid-phase composition gradients. It is therefore expected that the mass transfer
Figure 4. Comparison of mass transfer of acetone from an acetone + EG mixture with eq 4 (solid line). Broken lines denote the upper and lower limits of MTGog as calculated with eq 14.
Figure 5. Comparison of mass transfer of methanol from a methanol + EG mixture with eq 4 (solid line). Broken lines denote the upper and lower limits of MTGog as calculated with eq 14.
Figure 6. Comparison of mass transfer of acetone from a 40 mol % acetone + water mixture with eq 4 and eq 14.
should correlate closely with eq 5. The results for the evaporation of acetone-methanol are shown in Figure 1. The experimental and predicted MTG values are very close, verifying the analysis used in obtaining the masstransfer coefficients. The evaporation data for methanol + 1-octanol are shown in Figure 2. It can be seen that the mass-transfer resistance is less at Rel ) 33 than at Rel ) 58. This could be caused by the increase in liquid waviness at lower flow rates. It was observed that the distance for wave inception below the liquid entrance decreased as the
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liquid flow rate decreased. The overall mass-transfer coefficients are generally less than the predicted gasphase mass-transfer coefficients (solid line) but are greater than the predicted overall mass-transfer coefficients (broken lines) using Higbie’s theory7 to calculate the liquid side mass-transfer coefficient. The upper broken line corresponds to Shog calculated at the highest liquid flow rate for that system, and the lower broken lines correspond to Shog calculated at the lowest liquid flow rate for that system. The mass-transfer data for acetone + aniline, acetone + EG, methanol + EG, and acetone + water are shown in Figures 3-6. A surprising trend can be seen in these figures. The experimental overall mass-transfer coefficients are generally larger than predicted by eq 14, and even more surprising is the fact that the observed mass-transfer coefficients are even larger than predicted by the gas-phase mass-transfer correlation. This leads to the conclusion that not only is the liquid-phase masstransfer resistance very small compared with the gasphase resistance but also gas-phase mass-transfer enhancement takes place. Increased rippling of the liquid film (compared to pure component evaporation) was observed for the systems where the observed mass transfer was larger than the predicted one. The apparent amplitude of the ripples increased, and the distance of rippling inception decreased. It is quite possible that the increased liquid rippling reduces the liquid side resistance and increases the area available for mass transfer. When surface tension gradients exist in the liquid phase, Marangoni induced liquid turbulence can cause an increase in liquid-phase mass transfer (see e.g. Brain et al.2 and Imaishi et al.8 for experimental results, Golovin6 for theoretical modeling). Although Brain et al. measured gas- and liquid-phase mass-transfer coefficients under conditions of interfacial turbulence, they did not observe any increase in gas-phase mass transfer caused by interfacial turbulence. It must however be remembered that the gas flow was in the laminar region for their experiments. To observe the dependence of the mass-transfer enhancement on the Marangoni number (Ma), a masstransfer enhancement factor F is defined as the ratio of the experimentally observed mass-transfer coefficient to the gas-phase mass-transfer coefficient:
F)
kog,exp kg,eq4
(18)
The Marangoni number is defined as6
Ma )
(σi - σb) µl kl
(19)
Figure 7. Mass-transfer enhancement factor F of acetone for acetone + EG binary mixtures.
stant. These systems showed much more pronounced liquid turbulence and surface rippling, which may have increased the effective mass-transfer area and possibly increased the gas side turbulence. Whether this increase in surface rippling is caused by an increase in viscosity, the Marangoni effect, or a combination thereof is not clear. Although it was expected to observe an increase in F with an increase of Ma, using kl° in place of kl could have introduced unacceptable errors when calculating Ma. Although previous researchers have obtained correlations between Ma and liquid-phase mass-transfer enhancement, the conditions in this work (free rippling liquid film, turbulent gas stream) create a more complex relation between the enhancement of mass transfer and Ma. Conclusions The system methanol + acetone shows no masstransfer enhancement. Liquid-phase resistance was observed in the system methanol + 1-octanol. In these systems the differences between the pure component surface tensions are small. In the case of binary systems with large differences between the pure component surface tensions, the masstransfer coefficients were significantly higher than those of the pure components. This enhancement was observed for the systems acetone + aniline, acetone + water, acetone + EG, and methanol + EG. In the binary cases, the mass-transfer coefficients were up to 60% higher than those of the pure components. These systems showed much more pronounced liquid turbulence and surface rippling, which may have increased the effective mass-transfer area and possibly increased the gas side turbulence. Acknowledgment
However, since no meaningful experimental liquidphase mass-transfer coefficients could be calculated from the results, it was decided to use kl° to calculate Ma (Imaishi et al.8). In Figure 7 the F factors for the acetone + EG runs are plotted versus Ma. From this figure it can be seen that the enhancement factors are approximately constant for a series of experiments with the same bulk concentration and increase with an increase in EG concentration. The same trends hold for the methanol + EG data. The enhancement factors for acetone + aniline and acetone + water are approximately con-
The financial and in-kind support of Sastech R&D and Sulzer Chemtech is gratefully acknowledged. Nomenclature d ) diameter, m DA ) diffusion coefficient of A in air, m2/s DAB ) diffusion coefficient of A in B, m2/s F ) enhancement factor k ) mass-transfer coefficient, m/s m ) ratio of the gas and liquid concentration Ma ) Marangoni number, Ma ) (σi - σb)/µlkl
Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4937 Mr ) molecular weight, g/mol MTG ) mass-transfer group, MTG ) Sh/Scg0.5Rel0.08 N ) molar flux, mol/(m2 s) P ) pressure, Pa PBM ) mean pressure of B, Pa Q ) volumetric flow rate, m3/s R ) universal gas constant, 8.314 J/(mol K) R ) ratio of gas-phase transfer resistances for A and B, R ) kg,A/kg,B ) (DB/DA)0.5 Reg ) gas-phase Reynolds number, Reg ) Fgug(d - 2δ)/µg Rel ) liquid Reynolds number, Rel ) FlQl/[πµl(d - 2δ)] Scg ) gas-phase Schmidt number, Scg ) µg/FgDAB Shg ) gas-phase Sherwood number, Shg ) kg(d - 2δ)/DAB Shog ) overall gas-phase Sherwood number, Shog ) kog(d - 2δ)/DAB T ) temperature, °C t ) time, s u ) velocity, m/s yA ) fraction of A in gas phase zA ) fraction of A that evaporates Greek Symbols δ ) liquid film thickness, m µ ) viscosity, Pa‚s F ) density, kg/m3 σ ) surface tension, N/m Subscripts A ) component A avg ) average B ) component B b ) bulk g ) gas phase i ) interface l ) liquid phase m ) mean og ) overall gas phase t ) total
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Received for review January 11, 1999 Revised manuscript received August 17, 1999 Accepted August 22, 1999 IE990030E
