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Ind. Eng. Chem. Res. 2001, 40, 2310-2321
Mass Transfer in Structured Packing: A Wetted-Wall Study Andre´ B. Erasmus and Izak Nieuwoudt* Institute for Thermal Separation Technology, Department of Chemical Engineering, University of Stellenbosch, Stellenbosch, 7600 South Africa
A short wetted-wall column was used to measure and correlate gas-phase mass transfer coefficients for various pure components evaporating counter current into an air stream. Mass transfer coefficients were also measured for binary mixtures. Both a smooth and a complex surface, similar to the surface of the structured packing Mellapak, were used in the study. The gas-phase mass transfer coefficients for the smooth surface were correlated with Shg ) 0.0044RegScg0.5Wel0.111. The results for the complex surface were correlated with Shg ) 0.0036Reg0.76Scg0.5Rel0.41Bo-0.13. Mass transfer coefficients for binary mixtures were compared with these gas-phase mass transfer coefficients. Enhanced mass transfer was observed for systems with large differences in pure-component surface tensions. This was not the case for binary systems with small differences in the pure-component surface tensions. Negligible liquidside resistance to mass transfer was found in all systems in this study. High-viscosity liquids deviated from the proposed correlations. Introduction For investigations of the mass transfer efficiency of structured packing, there are three common approaches used to predict the HETP (height equivalent to a theoretical plate): mass transfer models, general rules, and data interpolation. The state of existing mass transfer models is such that Kister20 recommends using general rules, or data interpolation to obtain design HETP. In recent years, some progress has been made in understanding the theory describing the process, most notably by Bravo et al.6 and Rocha et al.30 Their proposed models are based on the two-film theory and assume resistance to mass transfer in both phases. This is a step in the right direction, but there is some concern as to whether the correlations used in obtaining these resistances are valid in a column containing structured packing. For example, the resistance to mass transfer in the vapor phase is calculated by using the empirical correlation developed by Gilliland and Sherwood14 or fitted to distillation data.30 The correlation of Gilliland and Sherwood14 was developed in a long wetted-wall column where the flow was completely developed, which is not necessarily the case in structured packing. In these mass transfer models, Higbie’s16 penetration theory is used to model the liquid-side mass transfer resistance. It was found, however, that, in rippling liquid films, Higbie’s penetration theory underpredicts the mass transfer coefficient quite substantially.1,13,19,21,25,37 More recently, Crause and Nieuwoudt8,23 used a much shorter wetted-wall column to obtain a correlation for the mass transfer resistance in the vapor phase and used this correlation, in turn, to investigate the liquidphase resistance. To the authors’ knowledge, all previous wetted-wall studies involving the evaporation of pure liquids into a gas stream were carried out using a smooth surface. Most sheet-structured packings have a certain surface structure that influences the liquid flow over it. Because numerous wetted-wall studies * Author to whom correspondence should be addressed. Fax: +27 (0)21 808 2059. E-mail:
[email protected].
indicated that a wavy liquid surface profile enhances the mass transfer rate,3,27,38 it was decided to investigate the mass transfer from “wavy’ surfaces. These complex surfaces induce a wavy profile at the gas-liquid interface, and it is expected that this will enhance the mass transfer rate compared to that of liquids flowing over smooth surfaces where only part of the surface area is covered in waves. A few attempts have been made at modeling the hydrodynamics of a liquid flowing over a complex surface.4,10,28,36,39 No attempt will be made at modeling the hydrodynamics of liquid flowing over a complex surface in this paper. A hydrodynamic model similar to that used by Crause and Nieuwoudt8,23 is used in this work for both the smooth and complex surfaces. Pure liquids were evaporated from both smooth and complex surfaces in a short wetted-wall column, similar to that used by Crause and Nieuwoudt.8,23 The results were correlated with a simple power law series, and an attempt was made to quantify the liquid-side resistance in binary systems with one volatile component, similar to systems used in extractive distillation. Experimental Setup A short wetted-wall column was used in this study. Figure 1 show the wetted-wall column assembly. The important features of this assembly are the diameter and length of the wetted-wall column. The center tube in this assembly is the wetted-wall column. It is made from precision glass with a diameter of 25.5 mm and a length of 110 mm. The study was undertaken using the same experimental setup as described by Crause and Nieuwoudt.8 The reader is referred to this article for a detailed description of the apparatus. Only minor modifications were made to the experimental setup in order that lower liquid flow rates could be used. The same assembly was used for the experimental work on complex surfaces. The glass unit consisting of the wetted wall tube and reservoir was replaced by another unit having a glass tube with a slightly larger diameter. A sheet of Sulzer Mellapak 350Y packing material (without holes) was cut and rolled to fit into the glass tube. At 27.3 mm, the diameter of this packing wetted-wall column is slightly larger than that of its
10.1021/ie000841e CCC: $20.00 © 2001 American Chemical Society Published on Web 04/20/2001
Ind. Eng. Chem. Res., Vol. 40, No. 10, 2001 2311
Experimental Procedure
Figure 1. Wetted-wall column.
The apparatus is filled with the desired liquid through the calibrated reservoir and pumped to the reservoir in the wetted-wall assembly. The air flow rate and the temperature of the water bath are adjusted to the desired values. The temperature of the air is adjusted to the operating temperature by varying the power to the electric heater. Before experimental work is started, the liquid is circulated until it reaches operating temperature. The evaporation rate of a liquid is measured at combinations of different air and liquid flow rates. The liquid level is allowed to build up between the bottom flange and the bottom of the wetted-wall tube to prevent air from being vented through the liquid return line. This liquid is drained before volumetric measurements are made. The total amount of liquid evaporated during a run is measured with the calibrated reservoir. The temperatures are registered several times during a run, and the average temperature is used in the calculations. For the binary mixtures with one volatile component, the liquid reservoir is topped off with the volatile component after each run in order to maintain a constant liquid concentration for a series of runs. The change in composition during an experimental run is accounted for by using an average in the calculations. The change in composition during an experimental run for binary mixtures in which both components are volatile is negligible. After each run, the liquid reservoir is topped off with the binary mixture, and after every second run, a sample is drawn from the liquid reservoir for GC analysis. The average composition for each run is determined by linear interpolation between the sampling points. Gas-Phase Mass Transfer The molar flux per unit area of species A diffusing through a stagnant gas B is calculated from7
NA ) Figure 2. Flow diagram: Wetted-wall column.
smooth counterpart. The total length of this column is 106 mm. The wavelength of the microstructure of the packing material is 3.75 mm, and its amplitude is 0.6 mm. Experiments were carried out with in both an inline and a staggered configuration of the microstructure. A flow diagram of the experimental setup is shown in Figure 2. The liquid feed to the wetted-wall column is pumped from a calibrated reservoir with a small centrifugal pump. The liquid is heated to the temperature of the water bath through a heating coil that is submerged in the constant-temperature bath. The liquid fills the reservoir and flows through the liquid inlet slot into the wetted-wall tube. It exits through the outlet slot and flows under gravity back to the calibrated reservoir. Dehumidified air is heated in an electric heater and enters the wetted-wall tube through the inlet calming section. It is vented to the atmosphere through the outlet calming section. The temperatures of the air and working liquid are measured at different points with type K thermocouples and registered on a recorder.
DAB P (P - PAb) ∆z PBmRT Ai
(1)
PBm is the logarithmic mean of PBi and PBb and is given by
PBm )
PBb - PBi PBb ln PBi
( )
(2)
The subscripts i and b refer to the interface and the bulk of the gas, respectively. ∆z is the thickness of the diffusional sublayer, and because this quantity is difficult to measure or correlate, a mass transfer coefficient is introduced
P NA ) kg (P - PAb) PBmRT Ai
(3)
To obtain the total rate of mass transfer from a liquid film on the inside of a pipe wall, the following integration has to be done:
n ) N AA )
[
]
∫0h ∫02π kgPBmPRT(PAi - PAb) r dθ dy
(4)
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Ind. Eng. Chem. Res., Vol. 40, No. 10, 2001
If it is assumed that the variables are independent of θ, the pressure drop is negligible, and k is independent of y, then eq 4 can be simplified to
n ) 2πrkgP
∫0
1 (P - PAb) dy RTPBm Ai
h
∆PA )
ln
[
]
(PAi - PAb)inlet (PAi - PAb)exit
(6)
The molar transfer rate is calculated by substituting ∆PA into eq 5 and integrating over the height of the column
kgPt∆PA n ) Ai RTPBm
(7)
In the calculation of the interfacial area, the thickness of the liquid film is taken into account, r ) rp - ∆
Ai ) 2πrh
The final form of the equation relating the overall mass transfer coefficient to the individual mass transfer coefficients is as follows:7
m)
( )( )
yA Mr,l Fg xA Mr,g Fl
(13)
The surface tension of the liquid at the interface, σi, is calculated for the interfacial concentration, Cli, that is calculated from
Cl
Cli )
(14)
(1 + B)
where B is a ratio of the mass transfer resistances in the liquid and the gas phases and is given by
B)
mkg kl
(15)
The liquid-side resistance in eq 15 is calculated using the penetration theory of Higbie. For a wetted-wall column, the liquid-phase mass transfer coefficient is given by13
(9)
x
DA u i πz
(16)
The gas-phase mass transfer coefficient in eq 15 is calculated from gas-phase mass transfer correlations fitted to experimental data. Results: Gas-Phase Mass Transfer
(10)
yA is calculated as PAi/Pt. PAi is the vapor pressure of component A corresponding to the mole fraction of xA in the liquid phase and is calculated with the NRTL equation. For binary mixtures with only one volatile component, the molar flux is simply the total mass evaporated. In binary mixtures in which both components are volatile, the estimation of the molar flux for each component is complicated somewhat. Nieuwoudt and Crause23 have shown that, for a binary mixture of component A and C evaporating into a gas B, the mole fraction of A (based on the total evaporation rate) that evaporates is given by
yAi zA ) yAi + KyCi
(12)
(σi - σl) µl kl
Ma )
kl ) 2
where m is the slope of the equilibrium line and is defined as24
c
The analysis was performed assuming that, at low mass transfer rates, the fluxes of the two components are independent. The exponent c in eq 12 is equal to the exponent of the Schmidt number in the gas-phase mass transfer correlation. In this work, this exponent is assumed to be equal to the theoretical value of 0.5. In binary systems in which there is a substantial difference between the surface tensions of the components, the Marangoni number is often used to correlate the observed enhancement. Imaishi et al.17 defines the Marangoni number as
(8)
Liquid-Phase Mass Transfer
1 m 1 ) + kog kg kl
( ) DCB DAB
K)
(5)
If isothermal operation is assumed, i.e., evaporative cooling is considered to be negligible, it is not necessary to numerically integrate eq 5. For short columns, this is a good approximation. If pure B enters the column and the mass transfer rate of A is small, (PAi - PAb) will vary more between the inlet and the outlet of the column than will PBm. An arithmetic mean between the inlet and outlet values of PBm will, therefore, be adequate. A logarithmic average of the inlet and outlet of the partial pressure driving force is used
(PAi - PAb)inlet - (PAi - PAb)exit
as
(11)
K is a ratio of the gas-phase diffusion coefficients defined
Smooth Surface. The results are plotted in terms of a dimensionless flow number (Reg or Rel) and a dimensionless mass transfer number (Shg). Figure 3 show the experimental results for six pure components at different air flow rates. Figure 4 show the influence of the liquid flow rate on the gas-phase Sherwood number. The remaining pure components showed the same trend as in Figure 4, except for 1,2-propanediol. For 1,2-propanediol, there was no increase in the mass transfer rate (Shg) with increasing liquid flow rate (Rel). The results are compared to the correlation developed by Crause and Nieuwoudt8 in Figure 5. In this figure, MTG is defined as
MTG )
(
Sh Sc Rel0.08 0.5
)
(17)
From Figure 5, it is clear that the correlation developed by Crause and Nieuwoudt8 gives a reasonable fit to the data, but a few of the data points lie well below their
Ind. Eng. Chem. Res., Vol. 40, No. 10, 2001 2313 Table 1. RMS Errors for Various Correlations (Smooth Surface)
Figure 3. Shg vs Reg for different pure components. Ranges of some important dimensionless numbers, physical properties: Scg ) 0.97-2.02, Rel ) 6-330, σ (N/m) ) 0.016-0.028, and µ (Pa s) ) 2.51-14.7 × 10-4.
Figure 4. Shg vs Rel for i-propanol. Reg ) 1785-5920, Rel ) 12153.
Figure 5. Experimental values (]) compared to predictions by Crause and Nieuwoudt8 (solid line).
predicted values. This suggests that Rel had a larger influence on the gas-phase mass transfer rate in the present work than was observed in their work. In Figure 5, there are a few points for which the mass transfer rate lies well above the value predicted by their correlation. These points represent the gas-phase mass transfer rate of 1,2-propanediol. The experimental gas-phase mass transfer rates for the different pure components were correlated by using a power law series similar to that used by previous investigators. Combinations of different dimensionless numbers were used in the correlating procedure. This was done in order to assess the influence of the different physical properties on the mass transfer rate. Nonlinear least-squares minimization of the squared sum of the differences between the calculated and experimental values of Shg was used to calculate the constants in the correlation.
correlation
RMS error
Shg ) 0.0044Reg0.992Scg0.583 Shg ) 0.0008Reg,r1.172Scg0.547 Shg ) 0.0030Reg0.959Scg0.485Rel0.145 Shg ) 0.0047Reg0.992Scg0.537Wel0.111
3.175 2.461 2.024 1.734
Relatively few experimental points were measured for 1,2-propanediol because of wetting problems at low liquid flow rates. It is also uncertain whether the available correlations for the binary diffusion coefficient are accurate for 1,2-propanediol/air at the experimental conditions of interest. It was therefore decided that this data set should not be included in the training set. Table 1 shows the results for the different combinations of dimensionless numbers. In the second correlation in the table, the velocity of the gas phase relative to the liquid surface was used in calculating the relative gas-phase Reynolds number. When the root-mean-square errors of the different correlations in Table 1 are compared, it can be seen that correlations in which the velocity of the liquid phase is accounted for or a dimensionless number for the liquid phase is included fit the data better than a simple Gilliland-Sherwood-type correlation (the first correlation in the table). This is also evident from Figure 4, which shows that Shg is influenced by the liquid flow rate. The correlation in which the liquid flow term incorporates the velocity of the film and the surface tension, through the Weber number, gives the best fit to the experimental data (the last correlation in Table 1). This is in contrast to the correlations employed by previous investigators8,18,22,32 who used Rel to characterize the influence that the liquid film has on the gas-phase mass transfer. It is expected, however, that this correlation will not extrapolate well to liquids having viscosities that fall outside the range over which it was fitted (2.51-7.65 10-4 Pa s). Further discussions of the results will focus on this correlation, unless stated otherwise. The effect that the surface tension has on the gasphase mass transfer is not yet fully understood. Peramanu et al.26 link the surface tension to the instability of a falling liquid film. They found that, for a decrease in surface tension, there is an increase in the amplitude of the waves on the surface of the film. This might have the effect of inducing more turbulence in the gas layer close to the interface and thereby enhancing the rate of mass transfer. One can not ignore, however, the effect that the viscosity of the liquid phase has on the mass transfer rate. Figure 4 shows that the mass transfer rate for 1,2propanediol is higher than that for the other pure liquids. Crause and Nieuwoudt8 also found this to be the case with ethylene glycol when compared to the gasphase mass transfer rate of liquids of lower viscosity. If it is assumed that this effect is not due to experimental error or inaccuracies in the estimation of the binary gas-phase diffusion coefficient, then the following analysis can be made. The viscosity of 1,2-propanediol is almost twice that of the highest pure-liquid viscosity in the training set (1.47 × 10-3 Pa s compared to 7.65 × 10-4 Pa s). The surface tension is 25% higher than the highest surface tension (0.028 N/m compared to 0.023 N/m). To verify that it is the viscosity, and not the surface tension, that causes the enhanced mass transfer rate, experimental
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Figure 6. Plot of experimental data for water (σ ) 0.065 N/m, µ ) 4.55 × 10-4 Pa s), acetonitrile (σ ) 0.028 N/m, µ ) 3.06 × 10-4 Pa s), and toluene (σ ) 0.024 N/m, µ ) 4.03 × 10-4 Pa s) with proposed correlation (s).
Figure 7. Plot of experimental data and proposed correlation (s).
data for liquids having surface tensions higher than those of the liquids in the training set are compared with the proposed correlation in Figure 6. The viscosities of these liquids fall within the experimental range. The data were obtained from Crause and Nieuwoudt.8 In this figure, MTG is defined as
MTG )
(
Shg
Scg
0.537
Wel0.111
)
(18)
Figure 6 shows the excellent fit of the proposed correlation to the experimental data. The conclusion can be made that the viscosity has a definite effect on the mass transfer rate. More experimental work needs to be done in order to investigate this phenomenon. However, it is clear that the correlation developed in this work does not extrapolate well to liquids having a viscosities higher than those of the liquids in the training set. It does extrapolate well to liquids having surface tensions that are substantially higher, but with viscosities that fall within the experimental range. The proposed correlation is plotted with the experimental data in Figure 7, with the confidence intervals shown. MTG is defined as in eq 18. For the sake of simplicity, the exponents in the proposed correlation were rounded to give the following correlation, without a substantial increase in the rms error:
Shg ) 0.0044RegScg0.5Wel0.111
(19)
The exponent of the gas-phase Reynolds number (0.99
Figure 8. Shg vs Reg for different pure components, complex surface (staggered configuration).
≈ 1) is the same as in the correlation developed by Crause and Nieuwoudt.8 This is to be expected because the same column was used in both sets of experimental work. This exponent is substantially higher than the exponents reported by previous investigators:2,14,18 0.80.83. The difference can be contributed to the length of the column.8 The column used in this work (0.1 m) is shorter than those used by previous investigators (0.51.8 m). Entrance effects in a column shorter than six pipe diameters can be expected to dominate according to Crause and Nieuwoudt.8 As mentioned earlier, it is expected that entrance effects will have an influence on the mass transfer in structured packing, where the flow profile is never completely developed because of the geometry of the packing. The exponent of the gas-phase Schmidt number was rounded to 0.5 because it (0.537) compared favorably to this theoretical value. Dudukovic12 has shown that the widely used exponent of 1/3 is applicable not to mass transfer from a falling liquid interface, but rather to the mass transfer from a stationary interface. The exponent of the liquid-phase dimensionless number is higher than that found by Crause and Nieuwoudt.8 This can be expected because the mass transfer was investigated at lower flow rates. It was found that, as the flow rate decreased from that used by Crause and Nieuwoudt,8 the line of wave inception, or the point where waves can be visually observed, moves up the column.33 The influence that these waves have on the mass transfer rate is not yet fully understood. Some investigators attribute it to an increase in the surface area,29 whereas others argue that it increases interfacial turbulence.9 All agree, however, that it does have an effect on the mass transfer rate. It is therefore not surprising that, for an increase in the area covered by visually observable surface waves, there is an increase in the exponent of the liquid-phase dimensionless number. As previously stated, it was found that, in the viscosity range of this experimental work, Wel gave a better fit than Rel. Complex Surface. Figure 8 shows the results for the three pure components used. The ranges of some important dimensionless numbers and physical properties are as follows: Scg ) 0.97-1.93, Rel ) 50-200, σ (N/m) ) 0.017-0.021, and µ (Pa s) ) 2.61-5.54 × 10-4. The effect of the liquid flow rate on the rate of mass transfer is shown in Figure 9. The same trend was observed for the other liquids. No difference in the rate of mass transfer between the staggered and inline configurations could be found. It was however found that the surface of the liquid
Ind. Eng. Chem. Res., Vol. 40, No. 10, 2001 2315
Figure 9. Shg vs Rel for ethanol, complex surface (staggered configuration). Reg ) 1665-5515, Rel ) 50-140.
became unstable and breakaway droplets formed for the inline configuration at high liquid flow rates (Rel > 100). For the staggered configuration, the liquid flow rate could be increased to (Rel ) 140 without the formation of breakaway liquid droplets. The formation of breakaway droplets in the inline configuration at higher Rel values might be explained by the mean film thickness and the average surface velocity of the liquid phase. The mean thickness of the liquid film in this type of configuration is thought to be smaller than that in the staggered configuration, with most of the volume of the liquid flowing in the channels between inline peaks. The thickness of these films is comparable to that of a smooth surface. The staggered configuration induces liquid spreading, and therefore, the volume of the liquid film is more uniformly spread over this configuration. The mean thickness of these films is greater than that for smooth surfaces, and the average free surface velocity is smaller.39 It follows that, for an increase in the liquid flow rate, the average surface velocity of the liquid film will reach the critical value for breakaway sooner in the inline configuration than in the staggered configuration. It was again found that Shg is dependent on the liquid flow rate. Figure 9 shows this dependence quite clearly. It was also found that the liquid flow rate influences the mass transfer rate at lower Reg values than for the smooth surface. For the smooth surface, the slope of Shg vs Rel is smaller at low Reg (
