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Ind. Eng. Chem. Res. 1999, 38, 4928-4932
Mass Transfer in a Short Wetted-Wall Column. 1. Pure Components James C. Crause and Izak Nieuwoudt* Institute for Thermal Separation Technology, Department of Chemical Engineering, University of Stellenbosch, Stellenbosch, South Africa
It is believed that mass transfer in modern structured packing is not analogous to mass transfer in long wetted-wall columns used previously in mass-transfer studies. To model mass transfer in structured packing, gas-phase mass-transfer coefficients were measured by evaporation in a short wetted-wall column with a length of 110 mm and a diameter of 25.4 mm. The results were correlated as Shg ) 0.00283RegScg0.5Rel0.08. This correlation is based on the evaporation data of six low-viscosity pure liquids covering a wide range of surface tensions. In the case of a high-viscosity liquid such as ethylene glycol, systematic deviation from this correlation was observed. Introduction
Table 1. Previous Wetted-Wall Correlations
The geometry of structured packing enables one to approximate the mass transfer in these packings as mass transfer from a wetted-wall. To develop an accurate mass-transfer model for structured packing, one would require an accurate wetted-wall mass-transfer model. Previous investigators used long wetted-wall columns (>0.5 m) to obtain mass-transfer correlations. Since the structured packing segments are approximately 200 mm long and the corrugations are on the order of 20 mm wide, the need for a mass-transfer model suitable for use in these relatively short channels is obvious. In several studies the evaporation of pure liquids into air streams has been investigated. These experiments, as opposed to distillation in a wetted-wall column, are suited to measuring the gas-phase resistance, since there is no liquid side resistance to mass transfer. Gilliland and Sherwood1 pioneered the use of wettedwall columns for gas-phase mass-transfer studies in 1934. They evaporated several organic liquids and water into air. Their mass-transfer correlation, as well as the correlations of subsequent investigators, is listed in Table 1. The length of the wetted-wall columns used in the various experiments varied between 0.5 and 1.8 m. The diameter of the wetted-wall section varied between 2.5 and 3.7 cm. The height of a section of the structured packing used is about 200 mm. The height of the corrugations is approximately 20 mm. This is considerably shorter than the columns used by other researchers in obtaining mass-transfer correlations. It is possible that with such a relatively short contact length entrance effects could significantly influence mass transfer. It is also clear that the influence of liquid flow rate on mass transfer is ill understood and needs further investigation. All the above-mentioned researchers used an adiabatic setup to measure mass transfer. Most of them then used the logarithmic mean partial pressure to calculate the driving force for mass transfer. Reker et al.2 showed that the use of logarithmic partial pressures for the calculation of the mass-transfer coefficient in adiabatic systems can, under certain circumstances, * Corresponding author. Telephone: +27 21 808-4421. Fax: +27 21 808-2059. E-mail:
[email protected].
correlation
ref
Shg ) 0.023Reg0.83Scg0.44 Shg ) 0.02Reg0.83Scg0.44
( )
Shg
PBM P
0.83
1 10
) 0.021Reg0.83Scg0.44
Shg ) 0.024Re′g0.8Scg0.4 nonrippling films: Shg ) 0.013Re′g0.83 rippling films: Shg ) 0.0065Reg0.83Rel0.15 Shg ) 0.093Reg0.68Rel0.34 Shg ) 0.16Reg0.83Scg0.5Se
with S ) 0.721Rel5/3
( ) gµl Fl
1/3µ l
11 12 9 13 2, 14
σ
Shg ) 0.02Re′g0.83Scg0.44 Shg ) 0.0318Reg0.79Scg0.5 Shg ) 0.00031Reg1.05Rel0.207Scg0.5
15 7 16
lead to errors of up to 10% when compared to numerical integration of the differential mass-transfer equations for evaporation. In this study pure liquids were evaporated in an isothermal wetted-wall column to determine gas-phase mass-transfer coefficients. These experiments were designed to investigate the influence of parameters such as the liquid and gas Reynolds numbers and the gasphase Schmidt number on the gas-phase Sherwood number. Experimental Setup Since the aim is to model mass-transfer in packing where the changes in liquid flow occur every few centimeters (see Shetty and Cerro20), it was decided to use a short wetted-wall column and to use an isothermal configuration to simplify the mass transfer analysis. A drawing of the column assembly is shown in Figure 1. The wetted-wall section is a precision bore glass tube with an inside diameter of 25.4 mm and a length of 111 mm. The upper end of the wetted-wall tube is ground at a 45° angle. The bottom of the wetted-wall tube is flared at an angle of approximately 45° and fused to a 110 mm diameter glass tube that forms a mantle around the wetted-wall tube. The wetted-wall tube protrudes about 5 mm above the mantle. The gas inlet piece, length 145 mm, has a 45° bevel and when assembled forms an approximately 3 mm drainage slot with the
10.1021/ie990029f CCC: $18.00 © 1999 American Chemical Society Published on Web 10/23/1999
Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4929
Figure 1. Sketch of wetted-wall column.
centrifugal pump from a calibrated glass reservoir through a rotameter and a heating coil submerged in the constant-temperature bath. The flow rate is controlled with a needle valve at the centrifugal pump outlet. The liquid drains from the wetted-wall column and is returned to the calibrated reservoir via a needle valve that serves as a level control valve. The volume of the reservoir can be read with an accuracy of approximately 2 mL. The liquid flow rotameter was calibrated for each of the liquids and temperatures used. Compressed air is dried in a dryer filled with silica gel. The air flows through a valve and a rotameter to an electrical resistance heater. The temperature of the air supplied to the column is controlled by varying the electric power to the heater with a variable transformer. The exit of the electrical heater is connected to the lower calming section of the column. The air flow rotameter was calibrated for high flow rates by timing and measuring the mass loss from a bottle of compressed air and for low flow rates by measuring the volume of compressed air flowing through the rotameter with a Parkinson Cowan turbine gas totalizer. An estimated error of about 2% of the flow rate can be expected. The liquid and gas inlet and exit temperatures at the column are measured with thermocouples (TC1-TC4). The temperature in the liquid reservoir (TC5) and the air temperature (TC6) and pressure (PI) at the inlet of the air rotameter are also measured. All the thermocouples are of type K, and the temperature readings are registered on a Yokogawa HR1300 hybrid recorder. Comparison of the thermocouples with a glass thermometer accurate to 0.1 °C indicates that the thermocouples are accurate to within (0.2 °C. Experimental Procedure
Figure 2. Experimental setup of wetted-wall column.
bottom of the wetted-wall tube. The gas outlet piece, length 75 mm, has an inner 45° bevel and when assembled forms an approximately 2 mm inlet slot with the upper end of the wetted-wall tube. A gas inlet calming section of 475 mm and a gas outlet section of 205 mm are used. Both these sections and the inlet and outlet pieces have inside diameters of 25.0 mm. This compensates somewhat for the thickness of the liquid film flowing down the 25.4 mm wetted-wall tube. The gas outlet section is made from Teflon while the gas inlet section and the calming sections are made from phosphor bronze. The glass section is supported by two stainless steel flanges. During assembly all the sections are carefully aligned, and when clamped together, the distance between the top and bottom flanges along the circumference is measured with a vernier calliper to ensure that the two flanges are parallel. When in operation, liquid flows into the mantle, rises, and flows over onto the inside of the wetted-wall tube. The liquid then flows down the wetted-wall tube and through the drainage slot. The liquid is drained at the lower flange. A sketch of the experimental setup is given in Figure 2. The wetted-wall column is placed in a clear Perspex water bath. The water in the Perspex bath is heated and circulated with a MGW Lauda constant-temperature bath and circulating pump. The liquid feed to the column is pumped with a small
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 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 is adjusted to the desired rate. 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. Results The pure liquids used in this study were acetone, acetonitrile, carbon tertrachloride, ethylene glycol, methanol, toluene, and water. The purities of the chemicals are shown in Table 2. All chemicals were used without further purification. The results are presented as a plot
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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 Table 3. RMS Errors for Various Correlations correlation Shg ) Shg ) Shg ) Shg )
0.00526Reg0.978Scg0.532 0.00317Reg0.983Scg0.566Rel0.081 0.000797Re′g1.18Scg0.558 0.000809Re′g1.18Scg0.557Rel-0.003
RMS error 2.47 2.29 2.36 2.36
with Ai the interfacial area of the liquid film. The interfacial area used in the calculations was corrected for the film thickness:
Ai ) π(d - 2δ)h
(4)
of Shg versus Reg in Figure 3. The experimental data are available from the corresponding author.
No area correction for rippling was made. The calculation of the liquid film thickness and interfacial velocity is done as described in Appendix A. Equation 3 is used to obtain mass-transfer coefficients from evaporation experiments. Due to the fact that isothermal conditions were used, numerical integration of eq 1 yielded mass-transfer coefficients that are virtually the same as those of eq 3. The parameters of the correlations reported in this article were determined by the method of nonlinear least-squares regression. Table 3 shows various types of correlations with the associated errors. The following ranges of dimensionless numbers were covered in this work: Shg, 11-65; Re′g, 3000-10000; Reg, 2400-9100; Rel, 110-480; Scg, 0.62-1.93.
Calculations
Discussion
Starting with a differential height element in a wetted-wall, the rate of mass transfer can be described as3
Comparing the root-mean-square errors reported in Table 3, it can be seen that a simple GillilandSherwood type correlation using Reg (Re number of gas relative to tube wall) adequately describes the mass transfer in this work. The use of the relative Reynolds number (relative to the liquid interface) Re′g did not reduce the error by much. A combination of Reg and Rel decreased the error somewhat, while a combination of Rel and Re′g offered no improvement. A combination of Reg and Rel yielded the smallest root-mean-square error, and further discussion of the results will be at the hand of this correlation. Sh ∝ Reg0.983. Possibly the most important result of this wetted-wall study is the fact that, for the configuration used, the exponent of the gas Reynolds number was found to be significantly larger than the accepted value of 0.8-0.83. Even though air calming sections are used to allow the air profile to develop before entering the wetted-wall tube, the presence of ripples on the liquid surface might promote a different flow profile to develop. Schwarz and Hoelscher4 indicated that entrance effects are exhibited for about 6 pipe diameters. Since the wetted-wall tube used in this study is only 4 diameters long, entrance effects can be expected to dominate. Importantly, this exponent compares favorably with the value of 1.0 reported by Spiegel and Meier5 for distillation in structured packing (Sulzer Mellapak 125Y-500Y). A value of 1.02 was reported by Weiland et al.6 for absorption in structured packing (Montz A2). Sh ∝ Sc0.566. The Schmidt number exponent found in this work compares favorably with the results of Gilliland and Sherwood,1 who reported an exponent of 0.44, the results of Reker et al.,2 who reported a value of 0.5, and the value of 0.5 for the hydrodynamic theory for two-phase flow with a nonstationary interface as discussed by Dudukovic et al.7 and Hirata et al.8 Since
Figure 3. Gas-phase mass-transfer results. Table 2. Chemicals Used in Experiments chemical
supplier
purity
acetone acetonitrile aniline CCl4 EG methanol n-octanol toluene water
UniVAR UniLAB UniLAB Merck NT Labs UniVAR UniVAR UniLAB N/A
99.5% 98% 99% 99.8% CP grade 99.5% 99% 99.5% glass distilled
h)L 1 (P - PAb) dh ∫h)0 RTPB,M Ai
n ) AikgPt
(1)
The partial pressure driving force (PAi - PAb) varies with h because of the evaporation of A into the gas stream (influencing PAb) and also because of temperature gradients (influencing PAi) caused by evaporative cooling. Likewise, PB,M (mean partial pressure of nondiffusing component B) will also vary because of evaporation. If one assumes low mass-transfer rates and isothermal conditions, PB,M will vary little between the top and bottom of the wetted-wall column. This small variation of PB,M implies that an arithmetic mean of the inlet and exit values will be adequate for use in eq 1. For an isothermal setup the numerical integration of eq 1 is not necessary because the vapor pressure at the interface does not change due to evaporative cooling. Since PAi - PAb will vary more than PB,M between the inlet and exit (PAb < PAi , Pt for evaporation in a wetted-wall column), a logarithmic average of the inlet and exit partial pressure driving forces will be used:
∆PA )
(PAi - PAb)inlet - (PAi - PAb)exit ln
(
)
(PAi - PAb)inlet (PAi - PAb)exit
(2)
Substituting these simplifications into eq 1 and integrating gives the molar transfer rate
kgPt∆PA n ) Ai RTPB,M
(3)
Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4931
the effective interfacial area and the mass-transfer coefficient. This phenomenon is being researched further. Inclusion of a viscosity factor in the correlation could not reconcile the difference between the predicted and experimentally observed mass transfer of EG. Conclusions
Figure 4. Proposed correlation compared with experimental mass-transfer results.
the range of Sc in this work varied between 0.62 and 1.93, and the exact value of the exponent depends somewhat on the other dimensionless numbers used in developing the correlation (see Table 3), the exponent can be set equal to the theoretical value of 0.5 without increasing the error by much. The widely used Sc exponent of 1/3 corresponds to mass transfer from a stationary interface, such as the dissolution of benzoic acid into water, and is not applicable to mass transfer from a falling film into a gas stream, as pointed out by Dudukovic et al.7 In fact, fixing the Schmidt exponent as 1/3 and regressing the other constants in the proposed correlation increase the RMS error from 2.29 to 3.05. Sh ∝ Rel0.081. The exponent of the liquid Reynolds number agrees very well with the value of 0.08 quoted by Kafesjian.9 Since the liquid surface velocity, surface area enhancement, and interfacial turbulence enhancement, all caused by surface waves, are all dependent on Rel, it is very difficult to separate these effects. Since all these effects tend to increase mass transfer, one would expect a larger dependence of the mass-transfer coefficient on Rel (a larger exponent for Rel). However, it was observed that the distance of wave inception below the top of the wetted-wall column increases and the total wavy surface area decreases as the liquid flow rate increases. The observed small net dependency of Shg on Rel is thus the result of the sum of two opposing phenomena. Because of the scatter in the data, rounding of the exponential constants in the proposed correlation does not increase the RMS error by much. It was therefore decided to round the exponential constants and recalculate the pre-exponential constant:
Shg ) 0.00283RegScg0.5Rel0.08 (RMS error ) 2.37) (5) The experimental data are plotted in Figure 4, together with correlation 5. The vertical axis is defined as
MTG )
Shg 0.5
Scg Rel0.08
(6)
From Figure 4 it can be seen that the evaporation data of EG do not follow correlation 5. It is evident that the difference between the experimental and predicted Shg numbers increases significantly as the Reg values increase. The higher viscosity of EG may have caused changes in liquid waviness, which may have influenced
Gas side mass-transfer coefficients in an isothermal short wetted-wall column were studied. The masstransfer coefficients for a range of low-viscosity organic liquids, and water, were correlated with eq 5. The main difference between the Shg correlation of this work and previous correlations is the value of the Reg exponent. This study yielded an exponent of ≈1 whereas most previous researchers used an exponent of about 0.8. The mass transfer of a highly viscous liquid, ethylene glycol, could not be correlated with the same equation. Acknowledgment The financial and in-kind support of Sastech R&D and Sulzer Chemtech is gratefully acknowledged. Nomenclature A ) area, m d ) diameter, m DAB ) diffusion coefficient of A in B, m2/s e ) characteristic roughness, m e ) exponent used by Reker et al. f ) friction factor g ) gravitational acceleration, 9.8 m/s2 h ) height of wetted-wall column, m k ) mass-transfer coefficient, m/s n ) molar transfer rate, mol/s NA ) molar flux of component A, mol/(m2 s) P ) pressure, Pa PBM ) mean pressure of component B, Pa Q ) volumetric flow rate, m3/s R ) universal gas constant, 8.314 J/(mol K) Reg ) gas-phase Reynolds number, Reg ) Fgug(d - 2δ)/µg Re′g ) relative gas-phase Reynolds number, Re′g ) Fg(ug + ui)(d - 2δ)/µg Rel ) liquid Reynolds number, Rel ) FlQl/[πµl(d - 2δ)] S ) fractional area increase used by Portalski Scg ) gas-phase Schmidt number, Scg ) µg/FgDAB Shg ) gas-phase Sherwood number, Shg ) kg(d - 2δ)/DAB T ) temperature, °C u ) velocity, m/s z ) effective diffusion sublayer thickness, m Greek Symbols δ ) liquid film thickness, m µ ) viscosity, Pa‚s F ) density, kg/m3 τ ) interfacial shear force, N Subscripts A ) component A avg ) average B ) component B b ) bulk g ) gas phase i ) interface l ) liquid phase t ) total
Appendix Nieuwoudt17 took into account the effect of the buoyancy and interfacial friction forces on the flow
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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999
profile. His resulting equation (simplified for a vertical flat plate) for the film thickness is
τi 2 g(Fl - Fg) 3 δ δ - uavgδ ) 0 3µl 2µl
(A1)
and the expression for the interfacial velocity is
ui )
gδ2(Fl - Fg) τi - δ 2µl µl
(A2)
Equations A1 and A2 require the interfacial shear stress to calculate the film thickness and interfacial velocity. The interfacial shear stress is defined as follows:
fi τi ) Fgu2 2
(A3)
The friction factor fi is analogous to the Moody friction factor18 for fluid flow in pipes, with the appropriate velocity the air velocity relative to the liquid interface:
1
xfi
) -4 log10
[(
]
1.25 e + 3.7d Regxfi
)
(A4)
The roughness of the interface e must however be estimated. Richter19 quoted values for the ratio of wave height to film thickness of between 4 and 6. Wasden and Duckler21 noted that the wave height varied between 2 and 5 times the film thickness. For calculations the roughness of the interface in this work is taken to be equal to 4 times the film thickness. Literature Cited (1) Gilliland, E. R.; Sherwood, T. K. Diffusion of Vapors into Air Streams. Ind. Eng. Chem. 1934, 26, 516. (2) Reker, J. R.; Plank, C. A.; Gerhard, E. R. Liquid Surface Area Effects in a Wetted-Wall Column. AIChE J. 1966, 12, 1008. (3) Crause, J. C. A mass transfer model for an extractive distillation application. Masters thesis, University of Stellenbosch, South Africa, 1998. (4) Schwarz, W. H.; Hoelscher, H. E. Mass Transfer in a Wetted-Wall Column: Turbulent Flow. AIChE J. 1956, 2, 101.
(5) Spiegel, L.; Meier, W. Correlations of the Performance Characteristics of the Various Mellapak Types. In IChemE Symposium Series No. 104; Hemisphere Publishing Corporation: New York, 1988; p A203. (6) Weiland, R. H.; Ahlgren, K. R.; Evans, M. Mass Transfer Characteristics of some Structured Packings. Ind. Eng. Chem. Res. 1993, 32, 1411. (7) Dudukovic, A.; Milosevic, V.; Pjanovic, R. Gas-Solid and Gas-Liquid Mass Transfer Coefficients. AIChE J. 1996, 42, 269. (8) Hirata, A.; Kawakami, M.; Okana, Y. Effect of Interfacial Velocity and Interfacial Tension Gradient on Momentum, Heat and Mass Transfer. Can. J. Chem. Eng. 1989, 67, 777. (9) Kafesjian, R.; Plank, C. A.; Gerhard, E. R. Liquid Flow and Gas-Phase Mass Transfer in Wetted-Wall Towers. AIChE J. 1961, 7, 463. (10) Barnet, W. I.; Kobe, K. A. Heat and Vapor Transfer in a Wetted-Wall Tower. Ind. Eng. Chem. 1941, 33, 436. (11) Cairns, R. C.; Roper, G. H. Heat and Mass Transfer at High Humidities in a Wetted-Wall Column. Chem. Eng. Sci. 1954, 3, 97. (12) McCarter, R. J.; Stutzman, L. F. Transfer Resistance and Fluid Mechanics. AIChE. J. 1959, 5, 502. (13) Strumillo, C.; Porter, K. E. The Evaporation of Carbon Tetrachloride in a Wetted-Wall Column. AIChE J. 1965, 11, 1139. (14) Portalski, S. Eddy Formation in Film Flow Down a Vertical Plate. Ind. Eng. Chem. Fundam. 1964, 3, 49. (15) Spedding, P. L.; Jones, M. T. Heat and Mass Transfer in Wetted-Wall Columns: I. Chem. Eng. J. 1988, 37, 165. (16) Nielsen, C. H. E.; Kiil, S.; Thomsen, H. W.; Dam-Johansen, K. Mass Transfer in Wetted-Wall Columns: Correlations at High Reynolds Numbers. Chem. Eng. Sci. 1998, 53, 495. (17) Nieuwoudt, I. The fractionation of high molecular weight alkane mixtures with supercritical fluids. Ph.D. Dissertation, University of Stellenbosch, South Africa, 1994. (18) Brodkey, R. S.; Hershey, H. C. Transport phenomena; New York, McGraw-Hill: 1988. (19) Richter, H. J. Flooding in Tubes and Annuli. Int. J. Multiphase Flow 1981, 7, 647. (20) Shetty, S.; Cerro, R. L. Fundamental Liquid Flow Correlations for the Computation of Design Parameters for Ordered Packings. Ind. Eng. Chem. Res. 1997, 36, 771. (21) Wasden, F. K.; Duckler, A. E. A Numerical Study of Mass Transfer in Free Falling Wavy Films. AIChE J. 1990, 36, 1379.
Received for review January 11, 1999 Revised manuscript received August 17, 1999 Accepted August 22, 1999 IE990029F
