mass transfer in structured packing: a wetted-wall study

Mass Transfer in Structured Packing: A Wetted-Wall StudyAndre 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 transfercoefficients for various pure components evaporating counter current into an air stream. Masstransfer coefficients were also measured for binary mixtures. Both a smooth and a complexsurface, similar to the surface of the structured packing Mellapak, were used in the study. Thegas-phase mass transfer coefficients for the smooth surface were correlated with Shg )0.0044RegScg

0.5Wel0.111. The results for the complex surface were correlated with Shg )

0.0036Reg0.76Scg

0.5Rel0.41Bo-0.13. Mass transfer coefficients for binary mixtures were compared

with these gas-phase mass transfer coefficients. Enhanced mass transfer was observed forsystems with large differences in pure-component surface tensions. This was not the case forbinary systems with small differences in the pure-component surface tensions. Negligible liquid-side resistance to mass transfer was found in all systems in this study. High-viscosity liquidsdeviated from the proposed correlations.

Introduction

For investigations of the mass transfer efficiency ofstructured packing, there are three common approachesused to predict the HETP (height equivalent to atheoretical plate): mass transfer models, general rules,and data interpolation. The state of existing masstransfer models is such that Kister20 recommends usinggeneral rules, or data interpolation to obtain designHETP.

In recent years, some progress has been made inunderstanding the theory describing the process, mostnotably by Bravo et al.6 and Rocha et al.30 Theirproposed models are based on the two-film theory andassume resistance to mass transfer in both phases. Thisis a step in the right direction, but there is some concernas to whether the correlations used in obtaining theseresistances are valid in a column containing structuredpacking. For example, the resistance to mass transferin the vapor phase is calculated by using the empiricalcorrelation developed by Gilliland and Sherwood14 orfitted to distillation data.30 The correlation of Gillilandand Sherwood14 was developed in a long wetted-wallcolumn where the flow was completely developed, whichis not necessarily the case in structured packing. Inthese mass transfer models, Higbie’s16 penetrationtheory is used to model the liquid-side mass transferresistance. It was found, however, that, in ripplingliquid films, Higbie’s penetration theory underpre-dicts the mass transfer coefficient quite substan-tially.1,13,19,21,25,37

More recently, Crause and Nieuwoudt8,23 used a muchshorter wetted-wall column to obtain a correlation forthe mass transfer resistance in the vapor phase andused this correlation, in turn, to investigate the liquid-phase resistance. To the authors’ knowledge, all previ-ous wetted-wall studies involving the evaporation ofpure liquids into a gas stream were carried out using asmooth surface. Most sheet-structured packings havea certain surface structure that influences the liquidflow over it. Because numerous wetted-wall studies

indicated that a wavy liquid surface profile enhancesthe mass transfer rate,3,27,38 it was decided to investigatethe mass transfer from “wavy’ surfaces. These complexsurfaces induce a wavy profile at the gas-liquid inter-face, and it is expected that this will enhance the masstransfer rate compared to that of liquids flowing oversmooth surfaces where only part of the surface area iscovered in waves. A few attempts have been made atmodeling the hydrodynamics of a liquid flowing over acomplex surface.4,10,28,36,39 No attempt will be made atmodeling the hydrodynamics of liquid flowing over acomplex surface in this paper. A hydrodynamic modelsimilar to that used by Crause and Nieuwoudt8,23 is usedin this work for both the smooth and complex surfaces.

Pure liquids were evaporated from both smooth andcomplex surfaces in a short wetted-wall column, similarto that used by Crause and Nieuwoudt.8,23 The resultswere correlated with a simple power law series, and anattempt was made to quantify the liquid-side resistancein binary systems with one volatile component, similarto 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. Theimportant features of this assembly are the diameterand length of the wetted-wall column. The center tubein this assembly is the wetted-wall column. It is madefrom precision glass with a diameter of 25.5 mm and alength of 110 mm. The study was undertaken using thesame experimental setup as described by Crause andNieuwoudt.8 The reader is referred to this article for adetailed description of the apparatus. Only minormodifications were made to the experimental setup inorder that lower liquid flow rates could be used.

The same assembly was used for the experimentalwork on complex surfaces. The glass unit consisting ofthe wetted wall tube and reservoir was replaced byanother unit having a glass tube with a slightly largerdiameter. A sheet of Sulzer Mellapak 350Y packingmaterial (without holes) was cut and rolled to fit intothe glass tube. At 27.3 mm, the diameter of this packingwetted-wall column is slightly larger than that of its

* Author to whom correspondence should be addressed.Fax: +27 (0)21 808 2059. E-mail: [email protected].

2310 Ind. Eng. Chem. Res. 2001, 40, 2310-2321

10.1021/ie000841e CCC: $20.00 © 2001 American Chemical SocietyPublished on Web 04/20/2001

smooth counterpart. The total length of this column is106 mm. The wavelength of the microstructure of thepacking material is 3.75 mm, and its amplitude is 0.6mm. Experiments were carried out with in both aninline and a staggered configuration of the microstruc-ture.

A flow diagram of the experimental setup is shownin Figure 2. The liquid feed to the wetted-wall columnis pumped from a calibrated reservoir with a smallcentrifugal pump. The liquid is heated to the temper-ature of the water bath through a heating coil that issubmerged in the constant-temperature bath. The liquidfills the reservoir and flows through the liquid inlet slotinto the wetted-wall tube. It exits through the outletslot and flows under gravity back to the calibratedreservoir. Dehumidified air is heated in an electricheater and enters the wetted-wall tube through the inletcalming section. It is vented to the atmosphere throughthe outlet calming section. The temperatures of the airand working liquid are measured at different pointswith type K thermocouples and registered on a recorder.

Experimental Procedure

The apparatus is filled with the desired liquid throughthe calibrated reservoir and pumped to the reservoir inthe wetted-wall assembly. The air flow rate and thetemperature of the water bath are adjusted to thedesired values. The temperature of the air is adjustedto the operating temperature by varying the power tothe electric heater. Before experimental work is started,the liquid is circulated until it reaches operating tem-perature.

The evaporation rate of a liquid is measured atcombinations of different air and liquid flow rates. Theliquid level is allowed to build up between the bottomflange and the bottom of the wetted-wall tube to preventair from being vented through the liquid return line.This liquid is drained before volumetric measurementsare made. The total amount of liquid evaporated duringa run is measured with the calibrated reservoir. Thetemperatures 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 volatilecomponent after each run in order to maintain aconstant liquid concentration for a series of runs. Thechange in composition during an experimental run isaccounted for by using an average in the calculations.

The change in composition during an experimentalrun for binary mixtures in which both components arevolatile is negligible. After each run, the liquid reservoiris topped off with the binary mixture, and after everysecond run, a sample is drawn from the liquid reservoirfor GC analysis. The average composition for each runis determined by linear interpolation between thesampling points.

Gas-Phase Mass Transfer

The molar flux per unit area of species A diffusingthrough a stagnant gas B is calculated from7

PBm is the logarithmic mean of PBi and PBb and is givenby

The subscripts i and b refer to the interface and the bulkof the gas, respectively.

∆z is the thickness of the diffusional sublayer, andbecause this quantity is difficult to measure or correlate,a mass transfer coefficient is introduced

To obtain the total rate of mass transfer from a liquidfilm on the inside of a pipe wall, the following integra-tion has to be done:

Figure 1. Wetted-wall column.

Figure 2. Flow diagram: Wetted-wall column.

NA )DAB

∆zP

PBmRT(PAi - PAb) (1)

PBm )PBb - PBi

ln(PBb

PBi)

(2)

NA ) kgP

PBmRT(PAi - PAb) (3)

n ) NAA ) ∫0

h ∫0

2π[kgP

PBmRT(PAi - PAb)]r dθ dy (4)

Ind. Eng. Chem. Res., Vol. 40, No. 10, 2001 2311

If it is assumed that the variables are independentof θ, the pressure drop is negligible, and k is indepen-dent of y, then eq 4 can be simplified to

If isothermal operation is assumed, i.e., evaporativecooling is considered to be negligible, it is not necessaryto numerically integrate eq 5. For short columns, thisis a good approximation. If pure B enters the columnand the mass transfer rate of A is small, (PAi - PAb)will vary more between the inlet and the outlet of thecolumn than will PBm. An arithmetic mean between theinlet and outlet values of PBm will, therefore, be ad-equate. A logarithmic average of the inlet and outlet ofthe partial pressure driving force is used

The molar transfer rate is calculated by substituting∆PA into eq 5 and integrating over the height of thecolumn

In the calculation of the interfacial area, the thicknessof the liquid film is taken into account, r ) rp - ∆

Liquid-Phase Mass Transfer

The final form of the equation relating the overallmass transfer coefficient to the individual mass transfercoefficients is as follows:7

where m is the slope of the equilibrium line and isdefined as24

yA is calculated as PAi/Pt. PAi is the vapor pressure ofcomponent A corresponding to the mole fraction of xAin the liquid phase and is calculated with the NRTLequation.

For binary mixtures with only one volatile component,the molar flux is simply the total mass evaporated. Inbinary mixtures in which both components are volatile,the estimation of the molar flux for each component iscomplicated somewhat. Nieuwoudt and Crause23 haveshown that, for a binary mixture of component A and Cevaporating into a gas B, the mole fraction of A (basedon the total evaporation rate) that evaporates is givenby

K is a ratio of the gas-phase diffusion coefficients defined

as

The analysis was performed assuming that, at low masstransfer rates, the fluxes of the two components areindependent. The exponent c in eq 12 is equal to theexponent of the Schmidt number in the gas-phase masstransfer correlation. In this work, this exponent isassumed to be equal to the theoretical value of 0.5.

In binary systems in which there is a substantialdifference between the surface tensions of the compo-nents, the Marangoni number is often used to correlatethe observed enhancement. Imaishi et al.17 defines theMarangoni number as

The surface tension of the liquid at the interface, σi, iscalculated for the interfacial concentration, Cli, that iscalculated from

where B is a ratio of the mass transfer resistances inthe liquid and the gas phases and is given by

The liquid-side resistance in eq 15 is calculated usingthe penetration theory of Higbie. For a wetted-wallcolumn, the liquid-phase mass transfer coefficient isgiven by13

The gas-phase mass transfer coefficient in eq 15 iscalculated from gas-phase mass transfer correlationsfitted to experimental data.

Results: Gas-Phase Mass Transfer

Smooth Surface. The results are plotted in termsof a dimensionless flow number (Reg or Rel) and adimensionless mass transfer number (Shg). Figure 3show the experimental results for six pure componentsat different air flow rates. Figure 4 show the influenceof the liquid flow rate on the gas-phase Sherwoodnumber. The remaining pure components showed thesame trend as in Figure 4, except for 1,2-propanediol.For 1,2-propanediol, there was no increase in the masstransfer rate (Shg) with increasing liquid flow rate (Rel).The results are compared to the correlation developedby Crause and Nieuwoudt8 in Figure 5. In this figure,MTG is defined as

From Figure 5, it is clear that the correlation developedby Crause and Nieuwoudt8 gives a reasonable fit to thedata, but a few of the data points lie well below their

n ) 2πrkgP∫0

h 1RTPBm

(PAi - PAb) dy (5)

∆PA )(PAi - PAb)inlet - (PAi - PAb)exit

ln[(PAi - PAb)inlet

(PAi - PAb)exit]

(6)

n ) Ai

kgPt∆PA

RTPBm(7)

Ai ) 2πrh (8)

1kog

) 1kg

+ mkl

(9)

m )yA

xA(Mr,l

Mr,g)(Fg

Fl) (10)

zA )yAi

yAi + KyCi(11)

K ) (DCB

DAB)c

(12)

Ma )(σi - σl)

µlkl(13)

Cli )Cl

(1 + B)(14)

B )mkg

kl(15)

kl ) 2xDAui

πz(16)

MTG ) ( ShSc0.5Rel

0.08) (17)

2312 Ind. Eng. Chem. Res., Vol. 40, No. 10, 2001

predicted values. This suggests that Rel had a largerinfluence on the gas-phase mass transfer rate in thepresent work than was observed in their work. In Figure5, there are a few points for which the mass transferrate lies well above the value predicted by their cor-relation. These points represent the gas-phase masstransfer rate of 1,2-propanediol.

The experimental gas-phase mass transfer rates forthe different pure components were correlated by usinga power law series similar to that used by previousinvestigators. Combinations of different dimensionlessnumbers were used in the correlating procedure. Thiswas done in order to assess the influence of the differentphysical properties on the mass transfer rate. Nonlinearleast-squares minimization of the squared sum of thedifferences between the calculated and experimentalvalues of Shg was used to calculate the constants in thecorrelation.

Relatively few experimental points were measured for1,2-propanediol because of wetting problems at lowliquid flow rates. It is also uncertain whether theavailable correlations for the binary diffusion coefficientare accurate for 1,2-propanediol/air at the experimentalconditions of interest. It was therefore decided that thisdata set should not be included in the training set.

Table 1 shows the results for the different combina-tions of dimensionless numbers. In the second correla-tion in the table, the velocity of the gas phase relativeto the liquid surface was used in calculating the relativegas-phase Reynolds number.

When the root-mean-square errors of the differentcorrelations in Table 1 are compared, it can be seen thatcorrelations in which the velocity of the liquid phase isaccounted for or a dimensionless number for the liquidphase is included fit the data better than a simpleGilliland-Sherwood-type correlation (the first correla-tion in the table). This is also evident from Figure 4,which shows that Shg is influenced by the liquid flowrate.

The correlation in which the liquid flow term incor-porates the velocity of the film and the surface tension,through the Weber number, gives the best fit to theexperimental data (the last correlation in Table 1). Thisis in contrast to the correlations employed by previousinvestigators8,18,22,32 who used Rel to characterize theinfluence that the liquid film has on the gas-phase masstransfer. It is expected, however, that this correlationwill not extrapolate well to liquids having viscositiesthat fall outside the range over which it was fitted(2.51-7.65 10-4 Pa s). Further discussions of the resultswill focus on this correlation, unless stated otherwise.

The effect that the surface tension has on the gas-phase mass transfer is not yet fully understood. Pera-manu et al.26 link the surface tension to the instabilityof a falling liquid film. They found that, for a decreasein surface tension, there is an increase in the amplitudeof the waves on the surface of the film. This might havethe effect of inducing more turbulence in the gas layerclose to the interface and thereby enhancing the rate ofmass transfer.

One can not ignore, however, the effect that theviscosity of the liquid phase has on the mass transferrate. Figure 4 shows that the mass transfer rate for 1,2-propanediol is higher than that for the other pureliquids. Crause and Nieuwoudt8 also found this to bethe case with ethylene glycol when compared to the gas-phase mass transfer rate of liquids of lower viscosity.If it is assumed that this effect is not due to experimen-tal error or inaccuracies in the estimation of the binarygas-phase diffusion coefficient, then the following analy-sis can be made.

The viscosity of 1,2-propanediol is almost twice thatof the highest pure-liquid viscosity in the training set(1.47 × 10-3 Pa s compared to 7.65 × 10-4 Pa s). Thesurface tension is 25% higher than the highest surfacetension (0.028 N/m compared to 0.023 N/m). To verifythat it is the viscosity, and not the surface tension, thatcauses the enhanced mass transfer rate, experimental

Figure 3. Shg vs Reg for different pure components. Ranges ofsome 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 ) 12-153.

Figure 5. Experimental values (]) compared to predictions byCrause and Nieuwoudt8 (solid line).

Table 1. RMS Errors for Various Correlations (SmoothSurface)

correlation RMS error

Shg ) 0.0044Reg0.992Scg

0.583 3.175Shg ) 0.0008Reg,r

1.172Scg0.547 2.461

Shg ) 0.0030Reg0.959Scg

0.485Rel0.145 2.024

Shg ) 0.0047Reg0.992Scg

0.537Wel0.111 1.734


data for liquids having surface tensions higher thanthose of the liquids in the training set are comparedwith the proposed correlation in Figure 6. The viscositiesof these liquids fall within the experimental range. Thedata were obtained from Crause and Nieuwoudt.8 Inthis figure, MTG is defined as

Figure 6 shows the excellent fit of the proposedcorrelation to the experimental data. The conclusion canbe made that the viscosity has a definite effect on themass transfer rate. More experimental work needs tobe done in order to investigate this phenomenon.However, it is clear that the correlation developed inthis work does not extrapolate well to liquids having aviscosities higher than those of the liquids in thetraining set. It does extrapolate well to liquids havingsurface tensions that are substantially higher, but withviscosities that fall within the experimental range. Theproposed correlation is plotted with the experimentaldata in Figure 7, with the confidence intervals shown.MTG is defined as in eq 18.

For the sake of simplicity, the exponents in theproposed correlation were rounded to give the followingcorrelation, without a substantial increase in the rmserror:

The exponent of the gas-phase Reynolds number (0.99

≈ 1) is the same as in the correlation developed byCrause and Nieuwoudt.8 This is to be expected becausethe same column was used in both sets of experimentalwork. This exponent is substantially higher than theexponents reported by previous investigators:2,14,18 0.8-0.83. The difference can be contributed to the length ofthe column.8 The column used in this work (0.1 m) isshorter than those used by previous investigators (0.5-1.8 m). Entrance effects in a column shorter than sixpipe diameters can be expected to dominate accordingto Crause and Nieuwoudt.8 As mentioned earlier, it isexpected that entrance effects will have an influence onthe mass transfer in structured packing, where the flowprofile is never completely developed because of thegeometry of the packing. The exponent of the gas-phaseSchmidt number was rounded to 0.5 because it (0.537)compared favorably to this theoretical value. Duduk-ovic12 has shown that the widely used exponent of 1/3 isapplicable not to mass transfer from a falling liquidinterface, but rather to the mass transfer from astationary interface. The exponent of the liquid-phasedimensionless number is higher than that found byCrause and Nieuwoudt.8 This can be expected becausethe mass transfer was investigated at lower flow rates.It was found that, as the flow rate decreased from thatused by Crause and Nieuwoudt,8 the line of waveinception, or the point where waves can be visuallyobserved, moves up the column.33 The influence thatthese waves have on the mass transfer rate is not yetfully understood. Some investigators attribute it to anincrease in the surface area,29 whereas others argue thatit increases interfacial turbulence.9 All agree, however,that it does have an effect on the mass transfer rate. Itis therefore not surprising that, for an increase in thearea covered by visually observable surface waves, thereis an increase in the exponent of the liquid-phasedimensionless number. As previously stated, it wasfound that, in the viscosity range of this experimentalwork, Wel gave a better fit than Rel.

Complex Surface. Figure 8 shows the results for thethree pure components used. The ranges of someimportant dimensionless numbers and physical proper-ties 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 masstransfer is shown in Figure 9. The same trend wasobserved for the other liquids.

No difference in the rate of mass transfer betweenthe staggered and inline configurations could be found.It was however found that the surface of the liquid

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) withproposed correlation (s).

Figure 7. Plot of experimental data and proposed correlation (s).

MTG ) ( Shg

Scg0.537Wel

0.111) (18)

Shg ) 0.0044RegScg0.5Wel

0.111 (19)

Figure 8. Shg vs Reg for different pure components, complexsurface (staggered configuration).


became unstable and breakaway droplets formed for theinline configuration at high liquid flow rates (Rel > 100).For the staggered configuration, the liquid flow ratecould be increased to (Rel ) 140 without the formationof breakaway liquid droplets. The formation of break-away droplets in the inline configuration at higher Relvalues might be explained by the mean film thicknessand the average surface velocity of the liquid phase. Themean thickness of the liquid film in this type ofconfiguration is thought to be smaller than that in thestaggered configuration, with most of the volume of theliquid flowing in the channels between inline peaks. Thethickness of these films is comparable to that of asmooth surface. The staggered configuration inducesliquid spreading, and therefore, the volume of the liquidfilm is more uniformly spread over this configuration.The mean thickness of these films is greater than thatfor smooth surfaces, and the average free surfacevelocity is smaller.39 It follows that, for an increase inthe liquid flow rate, the average surface velocity of theliquid film will reach the critical value for breakawaysooner in the inline configuration than in the staggeredconfiguration.

It was again found that Shg is dependent on the liquidflow rate. Figure 9 shows this dependence quite clearly.It was also found that the liquid flow rate influencesthe mass transfer rate at lower Reg values than for thesmooth surface. For the smooth surface, the slope of Shgvs Rel is smaller at low Reg (<2700) than it is for thecomplex surface (see Figures 4 and 9). A possibleexplanation for this might be the formation of stagnantand recirculating pockets of air in the valleys betweenpeaks for the complex surface at low Reg. At higherliquid flow rates, these pockets no longer exist becauseof flatter surface profile.39 This explains the increasein the rate of mass transfer with liquid flow rate. Thisargument also holds for the smooth surface where theliquid film surface profile is wavy. It must be remem-bered, however, that the wavy interface extends for theentire length of the column in the case of the complexsurface at low flow rates.

Figure 10 compares Shg vs Reg for the smooth andcomplex surfaces. The data are for n-hexane at aconstant liquid flow rate (relatively low, Rel ≈ 70). Thesharp increase of Shg with Reg for the complex surface,above that measured for smooth surfaces, might becaused by the onset of and increase in interfacialturbulence with an increase in Reg. This has a moreprofound effect on the complex surface because thesurface profile of the liquid film is wavy for the entire

length of the column, especially at low liquid flow rates.This waviness is induced and cannot “fall flat” as in thecase of flat surfaces.

The correlation developed for smooth surfaces (eq 19)is compared to the experimental data in Figure 11. Inthis figure, MTG is defined as in eq 18, but with theexponent of the Schmidt number set equal to thetheoretical value of 0.5.

Figure 11 show that eq 19 underpredicts the masstransfer rate, as expected.

The experimental data were correlated in the samemanner and using the same dimensionless numbers asdiscussed in the previous section. The capillary numberwas included in the correlating procedure becausevarious investigators31,34 claim that capillary forces willhave an effect on the surface profile of the liquid. Thecapillary number used in this work is defined as theratio of the viscous forces to the surface tension forces.

The root-mean-square error values in Table 2 showthat correlations without a dimensionless liquid flowterm fail to correlate the data. Correlations containingthe Weber number, similar to that used in the previoussection, or the Capillary number, did not accurately fitthe data. A reasonable fit was obtained by using the

Figure 9. Shg vs Rel for ethanol, complex surface (staggeredconfiguration). Reg ) 1665-5515, Rel ) 50-140. Figure 10. Shg vs Reg for n-hexane. Rel (smooth) ) 75, Rel

(complex) ) 67.

Figure 11. Experimental values for complex surface (]) com-pared to values predicted by eq 19 (solid line).

Table 2. RMS Errors for Various Correlations (ComplexSurface)

correlation RMS error

Shg ) 0.0413Reg0.761Scg

0.576 4.417Shg ) 0.0069Reg,r

0.958Scg0.615 3.744

Shg ) 0.095Reg0.769Scg

0.720Cal0.184 4.196

Shg ) 0.0375Reg0.776Scg

0.755Wel0.210 2.968

Shg ) 0.0067Reg0.772Scg

0.618Rel0.364 2.158

Shg ) 0.0047Reg0.752Scg

0.547Rel0.393Bo-0.099 2.069


liquid Reynolds number in the correlation. It wasslightly improved by adding the Bond number to thiscombination.

It is assumed that the last correlation in Table 2 bestdescribes the mass transfer data measured in this workfor liquid films flowing down a complex surface. Thiscorrelation is plotted with the experimental data inFigure 12. The confidence intervals are also shown.MTG is defined as

If the exponent of the gas-phase Schmidt number in theproposed correlation is set equal to the theoretical value(0.5) and the remaining constants are regressed on theexperimental data, the error value is not increased bymuch.

Results: Liquid-Phase Mass Transfer

Smooth Surface. Several binary mixtures with onevolatile component were investigated. They includemethanol/ethylene glycol, methanol/1-octanol, ethanol/tridecane, and n-hexane/tridecane. Two binary mixtures

with both components volatile were also investigated.They were methanol/ethanol and acetone/methanol.

Figures 13-16 show the results of the experimentaland predicted mass transfer coefficients for the binarysystems with one volatile component. VLE data forthese systems were obtained from the SIMSCI databankin the simulation package Pro Π. If no experimentallyfitted interaction parameters could be found either inthe literature or in the SIMSCI databank, then thebinary interaction parameters for the NRTL model wereestimated from the UNIFAC group contribution methodin Pro Π. This was the case for the systems methanol/1-octanol, ethanol/tridecane, and hexane/tridecane.

It is evident from Figures 13-16 that the liquid-sideresistance, calculated with Higbie’s penetration theory,is negligible in the binary systems investigated. Thisconclusion can be made because, in all of the plots ofkog (experimental) versus kog (predicted), the points lieabove the diagonal, i.e., the experimentally measuredkog is higher than the predicted kog.

What is surprising to see is that, in most of the binarysystems with one volatile component, the measured kogis higher than the predicted kg. Nieuwoudt and Crause23

also observed this phenomenon. For the system methanol/ethylene glycol the measured mass transfer coefficientis much higher than the predicted value at low concen-trations of methanol (see Figure 13b). This also seemsto be true for the n-hexane/tridecane system (Figure16b).

For the system methanol/1-octanol (Figure 14b), thereis some enhancement of the measured value over thepredicted value, although it is not as composition-dependent as in the methanol/ethylene glycol andn-hexane/tridecane systems.

The binary system ethanol/tridecane is an exception.At low mass transfer rates, there is good agreementbetween the measured and predicted mass transfercoefficients (see Figure 15b). At higher mass transferrates, some liquid-side resistance develops, but it ismuch smaller than predicted by penetration theory. Itmust, however, be mentioned that the binary interactionparameters used in the NRTL equation to calculate thevolatile component’s vapor pressure were estimatedusing the UNIFAC method (this is also the case for then-hexane/tridecane and methanol/1-octanol systems).Experimental vapor/liquid equilibrium data will verifywhether the observed resistance is meaningful.

Figure 12. Plot of experimental data and proposed correlation(s).

MTG ) ( Shg

Scg0.547Rel

0.393Bo-0.1)1/0.75

(20)

Shg ) 0.0036Reg0.76Scg

0.5Rel0.41Bo-0.13 (21)

Figure 13. Plot of measured kog vs (a) predicted kog and (b) predicted kg for methanol/ethylene glycol. Reg ) 1950-6490, Rel ) 6-91.


The results for the binary systems with both compo-nents volatile are presented in the same format. Figure17 show the results for the binary system acetone/methanol. The composition in the liquid phase is near

the azeotropic composition (89.5 mol % acetone at 37.1°C). Because the azeotropic composition is used, theliquid composition does not change, and no liquidresistance exists.

Figure 14. Plot of measured kog vs (a) predicted kog and (b) predicted kg for methanol/1-octanol. Reg ) 1950-7240, Rel ) 18-142.

Figure 15. Plot of measured kog vs (a) predicted kog and (b) predicted kg for ethanol/tridecane. Reg ) 1945-6480, Rel ) 19-103.

Figure 16. Plot of measured kog vs (a) predicted kog and (b) predicted kg for n-hexane/tridecane. Reg ) 2215-7360, Rel ) 15-165.


Figure 18 shows the result for the binary mixturemethanol/ethanol at an average methanol concentrationof 51 mol %.

In the binary systems with both components volatile,there is close agreement between the measured overallgas-phase mass transfer coefficient (kog) and the pre-dicted gas-phase mass transfer coefficient (kg) (Figures17 and 18). Both of these figures are for the componentthat forms the bulk of the evaporating mixture (themore volatile component). The acetone/methanol systeminvestigated had a liquid-phase concentration of ap-proximately 89.5 mol % acetone. Because this concen-tration is close to the azeotropic point, the concentrationof acetone in the gas layer next to the interface is almostthe same. In both instances, the concentration of themore volatile component (methanol, acetone) is muchhigher than that of the less volatile component (ethanol,methanol). It is therefore a good approximation toassume that the flux of the more volatile component isindependent of the flux of the less volatile component.The opposite, however, is not true. To evaluate the gas-phase mass transfer coefficient for the less volatilecomponent, the molar flux of the two components willhave to be coupled. This falls outside the scope of thiswork.

A mass transfer enhancement factor is defined in anattempt to correlate the observed enhancement with

some physical property (or properties). The enhance-ment factor is defined as

Table 3 shows the enhancement factors calculated forbinary mixtures with one volatile component.

The enhancement factors shown in Table 3 werecalculated as averages for specific compositions.

A possible explanation for the enhancement is theMarangoni effect.5,11,15,17,35 Because no liquid-side re-sistance could be detected in the systems investigated,it is believed that the Marangoni effect might enhancethe gas-phase mass transfer rate by causing interfacialturbulence. However, no difference could be detected inthe appearance of the liquid surface between differentconcentrations of the solute, as observed by Nieuwoudtand Crause.23 No correlation between the observedenhancement and Ma could be found.

There are, however, some difficulties involved incalculations of the Marangoni number:9 (1) The liquid-side resistance was calculated using Higbie’s penetra-tion theory, which was developed for laminar flow. Nocorrelation exists for turbulent conditions. (The logicbehind the use of Higbie’s theory is that it will estimatekl within an order of magnitude for the differentsystems.) (2) The liquid-phase diffusion coefficient isrequired. The accuracy of existing correlations is doubt-ful. (3) To calculate the interfacial surface tension, theconcentration gradient in the liquid phase must beknown.

The Marangoni number fails to predict the observedenhancement, but there does seem to be a link betweenthe surface tension and the enhancement. Figure 19shows the effect of the quantity (σmixture - σvolatile) on F(from Table 3). Points where the mixture viscosity liesoutside the experimental range were not included in thisgraph (25 and 50 mass % ethylene glycol/methanolmixtures).

Figure 19 shows a scatter in the data at low differ-ences in surface tension. For differences higher than 3.5mN/m there seems to be an upward trend.

The conclusion can be made that the observed en-hancement is coupled to the difference in surface tensionbetween the solute and the solvent. It could be thatliquid-phase mass transfer coefficients calculated withHigbie’s penetration theory are faulty and mask thiseffect (surface tension difference) in the Marangoninumber. This idea is supported by the results obtained

Figure 17. Plot of measured kog vs predicted kg for acetone in abinary mixture of acetone/methanol containing 89.5 mol % acetone.Reg ) 3020-6720, Rel ) 66-297.

Figure 18. Plot of measured kog vs predicted kog and kg formethanol in a binary mixture of methanol/ethanol containing 51mol % methanol. Reg ) 1870-6180, Rel ) 28-155.

Table 3. F for Binary Mixtures Containing One VolatileComponent (Smooth Surface)

system

mass %(volatile

component)

viscosity× 104

(Pa s)

surfacetension(N/m) F

methanol/ 25 30.1 0.037 2.27ethylene glycol 50 13.5 0.030 1.67

75 7.1 0.025 1.32

methanol/ 25 8.3 0.024 1.441-octanol 50 5.4 0.023 1.28

75 4.6 0.022 1.23

ethanol/ 25 6.0 0.021 1.00tridecane 50 5.6 0.021 1.05

75 5.5 0.020 1.02

n-hexane/ 25 7.9 0.022 1.48tridecane 50 5.0 0.020 1.23

75 3.5 0.018 1.08

F )kog (measured)

kg (predicted)(22)


for the binary mixtures with both components volatile.Because there is almost no difference in the surfacetension of the components in both the acetone/methanoland the methanol/ethanol mixtures, it is expected thatF ≈ 1. This was indeed found to be the case, with F )1.1 for acetone/methanol and F ) 1.06 for methanol/ethanol (see Figures 17 and 18).

The reason behind the enhancement observed whenthere is a substantial difference in the surface tensions

of the solute and solvent is still uncertain. It is believedthat this difference will cause some kind of hydrody-namic instability at the interface that will lead tointerfacial turbulence in the gas phase. It is possiblethat this instability will be in the form of surface wavesthat might also increase the mass transfer area.

Complex Surface. For complex surfaces, the inves-tigation of liquid-side resistance was limited to binarymixtures with one volatile component. The mixturesinvestigated were methanol/ethylene glycol and n-hexane/tridecane. Figure 20 shows the results for thebinary mixture methanol/ethylene glycol. Figure 21shows the results for n-hexane/tridecane.

It is again evident from Figures 20a and 21a thatthere is no liquid-side resistance to mass transfer. Inboth of these figures, the experimentally measured kog

values are higher than the predicted values (the mark-ers lie above the diagonal). The experimentally mea-sured kog value is also higher than the predicted kg value(see Figures 20b and 21b), as was the case for smoothsurfaces. An enhancement factor is defined as in eq 22,and the results are shown in Table 4. The correlationused to calculate kg is the second correlation in Table 2

Figure 19. Enhancement (F) vs (σmixture - σvolatile).

Figure 20. Plot of measured kog vs (a) predicted kog and (b) predicted kg for methanol/ethylene glycol, complex surface. Reg ) 1800-6740, Rel ) 5-97.

Figure 21. Plot of measured kog vs (a) predicted kog and (b) predicted kg for n-hexane/tridecane, complex surface. Reg ) 2200-7160, Rel) 24-172.


and has the following form:

This form was used because eq 21 was fitted in a narrowrange of liquid viscosity and only two of the data pointswould fall inside this range. Equation 23 uses a relativegas-phase Reynolds number to account for the influencethat the liquid phase has on the mass transfer rate. Itwill therefore not be too sensitive to physical propertiessuch as liquid viscosity. The enhancement factorscalculated with eq 21 are also shown.

A comparison between the two enhancement factorsshows that eq 21 is extremely sensitive to the liquidviscosity and surface tension. Where these propertiesare within the experimental range, good agreement isobtained between the two enhancement factors (50 and75 mass % n-hexane/tridecane).

It is again evident that the enhancement is coupledwith the difference in surface tension between the solute(volatile component) and the solvent. No experimentalwork was done for systems where there is only a smalldifference in surface tension between the solvent andsolute, but the same trend observed for the smoothsurface is expected. Because there is some doubt as tothe accuracy of eq 21 in calculating kg (see Table 2), nocomparison between the smooth and complex surfaceswill be made. This awaits future work.

Conclusions

Gas-phase mass transfer coefficients were measuredand correlated in a short wetted-wall column underisothermal conditions. These correlations were used toquantify the liquid-side resistance in binary mixtureswith one or both components volatile. Both a smoothand a complex surface were investigated in the study.The gas-phase mass transfer rate was found to be higherand more dependent on the liquid flow rate for liquidsflowing down a complex surface (similar to the surfaceof the structured packing Mellapak) than for liquids ona smooth glass surface. The experimental data werecorrelated with a power law series similar to that usedby previous investigators. For the smooth surface, it wasfound that, by using the liquid Weber number insteadof the liquid Reynolds number in the power law series,there was an improvement in the correlation of the data.The proposed correlation extrapolates well to liquidshaving surface tensions substantially higher than thosein the experimental range, provided that their viscosi-ties lie within the experimental range. A combinationof the liquid Reynolds number and the Bond number,together with the gas-phase Reynolds and Schmidtnumbers, gave the best fit to the data for the complexsurface. Care should, however, be taken when applyingthese correlations outside the range in which they werefitted.

Binary systems with one or both components volatilewere investigated in the smooth surface setup. In thecomplex surface setup, this was limited to systems withone volatile component. In most of the binary systemsinvestigated, the liquid-side resistance was found to benegligible. The system ethanol/tridecane is an exception.Some liquid-side resistance was observed at low con-centrations of ethanol and high mass transfer rates.However, it was much less than predicted by Higbie’spenetration theory. For both the smooth and complexsurfaces, the experimentally determined overall masstransfer coefficients were found to be higher than thepredicted gas-phase mass transfer coefficients (ethanol/tridecane being the only exception). This enhancementis coupled to the difference in surface tension betweenthe solvent and solute. No correlation could be obtainedbetween the observed enhancement and the Marangoninumber. Inaccurate values for the liquid-phase masstransfer coefficient might mask the effect.

Acknowledgment

The financial support of Sasol and Sulzer Chemtechis gratefully acknowledged.

Nomenclature

A ) area, m2

Bo ) Bond number, Bo ) [g(Fl - Fg)δ2]/σC ) concentration, mol/m3

Cal ) Capillary number, Cal ) ulµl/σD ) diameter, mDAB ) diffusion coefficient of A in B, m2/sDl ) liquid-phase diffusion coefficient, m2/sF ) enhancement factorg ) gravitational acceleration, 9.81 m/s2

h ) height, mK ) distribution coefficientk ) mass transfer coefficient, m/sm ) slope of equilibrium lineMa ) Marangoni number, Ma ) (σi - σl)/(µkl)Mr ) molecular weight, g/molMTG ) mass transfer groupn ) molar transfer rate, mol/sN ) molar flux, mol/(m2 s)P ) pressure, PaPBm ) mean pressure of B, Par ) radius, mR ) universal gas constant, 8.314 J/(mol K)Reg ) gas-phase Reynolds number, Reg ) Fgug(D - 2δ)/µgRel ) liquid-phase Reynolds number, Rel ) Flulδ/µlScg ) gas-phase Schmidt number, Scg ) µg/(FgDAB)Shg ) gas-phase Sherwood number, Shg ) kgδ/DABT ) temperature, Ku ) velocity, m/sWel ) liquid-phase Weber number, Wel ) Flul

2δ/σx ) liquid mole fractiony ) vapor/gas mole fractionz ) mole fraction in gas phase

Greek Symbols

θ ) angle, radυ ) kinematic viscosity, m2/s∆ ) differenceδ ) thickness, mµ ) viscosity, Pa sF ) density, kg/m3

σ ) surface tension, N/mτ ) interfacial shear force per area, Pa

Table 4. F for Binary Mixtures Containing One VolatileComponent (Complex Surface)

system

mass %(volatile

component)

viscosity× 104

(Pa s)

surfacetension(N/m)

F(eq 21)

F(eq 23)

methanol/ 25 29.8 0.038 4.63 2.00ethylene glycol 50 13.4 0.031 2.28 1.48

75 7.1 0.025 1.48 1.21

n-hexane/ 25 8.0 0.021 1.74 1.34tridecane 50 5.1 0.019 1.30 1.28

75 3.5 0.018 1.16 1.24

Shg ) 0.0069Reg,r0.958Scg

0.615 (23)


Superscripts

liq ) liquidvap ) vapor

Subscripts

avg ) averageb ) bulkg ) gas phasei ) interfaciall ) liquid phasem ) meano ) overallp ) piper ) relativet ) total

Literature Cited

(1) Banerjee, S.; Rhodes, E.; Scott, D. S. Mass transfer to fallingwavy liquid films at low Reynolds numbers. Chem. Eng. Sci. 1967,22, 43.

(2) Barnet, W. I.; Kobe, K. A. Heat and vapour transfer in awetted-wall tower. Ind. Eng. Chem. 1941, 33, 436.

(3) Barrdahl, R. A. G. Mass transfer in falling films: Influenceof finite-amplitude waves. AIChE J. 1988, 34, 493.

(4) Bontozoglou, V.; Papapolymerou, G. Laminar film flow downa wavy incline. Int. J. Multiphase Flow 1997, 23, 69.

(5) Brain, P. L. T.; Vivian, J. E.; Mayr, S. T. Cellular convectionin desorbing surface tension lowering solutes from water. Ind. Eng.Chem. Fundam. 1971, 10, 75.

(6) Bravo, J. L.; Rocha, J. A.; Fair, J. R. Mass transfer in gauzepackings. Hydrocarbon Process. 1985, 1, 91.

(7) Coulson, J. M.; Richardson, J. F. Chemical Engineering, 4thed.; Pergamon Press: New York, 1990; Vol. 2, Chapter 12.

(8) Crause, J. C.; Nieuwoudt, I. Mass Transfer in a ShortWetted-Wall Column. 1. Pure Components. Ind. Eng. Chem. Res.1999, 38, 4928.

(9) Crause, J. C. A fundamental mass transfer model for anextractive distillation application, M. Ing. Thesis, University ofStellenbosch, Stellenbosch, South Africa, January 1998.

(10) Dassori, C. G.; Deiber, J. A.; Cassano, A. E. Slow two-phaseflow through a sinusoidal channel. Int. J. Multiphase Flow 1984,10, 184.

(11) Drinkenburg, A. A. H. Marangoni convection by evapora-tion in Spacelab; Institution of Chemical Engineers SymposiumSeries No. 104; Hemisphere Publishing Corporation: New York,1988; p B179.

(12) Dudukovic, A.; Milosevic, V.; Pjanovic, R. Gas-solid andgas-liquid mass transfer coefficients. AIChE J. 1996, 42, 269.

(13) Emmert, R. E.; Pigford, R. L. Interfacial resistance. Chem.Eng. Prog. 1954, 50, 87.

(14) Gilliland, E. R.; Sherwood, T. K. Diffusion of vapors intoan air stream. Ind. Eng. Chem. 1934, 26, 516.

(15) Golovin, A. A. Mass transfer under interfacial turbu-lence: Kinetic regularities. Chem. Eng. Sci. 1992, 47, 2069.

(16) Higbie, R. The Rate of Absorption of Pure Gas into a StillLiquid during Short Periods of Exposure. Trans. Am. Inst. Chem.Eng. 1935, 31, 365.

(17) Imaishi, N.; Suziki, Y.; Hozawa, M.; Fujinawa, K. Inter-facial turbulence in gas-liquid mass transfer. Int. Chem. Eng.1982, 22, 659.

(18) Kafesjian, R.; Plank, C. A.; Gerhard, E. R. Liquid flow andgas-phase mass transfer in wetted-wall towers. AIChE J. 1961,7, 463.

(19) King, C. J. Turbulent liquid-phase mass transfer at a freegas-liquid interface. Ind. Eng. Chem. Fundam. 1966, 5, 1.

(20) Kister, H. Z. Distillation Design; McGraw-Hill: New York,1992; Chapter 9.

(21) Lamourelle, A. P.; Sandall, O. C. Gas absorption into aturbulent liquid. Chem. Eng. Sci. 1972, 27, 1035.

(22) Nielsen, C. H. E.; Kiil, S.; Thomsen, W.; Dam-Johansen,K. Mass transfer in wetted-wall columns: Correlations at highReynolds numbers. Chem. Eng. Sci. 1998, 53, 495.

(23) Nieuwoudt, I.; Crause, J. C. Mass Transfer in a ShortWetted-Wall Column. 2. Binary Systems. Ind. Eng. Chem. Res.1999, 38, 4933.

(24) Nieuwoudt, I. The fractionation of high molecular weightalkane mixtures with supercritical fluids. Ph.D. Dissertation,University of Stellenbosch, Stellenbosch, South Africa, March1994.

(25) Oliver, D. R.; Atherinos, T. E. Mass transfer to liquid filmson an inclined plane. Chem. Eng. Sci. 1968, 23, 525.

(26) Peramanu, S.; Sharma, A. Nonlinear instabilities of fallingfilms on a heated vertical plane with gas absorption. Can. J. Chem.Eng. 1998, 76, 211.

(27) Portalski, S.; Clegg, A. J. Interfacial area increase inrippled film flow on wetted wall columns. Chem. Eng. Sci. 1971,26, 773.

(28) Pozrikidis, C. The flow of a liquid film along a periodic wall.J. Fluid Mech. 1988, 188, 275.

(29) Reker, J. R.; Plank, C. A.; Gerhard, E. R. Liquid surfacearea effects in a wetted-wall column. AIChE J. 1966, 12, 1008.

(30) Rocha, J. A.; Bravo, J. L.; Fair, J. R. Distillation columnscontaining structured packings: A comprehensive model for theirperformance. 2. Mass-transfer model. Ind. Eng. Chem. Res. 1996,35, 1660.

(31) Shetty, S.; Cerro, R. L. Flow of a thin film over a periodicsurface. Int. J. Multiphase Flow 1993, 19, 1013.

(32) Strumillo, C.; Porter, K. E. The evaporation of carbontetrachloride in a wetted-wall column. AIChE J. 1965, 11, 1139.

(33) Tailby, S. R.; Portalski, S. Wave inception on a liquid filmflowing down a hydrodynamically smooth plate. Chem. Eng. Sci.1962, 17, 283.

(34) Trifonov, Y. Viscous liquid film flows over a periodicsurface. Int. J. Multiphase Flow 1998, 24, 1139.

(35) Vazquez, G.; Antorrena, G.; Navaza, J. M.; Santos, V.Effective interfacial area in the presence of induced turbulence.Int. Chem. Eng. 1994, 34, 247.

(36) Wang, C. Y. Liquid film flowing slowly down a wavyincline. AIChE J. 1981, 27, 207.

(37) Wasden, F. K.; Duckler, A. E. A numerical study of masstransfer in free falling wavy films. AIChE J. 1990, 36, 1379.

(38) Yoshimura, P. N.; Nosoko, T.; Nagata, T. Enhancement ofmass transfer into a falling liquid film by two-dimensional surfacewavessSome experimental observations and modelling. Chem.Eng. Sci. 1996, 51, 1231.

(39) Zhao, L.; Cerro, R. L. Experimental characterization ofviscous film flows over complex surfaces. Int. J. Multiphase Flow1992, 18, 495.

Received for review September 25, 2000Accepted February 28, 2001

IE000841E


mass transfer in structured packing: a wetted-wall study

Documents