Coeficientes Agua Aire Hl

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PREDICTING MASS TRANSFER IN PACKED COLUMNS

CONTAINING STRUCTURED PACKINGS

Z.P. XU, A. AFACAN and K.T. CHUANG

Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada

Amodel has been developed for predicting mass transfer in packed columns containingstructured packings. The model was veried by experimental results from a 300 mmdiameter distillation column installed with three types of structured packings (Gempak

2.5A, AW7 and AW12). Three systems (methanol/isopropanol, water/acetic acid and methanol/water) and two operating pressures (710 and 260 mmHg) were used in the tests. Hence, a largerange of physical properties were covered for the modeling.

A total of 62 data points was obtained from the distillation tests. The average deviationbetween the measured values of HOGand the predicted values is 610.2%. The deviations arewithin 620% for 90% of the data points.

Keywords: mass transfer; structured packings; efciency

INTRODUCTION

Structured packings have been widely used in chemical andpetrochemical processes for separation purposes, especiallyin distillation. Accurate prediction of the mass transferefciency is essential for successful design and operation ofpacked columns.

The rst fundamental model for structured packingefciency is attributed to Bravo et al.1 For Sulzer gauzepackings, they assumed that effective interfacial area wasequal to packing surface area. Obviously, this is anoversimplied assumption. Later, Fair and Bravo2 used asimilar procedure for predicting the efciency of structuredpackings constructed with sheet metals. They proposed thefollowing equations to calculate effective interfacial area:

ae = bap (1)

where

b= 0.50 + 0.0058 (% flood) (2)

and b= 1.0 for above 85% flood (3)

This means that for sheet metal packings, effectiveinterfacial area is always lower than packing surface area.Henriques de Brito et al.3measured the effective interfacialarea of sheet metal structured packings: Mellapak 125,Mellapak 250 and Mellapak 500. Their results showed thatthe effective area of the structured packings can be muchhigher than packing surface area due to the instabilities inliquid ow (ripples or waves, detachment and subsequentfragmentation of the lm into copious liquid showers, etc.).Shi and Mersmann4 noted that the effective interfacial

area should include surface of drops and jets which owthrough the voids of the packed bed. Therefore, it is possiblethat the effective interfacial area is higher than the packingsurface area. Billet and Schultes5 proposed an efciencymodel for both structured and random packings. But theirmodel can only be used below the loading point. For

structured packings, it can be difcult to locate the loadingpoints.

The purpose of this work is to develop a model which canpredict the mass transfer efciency of structured packings ofvarious geometries over a range of vapour/liquid ows andphysical properties. The model should take the columnconcentration prole into consideration and be validated bydistillation test results.

Basic Equations

The packing efciency can be expressed by the overallheight of a transfer unit (HOG) or the height equivalent to atheoretical plate (HETP). The relationship between HETPand HOGis given by

HETP = HOGlnl

l

1(4)

where l= m/(L/G). Equation (4) is valid when both the

equilibrium line and operating line are straight.In distillation columns, mixture composition and vapour/

liquid rates vary with column position. Their inuence onHOGor HETP can be taken into account by dividing thecolumn into sections of height or concentration. In eachsection, both the equilibrium line and the operating line canbe treated as straight lines. Therefore, equation (4) can beused for calculating HETP from HOGfor each section. Thevalues ofHOGor HETP for the entire column can be foundby proper averaging of the values from each section. In thesubsequent text, only HOGis considered.

The mass transfer process in packed columns is

dependent on many factors, such as vapour/liquid rates,physical properties (composition), vapour-liquid equilibriumvalue. All these factors change from location to locationalong the column. Most of the existing models for theprediction ofHOGwere derived from the use of average owrates, composition and physical properties (Rocha et al.6

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Wagner et al.7). Therefore, these models may not be reliablyapplied to the system if the factors stated above alongthe column change signicantly. This is especially true fornon-ideal, chemical systems.

In this work, the column was divided into fty sections ofconcentrations between the top and the bottom of thecolumn. Vapour/liquid rates, physical properties, vapour-liquid equilibrium, mass transfer coefcients, effective

interfacial area, and nally HOGwere calculated for eachsection. The value ofHOGfor the entire column was obtainedby arithmetic averaging of the HOGfor each section.

Two-lm and Higbie penetration theories have beenapplied with success to complex forms of processes such aspacked towers and even bubble-cup or sieve tray columns(e.g.,AIChE11,ChanandFair12,PradoandFair13, Zuiderweg14,Billet and Schultes5, Wagner et al.7, Rocha et al.6and Bravoet al.

1).The overall height of a transfer unit can be calculatedby

HOG = HG + lHL (5)

whereHG = UG/kGae (6)

HL = UL/kLae (7)

Billet and Schultes5proposed the following relationshipsfor calculating mass transfer coefcients, kGand kL:

kG =

4DGptG

s(8)

kL = 4DLptL

s (9)where

tG = (ehL)l/UG (10)

tL = hLl/UL (11)

Structure packings have a corrugated nature. The cross-section of the ow channel is considered to be diamondshape with a side length of l. The liquid which ows downthe side length of the corrugated sheet channels mixes andredistributes itself. It is generally assumed that the exposuretime is the residence time for liquid between corrugated

channels. Therefore, the characteristic length of packings, l,can be described by the hydraulic diameter deqor the sidedimension of corrugation S for structured packings (Billetand Schultes5, Rocha et al.8).

Based on the classical falling lm equation and theexpression for packing wetting area proposed by Shi andMersmann4, Rocha etal.8developedthe following expressionto calculate liquid holdup for structured packings:

hL = 4Ft

S

2/33mLUL

L(sin u)geff(12)

where

Ft =29.12(WeLFrL)

0.15S 0.359

Re0.2L 0.6(1

0.93 cosc)(sin u)0.3

(13)

geff = g 1

G

L K1

Dp

Dz

1

Lg(14)

K1 =(L

G)g

(DpDz)flood(15)

To the best of our knowledge, this is the best modelavailable for predicting liquid holdup in structured pack-ings. It can be applied in a wide range of vapour/liquid ratesup to ooding points. Because the model is based on thefundamental expression for packing wetting area developed

by Shi and Mersmann4

, the effect of liquid physicalproperties on liquid holdup was also considered in themodelling. This model has been validated by the measuredliquid holdup in Glitsch structured packings similar to thoseused in this study (Rocha et al.8) Billet and Schultes5 andBillet9developed several expressions for calculating liquidholdup, but they can only be used below the loading pointand the effect of vapour rates on liquid holdup (whichshould be signicant) was not considered.

Although several equations have been proposed forcalculating effective interfacial area (Onda et al.10, Shiand Mersmann4, Billet and Schultes5), none of those modelsconsidered the effect of vapour ow and thus can only beused with low vapour rates. However, since industrialcolumns often operate above the loading point, it is necessaryto develop a new correlation for effective interfacial areawhich is valid for a wide range of vapour rates.

The model for effective interfacial area proposed by Billetand Schultes5is very similar to Shi and Mersmann4, but theformer have been validated with experimental data. Thisnew correlation is based on Billet and Schultes5work.

From Billet and Schultes5,

ae

ap= 1.5(ap dh)

0.5 ULdh

nL

0.2

U2L Ldh

sL

0.75U2L

gdh

0.45

= 1.5(ap dh)0.5

Re0.2

L We0.75

L Fr0.45

L (16)

For surface tension negative systems,

ae

ap=

ae

ap Eq.(16)1

2.4 104jMaLj

0.5)

(17)

For surface tension positive and neutral systems,

ae/ap = (ae/ap)Eq.(16) (18)

The effective interfacial area may be affected by thevapour ow due to: (a) improvement of packing wetting byincreasing liquid holdup; (b) instabilities in liquid ow

resulting in higher interfacial area. These effects areespecially signicant at high vapour rates. To apply theabove model for the prediction of effective interfacial areawithin a wide range of operating conditions, the inuence ofvapour ow on ae should be introduced. This can beachieved by adding another term of vapor Reynolds numberinto equation (16). Equation (17) indicates that for surfacetension negative systems, the Marangoni effect will cause areduction in effective interfacial area. Equation (18) showsthat effective interfacial area is the same for positive andneutral systems. However, it is considered that the surfacetension positive systems should have a higher interfacial

area than the neutral and negative systems because theliquid lm is more stable. In addition, it was found thatusing the relative stability index SR, as dened below,results in better correlation with the experimental data. Thisindicates that the interfacial area may more dependent onthe relative surface tension gradient than on absolute values.

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Based on the above discussions, a new equation for effectiveinterfacial area is proposed:

ae/ap = C1(apdh)0.5

Re0.2

L WeC2

L Fr0.45

L ReC3G (1 6 S

C4R )

(19)

where

SR relative stabilizing index =

ds

sdx(x

x )

6

for surface tension positive and negative

system, respectively

The constants C1, C2, C3and C4can be obtained by best tof the measured HOGvalues using equations (4) to (19).

Choice of Test Systems

Three systems (methanol/water, methanol/isopropanoland water/acetic acid) were chosen for the distillation tests.These systems include organic and aqueous systems,surface tension positive (methanol/water), neutral (metha-nol/isopropanol) and negative (water/acetic acid) systems.

They cover a broad range of physical properties as listed inTable 1.

EXPERIMENTAL STUDIES

Three structured packings (Gempak 2.5 A, AW7 andAW12) were tested in a 300 mm diameter distillationcolumn with the methanol/isopropanol system. PackingAW12 was also tested with the methanol/water and thewater/acetic acid systems. All the packings were installed toa height of 2.15 m with 908 rotation between packingelements. A cross type liquid sample collector was installedunder the packed bed with a space of 50 mm between thecollector and the packing support. The test ow diagram is

shown in Figure 1. The geometrical dimensions of the testpackings are listed in Table 2.

The tests were conducted under total reux conditions atpressures of 710 mm Hg and 260 mm Hg. The column wascontrolled by an Opto-22 sub I/O system interfaced with apersonal computer. The temperatures and ow rates weremeasured by thermocouples and orices respectively, andlogged through the Opto-22 system. The packing pressuredrops were measured with a U-type manometer with wateras an indicator liquid. Precautions were taken to preventsystem vapour condensation in the collecting lines from thecolumn to the manometer. For each run, temperatures

(cooling water, steam, column top vapour and bottomliquid, reux), ow rates (cooling water, steam, reux) andpacking pressure drop were recorded. The steady state (asindicated by the steady uid rates and temperature prole)for column operation could usually be reached in one hour.Then liquid samples were taken from the condenser bottomand the bottom of the packed bed. For the methanol/isopropanol system, the samples were analysed with a gaschromatograph (HP5890 Series II). The samples for thewater/acetic acid system were analysed by gas chromato-graphy as well as by the titration method. For the methanol/water system, all the top samples were analysed with a

Mitsubishi Moisture Meter (CA-02) because of the lowwater content in methanol. Bottom samples and some topsamples for the methanol/water system were analysed usinga gas chromatograph (HP5890 Series II).

From the measured liquid compositions of the top andbottom of the packed bed, the overall height of a transferunit can be calculated using the following equations:

93PREDICTING MASS TRANSFER IN PACKED COLUMNS


Table 1. Physical properties of the test systems.

L G mL 103

mG105

s103 DL109

DG105

(kgm3) (kg m3) (kg m1s1) (kg m1s1) (N m1) (m2s1) (m2s1)

730975 0.221.95 0.280.84 0.861.20 17.064.0 1.134.59 0.865.28

Figure 1. Schematic diagram of the experimental set-up.

Table 2. Geometric data of Glitsch Gempak structured packings.

Packing 2.5 A AW7 AW12

Crimp height, h, mm 10.4 7.0 11.7Channel base, B, mm 31.0 26.4 37.5Side of corrugation, S, mm 18.7 14.9 22.1Void fraction, e 0.983 0.978 0.985Surface area, ap, m

2m3 250 345 227Channel angle, u, deg. 45 45 45


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From mass balance for an element in a packed column,

Gdy

dz= Kyae(y

y) (20)

At total reux conditions,

G = L and y = x (21)

From vapour-liquid equilibrium,

y = f(x) (22)

Substituting equations (21) and (22) into equation (20)and assuming G/ky ae is constant, integration of equation(20) gives,

HOG =Z

xT

xB

dx

f(x)

x

=

Z

NOG(23)

NOG can be found by numerical integration withmeasured liquid compositions at the top and bottom of thepacked bed. The measured overall height of a mass transferunit can then be calculated by equation (23).

RESULTS AND DISCUSSION

Estimation of model parameters

The model parameters C1, C2, C3and C4 in equation (19)were found by the best t method comparingcalculated valuesofHOGagainst measured values. A total of 62 data points fromthe three packings, three test systems and two operatingpressures were used in the parameter estimation. Thephysical properties covered in the experiment and modelingare listed in Table 1. The parameters were found to be

C1 = 0.00842 C2 = 0.614

C3 = 0.647 C4 = 0.358 (24)

The deviations between predictedHOGand the measured arewithin 20% for 90% of the data points. The averagedeviation is

E=1

N

XNi=1

jHOG,cal. HOG,meas.j

HOG,meas.= 10.2% (25)

Weber number reects the effect of surface tension oninterfacial area. The value ofC2is smaller than 0.75 of theoriginal value in equation (19). This is due to the introduction

of the relative stability index which also includes the surfacetension effect. The large positive value ofC3 indicates thateffective interfacial area increased signicantly with theincrease in vapour rate. The positive value ofC4shows thatsurface tension positive systems have a larger effective areathan that of negative systems under otherwise similaroperating conditions and physical properties.

Liquid holdup

Figure 2 shows the predicted liquid holdup in packingAW12 with dimensionless concentration for the three testsystems at the pressure of 710 mm Hg. The predicted liquid

holdup was calculated using equations (12) to (15). Thedimensionless concentration is dened as:

X=x

xB

xT xB

(26)

at column top, X= 1; at column bottom, X= 0.

The predicted liquid holdup increases from column top tobottom for the methanol/isopropanol system while themethanol/water system shows the opposite affect. Liquidholdup increases slightly from column top to bottom for thewater/acetic acid system. Computer simulation indicatesthat for the methanol/isopropanol system, the columnbottom has higher liquid rates and higher vapour F-factors.The above simulation trends were veried by experimentalobservation of ooding tests. When the column oodingpoint was reached, it was noticed that pressure drop acrossthe packed bed gradually increased with time. This indicatesthat liquid holdup is building up from the column bottom.Without changing any operating parameters, it took about40 minutes to observe liquid ooding at the top of thepacked bed. At this time, a very high pressure drop wasmeasured across the packed bed. These observations indicatethat column ooding started from the column bottom due tothe higher liquid rate and higher vapour F-factor. Since liquidholdup increases with increasing liquid and vapour rates, itcan be expected that the column bottom will have a higherliquid loading as the model predicts. On the other hand,simulations indicated that the column top has a higher liquid

rate and higher vapour F-factor for methanol/water systembecause water, which has a higher boiling point thanmethanol, has a much higher enthalpy than methanol. Theexperiments also showed that when the ooding point wasreached, the pressure drop across the packed bed was stillquite low as compared with methanol/isopropanol systemand did not change with time. The ooding phenomena wereobserved by the crowds of large liquid drops suspended onthe top of the packed bed. As explained above, the higherliquid rates and higher vapour F-factor at the top of thepacked bed resulted in a higher liquid holdup for themethanol/water system. In addition, lower liquid surface

tension at the column top improved packing wetting andthus it also contributes to a higher liquid holdup at thatlocation. As shown in Figure 2, the model predicts thatliquid holdup at the column top is much higher than that atthe bottom. For the water/acetic acid system, liquid rate isslightly higher and surface tension slightly lower at the

94 XU et al.


Figure 2. Predicted liquid holdup as function of dimensionless con-centration.


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column bottom. Therefore, liquid holdup increases slowlyfrom column top to bottom as the model predicts.

It is expected that effective area will increase but liquidmass transfer coefcients may decrease with the increase inliquid holdup. Bravo et al.1 found that liquid-phaseresistance for gauze structured packings was very small.Because the structure of sheet-metal structured packings issimilar to that of gauze structured packings, it is expected

that in most cases, mass transfer for the sheet-metalstructured packings is also not liquid-phase controlled.Hence, the high liquid holdup should favour the masstransfer process.

Effective Interfacial Area

Figure 3 shows that the predicted effective interfacialarea increases with the increase in vapour F-factor. Undertotal reux conditions, the liquid rate increases proportion-ally with the vapour rate. Higher liquid rates improvepacking wetting and increase effective interfacial area. On

the other hand, higher vapour rate increases the instabilityin liquid ow and results in a higher effective interfacialarea.

As expected, the predicted effective interfacial area forthe methanol/isopropanol system is much higher than thatfor the water/acetic acid system due to its lower surfacetension and higher liquid holdup.

Figure 4 shows the ratio of the predicted effectiveinterfacial area to packing surface area along the packedbed. For the operating conditions listed in the gure, thepredicted effective interfacial area for the water/acetic acidsystem is always lower than the packing surface area. This ismainly due to high liquid surface tension, low liquid holdupand negative surface tension gradient. For the methanol/isopropanol system, the ratio ofae/apis between 0.9 to 1.5.If the liquid and vapour rates are reduced, the ratio ofae/apcan be less than unity. The predicted effective interfacialarea for the methanol/water system drops sharply fromcolumn top to bottom. At the column top, the ratio ofae/apisclose to 1.9 but the value is only about 0.4 at the column

bottom. This is due to the fact that surface tension increasesand liquid holdup decreases from top to bottom.

Comparison of Predicted and Measured HOG

Figures 5 to 9 show the measured HOG and thosepredicted by the model for the three packings, three testsystems at 710 mm Hg pressure. From the gures, it can beseen that the measured values ofHOGcan be well predictedby the model developed in this study. In most cases, HOGdecreases with the increase in vapour F-factors due to theincrease in interfacial area and vapour mass transfercoefcient. From equation (19), it can be seen that theeffective interfacial area increases with the increase inliquid and/or vapour rate. Therefore, it may increase moresignicantly with the increase in both liquid and vapourrates under total reux conditions.



Figure 3. Effect of vapour rate o n p redicted effective interfacial area.

Figure 4. Ratio of predicted effective interfacial area to packing surfacearea as a function of column position.

Figure 5. Measured and predicted HOGfor packing 2.5A with methanol/isopropanol system under 710mm Hg.


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Figure 10 shows the comparison of the measured valuesof HOG and those predicted for the 62 data points. Theoverall height of a transfer unit changes from as low as0.20 m to as high as 0.50 m dependingon the test system andconcentration, packing type and operating pressure. Themodel can predict HOGwithin a deviation of620%.

Effect of Concentration on Predicted HOG

In a distillation column, physical properties and thus HOGvalues vary with concentration at various column location.Most of the previous publications used the averagecompositions to calculate HOG. This method is simple, butcannot reect the changes ofHOGalong the column. In thisstudy, the column was divided into 50 sections of con-centration. The physical properties, vapour/liquid loadings,

and nally HOG were calculated for each section, based onthe concentration prole. This method gives readers someinsight into the changes in vapour/liquid loadings, physicalproperties, and HOG along the column. Designers maychoose adequate packing height for each section based onthis information.

Figure 11 shows the prediction of HOG at differentlocations along the packed bed for the three test systems. Itcan be seen that HOGchanges signicantly from column top

to bottom for the the methanol/water system but not for themethanol/isopropanol and acetic acid/water systems. Forthe methanol/water system, the concentration of methanolchanges dramatically from column top to bottom due to itshigh relative volatility. Vapour and liquid rates also changegreatly because of the large difference in enthalpies betweenmethanol and water. The high liquid and vapour rates and

96 XU et al.


Figure 6. Measured and predicted HOG

for packing AW7 with methanol/isopropanol system under 710mm Hg.

Figure 7. Measured and predicted HOGfor packing AW12 for Methanol/Isopropanol system under 710mm Hg.

Figure 8. Measured and predicted HOG

for Packing AW12 with water/acetic acid system under 710mm Hg.

Figure 9. Measured and predicted HOGfor packing AW12 with methanol/water system under 710 mm Hg.


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low liquid surface tension at the column top results in a largeeffective interfacial area and low values of HOG. Theopposite is true at the column bottom. Therefore, HOGincreases sharply from column top to bottom. Simulationresults are suggesting that for such a system, concentrationeffect on packing separation efciency be considered anddifferent types of packings be used for column top andbottom.

Figure 12 shows the relative mass transfer resistance from

the vapour phase. It can be seen that in most parts of thecolumn, mass transfer is vapour-phase controlled. At thecolumn bottom, liquid phase resistance is greater than at anyother locations in the column for all the three test systemsbecause of the larger slope of the vapour-liquid equilibriumline. Considering the steep vapour-liquid equilibrium line atcolumn bottom for the methanol/water system, the liquid

phase resistance there is not as high as expected. The reasonfor this is the lower liquid rate at column bottom versuscolumn top. Although the vapour-liquid equilibrium line forthe methanol/isopropanol system is not as steep as themethanol/water system at column bottom, the liquid phaseresistance for the methanol/isopropanol system is muchhigher due to its much higher liquid ow rate.

Comparison with Existing Models

There are four existing models for predicting structurepacking efciency (Fair and Bravo2, Billet and Schultes5,the Rocha et al.6, Bravo et al.1), in which only Rochaet al.6 model was intended for metal sheet packing (theothers were for gauze packing). The Rocha et al.6modelwas tested with their data bank consisting of six hydro-carbon systems. Since surface tension is similar for allhydrocarbons, the effects of surface tension and its gradientwere not incorporated into the model.

Figure 13 shows the comparison of our measured HOGvalues with those predicted by the Rocha et al.6model forthe methanol/isopropanol, methanol/water and acetic acid/

water systems. It can be seen that the proposed model in thepresent study is in reasonable agreement with the measured

HOGvalues. Rocha et al.6on the other hand, predict higher

HOGvalues than those measured, particularly for aqueoussystems. Obviously, surface tension is an important factorin the determination of packing wetability which in turnaffects the effective interfacial area. The authors considerthat the present model can predict the efciency for a widerange of physical properties. It is an improvement over theRocha et al.6model.

CONCLUSIONS

A fundamental model has been developed for predictingmass transfer efciency for packed columns containingstructured packings. The model consists of equations formass transfer coefcient, liquid holdup and effectiveinterfacial area. The model is validated by distillation tests



Figure 10. Comparison of measured and predicted HOGfor Gempak 2.5A,

AW7 and AW12 with methanol/water, methanol/isopropanol and aceticacid/water systems under 260 mm Hg and 710mm Hg.

Figure 11. Variation of predicted HOGas a function of packing height.

Figure12. Predicted mass transfer resistance from vapour and liquidp hases

as a function of packing height.


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in a 300 mm diameter column with three structuredpackings, three test systems and two operating pressures.The average deviation of model prediction for the 62measured data points is 10.2%.

NOMENCLATURE

ae effective interfacial area, m2m3

ap packing surface area, m2m3

B packing channel base, m mD molecular diffusivity, m

2s1

Ci model parametersdh hydraulic dimension (S for structured packings), mE average relative errorF-factor (UG

G

p), m s1(kgm3)0.5

FrL Froude number for liquidFt correction factor for total liquid holdupG vapor ow rate, mol m2s1

g gravitational constant, m s2

geff effective gravity, m s2

H height of a phase transfer unit, mh packing crimp height, m mHAc acet ic acid

HETP height equivalent to a theoretical plate, m

hL liquid holdup in packed bed, m3

m3

HOG overall height of a transfer unit, mIPA isop ro pan olk phase mass transfer coefcient, m s1

Ky overall vapuor mass transfer coefcient, mol m2s1

L liquid ow rate, mol m2s1

l packing characteristic length, mLV liquid ow density, m

3m2h1

m slope of equilibrium line

Ma Marangoni number,ds

dx

Dx

DLmL apMeOH methanol

N number of transfer unitsDp pressure drop across packed bed, Pa

Re Reynolds number,

dhU

n

S side dimension of corrugation, mSR relative stability index

U supercial velocity, m s1

WeL Weber number for liquid,U2LL dh

s

x mole fraction of more volatile component in liquid phasey mole fraction of more volatile component in vapour phasey equilibrium mole fraction of vapour with liquidz location of packed bed, mZ total height of packed bed, mX dimensionless concentration as d ened in equation (26 )

Greek letters

b constant dened in equations (2) and (3)l ratio of slope of vapour-liquid equilibrium line to operating linet phase contact time, se void fraction of packing, m3m3

density, kg m3

s surface tension, N m1

m viscosity, kg m1s1

n kinematic viscosity, m2s1

c contact angle between solid and liquid, degu angle with h orizontal for corrugation channel, deg

Subscripts

B column bottomcal. calculatedG vapour phase

L liquid phasemeas. measuredO overallT column top

REFERENCES

1. Bravo, J. L., Rocha, J. A. and Fair, J.R., 1985, HydrocarbonProcessing, 64(1): 91 95.

2. Fair, J. R.,and Bravo, J. L., 1990, Chem Eng Prog, 86(1): 1929.3. Henriques de Brito, M., von Stockar, U., Menendez, B. A., Bomio, P.

and Laso, M., 1994, Ind Eng Chem Res, 33: 647656.4. Shi. M. G. and Mersmann, A., 1985, Ger Chem Eng, 8: 8796.

5. Billet, R. and Schultes, M., 1993, Chem Eng Technol, 16: 19.6. Rocha, J. A., Bravo, J. L. and Fair, J. R., 1996, Ind Eng Chem Res, 35:

16601667.7. Wagner, I., Stichlmair, J. and Fair, J. R., 1997, Ind Eng Chem Res, 36:

227237.8. Rocha, J. A., Bravo, J. L. and Fair, J. R., 1993, Ind Eng Chem Res, 32:

641651.9. Billet, R., 1995, Packed T owers in Processing and Environmental

Technology (VCH Publishers, Inc, New York).10. Onda, K., Takeuchi, H. and Okumoto, Y., 1986, J Chem Eng Japan, 1:

5666.11. American Institute of Chemical Engineers, 1958, Bubble Tray Design

Manual, (AIChE, New York)12. Chan, H. and Fair, J. R., 1984, Ind Eng Chem Proc Des Dev, 23: 814

819.

13. Prado, M., and Fair, J. R., 1990, Ind Eng Chem Res, 29: 10311042.14. Zuiderweg, F. J., 1982, Chem Eng Sci, 37: 14411464.

ACKNOWLEDGEMENT

The authors wish to thank the Natural Sciences and EngineeringResearch Council of Canada for their nancial support.

ADDRESS

Correspondence concerning this paper should be addressed to ProfessorK.T. Chuang, Department of Chemical Engineering, 536 ChemicalMaterials Engineering Building, University of Alberta, Edmonton,Canada, T6G 2G6.

The manuscript was received 18 December 1998 and accepted for

publication after revision 1 June 1999

98 XU et al.

Trans IChemE Vol 78 Part A January 2000

Figure 13. Comparison of measured HOG

with those predicted values byRocha et al.6

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Coeficientes Agua Aire Hl