Chemical Engineering Science 76 (2012) 90–98

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

The effect of tray geometry on the sieve tray efficiency

Rahbar Rahimi n, Maryam Mazarei Sotoodeh, Elahe Bahramifar

Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, P.O. Box 98164-161, Iran

a r t i c l e i n f o

Article history:

Received 22 June 2011

Received in revised form

31 December 2011

Accepted 6 January 2012Available online 4 February 2012

Keywords:

Distillation

Hydrodynamics

Multiphase flow

Mass transfer

Efficiency

CFD

09/$ - see front matter & 2012 Published by

016/j.ces.2012.01.006

esponding author. Tel.: þ98 915 141 9052.

ail address: rahimi@hamoon.us.ac.ir (R. Rahim

a b s t r a c t

In this research a 3-D two phase CFD model in Eulerian–Eulerian framework was developed to study

sieve trays efficiency, hydraulics and mass transfer. To estimate the efficiency of the sieve trays, two

trays with similar geometry but unequal hole diameters were used while the effects of the holes and

bubbles diameters were observed. The results were compared with the available experimental data for

distillation of methanol and n-propanol mixture. Mass transfer coefficients were estimated by the

Higbie and surface renewal stretch (SRS) mass transfer models. It has been found that the liquid flow

pattern on the tray which had smaller hole diameter is closer to the plug flow pattern and tends to have

a larger mass transfer rate. In addition, while comparing the SRS model theory with the Higbie model,

it has been found that using the SRS model reduces the sensitivity of the simulation results to the

bubble diameters.

& 2012 Published by Elsevier Ltd.

1. Introduction

Sieve trays are commonly used in the distillation and absorp-tion towers. Prediction of tray efficiency is important because ofits role in reducing the number of mass transfer stages and energyrequirements.

The aim of the present work was to obtain a CFD model topredict the tray hydraulics and mass transfer, and also to studyeffects of the hole diameter on tray efficiency by providingcomparisons between the trays which have different holes dia-meters. An insight into the usage of SRS theory in prediction ofmass transfer efficiency of the sieve tray has been provided.

This paper is divided into following sections. Section 2 brieflyintroduces the previous works which have been done in multi-phase CFD models. In Section 3 research methods are described.Section 4 summarizes Flow Geometries and Boundary Conditionsused in this research. Section 5 describes the results and finally inSection 6 the research is concluded.

2. Previous works

In the early investigations, most attentions were on under-standing of the hydrodynamics of sieve trays (Mehta et al., 1988;Liu et al., 2000; Krishna et al., 1999; Van Baten et al., 2000; Gesitet al., 2003; Li et al., 2009; Zarei et al. 2009).

Elsevier Ltd.

i).

Lopez and Castells (1999) investigated the effects of traygeometry experimentally. They focused on the holes diametersand influence of liquid composition on tray efficiency. Theyreported that a quadruplicate increase in the holes diametersreduced tray efficiency by 25%. That was due to dependency ofbubble diameter, froth characteristics, froth height and subse-quently interfacial area on the tray holes diameters. But, bubblesdiameter depends on physical properties and flow rates of thepresent liquid and gas phases. Therefore, in CFD simulations, itwas desirable to employ relations for drag, heat and mass transfercoefficients that were independent of bubbles diameter.

Van Baten et al. (2000) presented a relation for drag coefficientwhich was independent of bubble diameter. Their model was usedextensively by many researchers and was proved to be valuable.

The applications of CFD in the estimation of tray efficiencywere considered by Wang et al. (2004). They represented a threedimensional CFD model to describe the liquid phase flow andconcentration distribution on the trays of the distillation columns.Rahimi et al. (2006a) studied the hydrodynamics of sieve trays bymeans of a three dimensional two fluid CFD simulation. The liquidvelocity, concentration and temperature distribution were deter-mined. Thereafter, to predict the hydrodynamics, heat and masstransfer of sieve trays, a 3-D two fluid CFD model in the Eulerian–Eulerian framework was developed by them (Rahimi et al., 2006b).

Jajuee et al. (2006) presented SRS1 theory to predict the liquidmass transfer coefficient that was independent of bubblediameter, thus these relations may be useful for CFD simulation.

1 Surface-renewal-stretch.

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–98 91

The SRS mass transfer model has not been tested in CFD simula-tion of distillation by the author’s knowledge.

In addition to previous works, Tray efficiency has beeninvestigated using computational fluid dynamics (CFD) techni-ques (Taylor, 2007). Sun et al. (2007) presented a computationalmass transfer model which was a combination of a basic differ-ential mass transfer equation and an appropriate accompanyingCFD formulation. Noriler et al. (2008) developed a CFD model inEulerian–Eulerian framework to predict momentum and heattransfer for multiphase flow. Consequently, they presented atwo-phase, three-dimensional and transient model with chemicalspecies, energy and momentum conservation balances. They usedsubroutines in FORTRAN language for the closure equations of themodel (Noriler, 2010). Also, they obtained experimental data ofclear liquid height in a distillation sieve tray column with waterand air (Noriler, 2010). However, lack of an appropriate masstransfer model for the calculation of mass transfer rates in CFDsimulation models was emphasized.

3. Research methods

3.1. Simulation

Eulerian simulations were adopted for rectangular sieve trays.A three-dimensional steady state model was developed todescribe the two phase flow and mass transfer on the tray withan outlet down comer. The hydraulic parameters such as the clearliquid height and froth height changes little over time and theyhave periodic manner ‘‘quasi-steady state’’. Even though, theseparameters have an effect on the gas–liquid contact time andmass transfer rates between two phases. Because these changesare negligible, the steady state assumption is acceptable. Also,Wang et al. (2004) and Rahimi et al. (2006) simulated masstransfer on sieve trays using this assumption for the sake ofsimplicity and reducing computational efforts.

The dispersed gas and the continuous liquid were modeled astwo interpenetrating phases having separate transport equations.The continuity, momentum and mass transfer equations werenumerically solved for each phase. Consequently, interphasetransfer quantities, momentum and mass transfer models wereused to develop the model. The solutions that used in CFDsimulations are consist of two alcohols, Methanol and n-Propanol.So, their solutions were ideal and the heats of mixing werenegligible (the changes in liquid and gas temperatures are alittle). Therefore, one can neglect the use of energy balanceequations. Hence, assumption of constant physical propertieswas used.

3.2. Governing equations

According to assumptions, governing equations are as follows:

3.2.1. Continuity equations

For gas phase:

r:ðrGrGVGÞþSLG ¼ 0 ð1Þ

For liquid phase:

r:ðrLrLVLÞ�SLG ¼ 0 ð2Þ

SLG is the rate of mass transfer from liquid phase to gas phaseand vice versa. Mass transfer between phases must satisfy thelocal balance condition, so SLG¼�SGL.

3.2.2. Momentum conservation

For gas phase:

r:ðrGðrGVGVGÞÞ ¼ �rGrPGþr:ðrGmef f ,GðrVGþðrVGÞTÞÞ�MGL ð3Þ

For liquid phase:

r:ðrLðrLVLVLÞÞ ¼�rLrPLþr:ðrLmef f ,LðrVLþðrVLÞTÞÞþMGL ð4Þ

MGL describes the interfacial forces acting on each phase due tothe presence of the other phase.

3.2.3. Volume conservation equation

This is simply the constraint that the volume fractions sum tounity:

rGþrL ¼ 1 ð5Þ

3.2.4. Pressure constraint

Two phases share the same pressure field:

PG ¼ PL ¼ P ð6Þ

3.2.5. Mass transfer equations

Transport equations for the mass fraction of light component Acan be written as:

For gas phase:

r:½rGðrGVGYA�rGDAGðrYAÞÞ��SLG ¼ 0 ð7Þ

For liquid phase:

r:½rLðrLVLXA�rLDALðrXAÞÞ�þSLG ¼ 0 ð8Þ

3.3. Closure models

3.3.1. Inter phase momentum models

The turbulence viscosities were related to the mean flowvariables using the standard k-e model. The equation to calculatethe inter phase momentum transfer MGL is as below:

MGL ¼3

4

CD

dGrGrL VG�VLj jðVG�VLÞ ð9Þ

The effect of drag force was considered using the dragcoefficient given by Van Baten et al. (2000).

CD ¼4

3

rL�rG

rL

gdG1

V2slip

ð10Þ

where the slip velocity, Vslip ¼ VG�VLj j is estimated from the gassuperficial velocity VS and the average gas hold up fraction in thefroth region:

Vslip ¼VS

rGð11Þ

For the average gas holdup fraction, Bennett et al. correlationwas used.

rG ¼ 1�exp �12:55 VS

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirG

rL�rG

r� �0:91" #

ð12Þ

By substituting Eqs. 10–12 in Eq. (9), the inter phase momen-tum transfer equation became:

MGL ¼ðraverage

G Þ2

ð1�raverageG ÞV2

S

gðrL�rGÞrGrL VG�VLj jðVG�VLÞ ð13Þ

This relation is suitable to use in CFD simulations because it isindependent from bubble diameter.

Fig. 1. Geometry of simulated rectangular sieve trays; (a) Geometry 1 and (b)

Geometry 2.

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–9892

3.3.2. Mass transfer models

The rate of local mass transfer SLG was expressed by Eq. (6)(Rahimi et al., 2006b):

SLG ¼ KOGaeMAðyA�yn

AÞ ¼ KOLaeMAðxn

A�xAÞ ð14Þ

The overall gas and liquid mass transfer coefficients, wereKOG ¼ 1=ð1=kGþm=kLÞ, and KOL ¼ 1=ð1=mkGþ1=kLÞ. yn

A ¼mxAþb

(Vapor composition), ynA, in equilibrium with the liquid composi-

tion, xA.The Higbie and the SRS mass transfer theories were used to

estimate the liquid mass transfer coefficient kL, and the Higbietheory was used to estimate the gas mass transfer coefficient kG.Eq. (15) calculates the average mass transfer coefficient fromHigbie penetration theory that has been widely used in simulat-ing the gas and liquid mass transfer in the distillation columns(Rahimi et al., 2006b). This theory assumes that the compositionof the film does not stay stagnant.

kL,av ¼ 2

ffiffiffiffiffiffiffiffiDAL

py

rð15Þ

The exposure time, y, were obtained from the hydrodynamicproperties of the system by the equation below: (Rahimi et al.,2006b)

y¼dG

VRð16Þ

where the average bubble rise velocity, VR, through the froth wasgiven by:

VR ¼VPðAP=ABÞ

ð1�rL_Þ

ð17Þ

AP/AB is the perforated area to the bubbling area ratio.The exposure time for the estimation of gas side mass transfer

coefficient from the Higbie theory were taken to be bubblediameter, dG, divided by the vapor velocity through the trayperforations, Vp (Rahimi et al., 2006b).

The SRS model is based on the equation of continuity, whichincludes both turbulent and convective mass transfer at the gas–liquid interface. In other words, it is the extension of thepenetration theory of mass transfer to fluid–fluid interactionsystems (Jajuee et al., 2006). The average mass transfer coefficientfrom SRS model for the case in which, gas was considered as adispersed phase is given by Eq. (18).

KL,av ¼ 2

ffiffiffiffiffiffiffiffiffiffiDALs

p

rð18Þ

where s is defined by Eq. (19)

s�ul

ð19Þ

In this case, the length l, and velocity scales of eddies, v,for isotropic turbulence can be written as:

l¼k3

_e

� �1=4

ð20Þ

u¼ k_eð Þ1=4ð21Þ

where, k¼ m=rL is kinematic viscosity and _e is viscous dissipationof energy per unit mass of eddies.

Substitution of Eqs. (20) and (21) for n and l in Eq. (18) yields:

s¼

ffiffiffiffi_ek

rð22Þ

Energy dissipation rate was calculated as follows:

_e ¼ Usg�eg

1�egUsl

� �:g ð23Þ

In systems with low superficial liquid velocity ðUsl � 0Þ theenergy dissipation rate can be approximated by:

_e ¼Usgg ð24Þ

Combination of Eqs. (18) and (22) provides an expression for s,and hence the time-average overall mass transfer coefficientbecomes (Jajuee et al., 2006):

KL,av ¼ 2DAL

p

ffiffiffiffiffiffiffiffiffiffiUsgg

k

r !1=2

ð25Þ

It is interesting to note that Eq. (25) does not show bubblediameter dependency explicitly.

4. Flow geometries and boundary conditions

In the simulations, methanol and n-propanol liquid mixturewith the average methanol concentration of Xm, were used.Experimental data were at total reflux and at atmosphericpressure. The entering gas and the leaving liquid concentrations,ynþ1 and xn,at total reflux are equal. Schematics of rectangularsieve trays are illustrated in Fig. 1a and b. The Characteristics ofthe two simulated trays are given in Table 1. (Dribika andBiddulph, 1986). Table 2 shows the physical properties formethanol and n-propanol. In this table, m is the equilibrium

Table 1Rectangular sieve trays specifications.

Characteristic Geometry1

Geometry 2, (Dribika and Biddulph,

1986)

Weir length (mm) 83 83

Liquid flow path (mm) 991 991

Tray spacing (mm) 154 154

Hole diameter (mm) 7.5 1.8

Hole number 132 2465

Percentage of free area

(%)

8 8

Weir height (mm) 25 25

Table 2Physical properties for methanol and n-propanol system.

Xm m rG rL DG DL

0.279 1.204 1.844 748 1.04�10�5 1.46�10�9

0.342 0.940 1.798 750 1.02�10�5 1.10�10�9

0.410 0.735 1.728 752 1.02�10�5 8.08�10�10

0.555 0.505 1.602 755 9.93�10�6 4.31�10�10

0.771 0.432 1.403 759 9.67�10�6 1.75�10�10

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–98 93

coefficient. Wilson’s equations were used for calculating the activitycoefficient (g). Non-ideal equilibrium coefficients were calculated bymultiplication of m with the activity coefficient. But, as it wasmentioned in Section 3.1, since the solutions are ideal the calculatedg was close to 1. Therefore, there was no significant differencebetween ideal and non-ideal equilibrium coefficients. The m valuesthat were presented in the table, were calculated from the equili-brium distribution curve, x y, as m¼dy/dx. The differentiation can beperformed if y¼ ax=ð1þða�xÞÞ were accepted. Where a is volatilitycoefficient.

Inlet liquid and gas flow rates were known. Constant molefraction values for entering gas and liquid phases were used. Theleaving concentrations are estimated by the CFD model. The gasand liquid outlet specification were in agreement with thespecification of inlet where only one fluid was assumed to enter.Atmospheric pressure and uniform velocity were selected for gasand liquid outlet boundaries, respectively. A no-slip wall bound-ary condition was specified for the liquid phase while a free slipwall boundary condition was used for the gas phase.

Fig. 2. CFD simulation and experimental data for: (a) froth height at

F-factor¼0.4(m/s(kg/m3)0.5) and (b) clear liquid height at F-factor¼0.4 (m/s(kg/

m3)0.5).

5. Results and discussion

In Section 5.1, the effect of hole diameter and in Section 5.2,the effect of mass transfer coefficient relations have beenexplained. In sections that fallow the model validated with theacceptable experimental data of Dribika and Biddulph (1986) thatapplies for Geometry 2.

5.1. Effects of hole diameter

According to Table 1, the trays were differed in the number ofholes and their sizes. Geometry 2 (tray with smaller holediameter) was in accordance with the experimental tray ofDribika and Biddulph (1986), Geometry 1 is mostly similar toGeometry 2 but it has larger holes. In order to remain thepercentage of bubbling area in Geometry 1 equal to Geometry2, the number of holes is reduced. Penetration or Higbie theorywas used to calculate the mass transfer coefficient.

5.1.1. Effects of holes diameters on tray hydraulics

Simulations runs were carried out at F-factor equal to 0.4 (m/s(kg/m3)0.5) and the results were compared with the experimental

data in Fig. 2. Froth height, Fig. 2a, and clear liquid height, Fig. 2b,versus average methanol concentration, Xm, were used for valida-tion of the hydrodynamics of the model. Froth height and clearliquid height were considered to be the key hydraulic parameters.Comparisons have showed that the model using either of thegeometries overestimates the experimental results by lessthan 15%. This percentage of error was acceptable and showedthat the model was validated.

The liquid flow pattern on the tray was close to plug flowbecause of the rectangular shape of the tray geometry. Appreci-able back mixing and stagnant zones were not observable.Reducing or eliminating back flows and stagnant zones that arecommon in circular sieve trays were the key factors to reach plugflow. Therefore good mass transfer and prevention of decreasingin concentration gradients increased the tray efficiency. As theresult, larger sieve tray holes diameters led to having fewer holeswith larger pitches and consequently having larger bubbles atcertain perforated area. Larger bubbles with far apart providemore irregular liquid flow pattern than smaller bubbles withless apart.

Fig. 3 shows horizontal liquid velocity values versus dimen-sionless width of tray, z/W, at y¼4.8 mm and x/L¼0.333, forXm¼0.41. Geometry 2 had more uniform velocity distributionprofile and behaved closer to plug flow. The values of liquidmixture velocity were zero at the first and the end points of thecurves or at walls of the tray.

The liquid volume fraction contours at x–z plane, whichrepresented the mixing and bubbling in the dispersion height is

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–9894

shown in Fig. 4a and b for two different distances from the traydeck. These figures showed that at heights above the deck of thetray, the froth is uniform. But near the wall the liquid volumefraction was larger due to wall liquid retardation. However asmovements of liquid versus the deck towards the outlet weiroccurred, the mass transfer coefficients are large for plug flow

Fig. 3. Horizontal component of liquid velocity across the tray at y¼4.8 mm,

x/L¼0.333 and for Xm¼0.41.

Fig. 4. (a) Liquid volume fraction contours for the Geometry 1 on a horizontal plane at

plane at y¼5 mm.

situations. A reduction in stagnant zone and more uniformity ofdistribution of gas in liquid phase were observed.

5.1.2. Mass transfer

Fig. 5 was used for validation of mass transfer model. Experi-mental methanol composition profile and CFD simulation results ofmodel (Geometry 2) were compared. Comparison showed that theexperimental data and CFD simulation results differ by about 14%.Also, mass transfer rate for the Geometry 1 was shown to be lowand the results were far from experimental data. Plug flow alongliquid flow path on the tray resulted in less back flow mixing andhigher concentration gradient. The overall effects were to increasemass transfer rates for Geometry 2 to be higher than Geometry1.Liquid flow path for Geometry 1 is not plug flow.

When the liquid moves over the tray, propanol in the gasphase is absorbed by the liquid phase and methanol is desorbedinto the gas phase. With fluid movement along the tray, theconcentration of propanol in the liquid phase increases, so theflux of mass transfer between two phases decreases. Therefore,concentration of propanol in the gas phase increases, this meansthat the discharged gas concentration from the tray is notuniform. These results were illustrated in the Fig. 6a and b.Comparison between Fig. 6a and b shows that mass transfer rate

y¼5 mm. (b) Liquid volume fraction contours for the Geometry 2 on a horizontal

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–98 95

in Geometry 2 which has smaller holes was more than masstransfer rate in Geometry 1 with larger holes. So, n-propanolconcentration had more decrease in gas phase in Geometry 2.

5.1.3. Efficiency

The Murphree tray efficiency which was defined by comparinga real tray with an ideal tray is the most applied definition of the

Fig. 5. Methanol mole fraction profile on the tray at Xm¼0.41.

Fig. 6. (a) Vapor phase propanol mole fraction for the Geometry 1 on a vertical plane at

2 on a vertical plane at z/W¼0.5 and Xm¼0.279.

tray efficiency. The average Murphree tray efficiency may be 100%greater than the Murphree point efficiency whilst point efficiencyis always less than 1 by definition (Lockett, 1986).

In this work Murphree tray efficiency was calculated by thefollowing equation:

EMV ¼yn�yn�1

ynn�yn�1

ð26Þ

where:

yn

n ¼mxnþb ð27Þ

and

yn ¼mxn

nþb ð28Þ

To estimate point efficiency, the tray was divided into six cellsin the liquid flow direction. By integration on the y and z

directions, the average value of concentration was calculated foreach cell (Rahimi et al., 2006b). The efficiency of each cell wascalculated by the point efficiency equation

EOG ¼yn�yn�1

ynn�yn�1

� �point

ð29Þ

z/W¼0.5 and Xm¼0.279. (b) Vapor phase propanol mole fraction for the Geometry

Fig. 9. Liquid phase methanol mole fraction on the tray for Xm¼0.279.

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–9896

Equations of Murphree tray efficiency and point efficiency canbe found in several books and papers in details (Rahimi et al.,2006b; Lockett, 1986; Kister, 1992).

Point efficiencies of the two geometries were compared inFig. 7. It is shown that the point efficiency for Geometry 2 is largerthan the point efficiency for Geometry 1. Fig. 4 showed that liquidvolume fraction was high near the outlet weir. Therefore, thereexists the possibility of increasing contact times of liquid andvapor which has led to more significant point efficiency in thatarea. This was observable in Fig. 7 when x/L towards 1.

The increase of point efficiency in Geometry 1 is more than theincreasing of point efficiency in Geometry 2 as x/L tends toward 1.Mass transfer rate in Geometry 2 was higher than mass transferrate in Geometry 1 or rate of decrease of mass transfer drivingforce in Geometry 2 was more than that of Geometry 1. Therefore,increases in contact time at the liquid exit end of the tray had alesser affect in point efficiency for Geometry 2 than that forGeometry 1.

Efficiency of simulated trays and experimental data werecompared in Fig. 8. According to Fig. 8, it is shown that the modelhas 15% overestimation which is a reasonable validation of themodel for the Geometry 2.

Also, it is shown that by increase of the holes diameter, trayefficiency is decreased. It can be argued that an increase inbubbles diameter can lead to a decrease in the interfacial area.The gas mal-distribution in liquid phase caused a subsequentnon-uniformity of liquid flow pattern on the tray. This fact hasbeen observed in Lopez and Castells (1999) study as well.

5.2. Effects of mass transfer theory

In this part of simulations, two theories of mass transfercoefficients were compared. Geometry 2 was employed and the

Fig. 7. Point efficiency on the tray for Xm¼0.41.

Fig. 8. Variation of Murphree efficiency with respect to changes of average liquid

mole fraction, Xm.

effects of bubble diameters were studied with bubbles of 2, 5 and10 mm in diameters.

5.2.1. Mass transfer

Changes in the methanol mole fraction of liquid phase on thetray are shown in Fig. 9. The chart is drawn for bubbles which are5 mm in diameter. Fig. 9 shows that application of SRS theory forthe Geometry 2 has improved the simulation results more thanapplying the Higbie theory.

Fig. 10 illustrates contour of methanol in liquid phase at x–z

plane for SRS theory. This figure shows that concentration ofmethanol has decreased along the tray and has reached its lowestvalue at the outlet weir.

5.2.2. Efficiency

Fig. 11 illustrates variation of tray efficiency along the traylength. This figure includes the simulations results using Higbiepenetration and SRS mass transfer theories with three differentbubble diameters. For 2 mm bubble diameter, penetration theoryhas predicted larger point efficiency than SRS theory.

For 5 mm bubble diameter point efficiency predictions wereunfavorable and theoretical efficiency of SRS increased. Theseresults illustrated that using SRS theory the sensitivity of simula-tions to bubble diameter has decreased. This was due to inde-pendency of SRS theory to bubble diameter. By increasing thebubble diameter to more than 10 mm this theory cannot predictsuitable results.

Fig. 12 represents calculated efficiency for Geometry 2 using bothHigbie and SRS theories for three bubble diameters of 2, 5 and10 mm. According to Fig. 12, calculated efficiencies for 2 and 5 mmbubbles diameters are equal as was predicted by SRS theory. Higbietheory is sensitive to bubble diameter, therefore calculated efficiencyfor 2 and 5 mm bubble diameters were different, using this theory.

6. Conclusion

In this study, a 3D two phase flow model was developed topredict the sieve tray hydraulics, mass transfer and efficiency.The tray geometries were based on the large rectangular tray ofDribika and Biddulph (1986). Two trays with different holesdiameters were simulated. The effects of holes diameters on thetray hydraulic and on the mass transfer were investigated. In hasbeen concluded that the tray with smaller holes diameters wouldgive more uniform liquid phase mixture, lower back mixing andhigher efficiency.

The study has shown that SRS mass transfer theory could beused in CFD modeling in the cases with bubble diameters whichare less than 10 mm. The results were compared by results of

Fig. 10. Profile of liquid phase methanol mole fraction on horizontal plane at y¼25 mm and for Xm¼0.279.

Fig. 11. Point efficiency along the tray deck with different bubble diameters,

Xm¼0.555.

Fig. 12. Variation of Murphree efficiency calculated using Higbie and SRS mass

transfer theories with respect to changes of bubble diameters, dG, Xm¼0.555.

R. Rahimi et al. / Chemical Engineering Science 76 (2012) 90–98 97

Higbie theory. SRS theory was less sensitive to the size of bubblesin froth region because this theory is independent of bubblediameter. It has been obtained that using the SRS theory is moresuitable for CFD simulation than Higbie theory.

Nomenclature

AB tray bubbling area, m2

AP total area of holes, m2

ae effective interfacial area per unit volume, 1/m

CD drag coefficientdG mean bubble diameter, mDAL liquid molecular diffusivity, m2/sFS F-factor¼ VS

ffiffiffiffiffiffirg

p, m/s(kg/m3)0.5

g gravity acceleration, m/s2

kG gas phase mass transfer coefficient, m/skL liquid phase mass transfer coefficient, m/sKL,av time-average overall mass transfer coefficient, m/sKOG gas phase overall mass transfer coefficient, m/sKOL liquid phase overall mass transfer coefficient, m/sl length scale of eddies in viscous dissipation range, mm slope of equilibrium lineMA molecular weight of component A, g/molMGL interphase momentum transfer, kg/(m2s2)rG average gas holdup fraction in frothrL average liquid holdup fraction in froths fractional rate of surface renewal, 1/sSLG rate of inter phase mass transfer, kg/m3sUsg superficial gas velocity, m/sUs1 superficial liquid velocity, m/sv molar average velocity; velocity scale of eddies in

viscous dissipation range, m/sVG gas phase velocity vector, m/sVL liquid phase velocity vector, m/sVS gas phase superficial velocity based on the bubbling

area, m/sVP vapor velocity through the tray perforations, m/sVR bubble rise velocity, m/sVslip slip velocity, m/seg gas volume fraction_e energy dissipation rate per unit mass, W/kgy liquid contact time, sk kinematic viscosity, m2/sm liquid phase viscosity, kg/m srG gas density, kg/m3

rL liquid density, kg/m3

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