Concentration profiles in a packed distillation column

CONCENTRATION PROFILES IN A PACKED DISTILLATION COLUMN L STEINER, H P BARENDREGHT and S HARTLAND SWISSFederal Institute of Technology, Department of Industrial and Engmeermg Chemistry, (Recerved

15 September

1976, accepted

11 August

Zurich, Switzerland

1977)

Abstract-Concentratloon profiles m a pdot plant-sized packed chstdlatlon column were measured by samplmg both the hqmd and the vapour m ten posItIons along the column The results were compared with the profiles obtamed by computer snnulatlon from the plug flow and backmrxmg models It was found that the stagewlse backflow model reproduced the experImental profiles well The correspondmg mass transfer coefficients were greater than those calculated for the plug-flow model and could be better correlated v&h the vapour velocity However, the correspondmg backrmxmg coefficients were rather low, the equivalent eddy dlffuslvlty m the llquld phase bemg of the order of lo-‘m*/s

INTRODUCTION

In llquld-hqutd extractlon effort has been expended m an attempt to Improve the assumption of plug flow mslde the column Backmlxmg models and their apphcatlon in this special field have been much dlscussed Hanson[l] compiled the prmclples, Mecklenburgh and Hartland[2] developed simplified procedures for column design and Ingham and Dunn[3] Introduced dlgltal slmulatlon to make direct numerical solution of the governing equations possible TheoretIcal concentration profiles along the column show devlatlons from the plug flow values, even in cases when the backmlxmg 1s relatively small Although there IS stdl not enough experlmental evtdence m the form of measured concentration profiles, the avallable results confirm the assumption that the flow pattern 1s of conslderable Importance and may even determine the separatmg ablhty of the column In dlstdlatlon, the backmrxmg of hquld on the contacting piates has been related to the plate efficiency However, only a few references to the longatudmal mixMecklenburgh and mg m packed columns exist Hartland[4], using the same procedures as in hqmdhquld extraction, extended the dlfferentlal and the backflow models for different dlstdlatlon cases, and Blddulph [5] simulated a large air-separatmg column using the dlfferentlal model However, no experimental results exist to demonstrate how Important the backmlxmg may be m dlstdlatlon To rectify this sltuatlon we have measured the concentration profiles m a pdot plant-sized packed datlllatlon column and attempted to simulate the results using the plug flow and backmlxmg models It was found that, although the amount of backmlxmg was srgndicant, it 15 smaller than m a slmllar extra&Ion coIumn

of steps which may be chosen sufficiently small to well represent the orlguud contmuous profiles In this model the back-mixing coefficients, f and g, are defined as the fractions of the actual mass or molar flows which move against the mam streams and give rise to the backmlxmg The detailed discussion may be found in the work of Mecklenburgh and Hartland cited above The backflow model may be used for a very general description of the column performance as It IS not really necessary to keep the flow rates or densltles constant along the column height However, to economtze in computer time, as many slmphficatlods as possible should be made For this reason, m our case of a binary distdlatlon of methyl alcohol-water mixtures, the constancy of the Rows was obtained using fictltlous mole fractions based on the fictltlous molecular weight of 38 for the methyl alcohol, in which case the molar heats of vapourization are approximately the same for both components Expressmg the equrhbrlum curve and all concentrations m these fictitious fractions, and assuming that the vapour phase behaves hke a perfect gas, the flow rates and the density of the vapour phase may be considered constant, while the density of the lrquld phase IS a function of the concentration and hence changes along the column The corresponding functions are plotted m Fag 1 Defining the molar flow rates as u, = L/&x) u, = GIAQ

vb =

G/(&d

u, = FIA,

THEORY

33 No 3-A

(L + FM&+)

I, = WlAi,,

In previous work[6] concerning hqmd-liquid extraction It was found that the backflow model IS the most versatile and most suitable for computer simulation Prmclpally, the column 1s divided into hypothetical stages m which perfect mlxrng 1s assumed The contmuous change m conc_e_nn_tratlonIS thus replaced by a series CES Vol

ub =

(1)

the followmg balances may be written for the situation shown m Fig 2 Assuming a total condenser with a very smal1 hold-up of the liquid placed so high above the upper surface of the packing that no entrainment can reach It, the un255

L

256

STEINER et 01 loo

9c-

SC-

YN+I

fL,

XN-1

(1 +g)G yn

t/_

x,

(1 + g)G.

Y”-r

fLc

(1 +g)G

YII

(1 + SW

*,:;;t,r t Bottom

X,-l

fb. Xl, tN YZ

4(1 + fk

t

of the upper

%!I

sectlon

IO

20

30

40

50

60

70

so

so

I 0

Rg 2 Vapour-hqmd equlhbrlum and molar density of the hquld F

r gG

(1 + f)L,.

YM

Cl+ g)G

YH-I

IL

xw-,

(1 +dG

ym

fL

x,

(1 + SW

ym-I

fL

x,_,

tl + g)G

~lb

fL

Xlb

t 1 Bottom

for the methyl alcohol/water fractions (a), Equdibnum

xF

x&4

system, expressed m fictltlous mole curve calculated from Van Laar’s

equanon (b), Molar densny of the hqurd mixtures, recalculated from the data of Kwang-Yu Chu and Thompson@] (c), Operatmghnes

for exp

No 3

In practice, the dBerence between eqns (3) and (3a) IS very small The balances for a typlcal stage m the upper section of the column are the same as for any other kmd of counter current column with backmlxmg (1 + f)L*

QG. YZ~

of the lower section

dyn _ 1 ut ~~tl+g)tY.-1-Y”)+8tYn+l-Y~~l+~ dt us t

X26

1

dxn _ 1

dr

Rg I Derlvatlon of the backflow model steady state balances for the last hypothetical the top of the column are

stage N, at

~xnt

ut I(1 +f1 t&*1 -x”)+f~x.-,-x”~l-~

3

I (5) 1

Assummg that no backmlxmg leaves the packed section of the column, the balance for the first stage m the upper sectlon is

dy,, -=&

b,{;bl. +gY,,-(L+gh,)l+~](7)

(2) (1 + f) (XZr- x,,) - $1 (3) where r = &a(~*

- y)

(4)

Alternatively, assummg that the backflow of the llquld phase enters the condenser as entramment and mixes with the dIstIllate, eqn (3) may be modified as follows dx N=

dt

piN[~(l+n(x,-x,)+f(X,_,-X,)-~}

-

Gal

(8)

At the steady state, the time derlvatlves on the left-hand side of the balance equations disappear and In this case the hquld concentration m the first stage ts related to the concentration of the entermg vapour by x,, = CR+ l)Y,. - & R In the lower section the balances for the feed plate are as follows, assuming that the feed IS Introduced as boiling hquid (the devlatlons for the case when the feed IS below Its boding pomt are neghglble)

Concentration profiles IIIa packed dlstdlatlon column

dy,_ -_-

dt

1 PY

{~[(l+g)(Y,_,,-Y,)l+~}

(10) A typlcal stage m the lower sectlon in the upper sectlon, so that

m analogous

to one

(13)

257

wg +4)

PYQ

=

AD,

= u&j +

;)

cw (21)

It may be seen that the eddy dtiustvlty coefficients are non zero, even If the backmixing coeficlents f and g disappear This shows that the stagewise model cannot be used for sltuatlons with lower backmlxmg than those correspondmg to some tnuumum value which 1s given by the number of stages and the flow velocity Theoretlcally, knowing the concentrations of both the hqmd and the vapour along the column, eqns (18) and (19) may be numerlcally integrated between selected points A and B to obtam the mass transfer coefficient and one of the eddy diffusion coefficients, If the other one IS independently available For example, d the backmlxmg in the hqmd phase IS independently measured by a steady state tracer method, the mass transfer coefficient may be obtained from

For the lowest stage it is assumed that no backmlxmg leaves the packed part of the column, so that dY,b -_dt

_

1 (lb pv

3

[Yw+ !?YZb-(1 + g) YI] + 2

(14)

(15)

and the backmlxmg

coefficient

tn the vapour phase from B

It 1s assumed that the reboller 1s equal to one theoretlcal stage and that it contains a constant volume of liquid Thrs corresponds to normal column constructlon with a ltquld level control In this case the concentration IS given by

dxw= Ab (‘% Ubx, - l, dt

and the amount

Vwpxw

vb

of residue withdrawn W=E(L+F)-kG X

Yw - &a

&v)

(16)

m unrt time by

P XWW)

(17)

This set of equations may be solved by numerical mtegration if the equlhbrmm curve IS suitably expressed The other possiblhty 1s to solve the set of equations numerlcally for the steady state condltlon when all the time derivatives are equal to zero For some purposes the contmuous model offers advantages It has been shown by Mlyaucha and Vermeulen[7] that eqns (5) and (6) or (12) and (13) may be rewritten m dlfferentlal form usmg the first two terms of the Taylor series For the steady state we have (18)

(19)

In these equations the eddy dlffusivltles D, and D, are related to the backmlxmg coel?iclents f and g by

I {dy/dz), - &dz),~

ly V(YB - YA) -

0,. =

PA

&a

(Y* - Y) dz

Unfortunately, the accuracy of the experimental required by the method IS dtfficult to achieve

data

EXPERIMENTAL,

A standard QVF glass column with the dlmenslons given in Table 1 and packed with glass spirals was used for the experimental study Sampling holes were drllled through the wall of the working sectlons at 10 pomts along the column from which both hquld and vapour could be continuously removed The collectors of the samphng devtces were of the same size as the packmg pteces, thetr construction IS shown m Fig 3 Each sample locatlon was equipped with a thermocouple and It was also possible to read the local pressure Heat was supphed by steam with precisely controlled pressure, constant values of the reflux ratlo and the feed rate were automatically mamtamed The test mixture was methyl alcohol and delomzed water, the mass fraction of the methyl-alcohol m the feed being about 0 25 In a typical run, about 2 hr were necessary to reach the steady state After thts period the samples were taken for 15 mm and collected m sealed bottles After tirushmg the run the samples were thoroughly mixed and their densities were measured usmg an automatic analyser with an accuracy of f 0 03 kg/m3 An attempt was made to measure the backmlxmg m the hquld phase drrectly by steady-stage inJectIon For this purpose a KC1 solution was InJected through a dlstrlbutor placed 80mm above the packtng support m the lower part of the column The conductlvlty of the

L STEINER et 01 Table 1 Column cbmenslons Material Diameter Length of packed sectIons Heat transferrmg areas Heatmg me&urn Packing matenal

Manufacturer

Pyrex glass 80 mm 100 mm

Upper sectIon Lower sectlon Upper Lower

1OOOmm 900mm

Reboder Condenser

0 15m2 10m’ steam up to 2 5 atm glass spuals 12X 12mm 430 mz/m3 84 8% Qmckfit Ltd

I)lmenslons Specdic surface area VoIdage

higher concentration than the average for the crossection, the mass transfer ~111 be Increased so that thus concentration will be reduced to the average value In this way, the concentration profiles for methyl alcohol are more reliable than those for the untransferable salt However, It must be recogmsed that samplmg IS the weak pomt of all mvestlgatlons of this type and the accuracy of the results IS hmlted, even d all the other operations, e g column control, sample handhng and analysis are done with utmost care RESULTSANDCOMFWTATION

profiles were obtained for different workmg condlhons of the column, as hsted m Table 2 The experlmental profiles were plotted and compared with those predicted by drfferent mass transfer and backmlxmg coefficients The common plug flow model was tested first, Integrating equations (18) and (19) numerlcally with 0, = D, = 0 and expressmg the equihbrmm curve using the Van Laar’s equation Starting from the composltlon of the dlstdlate m the upper part of the column and from the composltlon of the residue m the lower part of the column, profiles were generated for different mass transfer coefficients till the concentration of the vapour phase at the other end of the column sectlon agreed with the measured one As may be seen m Fig 4, curves of ddierent shape are generated for different coefficients If the mass transfer 1s sufficiently fast, a horizontal hne results m some part of the column, correspondmg to the “pm,ched region” lust before the operation hne cuts the equrhbrmm hne (The operation hnes for run No 3 are drawn tn Fig 2) Further examples of the agreement of the plug flow model with the experimental data may be seen m Figs 5 and 6 It was found that the curves fit the experimental data quite well along a greater part of the column height However, the measured concentrations close to the column ends were usually different from those predlcted by the model This may be seen m both Figs 5 and 6 In the latter Figure, the pomt marked (a) (upper part of the column) could not be reached with a curve bent to the right hand side, the results showed that there IS backmlxmg m the column However, from the fair fit of the plug flow curves it may be concluded that the correspondmg coefficients are rather small The mass transfer coefficients which correspond to the best fitting

Sixteen

Vapw Fig 3 Samplmg of the phases from the column 1, column wall, 2, collector, 3, cooler, 4 and 5, needle valves, 6, pressure gauge (to read pressure, valve 5 must be closed), 7, thermocouple, 8, gasket, 9, nut, 10, stamless steel tubing, 1 5 mm bore

samples wlthdrawn

from the four samphng points above this dlstnbutor was measured and the results evaluated Unfortunately, owmg to the large differences in the conductlvlty of the hqmd sampled from different points, no conclusion could be drawn It IS assumed that this fadure was caused by the unumformlty m the dlstrlbutlon of the hquld across the horizontal sectlon of the column, and that unless a mean sample from all the liquid m a column cross sectlon may be taken, the method ts not rehable In our case the samphng devices dehvered the point concentrations tn places about one third of the column diameter from the wall, and quite frequently the measured concentration upstream was higher than at the points closer to the dlstrlbutor The samples for measurmg the methyl alcohol concentratlon were obtamed m the same way The profiles were smooth and no unreasonable values were found This may be explamed by the mass transfer with IS proporttonal to the effective concentration difference between the two phases If there IS a local stream of a

Concentration

profiles

m a packed

Table 2 Operattng oondltlons Steam pressure atm

Exp No

Reflux ratio

13 16 19 2 23 13 16 19 22 13 16 19 22 13 1 62 19 22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10 10 10 1 14 164 167 164 1 59 303 3 13 250 2 86 5 26 50 5 56 256

dlstdlatlon

and expenmental

Flow rate m3 x 106/sec Feed Dlstlllate

Feed

4 50 4 83 7 50 8 67 4 57 7 50 10 0 3 33 7 50 9 33 2 33 5 17 5 17 2 67 5 33 700

0 215 0 243 0 265 0 285 0 210 0 212 0 260 0 250 0 247 0240 0 21s 0290 0 230 0 250 0 265 0 250

0 83 1 83 2 33 2 67 I 07 1 so 2 17 1 50 1 17 1 17 100 1 67 0 67 0 83 1 17 1 83

259

column results Concentration (mass fraction) DIstIllate 065 0 780 0 927 0 920 0970 0%7 0963 OS00 0984 0990 0660 0 973 0990 0960 0 980 0990

Restdue 001 0 018 0 027 0045 0 025 0046 0 070 0 015 0 101 0 11s 0 010 0 010 0 150 0 010 0040 0040

IO 09 06

9

IO -07

-

6

--_

7

06

9----

H

6

05 04 03 02 01

0

I

1

01

02

03

,

/b 05

04 x.

I

06

07

06

-A-----

10

Fq 4 Influence of mass transfer coefficients on concentration profiles calculated from the plug-flow model compared to exp data, exp No 3, upper part of the column The parameters on the curves show the value of K,a (mole/m’ s) Expenment 0, x,

0, y. Slmulatlon --,

63) 0

C)9

Y

x, -,

5-Sarrpltw devices

solved for a very small mass transfer co&bent After the prescrbed accuracy had been reached the mass

transfer coefficient was increased and the results from the calculation were used as a first estlmatlon for the new run w&h a larger mass transfer coefficient In this way, results significant to 5 digits were obtained with 4 to 6 iterations, so that the computation was relatively quick

-g_

_

8

_

7

4 --6

v

profiles for the plug flow assumption are given m Table 3, together with those obtained from the backflow model They may be correlated to some extent agamst the vapour velocity but the values are widely scattered This, together with the lmposslbdlty of slmulatmg the end concentrations m both phases, IS further proof of the backmlxmg m the column As a further step, the profiles from the backflow model were calculated It was found that the steady state numeric solution of eqns (7&(16) may easily be done by a standard computer subroutine, based on the NewtonRaphson method Usmg linear mterpolatlon between the end concentrations as a first estimate, the equations were

r------

Hypothet&l stages 2--

; -32 I

I --

-

-

WC-

Fig 5 Comparison of the simulated profiles with the expertmental data, exp No 4, (a) and (b) are the startmg pomts of the generated profile for the backflow and the plug-flow models respectively (A) --, plug flow model (K,a = 0 08S), -, backflow model (K,o = 0 17, f= g = 0) (B) --, plug flow model (K,a = 0 038) -, backflow model (K,a = 0 14, f = 1, l? =0)

The startmg pomt m this case was the vapour concentratlon at the mlet to the upper part of the column and the hquld concentration at the mlet to the lower part These points were marked m Figs 5 and 6 by (b) where the best fitting curves are gtven (Strictly speakmg it 1s not possible to have contmuous lmes from a stagewise

L

260

STEINERef al

Table 3 Calculated values of mass transfer and ddfuslon coefficients mole v-zT

mole uYiiT

EXP No 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

( >

( )

I

b

t

b

0084 0 155 0 172 0 229 0 123 0 182 0 249 0 176 0 275 0 272 0231 0 334 0 235 0299 0 437 0 325

07% 0 857 1 14 1058 0 659 1 01 1 217 0 315 0701 0 823 0 388 0 549 1381 1 247 1 355 1 583

00111 0 022 0 025 0031 0014 0021 003 0031 0 024 0 025 0 023 0 033 0021 0 026 0 039 0 033

00069 0 014 0 016 0 019 0009 0 013 0 019 0 019 0 016 0 016 0015 0 022 0013 0 016 0 025 0021

D, X 104 (m*/s) backflow t b

plug flow I b

-

0 05 004

0 01

0 082 0085 0048 0 059 01 0 072 01 008 0 11 0 075 008 00% 0 14

0045 0038 0043 004 008 004 0 08 002 004 008 0055

0 I

0076

016 016 017 011 012 0 16 -014 0 16 0 16 0 23 016 0 16 0 19 021

011 012 013 0 13 012 0 12 0 15 011 0 12 0 16 014

I

b

4 38 5 41 2 97 3 18 267 337 5 19 625 6 18 231 668 16 00 4 82

7 02 40 20 34 20 29 80 15 40 i 9 03 3 49 15 40 46 60 1100 16 90 17 90

1040 7 39

* = floodmg

----

----------

___

9 IO--

---

8

-7-

9 --

6

---

-5-

8 --

___ 7--_6 F

4

-=2

--I-

-

0

01

_

02

03

04

65

06

07

08

C

x. Y IO

Fig 7 Influence of the backmlxmg coeficlents on the concentration profile exp No 3, upper part of the column, backflow model with 10 hypothetlcal stages, K,a = 0 218 The parameters gave the values of the backmlxmg coefficients (f - g) f = 0, 0, = 2 fix ]o-~, f= 1, DX =737x 10-4, f= 2, Dr = 123x 10-3, g =0, D,=379~I0-~,g=1,D,=123~10-’

-9 saw; devkzes

-8 4-_

HyDothewca13 -stages L

-7 6 __ 5 _4

-

3 2 -_

I--

-2 --

I - -

‘I

L__________________ lb)

w-

01

02

03

04

05

06

07

06

09

Xf

Fig 6 Comparison

of the simulated profiles data, exp No 12 (A) --, plug flow (K,a = 0 (K,a = 0 22, f = g = 0) (B) --, plug flow backflow (K,o = 0 12, f = 2, g

model drawing

The curves contmuous

m Ftgs curves

with experImenta 111, -, backflow. (K,a = 0 02). -5 = 0)

5 and 6 were obtamed by through the pomts m the

mlddie of the hypothetlcal stages) To show the influence of the backmtxmg coefficients on the concentration profile, an example IS given m Fig 7

It may

be seen

that the curve

with

f = g = 0 car-

responds best to the expertmental points, although even here.the agreement IS only farr It 1s assumed for the case shown that the backmlxmg ts even lower than that correspondmg to the mnumum for the model used with 10 hypothetacal stages m each column sectlon Figure 8 shows the profiles for the least posstble amount of backmlxmg and different mass transfer coefficients In all cases, the best fitting curves were obtamed for g = 0 and the ma]onty for f = 0 As these coefficients are dependent on the chosen number of hypothetlcal stages, It 1s better to express them as eddy dlffuslvitles usmg eqn (21) The ddfuslvltles m the lrquld phase are given m Table 3 In some cases the mlmmum backmlxmg values avaIlable with the lo-stage model were too high and the actual profile was between that for plug flow and the one for f= g =0 m the lO-stage model This may be the situation m FWS 4. 7 and 8 ~~

Concentration

profiles m a packed dlstrllatlon column

07 06 z,m

05 04 03 02 01 I

0

01

02

I

03

I

I

04

-b5

x.

06

07

I

08

09

Y

Rg 8 Influence of the mass transfer coefficient on the concentratlon profile Backflow model, exp No 3, uppe.r seenon of the column, least poss&le backnuxmg m the 10 stage model (f = g = 0) The arrow shows the startmg pomt of the profile generatIon

Using the backmlxmg model with different values of the coefficient f, the resultmg mass transfer coefficients, which generally are greater than those correspondrng to the plug flow model, may be well correlated with the molar vapour velocity, u, as follows

K,a = 1 388 u” W’

(24)

Figure 9 shows the dependence of the mass transfer coefficients for both the plug flow and the backflow models on the vapour flow rate, together with the predlcted values It may be seen that the backflow pomts may be better correlated, the coefficient of determination being 0 87 against 0 63 for the plug flow model In both cases, no relation of the mass transfer coefficient with the hquld flow rate was found

Rg 9 Correlation of the mass transfer coeficlents obtamed for the plug flow and the backflow models agamst the vapour velo city 0, plug flow, +, backflow

261

A tinrd model was proposed for the case of rapld mass transfer and conslderabie backmlxmg, assummg eqmhbrmm concentrations in all stages In this case the profile IS determined by the backmlxmg coefficients only, If the mass transfer rate IS greater than some muumum value A program for this model was developed but the results did not compare well with the experiment and are therefore not Included However, they further support the claim that for the column m questlon the backmlxmg IS relatively low, the average eddy dlffuslon coefficrent for the hqmd phase bemg D, = 6 0 X lop4 m*/s in the upper, and 1 99 x lop3 m*/s m the lower column sectlon Smce backmlxmg coefficients were not independently measured no attempt was mode to correlate them with the other vanables DISCUSSION It has been shown that for the column and packmg in questlon, the concentrations at the column ends cannot be obtained from the plug flow model It follows that mass transfer coefficients (and he&s of transfer units) based on this model and calculated from the end concentratlons are not the true coefficients, but mvolve the Influence of the backmlxmg m the column They are widely scattered and It would hardly be possible to use them for a column of another stze The simple backflow model Improves the fit and yields coefficients which are generally greater than those calculated for the plug flow assumption and which correlate well agamst the vapour flow rate There are stdl devlatlons from the measured profiles, but these are smaller than m the plug flow case The devlatlons may be caused by the followmg facts As already mentloned, samphng IS d&cult If the hquld concentration IS not constant m each honzontal column cross sectlon The pomt samples are thus not necessarily quite representative, even d they were collected at the true steady state over a long time period Furthermore, the dlffuslvlty coefficients need not be constant along the column height if the composltlon of the hquld and the mass transfer rate varies There IS no posslblhty of measuring theu pomt values and mean values must therefore be used m the slmuiatlon To obtain acceptable mean values, independent measurement m both phases would be necessary, because eqns (22) and (23) are extremely sensltlve to the accuracy of the experlmental profiles The difference of the slopes at the boundary pomts IS especially drfficult to obtam accurately and unacceptable errors result m all the calculated coefficients Generatlon of the profiles with a computer, varying the values of the mass transfer and backmlxmg coefficients until agreement w&h the experimental results IS reached, is a laborious procedure, but m the only way avadable (On the other hand, knowing the coefficient calculation of the profiles IS easy and quick ) Concentratlon profiles predlcted by the backflow model agreed better with the experlmental profiles than those predlcted by the plug flow model and the resultmg mass transfer coefficients could be correlated against the gas phase velocny This shows that the use of the backmlxmg model 1s Justified In dlstlllatlon and that some expenmental work may be spared m scahng up the columns d

L

262

S~i3NEi3 et al

the true coefficients are used m the design together with a reahstlc model of the Internal flow CONCLUSZONS

1 Concentration profiles m a pilot plant sized packed dlsttllatlon column were expertmentally measured and compared with simulated profiles The results show that the column behavlour may be simulated by the backflow model with relatively low values of the backmlxmg coefficients 2 The plug flow model faded, especially close to the column ends, so that It could not be used to reproduce the end concentrattons of both phases 3 The mass transfer coefficients based on the backflow model are higher than those for the plug model and may be better correlated against the molar flow velocity of the vapour phase NOTATION

F

f :

KY

specific surface area of packmg, ma/m3 cross sectional area of column molar flux of dlstdlate, mole/s eddy dlffuslvltles m llquld and vapour phases respectively molar flux of feed backmlxmg coeffictents m hquld phase backmlxmg coefictent m vapour phase molar flux of the vapour phase m the column mass transfer coeffielent based on concentratlon dtfference m vapour phase, mole/m’s molar flux of hquld phase m column reflux ratio, = LID mass transfer rate defined by eqn (4) time molar velocity of hquld, mole/m’s molar velocity of vapour mole fraction of light component m hqmd phase

Y mole fraction of hght component phase y* eqmhbrmm mole fraction distance along column height z

m vapour

Greek symbols

E 8 p

fractum of unit volume occupied by a phase he&t of (hypothetical) stage m the back flow model density

Indrces

feed dlsttllatlon residue W hqmd phase X Y vapour phase mlet ltl m typtcal stage m the lower section typlcal stage m the upper sectlon AY last stage m the lower section (measured reboller) N last stage tn the upper sectlon (measured feed) b lower (stnpptng) part of the column t upper (enrichmg) part of the column f

d

from from

REFERJCNCES

[II Hanson C , Recent Advances rn Llqurd-Llquad Extractton Pergamon Press, Oxford 1971 [21 Mecklenburgh J C and Hartland S , The Theory of Backmumg Whey, London 1975 [31 Dunn I J and Ingham J , Verfahrenstechnlk 1972 6 399 I41 Mecklenburgh J C and Hartland S , Ckem Engng Scr I%9 24899 197521327 PI BlddulphM W,AZCkEJ bl Stemer L and Hartland S, Chemuche Rundschau 1974 28(3) [71 Mlyauchl T and Vermeulen T , Z LBE Ch Fund[ I%3 2 304 [gl Kwang-Yu Chu and Thompson A R ,J Ck Data I%2 7(3)