MURPHREE AND VAPORIZATION
EFFICIENCIES
IN MULTICOMPONENT
DISTILLATION
A G MEDINA,‘? N ASHTON and C MCDERMOTT
Chemical Engmeermg Department, Umverslty of Birmmgham, Bummgham BlS, England
(Recewed 19 Apnl 1977, accepted 14 June 1977)
quantitative comparison between Murphree and vaponzatlon
efficlencles IS presented based on ternary
chstdlatlon data for the systems acetone/methanol/ethanol,
acetone/benzene/chlorobenzene,
benzene/toluene/mxylene and n-hexanelmethylcyclopentanelbenzene
The Influence of expenmental
errors on calculated values of
Murphree efficiencies IS also analysed
It IS shown that the vaporlzatlon
efficiency model fads to descnbe the hehavlour of dlstdlatlon plates and It IS
suggested that Murphree’s model grves a more useful representation
of the behavlour of dlstdlatlon columns
Abstract-A
INTRODUCTION
the
design of dlsdlation
columns the knowledge of
accurate values of plate efficiencies 1s very Important as
they have a direct effect on the number of plates required
and an mdrrect effect on the runnmg costs of the eqmpment
Murphree’s model[l7] was the first of several models
leadmg to different efficiency defimttons
Vapour phase Murphree efficiency for component
I
and plate n can be defined as
In
Ynr-Yn+lt
%v,z= Y2
Y"+i
I
-
(1)
I
where y “I and y,,+, 1are the mole fractions of component I
m the vapour leaving and entering plate n respectively
and y* , IS the mole fraction of component
I In the
vapour m eqmhbrmm with the hqmd leaving plate R @us
liquid 1s considered to be a saturated hquld)
The ongmal Murpbree defimtlon was generahzed by
Taylor[20]
allowing
for unsaturated
llquld
and vapour
streams
Holland [ 11J defined the vaporlzatlon
efficiency for
component I and plate n as
E vnI =- y”’
*t
(2)
where Y,,, = K,,, A,, x,, IS the mole fraction of component 1 in the hqmd leavmg plate n and K,, IS the
vapour-hqmd
equllrbnum
ratio evaluated at the actual
temperature and pressure at which hqmd leaves plate n
Naturally Y,, , = y*nI If the hquld leavmg the plate IS a
saturated liquid
Several papers were pubhshed recently dlscussmg the
relative merits of Murphree and vaponzatlon
efficlencles
Holland and McMahon[12] attempted to show that m
the dlstlllatlon of multlcomponent
murtures, condltlons
could exist m which the values of Murphree efficIencles
were zero and mfimty while vaponzation
efficlencles had
finite, bounded values Their statements were later questloned by Standart [ 191
?Present address, Centro de Engenhana
de Engenhana, Porto, Portugal
Qmmwa,
Faculdade
Expenmental
values of vaporlzatlon efficlencles were
pubhshed by Gucalp[lO] and M&m ef al [16] for the
dlstlllatlon
of the ternary
system
n-hexanelmethylcyclopentane/benzene
in an Oldershaw column, it was
shown that average ternary
vaporlzatlon
efficiencies
were m close agreement with binary values obtamed m
the same column
Arguments
m favour of the vaporlzatlon
efficiency
concept were also put forward by Castells Pique et
al [3], pomtmg out that Its experlmental
determmatlon
1s
easier, above all for columns not operatmg at total reflux,
and by Ellis and Boyes [6]
Advantages of the use of vaporlzatlon
efficlencles m
dlstiatlon
calculations were referred to by Holland [ 111,
Yamada and Holland[24] and Yamada et al 1251
It 1s the purpose of the present work to present a
quantltatlve
comparison
between
Murphree
and
vaporlzatlon
efficlencles using published
ternary dlstlllatlon
data for the systems
acetone/methanol/ethanol [8], acetone/benzene/chlorobenzene
[8], benzeneltoluenelm-xylene[l81
and
n-hexanelmethylcyclopentane/benzene
[ 10,161
It IS important to emphasize that all the experlmental
work was carried out m small laboratory
columns m
which the hquld m each plate could be consldered completely mixed
VAPOUR-LIQUID
RQUlLLBRIlJM DATA
The calculation
of plate efficlencles
requires
the
knowledge of accurate vapour-hquld
equlhbrlum
data
As for each ternary system limited experimental
mformatlon IS normally available, It 1s common practice to
adopt correlating
equations
using the experlmental
vapour-hquld
equdlbrlum pomts to determme the constants m the equations
For this purpose a computer
program usmg the descent method of Davldon[5] for the
mnumlzatlon
of the differences between experlmental
and predicted
vapour mole fractions
was prepared
MarguIes three suffix equatlons[l3]
were used to correlate hquld phase actlvlty coefficients The vapour phase
was consldered to be ideal
Pure component
vapour pressures were evaluated m
A G
332
terms of the Antoine
equations
MEDINA
wrltten as
et ol
ted m Table 3 together with the numerical values of root
mean square devlatlons (r m s d ) for the mole fraction of
each component,
the bodmg point temperature and the
total pressure
B
hzmp: = A - C,+T
where pp IS the vapour
pressure
of component
I
(mm Hg), A,, B,, C, are the Antoine constants
for
component I and T IS the temperature (“C)
Values of the Antoine constants used are presented in
Table 1 Sources of ternary equlhbrmm
data for the
drfferent systems are hsted m Table 2 The system benzene/toluene/m-xylene
can be considered
as an Ideal
one[18, 231
A summary of the fitted Margules constants IS presen-
PtATE E%FIcIEW!IEs
Computer programs were developed[l41
for the calculatlon of vapour phase plate efficlencles from expenmental hquld composltlons
and temperatures
Neither
Nord [18] nor Free and Hutchlson[8]
measured
liquid
plate temperatures
and so, m the treatment
of their
results, the liquid in each plate was assumed to be a
saturated Ilqud
Table 1 Antome constants
component
A
B
C
Acetone
7
1171
1210
595
229
664
Benzene
6
90565
1211
033
220
790
Chlorobenzene
6
9781
1431
a53
217
55
Ethanol
8 1122
1592
864
226
184
n-Hexane
6
8778
1171
530
224
366
MCP
6
8628
1186
059
226
042
Methanol
8 0810
1582
271
239
726
Toluene
6
9580
1346
773
219
693
m-Xylene
7 0065
1460
183
214
a27
TabIe 2 Vapour-hqmd eqmhbrmm data
Author
system
Acetone/Methanol/Ethano~
Paxton
Amer,
Van
Free
n-Hexane/M
Eelknap
C P
/Benzene
and
1
Hutchxon
7
Wlnk1.e
Acetone/Benzene/Chlorobenzene
Benzene/Toluene/m-Xylene
Reference
and
Ga-jewskl
and
2.
Weber
and
Westephely
9,23
Table 3 Correlanon of vapour-llqmd equtibnum
Acetone
system
Methanol
Ethanol
<l)/
(2)/
(3)
Acetone
cl)/
n-Hexane
Benzene
<2)/
MCP
Chlorobenzene
(3)
(I)/
(2)/
Benzene
Margules
M
(1.2)
0 6334
0
4708
0
constants
M
(2,1>
a
6283
0
2602
0
1695
M
(1,3)
a
5600
0
2456
0
1772
N
(3,l)
0
3161
a
2530
0
2084
M
(2,3)
0 0794
0
0125
0
00133
M
(3,2)
a470
-a
la53
0 01578
RHSD
-0
007
0 007
0 006
ye
temp
press
0
341
0 008
0 005
0 009
0 375
9
531
8 471
a
Y2
YS
(OC)
(mm
Hg)
1499
0
0
0
0
005
005
007
168
4 012
(3)
333
Murphree and vaporlzatlon efficrenctes m multlcomponent disttllation
From the large number of results obtamed,
those
presented m Tables 47 were selected as typical examples
for
the
systems
benzeneltoluenelm-xylene,
acetonelbenzenelchlorobenacetone/methanol/ethanol,
zene and n-hexanelmethylcylcopentanelbenzene
respectlvely
Plots of expernnental
composltlon
protiles and calculated values of Murphree and vaponzation
efficlencles
for the first three systems are presented m Figs l-3
Sumlar plots for the system
n-hexane/methylcyclopentane/benzene
were pubhshed elsewhere [ 10,161
wrttten[l4]
to allow the defimtion
of the possible
extremes of calculated values of Murphree efficiencies
The followmg experimental errors were assumed
Liquid composlhon
Vapour-liquid
001 (mole fraction)
error-0
005 (mole fraction)
situations
1
of experrmental errors,
sampling and analysis)
errors, on calculated
computer program was
between Murphree efficiencies and vapormtion
xylene
efficlencles-system
benzeneltoluenelm-
Plate
number
x
Component
0
E”
EMV
926
0 058
2
10
11
were defined, as
ERRORS ON CALCULATED
EFFIclENcm
In order to assess the influence
hquld composltlon errors (due to
and vapour-liquid
eqmhbnum
values of Murphree efficiencies, a
Table 4 Companson
eqmhbnum
For any plate n two extreme
follows
Sttuatton
INFLUENCE OF -AL.
VALUES OF -
error4
0
016
Benzene
0
906
0
0
322
0
Toluene
0
066
0 027
0
207
2 12
m-Xylene
0 028
0
005
0
512
3
52
Benzene
0
808
0
963
0
239
0
941
Toluene
0
071
0
030
0
122
2
21
m-Xylene
0
041
0
007
0
380
4
12
968
960
Benzene
0
868
0
957
0
224
0
928
Toluene
0
079
0
034
0 177
2
09
m-Xylene
0.053
0
009
0
272
4
58
912
Benzene
0
a50
0
952
0
176
0
Toluene
0 083
0
036
0
086
2 18
m-Xylene
0 067
0 012
0
253
4
59
Benzene
0
a35
0 947
0 134
0
a97
Toluene
0
089
0 040
0
121
2
11
m-Xylene
0
076
0
013
0
144
5 03
Benzene
0
814
0 940
0
166
0
888
Toluene
0
097
0
044
0 150
2
03
m-Xylene
0 089
0
016
0
178
4
76
Benzene
0
786
0
931
0 193
0
874
Toluene
0
104
0
048
0
126
2 01
m-Xylene
0
110
0
021
0
7.34
4
37
Benzene
0
664
0
891
0
537
0
882
Toluene
0
113
0
061
0
171
1
72
m-Xylene
0
223
0
048
0
647
2
28
Benzene
0
46s
0 792
0
609
0
839
Toluene
0
129
0 090
0 410
1
26
m-Xylene
0
406
0 iia
0
636
1
89
Benzene
0
252
0
596
0
619
0 780
Toluene
0
132
0 133
2
77
0
969
m-Xylene
0
616
0
0
608
1
50
271
334
A G MEDINA et al
Table
5 Companson
Plate
between
Murphree
efficrencles
and
methanol/ethanol
Component
x
vaporization
efficlencres-system
Y+
6
Comparison
Plate
2
7
"
Acetone
0
420
Methanol
0
464
Ethanol
0
116
Acetone
0
351
0
495
0
481
0
Methanol
0
495
0
435
0
517
1 07
849
Ethanol
0
154
0 070
0
454
1
Acetone
0
262
0
419
0
566
0.837
Methanol
0
519
0 473
0
522
105
Ethanol
0 219
0
0
584
1 43
Acetone
0
201
0.356
0
393
0
Methanol
0
526
0
0
268
1 04
log
500
65
735
Ethanol
0
273
0
144
0
418
1
52
Acetone
0
135
0
272
0
481
0
738
Methanol
0
519
0
528
0
829
0
997
Ethanol
0
346
0
200
0
501
1
36
Acetone
0
073
0
170
0
637
0
793
Methanol
0
464
0 541
0 616
0
960
Ethanol
0 443
0
0.630
1
20
Acetone
0
0 117
0
361
0
625
"lethanol
0 4J_4
0 499
0
821
0
969
Ethanol
0
0
0
622
1
15
between
Murphree
046
540
289
384
efficlencles
and vapomatlon
zenelchlorobenzene
efficlencles-system
acetone/ben-
+
Component
x
E
Y
number
1
E
%V
number
Table
acetouel-
Acetone
0
Benzene
0
574
Chlorobenzene
0
022
YV
E"
404
Acetone
0
263
0 491
0
620
0
Benzene
0
684
0
0
608
1 14
503
824
Chlorobenzene
0
053
0 006
0
664
3 47
Acetone
0
134
0
333
0
650
0
791
Benzene
0
750
0
650
0
660
1
05
Chlorobenzene
0
116
0
017
0
640
3 02
Acetone
0
062
0 199
0
526
0
Benzene
0
713
0
756
0
866
0 992
Chlorobenzene
0
225
0
045
0 607
2
55
Acetone
0
020
0 084
0
655
0
737
Benzene
0
570
0
795
0
637
0
898
Chlorobenzene
0 410
0
121
0
641
1
85
Acetone
0
008
0
041
0
362
0
486
Benzene
0 408
0
723
0
514
0
788
Chlorobenzene
0
0 236
0
500
1
74
Acetone
0 002
0
013
0
529
0
599
Benzene
0
212
0
520
0 636
0
785
Chlorobenzene
0
786
0
467
0
1
25
564
632
673
Murphree
Table 7
Comparison
Plate
between
and vaponzatlon
Murphree
efficiencies
in multicomponent
efficlencles and vaponzatton
pentane (M C P )/benzene
Component
x
distdlation
efficlencles-system
Y
2
3
4
5
6
11
12
13
14
15
CESVol 33 No fF
E"
n-Hexane
0
476
0 505
0
577
0
MCP
0
305
0
293
1
07
0
977
Benzene
0
219
0 204
0
126
1
07
n-Hexane
0
449
0
480
0
905
0
994
MCP
0
313
0
302
0
672
1
01
Benzene
0
238
0
220
0
988
1
00
570
977
n-Hexane
0
431
0
464
0
MCP
0
318
0
308
0 470
1
02
BelIZZ.%le
0
251
0
231
0 6011
1
04
!-l-HeXaIle
0
396
0
431
1
02
1
00
MCP
0
334
0
326
1
92
0
976
Benzene
0
270
0
246
0
778
1 07
n-Hexane
0
382
0
416
YCP
0
331
0
323
-0
359
1
B.XlZene
0
287
0
258
0
580
1 05
0 417
0 971
0 953
04
II-Hexane
0
353
0
392
0
744
0
974
MCP
0
346
0
343
5
61
0
964
1 05
Aenzene
10
n-hexanelmethylcyclo-
=MV
number
1
335
0
301
0
272
0
487
0
326
0
369
0
622
0 956
0
349
0
352
-0
933
0 982
0
325
0
294
0
770
1 02
0
282
0
324
1
05
1 00
0
357
0
363
-1
31
0
0
361
0
320
0
878
1 02
Il-HeXane
0
249
0
298
0
667
0
MCP
0
332
0
350
1
36
1 02
419
0
961
944
Benzene
0
369
1
17
0 977
n-Hexane
0 214
0 263
0
713
0
MCP
0
308
0
331
104
946
1 00
Benzene
0
478
0
411
0
876
1
02
n-HeXaTIe
0
178
0 231
0
674
0
925
MCP
0 279
0
315
0
807
0
970
BeKl2ene
0
0 467
0
850
1
02
988
543
I-l-HeXane
0
132
0
180
0
956
0
MCP
0
238
0
279
0
994
0
999
Benzene
0
630
0
525
0
831
1
03
879
n-Hexane
0 097
0
150
0 658
0
MCP
0
183
0
242
0
0 985
Ben2eIle
0
720
0
Z-l-HeXaIle
0 054
939
631
1
01
0
999
0 092
1
14
1
06
752
MCP
0 138
0
198
0
Benzene
0
808
0
716
0 952
1
n-Hexane
0
032
0
059
0
825
0
920
MCP
0 093
0
143
0
898
0
964
Benzene
0
0
787
0
766
1
03
875
0 925
00
A
336
G
MEDINA et nl
50
45
40
35
30
5
g
25
OS
00
*
00
2
I
3
4
5
6
7
04
02
00
Plate nunbet
Ag 1 Vanation of plate efficiency and composition
with plate
number-system
benzene/toluene/m-xylene
-,
Murphree eff ,
--0, vaponzahon eff , 0, benzene, 0, toluene, +, m-xylene
Fig 3 Variation of plate efficiency and composition
with plate
number-system
acetone/benzene/chlorobenzene
-,
Murphree
vaportzatron eff , q, acetone, 0, benzene, +, chlorobeneff ,-,
zene
where x,_, , and X, , are the mole fractions of component
I m the lqutd entermg and leavmg plate n respectively
and (K,, ,)1 and (K, ,)> are the vapour hquld eqmhbnum
ratios for sltuatlons 1 and 2
For total reflux the equations defining vapour phase
Murphree efficlencles for sltuatlons 1 and 2 can be wntten as
(EM””
t)l
=
0 002
Xn-14 - X”,, +
w”,h(~“#)1-x,,--~
00
-
06
-
04
-
02
-
0°0
I
2
x
I
2
3
4
5
6
x"_,,~-x",,-ooo2
u%.ivn
‘12=
W” Mxn J2 - x,
7
I
+
0 004
The extreme values based on the assumed errors are
plotted m Fig 4 for benzene (system n-hexanelmethylcyclopentanelbenzene)
DISCUSSION OF RFSULTS
of the calculated
values of plate efficiencles allows the followmg comments to be made
An
3
4
5
6
7
analysts
Platellumber
Fig 2 Vaflatlon of plate eficlency and composltlon
with plate
number-system
acetone/methanol/ethanol
-,
Murphree eff ,
---7 vaporlzauon eff , 0, acetone, 0, methanol, +, ethanol
(a) Murphree eficrencres
(I) Most of the calculated
ties lie in the tnterval (0,l)
values of Murphree efficlen-
Murphree and vapowatlon
efficiencies
m multlcomponent
337
dlstdlation
three sets of efficlencles, calculated vapour composltlons
vary only slightly This 1s because the wide vacation m
the efficiency values IS due to the low dependence
of
efficiency
vapour
composition
on
Conversely
a well defined
efficiency
value
results
from
the
case
where
the
vapour
composition
is heavdy
dependent on efficiency The resultmg error m the computed vapour composltlon 1s naturally of the same size m
both cases
These results explain the observations
of
Cllianu et al [4]
(b) Vaponzatton eficlencres
(1) Vaponzatlon
efficiencies are normally smaller than
unity for the more volatile component (MVC) the concentration of which IS rncreasmg upwards and
hm
00
0
I
n
2
4
6
6
IO
12
14
(E,v,)
= 1
(4)
t
16
Flat6nunb6r
Fig 4 Influence of experunental
errors on Murphree efficienn-hexane~methylcyclopentane/benzene-component
cies-system
benzene
-,
Extreme situations
1 and 2, ---,
expenmental
values
(u) The largest varmtions
of Murphree efficiencies
with composltlon
occur for the intermediate component
for which calculated
values of Murphree efficiencies
often fall outside
this interval
This is particularly
evident for methylcyclopentane
as, m this case, negative
values appear together with very high positive values
(m) The influence that expenmental
errors have on
calculated
values
of Murphree
efficiencies
may be
enormous
TIN is particularly important for the mtermediate component m the regon m wluch a maximum or
a minimum of concentration
occurs In fact the range of
possible
values
can be mfimte when the difference
appearmg m the denominator of Murphree’s definitions 1s
smaller than the expenmental
error
(iv) Though the consideration of the possible range of
experimental errors can lead to a wide range of values of
Murphree efficiencies there IS often an interval of this
range which lies between zero and one
(v) Some negative values of efficiencies as well as
some high positive values can be explamed by previous
conslderatlons
The above comments do not imply the non-existence
of negative point efficiencies
or of point efficiencies
greater than umty Such situations can occur[ 15,21,22]
and will be discussed later m detati[l5]
The previous evidence shows the ddficulty m assigmng
a specific numerical value to a Murphree efficiency m
some circumstances
and It raises the question of whether
the error on the evaluation
of Murphree efficiencies
affects the determination of composltlon profiles Table 8
summarizes
the results of the evaluation
of the composItion of the vapour leavmg a plate (system n-hexane/methylcyclopentane/benzene-plate
6) using three
different sets of efficiency, i&v, (EW)t, (Em)2
It can
be seen that, in spite of the large differences between the
(II) Vaporization
efficiencies of the less volatile
ponent (LVC) are normally greater than umty and
hm
6% ,_vc) = 1
com-
(5)
xI_vc + 1
(m) Vaponzatlon
efficiencies of the intermediate component are less than umty when the concentration of the
component 1s increasing upwards and greater than unity
when the concentration
1s decreasing
In fact the
vaporization
efficiency 1s bound to be equal to unity
whenever a maximum or mlmmum of concentration
1s
reached
(iv) For the less volatde component calculated values
of vaponzation
efficiencies spread over a wide range,
typical
examples
occur
for
the
systems
benzeneltoluenelm-xylene
and acetonejbenzenejchlorobenzene Table 9 shows the limits of vanation for these two
systems and shows that the results of Ml&m et al [la]
cannot be generalized
(v) It 1s mterestmg
to note that m a hypothetical
column m which no separation occurs, that 1s to say plate
composltlons are the same for plates 1 to N, vaporization
efficlencles
are dtierent
from zero
An example
IS
presented
m Table 10 for acetone/benzene/chlorobenzene
It IS clear that the range of possible
values
of
vaponzatlon
efficlencles say for the more volatile component 1s smaller than the interval (0, 1) and depends on
the component mole fraction As the mole fraction of the
more volatde component approaches unity the size of the
interval of possible values of vaponzatlon
efficiencies
tends to zero
Expenmental
data obtamed by Nord[l8],
Free and
Hutchlsoni83
and Gucalp [lo] for the ternary systems
benzene/toluenejm-xylene,
acetone/methanol/ethanol,
acetonelbenzenelchlorobenzene
and n-hexanelmethyl-
A G MEDINA ef al
338
Table 8 Iduence
of experimental
errors on piate to plate calculations
zene-plate 6)*
Murphree
Component
(system
ir-hexane methylcyclopentane/ben-
Predtcted
vapour
composltlon
efflclency
i-t-HeXZdne
0 744
0 382
M C P.
5 61
0 331
Benzene
0 487
0 287
0 381
n-Hexane
0
MCP
1 72
0 330
Benzene
0 355
0 289
n-Hexane
MCP
0 613
0 380
-7 712
0 336
0 677
0 284
Benzene
* Plate
composltlon
- xH
912
= 0 353,
‘Fable 9 Llmlts of variation
component
System
Benzene
Toluene
m-Xylene
Lower
(l)/
(2)/
xM
C p
= 0 346,
of vamzaticm
1
XB
= 0 301
efficlencles
Component
2
Component
3
UPPep
11m1t
Lower
llrnlt.
11m1t
Upper
llmlt
1un1t
1lrnl-t
0 780
0 960
0.969
2 21
1 50
5 03
0 486
0 824
0 785
1 14
1 25
3 47
LOWeP
Upper
(3)
Acetone
(l)/
Benzene
<?I/
Chlorobenzene
i
Table 10 Vaporuation
(3)
efficlencles
for a zero separation
situation
(system acetone/benzene/chlorobenzene)
Plate
Plate
number
composlt1on
1
2
3
Vaporization
Component
efflclencl0s
150
0 407
Acetone
Benzene
Chlorobenzene
0 002
0 212
0 786
1 685
Acetone
Benzene
Chlorobenzene
0 002
0 150
0 212
0 786
0 407
0
1 685
150
Acetone
0 002
0
Benzene
Chlorobenzene
0 212
0 786
0 407
1 685
339
Murphree and vaponzatlon efficrenclesm multwomponent dlstdlatlon
cyclopentane/benzene
were used on a quantltatlve
compamon between Murphree efficlencles and vaponzatlon
efficiencies It was shown that
(a) The vaponzatlon
efficiency concept fads to descnbe the behavlour of the phases m a dlstflatlon
plate
due to its mathematical
hmltatlons
The pattern of calculated values of vaponzation
efficlencles IS the same for
all the systems as the vaponzatlon
efficiency of the more
volatile component
IS normally
less than umty, the
vaporlzatlon
efficiency of the less volatde component 1s
normally greater than unity and the vapomation
efficiency
of the intermediate component takes values close to unity
(b) A wide variation of the vaporlzatlon efficiency with
composition
can exist above all for the more volatde
component
(c) The range of possible
values of vaponzatlon
efficiencies IS limited and depends on the component
mole fraction
(d) Vaponzatron
efficiencies differ from zero m sltuatlons m which no separation occurs
(e) “Murphree type” efficiencies are m agreement with
physical reality as their values normally belong to the
interval (0,l)
Values falling outside this interval can
normally
be Justtied
in terms of the influence that
experimental
errors
have on calculated
Murphree
efficlencles, alternatively
such values hlghhght mterestmg physical
situations
(reverse
diffusion,
dtiuslon
barriers)
(f) The influence that experimental errors (hquld composttlon errors and vapour-hqmd
eqmllbrmm errors)
have on calculated values of Murphree efficlencles may
be enormous This effect IS particularly Important for the
intermediate
component m the regon m which a maxlmum of concentration
occurs
(g) Although experimental
errors seriously affect calculated values of Murphree efficlencles their influence on
plate to plate cakulatlons
IS llmlted Such mfluence 1s of
the order of magnitude of the experlmental errors
of the authors (AGM) wishes to thank
Junta Naclonal de Inveshga@o
Clentlfica e Tecnologlca-ComlssHo Invotan-Portugal
for the award of a research scholarshlp
Acknowledgements-One
NOTATION
A, B, C
Ehnv
E,
K
Antome constants
Murphree vapour phase plate efficiency
vaporlzatlon efficiency
vapour-liquid
eqmllbnum ratio
P0
T
x
y
Y*
Subscripts
n
I
vapour pressure
temperature
hquid mole fraction
vapour mole fraction
eqmhbnum vapour composition
plate number
component
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