kjo(amyo l^jjlyyni/na^
TRANSCRIPT
ETHANOL DEHYDRATION USING POTASSIUM ACETATE SALT EFFECT, EXTRACTIVE DISTILLATION
by
FRANK lUELIEN FAN, B.S. in Ch.E.
A THESIS
IN
CHEMICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
CHEMICAL ENGINEERING
Approved
^ kJo(AMyo L^Jjlyyni/nA^ Cha i rman o f t h e CommiiTtee
A u q u s t , 1^8^
l<Min WSrl
ACKNOWLEDGEMENTS
I am deeply indebted to Dr. Clements for his
guidance in the course of this research and for his
patience during the preparation of this thesis.
Special thanks are also extended to Dr. Beck and Dr.
Desrosiers for their helpful criticism and encourage
ment.
Sincere appreciation goes to my parents and my
brothers for their moral and financial support
throughout my college career. Finally, I would also
like to thank my wife, Chia-Ping Yao, whose sacrifice
and encouragement made my success possible.
11
ABSTRACT
This thesis describes the physical chemistry of
recovering absolute ethanol using extractive distilla
tion. The process being evaluated uses a dissolved
salt, potassium acetate, as the separating agent. The
research includes the first successful use of a thermo
dynamic consistency test for the ethanol-water-potassium
acetate (E-W-KOAc) system. This work shows that the
Meranda and Furter [1966] data are thermodynamically
consistent, while the Costa Novella [1952] data are not.
The solvation method is used to predict vapor-liquid
equilibrium (VLE) data for the saturated or unsaturated
E-W-KOAc ternary system for the first time. The VLE
prediction is used in a computer simulation of salt
effect, extractive distillation. In order to simulate
extractive distillation, measurements of the solubility
of potassium acetate in the ethanol-water system at 6
temperatures, 79, 74, 72.5, 65, 61, 59°C and 1 atm were
made.
Ill
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT ill
LIST OF TABLES vi
LIST OF FIGURES ix
NOTATION xi
CHAPTER
I. INTRODUCTION 1
Application of the Salt Effect to Extractive Distillation 4
Scope of Research 9
II. VLE THERMODYNAMIC CONSISTENCY TEST 12
Thermodynamic Systems Studies 12
Thermodynamic Consistency Tests for Salt
Solutions 16
Thermodynamic Consistency Test 17
Solvent Vapor Pressure of the Saturated Salt Solutions 22
Heat of Mixing and Solution in the E-W-KOAc System 29
Thermodynamic Consistency Test with
Herington and Rigorous Method 35
III. VLE DATA PREDICTION AND THE SOLVATION METHOD 43
The Salt Effect in Solution 43
Correlation and Prediction Review 44
Solvation and Solvation Number 53
VLE Prediction by the Solvation Method ... 53
Prediction and Comparison with Experimental Data 60
Testing of the Solvation Method 64 iv
%^
Conversion from Saturated VLE to Unsaturated VLE Data 72
IV. THE SALT EFFECT IN EXTRACTIVE DISTILLATION
AND ITS COMPUTER SIMULATION 78
Computer Simulation 80
Salt Effect Distillation Studies 81
Simulation Validation 81
Simulation Studies 87
Process Evaluation 92
V. CONCLUSIONS 100
VI. RECOMMENDATIONS 102
BIBLIOGRAPHY 104
APPENDIX
A. THERMAL PHYSICAL PROPERTIES DATA REFERENCES 111
B. THERMODYNAMIC CONSISTENCY TEST 112
C. SOLUBILITY OF KOAc IN E-W-KOAc SYSTEM 119
D. SALT EFFECT DISTILLATION EMPIRICAL DATA
(FURTER) 125
E. HERINGTON METHOD DERIVATION 130
F. COMPUTER SIMULATION PROGRAM FOR SALT EFFECT, EXTRACTIVE DISTILLATION 134
LIST OF TABLES
1. VLE Data for Ethanol-Water-Salt Systems 6
2. Relative Volatility of E-W-KOAc System 8
3. Solubility for the Potassium Acetate-Water
System 13
" 4. Thermodynamic Consistency Test and Correlation 18
5. Thermodynamic Consistency Test (JAQUES AND FURTER) 19
6. Solubility of KOAc in Aqueous Ethanol Solution
at 25°C 25
7. VLE Data for Saturated E-W-KOAc System I 37
8. VLE Data for Saturated E-W-KOAc System II 40
9. Thermodynamic Consistency Test for the VLE of E-W-KOAc System 42
10. Correlation and Prediction on VLE for Salt-Containing Systems 45
11. Correlation and Prediction Using Activity
Coefficient Methods 51
12. Correlation by Solvation Method (OHE) 52
13. Isobaric VLE Data for E-W-KOAc at X^ = 0.313 .. 56
14. Standard Solvation Number 58
15. Comparison of Calculated and Literature Values of Solvation Number 62
16. VLE Prediction of Salt Effect by the
Solvation Method 65
17. Isobaric VLE Data for E-W-KOAc System I 66
18. Isobaric VLE Data for E-W-KOAc System II 67 vi
19. Isobaric VLE Data for E-W-KOAc System III 68
20. Isobaric VLE Data for E-W-KOAc System IV 69
21. Isobaric VLE Data for E-W-KOAc System V 70
22. Salt Effect in Extractive Distillation Studies I 88
23. Salt Effect in Extractive Distillation Studies II 88
24. Salt Effect in Extractive Distillation Studies III 90
25. Energy Requirement for Concentrated Ethanol
in the Feed Stream 95
26. Energy Requirement for X«. = 0.0213 98
27. Thermodynamic Data References •.. Ill
28. Activity Coefficient of Ethanol in E-W-KOAc System (MERANDA AND FURTER) 113
29. Activity Coefficient of Water in E-W-KOAc System (MERANDA AND FURTER) 11^
30. Thermodynamic Consistency Test (MERANDA AND FURTER) • 115
31. Activity Coefficient of Ethanol in E-W-KOAc System (COSTA NOVELLA) 116
32. Activity Coefficient of Water in E-W-KOAc System (COSTA NOVELLA) 117
33. Thermodynamic Consistency Test (COSTA NOVELLA) 118
34. Solubility of KOAc in E-W-KOAc System at 1 atm 121
35. Solubility Data for KOAc in Boiling E-W-KOAc at 1 atm 123
36. Distillation Profile for the Ethanol-Water System I 126
37. Distillation Profile for the Ethanol-Water System II 127
Vll
%:
<'-m:m
38. Distillation Profile for the E-W-KOAc System I 128
39. Distillation Profile for the E-W-KOAc System System II 129
40. Typical Values of* |AHm/Gm^l 133
Vlll
i -
LIST OF FIGURES
1. VLE Data for the Saturated E-W-KOAc System 10
y 2. Thermodynamic Consistency Test Using Herington Equation 23
' 3. The Saturated Water Vapor Pressure 28
4. Heat of Solution for the Ethanol-Water System 30
' 5. Heat of Solution for the Ethanol-Water System (MERANDA AND FURTER) 31
' 6. Heat of Solution for the Ethanol-Water System (COSTA NOVELLA) 32
7. Heat of Solution for the KOAc-Water System at 25°C 33
' 8. Thermodynamic Consistency Test for Meranda and Furter's Data 39
' 9. Thermodynamic Consistency Test for Costa
Novella's Data 41
10. Standard Solvation Number Calculation 59
11. Standard Solvation Number for KOAc in Pure Water 61
12. VLE Curve Generation for Constant Salt Concentration 63
13. Conversion from Saturated VLE to Unsaturated VLE I 74
14. Conversion from Saturated VLE to Unsaturated VLE II 76
15. Distillation Profile for Ethanol-Water System I 82
IX
16. Distillation Profile for Ethanol-Water
System II 83
17. Distillation Profile for E-W-KOAc System I ... 85
18. Distillation Profile for E-W-KOAc System II .. 86
19. The Theoretical Equilibrium Stages Requirement for E-W-KOAc Distillation 91
20. Salt Effect, Extractive Distillation Process Design I 94
21. Salt Effect, Extractive Distillation Process Design II 97
22. Salt Effect, Extractive Distillation Process Design III 99
23. Solubility of KOAc in E-W-KOAc System at Reflux Temperature at 1 atm 122
24. Solubility of KOAc in Boiling E-W-KOAc Solution 124
a "
J-,'<,<-
NOTATION
Symbol Unit
B. . 11
E-W-KOAc
Hmix
Hsolu,
HsolUo
K
KOAc
M
N
P.o 1
cm'/mole
Expression
Second virfal coefficient for component i
Moles of water of crystallization in one formula weight of the solid phase
Percentage deviation in the thermodynamic consistency plots, 100* III/I
Ethanol
Ethanol-water-potassium acetate
Heat of mixing J/mole
Heat of solution in ethanol-water system J/mole
Heat of solution in KOAc-water system J/mole
Difference between the area above and below the abscissa in the thermodynamic consistency test plots
Empirical parameter in consistency test
Salt effect parameter
Potassium acetate
Total moles of water containing one mole anhydrous solute
Mole fraction of salt in ethanol-water-salt solution
Saturated vapor pressure of pure component i mmHg
XI
Pi '
q
R
S
Tmin
V
VLE
W
X
The vapor pressure of component i in the saturated salt solution mmHg
Heat of vaporization of water
Gas constant
Kcal/mole
Preferential solvation number
Temperature
Lowest boiling point in the system °K
Molar volume cm'/mole
Vapor-liquid equilibrium
Water
Mole fraction of component in liquid phase (salt-free basis)
Mole fraction of component which is not solvated on the salt-free basis
Mole fraction of component in liquid phase
Mole fraction of component in vapor phase
Greek Letters
H
r
£
e
Total pressure
Activity coefficient of component
Relative volatility
1l/Pi°
Difference between maximum and minium boiling point
Total area irrespective of the sign of the integrals in consistency test plots
mmHg
K
Xll
Subscripts
° Water-salt system
i Component i
s Ethanol-water-salt system
1 Ethanol
2 Water
3 Salt, potassium acetate
xiii
l^^^sr;^^
CHAPTER I
INTRODUCTION
Ethanol is one of.the largest-volume organic
chemicals used in industry. The total production of
synthetic ethanol in 1982 was 1.02 billion pounds
[Synthetic Organic Chemicals, 1983]. Ethanol was 50th
in the ranking of chemicals produced in 1982 [Chem &
Eng News, 1983]. The principal use of ethanol is as an
intermediate for other chemicals, including acetaldehyde,
acetic acid, ethyl ether, and ethyl acetate. Ethanol is
second only to water in use as a solvent. It is used in
production of lacquers, varnishes and pharmaceuticals.
Large volumes of ethanol are employed in the production
of synthetic drugs, and as motor fuels. The detailed
use of ethanol was reviewed by Monick [1968].
Ethanol is manufactured commercially by biological
fermentation and by chemical synthesis. In the U.S.,
20% of ethanol was manufactured by fermentation in 1981
[Chemical Marketing Reporter, 1983]. In the production
of ethanol by fermentation, the main reactions are:
' "^°°5^" - d l ^ s b r ' ' 2^22°u - ™ ; - > 2C5H120, (1-1) starch diastase maltose '"a ase gi^cose
HjO ^12^22°ll -IRvi?iiii> ^^6^12°6 (1-2) molasses glucose
^6"l2°6 -zymiie-> 2C2H3OH . 200^ (1-3)
N-propyl,.. iso-butyl and iso-a/nyl alcohol are by-prod
ucts of this process.
The starting material for the fermentation process
may be any raw material containing hexose sugars, or
materials that can be transformed into hexose sugars.
The fermentation product (mash) contains 6 to 12%
ethanol. The mash may be fed into a continuous distil
lation unit, and enriched ethanol separated from the
residue by steam distillation. Small quantities of
impurities (such as aldehydes, esters and fusel oil)
distill overhead with the ethanol and impart an unde
sirable taste and odor to beverage alcohol. Although
this enriched ethanol is satisfactory for a variety of
uses, an anhydrous grade is necessary for many proc
esses. Since ethanol and water form an azeotrope at
95.6% by weight at 1 atm, the final dehydration can not
be performed by simple distillation.
Absolute ethanol may be recovered by azeotropic,
vacuum, or extractive distillation, or by other non-
distillation means. Extractive distillation is prefer
able because of two reasons:
1. There is no need to choose a third component
which can form an azeotrope with water, and
2. The mole fraction of ethanol in the feedstock
may be low and save the operating cost.
Extractive distillation can employ two different kinds
of separating agent, a liquid or a soluble salt.
Extractive distillation employing a dissolved salt
as a separating agent is recommended because of the
potential for a high separation efficiency and a low
energy requirement. In other words, the cost saving is
the greatest advantage [Furter, 1977]. The detailed
discussion of advantages and disadvantages of a salt
effect dehydration process is in Chapter IV. The
merits of this process in industry have been reviewed
by Furter [1977].
To apply the salt effect to fractional distilla
tion, the salt is introduced into the reflux stream.
Recovery of salt from the bottom products requires a
simple vaporization process. The salt, being nonvola
tile, appears only in the liquid phase. Hence, the
salt effect distillation yields a product completely
free of the salt. Although salt effect extractive
distillation processes are not new, they have not been
widely used in the industry. The reasons are that the
technology has tended to be closely held, and the chem
istry involved is not well understood. As a result,
the literature relating to this technology and its
chemistry is fragmentary.
Application of the Salt Effect to Extractive
Distillation
When a nonvolatile electrolyte is dissolved in a
binary mixture of miscible, volatile liquids, the activ-
ity of the volatile components is affected by the for
mation of association complexes in the liquid phase
with the salt. The degree of selective association
(solvation) with a salt is related to the salt's rela
tive solubility in each liquid. The higher the salt's
solubility in each phase, the greater the selectivity.
The difference in selectivity affects the relative
volatility of the two solvents. If the volatility of
the less volatile component is reduced by an amount
which is proportionally greater than that of the more
volatile component, the relative volatility is increas
ed. If an azeotrope exists, it may be altered in com
position and even eliminated if the difference in se
lectivity is sufficiently large.
The major research issues in salt effect distilla
tion can be classified as:
1. Determining the best 'salting out' salt
2. Predicting activity coefficients for concentrat
ed salt solutions
3. Developing a reliable vapor-liquid equilibrium
(VLE) consistency test for salt solutions
4. Defining the mechanism of the salt effect in VLE
5. Predicting the effect of salt on VLE
6. Designing extractive distillation processes
based on salt effects.
A number of investigators have measured VLE data
for the ethanol-water-salt system. Table 1 lists the
previous work. The relative volatility of the ethanol-
water-potassium acetate (E-W-KOAc) system is large
compared to that of the ethanol-water system (see Table
1 and 2). The E-W-KOAc system shows the strongest salt
effect of any of the ethanol-water-salt systems studied
to date.
Before using any VLE data for developing predic
tive models or for process design, it is important to
verify the thermodynamic consistency of the basic data.
No one has reported successful use of a VLE thermody
namic consistency test or has had success in VLE data
prediction for the E-W-KOAc system because of the
following reasons:
1. The physical property differences between KOAc-
water and KOAc-ethanol are large.
2. Thermodynamic data are insufficient. Only
limited water vapor pressure data for saturated
KOAc aqueous solutions and heat capacity data of
KOAc-water solutions are available.
TABLE 1
VLE DATA FOR ETHANOL-WATER-SALT SYSTEMS
Salts s(#) Azeotrope Broken
Reference-
Ammonium bromide 4.51 Ammonium chloride 5.77 Barium acetate 2.85 Calcium acetate 3.09 Calcium fchloride
Calcium chloride(*)
Calcium nitrate
Cobaltous chloride Cupric chloride 7.91
Cupric chloride(*)
Dimethylglyoxime Lithium bromide
Lithium chloride 4.01 Mercuric chloride 2.32
Nickelous chloride
yes
yes
yes yes
yes
Johnson [1960] Johnson [I960] Meranda [1971] Meranda [1971] Jost [1951], Yamamoto [1952]
Hollo [1952] Dobroserdov [1958a] Ciparis [1966], Baranov [1971] Alvarez Gonzales [1973] Costa Novella [1952], Labradov [1976] Rouleau [1957]
Alvarez Gonzales [1973] Sabarathianam [1975], Rudakoff [1972] Decker [1972] Alvarez Gonzales [1974], Furter [1957] Labradov [1976]
Phenolphthalein Potassium acetate(*)
Potassium acetate
Potassium bromide Potassium chloride
Potassium iodide
Potassium nitrate Potassium sulfate Sodium acetate
Sodium acetate(*)
Sodium bromide
Sodium chloride
14.60
6.00 4.15
7.00
3.80 3.09 7.81
6.05
4.74
yes
yes
yes
yes
yes
yes
Alvarez Gonzales [1974] Costa Novella [1952], Meranda [1966] Dobroserdov [1958b], Klar [1958] Meranda [1972] Hahn [1975]
Hahn [1975], Meranda [1972b] Rieder [1950] Tursi [1975] Dobroserdov [1958c], Meranda [1971] Bedrossian [1974]
Meranda [1972], Hahn [1975] Dobroserdov [1958b].
TABLE 1 -Con t i nued
Salts
Sodium chloride
Sodium iodide
Sodium nitrate Sodium sulfate
Strontium chloride
Sucrose Zinc chloride Calcium and ammonium nitrate Sodium and potassium bromide Sodium and potassium iodide
s(#) Azeotrope Broken
Reference
14.56
5.27 3.06
yes
Ghosh [1964], Decher [1972], Johnson [I960] Meranda [1972], Hahn [1975] Tursi [1975] Tursi [1975] Ciparis [1966] Labrador [1976]
Kharin [1964] yes Dobroserdov [1958d]
Proinova [1966]
yes Meranda [1972]
Meranda [1972]
NOTE: (*) Unsaturated salt concentration
(#) X, = 0.3, liquid mole fraction of ethanol
ds Relative volatility of ethanol/water in
ethanol-water-salt solution
f^^<U-$iH^
TABLE 2
RELATIVE VOLATILITY OF E-W-KOAc SYSTEM
OC(760 mmHg) o(s(755 mmHg)
0.05 0.10 0.15 0.20 0.25
0.30 0.35 0.40 0.45 0.50
0.55 0.60 0.65 0.70 0.75
0.80 0.85 0.90 0.95 0.99
SOURCE;
NOTE:
9.358 7.071 5.554 4.457 3.696
3.144 2.728 2.396 2.108 1.867
1.676 1.519 1.385 1.286 1.217
1.124 1.041 0.960 0.912 0.832
; Meranda a
X.: The mo
8
(^s/d<
25.186 21.000 18.550 17.053 15.750
14.575 13.365 12.136 10.879 9.526
8.479 7.463 6.455 5.694 5.043
4.295 3.745 3.063 2.579 2.010
2.691 2.970 3.340 3.826 4.261
4.636 4.899 5.065 5.161 5.130
5.059 4.913 4.661 4.428 4.144
3.821 3.598 3.191 2.828 2.416
The mole fraction of ethanol (salt-free
basis)
oi. : Relative volatility of ethanol-water
oLs:
system without salt
Relative volatility of ethanol-water^
salt system
Scope of Research
The original goal in this work was to develop a
basis for simulation of salt effect, extractive distil
lation for the ethanol-^ater-potassium acetate (E-W-
KOAc) system. This simulation would then be available
to define optimal operating policies for salt effect
distillation for the ethanol-water system. In order to
achieve this goal, a number of tasks were necessary.
1.. Data selection based on thermodynamic consisten
cy test
Two sets of vapor-liquid equilibrium data
for the saturated E-W-KOAc system have been
reported (see Figure 1). These data are quite
different. In order to choose which data are
more correct, thermodynamic consistency was
tested using the Herington equation [Herington,
1951].
2. Saturation measurements
The salt concentration is limited by the
solubility of salt at the reflux temperature,
hence the salt concentration affects the degree
of salt effect and separation efficiency. Sol
ubility measurements were made for KOAc in the
ethanol-water system between 59°C and 79°C.
10
(0 CO
JZ Q_
O Q. CO >
-p
c •H
O c CO
LU
< t -
O
c o
o CO u
0)
o
-O- Meranda and Furter [1966] Q Costa Novella [1952]
Salt-free system
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
X,- Mole Fraction of Ethanol in the Liquid phase
Figure 1. VLE data for the saturated E-W-KOAC system.
m^m
11
3. VLE prediction by the solvation method
Because the solubility of KOAc in ethanol
is very small and the solvation nUmber is nearly
independent of the temperature, the solvation
number can be calculated with a. set VLE data
with a constant mole fraction of ethanol. Then,
the VLE properties of saturated or unsaturated
solutions can be predicted based on these calcu
lated solvation numbers.
4. Computer simulation of extractive distillation
A computer simulation for extractive, salt
effect distillation was developed and compared
with four sets of experimental data. The simu
lator was then used to suggest operating poli
cies for salt effect distillation in the E-W-
KOAc system.
CHAPTER II
VLE THERMODYNAMIC CONSISTENCY TEST
It is very difficult to measure VLE data for the
ethanol-water-salt system. The reasons are:
1. At low ethanol/water ratios, the saturated solu
tion becomes very viscous and tends to superheat.
One needs to•control.the heating rate carefully
to prevent local hot spots in the solution which
cause sudden fast bumping and excursions from
equilibrium.
2. Traces of excess solid salt tend to adhere to
glass surfaces including the bulb and stem of the
thermometer. This alters the ethanol-water ratio
in the liquid phase as a result of hydration or
selective adsorption.
3. KOAc is hygroscopic and the solubility of KOAc in
water is very high (see Table 3). This makes
precise composition determination and control
difficult.
Thermodynamic Systems Studies
For a system consisting of two volatile components
and a salt, there have been controversies over whether
binary or ternary forms of the correlating equation
12
13
TABLE 3
SOLUBILITY FOR THE POTASSIUM ACETATE-WATER SYSTEM
Temperature (°C)
5
25
30
40
42
50
60
70
Grams 100
of KOAc per Grams Water
223.9
269.4
283.8
323.3
329.0
337.3
350.0
364.8
Solid Phase
2KOAC.3H2O
II
II
II
2K0AC-H20
II
II
II
80 380.1
90 396.3
96 406.5
SOURCE: Linke [1965]
II
II
14
should be used. Also at issue is whether the salt
should be included in the liquid mole fraction data
used to calculate liquid activity coefficient values
for the two volatile components. Hence, it is impor
tant to discuss the following assumptions for solving
these two controversies.
If the two volatile components are designated A
and B respectively, three composition definitions can
be considered:
1. Salt-free basis
y^ moles A , . A moles A + moles B ^2-1;
However, if activity was calculated for compo
nent A using the pure component vapor pressure
and liquid composition data on a salt-free basis,
the activity coefficient would not normalize
unless the salt were insoluble in component A.
2. Dissolved salt basis
X moles A , .
A " moles A + moles B + moles salt ^ -< -'
In this definition, it is not clear whether the
salt should be considered as a molecular or ionic
consitituent. Solution theory suggests using
the ionic species. However, unless the salt is
either fully associated or fully dissociated
over the entire liquid composition range, the
15
degree of salt dissociation is important, but
typically unknown.
3. Partially dissociated, dissolved salt basis
moles A (2-3)
A moles A + moles B + n moles salt
This definition considers the salt effect to be
caused by a partially dissociated salt. The
total number of salt particles (ions and mole
cules) should be considered. The problem is to
know the degree of salt dissociation as a func
tion of liquid composition in a boiling system.
In summary, when salt dissolves in a solvent, the
non-dissociated, dissolved salt basis does not repre
sent reality, because there is some measure of dissoci
ation. Although the partially dissolved basis is the
real case, it is impractical to use because the actual
dissociation number, n, is unknown. The salt's pres
ence must be considered in calculating activity coeffi
cients in thermodynamic studies, invalidating use of
the salt-free basis. An alternative approach, which
may be considered a compromise is to treat the ternary
system as a pseudo-binary system of salt saturated
solvent 1 and salt saturated solvent 2. The pseudo-
binary approach is used in this work, but has its
origins in the work of Chen [1970], Jaques and Furter
[1972a], and Jaques [1974] as described in the next
16
section.
Thermodynamic Consistency Tests for Salt Solutions
Because of the experimental inaccuracies involved,
thermodynamic consistency tests are used to check
whether the experimental VLE data are valid, based on
the thermodynamic consistency test for salt systems.
Kogan [1960] used the 'slope' method. It was used to
calculate the activity coefficient of water for ethanol
water-salt systems. The salts used were potassium
nitrate, and sodium and mercurous chloride. The Kogan
slope method used Equation (2-4) to test thermodynamic
consistency (based on Gibbs-Duhem equation).
Here b is equal to the logarithm of the activity coef
ficient of the less volatile component in a saturated
salt solution. Both calculated and experimental activ
ity coefficients, T^'s should lie on parallel curves.
The biggest drawback of the 'slope' method is the
difficulty to measure slopes with sufficient accuracy.
Hence, the slope method is of little practical value.
Lindberg [1971] and Costa Novella [1952] had tried
to test thermodynamic consistency of VLE data with ac
tivity coefficient, using van Laar, Margules equations
17
and Redlich Kister area test. They had met difficul
ties doing thermodynamic consistency tests or fitting
data on a salt-free liquid basis. Table 4 summarizes
their tests.
Chen [1970], Jaques and Furter [1972a] and Jaques
[1974] redefined the saturated states of the E-W-Salt
systems by considering the ternary system as two bina
ry systems. Ethanol saturated with salt is one binary,
water saturated with salt is another binary. The
pseudo-binary approach was successfully applied to a
number of systems (see Table 5), using the Herington
method to be described below. The binary system as
sumption and the Herington test for thermodynamic
consistency for isobaric, E-W-KOAc VLE data have been
adopted for use in this work.
Thermodynamic Consistency Test
Isobaric VLE data are more useful than iscthermal
VLE data in distillation studies because distillations
are nearly isobaric but not isothermal. For this rea
son, Herington [1951] derived a rigorous equation which
can test thermodynamic consistency for an isobaiic,
binary system. The derivation is as follows:
From the general Gibbs-Duhem equation for an
isobaric system.
18
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•H 00 :^ <r
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r H CO B M (U
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r H O c CO
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u 0)
- p CO s I
I—• o c CO
J C 4-> 0)
19
TABLE 5
THERMODYNAMIC CONSISTENCY TEST (JAQUES AND FURTER)
Solvent Pair Salt Comments
methanol-water ammonium chloride sodium chloride sodium bromide sodium iodide sodium nitrate
potassium chloride potassium bromide potassium iodide mercuric chloride lead nitrate
1-propanol-water ammonium chloride sodium chloride sodium nitrate potassium chloride mercuric chloride lead nitrate
2-propanol water ethanol-water
calcium nitrate ammonium chloride ammonium sulfate sodium chloride sodium bromide
sodium nitrate sodium iodide potassium chloride potassium bromide potassium iodide
potassium sulfate calcium nitrate barium nitrate cuprious chloride mericuric chloride
mericuric bromide * mericuric iodide lithium chloride * sodium flouride sodium sulfate barium chloride
NOTE: (•) The data are thermodynamically inconsistent
20
Xx^dlnjr^ = -(Hmix/RT')dT (2-5a)
In the case of a binary system. Equation (2-5a) becomes
X dlnr" + y.^6lnlf^ = -(Hmix/RT')dT (2-5b)
By substituting X^ = 1.0 - X , Equation (2-5b) can be
rearranged to give
X (dln'2r - dlnr^) = -(Hmix/RT^)dT - dln2 2 (2-5c)
Since the total derivative of X (Inr^^ - InT ) is
d[X (lnJr - lnr2)] = X^(dlnr^ - dlnT^) + (InJ ^ - ln2r2)dX
(2-5d)
Equation (2-5c) can be combined with (2-5d), and
rearranged to give
ln(f /2r2)dXj - (Hmix/RT^)dT = d[X^(lnr^ - Inr^)] + dln7'2
(2-5e)
Integrating Equation (2-5e) from 0 to 1 with the limits
Infj = 0 at Xj = 1
ln/2 = 0 at X^ = 0
gives
[ln(r^/r ) - (Hmix/RT^)dT/dX^]dX^ = -lnr2 + lnr2 - 0 - 0
and f' ll^{r^/lf^) - (Hmix/RT')dT/dX^]dX^ = 0 (2-6)
where "T. : activity coefficient of component i
Hmix: heat of mixing
R: gas constant
T: temperature, °K
The activity coefficient, T., is Y
Inf. = ln(-57i|-T) + (B^. - V.)(1I - P.°)/RT (2-7) i i
21
where Y.: mole fraction of component i in Jthe vapor
phase
11: total pressure
X.: mole fraction*of component i in the liquid
phase on a salt-free basis
ii second virial coefficient of component i
molar volume of component i
vapor pressure of pure component i
Equation (2-6) is a binary, rigorous equation.
^i
P.o 1.
However, in most cases, Hmix is not available. For
this reason, a semiempirical test for the thermodynamic
consistency for binary, isobaric VLE data has been
proposed by Herington. He suggested use of a plot of
ln{r-^/f ) vs. Xj (see Equation (2-6)) from X^ = 0 to 1.
The parameter D is defined as
D = 100 *|I|/I (2-8)
where I = area above x-axis - area below x-axis
L = total area irrespective of the sign of the
integral
Another parameter, J, is defined as
J = 150 * 8/Tmin (2-9)
where 9 is the boiling point range between two pure
components and Tmin is the lowest boiling point in the
component range. The value 150 is empirical, based on
Herington's analysis of 15 binary VLE data sets. VLE
data are considered consistent if J > D. The detailed
22
discussion is in Appendix E.
An example of the Herington test is shown in
Figure 2. Because J > D, the data are thermodynamically
consistent. Chen [1970] *used the glycerol-water-sodium
chloride system to perform a consistency test with
Equation (2-6). Ohe [1971] used methanol-ethyl acetate-
calcium chloride data with the same equation. Both
data were showed to be not thermodynamically inconsist
ent based on the Herington method.
Before testing thermodynamic consistency for the
E-W-KOAc system using either the Herington or the rig
orous method (Equation (2-6)), there are two problems
to be solved. Limited water vapor pressure data are
available for saturated KOAc aqueous solutions. Sim
ilarly, few heat capacity data for KOAc-water solutions
are available. Hence, the estimation of the solvent vapor
pressure for saturated salt solutions and prediction
of heats of mixing for the E-W-KOAc system are necessary.
Solvent Vapor Pressure of the Saturated Salt
Solutions
The approach of treating the E-W-KOAc system as two
binaries, divides the mixture into one binary system
consisting of ethanol saturated with KOAc, and another
which is water saturated with KOAc. When using a ther-
23
vT-
O
If area A = 30 and area B = 20 th^n, I = area A - area B = 10
Z = area A + area B = 50 D = 100 * lll/z = 20
For the temperature range 86.85 to 156.850C
Tmin = 86.85 + 273.15 = 360 8 = 156.85 - 86.85 = 70 J = 150 * 70/360 = 29.16
± 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Figure 2. Thermodynamic consistency test using Herington equation.
24
modynamic consistency test for the E-W-KOAc system, use
of the saturated pure solvent vapor pressure, P.°, is
not applicable because the solvent is saturated with
KOAc. Instead, the solvent vapor pressure of the sat
urated salt solution, P^', must be used. However, both
ethanol and water vapor pressure data for saturated
KOAc solutions are unavailable. It means that before
applying a consistency test, vapor pressure data for
both saturated ethanol-KOAc and water-KOAc solutions
must be estimated.
KOAc-Ethanol System
The solubility of KOAc in ethanol is much smaller
than its solubility in water (see Table 6). The previ
ous investigators' method (Furter [1972], Chen [1970],
Jaques [1974], Jaques and Furter [1972]) of correcting
the ethanol vapor pressure of the saturated KOAc solu
tion will be used in preparing vapor pressures for the
thermodynamic consistency test.
This method calculates a corrected ethanol vapor
pressure as follows: First of all, we define £ as the
ratio of vapor pressure of ethanol saturated with salt
to the vapor pressure of pure ethanol at the salt solu
tion boiling point. We also assume £ is independent of
temperature. Then, the vapor pressure of the ethanol
saturated with the salt at any temperature is equal to
the vapor pressure of pure ethanol at that temperature
25
TABLE 6
SOLUBILITY OF KOAc IN AQUEOUS ETHANOL SOLUTION AT 25°C
Wt% Of Ethanol in Solvent
0
40
50
60
70
80
90
95
100
SOURCE: Linke [1965]
G rams KOAc Grams So
219
192
171
147
118
87,
52,
34.
16.
per 100 Ivent
.6
.4
.8
.5
.3
.6
.9
.2
.3
26
multiplied by £. For example, given
1. The boiling point of the saturated salt solution
is 150OC at 760 mmHg
2. The vapor pressure* of pure solvent is 2280 mmHg
at 1500C
3. The vapor pressure of pure solvent is 1520 mmHg
at 120°C
Then, the vapor pressure of the saturated salt solution
at 120°C may be found from
£ = 760/2280 = 1/3
and P'i20°C ^ ^^'^^ * € = 506.7 mmHg
KOAc-Water System
Jaques [1974, 1975b] has also applied the ratio
method to the water-salt system if the water vapor
pressure of the saturated salt solution was unavailable.
However, this method is not appropriate in this work
because the solubility of KOAc in water is large (see
Table 3), violating a fundamental assumption of the
method (6. is independent of temperature).
In order to estimate the effect of salt concentra
tion on the vapor pressure of water, the Roozeboom
equation as modified by West and Menzies [1937] may be
used.
dloqP -[q + Hsolu/(M - Q ] d(l/T) = - ^ 476 (2-10)
where q: molar heat of vaporization of water at 1 atm
27
Hsolu: the integral heat of solution for one formula
weight of a solid phase in forming its satu
rated solution from pure water
M: total moles of water containing one mole
anhydrous solute
C: mole of water of crystallization in one
formula weight of the solid phase
Equation (2-10) is a semi-empirical equation.
When one plots logP vs. 1/T, the slope of the curve
will not be retroflex if the Hsolu/(M - C) is very
small in comparison with q. The slope will be similar
to that of water. Rossini [1952] reported that the
heat of solution of KOAc in water is very small compared
with the heat of vaporization of water at 25°C. This
means the slope of the vapor pressure as a function of
temperature for saturated KOAc aqueous solutions should
be nearly constant. The few experimental data for water
vapor pressure over a saturated KOAc solution shown in
Figure 3 support the assumption that the slope is con
stant. The water vapor pressure, lower line in Figure
3, of the saturated KOAc aqueous solution will be used
for testing the thermodynamic consistency of VLE data
(refer to Equation (2-6)).
28
CO CO
o 1.6
1.4
1.2h
1.0
0.8
0.6
0.4f-
® Salt-free system ° Lang's Handbook [1973] V Rees [1939] ^ Meranda and Furter [1966]
2.5 3.0 3.5
Temperature (1/T)»1000, °K
Figure 3. The saturated water vapor pressure
29
Heat of Mixing and Solution in the E-W-KOAc System
The rigorous method for thermodynamic consistency
testing requires use of the heat of mixing for the
system. The heat of mixing will be contributed by the
various heats of solution. Unfortunately, measurements
of the heats of solution are unavailable for the E-W-
KOAc system. The contributors to the heat of mixing
include the binary heats of solution of (1) ethanol-
water (Hsolu,); (2) KOAc-water (HS0IU2); (3) KOAc-
ethanol. Because the solubility of KOAc in ethanol is
extremely small compared with the other two, the heat
of solution of ethanol-KOAc is ignored here.
Larkin [1975] measured the Hsolu, for a number of
temperatures (see Figure 4). The heat, Hsolu, based on
the Larkin's data is 0 to 400 J/mole (0 to 0.1 Kcal/
mole), depending on temperature and composition (see
Figure 5 and 6).
The heat of solution for KOAc-water, HS0IU2, may be
estimated from the Rossini data in Figure 7. It is
about -0.85 Kcal/mole at 25°C. This is 8.5 times great
er than the heat of solution for the ethanol-water sys
tem. Hence, the heat of solution for the KOAc-water
system can not be ignored in testing thermodynamic
consistency using the rigorous method.
Since an exact heat of solution of KOAc-water sys-
30
i j i )
^ i i t i
uu
300 -
0)
o E
n ^
c o
•H 4-> o
r-\
O CO
(*-
o -p CO (D X
200
100
0
l u l l
- i uO
- iCJU
-nil I
•^LIO
^x
'^^sr^^ , & *« JSi——'^^~^--„^
L a r k i n [ l y / " ]
-
- . ._. 1 . -1 1 u .
v V
- 0
B >v
^^. * ^N
1 ,
\ r
1 . .
•7 \ i u \
V 5 700C
X > 58°C
\ ± 50°C
\ A y '
1 1 . J 0 . 1 n . 2 0 . 3 O.^t 11 . ' - i i . t .
Mole Fraction of Water
0.8 0 . • ? 1 . f I
Figure 4. Heat of solution for the ethanol-water system.
31
Mole Fraction of Water
0.466
0.648
0.255
0.574
60 70 80 ^0 100 110 120^^3^
T (°C)
thanoi-'w'at'er'sys't'lm' " ( W ' . ' ' ' ' ' ' ' ' '^^ sysiem (Meranda and Furter
" I *
32
500
400 -
Qi
300 -
o 200 •H -P D
O cn
o
- p CO
100 -
-100 _
-200 L
Figure 6. Heat of solution for the ethanol-water system (Costa Novella).
1 7 7 -
176
0}
o E
CO
o
175 -
174 CN
o U)
173
33
Rossini [1952]
X I J. 1 1 10 15 20 25 30 35 40
Moles Water/Moles KOAc
45 50
Figure 7. Heat of solution for the KOAc-water system at 25°C.
34
tern is unavailable from the literature (except at 250C),
the heat of solution of saturated KOAc in aqueous solu
tion must be estimated from the slope of dlogP/d(l/T)
from Figure 3 using Equation (2-10).
Before predicting the heat of solution; however,
it is necessary to check whether Equation (2-10) applies
to this system. The following data are available from
the literature:
1. dlogP/d(l/T) = -2100 from Figure 3
2. C = 1.5 at 25°C and C = 0.5 over 500C from Table
3. The formula weight of KOAc is 98.15, M = (100/
18.02)/(219.6/98.15) = 2.48, where 219.6 is the
solubility of KOAc in water at 25°C from Table 6
4. The heat of solution for KOAc-water at 25°C is
-0.88 Kcal/mole from Rossini [1952]
5. The heat of vaporization of water is 583.2 cal/g
(10509 cal/mole).
Using Equation (2-10),
dlogP/d(l/T) = -2100 = -[10509 + HsolU2/(2.48 - 1.5)]
1.987 * 2.303
Then, the calculated value for Hsolu« is -881.3 cal/
mole, only 1.3 cal/mole difference from the experimental
data.
Based on the agreement between calculation and
experiment, Equation (2-10) is used in this work to