J. Chem. Thermodynamics 2001, 33, 1285–1308
doi:10.1006/jcht.2001.0837
Available online at http://www.idealibrary.com on
Experimental determination of oxygen and
nitrogen solubility in organic solvents up to
10 MPa at temperatures between 298 K and
398 K
Kai Fischer,a
Laboratory for Thermophysical Properties LTP GmbH, Institute at the
University of Oldenburg, FB9-TC, P.O. Box 2503, D-26111 Oldenburg,
F.R.G.
and Michael Wilken
University of Oldenburg, Department of Industrial Chemistry,
P.O. Box 2503, D-26111 Oldenburg, F.R.G.
Oxygen solubility in methanol, n-propanol, dibutyl ether, toluene, and octane, and nitrogen
solubility in ethanol, n-propanol and 2-methyltetrahydrofuran was measured at pressures
up to 10 MPa in the temperature range between 298 K and 398 K using the static
synthetic method. The experimental results were used to extend the range of applicability
of the Soave–Redlich–Kwong (PSRK) model for the prediction of air solubility in
organic solvents and solvent mixtures by fitting the missing gas–solvent group interaction
parameters. The required pressure range of gas solubility data for fitting the PSRK group
interaction parameters was defined by analysing the significance of the data for the
optimized parameters. The applied experimental method was analysed in detail since its use
at higher pressures requires the consideration of the partial molar volumes of the dissolved
gases when solving the mass and volume balance equations during the data treatment.
c 2001 Academic Press
KEYWORDS: gas solubility; PSRK group contribution; equation of state; oxygen;
nitrogen; organic solvents
1. Introduction
The correlation and prediction of (vapour, or gas + liquid) equilibria is possible with
cubic equations of state (EoS) combined with so-called G E mixing rules. These methods
combine the advantages of the local composition concept of G E models with those of
equations of state. (Vapour + liquid) equilibria at high or low pressure of multicomponent
a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/01/101285 + 24 $35.00/0
c 2001 Academic Press
1286
K. Fischer and M. Wilken
systems can be predicted using only binary interaction parameters, regardless of the
polarity of the components, and whether they are sub- or super-critical. Also group
contribution approaches such as UNIFAC can be used, so that the applicability of methods,
for example the PSRK group contribution equation of state, (1) is not restricted to systems
where experimental data are available. Furthermore, an equation of state allows the
calculation of other properties such as enthalpies and densities which are also required
for the design of separation processes. The range of applicability was extended by the
introduction of new structural groups and the fitting of the group interaction parameters
between the new groups and the already existing groups. (2–6) Up to now, 31 new PSRK
main groups (epoxy group and 30 gases such as CO2 , CO, O2 , N2 , CH4 , etc.) have been
introduced. An improvement of the results for strongly asymmetric systems (mixtures with
compounds different in size) was achieved by Li et al. (7) A detailed analysis of different
thermodynamic properties like enthalpy and volume effects and their representation by
PSRK was given for (carbon dioxide + ethane) by Horstmann et al. (8)
Most of the available experimental information for gas solubility is given in terms of
solubility coefficients, which are based on the approximate linearity of gas solubility with
its partial pressure at low concentration and low pressure. They can be used to fit the
interaction parameter for the classical mixing rules for cubic equations of state. But for
the optimization of the two or three parameters required by G E mixing rules a larger
composition and pressure range should be covered. Therefore, in this work gas solubility
data for oxygen in n-octane, toluene, n-propanol, dibutyl ether, and methanol, and nitrogen
in ethanol, 2-methyltetrahydrofuran (2-methylTHF), and n-propanol were measured using
a static apparatus in the temperature range between 298 K and 398 K and at pressures
up to 10 MPa. These data were used to fit the required interaction parameters for the
PSRK model. The calculated results were compared with all the available experimental
information stored in the Dortmund Data Bank (DDB) in terms of Henry coefficients.
Since the applied experimental static synthetic method was used before only at low
pressure, the treatment of raw data was carefully analysed in order to provide reliable
( p, x) data.
2. Experimental
2.1. MATERIALS
Oxygen (mole fraction purity: 0.99995) and nitrogen (mole fraction purity: 0.99999) were
purchased from Messer Griesheim. They were used without further purification. The purity
and the suppliers of the different solvents are given in table 1. All the solvents were distilled
and degassed after drying over molecular sieves by low-pressure distillation as described
previously. (9)
2.2. APPARATUS AND PROCEDURE
The apparatus used was previously described in detail by Fischer and Gmehling. (9) Since
it was previously used only for the measurement of v.l.e. for subcritical systems, a few
modifications were made. A schematic view of the apparatus is shown in figure 1. The
Experimental determination of oxygen and nitrogen solvents
1287
TABLE 1. Suppliers, mole fraction purity x and mole
fraction of water x(H2 O)
106 · x(H2 O)
Solvent
Supplier
x
Methanol
Scharlau
>0.999
71
Ethanol
Scharlau
>0.999
230
n-Propanol
Aldrich
0.999
228
Toluene
Fluka
0.999
273
Dibutyl ether
Fluka
0.999
289
n-Octane
Aldrich
0.999
104
2-Methyl tetrahydrofuran
Aldrich
0.995
445
F
A
E
Pressure
R
K
D
M
H
K
O
N2
Pressure
balance
<1 MPa
N
Gas
H
Vacuum
Pressure
balance
<12 MPa
H
B
C
G
FIGURE 1. Schematic diagram of the static apparatus. A, buffer volume; B, pressure regulator;
C, vacuum tubes; D, gas container; E, pressure display; F, container for degassed liquids; G, pump;
H, constant temperature bath; K, thermometer; M, differential pressure null indicator; N, equilibrium
cell; O, piston injectors; R, pressure balance gauge.
1288
K. Fischer and M. Wilken
Input
Vcell VGas tank TCell TGas tank v1 p 2s
Bii pCell pGas tank Solvent
Calculation of the injected masses
V
2B11
n 1a e
2
V
2B11
Starting values: x 2
n 2T
n 2l
1 y1
n 2T v2
n 1T
pV 2
RT B11
n 2T
p 2s
1 p2
V
l
V
n a1 n e1
v
M
V
VCell
Vl
V
Mass balance of solvent, calculation of n2
2
}
v1 n 1L




p2 V V 2 
l
 n2
RT B22 

VV
2B22

VV
2B22
n 2V
Volume calculation
VL
n 2l v2l
{1
VV
VCell
VL
2
p
p
VV
2B11
VV
2B11
2
n 2V
Calculation of the
partial pressures
p2
Mass balance of gas, calculation of
n 1V
n 2T
x 2 p 2s p 1
p
p2
n1V
p1 V V 2
RT B11
n 1L
n 1T
n 1V
Calculation of xi
no
p i ,V L
const ?
yes
FIGURE 2. Flow diagram of the raw data treatment by the first procedure.
Output:
x i yi V L p
Experimental determination of oxygen and nitrogen solvents
GLEFLASH
Input:
Pure component data,
starting values
of mixing rule parameters,
feed masses, T, p
Estimating unknown
Péneloux-corrections
Flash calculation with
starting values of
mixing rule parameters
Optimization of
mixing rule parameters
Flash calculation
Flash calculation with
optimized
mixing rule parameters
Conversion of
saturation vapour pressures
to average temperature
Output:
x i yi V L V V p
END
FIGURE 3. Flow diagram of the raw data treatment by the second procedure, main loop.
1289
1290
K. Fischer and M. Wilken
FLASH
for constant mixing rule parameters
Input :
zi T p
Starting values: xi, yi
1. Iteration ?
Calculation with
equation of state :
ViL ViV
Ki
yi
xi
Ki
L
i
L
i
V
i
L
i
One phase?
V L = VV
yes
no
Mass balance :
calculation of
xi, yi
from Ki, zi
x i new
xi
xi
yi new
STOP
yi
yi
no
xi, yi = const
yes
Output :
xi, yi, VL, VV
FIGURE 4. Flow diagram of the raw data treatment by the second procedure, flash loop.
Experimental determination of oxygen and nitrogen solvents
1291
TABLE 2. Critical temperatures T1,c , critical
pressure p1,c and parameters A and B of equation (12)
T1,c /K
p1,c /MPa
A
B
Oxygen
154.6
5.043
0.0525
3.808
Nitrogen
126.2
3.39
0.0411
4.71
TABLE 3. Isothermal compressibility βT , isobaric thermal expansion α, calculated
partial molar volumes of oxygen in the solvents used v1 , and values of the internal
pressure p in {equation (12)} at temperature T
Methanol
n-Propanol
n-Octane
Toluene
T /K
βT /(10−3 · MPa−1 )
α p /(10−3 · K−1 )
pin /MPa
v1 /cm3
298.15
1.182
1.172
295.6
45.3
323.15
1.420
1.218
277.1
50.3
348.15
1.730
1.321
265.7
54.9
298.15
0.964
0.982
303.8
44.5
323.15
1.118
1.059
305.9
46.8
348.15
1.327
1.136
297.8
50.4
298.15
1.207
1.147
283.4
46.7
323.15
1.475
1.233
269.9
51.3
348.15
1.812
1.318
253.2
56.9
298.15
0.908
1.105
362.8
39.4
323.15
1.107
1.132
330.4
44.3
348.15
1.375
1.184
299.9
50.1
principle of the synthetic measurement is to inject precisely known amounts of the pure
components into a thermoregulated equilibrium chamber, and to measure the system
pressure as a function of composition in the (gas, or vapour + liquid) system. The
degassed pure liquid solvents were injected at the beginning of each experimental run into
the evacuated equilibrium cell using displacement pumps. Then, the gases were injected
stepwise from a gas container with constant volume (about 1 dm3 ) filled directly from gas
bottles to a pressure greater than the pressure in the equilibrium cell. The temperature
and pressure in the gas container at ambient temperature were monitored by using a
Pt 100 resistance thermometer (model 1560, Hart Scientific), and a calibrated piezoelectric
pressure sensor (model PDCR 911, Druck). The total volumes of the gas injection system,
and of the equilibrium cell were determined by displacing the complete volume under
reduced pressure with pure compressed water. The estimated accuracy of the volumes
determined with this procedure was better than ±0.05 per cent . After recording the initial
pressure in the gas injection system, the valve to the equilibrium chamber was opened
1292
K. Fischer and M. Wilken
TABLE 4. Calculated partial molar volumes of nitrogen in the solvents used, and
values of the internal pressure pin {equation (12)}
n-Propanol
Ethanol
T /K
β/(10−3 · MPa−1 )
α/(10−3 · K−1 )
pin /MPa
v1 /cm3
298.15
0.964
0.982
303.8
51.2
348.15
1.327
1.136
297.8
58.5
398.15
1.909
1.289
268.7
70.7
298.15
1.117
1.074
286.6
46.3
348.15
1.675
1.077
223.8
62.6
398.15
2.866
1.531
212.5
72.7
for several seconds so that the pressure in the equilibrium chamber became equal to the
pressure in the gas injection system. Then the valve was closed, and the pressure of the gas
injection system was measured again. From the ( p, V, T ) data before and after injection,
the amount of the gaseous compound injected can be calculated using suitable equations of
state, which are available for most of the common gases. We have used the virial equation
with the second virial coefficients recommended by DIPPR. (10) Liquid densities of the
pure solvents were required to calculate the solvent loading from the volume displaced
during injection. From the volume change with pressure in the displacement pumps, the
liquid compressibility could be determined and taken into account, since the injection of
the compressed pure liquids was performed at about 2 MPa. The amount of solvent initially
injected into the equilibrium chamber was chosen to be large enough to fill the major part
of the equilibrium chamber because most of the gas injected would be in the liquid phase.
For each loading of the equilibrium cell the temperature and pressure were monitored
while stirring the mixture. After about (30 to 45) min equilibrium was indicated by stable
readings of temperature and pressure. Then the next gas injection could be made.
2.3. TREATMENT OF RAW DATA
Since only temperature, pressure, total loadings n Ti , and the total volume V T are measured,
the composition of the coexisting phases must be determined by an isothermal and
isochoric flash calculation. The following balance equations must be fulfilled:
n Ti = n li + n V
i ,
(1)
V =V +V .
(2)
T
l
V
We have compared two different methods for treating the raw data:
In the first procedure (a), the liquid phase volume V l is calculated from the solvent
density at a given temperature. The remaining gas phase volume V V is given by
equation (2), and allows the calculation of the amount of gas in the gas phase n V
1 at given
pressure and temperature. Then equation (1) allows the calculation of the amount of gas in
the liquid phase n l1 . It is necessary to consider the following effects in this procedure: the
amount of solvent in the liquid phase must be reduced because a certain amount evaporates;
Experimental determination of oxygen and nitrogen solvents
10
10
8
8
6
6
p / MPa
p / MPa
a
4
2
1293
b
4
2
0
0
0
0.1
0.2
0
0.1
x
0.2
x
FIGURE 5. Pressure against the mole fraction of oxygen x for (oxygen+n-octane) at T = 348.15 K:
a, without consideration of v1 and βT ; b, with consideration of v1 and βT ; , first procedure;
, second procedure.
12
a
10
10
8
8
p / MPa
p / MPa
12
6
6
4
4
2
2
0
0
b
0
0.025
x
0.05
0
0.025
0.05
x
FIGURE 6. Pressure against mole fraction of nitrogen x for (nitrogen + ethanol) at T = 348.15 K:
a, without consideration of v1 and βT ; b, with consideration of v1 and βT ; ♦, first procedure;
, second procedure.
the liquid volume is reduced at high pressures due to the compressibility of the solvent; the
total pressure p is not equal to the partial pressure of the gas p1 because the solvent has
a significant partial pressure p2 which can be estimated from the vapour pressure p2s ; the
liquid phase volume increases when a gas is dissolved due to the partial molar volume
of dissolution.
These effects become important when either the solubility or the pressure is high, or the
solvent is volatile or compressible. When the solvent activity coefficient is assumed to be
equal to unity (solvent mole fraction x2 → 1), equation (3) can be used to estimate the
1294
K. Fischer and M. Wilken
TABLE 5. Comparison of the resulting mole fraction solubility data x for
the procedures
T /K
xb
xa
102 · δ c
b
V l /cm3
a
V l /cm3
102 · δ c
xO2 + (1 − x)CH3 (CH2 )6 CH3
298.42
323.29
348.31
0.00183
0.00179
2.1
93.53
93.54
−0.01
0.18445
0.17956
2.7
98.79
98.23
0.57
0.00206
0.00206
0.1
97.01
97.02
−0.01
0.18440
0.17771
3.6
102.51
102.09
0.41
0.00183
0.00179
2.1
100.04
100.06
−0.02
0.18445
0.17956
2.7
105.85
105.60
0.23
0.00026
0.00025
4.7
142.63
142.64
−0.01
0.03347
0.03173
5.2
145.2
144.83
0.25
0.00038
0.00039
−1.9
141.24
141.28
−0.03
0.03949
0.03971
−0.6
144.06
144.78
−0.50
0.00059
0.00057
3.0
142.68
142.51
0.12
0.04364
0.04348
0.4
145.56
145.92
−0.25
xN2 + (1 − x)CH3 CH2 OH
298.22
348.20
398.02
a First procedure; b Second procedure; c δ is the deviation per cent between experimental and calculated values. Total volume of the equilibrium cell is 167.08 cm3 .
solvent partial pressure:
p2 = x2 · p2s ,
(3)
p1 = p − p2 .
(4)
and the partial pressure of the gas:
The liquid volume is calculated from the liquid molar volume of the pure solvent v2l,∗ at a
reference pressure p ∗ (usually 1 atmosphere), its compressibility β2 , and the partial molar
volume of the dissolved gas v1 (see Section 2.4).
V l = n l2 v2l,∗ · {1 − β2 ( p − p ∗ )} + v1 n l1 .
(5)
Since these calculations depend on the mole numbers of the components in the liquid
phase, the solution for the solubility data can only be found iteratively, where the mole
numbers of the compounds in the vapour phase must be calculated using suitable equations
of state by the following relation:
V∗
n iV = V V /[RT {(∂ ln ϕi i /∂ pi )T + (1/ pi )}].
(6)
For nitrogen and oxygen we have used the virial equation, where equation (6) transformed
Experimental determination of oxygen and nitrogen solvents
1295
TABLE 6. Henry coefficients H12 derived from the experimental pressure
and mole fraction at temperature T and deviation δ
System
Methanol + oxygen
Toluene + oxygen
Octane + oxygen
T /K
a /MPa
H12
b /MPa
H12
102 · δ
298.34
252.8
247.4
2.1
323.32
257.5
247.4
3.9
348.29
233.4
239.1
−2.4
298.41
104.5
103.9
0.6
323.30
96.4
99.2
−3.0
348.29
89.2
94.3
−5.7
−0.7
298.43
45.9
46.3
323.29
46.9
46.6
0.7
348.29
46.4
46.5
−0.1
Dibutylether + oxygen
298.30
47.6
47.3
0.7
n-Propanol + oxygen
298.20
150.2
152.4
−1.5
323.56
141.2
145.5
−3.1
348.20
139.7
139.3
0.2
311.03
135.8
136.1
−0.2
2-Methyltetrahydrofuran + nitrogen
n-Propanol + nitrogen
Ethanol + nitrogen
298.34
254.0
257.7
−1.5
348.18
213.9
217.6
−1.7
398.29
164.2
168.3
−2.5
298.02
296.5
290.8
1.9
348.20
252.3
254.9
−1.0
398.02
198.3
208.3
−5.0
h102 · δi
−0.9
a SRK + Huron-Vidal mixing rules + UNIQUAC; b virial equation.
to equation (7), where the second virial coefficient Bii must be known at the temperature
T to calculate the fugacity coefficient φiV .
n iV = −V V /2Bii ± [(V V /2Bii )2 + { pi (V V )2 /RT Bii }].
(7)
This iterative treatment of the raw data is applied for each single data point.
In the second procedure (b), equations of state allow the calculation of the desired
auxiliary quantities given above. They even allow a further refinement of the first procedure
because for the expression of the solvent activity coefficient γi {assumed to be unity in
equation (3)} and the real mixture behaviour of the gas phase (cross virial coefficients) no
assumptions are required. But knowledge of the EoS mixture parameters is required and
these parameters must be obtained from solubility data. Consequently, another iterative
1296
K. Fischer and M. Wilken
TABLE 7. Experimental pressure p and mole fraction x of
oxygen for (oxygen + methanol) at temperature T
T /K 298.34
323.32
348.29
x
p/MPa
x
p/MPa
x
p/MPa
0.00000
0.0169
0.00000
0.0557
0.00000
0.1511
0.00041
0.1197
0.00029
0.1296
0.00045
0.2582
0.00072
0.1976
0.00081
0.2652
0.00076
0.3295
0.00098
0.2644
0.00112
0.3455
0.00102
0.3923
0.00128
0.3403
0.00138
0.4112
0.00132
0.4616
0.00194
0.5046
0.00179
0.5173
0.00163
0.5351
0.00357
0.9113
0.00329
0.8980
0.00311
0.8843
0.00542
1.3680
0.00513
1.3613
0.00479
1.2822
0.00989
2.4517
0.00968
2.4824
0.00936
2.3578
0.01523
3.7108
0.01476
3.6939
0.01499
3.6791
0.02102
5.0358
0.02048
5.0104
0.02055
4.9808
0.02714
6.3933
0.02675
6.3994
0.02648
6.3642
0.03353
7.7667
0.03326
7.7863
0.03213
7.6782
0.04014
9.1409
0.04028
9.2255
0.03839
9.1293
TABLE 8. Experimental pressure p and mole fraction x of
propanol for (oxygen + propanol) at temperature T
T /K 298.2
323.56
348.2
x
p/MPa
x
p/MPa
x
p/MPa
0.00000
0.0028
0.00000
0.0125
0.00000
0.0414
0.00073
0.1117
0.00029
0.0535
0.00049
0.1100
0.00129
0.1954
0.00072
0.1151
0.00100
0.1816
0.00172
0.2604
0.00121
0.1843
0.00158
0.2629
0.00226
0.3396
0.00171
0.2542
0.00208
0.3324
0.00300
0.4499
0.00228
0.3361
0.00291
0.4469
0.00601
0.8909
0.00406
0.5887
0.00601
0.8728
0.00925
1.3568
0.00671
0.9683
0.01021
1.4417
0.01734
2.4833
0.01194
1.7212
0.01772
2.4321
0.02654
3.7065
0.01884
2.7253
0.02796
3.7316
0.03692
5.0188
0.02714
3.9532
0.04025
5.2208
0.04843
6.3991
0.03557
5.2221
0.05030
6.3848
0.06113
7.8387
0.04341
6.4211
0.06316
7.8107
0.07379
9.1978
0.05251
7.8376
0.07663
9.2338
Experimental determination of oxygen and nitrogen solvents
TABLE 9. Experimental pressure p and mole fraction x of
oxygen for (oxygen + octane) at temperature T
T /K 298.43
323.29
348.29
x
p/MPa
x
p/MPa
x
p/MPa
0.00000
0.0020
0.00000
0.0069
0.00000
0.0198
0.00220
0.1030
0.00206
0.1035
0.00183
0.1049
0.00405
0.1882
0.00377
0.1838
0.00341
0.1784
0.00546
0.2530
0.00519
0.2508
0.00488
0.2475
0.00702
0.3249
0.00673
0.3233
0.00633
0.3151
0.01042
0.4820
0.01002
0.4778
0.00961
0.4683
0.01852
0.8570
0.01803
0.8560
0.01066
0.5173
0.02840
1.3159
0.02635
1.2495
0.01773
0.8481
0.04985
2.3201
0.04805
2.2822
0.02664
1.2668
0.07644
3.5800
0.07421
3.5382
0.04723
2.2390
0.10390
4.8984
0.10124
4.8484
0.07317
3.4741
0.13054
6.1951
0.12889
6.2029
0.10114
4.8190
0.15897
7.5988
0.15640
7.5643
0.12874
6.1587
0.18629
8.9671
0.18440
8.9633
0.15651
7.5202
0.18445
8.9026
TABLE 10. Experimental pressure p and mole fraction x
of oxygen for (oxygen + toluene) at temperature T
T /K 298.41
323.3
348.29
x
p/MPa
x
p/MPa
x
p/MPa
0.00000
0.0039
0.00000
0.0124
0.00000
0.0329
0.00101
0.1094
0.00103
0.1117
0.00090
0.1139
0.00177
0.1884
0.00191
0.1961
0.00170
0.1851
0.00244
0.2589
0.00263
0.2657
0.00247
0.2538
0.00318
0.3359
0.00334
0.3337
0.00332
0.3302
0.00473
0.4969
0.00502
0.4954
0.00507
0.4868
0.00852
0.8893
0.00916
0.8908
0.00934
0.8679
0.01242
1.2916
0.01370
1.3227
0.01417
1.2989
0.02323
2.3942
0.02501
2.3851
0.02604
2.3539
0.03603
3.6801
0.03895
3.6711
0.04029
3.6155
0.04953
5.0137
0.05462
5.089
0.05538
4.9427
0.06373
6.3922
0.06875
6.3427
0.07081
6.2938
0.07825
7.7775
0.08470
7.7304
0.08691
7.6947
0.09267
9.1293
0.10156
9.1671
0.10282
9.0705
1297
1298
K. Fischer and M. Wilken
TABLE 11. Experimental pressure
p and mole fraction x of oxygen
for (oxygen + diethylether) at T =
298.3 K
x
p/MPa
x
p/MPa
0.00000
0.0007
0.01229
0.5929
0.00172
0.0829
0.01460
0.7057
0.00262
0.1256
0.01900
0.9225
0.00343
0.1644
0.02323
1.1320
0.00415
0.1991
0.02538
1.2392
0.00533
0.2559
0.03153
1.5488
0.00669
0.3212
0.03470
1.7096
0.00806
0.3874
0.03851
1.9049
0.00948
0.4565
0.04255
2.1129
0.01093
0.5266
TABLE 12. Experimental pressure p
and mole fraction x of 2-methyltetrahydrofuran at T = 311.03 K
x
p/MPa
x
p/MPa
0.00000
0.0222
0.00743
1.0383
0.00041
0.0782
0.01349
1.8712
0.00089
0.1435
0.02309
3.2009
0.00138
0.2107
0.03646
5.0715
0.00192
0.2841
0.04985
6.9650
0.00283
0.4082
0.06069
8.5140
0.00480
0.6771
0.06452
9.0650
data treatment has to be applied, where in addition to the balance equations the isofugacity
criterion is considered:
f il = f iV .
(8)
There are two important conditions which must be satisfied before applying the second
procedure: the EoS model should describe the phase equilibrium and solubility behaviour
reliably and especially the liquid volumes. The first condition is proved to be correct
for the majority of systems when suitable mixing rules (e.g. G E mixing rules) are used.
Of course, the interaction parameters must be fitted, and experimental data covering a
considerable concentration or pressure range must be used to fit the two or three G E
model parameters for the NRTL, UNIQUAC, or Wilson models introduced in the G E
mixing rule. A significance analysis given in Section 3 demonstrates this requirement.
Experimental determination of oxygen and nitrogen solvents
TABLE 13. Experimental pressure p and mole fraction x
of nitrogen for (nitrogen + ethanol) at temperature T
T /K 298.02
348.2
398.02
x
p/MPa
x
p/MPa
x
p/MPa
0.00000
0.0080
0.00000
0.0894
0.00000
0.5000
0.00026
0.0849
0.00038
0.1869
0.00059
0.6195
0.00052
0.1623
0.00073
0.2740
0.00121
0.7464
0.00075
0.2295
0.00132
0.4241
0.00190
0.8878
0.00100
0.3028
0.00257
0.7413
0.00313
1.1387
0.00145
0.4387
0.00407
1.1237
0.00532
1.5845
0.00254
0.7589
0.00754
1.9996
0.00813
2.1556
0.00390
1.1592
0.01222
3.1767
0.01270
3.0853
0.00691
2.0333
0.01728
4.4395
0.01834
4.2250
0.01225
3.5671
0.02293
5.8378
0.02455
5.4741
0.01883
5.4153
0.02835
7.1687
0.03122
6.8087
0.02593
7.3565
0.03397
8.5370
0.03771
8.0977
0.03347
9.3637
0.03950
9.8705
0.04364
9.2690
TABLE 14. Experimental pressure p and mole fraction x
of nitrogen for (nitrogen + propanol) at temperature T
T /K 298.34
348.18
398.29
x
p/MPa
x
p/MPa
x
p/MPa
0.00000
0.0029
0.00000
0.0415
0.00000
0.2690
0.00045
0.1171
0.00037
0.1219
0.00063
0.3737
0.00076
0.1953
0.00074
0.2000
0.00118
0.4664
0.00104
0.2671
0.00106
0.2694
0.00158
0.5332
0.00135
0.3445
0.00140
0.3421
0.00274
0.7244
0.00201
0.5136
0.00215
0.5036
0.00432
0.9865
0.00371
0.9415
0.00419
0.9376
0.00656
1.3530
0.00544
1.3761
0.00630
1.3865
0.01305
2.3926
0.00571
1.4446
0.01148
2.4816
0.02131
3.6724
0.01015
2.5481
0.01761
3.7626
0.02975
4.9305
0.01567
3.9068
0.02441
5.1632
0.03984
6.3712
0.02087
5.1648
0.03114
6.5302
0.04956
7.6988
0.02690
6.6036
0.03811
7.9251
0.06040
9.1144
0.03242
7.8973
0.04503
9.2890
0.06720
9.9682
0.03849
9.2950
1299
1300
K. Fischer and M. Wilken
10
10
b
8
8
6
6
p / MPa
p / MPa
a
4
4
2
2
0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0
0.00
0.01
0.02
x
10
0.04
0.05
0.03
0.04
0.05
2.5
c
d
8
2.0
6
1.5
p / MPa
p / MPa
0.03
x
4
1.0
2
0.5
0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07
x
0.0
0.00
0.01
0.02
x
FIGURE 7. Experimental and calculated pressure p and mole fraction of nitrogen or oxygen x
for: a, (nitrogen + 2-methyltetrahydrofuran); b, (nitrogen + ethanol); c, (nitrogen + n-propanol);
d, (oxygen + dibutyl ether); , T = 298.15 K; , T = 311.03 K; , T = 348.15 K; ♦, T =
398.15 K; ———, PSRK.
◦
•
The latter condition (liquid density representation) is known to be poorly obeyed using
simple cubic equations of state, but recognizing the importance of this property when
solving the volume balance equation (2), the Péneloux volume translation can be used
to overcome this weakness.
Unfortunately, it is not possible to separate the different contributions for the various
effects described in the first procedure, so that the EoS flash procedure (b) remains difficult.
This is the reason why we have extensively studied the resulting solubility data in order to
verify procedure (b). The iterative treatment of the raw data by procedure (b) is applied to
Experimental determination of oxygen and nitrogen solvents
10
10
b
8
8
6
6
p / MPa
p / MPa
a
4
4
2
2
0
0.00
0.01
0.02
0.03
0.04
0
0.00
0.05
0.04
0.08
x
0.16
0.20
10
c
d
8
8
6
6
p / MPa
p / MPa
0.12
x
10
4
4
2
2
0
0.00
1301
0.02
0.04
0.06
x
0.08
0.10
0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
x
FIGURE 8. Experimental and calculated pressure p and mole fraction x for: a, (oxygen + methanol);
b, (oxygen + n-octane); c, (oxygen + n-propanol); d, (oxygen + toluene}; , T = 298.15 K;
4, T = 323.15 K; ♦, T = 348.15 K; ——, PSRK.
◦
all the data points together, which allows the use of the implied information on the mixture
behavior.
The flow diagrams of both data treatment procedures are shown in figures 2, 3, and 4.
2.4. PARTIAL MOLAR VOLUMES OF GASES DISSOLVED IN LIQUIDS
It is important that the liquid phase volume increases significantly when the gas solubility
is high. Therefore, the partial molar volumes of these gases must be considered for the data
treatment in procedure (a). Fortunately, there are reliable methods for estimating the partial
molar volumes (11–14) from the critical data Tc and pc of the gases and the internal pressure
1302
K. Fischer and M. Wilken
1
0.9
0.8
0.7
F ′ (rel)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
p / MPa
FIGURE 9. Significance of pressure for the regression of PSRK interaction parameters fitted to
solubility data of oxygen (1) in n-propanol (2): , F 0 (rel) for a21 ; , F 0 (rel) for a12 ; F 0 (rel) for
a21 and a12 normalized by the value of F 0 (rel) for a12 at the pressure limit of 10 MPa.
pin of the solvents defined by:
pin = (∂U/∂ V )T = T · (∂ p/∂ T )V − p,
(9)
or:
pin = (T · α P /βT ) − p,
(10)
where βT is the isothermal compressibily coefficient, and α p is the isobaric thermal
expansion. Handa et al. (12) proposed the following expression for estimating the partial
molar volumes with a ±10 per cent accuracy:
v1 p1,c /(RT1,c ) = 0.088 + 2.763 · T · p1,c /(T1,c p2,in ).
(11)
The use of specific parameters A and B for the different gases permits an increase in
accuracy to about ±1 per cent (Cibulka and Heintz, 1995). (13,14)
v1 p1,c /(R · T1,c ) = A + B · T · p1,c /(T1,c p2,in ),
T < T2,c .
(12)
The parameters for oxygen and nitrogen are given in table 2.
The partial molar volume of a gas usually decreases when the size of the solvent
molecule of a certain class of substances (e.g. alcohols) increases. It increases by about
0.3 cm3 · mol−1 · K−1 with temperature, as Walkley and Jenkins (1968) (15) found. This
effect is caused by the solvent properties (internal pressure). The values used for the data
treatment are listed in tables 3 and 4.
When the first procedure is used in the data treatment, neglecting the partial molar
volume of the gas leads to a significant error in the volume balance. The reason for this
Experimental determination of oxygen and nitrogen solvents
1303
TABLE 15. New PSRK group interaction parameters
n
m
anm /K
bnm
amn /K
bmn
CH2
O2
−19.628
1.8192
104.28
ACH
O2
285.26
0.0000
−0.6989
0.0000
ACH2
O2
130.37
63.323
384.98
−2.1163
−1.2191
OH
O2
2018.6
0.0000
382.59
0.0000
CH3 OH
O2
1061.4
−1.2561
−516.85
1.1696
CH2 O
O2
147.51
0.0000
1986.8
0.0000
OH
N2
589.20
2.6810
2836.9
−5.2997
CH2 O
N2
3191.3
0.0000
266.63
0.0000
is that the vapour volume is assumed to be larger than it actually is. Thus, the amount of
gas calculated for the gas phase will be too high, and the solubility in the liquid solvent
too small. Furthermore, the compressibility of the solvent must be considered in order to
obtain an accurate value for the liquid volume. It is important to take into account all
the different effects having an influence on the liquid volume, as can be judged from
figures 5 to 6, where the resulting solubility data (with and without consideration of the
effects of the liquid volume) are plotted. When these results are compared with those
obtained by the second procedure, a good agreement is observed. This makes the second
procedure a very attractive alternative for obtaining reliable solubility data, because the
effects mentioned above are automatically part of the equation of state model used for the
isochoric flash calculation. Its reliability is demonstrated in table 5 for the examples of
oxygen and nitrogen solubility in ethanol and n-octane. From figures 5 to 6 it can also be
seen that both procedures provide almost the same results for the solubility data when they
are applied correctly. The experimental data listed in tables 7 to 14 and plotted in figures 7
and 8 were obtained with the help of the second procedure.
2.5. EXPERIMENTAL RESULTS
In table 6 the Henry coefficients and their deviations for both procedures are presented. It
can be seen that the results are almost identical, because at low pressure the solubility is
small and thus the partial molar volume is not significant.
In figures 7 and 8 the experimental and predicted ( p, x) data are shown for all investigated system at pressures up to 10 MPa and over the temperature range between 298 K
and 398 K. Three isothermal data sets for each system were measured. For (oxygen +
n-octane) it can be seen that the solubility is nearly identical at different temperatures
because the experimental solubility data are close to the maximum of the Henry coefficient
at T = 325 K, as shown in figure 10(c).
In tables 7 to 14 the experimental ( p, x) data for the solubility of the gases in the organic
solvents are listed.
1304
K. Fischer and M. Wilken
350
170
a
160
300
150
140
H12 / MPa
250
H12 / MPa
b
200
150
130
120
110
100
90
100
80
50
200
250
300
350
70
200
400
250
T/K
55
350
400
350
400
140
c
130
50
d
120
H12 / MPa
45
H12 / MPa
300
T/K
40
35
110
100
90
30
80
25
200
250
300
T/K
350
400
70
200
250
300
T/K
FIGURE 10. Experimental and calculated Henry coefficients H12 against temperature T for:
a, (oxygen + methanol}; b, (oxygen + n-propanol); c, (oxygen + n-octane); d, (oxygen + toluene);
experimental: , this work; +, literature data from DDB; ——, PSRK.
•
3. Fitting of the PSRK group interaction parameters
The details of the optimization procedure for the interaction parameters are available
elsewhere. (1–3) Temperature-dependent interaction parameters bi j are introduced in the
UNIFAC expression
ψi j = exp{(ai j + bi j · T )/T }.
The new PSRK group interaction parameters are listed in table 15.
(13)
Experimental determination of oxygen and nitrogen solvents
50
1305
160
a
b
150
45
H12 / MPa
H12 / MPa
140
40
130
120
35
110
30
200
250
300
350
100
200
400
250
T/K
c
260
350
400
d
240
280
H12 / MPa
H12 / MPa
400
340
300
260
240
220
200
180
220
160
200
180
200
350
T/K
340
320
300
250
300
350
400
T/K
140
200
250
300
T/K
FIGURE 11. Experimental and calculated Henry coefficients H12 against temperature T
for: a, (oxygen + dibutylether); b, (nitrogen + 2-methyltetrahydrofuran); c, (nitrogen + ethanol};
d, (nitrogen+n-propanol}; experimental: , this work; +, literature data from DDB; ——, PSRK.
•
The gradient F 0 of the objective function F with respect to the interaction parameters
ai j , F 0 = (dF/dai j ), contains information on the significance of these parameters for
the correlation of experimental data. As an example, the solubility data of (oxygen + 1propanol) were used in the following procedure: for given starting values of the interaction
parameters the gradient of the objective function with respect to these parameters was
calculated. This was repeated while the experimental database used in the fit was limited
to different pressure values. The relative gradients of F 0 (rel) with respect to a12 and a21 ,
normalized by the value of F 0 (rel) for a12 at the pressure limit of 10 MPa, are plotted
against this pressure limit. Figure 9 shows that for fitting reliable interaction parameters,
1306
K. Fischer and M. Wilken
160
95
a
150
b
140
90
120
H12 / MPa
H12 / MPa
130
110
100
85
80
90
75
80
70
60
200
250
300
T/K
70
200
400
350
170
300
T/K
400
350
100
c
160
d
90
150
140
H12 / MPa
H12 / MPa
250
130
120
80
70
110
100
250
300
350
T/K
400
60
180
230
280
T/K
330
380
FIGURE 12. Experimental and calculated Henry coefficients H12 against temperature
T for: a, (nitrogen + benzene}; b, (oxygen + ethylbenzene}; c, (nitrogen + n-heptanol};
d, (nitrogen + diethyl ether); +, experimental literature data from DDB; ——, PSRK.
solubility data up to (2 to 4) MPa are required. If only solubility data at atmospheric
pressure are used, the significance of the parameters is not guaranteed, because two
parameters are used to represent one property, the Henry coefficient. The significance for
the 1-propanol–oxygen parameter (a12 ) is lower than for the oxygen–1-propanol parameter
(a21 ), because of the limited mole fraction range (about 0.1) of (oxygen + n-propanol).
To check the reliability of the PSRK method for this application, experimental values
for Henry coefficients (from this work and literature data from DDB) are compared with
the calculated results in figure 10 to 13. All these examples demonstrate the reliability of
PSRK.
Experimental determination of oxygen and nitrogen solvents
95
1307
50
a
b
45
H12 / MPa
H12 / MPa
90
85
40
35
30
80
25
20
200
75
300
325
T/K
350
375
60
250
300
T/K
350
400
80
c
d
70
50
H12 / MPa
H12 / MPa
60
40
50
40
30
30
20
200
250
300
T/K
350
400
20
200
250
300
T/K
350
400
FIGURE 13. Experimental and calculated Henry coefficients for: a, (oxygen + n-octanol);
b, (oxygen + 2, 2, 4-trimethylpentane); c, (oxygen + n-hexane}; d, (oxygen + n-decane); +, experimental literature data from DDB; ——, PSRK.
4. Conclusion
The present study was carried out in order to extend the applicability of PSRK for the
prediction of air solubility in organic substances and their mixtures. The solubility of gases
up to 10 MPa in the temperature range between 298 K and 398 K was measured with a
static synthetic apparatus. To obtain the desired ( p, x) data from the raw data two different
methods were used and compared with each other. Both methods gave reliable and almost
identical results. PSRK now enables the prediction of oxygen and nitrogen solubilities in
organic solvents with the newly fitted interaction parameters. These solubilities find an
important application in the field of storage and transportation of organic liquids where,
1308
K. Fischer and M. Wilken
for example, the oxygen solubility can be decisive for the purity or stability of products, or
the pressure changes with temperature in closed containers must be known.
The authors thank the “Bundesministerium für Wirtschaft” for financial support via
“Arbeitsgemeinschaft industrieller Forschungsvereinigungen” (AiF project 10931N).
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Holderbaum, T.; Gmehling, J. Fluid Phase Equilib. 1991, 70, 251–265.
Fischer, K.; Gmehling, J. Fluid Phase Equilib. 1996, 121, 185–206.
Gmehling, J.; Li, J.; Fischer, K. Fluid Phase Equilib. 1997, 141, 113–127.
Horstmann, S.; Fischer, K.; Gmehling, J. Fluid Phase Equilib. 2000, 167, 173–186.
Horstmann, S. Ph.D. Thesis, University of Oldenburg. 2000.
Guilbot, P.; Théveneau, P.; Baba-ahmed, A.; Horstmann, S.; Fischer, K.; Richon, D. Fluid Phase
Equilib. 2000, 170, 193–202.
Li, J.; Fischer, K.; Gmehling, J. Fluid Phase Equilib. 1998, 143, 71–82.
Horstmann, S.; Fischer, K.; Gmehling, J. J. Chem. Thermodynamics 2000, 32, 451–464,
doi:10.1006 jcht.2000.0611.
Fischer, K.; Gmehling, J. J. Chem. Eng. Data 1994, 39, 309–314.
Daubert, T. E.; Danner, R. R. Physical and Thermodynamic Properties of Pure Chemicals.
Taylor & Francis: Washington D.C. 1989.
Handa, Y. P.; Benson, G. C. Fluid Phase Equilib. 1982, 8, 161–180.
Handa, Y. P.; D’Arcy, P. J.; Benson, G. C. Fluid Phase Equilib. 1982, 8, 181–196.
Cibulka, I.; Heintz, A. Fluid Phase Equilib. 1995, 107, 235–255.
Izák, P.; Cibulka, I.; Heintz, A. Fluid Phase Equilib. 1995, 109, 227–234.
Walkley, J.; Jenkins, W. I. Trans. Faraday Soc. 1968, 64, 19–22.
(Received 27 July 2000; in final form 24 January 2001)
WA 00/039