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Excess enthalpies of mixing methane with methanol, n-heptane, toluene and methylcyclohexane at 255.4 and 310.9 K and 13.8 MPa
ILUlOPml [QUIUHIA ELSEVIER
Fluid Phase Equilibria 114 (1996) 161- 174
Excess enthalpies of mixing methane with methanol, n-heptane, toluene and methylcyclohexane at 255.4 and 310.9 K and 13.8 MPa J.L. Oscarson a,*, j . y . Coxam b, S.E. Gillespie ~, R.M. Izatt c a Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, USA b Laboratoire de Thermodynamique et Gdnie Chemique, Universitd Blaise Pascal, 63177 Aubibre Cedex, France c Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA
Received 5 January 1995; accepted 18 June 1995
Abstract Excess molar enthalpies, H E, have been measured for methane with methanol, n-heptane, toluene, and methylcyclohexane at 310.9 and 255.4 K and at 13.8 MPa. Four ternary systems were also studied. These included (methane + (88.2% toluene + 11.8% methanol)), (methane + (93.4% toluene + 6.6% methanol)), (methane +(87.8% methylcyclohexane + 12.2% methanol)), and (methane + (93.8% methylcyclohexane + 6.2% methanol)). The H E values have been fitted using an ordinary Redlich-Kister equation and a linear least-squares method over the one-phase and the two-phase regions, respectively. A modified Redlich-Kister equation was used to fit H E values for (methane + n-heptane). The solubility of methane in the liquid phase has been determined from the plot of H E VS. the mole fraction. Keywords: Experimental; Excess enthalpies; Data thermal; Data VLE
1. I n t r o d u c t i o n Heat o f mixing, H E, data for methane with hydrocarbons are o f interest for calculations needed for process optimization in the natural gas industry. Methanol is used in the gas industry to inhibit the formation o f hydrates in transporting and processing natural gas, as well as to r e m o v e water and acid gases from unprocessed gases. Only limited information about the thermodynamic properties of these systems is available. The H E data were measured using an isothermal flow calorimeter at 255.4 and 310.9 K and 13.8 MPa. At these temperature and pressure conditions methane is in a supercritical state and the hydrocarbons are in the liquid state. Values of H E for (methane + methanol), (methane + n-heptane), (methane + toluene), (methane + methylcyclohexane) together with (methane + (88.2% toluene
* Corresponding author. Tel.: 801 378 6243; Fax.: 801 378 7799. 0378-3812/96/$15.00 © 1996ElsevierScienceB.V. All rights reserved SSDI 0378-3812(95)02813-7
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174
162 + 11.8%
methanol)),
(methane
clohexane
+ 12.2%
methanol)),
reported.
The
one-phase
H E values
region
and
(methane
+ n-heptane)
behavior
has been
the two-phase phase
have
a linear where
discussed
region
equilibrium
+ (93.4% and been
least squares a modified
has been
using
when
methanol)),
method
from
(methane
methylcyclohexane an ordinary
over
equation
physical,
+ (87.8%
+6.2%
Redlich-Kister
the two-phase
Redlich-Kister
of chemical,
determined
values,
+ 6.6%
+ (93.8%
curve-fitted
in terms
literature
toluene
(methane
was
region used.
methylcy-
methanol)) equation
over
for all systems The
enthalpy
except
of mixing
and structural
effects.
The composition
the plot of H E vs. mole
fraction
and compared
available.
The
agreement
is better
are the
of with
than 2%.
2. Experimental The 1986a).
isothermal The
flow
mixing
calorimeter
tubing
used
is made
has
been
of hastelloy-C.
described A water
(Christensen and
50%
(water
et al.,
1976;
+ glycol)
Ott
mixture
et al., were
Table l E x c e s s m o l a r e n t h a l p i e s ( H E) for ( x m e t h a n e + ( 1 - x ) m e t h a n o l ) H E (j t o o l - i ) x
0.0088 0.0175 0.0323 0.0426 0.0528 0.0625 0.0817 0.0910 0.1003 0.1177 0.1347 0.0062 0.0087 0.0230 0.0319 0.0319 0.0319 0.0616 0.0619 0.0805 0.0896 0.0900 0.0900 0.1148 0.1155 0.1155
Exp a 2 5 5 . 4 K, 13.8 M P a 0 -7 -22 - 29 - 47 - 56 - 70 - 79 - 91 - 110 - 117 310.9 K, 13.8 M P a - 5 - 9 -21 -34 -30 -27 -64 - 72 - 91 - 101 - 101 - 96 - 97 - 96 - 106
H E (j m o l - 1) Calc b
X
Exp
-5.8 - 12.0 -23.6 - 32.3 - 41.5 - 50.7 - 70.1 - 80.1 - 90.5 - 110.7 - 124.2
0.1514 0.2106 0.2379 0.3078 0.4008 0.5009 0.6008 0.7007 0.8006 0.9003 0.9475
- 121 - 112 - 110 - 99 - 85 - 72 - 54 - 40 - 26 - 12 - 4
- 121.7 - 113.0 - 109.0 - 98.6 - 84.9 - 70.1 - 55.3 - 40.5 - 25.8 - 11.0 - 4.1
- 5.8 - 8.2 - 22.5 -31.8 -31.8 -31.8 -65.5 - 65.9 - 88.7 - 100.3 - 100.8 - 100.8 - 115.9 - 115.7 - 115.7
0.1160 0. 1165 0.1273 0.1409 0.1415 0.1415 0.1416 0.1652 0.1875 0.1876 0.2087 0.2289 0.2289 0.2480 0.2662
-
-
a E s t i m a t e d uncertainties are ± 5 J m o l - 1 , Eq. 2 over r e g i o n s specified in T a b l e 10.
b
a
110 109 115 105 115 102 103 - 99 - 93 -93 - 89 - 85 - 82 - 79 - 75
Calc b
115.6 115.4 I 11.8 107.4 107.2 107.2 107.2 - 99.4 - 92.1 -92.1 - 85.1 - 78.5 - 78.5 - 72.2 - 66.3
H E values were calculated u s i n g Eq. 1 over regions specified in Table 9 and
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174 Table
163
2
Excess
molar
enthalpies
(H E) for (x
methane+(1-
x) n-heptane)
H z (Jmol-l) x
H E (Jmol
Exp a
Calc b
i)
x
Exp
a
Calc b
255.4 K, 13.8MPa 0.0226
- 2
0.0545
-
-44 101
16.7
0.3076
- 352
--371.1
- 44.9
0.3542
- 454
- 430.8
-95.9
0.4070
- 483
- 499.1
-54.5
0.4464
- 559
- 552.3
0.1014
-
0.1475
-147
0.2051
- 236
- 233.4
0.5020
- 637
- 630.1
0.2507
- 295
- 296.0
0.5478
- 691
- 689.7
0.2530
- 307
- 299.1
0.6019
- 729
- 729.4
0.3073
- 369
- 370.7
310.9 K, 13.8MPa 0.0196
- 25
- 27.0
0.2184
- 354
- 348.8
0.0384
- 53
- 54.4
0.2421
- 396
- 387.0 - 421.7
0.0736
-
109
-
108.7
0.2643
- 430
0.0739
-
112
-
109.2
0.2844
- 451
- 452.1
0.1065
-
162
-
162.2
0.3229
-499
- 507.4
0.1226
-
198
-
189.0
0.3585
- 557
- 554.1
0.1372
- 216
- 213.4
0.3887
- 577
- 589.7
0.1664
- 257
- 262.6
0.4181
- 618
- 620.0
0.1926
- 309
- 306.4
0.4429
- 656
- 641.5
,~.b S e e f o o t n o t e s Table Excess
in T a b l e
1.
3 molar
enthalpies
(H E) for (x
(j
HE x
mol
methane
+ (1 -
x) toluene)
l)
Exp a
HE (j mol Calc b
X
Exp a
i) Calc
b
255.4 K, 13.8 MPa 0.0128
4
3.6
0.2403
9
7.6
0.0257
10
6.8
0.2757
0
0.7
0,0319
10
8.2
0.3191
0.0394
11
9.7
0.3500
-
16
-
17.3
0.0808
16
15.8
0.3545
-
11
-
11.9
0.1001
19
17.3
0.4127
-
11
-
10.7
0.1409
17
17.9
0.4505
-
11
-
0.1701
16
16.5
0.4989
- 9
- 9.0
0.1898
15
14.8
0.7008
- 5
- 5. I
0.2093
10
12.4
0.8241
- 3
- 2.6
0.2194
14
11.0
0.9036
2
0.2300
5
9.3
- 9
- 9.3
10.0
-
1. I
310.9 K, 13.8 MPa 0.0552
-
13.5
0.1791
-59
-60.2
0.0802
- 22
- 21.3
0.1887
- 64
- 64.4
0.0805
- 22
- 21.4
0.2253
- 82
- 81.3
0.0983
- 29
- 27.5
0.2587
- 96
0.1042
- 29
- 29.7
0.2595
- 97
0.1486
- 47
- 47.1
:,.b S e e f o o t n o t e s
12
in T a b l e
-
1.
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174
164
Table 4 Excess molar enthalpies
(H E) for ( x
methane
+ (1-
x)methylcyclohexane)
H E (J m o l - 1) x
Exp
H E (J m o l - l)
a
Calc
255.4 K, 13.8
b
x
Exp
a
Calc b
MPa
0.0435
- 30
- 37.2
0.3986
- 468
0.0568
- 59
- 50.0
0.3996
- 485
- 476.8
0.0885
- 92
- 83.2
0.4985
- 584
- 572.8 - 573.6
130
-
- 475.7
0.1363
-
138.8
0.4996
- 574
0.2019
- 228
- 222.4
0.6010
- 472
- 473.4
0.2026
- 242
- 223.3
0.6020
- 476
- 472.3
0.2256
- 238
- 253.8
0.7067
- 356
- 355.2
0.2403
- 263
- 273.5
0.7991
- 250
- 251.9
0.3026
- 349
- 356.5
0.7998
- 247
- 251.1
0.3035
- 362
- 357.7
0.9060
-
-
0.3516
- 406
- 419.5
310.9 K, 13.8 0.0415
136
132.4
MPa
- 89
- 74.5
0.2378
- 369
- 378.1
0.0648
-
130
-
115.0
0.2575
- 430
- 402.9
0.0798
-
152
-
14 0 . 6
0.2586
- 405
- 404.3
0.1218
-
197
- 209.7
0.2941
- 442
- 445.8
0.1477
- 265
- 250.3
0.2950
- 452
- 446.8
0.1485
- 232
- 251.5
0.4098
- 554
- 549.7
0.1722
- 284
- 287.2
0.4109
- 527
- 550.4
0.2181
-340
-352.1
a.b See footnotes in Table
1.
used as bath fluids for the experiments at 310.9 K and 255.4 K, respectively. The bath temperatures were set and monitored with a Hart model 1006 platinum resistance thermometer calibrated against a Rosemount thermometer (ITS 68). The pressure was read from a 20 MPa 3D Instrument Inc. gauge with 0.25 of 1% accuracy. The back pressure regulator used to control the pressure provided a constant pressure within less than 0.1 MPa fluctuations. Alphagaz 99.9 mass per cent pure methane was used without further purification. Aldrich Reagent Grade n-heptane, methylcyclohexane, toluene and Aldrich Spectranalized methanol were stored over 0.3 nm molecular sieves to remove water and degassed for 10 min in an ultrasonic bath before use. The volumetric flow rates were converted to mass flow rates and to mole fractions using the densities of the pure components at 298.15 K and 13.8 MPa estimated as follows. The densities of methane were calculated using an equation of state (Sievers and Schulz, 1980). Densities for C 7 hydrocarbons were estimated using the densities at 298.15 K and 0.101 MPa (Handbook of Chemistry and Physics, 1993) and the isothermal compressibilities at 298.15 K of pure n-heptane (Handbook of Chemistry and Physics, 1993), methylcyclohexane (Wilhelm et al., 1979) and toluene (Riddick et al., 1986). Densities of methanol were calculated using an equation of state for the liquid (Machado and Streett, 1983). Concerning the systems (methane + (88.2% toluene + 11.8% methanol)), (methane + (93.4% toluene + 6.6% methanol)), (methane+ (87.8% methylcyclohexane + 12.2% methanol)), and (methane+ (93.8% methylcyclohexane + 6.2% methanol)) the binary mixtures containing methanol were made before entering the mixing cell. The heat of mixing methane with the liquid mixtures was then measured. The densities of
165
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174
Table 5 Excess molar enthalpies ( H E) for ( x methane + (1 - x) (88.2% toluene + 11.8% methanol)) H E (j mol 1)
H E (j m o l - 1) x
Exp '~
Calc b
255.4 K, 13.8 MPa 3.7 3 5.6 5 6.9 8 8.8 9 9.9 12 10.4 14 9.4 13 8.1 10 6.3 11 4.2 5 - 2.7 - 11 - 4.8 - 10 -4.8 - 14 310.9 K, 13.8 MPa - 12.7 - 15 - 12.8 - 10 - 25.7 - 25 - 25.9 - 30 - 38.4 - 35 -47.6 -54 - 50.5 - 49 - 50.8 - 49 -61.8 -58
0.0201 0.0330 0.0435 0.0639 0.0835 0.1022 0.1408 0.1605 0.1793 0.1973 0.2430 0.2545 0.2548 0.0511 0.0515 0.0973 0.0979 0.1392 0.1683 0.1773 0.1783 0.2123
x
Exp a
Calc b
0.3128 0.3533 0.4504 0.5004 0.5604 0.6455 0.7014 0.7445 0.8999 0.8310 0.9291 0.9425
-
-
0.2444 0.2456 0.2739 0.2753 0.3016 0.3016 0.3269 0.3502
- 71 - 76 - 84 - 90 - 80 -81 - 76 - 66
14 20 15 13 - 9 - 6 - 4 0 0 5 1I 10
16.8 20.7 15.6 13.0 - 9.9 - 5.4 - 2.5 - 0.3 7.8 4.2 9.4 10.1
- 72.2 - 72.6 - 81.6 - 82.1 - 81.2 -81.2 - 73.8 - 67.(11
,~.b See footnotes in Table 1.
the liquid mixtures were estimated using a linear combination values for ethanol-water
obtained from this calorimeter
v a l u e s r e p o r t e d b y ( O t t e t al., 1 9 8 6 b ) . T h e u n c e r t a i n t y systems
than for liquid-liquid
constant known temperature
systems
± 5% or 5 J mol-1,
in t h e p u m p
whichever
in the measured
h e a t s is g r e a t e r f o r g a s - l i q u i d
due to the difficulty of delivering
flow rate. The amount
or pressure
of pure liquid densities. Heat of mixing
were within 2 per cent of the ethanol-water
of gaseous much
more
reactant delivered
the gaseous
reactant
at a
changes with any fluctuation
so than in a liquid. The estimated
uncertainty
in is
is g r e a t e r .
3. Results and discussion The toluene),
H E data for the binary and
(methane+
ternary systems (methane methanol)),
(methane
systems
(methane
methylcyclohexane)
+ methanol),
are reported
+ (88.2% toluene + 11.8% methanol)),
+ (87.8%
methylcyclohexane
+ 12.2%
(methane
in Tables
+ n-heptane),
1-4.
(methane methanol)),
+
The
(93.4% and
(methane
H E data
+
for the
toluene + 6.6%
(methane
+ (93.8%
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174
166
Table 6 Excess molar enthalpies ( H E) for ( x methane+(1 - x)) (93.4% toluene +6.6% methanol) H E (j mol - J) Exp a
x 0.0235 0.0326 0.0430 0.0631 0.0729 0.0743 0.1010 0.1442 0.1826 0.2017 0.2192 0.0338 0.0530 0.0775 0.1007 0.1438 0.1829 0.2187 0.2187
Calc b
255.4 K, 13.8 MPa 5 5.6 6 7.4 7 9.2 12 12.0 12 13.0 11 13.1 14 14.8 16 14.6 17 11.7 10 9.4 7 6.8 310.9 K, 13.8 MPa - 5 - 6.2 - 9 - 10.6 - 17 - 17.0 - 26 - 23.9 - 36 - 38.5 - 59 - 53.3 - 65 - 67.8 - 67 - 67.8
x
H E (j mol - a) Exp a
Calc b
0.2313 0.2509 0.2520 0.3087 0.3188 0.3958 0.4835 0.6518 0.8179 0.8999
6 3 - 5 - 10 - 16 - 13 - 10 - 3 - 3 7
4.8 1.2 1.0 - 14.3 - 14.0 - 11.4 -8.4 - 2.7 3.0 5.7
0.2514 0.2514 0.2815 0.3093 0.3350 0.3589
-
-
84 82 85 82 77 74
91.3 91.3 86.4 81.9 77.8 77.1
a,b See footnotes in Table 1.
methylcyclohexane
+ 6 . 2 % m e t h a n o l ) ) a r e r e p o r t e d in T a b l e s 5 - 8 .
r e g i o n h a v e b e e n f i t t e d to t h e m o d i f i e d R e d l i c h - K i s t e r
T h e H E v a l u e s in t h e o n e - p h a s e
equation
N Y'~ C . ( 1 - 2 x ) n HE(Jmol-')=x(1-x)
n=OM 1 +
(1)
E Dm(1m=l
2x)m
w h e r e x is t h e m o l e f r a c t i o n o f m e t h a n e in t h e m i x t u r e s . T h e R e d l i c h - K i s t e r and standard deviations
C, and D m parameters
s a r e g i v e n in T a b l e 9 a l o n g w i t h t h e m o l e f r a c t i o n r e g i o n s f o r w h i c h t h e
equation applies. The modified Redlich-Kister an o r d i n a r y R e d l i c h - K i s t e r
e q u a t i o n w a s u s e d to fit ( m e t h a n e + n - h e p t a n e ) w h i l e
equation was used for the remaining systems. In the two-phase region the
H E v a l u e s w e r e f i t t e d to t h e e q u a t i o n
(2)
HE=Ao+AIx
T h e A n p a r a m e t e r s f o r E q . (2) a n d s t a n d a r d d e v i a t i o n s s a r e g i v e n in T a b l e 10 a l o n g w i t h t h e m o l e fraction regions for which
the equation
applies. The
experimental
and calculated
H E values are
p l o t t e d v s . t h e m e t h a n e m o l e f r a c t i o n x in F i g s . 1 - 8 . T h e s o l u b i l i t i e s o f m e t h a n e in t h e l i q u i d p h a s e have been determined
from the curves. The basis for this determination
is that, w h e n a r e g i o n o f
J.L. Oscarson et al. / Fluid Phase Equilihria 114 (1996) 161-174 Table
167
7
Excess molar enthalpies
( H E) f o r ( x
H E (j tool x
methane
x) (87.8%
methylcyclohexane
1)
+ 12.2% HE
Exp a 255.4
+ (1 -
Calc
6
(j
tool
methanol)) i)
x
E x p '~
Calc
b
- 445.9
K, 13.8 MPa
0.0526
- 42
- 43. l
0.3997
- 436
0.0561
- 50
- 46.3
0.4500
- 521
- 495.6
0.0999
- 99
- 89.9
0.4996
- 527
- 536. I
0.1508
-
14 6 . 7
0.5997
- 400
- 405.4
0.2033
- 210
146
- 209.9
0.703(/
- 288
- 295.2
0.2497
- 269
- 267.7
0.7998
-
194
-
0.3007
-321
-331.2
0.8498
-
127
-
0.3522
- 391
- 393.0
0.8999
- 73
- 85.3
- 268.8
310.9
-
K, 13.8
192.0 138.7
MPa
0.0308
- 53
- 42.3
0.2037
- 284
0.0598
- 98
- 82.0
0.2234
- 294
- 292.2
0.0870
-
130
-
118.8
0.2412
- 317
- 312.8
0.(/870 0.1128
-
108
-
118.8
0.2422
- 321
- 313.9
-
154
-
153.2
0.2761
-330
-351.2
0.1371
-
163
-
185.1
0.3092
-399
-385.1
0.1371
-
188
-
185.1
0.3092
-404
-385.1
0.1378
- 205
-
186.0
0.3371
- 383
- 411.6
0.1378
-
-
186.0
0.3384
-416
0.1602
- 218
- 214.8
0.3900
- 450
- 455.6
0.1820
- 241
- 242.2
0.3900
- 466
- 455.6
0.2027
- 266
- 267.6
~'~' S e e
footnotes in
155
Table
412.8
1.
immiscibility exists, the H E v s . x curve is linear. The composition of the two-phase region is then given by the intersection of the curve with the linear regions. The negative H E values observed for the systems (methane + methanol), (methane + n-heptane), (methane + methylcyclohexane) and (methane + (methylcyclohexane + methanol)) result from the condensation of the supercritical methane into the liquid phase. The H E regions with curvature correspond to a single liquid phase and H E regions with a straight line correspond to a (vapor + liquid) phase equilibrium where the composition of each phase is fixed. Measurements in the single vapor phase region were not possible due to high flow rates necessary for the gas. Mixing problems occur when high flow rates are used for the gas. For (methane + methanol) the curve represented in Fig. 1 shows a phase separation for methane mole fractions 0.10 and 0.13 at temperatures 310.9 K and 255.4 K, respectively. These results agree with those found by Hong et al. (1987), i.e., 0.1018 and 0.1224 at 310 and 250 K, respectively. The H E values are lower than those where the pure liquid is less associated. Heat of mixing data for (methane + toluene) vs. methane mole fraction represented in Fig. 3 show at 255.4 K positive or low negative values before the phase split. This results from the competition between the exothermic effect due to the condensation of gaseous methane into liquid toluene and the endothermic effect of breaking rr-Tr interactions in pure toluene. At 310.9 K, these aromatic interactions are weaker and the measured H E values are slightly negative. The methane mole fraction where two phases appear is
J.L. Oscarson et aL /Fluid Phase Equilibria 114 (1996) 161-174
168
Table 8 E x c e s s m o l a r e n t h a l p i e s ( H E) for ( x m e t h a n e + (1 - x ) (93.8% m e t h y l c y c l o h e x a n e + 6.2% m e t h a n o l ) ) H E (Jmol-l) x
Exp a
H E (Jmol-i) Calc b
x
Exp a
Calc b
255.4 K, 1 3 . 8 M P a 0.1044
- 117
- 112.4
0.5026
- 555
- 541.0
0.1481
- 168
- 165.0
0.5019
- 537
- 540.6
0.2041
- 234
- 234.3
0.6078
-449
- 447.7
0.2 527
- 291
-294.6
0.6992
- 342
- 343.6
0.3014
- 354
- 353.3
0.8027
- 224
- 225.8
0.3523
- 416
- 410.9
0.9029
- 115
- 111.7
-472
- 486.8 - 331.4
0.4293
310.9 K, 1 3 . 8 M P a 0.0321
- 52
- 48.0
0.2301
- 333
0.0623
-97
- 93.2
0.2493
- 351
- 356.0
0.0 906 0.1172
- 137 - 178
- 135.3 - 174.4
0.2849 0.2861
- 427 - 412
- 399.5 -400.9
0.1424
- 196
- 210.9
0.3173
- 432
- 436.3
0.1661
- 230
- 244.6
0.3469
- 456
-467.3
0.1669
- 241
- 245.7
0.3469
-475
-467.3
0.1895 0.2 099
- 278 - 308
- 277.1 - 304.7
0.3991 0.4050
- 548 -479
-515.2 -520.0
a.b See fo otnotes in Table 1. Table 9 C o e f f i c i e n t s C n, D m and s t a n d a r d d e v i a t i o n s s for l e a s t - s q u a r e s r e p r e s e n t a t i o n of H E (J m o l - ~ ) by Eq. (1) X
0<
x<0.10
0
T (K) CO (xmethane+(lx)methanol) 310.9 -2640.5
Cl
255.4
1820.7
-2458.3
S
1719.1
3 4
(x methane+(l - x)toluene) 0< 0<
x < 0.22 x < 0.33
0< 0<
x<0.41 x<0.51
310.9 255.4
-800.59 -237.07
609.78 536.80
1
3
(x methane+(1 - x)methylcyclohexane) 310.9 255.4
- 2370.5 2295.6
(x methane+(10< x<0.28 0< x<0.28
5423.9 1535.4
x)(88.2%toluene+
310.9 255.4
-560.87 -248.11
14 11
ll.8%methanol)) 332.61 453.83
4 5
(x methane+(1 - x)(93.4%toluene+6.6%methanol)) 0< 0<
x<0.26 x < 0.32
310.9 255.4
- 713.81 -253.78
563.15 522.88
(x methane+(l - x)(87.8%methylcyclohexane+ 0< x<0.39
310.9
0<
255.4 (xmethane+(1
x < 0.49
-
2067.4
12.2%methanol))
692.08
-2145.7 1431.7 x)(93.8%methylcyclohexane+6.2% 2314.0 821.14
0<
x < 0.41
310.9
0<
x<0.52
255.4 T(K)
- 2157.8
- 2509.2
0<
x<0.44
CO ( x m e t h a n e + ( 1 - x) n-heptane) 310.9 - 2690.3
0<
x<0.60
255.4
X
5 3 15 11 methanol)) 17
1208.3 Dj
8 D2
D3
0 4
1.0391
0.20604
0.99126
- 1.2235
1.1117
0.54549
- 2.5962 3.6327
8
13
169
J.L. Oscarson et a l . / Fluid Phase Equilibria 114 (1996) 161-174 Table 10 Coefficients A , a n d standard deviations s for l e a s t - s q u a r e s representation o f H E (J m o l - i ) T (K) 310.9 255.4 255.4 255.4 310.9 255.4 310.9 255.4 255.4 255.4
region ( x m e t h a n e + (1 0.10 < x < 0.99 0.13 < x < 0.99 ( x m e t h a n e + (1 0.33 < x < 0.99 ( x m e t h a n e + (1 0.51 < x < 0.99 ( x m e t h a n e + (1 0.28 < x < 0.99 0.28 < x < 0.99 ( x m e t h a n e + (1 0.26 < x < 0.99 0.32 < x < 0.99 ( x methane + ( 10.49 < x < 0.99 ( x m e t h a n e + (1 0.52 < x < 0.99
by Eq. (2)
Ao
Ai
s
- 144.04 - 144.12
263.36 147.82
9 3
x) methanol)
x ) toluene) - 18.903 19.756 x) methylcyclohexane) - 1145.4 1.1181 x ) (88.2% toluene + 11.8% m e t h a n o l ) - 169.43 292.54 -39.184 52.261 x ) 9 9 3 . 4 % toluene + 6.6% m e t h a n o l ) ) - 131.89 161.56 - 24.819 33.957 x ) (87.8% m e t h y l c y c l o h e x a n e + 12.2% m e t h a n o l ) ) - 1044.8 1066.3 x ) (93.8% m e t h y l c y c l o h e x a n e + 6.2% m e t h a n o l ) ) - 1139.7 1138.5
1 4 2 3 2 4 11 3
0.33 at 255.4 K. Chang and Kobayashi (1967a) report 0.3500 for the [methane + toluene] binary system at the same temperature. The same behavior was observed with the (methane + (toluene + methanol)) systems ( Figs. 5 and 6). The H E values measured for the (methane + 0
t
-50
g/ {
-100
-150
i
0.0
3' *o
I
0.2
i
I
/
i
0.4
i
0.6
0
I
0.8
1.0
X methane
Fig. 1. Plot o f H z for ( x m e t h a n e + (1 - x ) m e t h a n o l ) at 13.8 MPa; O , 310 K; z~, 255 K; - o v e r region specified in Table 9 and calculated u s i n g Eq. 2 o v e r region specified in T a b l e 10.
, calculated u s i n g Eq. 1
170
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174 •
i
•
i
'
i
-200
E
A
311~~
-400
-600
-800
i
0.0
I
,
0.2
I
,
0.4 x
I
=
0.6
I
1.0
0.8
methane
Fig. 2. Plot of H E for ( x methane +(1 - x) n-heptane) at 13.8 MPa; ©, 310 K; A, 255 K; - 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
50
.
i
•
I
i
i
,
I
,
i
, calculated using Eq.
i
A
o
-100
-150
, 0.0
0.2
0.4
I 0.6
x
~
I 0.8
,
1.0
methane
Fig. 3. Plot of H E for ( x m e t h a n e + ( l - x) toluene) at 13.8 MPa; C), 310 K; A, 255 K; - over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
, calculated using Eq. 1
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174
'
f
'
I
'
I
'
I
171
'
-200 K
E
-400
311K ~
~
0.2
0.4
-600 0.0
0.6
0.8
1.0
x methane
Fig. 4. Plot of H E for (x methane+(l - x) methylcyclohexane) at 13.8 MPa; O, 310 K; A, 255 K; - using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
, calculated
50
E
-50
311°K~ 0
-100
-150
=
0.0
I
0.2
=
I
,
0.4
I
0.6
i
I
0.8
J
1.0
x methane
Fig. 5. Plot of H E for (x methane+ ( 1 - x ) (88.2% toluene+ 11.8% methanol)) at 13.8 MPa; ©, 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174
172
50
,
"5 E "~ -50
,
,
311K
-100
i
- 150
I
0.0
i
f
0.2
i
I
0.4 x
I
i
0.6
i
0.8
1.0
methane
Fig. 6. Plot of H E for ( x m e t h a n e + ( 1 - x ) ( 9 3 . 4 % toluene+6.6% methanol)) at 13.8 MPa; O, 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
0
'
I
'
i
,
i
,
,
I
i
i
,
5K
-200
~.~
311K ~
%
~
-400
-600
,
0.0
I
0.2
~
I
0.4 0.6 x methane
I
0.8
1.0
Fig. 7. Plot of H E for ( x methane+(1 - x) (87.8% methylcyclohexane + 12.2% methanol)) at 13.8 MPa; O, 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
173
I.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174 '
I
'
I
'
I
'
I
i
I
'
I
i
-200
E
-400
o -600
i
0.0
I
0.2
i
[
,
0.4
0.6
0.8
1.0
x methane
Fig. 8. Plot of H E for (x methane+(l - x) (93.8% methylcyclohexane+6.2% methanol)) at 13.8 MPa; C), 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
(methylcyclohexane + methanol)) system were smaller than those for the binary system where smaller interaction forces exist. The phase splitting on the (methane + methylcyclohexane) plot in Fig. 4 appears for a methane mole fraction of 0.51 and can be compared with the value 0.4950 found by Chang and Kobayashi (1967b).
4. List of symbols
Ao Cn
coefficients in Eq. (2) coefficients in Eq. (1) O m coefficients in Eq. (1) H E excess molar enthalpy (J mol- l) s standard deviation T temperature (K) x mole fraction
Acknowledgements
This work was supported by the Gas Processors Association. J.Y. Coxam is grateful to the service des bourses de Recherche Scientifique et Technique de I'OTAN and the Fulbright Program for financial support.
174
J.L. Oscarson et aL / F l u i d Phase Equilibria 114 (1996) 161-174
References Chang, H.L. and Kobayashi, R., 1967a. Vapor-liquid equilibria of the methane-toluene system at low temperatures and high pressures. J. Chem. Eng. Data, 12: 517-520. Chang, H.L. and Kobayashi, R., 1967b. Vapor-liquid equilibria of the methane-methylcyclohexane system at low temperatures and high pressures. J. Chem. Eng. Data, 12: 520-523. Christensen, J.J., Hansen, L.D., Eatough, D.J., Izatt, R.M. and Hart, R.M., 1976. Isothermal high-pressure flow calorimeter. Rev. Sci. Instrum., 47: 730-734. CRC Handbook of Chemistry and Physics, 1993. Lide, D.R. (Editor), 74th edn., CRC Press, Boca Raton, FL. Hong, J.H., Malone, P.V., Jett, M.D. and Kobayashi, R., 1987. The measurement and interpretation of the fluid-phase equilibria of a normal fluid in a hydrogen bonding solvent: the methane-methanol system. Fluid Phase Equilibria, 38: 83-96. Machado, J.R.S. and Streett, W.B., 1983. Equation of state and thermodynamic properties of liquid methanol from 298 to 489 K and pressure to 1040 bar. J. Chem. Eng. Data, 28: 218-223. Ott, J.B., Stouffer, C.E., Cornett, G.V., Woodfield, B.F., Wirthlin, R.C., Christensen, J.J. and Deiters, U.K., 1986a. Excess enthalpies for (Ethanol+water) at 298.15 K and pressures 0.4, 5, 10, 15 MPa. J. Chem. Thermodyn., 18: 1-12. Ott, J.B., Comett, G.V., Stouffer, C.E., Woodfield, B.F., Guanquan, C. and Christensen, J.J., 1986b. Excess enthalpies for (Ethanol+water) at 323.15, 333.15, 348.15, and 373.15 K and from 0.4 and 15 MPa. J. Chem. Thermodyn., 18: 867-875. Riddick, J.A., Bunger, W.B. and Sakano, T.K., 1986. Organic Solvent, Physical Properties and Methods of Purification, 4th edn., Wiley, New York. Sievers, U. and Schulz, S., 1980. An equation of state for methane in the form of Bender's equation for temperatures between 91 K and 625 K and pressure up to 500 bar. Fluid Phase Equilibria, 5: 35-54. Wilhelm, E., Grolier, J.-P.E. and Karbalai Ghassemi, M.H., 1979. Molar heat capacity of binary liquid mixtures: 1,2-dichloroethane + cyclohexane and 1,2-dichloroethane and methylcyclohexane. Thermochim. Acta, 28: 59-69.
Fluid Phase Equilibria 114 (1996) 161- 174
Excess enthalpies of mixing methane with methanol, n-heptane, toluene and methylcyclohexane at 255.4 and 310.9 K and 13.8 MPa J.L. Oscarson a,*, j . y . Coxam b, S.E. Gillespie ~, R.M. Izatt c a Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, USA b Laboratoire de Thermodynamique et Gdnie Chemique, Universitd Blaise Pascal, 63177 Aubibre Cedex, France c Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA
Received 5 January 1995; accepted 18 June 1995
Abstract Excess molar enthalpies, H E, have been measured for methane with methanol, n-heptane, toluene, and methylcyclohexane at 310.9 and 255.4 K and at 13.8 MPa. Four ternary systems were also studied. These included (methane + (88.2% toluene + 11.8% methanol)), (methane + (93.4% toluene + 6.6% methanol)), (methane +(87.8% methylcyclohexane + 12.2% methanol)), and (methane + (93.8% methylcyclohexane + 6.2% methanol)). The H E values have been fitted using an ordinary Redlich-Kister equation and a linear least-squares method over the one-phase and the two-phase regions, respectively. A modified Redlich-Kister equation was used to fit H E values for (methane + n-heptane). The solubility of methane in the liquid phase has been determined from the plot of H E VS. the mole fraction. Keywords: Experimental; Excess enthalpies; Data thermal; Data VLE
1. I n t r o d u c t i o n Heat o f mixing, H E, data for methane with hydrocarbons are o f interest for calculations needed for process optimization in the natural gas industry. Methanol is used in the gas industry to inhibit the formation o f hydrates in transporting and processing natural gas, as well as to r e m o v e water and acid gases from unprocessed gases. Only limited information about the thermodynamic properties of these systems is available. The H E data were measured using an isothermal flow calorimeter at 255.4 and 310.9 K and 13.8 MPa. At these temperature and pressure conditions methane is in a supercritical state and the hydrocarbons are in the liquid state. Values of H E for (methane + methanol), (methane + n-heptane), (methane + toluene), (methane + methylcyclohexane) together with (methane + (88.2% toluene
* Corresponding author. Tel.: 801 378 6243; Fax.: 801 378 7799. 0378-3812/96/$15.00 © 1996ElsevierScienceB.V. All rights reserved SSDI 0378-3812(95)02813-7
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174
162 + 11.8%
methanol)),
(methane
clohexane
+ 12.2%
methanol)),
reported.
The
one-phase
H E values
region
and
(methane
+ n-heptane)
behavior
has been
the two-phase phase
have
a linear where
discussed
region
equilibrium
+ (93.4% and been
least squares a modified
has been
using
when
methanol)),
method
from
(methane
methylcyclohexane an ordinary
over
equation
physical,
+ (87.8%
+6.2%
Redlich-Kister
the two-phase
Redlich-Kister
of chemical,
determined
values,
+ 6.6%
+ (93.8%
curve-fitted
in terms
literature
toluene
(methane
was
region used.
methylcy-
methanol)) equation
over
for all systems The
enthalpy
except
of mixing
and structural
effects.
The composition
the plot of H E vs. mole
fraction
and compared
available.
The
agreement
is better
are the
of with
than 2%.
2. Experimental The 1986a).
isothermal The
flow
mixing
calorimeter
tubing
used
is made
has
been
of hastelloy-C.
described A water
(Christensen and
50%
(water
et al.,
1976;
+ glycol)
Ott
mixture
et al., were
Table l E x c e s s m o l a r e n t h a l p i e s ( H E) for ( x m e t h a n e + ( 1 - x ) m e t h a n o l ) H E (j t o o l - i ) x
0.0088 0.0175 0.0323 0.0426 0.0528 0.0625 0.0817 0.0910 0.1003 0.1177 0.1347 0.0062 0.0087 0.0230 0.0319 0.0319 0.0319 0.0616 0.0619 0.0805 0.0896 0.0900 0.0900 0.1148 0.1155 0.1155
Exp a 2 5 5 . 4 K, 13.8 M P a 0 -7 -22 - 29 - 47 - 56 - 70 - 79 - 91 - 110 - 117 310.9 K, 13.8 M P a - 5 - 9 -21 -34 -30 -27 -64 - 72 - 91 - 101 - 101 - 96 - 97 - 96 - 106
H E (j m o l - 1) Calc b
X
Exp
-5.8 - 12.0 -23.6 - 32.3 - 41.5 - 50.7 - 70.1 - 80.1 - 90.5 - 110.7 - 124.2
0.1514 0.2106 0.2379 0.3078 0.4008 0.5009 0.6008 0.7007 0.8006 0.9003 0.9475
- 121 - 112 - 110 - 99 - 85 - 72 - 54 - 40 - 26 - 12 - 4
- 121.7 - 113.0 - 109.0 - 98.6 - 84.9 - 70.1 - 55.3 - 40.5 - 25.8 - 11.0 - 4.1
- 5.8 - 8.2 - 22.5 -31.8 -31.8 -31.8 -65.5 - 65.9 - 88.7 - 100.3 - 100.8 - 100.8 - 115.9 - 115.7 - 115.7
0.1160 0. 1165 0.1273 0.1409 0.1415 0.1415 0.1416 0.1652 0.1875 0.1876 0.2087 0.2289 0.2289 0.2480 0.2662
-
-
a E s t i m a t e d uncertainties are ± 5 J m o l - 1 , Eq. 2 over r e g i o n s specified in T a b l e 10.
b
a
110 109 115 105 115 102 103 - 99 - 93 -93 - 89 - 85 - 82 - 79 - 75
Calc b
115.6 115.4 I 11.8 107.4 107.2 107.2 107.2 - 99.4 - 92.1 -92.1 - 85.1 - 78.5 - 78.5 - 72.2 - 66.3
H E values were calculated u s i n g Eq. 1 over regions specified in Table 9 and
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174 Table
163
2
Excess
molar
enthalpies
(H E) for (x
methane+(1-
x) n-heptane)
H z (Jmol-l) x
H E (Jmol
Exp a
Calc b
i)
x
Exp
a
Calc b
255.4 K, 13.8MPa 0.0226
- 2
0.0545
-
-44 101
16.7
0.3076
- 352
--371.1
- 44.9
0.3542
- 454
- 430.8
-95.9
0.4070
- 483
- 499.1
-54.5
0.4464
- 559
- 552.3
0.1014
-
0.1475
-147
0.2051
- 236
- 233.4
0.5020
- 637
- 630.1
0.2507
- 295
- 296.0
0.5478
- 691
- 689.7
0.2530
- 307
- 299.1
0.6019
- 729
- 729.4
0.3073
- 369
- 370.7
310.9 K, 13.8MPa 0.0196
- 25
- 27.0
0.2184
- 354
- 348.8
0.0384
- 53
- 54.4
0.2421
- 396
- 387.0 - 421.7
0.0736
-
109
-
108.7
0.2643
- 430
0.0739
-
112
-
109.2
0.2844
- 451
- 452.1
0.1065
-
162
-
162.2
0.3229
-499
- 507.4
0.1226
-
198
-
189.0
0.3585
- 557
- 554.1
0.1372
- 216
- 213.4
0.3887
- 577
- 589.7
0.1664
- 257
- 262.6
0.4181
- 618
- 620.0
0.1926
- 309
- 306.4
0.4429
- 656
- 641.5
,~.b S e e f o o t n o t e s Table Excess
in T a b l e
1.
3 molar
enthalpies
(H E) for (x
(j
HE x
mol
methane
+ (1 -
x) toluene)
l)
Exp a
HE (j mol Calc b
X
Exp a
i) Calc
b
255.4 K, 13.8 MPa 0.0128
4
3.6
0.2403
9
7.6
0.0257
10
6.8
0.2757
0
0.7
0,0319
10
8.2
0.3191
0.0394
11
9.7
0.3500
-
16
-
17.3
0.0808
16
15.8
0.3545
-
11
-
11.9
0.1001
19
17.3
0.4127
-
11
-
10.7
0.1409
17
17.9
0.4505
-
11
-
0.1701
16
16.5
0.4989
- 9
- 9.0
0.1898
15
14.8
0.7008
- 5
- 5. I
0.2093
10
12.4
0.8241
- 3
- 2.6
0.2194
14
11.0
0.9036
2
0.2300
5
9.3
- 9
- 9.3
10.0
-
1. I
310.9 K, 13.8 MPa 0.0552
-
13.5
0.1791
-59
-60.2
0.0802
- 22
- 21.3
0.1887
- 64
- 64.4
0.0805
- 22
- 21.4
0.2253
- 82
- 81.3
0.0983
- 29
- 27.5
0.2587
- 96
0.1042
- 29
- 29.7
0.2595
- 97
0.1486
- 47
- 47.1
:,.b S e e f o o t n o t e s
12
in T a b l e
-
1.
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174
164
Table 4 Excess molar enthalpies
(H E) for ( x
methane
+ (1-
x)methylcyclohexane)
H E (J m o l - 1) x
Exp
H E (J m o l - l)
a
Calc
255.4 K, 13.8
b
x
Exp
a
Calc b
MPa
0.0435
- 30
- 37.2
0.3986
- 468
0.0568
- 59
- 50.0
0.3996
- 485
- 476.8
0.0885
- 92
- 83.2
0.4985
- 584
- 572.8 - 573.6
130
-
- 475.7
0.1363
-
138.8
0.4996
- 574
0.2019
- 228
- 222.4
0.6010
- 472
- 473.4
0.2026
- 242
- 223.3
0.6020
- 476
- 472.3
0.2256
- 238
- 253.8
0.7067
- 356
- 355.2
0.2403
- 263
- 273.5
0.7991
- 250
- 251.9
0.3026
- 349
- 356.5
0.7998
- 247
- 251.1
0.3035
- 362
- 357.7
0.9060
-
-
0.3516
- 406
- 419.5
310.9 K, 13.8 0.0415
136
132.4
MPa
- 89
- 74.5
0.2378
- 369
- 378.1
0.0648
-
130
-
115.0
0.2575
- 430
- 402.9
0.0798
-
152
-
14 0 . 6
0.2586
- 405
- 404.3
0.1218
-
197
- 209.7
0.2941
- 442
- 445.8
0.1477
- 265
- 250.3
0.2950
- 452
- 446.8
0.1485
- 232
- 251.5
0.4098
- 554
- 549.7
0.1722
- 284
- 287.2
0.4109
- 527
- 550.4
0.2181
-340
-352.1
a.b See footnotes in Table
1.
used as bath fluids for the experiments at 310.9 K and 255.4 K, respectively. The bath temperatures were set and monitored with a Hart model 1006 platinum resistance thermometer calibrated against a Rosemount thermometer (ITS 68). The pressure was read from a 20 MPa 3D Instrument Inc. gauge with 0.25 of 1% accuracy. The back pressure regulator used to control the pressure provided a constant pressure within less than 0.1 MPa fluctuations. Alphagaz 99.9 mass per cent pure methane was used without further purification. Aldrich Reagent Grade n-heptane, methylcyclohexane, toluene and Aldrich Spectranalized methanol were stored over 0.3 nm molecular sieves to remove water and degassed for 10 min in an ultrasonic bath before use. The volumetric flow rates were converted to mass flow rates and to mole fractions using the densities of the pure components at 298.15 K and 13.8 MPa estimated as follows. The densities of methane were calculated using an equation of state (Sievers and Schulz, 1980). Densities for C 7 hydrocarbons were estimated using the densities at 298.15 K and 0.101 MPa (Handbook of Chemistry and Physics, 1993) and the isothermal compressibilities at 298.15 K of pure n-heptane (Handbook of Chemistry and Physics, 1993), methylcyclohexane (Wilhelm et al., 1979) and toluene (Riddick et al., 1986). Densities of methanol were calculated using an equation of state for the liquid (Machado and Streett, 1983). Concerning the systems (methane + (88.2% toluene + 11.8% methanol)), (methane + (93.4% toluene + 6.6% methanol)), (methane+ (87.8% methylcyclohexane + 12.2% methanol)), and (methane+ (93.8% methylcyclohexane + 6.2% methanol)) the binary mixtures containing methanol were made before entering the mixing cell. The heat of mixing methane with the liquid mixtures was then measured. The densities of
165
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174
Table 5 Excess molar enthalpies ( H E) for ( x methane + (1 - x) (88.2% toluene + 11.8% methanol)) H E (j mol 1)
H E (j m o l - 1) x
Exp '~
Calc b
255.4 K, 13.8 MPa 3.7 3 5.6 5 6.9 8 8.8 9 9.9 12 10.4 14 9.4 13 8.1 10 6.3 11 4.2 5 - 2.7 - 11 - 4.8 - 10 -4.8 - 14 310.9 K, 13.8 MPa - 12.7 - 15 - 12.8 - 10 - 25.7 - 25 - 25.9 - 30 - 38.4 - 35 -47.6 -54 - 50.5 - 49 - 50.8 - 49 -61.8 -58
0.0201 0.0330 0.0435 0.0639 0.0835 0.1022 0.1408 0.1605 0.1793 0.1973 0.2430 0.2545 0.2548 0.0511 0.0515 0.0973 0.0979 0.1392 0.1683 0.1773 0.1783 0.2123
x
Exp a
Calc b
0.3128 0.3533 0.4504 0.5004 0.5604 0.6455 0.7014 0.7445 0.8999 0.8310 0.9291 0.9425
-
-
0.2444 0.2456 0.2739 0.2753 0.3016 0.3016 0.3269 0.3502
- 71 - 76 - 84 - 90 - 80 -81 - 76 - 66
14 20 15 13 - 9 - 6 - 4 0 0 5 1I 10
16.8 20.7 15.6 13.0 - 9.9 - 5.4 - 2.5 - 0.3 7.8 4.2 9.4 10.1
- 72.2 - 72.6 - 81.6 - 82.1 - 81.2 -81.2 - 73.8 - 67.(11
,~.b See footnotes in Table 1.
the liquid mixtures were estimated using a linear combination values for ethanol-water
obtained from this calorimeter
v a l u e s r e p o r t e d b y ( O t t e t al., 1 9 8 6 b ) . T h e u n c e r t a i n t y systems
than for liquid-liquid
constant known temperature
systems
± 5% or 5 J mol-1,
in t h e p u m p
whichever
in the measured
h e a t s is g r e a t e r f o r g a s - l i q u i d
due to the difficulty of delivering
flow rate. The amount
or pressure
of pure liquid densities. Heat of mixing
were within 2 per cent of the ethanol-water
of gaseous much
more
reactant delivered
the gaseous
reactant
at a
changes with any fluctuation
so than in a liquid. The estimated
uncertainty
in is
is g r e a t e r .
3. Results and discussion The toluene),
H E data for the binary and
(methane+
ternary systems (methane methanol)),
(methane
systems
(methane
methylcyclohexane)
+ methanol),
are reported
+ (88.2% toluene + 11.8% methanol)),
+ (87.8%
methylcyclohexane
+ 12.2%
(methane
in Tables
+ n-heptane),
1-4.
(methane methanol)),
+
The
(93.4% and
(methane
H E data
+
for the
toluene + 6.6%
(methane
+ (93.8%
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174
166
Table 6 Excess molar enthalpies ( H E) for ( x methane+(1 - x)) (93.4% toluene +6.6% methanol) H E (j mol - J) Exp a
x 0.0235 0.0326 0.0430 0.0631 0.0729 0.0743 0.1010 0.1442 0.1826 0.2017 0.2192 0.0338 0.0530 0.0775 0.1007 0.1438 0.1829 0.2187 0.2187
Calc b
255.4 K, 13.8 MPa 5 5.6 6 7.4 7 9.2 12 12.0 12 13.0 11 13.1 14 14.8 16 14.6 17 11.7 10 9.4 7 6.8 310.9 K, 13.8 MPa - 5 - 6.2 - 9 - 10.6 - 17 - 17.0 - 26 - 23.9 - 36 - 38.5 - 59 - 53.3 - 65 - 67.8 - 67 - 67.8
x
H E (j mol - a) Exp a
Calc b
0.2313 0.2509 0.2520 0.3087 0.3188 0.3958 0.4835 0.6518 0.8179 0.8999
6 3 - 5 - 10 - 16 - 13 - 10 - 3 - 3 7
4.8 1.2 1.0 - 14.3 - 14.0 - 11.4 -8.4 - 2.7 3.0 5.7
0.2514 0.2514 0.2815 0.3093 0.3350 0.3589
-
-
84 82 85 82 77 74
91.3 91.3 86.4 81.9 77.8 77.1
a,b See footnotes in Table 1.
methylcyclohexane
+ 6 . 2 % m e t h a n o l ) ) a r e r e p o r t e d in T a b l e s 5 - 8 .
r e g i o n h a v e b e e n f i t t e d to t h e m o d i f i e d R e d l i c h - K i s t e r
T h e H E v a l u e s in t h e o n e - p h a s e
equation
N Y'~ C . ( 1 - 2 x ) n HE(Jmol-')=x(1-x)
n=OM 1 +
(1)
E Dm(1m=l
2x)m
w h e r e x is t h e m o l e f r a c t i o n o f m e t h a n e in t h e m i x t u r e s . T h e R e d l i c h - K i s t e r and standard deviations
C, and D m parameters
s a r e g i v e n in T a b l e 9 a l o n g w i t h t h e m o l e f r a c t i o n r e g i o n s f o r w h i c h t h e
equation applies. The modified Redlich-Kister an o r d i n a r y R e d l i c h - K i s t e r
e q u a t i o n w a s u s e d to fit ( m e t h a n e + n - h e p t a n e ) w h i l e
equation was used for the remaining systems. In the two-phase region the
H E v a l u e s w e r e f i t t e d to t h e e q u a t i o n
(2)
HE=Ao+AIx
T h e A n p a r a m e t e r s f o r E q . (2) a n d s t a n d a r d d e v i a t i o n s s a r e g i v e n in T a b l e 10 a l o n g w i t h t h e m o l e fraction regions for which
the equation
applies. The
experimental
and calculated
H E values are
p l o t t e d v s . t h e m e t h a n e m o l e f r a c t i o n x in F i g s . 1 - 8 . T h e s o l u b i l i t i e s o f m e t h a n e in t h e l i q u i d p h a s e have been determined
from the curves. The basis for this determination
is that, w h e n a r e g i o n o f
J.L. Oscarson et al. / Fluid Phase Equilihria 114 (1996) 161-174 Table
167
7
Excess molar enthalpies
( H E) f o r ( x
H E (j tool x
methane
x) (87.8%
methylcyclohexane
1)
+ 12.2% HE
Exp a 255.4
+ (1 -
Calc
6
(j
tool
methanol)) i)
x
E x p '~
Calc
b
- 445.9
K, 13.8 MPa
0.0526
- 42
- 43. l
0.3997
- 436
0.0561
- 50
- 46.3
0.4500
- 521
- 495.6
0.0999
- 99
- 89.9
0.4996
- 527
- 536. I
0.1508
-
14 6 . 7
0.5997
- 400
- 405.4
0.2033
- 210
146
- 209.9
0.703(/
- 288
- 295.2
0.2497
- 269
- 267.7
0.7998
-
194
-
0.3007
-321
-331.2
0.8498
-
127
-
0.3522
- 391
- 393.0
0.8999
- 73
- 85.3
- 268.8
310.9
-
K, 13.8
192.0 138.7
MPa
0.0308
- 53
- 42.3
0.2037
- 284
0.0598
- 98
- 82.0
0.2234
- 294
- 292.2
0.0870
-
130
-
118.8
0.2412
- 317
- 312.8
0.(/870 0.1128
-
108
-
118.8
0.2422
- 321
- 313.9
-
154
-
153.2
0.2761
-330
-351.2
0.1371
-
163
-
185.1
0.3092
-399
-385.1
0.1371
-
188
-
185.1
0.3092
-404
-385.1
0.1378
- 205
-
186.0
0.3371
- 383
- 411.6
0.1378
-
-
186.0
0.3384
-416
0.1602
- 218
- 214.8
0.3900
- 450
- 455.6
0.1820
- 241
- 242.2
0.3900
- 466
- 455.6
0.2027
- 266
- 267.6
~'~' S e e
footnotes in
155
Table
412.8
1.
immiscibility exists, the H E v s . x curve is linear. The composition of the two-phase region is then given by the intersection of the curve with the linear regions. The negative H E values observed for the systems (methane + methanol), (methane + n-heptane), (methane + methylcyclohexane) and (methane + (methylcyclohexane + methanol)) result from the condensation of the supercritical methane into the liquid phase. The H E regions with curvature correspond to a single liquid phase and H E regions with a straight line correspond to a (vapor + liquid) phase equilibrium where the composition of each phase is fixed. Measurements in the single vapor phase region were not possible due to high flow rates necessary for the gas. Mixing problems occur when high flow rates are used for the gas. For (methane + methanol) the curve represented in Fig. 1 shows a phase separation for methane mole fractions 0.10 and 0.13 at temperatures 310.9 K and 255.4 K, respectively. These results agree with those found by Hong et al. (1987), i.e., 0.1018 and 0.1224 at 310 and 250 K, respectively. The H E values are lower than those where the pure liquid is less associated. Heat of mixing data for (methane + toluene) vs. methane mole fraction represented in Fig. 3 show at 255.4 K positive or low negative values before the phase split. This results from the competition between the exothermic effect due to the condensation of gaseous methane into liquid toluene and the endothermic effect of breaking rr-Tr interactions in pure toluene. At 310.9 K, these aromatic interactions are weaker and the measured H E values are slightly negative. The methane mole fraction where two phases appear is
J.L. Oscarson et aL /Fluid Phase Equilibria 114 (1996) 161-174
168
Table 8 E x c e s s m o l a r e n t h a l p i e s ( H E) for ( x m e t h a n e + (1 - x ) (93.8% m e t h y l c y c l o h e x a n e + 6.2% m e t h a n o l ) ) H E (Jmol-l) x
Exp a
H E (Jmol-i) Calc b
x
Exp a
Calc b
255.4 K, 1 3 . 8 M P a 0.1044
- 117
- 112.4
0.5026
- 555
- 541.0
0.1481
- 168
- 165.0
0.5019
- 537
- 540.6
0.2041
- 234
- 234.3
0.6078
-449
- 447.7
0.2 527
- 291
-294.6
0.6992
- 342
- 343.6
0.3014
- 354
- 353.3
0.8027
- 224
- 225.8
0.3523
- 416
- 410.9
0.9029
- 115
- 111.7
-472
- 486.8 - 331.4
0.4293
310.9 K, 1 3 . 8 M P a 0.0321
- 52
- 48.0
0.2301
- 333
0.0623
-97
- 93.2
0.2493
- 351
- 356.0
0.0 906 0.1172
- 137 - 178
- 135.3 - 174.4
0.2849 0.2861
- 427 - 412
- 399.5 -400.9
0.1424
- 196
- 210.9
0.3173
- 432
- 436.3
0.1661
- 230
- 244.6
0.3469
- 456
-467.3
0.1669
- 241
- 245.7
0.3469
-475
-467.3
0.1895 0.2 099
- 278 - 308
- 277.1 - 304.7
0.3991 0.4050
- 548 -479
-515.2 -520.0
a.b See fo otnotes in Table 1. Table 9 C o e f f i c i e n t s C n, D m and s t a n d a r d d e v i a t i o n s s for l e a s t - s q u a r e s r e p r e s e n t a t i o n of H E (J m o l - ~ ) by Eq. (1) X
0<
x<0.10
0
T (K) CO (xmethane+(lx)methanol) 310.9 -2640.5
Cl
255.4
1820.7
-2458.3
S
1719.1
3 4
(x methane+(l - x)toluene) 0< 0<
x < 0.22 x < 0.33
0< 0<
x<0.41 x<0.51
310.9 255.4
-800.59 -237.07
609.78 536.80
1
3
(x methane+(1 - x)methylcyclohexane) 310.9 255.4
- 2370.5 2295.6
(x methane+(10< x<0.28 0< x<0.28
5423.9 1535.4
x)(88.2%toluene+
310.9 255.4
-560.87 -248.11
14 11
ll.8%methanol)) 332.61 453.83
4 5
(x methane+(1 - x)(93.4%toluene+6.6%methanol)) 0< 0<
x<0.26 x < 0.32
310.9 255.4
- 713.81 -253.78
563.15 522.88
(x methane+(l - x)(87.8%methylcyclohexane+ 0< x<0.39
310.9
0<
255.4 (xmethane+(1
x < 0.49
-
2067.4
12.2%methanol))
692.08
-2145.7 1431.7 x)(93.8%methylcyclohexane+6.2% 2314.0 821.14
0<
x < 0.41
310.9
0<
x<0.52
255.4 T(K)
- 2157.8
- 2509.2
0<
x<0.44
CO ( x m e t h a n e + ( 1 - x) n-heptane) 310.9 - 2690.3
0<
x<0.60
255.4
X
5 3 15 11 methanol)) 17
1208.3 Dj
8 D2
D3
0 4
1.0391
0.20604
0.99126
- 1.2235
1.1117
0.54549
- 2.5962 3.6327
8
13
169
J.L. Oscarson et a l . / Fluid Phase Equilibria 114 (1996) 161-174 Table 10 Coefficients A , a n d standard deviations s for l e a s t - s q u a r e s representation o f H E (J m o l - i ) T (K) 310.9 255.4 255.4 255.4 310.9 255.4 310.9 255.4 255.4 255.4
region ( x m e t h a n e + (1 0.10 < x < 0.99 0.13 < x < 0.99 ( x m e t h a n e + (1 0.33 < x < 0.99 ( x m e t h a n e + (1 0.51 < x < 0.99 ( x m e t h a n e + (1 0.28 < x < 0.99 0.28 < x < 0.99 ( x m e t h a n e + (1 0.26 < x < 0.99 0.32 < x < 0.99 ( x methane + ( 10.49 < x < 0.99 ( x m e t h a n e + (1 0.52 < x < 0.99
by Eq. (2)
Ao
Ai
s
- 144.04 - 144.12
263.36 147.82
9 3
x) methanol)
x ) toluene) - 18.903 19.756 x) methylcyclohexane) - 1145.4 1.1181 x ) (88.2% toluene + 11.8% m e t h a n o l ) - 169.43 292.54 -39.184 52.261 x ) 9 9 3 . 4 % toluene + 6.6% m e t h a n o l ) ) - 131.89 161.56 - 24.819 33.957 x ) (87.8% m e t h y l c y c l o h e x a n e + 12.2% m e t h a n o l ) ) - 1044.8 1066.3 x ) (93.8% m e t h y l c y c l o h e x a n e + 6.2% m e t h a n o l ) ) - 1139.7 1138.5
1 4 2 3 2 4 11 3
0.33 at 255.4 K. Chang and Kobayashi (1967a) report 0.3500 for the [methane + toluene] binary system at the same temperature. The same behavior was observed with the (methane + (toluene + methanol)) systems ( Figs. 5 and 6). The H E values measured for the (methane + 0
t
-50
g/ {
-100
-150
i
0.0
3' *o
I
0.2
i
I
/
i
0.4
i
0.6
0
I
0.8
1.0
X methane
Fig. 1. Plot o f H z for ( x m e t h a n e + (1 - x ) m e t h a n o l ) at 13.8 MPa; O , 310 K; z~, 255 K; - o v e r region specified in Table 9 and calculated u s i n g Eq. 2 o v e r region specified in T a b l e 10.
, calculated u s i n g Eq. 1
170
J.L. Oscarson et al./Fluid Phase Equilibria 114 (1996) 161-174 •
i
•
i
'
i
-200
E
A
311~~
-400
-600
-800
i
0.0
I
,
0.2
I
,
0.4 x
I
=
0.6
I
1.0
0.8
methane
Fig. 2. Plot of H E for ( x methane +(1 - x) n-heptane) at 13.8 MPa; ©, 310 K; A, 255 K; - 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
50
.
i
•
I
i
i
,
I
,
i
, calculated using Eq.
i
A
o
-100
-150
, 0.0
0.2
0.4
I 0.6
x
~
I 0.8
,
1.0
methane
Fig. 3. Plot of H E for ( x m e t h a n e + ( l - x) toluene) at 13.8 MPa; C), 310 K; A, 255 K; - over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
, calculated using Eq. 1
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174
'
f
'
I
'
I
'
I
171
'
-200 K
E
-400
311K ~
~
0.2
0.4
-600 0.0
0.6
0.8
1.0
x methane
Fig. 4. Plot of H E for (x methane+(l - x) methylcyclohexane) at 13.8 MPa; O, 310 K; A, 255 K; - using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
, calculated
50
E
-50
311°K~ 0
-100
-150
=
0.0
I
0.2
=
I
,
0.4
I
0.6
i
I
0.8
J
1.0
x methane
Fig. 5. Plot of H E for (x methane+ ( 1 - x ) (88.2% toluene+ 11.8% methanol)) at 13.8 MPa; ©, 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
J.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174
172
50
,
"5 E "~ -50
,
,
311K
-100
i
- 150
I
0.0
i
f
0.2
i
I
0.4 x
I
i
0.6
i
0.8
1.0
methane
Fig. 6. Plot of H E for ( x m e t h a n e + ( 1 - x ) ( 9 3 . 4 % toluene+6.6% methanol)) at 13.8 MPa; O, 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
0
'
I
'
i
,
i
,
,
I
i
i
,
5K
-200
~.~
311K ~
%
~
-400
-600
,
0.0
I
0.2
~
I
0.4 0.6 x methane
I
0.8
1.0
Fig. 7. Plot of H E for ( x methane+(1 - x) (87.8% methylcyclohexane + 12.2% methanol)) at 13.8 MPa; O, 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
173
I.L. Oscarson et al. / Fluid Phase Equilibria 114 (1996) 161-174 '
I
'
I
'
I
'
I
i
I
'
I
i
-200
E
-400
o -600
i
0.0
I
0.2
i
[
,
0.4
0.6
0.8
1.0
x methane
Fig. 8. Plot of H E for (x methane+(l - x) (93.8% methylcyclohexane+6.2% methanol)) at 13.8 MPa; C), 310 K; A, 255 K; - - , calculated using Eq. 1 over region specified in Table 9 and calculated using Eq. 2 over region specified in Table 10.
(methylcyclohexane + methanol)) system were smaller than those for the binary system where smaller interaction forces exist. The phase splitting on the (methane + methylcyclohexane) plot in Fig. 4 appears for a methane mole fraction of 0.51 and can be compared with the value 0.4950 found by Chang and Kobayashi (1967b).
4. List of symbols
Ao Cn
coefficients in Eq. (2) coefficients in Eq. (1) O m coefficients in Eq. (1) H E excess molar enthalpy (J mol- l) s standard deviation T temperature (K) x mole fraction
Acknowledgements
This work was supported by the Gas Processors Association. J.Y. Coxam is grateful to the service des bourses de Recherche Scientifique et Technique de I'OTAN and the Fulbright Program for financial support.
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J.L. Oscarson et aL / F l u i d Phase Equilibria 114 (1996) 161-174
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