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Measurements on the phase behavior of binary mixtures for modeling the condensation behavior of natural gas
Fluid Phase Equilibria, 85 (1993) 335-345 Elsevier Science Publishers B.V.. Amsterdam
335
Measurements on the phase behavior of binary mixtures for modeling the condensation behavior of natural gas. Part III. The system methane
M.P.W.M.
Rijkers,
+ hexadecane
C.J. Peters and J. de Swaan Arons
DeCft University of Technology, Faculty of Chemical Engineering and Materials Science, Laboratory of Applied Thermodynamics and Phase Equilibria, Julianalaan 136, 2628 BL Delft (The Netherlands) (Received
January
3. 1992; accepted
in final form September
27, 1992)
ABSTRACT Rijkers, M.P.W.M., Peters, C.J. and De Swaan Arons, J., 1993. Measurements on the phase behavior of binary mixtures for modeling the condensation behavior of natural gas. Part III. The system methane + hexadecane. Fluid Phase Equilibria, 85: 335-345. This paper reports measurements on the solubility of hexadecane in methane at temperatures between 285 and 315 K and at pressures up to 25 MPa. The data were obtained with the gas saturation method, as described in Part I of this series (Rijkers, M.P.W.M., Malais, M.. Peters, C.J. and De Swaan Arons, J., 1992. Fluid Phase Equilibria, 71: 143-168). Concentrations between 0.1 and 700 ppm hexadecane in methane (on a molar basis) were measured with, in general, a reproducibility better than 2%. The experimental data are complementary to the bubble-point data of Glaser et al. (Glaser, M., Peters, C.J.. van der Kooi, H.J. and Lichtenthaler, R.N., 1985. J. Chem. Thermodyn., 17: 803815). The latter data were combined with the data reported in this contribution and are presented in a p,T, (x, y) space diagram, from which the p, T and p, (x, y) sections can be derived.
INTRODUCTION
In this paper new experimental data are reported on the solubility of hexadecane in supercritical methane. The data obtained will be applied to model the condensation behavior of natural gas. In earlier papers on this subject (Parts I and II) the experimental approach was discussed and data were reported for the systems methane + decane and methane + dodecane (Rijkers et al., 1992a, 1992b). With respect to the primary objective of this
Correspondence to: C.J. Peters, Delft University of Technolgy, Faculty ing and Materials Science, Laboratory of Applied Thermodynamics Julianalaan 136, 2628 BL Delft, The Netherlands. 0378-3812/93/$06.00
0
1993 - Elsevier
Science Publishers
of Chemical Engineerand Phase Equilibria,
B.V. All rights reserved
336
M.P. W.M. Rijkers et al. 1 Fltaid Phase E~~i~~b~~a8.5 (1993) 335-345
project, the binary methane + hexadecane was chosen to add to the “natural gas database” for the following reasons. (1) In particular, the very small amounts of heavy hydrocarbons present in natural gas play an important role in the phenomenon of retrograde condensation. (2) Modeling the phase behavior of three binary systems containing methane and a normal paraffin may allow a correlation between carbon number and equation of state parameters to be found. (3) Data on the solubilities of methane in liquid hexadecane have already been obtained by Glaser et al. (1985) in the same temperature region; therefore the gas saturation measurements are complementary to these. PHASE BEHAVIOR
The system methane + hexadecane shows qualitatively the same phase behavior as the binaries methane + decane and methane + dodecane. At 291.3 K and 0.10 Pa, hexadecane has a triple point (Research Project 44 of the API, 1988). Glaser et al. (19S5) reported that a three-phase equilibrium, solid hexadecane + liquid + gas (s,lg), originates from the triple point of hexadecane and that this, with a minimum in temperature, continues to a second critical end point (se + 1 = g) located at T = 286.4 K and p = 71.5 MPa. This three-phase equilibrium limits to lower temperatures the region where liquid + gas equilibria, of interest in natural gas transport, can be determined experimentally. This three-phase equilibrium was determined from data on freezing point depression by Glaser et al. (1985). Because traces of hexadecane in natural gas are not expected to cause precipitation of a solid phase, the sg + g equilibria are not considered in this work. Therefore, for temperatures below those of the three-phase equilibrium sBlg (approximately 285 K), the properties of hexadecane and its mixtures with methane will have to be obtained by extrapolation. For more general details on the type of phase diagrams occurring in this work, the reader is referred to Davenport and Rowlinson ( 1963) and in particular to Luks (1980), Van der Kooi (1981), Glaser et al. (1985), Peters et al. (1986) and Rijkers et al. ( 1992a, 1992b). EXPERIMENTAL
The experimental data reported here were all obtained utilizing the gas saturation apparatus. The hardware and the experimental procedure were described earlier in Part I of this series (Rijkers et al., 1992a). All measurements were carried out in triplicate, while each analysis of the gas washer solvent was automated and programmed to be executed in quadrupIicate_ The methane used in this work was an Air Product research-grade chemical. Its specified purity of 99.995% was verified by means of a GC
M.P. WM.
Rijkers et al. 1 Fluid Phase Equilibria
85 (1993) 335-345
337
analysis. Heptane (Janssen Chemie), which served as the gas washer solvent, hexadecane (Merck) and heptadecane (Janssen Chemie), which served as an internal standard, all had a specified purity of better than 99%. Any low volatile contaminants in the heptane, which could possibly interfere with hexadecane or heptadecane in the GC analyses, were removed by vacuum distillation. The purity of the hexadecane and heptadecane appeared to be better than 99.8% and 99.6% respectively; therefore they were used without further purification.
RESULTS
Solubilities in the gas phase were measured as a function of temperature (285 < T < 315 K) in the gas saturation apparatus at 11 pressures ranging from 0.1 to 25 MPa. Numerical values of the 1 + g equilibrium data are given in Table 1 and are shown in Fig. 1. The data obtained in this work are shown with the measurements of Glaser et al. (1985) in Fig. 2. Interpolated data at constant temperature are given in Table 2 and in Figs. 2-4. From
-3 0
25 OOMPa 0
0 2000~
ls.oo
-------
-5 -
-6 -
-7
1 280
I
1 290
I
I 300
I
1 310
1 -T/K
Fig. 1. Measured T, y sections of the system methane + hexadecane experimental points; -, least-squares best fit to low-degree pressure are shown.
at constant pressure: 0, polynomials. Values of
M.P. WM.
338 TABLE
p =0.106 291.7 294.1
et al. 1 Fluid Phase Equilibria
85 (1993)
335-345
1
Gas saturation measurements methane + hexadecane
T(K)
Rijkers
Y
MPa 7.305 x 10-7 ‘% 9.689 x lo-’ b
of
the
1+ g
phase
boundaries
of
the
system
T(K)
.I
T(K)
Y
299.2 303.4
1.819 x 10-6 2.785 x lO-‘j a
308.0 314.6
4.046 x 1O-6 8.166 x 10-6
303.4 308.0 308.5
1.534 x 10-6 2.297 x 10m6 2.325 x 1O-6 a
314.7
4.600 x 1O-6
299.0 303.5
4.275 x 10m7 7.323 x 10m7
308.4 314.6
1.123 x lo-’ 2.155 x 10m6 d
299.0 303.5 308.4
2.704 x lo-’ b 4.978 x 1O-7 a 7.803 x 1O-7 a
314.7
1.389 x 1o-6
299.1 303.5
2.625 x 10m7 4.188 x 10m7
308.5 314.8
6.685 x 1O-7 1.149 x 10-6
299.0 303.6
4.264 x lo-’ 6.025 x 1O-7 a
308.6 314.8
9.211 x 10-7 a 1.561 x 1O-6
299.6 303.8
1.468 x 1O-6 1.987 x lO-6
309.3 314.6
2.920 x 1O-6 b 3.865 x 10m6
298.9 303.7
5.277 x 10m6 6.598 x 1O-6
309.0 315.1
8.665 x 1O-6 a 1.183 x 10-5 a
298.2 303.6
3.688 x 1O-5 4.315 x 10-s
308.9 314.1
5.218 x 10ms d 6.058 x 1O-5
298.2 303.6
2.024 x 1O-4 2.132 x 10-4
309.0 314.1
2.197 x 1O-4 2.389 x 1O-4
297.9 303.8
5.120 x 1O-4 a 5.627 x 1O-4 d
308.7 314.3
5.985 x 10-4 6.243 x 1O-4 A
p = 0.200 MPa
291.3 294.3 299.2
3.819 x 10-7 d 5.662 x lo-’ a 9.148 x 10-7
p = 0.500 MPa
291.3 294.1
1.838 x 10-7 d 2.831 x 10m7
p = 1.000 MPa
291.4 294.0 294.2
1.125 x 10-7 b 1.778 x 10-7 b 1.796 x 1O-7
p = 2.000 MPa
291.3 294.1
1.173 x 10-7 b 1.544 x 10-7 ‘+
p = 4.000 MPa
289.3 293.9
1.667 x lo-’ 2.593 x lo-’
d d
p = 7.00 MPa
288.9 294.1
7.311 x 10-7 9.798 x 10-7
p = 10.00 MPa
287.8 293.7
3.208 x 1O-6 4.210 x 1O-6
p = 15.00 MPa
286.3 292.5
2.839 x 10m5 3.170 x 10-S
p = 20.00 MPa
285.6 291.9
1.813 x 10-4 1.923 x 10m4
p = 25.00 MPa
285.5 292.2
5.039 x 10-4 a 5.134 x 10-4 d
a Reproducibility b Reproducibility
better than 2%. better than 5%.
M.P. W.M.
Rijkers et al. 1 Fluid Phase Equilibria
85 (1993) 335-345
339
Fig. 2. Experimental two-phase boundaries of the methane + hexadecane system: 0, experimental points; -, least-squares best fit to low degree polynomials; 0, interpolations at constant temperature. Values of pressure and compositions are shown. Data at constant composition were measured by Glaser et al. (1985).
the data summarized in Table 2, the p, T phase envelopes at constant composition can be compiled. These data are given in Table 3 and are shown graphically in Fig. 5.
DISCUSSION
AND CONCLUSION
Solubility data for the binary methane + hexadecane have been measured with the gas saturation apparatus. The results reported in this work are shown together with the data obtained by Glaser et al. (1985) in Figs. 2 and 4. At pressures between 25 and 60 MPa, no solubility data could be measured in the vapor phase, because under these conditions the gas mixtures contain 700- 10 000 ppm hexadecane on a molar basis. However, the hexadecane concentration is too low for visual observation of any liquid dropout on pressure reduction in the autoclave equipment and, moreover, methane densities corresponding to pressures exceeding the pressure rating of the gas saturation apparatus are required to dissolve such quantities of solute. Nonetheless, all the data of the methane + hexadecane system needed to model the condensation behavior of natural gas (p < 10 MPa) were obtained.
M.P. WM. Rijkers et al. 1 Fluid Phase Equilibria 85 (1993) 335-345
340 TABLE
2
p, (x, y) sections temperatures
of 1+ g equilibria
for the binary
methane
+ hexadecane
at interpolated
P OfPa)
x, y
P Ofpa)
x7 Y
T = 293.15 K y = 8.766 x lo-’ y = 4.817 x 1O-7 y = 2.357 x lo-’ y = 1.493 x 10-7 y = 1.416 x lo-’ y =2.418 x lo-’ y = 9.258 x lo-’ y =4.068 x 1O-6
0.106 0.200 0.500 1.ooo 2.000 4.000 7.00 10.00
y y y y y y x x
= 3.213 x 1O-5 = 1.932 x 1O-4 = 5.130 x 10-4 = 0.023 = 0.038 = 0.048 = 0.073 =0.113
15.00 20.00 25.00 64.563 68.370 69.546 69.520 68.605
x x x x x x x x
= = = = = = = =
0.176 0.297 0.400 0.503 0.658 0.704 0.816 0.889
58.554 36.324 23.030 15.678 8.2837 6.6273 4.0157 2.0911
T=303.15K y = 2.656 x y = 1.416 x y = 7.019 x y = 4.644 x y = 3.994 x y = 5.920 x y = 1.902 x y = 6.470 x
1O-6 lo-” lo-’ lo-’ 10-7 lo-’ 10m6 1O-6
0.106 0.200 0.500 1.ooo 2.000 4.000 7.00 10.00
y y y y y v x x
=4.291 x IO-’ = 2.114 x 10-4 = 5.513 x 10-4 = 0.023 = 0.038 = 0.048 = 0.073 =0.113
15.00 20.00 25.00 62.430 66.024 67.153 67.153 66.329
x x x x x x x x
= = = = = = = =
0.176 0.297 0.400 0.503 0.658 0.704 0.816 0.889
57.096 36.719 23.427 16.185 8.6393 6.9365 4.1979 2.1859
T = 313.15 K y = 7.007 x 10-6 y = 3.874 x 1O-6 y = 1.890 x 1O-6 y = 1.213 x 1O-6 y = 1.004 x 10-6 y = 1.355 x 10-6 y = 3.622 x 1O-6 y = 1.068 x 10-5
0.106 0.200 0.500 1.ooo 2.000 4.000 7.00 10.00
y y y y y y y x
= 5.906 x 1O-5 =2.341 x 1O-4 = 6.223 x 1O-4 = 0.023 = 0.038 = 0.048 = 0.073 =0.113
15.00 20.00 25.00 60.527 63.964 65.067 65.099 64.380
x x x x x x x x
= = = = = = = =
0.176 0.297 0.400 0.503 0.658 0.704 0.816 0.889
55.848 36.580 23.791 16.651 8.9705 7.2228 4.3693 2.2763
x9 Y
P OW
Consistency tests proposed by Prausnitz and Keeler (1961) were performed on our data at three temperatures, resulting in the calculation of B12and CIIz, i.e. the second and third cross-virial coefficient respectively. Figure 6 shows, for one temperature, the reciprocal molar volume plotted against the logarithm of the product of the compressibility factor (Z) and the fugacity coefficient of hexadecane in methane. The fugacity coefficient was calculated with the virial equation of state. At low densities, the slope of the resulting straight line yields 2B,*, while deviations from the straight line at high densities are a result of the influence of Cr12. The data points in Fig. 6 show little scattering and therefore are well described by the virial equation of state. Figure 7 compares vapor pressure data derived from our solubility data, applying Raoult’s Law (Table 4), and values measured by Parks and Moore
M.P. WM.
341
Rijkers et al, / Fluid Phase Equilibria 85 (1993) 335-345
-
P'tlPa
Fig. 3. Interpolated p, y sections of the methane + hexadecane system at constant temperature: 0, interpolated data points. Values of temperature are shown. TABLE 3 p, T sections of 1 + g equilibria of the system methane + hexadecane at interpolated compositions: the broken line indicates the limit between interpolated and extrapolated values P
WP4
T(K) 0.1 a
0.2 =
Extrapolated 0.106 0.200 0.500
285.88
285.45 291 .I2
1.ooo 2.000 4.000
289.94 290.02 283.96
295.58 296.36 291.12
7.00 10.00 a y, in parts per million.
0.5 a
1”
2”
5”
10 a
Extrapolated I Interpolated 309.51 i 317.22 300.47 288.51 ,i 294.28 ,____________’ 306.50 ]--?i:;t-- 323.30 299.85 j 293.48 306.61 313.75 ! 324.15 / 299.94 .-______----310.99 319.26 i 303.86 321.60 313.11 i 305.48 309.39 318.16 j 301.21 .___ ____-----, 294.34 303.83 [ ________________________----311.88 297.70
-
T/‘K
b ~~~~A~E
-x
H~XA~~CA~E
Fig. 5. Int~~olat~ p, T sections of the methane + hexadecane system at constant composid~wp~~nt curves, tion: 0, interpolated data points: --,
M.P. W.M.
Rijkers et al. / Fluid Phase Equilibria
8.5 (1993) 335-345
343
-4
-6
- 8
-10
-12 20000 2/v~moi.m-3~
10000
-
30000
Fig. 6. Calculation of second and third cross-virial coefficients of the methane + hexadecane system at T = 293.15 K, according to Prausnitz and Keeler (1961): 0, data points; __ B,2 = -(618 & 8) x 10e6 m3 mol-‘; =, B,, = -(655 + 4) x 10m6m3 mol-‘; C,rz = (265’k 5) x 1O’Om6 molm2.
10
05 InpIPal
0.0
t
-
10
-15
-20
-25
0
31
32
33 -
34 lOOO/T[Kl
Fig. 7. Experimental vapor pressures of hexadecane: 0, this work; -, Antoine curve from the Research Project 44 of the API (1988); 0, data of Parks and Moore (1949).
M.P. WM. Rijkers et al. / Fluid Phase Equilibria 85 (1993) 335-345
344 TABLE
4
Raoult’s
law vapor pressures
derived
from 1+ g solubility
T(K)
P NV
Y
291.7 294.1 299.2 303.4 308.0 314.6
105.7 104.5 106.4 106.4 105.7 106.4
7.305 9.689 1.819 2.785 4.046 8.166
* Saturated
x x x x x x
IO-’ lo-’ 10m6 1O-6 10m6 10-6
data X
P* (PaI
0.9944 0.9945 0.9945 0.9946 0.9947 0.9948
0.07765 0.1018 0.1946 0.2979 0.4299 0.8734
property.
(1949). The API Antoine curve of hexadecane obtained from these data (Research Project 44 of the API, 1988) is included. Vapor pressures obtained in this work are found to be about 10% lower than the accepted API values. However, it should be noted that the data reported in this contribution show much less scattering than the data measured by Parks and Moore ( 1949). ACKNOWLEDGMENTS
The authors gratefully acknowledge the “Stichting Technische Wetenschappen” and “Gasunie Nederland N.V.” for financially supporting this project. AKZO Chemie provided free the solute supporting material. LIST OF SYMBOLS
B C f: P S
T X Y
z
second virial coefficient third virial coefficient refers to gas phase refers to liquid phase pressure refers to solid phase temperature mole fraction in the liquid phase mole fraction in the gaseous phase compressibility factor
Greek letter q5 fugacity
coefficient
Subscript B
refers to second
(heavy)
component
M.P. WM.
Rijkers et ai. j Fluid Phase Eq~ili~r~
85 (1993) 335-345
345
REFERENCES Davenport, A.J. and Rowlinson, J.S., 1963. The solubility of hydrocarbons in liquid methane. Trans. Faraday Sot., 59: 67-84. De Loos, Th.W., Wijen, A.J.M. and Diepen, G.A.M., 1980. Phase equilibria and critical phenomena in fluid (propane + water) at high pressures and temperatures. J. Chem. Thermodyn., 12: 193-204. Glaser, M., Peters, C.J., Van der Kooi, H.J. and Lichtenthaler, R.N., 1985. Phase equilibria of (methane + n-hexadecane) and (p, Y,, T) of n-hexadecane. J. Chem. Thermodyn., 17: 803-815. Luks, K.D., 1980. Proc. 2nd Int. Conf. on Phase Equilibria and Fluid Properties in the Chemical Industry, Berlin, 17-21 March. Dechema, Frankfurt am Main, pp. 699-712. Parks, G.S. and Moore, G.E., 1949. Vapor pressure and other thermodynamic data for n-hexadecane and n-dodecylcyclohexane near room temperature. J. Chem. Phys., 17( 11): 1151-1153. Peters, C.J., Lichtenthaler, R.N. and De Swaan Arons, J., 1986. Three-phase equilibria in binary mixtures of ethane and higher n-alkanes. Fluid Phase Equilibria, 29: 495-504. Prausnitz, J.M. and Keeler, R.N., 1961. Application of the Kihara potential to high pressure phase equilibria. AIChE J., 7( 3) : 399-405. Research Project 44 of the API, 1988. Selected Values of Properties of Hydrocarbons and Related Compounds. Texas A&M University, College Station TX. 23-2-f 1.lOl)-ka, p. 2. Rijkers, M.P.W.M., Malais, M., Peters, C.J. and De Swaan Arons, J., 1992a. Measurements on the phase behavior of binary hydrocarbon mixtures for modelhng the condensation behavior of natural gas. Part I. The system methane + decane. Fluid Phase Equihbria, 71: 143-168. Rijkers, M.P.W.M., Malais, M., Peters, C.J. and De Swaan Arons, J., 1992b. Measurements on the phase behavior of binary hydrocarbon mixtures for modelling the condensation behavior of natural gas. Part II. The system methane + dodecane. Fluid Phase Equilibria, 72: 309-324. Van der Kooi, H.J., 1981. Ph.D. Dissertation, Delft University of Technology (in Dutch).
335
Measurements on the phase behavior of binary mixtures for modeling the condensation behavior of natural gas. Part III. The system methane
M.P.W.M.
Rijkers,
+ hexadecane
C.J. Peters and J. de Swaan Arons
DeCft University of Technology, Faculty of Chemical Engineering and Materials Science, Laboratory of Applied Thermodynamics and Phase Equilibria, Julianalaan 136, 2628 BL Delft (The Netherlands) (Received
January
3. 1992; accepted
in final form September
27, 1992)
ABSTRACT Rijkers, M.P.W.M., Peters, C.J. and De Swaan Arons, J., 1993. Measurements on the phase behavior of binary mixtures for modeling the condensation behavior of natural gas. Part III. The system methane + hexadecane. Fluid Phase Equilibria, 85: 335-345. This paper reports measurements on the solubility of hexadecane in methane at temperatures between 285 and 315 K and at pressures up to 25 MPa. The data were obtained with the gas saturation method, as described in Part I of this series (Rijkers, M.P.W.M., Malais, M.. Peters, C.J. and De Swaan Arons, J., 1992. Fluid Phase Equilibria, 71: 143-168). Concentrations between 0.1 and 700 ppm hexadecane in methane (on a molar basis) were measured with, in general, a reproducibility better than 2%. The experimental data are complementary to the bubble-point data of Glaser et al. (Glaser, M., Peters, C.J.. van der Kooi, H.J. and Lichtenthaler, R.N., 1985. J. Chem. Thermodyn., 17: 803815). The latter data were combined with the data reported in this contribution and are presented in a p,T, (x, y) space diagram, from which the p, T and p, (x, y) sections can be derived.
INTRODUCTION
In this paper new experimental data are reported on the solubility of hexadecane in supercritical methane. The data obtained will be applied to model the condensation behavior of natural gas. In earlier papers on this subject (Parts I and II) the experimental approach was discussed and data were reported for the systems methane + decane and methane + dodecane (Rijkers et al., 1992a, 1992b). With respect to the primary objective of this
Correspondence to: C.J. Peters, Delft University of Technolgy, Faculty ing and Materials Science, Laboratory of Applied Thermodynamics Julianalaan 136, 2628 BL Delft, The Netherlands. 0378-3812/93/$06.00
0
1993 - Elsevier
Science Publishers
of Chemical Engineerand Phase Equilibria,
B.V. All rights reserved
336
M.P. W.M. Rijkers et al. 1 Fltaid Phase E~~i~~b~~a8.5 (1993) 335-345
project, the binary methane + hexadecane was chosen to add to the “natural gas database” for the following reasons. (1) In particular, the very small amounts of heavy hydrocarbons present in natural gas play an important role in the phenomenon of retrograde condensation. (2) Modeling the phase behavior of three binary systems containing methane and a normal paraffin may allow a correlation between carbon number and equation of state parameters to be found. (3) Data on the solubilities of methane in liquid hexadecane have already been obtained by Glaser et al. (1985) in the same temperature region; therefore the gas saturation measurements are complementary to these. PHASE BEHAVIOR
The system methane + hexadecane shows qualitatively the same phase behavior as the binaries methane + decane and methane + dodecane. At 291.3 K and 0.10 Pa, hexadecane has a triple point (Research Project 44 of the API, 1988). Glaser et al. (19S5) reported that a three-phase equilibrium, solid hexadecane + liquid + gas (s,lg), originates from the triple point of hexadecane and that this, with a minimum in temperature, continues to a second critical end point (se + 1 = g) located at T = 286.4 K and p = 71.5 MPa. This three-phase equilibrium limits to lower temperatures the region where liquid + gas equilibria, of interest in natural gas transport, can be determined experimentally. This three-phase equilibrium was determined from data on freezing point depression by Glaser et al. (1985). Because traces of hexadecane in natural gas are not expected to cause precipitation of a solid phase, the sg + g equilibria are not considered in this work. Therefore, for temperatures below those of the three-phase equilibrium sBlg (approximately 285 K), the properties of hexadecane and its mixtures with methane will have to be obtained by extrapolation. For more general details on the type of phase diagrams occurring in this work, the reader is referred to Davenport and Rowlinson ( 1963) and in particular to Luks (1980), Van der Kooi (1981), Glaser et al. (1985), Peters et al. (1986) and Rijkers et al. ( 1992a, 1992b). EXPERIMENTAL
The experimental data reported here were all obtained utilizing the gas saturation apparatus. The hardware and the experimental procedure were described earlier in Part I of this series (Rijkers et al., 1992a). All measurements were carried out in triplicate, while each analysis of the gas washer solvent was automated and programmed to be executed in quadrupIicate_ The methane used in this work was an Air Product research-grade chemical. Its specified purity of 99.995% was verified by means of a GC
M.P. WM.
Rijkers et al. 1 Fluid Phase Equilibria
85 (1993) 335-345
337
analysis. Heptane (Janssen Chemie), which served as the gas washer solvent, hexadecane (Merck) and heptadecane (Janssen Chemie), which served as an internal standard, all had a specified purity of better than 99%. Any low volatile contaminants in the heptane, which could possibly interfere with hexadecane or heptadecane in the GC analyses, were removed by vacuum distillation. The purity of the hexadecane and heptadecane appeared to be better than 99.8% and 99.6% respectively; therefore they were used without further purification.
RESULTS
Solubilities in the gas phase were measured as a function of temperature (285 < T < 315 K) in the gas saturation apparatus at 11 pressures ranging from 0.1 to 25 MPa. Numerical values of the 1 + g equilibrium data are given in Table 1 and are shown in Fig. 1. The data obtained in this work are shown with the measurements of Glaser et al. (1985) in Fig. 2. Interpolated data at constant temperature are given in Table 2 and in Figs. 2-4. From
-3 0
25 OOMPa 0
0 2000~
ls.oo
-------
-5 -
-6 -
-7
1 280
I
1 290
I
I 300
I
1 310
1 -T/K
Fig. 1. Measured T, y sections of the system methane + hexadecane experimental points; -, least-squares best fit to low-degree pressure are shown.
at constant pressure: 0, polynomials. Values of
M.P. WM.
338 TABLE
p =0.106 291.7 294.1
et al. 1 Fluid Phase Equilibria
85 (1993)
335-345
1
Gas saturation measurements methane + hexadecane
T(K)
Rijkers
Y
MPa 7.305 x 10-7 ‘% 9.689 x lo-’ b
of
the
1+ g
phase
boundaries
of
the
system
T(K)
.I
T(K)
Y
299.2 303.4
1.819 x 10-6 2.785 x lO-‘j a
308.0 314.6
4.046 x 1O-6 8.166 x 10-6
303.4 308.0 308.5
1.534 x 10-6 2.297 x 10m6 2.325 x 1O-6 a
314.7
4.600 x 1O-6
299.0 303.5
4.275 x 10m7 7.323 x 10m7
308.4 314.6
1.123 x lo-’ 2.155 x 10m6 d
299.0 303.5 308.4
2.704 x lo-’ b 4.978 x 1O-7 a 7.803 x 1O-7 a
314.7
1.389 x 1o-6
299.1 303.5
2.625 x 10m7 4.188 x 10m7
308.5 314.8
6.685 x 1O-7 1.149 x 10-6
299.0 303.6
4.264 x lo-’ 6.025 x 1O-7 a
308.6 314.8
9.211 x 10-7 a 1.561 x 1O-6
299.6 303.8
1.468 x 1O-6 1.987 x lO-6
309.3 314.6
2.920 x 1O-6 b 3.865 x 10m6
298.9 303.7
5.277 x 10m6 6.598 x 1O-6
309.0 315.1
8.665 x 1O-6 a 1.183 x 10-5 a
298.2 303.6
3.688 x 1O-5 4.315 x 10-s
308.9 314.1
5.218 x 10ms d 6.058 x 1O-5
298.2 303.6
2.024 x 1O-4 2.132 x 10-4
309.0 314.1
2.197 x 1O-4 2.389 x 1O-4
297.9 303.8
5.120 x 1O-4 a 5.627 x 1O-4 d
308.7 314.3
5.985 x 10-4 6.243 x 1O-4 A
p = 0.200 MPa
291.3 294.3 299.2
3.819 x 10-7 d 5.662 x lo-’ a 9.148 x 10-7
p = 0.500 MPa
291.3 294.1
1.838 x 10-7 d 2.831 x 10m7
p = 1.000 MPa
291.4 294.0 294.2
1.125 x 10-7 b 1.778 x 10-7 b 1.796 x 1O-7
p = 2.000 MPa
291.3 294.1
1.173 x 10-7 b 1.544 x 10-7 ‘+
p = 4.000 MPa
289.3 293.9
1.667 x lo-’ 2.593 x lo-’
d d
p = 7.00 MPa
288.9 294.1
7.311 x 10-7 9.798 x 10-7
p = 10.00 MPa
287.8 293.7
3.208 x 1O-6 4.210 x 1O-6
p = 15.00 MPa
286.3 292.5
2.839 x 10m5 3.170 x 10-S
p = 20.00 MPa
285.6 291.9
1.813 x 10-4 1.923 x 10m4
p = 25.00 MPa
285.5 292.2
5.039 x 10-4 a 5.134 x 10-4 d
a Reproducibility b Reproducibility
better than 2%. better than 5%.
M.P. W.M.
Rijkers et al. 1 Fluid Phase Equilibria
85 (1993) 335-345
339
Fig. 2. Experimental two-phase boundaries of the methane + hexadecane system: 0, experimental points; -, least-squares best fit to low degree polynomials; 0, interpolations at constant temperature. Values of pressure and compositions are shown. Data at constant composition were measured by Glaser et al. (1985).
the data summarized in Table 2, the p, T phase envelopes at constant composition can be compiled. These data are given in Table 3 and are shown graphically in Fig. 5.
DISCUSSION
AND CONCLUSION
Solubility data for the binary methane + hexadecane have been measured with the gas saturation apparatus. The results reported in this work are shown together with the data obtained by Glaser et al. (1985) in Figs. 2 and 4. At pressures between 25 and 60 MPa, no solubility data could be measured in the vapor phase, because under these conditions the gas mixtures contain 700- 10 000 ppm hexadecane on a molar basis. However, the hexadecane concentration is too low for visual observation of any liquid dropout on pressure reduction in the autoclave equipment and, moreover, methane densities corresponding to pressures exceeding the pressure rating of the gas saturation apparatus are required to dissolve such quantities of solute. Nonetheless, all the data of the methane + hexadecane system needed to model the condensation behavior of natural gas (p < 10 MPa) were obtained.
M.P. WM. Rijkers et al. 1 Fluid Phase Equilibria 85 (1993) 335-345
340 TABLE
2
p, (x, y) sections temperatures
of 1+ g equilibria
for the binary
methane
+ hexadecane
at interpolated
P OfPa)
x, y
P Ofpa)
x7 Y
T = 293.15 K y = 8.766 x lo-’ y = 4.817 x 1O-7 y = 2.357 x lo-’ y = 1.493 x 10-7 y = 1.416 x lo-’ y =2.418 x lo-’ y = 9.258 x lo-’ y =4.068 x 1O-6
0.106 0.200 0.500 1.ooo 2.000 4.000 7.00 10.00
y y y y y y x x
= 3.213 x 1O-5 = 1.932 x 1O-4 = 5.130 x 10-4 = 0.023 = 0.038 = 0.048 = 0.073 =0.113
15.00 20.00 25.00 64.563 68.370 69.546 69.520 68.605
x x x x x x x x
= = = = = = = =
0.176 0.297 0.400 0.503 0.658 0.704 0.816 0.889
58.554 36.324 23.030 15.678 8.2837 6.6273 4.0157 2.0911
T=303.15K y = 2.656 x y = 1.416 x y = 7.019 x y = 4.644 x y = 3.994 x y = 5.920 x y = 1.902 x y = 6.470 x
1O-6 lo-” lo-’ lo-’ 10-7 lo-’ 10m6 1O-6
0.106 0.200 0.500 1.ooo 2.000 4.000 7.00 10.00
y y y y y v x x
=4.291 x IO-’ = 2.114 x 10-4 = 5.513 x 10-4 = 0.023 = 0.038 = 0.048 = 0.073 =0.113
15.00 20.00 25.00 62.430 66.024 67.153 67.153 66.329
x x x x x x x x
= = = = = = = =
0.176 0.297 0.400 0.503 0.658 0.704 0.816 0.889
57.096 36.719 23.427 16.185 8.6393 6.9365 4.1979 2.1859
T = 313.15 K y = 7.007 x 10-6 y = 3.874 x 1O-6 y = 1.890 x 1O-6 y = 1.213 x 1O-6 y = 1.004 x 10-6 y = 1.355 x 10-6 y = 3.622 x 1O-6 y = 1.068 x 10-5
0.106 0.200 0.500 1.ooo 2.000 4.000 7.00 10.00
y y y y y y y x
= 5.906 x 1O-5 =2.341 x 1O-4 = 6.223 x 1O-4 = 0.023 = 0.038 = 0.048 = 0.073 =0.113
15.00 20.00 25.00 60.527 63.964 65.067 65.099 64.380
x x x x x x x x
= = = = = = = =
0.176 0.297 0.400 0.503 0.658 0.704 0.816 0.889
55.848 36.580 23.791 16.651 8.9705 7.2228 4.3693 2.2763
x9 Y
P OW
Consistency tests proposed by Prausnitz and Keeler (1961) were performed on our data at three temperatures, resulting in the calculation of B12and CIIz, i.e. the second and third cross-virial coefficient respectively. Figure 6 shows, for one temperature, the reciprocal molar volume plotted against the logarithm of the product of the compressibility factor (Z) and the fugacity coefficient of hexadecane in methane. The fugacity coefficient was calculated with the virial equation of state. At low densities, the slope of the resulting straight line yields 2B,*, while deviations from the straight line at high densities are a result of the influence of Cr12. The data points in Fig. 6 show little scattering and therefore are well described by the virial equation of state. Figure 7 compares vapor pressure data derived from our solubility data, applying Raoult’s Law (Table 4), and values measured by Parks and Moore
M.P. WM.
341
Rijkers et al, / Fluid Phase Equilibria 85 (1993) 335-345
-
P'tlPa
Fig. 3. Interpolated p, y sections of the methane + hexadecane system at constant temperature: 0, interpolated data points. Values of temperature are shown. TABLE 3 p, T sections of 1 + g equilibria of the system methane + hexadecane at interpolated compositions: the broken line indicates the limit between interpolated and extrapolated values P
WP4
T(K) 0.1 a
0.2 =
Extrapolated 0.106 0.200 0.500
285.88
285.45 291 .I2
1.ooo 2.000 4.000
289.94 290.02 283.96
295.58 296.36 291.12
7.00 10.00 a y, in parts per million.
0.5 a
1”
2”
5”
10 a
Extrapolated I Interpolated 309.51 i 317.22 300.47 288.51 ,i 294.28 ,____________’ 306.50 ]--?i:;t-- 323.30 299.85 j 293.48 306.61 313.75 ! 324.15 / 299.94 .-______----310.99 319.26 i 303.86 321.60 313.11 i 305.48 309.39 318.16 j 301.21 .___ ____-----, 294.34 303.83 [ ________________________----311.88 297.70
-
T/‘K
b ~~~~A~E
-x
H~XA~~CA~E
Fig. 5. Int~~olat~ p, T sections of the methane + hexadecane system at constant composid~wp~~nt curves, tion: 0, interpolated data points: --,
M.P. W.M.
Rijkers et al. / Fluid Phase Equilibria
8.5 (1993) 335-345
343
-4
-6
- 8
-10
-12 20000 2/v~moi.m-3~
10000
-
30000
Fig. 6. Calculation of second and third cross-virial coefficients of the methane + hexadecane system at T = 293.15 K, according to Prausnitz and Keeler (1961): 0, data points; __ B,2 = -(618 & 8) x 10e6 m3 mol-‘; =, B,, = -(655 + 4) x 10m6m3 mol-‘; C,rz = (265’k 5) x 1O’Om6 molm2.
10
05 InpIPal
0.0
t
-
10
-15
-20
-25
0
31
32
33 -
34 lOOO/T[Kl
Fig. 7. Experimental vapor pressures of hexadecane: 0, this work; -, Antoine curve from the Research Project 44 of the API (1988); 0, data of Parks and Moore (1949).
M.P. WM. Rijkers et al. / Fluid Phase Equilibria 85 (1993) 335-345
344 TABLE
4
Raoult’s
law vapor pressures
derived
from 1+ g solubility
T(K)
P NV
Y
291.7 294.1 299.2 303.4 308.0 314.6
105.7 104.5 106.4 106.4 105.7 106.4
7.305 9.689 1.819 2.785 4.046 8.166
* Saturated
x x x x x x
IO-’ lo-’ 10m6 1O-6 10m6 10-6
data X
P* (PaI
0.9944 0.9945 0.9945 0.9946 0.9947 0.9948
0.07765 0.1018 0.1946 0.2979 0.4299 0.8734
property.
(1949). The API Antoine curve of hexadecane obtained from these data (Research Project 44 of the API, 1988) is included. Vapor pressures obtained in this work are found to be about 10% lower than the accepted API values. However, it should be noted that the data reported in this contribution show much less scattering than the data measured by Parks and Moore ( 1949). ACKNOWLEDGMENTS
The authors gratefully acknowledge the “Stichting Technische Wetenschappen” and “Gasunie Nederland N.V.” for financially supporting this project. AKZO Chemie provided free the solute supporting material. LIST OF SYMBOLS
B C f: P S
T X Y
z
second virial coefficient third virial coefficient refers to gas phase refers to liquid phase pressure refers to solid phase temperature mole fraction in the liquid phase mole fraction in the gaseous phase compressibility factor
Greek letter q5 fugacity
coefficient
Subscript B
refers to second
(heavy)
component
M.P. WM.
Rijkers et ai. j Fluid Phase Eq~ili~r~
85 (1993) 335-345
345
REFERENCES Davenport, A.J. and Rowlinson, J.S., 1963. The solubility of hydrocarbons in liquid methane. Trans. Faraday Sot., 59: 67-84. De Loos, Th.W., Wijen, A.J.M. and Diepen, G.A.M., 1980. Phase equilibria and critical phenomena in fluid (propane + water) at high pressures and temperatures. J. Chem. Thermodyn., 12: 193-204. Glaser, M., Peters, C.J., Van der Kooi, H.J. and Lichtenthaler, R.N., 1985. Phase equilibria of (methane + n-hexadecane) and (p, Y,, T) of n-hexadecane. J. Chem. Thermodyn., 17: 803-815. Luks, K.D., 1980. Proc. 2nd Int. Conf. on Phase Equilibria and Fluid Properties in the Chemical Industry, Berlin, 17-21 March. Dechema, Frankfurt am Main, pp. 699-712. Parks, G.S. and Moore, G.E., 1949. Vapor pressure and other thermodynamic data for n-hexadecane and n-dodecylcyclohexane near room temperature. J. Chem. Phys., 17( 11): 1151-1153. Peters, C.J., Lichtenthaler, R.N. and De Swaan Arons, J., 1986. Three-phase equilibria in binary mixtures of ethane and higher n-alkanes. Fluid Phase Equilibria, 29: 495-504. Prausnitz, J.M. and Keeler, R.N., 1961. Application of the Kihara potential to high pressure phase equilibria. AIChE J., 7( 3) : 399-405. Research Project 44 of the API, 1988. Selected Values of Properties of Hydrocarbons and Related Compounds. Texas A&M University, College Station TX. 23-2-f 1.lOl)-ka, p. 2. Rijkers, M.P.W.M., Malais, M., Peters, C.J. and De Swaan Arons, J., 1992a. Measurements on the phase behavior of binary hydrocarbon mixtures for modelhng the condensation behavior of natural gas. Part I. The system methane + decane. Fluid Phase Equihbria, 71: 143-168. Rijkers, M.P.W.M., Malais, M., Peters, C.J. and De Swaan Arons, J., 1992b. Measurements on the phase behavior of binary hydrocarbon mixtures for modelling the condensation behavior of natural gas. Part II. The system methane + dodecane. Fluid Phase Equilibria, 72: 309-324. Van der Kooi, H.J., 1981. Ph.D. Dissertation, Delft University of Technology (in Dutch).