Measurements on the phase behavior of binary hydrocarbon mixtures for modelling the condensation behavior of natural gas

Fluid Phase Equilibria, 71 (1992) 143-168 Elsevier Science Publishers B.V., Amsterdam

143

Measurements on the phase behavior of binary hydrocarbon mixtures for modelling the condensation behavior of natural gas Part I. The system methane + decane

M.P.W.M. Rijkers, M. Malais, C.J. Peters ’ and J. de Swaan Arons Faculty of Chemical Engineering and Materials Science, Laboratory of Applied Thermodynamics and Phase Equilibria, Delft University of Technology, Julianalaan 136, 2628 BL Delft (The Netherlands) (Received

January

9, 1991; accepted

in final form July 8, 1991)

ABSTRACT Rijkers, M.P.W.M., Malais, M., Peters, C.J. and de Swaan Arons, J., 1992. Measurements on the phase behavior of binary hydrocarbon mixtures for modelling the condensation behavior of natural gas. Part I. The system methane + decane. Fluid Phase Equilibria, 71: 143-168. This paper reports on data obtained with a recently developed apparatus to measure small amounts of heavy hydrocarbons in compressed methane. The apparatus operates according to the saturation technique. Experimental data are presented for the solubility of decane in methane. In addition experimental data are presented for the solubility of methane in the coexisting liquid phase. The latter work was carried out in a windowed autoclave. The data obtained cover a temperature region of interest for the natural gas industry, i.e. from about 240 to 315 K. Pressures up to 40 MPa have been applied.

INTRODUCTION

Data on solubilities in supercritical fluids are increasingly demanded mainly for predicting extraction processes. For hydrocarbons, the solubility will primarily depend on the density of the solvent and the saturated vapor pressure of the solute. An attractive feature of the supercritical region is

’ Author

to whom correspondence

0378-3812/92/$05.00

should be addressed.

0 1992 Elsevier

Science

Publishers

B.V. All rights reserved

144

that, near the critical point of the solvent, the solvent density can be varied continuously over a wide range of values with only minor changes in operating conditions. It is interesting to observe the analogy between a supercritical extraction process, such as the decaffeination of coffee beans and the so-called retrograde condensation phenomenon of natural gas, that is the appearance of gas condensate when pressure is lowered. In both processes we operate with a supercritical solvent and consider solubility dependencies on temperature and pressure. However, the objectives of the two processes are quite different. In a supercritical extraction process it is endeavoured to enrich the solvent with the solute to give the best yield possible, while in natural gas transportation we wish that the “solvent” (predominantly methane) is capable of keeping the solutes in solution. As the temperature of operation is imposed by the climate, very little can be done to change solvent capacities in natural gases apart from mixing gases from several production wells. Because the operating conditions are often far removed from the critical point of pure methane (T, = 190.55 K, pc = 4.604 MPa), solvent capacity is generally low, which necessitates gas treatment prior to transport. The objective of this study is to supply experimental data of key binaries of interest and to develop a predictive model for calculating the condensation behavior of natural gas, based on the experimental information obtained. The input of this model should be an accurate gas analysis. When the composition is known, the dew point can be predicted by an algorithm embodying a suitable equation of state. Our thesis in this approach is that, within the area of applicability, a predictive equation of state should be well supported by accurate experimental data. Such an equation we like to call “dedicated”. Many important observations can be made concerning gas analysis. For example Dutch natural gas consists predominantly of methane and nitrogen. Apart from these main constituents, a great variety of heavier hydrocarbons are present in the gas. The larger the carbon number, the smaller the concentration. Light components like ethane, ethylene and propane are usually present in concentrations in the order of mole per cents. It can be argued that the presence of these light hydrocarbons enhances the solubility of the heavy ones, while nitrogen will reduce the solubility. Hydrocarbons with a carbon number of six and larger are only present in minute quantities, so that for the CT, fraction the concentrations are typically in the ppm range. As discussed by Cramers (1986), often the normal paraffins are all present as well as their branched and unsaturated counterparts. The condensation behavior seems to depend on both the carbon number and the concentration of the heavy hydrocarbons.

145

In order to obtain an accurate model for the prediction of the condensation behavior of natural gas, it is assumed that only a limited number of key binaries is required as input for the thermodynamic model. This supposition is based on the assumption that the experimental data obtained for the key binaries can be generalized to real natural gas. Preliminary calculations on the phase behavior of a typical natural gas system under pipeline conditions show that natural gas does not behave as an ideal solution, that is the solubility is not dictated only by the vapor pressure of the solute. Raising the pressure above a few bars results in a competition between repulsive and attractive forces and leads to an enhancement in solubility. This effect becomes predominant at higher pressures, at which the minimum solubility occurs, and consequently gives rise to the retrograde region. If the pressure further increases and approaches the critical pressure of the mixture, the solubility increases to a much greater extent. In natural gases under the conditions of interest in this study, the density is always less than about half the critical density of pure methane. Under these circumstances molecular interaction can be approximated by binary interactions only. Table 1 gives an overview of the availability of experimental p,T,x and p,T,y data of binaries of methane + n-paraffin in the temperature region 243.15 K < T < 313.15 K. From this Table some important conclusions can be drawn. (1) The number of data points available decreases if the carbon number of the solute becomes larger. (2) Fewer data are available on solubilities in the gaseous phase than on solubilities in the liquid phase. Often the former type of data is less accurate in terms of solute mole fractions. If the carbon number becomes greater than six, no solubility data exist at all for the gaseous phase. If a heavy hydrocarbon is branched or unsaturated, the number of data points generally decreases dramatically, especially for solubilities in the gaseous phase. Hence it can be concluded that, even for the key systems of interest in this study, a significant experimental gap exists. In the underlying study solubilities in the liquid phase could be measured by the application of high-pressure windowed autoclaves. As solubilities in the gaseous phase can be quite low, typically in the ppm range, a new experimental apparatus was developed for measuring this type of data. The objective of this paper is to discuss both types of experiment. Furthermore, experimental results for the system methane + decane are presented in the present paper. In subsequent papers similar experimental results for the methane binaries of dodecane, hexadecane, benzene, cyclohexane and 3-methylpentane will be presented.

146 TABLE

1

Compilation of the number of literature data points on the phase n-paraffin systems in the temperature range of 243.15-313.15 K Heavy hydrocarbon

Number

Dew points

n-c,

88

88

n-c,

153

153

n-c,

54

12

n-c,

146

29 *

n-c,

22 49 78

0

27’

24

0

n-C,

n-Cl0

a l = not accurate

PHASE

of methane+

Reference

of data points a

Bubble-points/ near-critical phenomena

behavior

0

l

Sage et al., 1940; Roberts et al., 1962; Kahre, 1974; Elliot et al., 1974 Berry and Sage, 1970; Kahre, 1975; Chu et al., 1976 Shim and Kohn, 1962; Lin et al., 1977 Chang et al., 1966; Reamer et al., 1956; Kohn, 1961; Koonce and Kobayashi, 1964a Kohn and Bradisch, 1964 Shipman and Kohn, 1966 Koonce and Kobayashi, 1964b Beaudoin and Kohn, 1967; Reamer et al., 1942 Glaser et al., 1985

at low temperatures.

BEHAVIOR

In the systems to be considered in this work the n-paraffin has a carbon number larger than seven. Because the melting temperatures of the chosen solutes are all much higher than the critical temperature of methane, the phase behavior is of the type shown in Fig. 1. It is of interest to know that the location of the liquid-gas dome is bounded at low temperatures by the three-phase equilibrium sn-l-g. When this dome is intersected at constant composition or temperature, two-phase boundaries appear which can be determined experimentally. Typical phase diagrams and data points, indicated by open circles, are illustrated schematically in Fig. 2. It proved to be useful to present T,x-sections at constant pressure on a logarithmic scale, because of the large differences in solubility as a function of temperature and pressure. For details with respect to the phase diagrams of interest in this study, reference should be made to Davenport and Rowlinson (1963), Luks (19801, Van der Kooi (1981) and Peters et al. (1986).

147

-T Fig. 1. Schematic p,T,x-projection with carbon number > 7.

of the phase behavior

of a system methane

+ n-paraffin,

EXPERIMENTAL

Windowed autoclave

Under vacuum conditions samples of known composition were introduced into a glass vessel, which was subsequently mounted into a stainless steel autoclave. To observe the sample visually, the autoclave was equipped with two sapphire windows. Pressure and temperature can be controlled independently and measured within the ranges 0.2-100 MPa and 250-350 K respectively. Phase boundaries between a homogeneous fluid phase (either liquid or gas) and two fluid phases can be located by varying the pressure at constant temperature. The phase boundaries obtained in this way are schematically illustrated by means of open circles in Figs. 2(b) and 2(c). Facilities were available for sample preparation, which can be subdivided into a liquid supply system, a dedicated gas burette and a sample sealing system. Details about the instrumentation involving both the windowed autoclave and the sample preparation system are described by Van Hest and Diepen (19621, De Loos et al. (19801, Van der Kooi (19811, Glaser et al. (1985) and Sassen et al. (1990).

A P=P,

-log

x0 B

(6 P t

x=x,

-T

Fig. 2. Illustration of phase boundaries obtained by intersecting 1 at (a) p = pl, (b) x = x1 and 63 x = x2.

the p,T,x projection of Fig.

Phase boundaries between a homogeneous vapor phase and two fhtid phases, removed from the critical region, can be located with a dynamic apparatus developed for this purpose, operating according to the so-called saturation technique. In Fig. 3 the principle of operation is shown schematically. A supercritical gas is supplied at constant temperature, pressure and flow rate to a saturation system, in which the gas stream is intensively contacted with the solute. After achieving saturation, the gas is withdrawn from the thermostatted saturators and heated in order to prevent premature condensation. Subsequently the gas stream is allowed to expand to atmospheric pressure. Downstream the gas can either be directed to a solute recovery system or to an absolute flow measuring device. A gas washing unit filled with a suitable solvent appeared to recover the solute

149 Apparatus for the measurement

of

very low solubilities

Compressed gas

Samples

to

GC analysis

Fig. 3. Schematic illustration

of the saturation

apparatus.

fully from the gas stream. The concentration of the solute can be monitored readily by gas chomatography. The supercritical gas, methane in this work, was withdrawn from a gas cylinder and, if necessary, compressed with a membrane compressor (Nova Swiss, model 554.2121) into a 50 ml buffer vessel. The compressor was on/off controlled by a contact pressure gauge. A supply pressure between 3 and 40 MPa could be established. Downstream of the buffer vessel a mechanical pressure controller (Tescom, model 26.1012.14) was installed to dampen the pressure fluctuations induced by the compressor to a constancy better than 0.1 MPa. The flow was subsequently controlled by a mass flow controller (Bronkhorst High Tech, type F-231-FA) in the range of 50-500 ml STP per minute with a constancy better than 1% (relative). Two saturation columns were applied with a volume of 250 ml each and facilities were provided to link the columns either in series or in parallel, or to isolate them from the gas stream through a bypass system. Each column was charged with a solute-supporting material (Si-5-5P pellets, supplied by AKZO Chemie), and approximately 50 g of solute. In this fashion the supporting material was wetted to such an extent that transportation of the solute into the gas stream was not expected to be influenced by adsorption

150

effects. The volume accessible to the gas was estimated to be at least 100 ml for each column. The saturation columns and the valving system were thermostatted by a Lauda thermostat/cryostat (type UK-40DW). Ethanol was used as the thermostatting fluid. The temperature was controlled at a constancy of better than 0.1 K between 240 and 320 K. The pressure was measured by either a digital pressure gauge (Heise, model 710B), calibrated either against a Heise dead weight pressure balance in the range l-30 MPa, with an accuracy of 0.02 MPa, or a dead weight pressure balance (Barnet, type 4050/2) in the range 0.2-l MPa, with an accuracy of 0.01 MPa, or a mercury manometer at atmospheric conditions, with an accuracy better than 0.0001 MPa. The pressure drop over the saturator columns never exceeded 0.001 MPa. The temperature was measured with either a chromel-alumel thermocouple (Thermocoax), calibrated against a Pt-100 resistance thermometer, or a Pt-100 resistance thermometer with a digital reading. In both alternatives the temperature was measured to an accuracy of better than 0.1 K. Downstream of the thermostat the gas is heated to approximately 420 K by application of heating tape and glass wool fiber insulation. At several locations the temperature of the gas stream is monitored to prevent over-heating and to ascertain that no cold spots were present. The pressure is released through a needle valve (Whitey, type SS 21RS4). Right at the downstream side of the needle valve the temperature is monitored. The Joule-Thompson effect appeared to be limited to causing a temperature drop which never exceeded 2 K. A three-way valve (Whitey, type SS 83 XTS4) was built in to direct the gas flow to either a solute collection system or a flow measurement device, preceded by a cold trap. The gas-washing unit consists of a glass column provided with calibration marks, to allow solvent mass calculation and a stirring facility. The heated gas flows into a glass supply tube which is left at ambient temperature. A fine fritted glass bubbler is immersed in the solvent, so that the gas stream is well contacted with the solvent. The solvent chosen was pure heptane and was supplied with a known concentration of undecane. Undecane served as an internal standard in the GC-analyses. The gas washing unit was able to recover at least 99.5% of the solute, as was verified by analysis of the output stream by application of either a cold trap or a second identical gas washer. Under most conditions the solute recovery was much better than this, depending on both the flow rate and the solute concentration. Most of the solute was observed to condense in the gas-washer supply tube, which was rinsed with the solvent after each sample collection, The volume of the solvent ranged from 130 to 170 ml and could be determined to an accuracy of better than 0.2 ml. The samples can be withdrawn manually from the gas washer. A gas chromatograph (Hewlett Packard,

151

type 589OA4)and an integrator (Spectra Physics, type 4290) were used for measuring solute concentrations. The gas chromatograph was equipped with an on-column injector, a fused silica wide-bore column (HP-l Methyl Silicone Gum, 5 m X 0.53 mm X 2.65 PM) and an FID detector (all Hewlett Packard products). The sample analysis was calibrated by employing a quadratic fit between the output signal and concentration, so that concentrations could be accurately measured over a wide range (lop2 to 1O-7 mole fraction, to an estimated accuracy of lop8 mole fraction). Helium was used as the carrier gas. For flow measurement an electronic precision film flow meter (Stec, model SF-101) was used, which was calibrated against a mercury ring volumeter. The time a soap film needed to pass through a calibrated volume was electronically measured and recorded. The temperature of the gas was measured by a chromel-alumel thermocouple, and the pressure was read from a barometer. The moisture content of the gas was found to depend on the flow rate. A dedicated correction formula for the flow rate was derived and reported by De Leeuw and Rijkers (1988) which led to the determination of the flow rate to an accuracy of better than 0.2%. Experimental procedure (windowed autoclave)

A concise description will be given here of the experimental technique involving autoclave measurements, because similar procedures are already described by De Loos et al. (1980), Van der Kooi (1981), Glaser et al. (1985) and Sassen et al. (1990). Samples used for autoclave measurements were prepared by introducing the decane as a liquid phase and methane as a gas. A glass vessel suitable for mounting into the high pressure autoclave was equipped with a nickel spherical stirrer. When immersed in hydrocarbon fluids nickel proved to be an inert material. Liquid decane was injected into the vessel using a volumetric technique. The quantity never exceeded 0.15 ml, while the accuracy was estimated to be better than 0.1 ~1. Subsequently the glass vessel was cooled by liquid nitrogen and evacuated, so that the decane remained as a solid in the glass vessel. Residual air, captured in the solid, was removed by gently melting the decane, followed by the liquid nitrogen treatment and evacuation. The methane was supplied in the gaseous state in a calibrated vessel at a known temperature and pressure. The quantity of methane was accurately determined by application of the virial equation of state. Finally the methane was forced to flow into the evacuated vessel by a mercury drive. To keep the methane in the gas phase, the liquid nitrogen coolant was replaced by a carbon dioxide-ethanol coolant. At atmospheric conditions the glass vessel was decoupled from the dedicated gas burette

152

and evacuation system, and placed into a stainless steel vessel containing distilled and degassed mercury. Finally the coolant was removed, the combination slid into the autoclave bomb and the autoclave sealed and pressurized. Gas solubilities were measured by varying the autoclave pressure at constant temperature. The temperature was controlled and measured in the range 240-360 K with an accuracy of 0.05 K, while the pressure was controlled and measured by a pressure balance (Budenberg) in the range 5-40 MPa with an accuracy of 0.005 MPa. The disappearance of the gas phase in the sample was observed visually at increasing pressures. The accuracy was estimated to be better than 0.02 MPa. Phase boundaries near the critical point were also determined by the same measuring technique. Liquid solubilities in a dense gas phase were measured in a slightly different fashion. First the pressure was lowered in a homogeneous gas phase until a liquid mist, usually very thin, was perceived. Then the pressure was raised until the mist disappeared. The pressure hysteresis could achieve values up to 0.1 MPa for the mixture rich in methane. Mixtures richer in methane could not be treated in this way without an unacceptable loss in accuracy. The circumstances are now suitable for the saturation technique. Experimental procedure (saturation apparatus)

Prior to the measurements on gas-phase solubilities of a selected binary system the following preparations are necessary. (1) The saturation columns are charged with the supporting material, carrying the solute. To rule out liquid entrainment, the columns are charged with dry pellets at both ends, while approximately 400 ml of cell volume is charged with the impregnated pellets. (2) A stock gas-washing solvent, containing a known quantity of internal standard, is prepared. (3) The gas-washer sample analysis is calibrated by preparing at least six mixtures with a known concentration of the solute to be measured. After the saturation columns are installed and the gas washer is filled with the solvent (heptane) containing the internal standard (undecane), the entire flow apparatus is flushed with methane at a low pressure. The temperature and the methane flow are kept constant. Pressure is generated by restricting the methane flow from the columns by turning the needle valve. The saturation columns are connected in series and after they have reached the desired temperature, at least 15 minutes are allowed to equilibrate the flow system. A solubility measurement in the gas phase involves the determination of the time (t ), solvent level in the gas washer

1.53

(h), solute concentration (c) and flow (a). Obtaining this information before and after the sample collection (referring to subcripts 1 and 2, respectively) will lead to the desired solubility in the following straightforward fashion: Am = (A + Bh,)pc, il.solute

=

Am/M

n solvent= ~ww~* x solute

- (A + Bh,)pc,

=?Z

solute/(%olvent

(1) (2)

-

wYne.ttla”e(STP) +

%hlte)

(3) (4)

where Am denotes the solute mass increase during collection, A and B are calibration constants for the gas washer volume and p stands for the solvent density at ambient temperature. (M is the molar mass of the solute and u is the molar volume under standard conditions.) At the same system temperature and pressure the procedure is repeated. Generally the two values agreed within 2%, which can be shown by performing an error and sensitivity analysis. Some measurements, however, did not agree within the desired reproducibility, but when there was no reason to discard poorly reproducible data points the results were averaged. Chemicals

The methane used in this work was an AGA Research-Grade chemical. Its specified purity of 99.995 mol.% was verified by means of GC-analysis. Decane and undecane were purchased from Janssen Chemie (Tilburg, The Netherlands) with a specified purity of better than 99%. GC-analyses showed that the purity of both chemicals was 99.8%. All chemicals were used without further purification.

RESULTS

Autoclave measurements

Phase boundaries were measured at constant composition for fourteen mixtures in the temperature region from 240 to 360 K, covering a composition range between 0.01 and 1 mole fraction of decane. Numerical values for the data points are given in Table 2, while the data are displayed in Fig. 4. The phase behavior of three mixtures, all having a mole fraction of decane less than 0.05 correspond to Fig. 2(b), that is the liquid phase

154 TABLE 2 Autoclave measurements of the liquid-gas system. * Dew point lines T (K>

p (MPa)

y = 0.0124 * 22.845 248.07 23.645 259.29 y = 0.0247 * 29.105 245.61 256.84 29.665 267.48 29.905 y = 0.0498 * 248.98 33.675 33.585 260.58 272.15 33.565 x = 0.0994 36.945 244.79 36.645 256.08 267.05 36.485 x = 0.1414 36.545 249.26 260.18 36.355 36.285 271.14 x = 0.1986 34.345 246.90 259.14 34.275 34.295 260.06 x = 0.2507 30.095 247.90 259.03 30.315 30.640 271.60 x = 0.3470 245.28 21.505 22.425 258.59 x = 0.4544 14.215 246.95 15.105 256.17 15.935 265.07 x = 0.5241 247.11 10.675 11.615 257.67 12.445 267.62 x = 0.5951 8.035 246.41 258.55 8.955 269.12 9.695

phase boundaries of the methane+decane

T (K)

p (MPa)

T (K>

p (MPa)

T (K)

p @@a)

272.38 283.95

24.245 24.445

295.42 309.34

24.345 23.445

321.87 335.68

21.145 17.745

278.90 289.31 302.54

29.975 30.035 29.745

315.27 326.84 338.38

29.420 28.645 27.770

350.33

26.745

283.91 296.65 308.67

33.555 33.465 33.225

321.26 334.88 351.51

32.755 32.135 30.955

274.99 285.75 292.72

36.435 36.365 36.315

306.75 317.58 329.32

36.165 35.975 35.695

339.12 350.67

35.375 34.895

281.34 295.21 307.61

36.245 36.215 36.105

320.77 333.58 350.26

35.925 35.595 35.015

271.23 271.33 281.28

34.355 34.365 34.465

288.17 305.18 316.74

34.535 34.705 34.705

328.00 339.42 350.15

34.635 34.475 34.215

282.50 293.01 302.12

30.905 31.205 31.465

314.12 325.43 336.13

31.695 31.845 31.905

348.23

31.875

273.37 287.39

23.475 24.315

305.86 321.37

25.295 25.895

334.91 349.40

26.275 26.555

275.37 285.06 294.82

16.795 17.495 18.225

306.23 316.27 327.05

18.895 19.385 19.845

337.42 347.60

20.215 20.525

278.12 289.54 299.06

13.215 14.085 14.655

311.47 323.96 336.11

15.315 15.865 16.335

348.12

16.705

279.40 291.26 303.08

10.350 11.065 11.665

315.42 327.91 338.48

12.215 12.705 13.065

348.32

13.335

155 TABLE

2 (continued)

T (K)

p (MPa)

T (K)

P

5.285 5.835 6.315

281.15 293.21 304.96

2.955 3.235 3.445 1.405 1.525 1.665

x = 0.6950 247.81 259.08 269.51 x = 0.8066 245.91 255.47 264.70 x = 0.9008 248.33 258.15 268.35

T (K)

p (MPa)

T (K)

p (MPa)

6.825 7.355 7.805

316.15 326.30 338.00

8.165 8.465 8.785

348.92

9.025

276.08 285.19 299.46

3.755 3.985 4.295

308.61 319.10 329.83

4.495 4.695 4.885

340.60 349.43

5.055 5.195

281.03 291.76 303.54

1.805 1.935 2.045

319.58 333.71 347.39

2.195 2.325 2.435

(MPa)

dissolved in the gaseous phase. In the remaining eleven mixtures a gaseous phase is dissolved in the liquid phase (Fig. 2(c)). The critical composition is located between y = 0.0498 and x = 0.0994 over the entire range of tem-

Fig. 4. Experimental two-phase boundaries of the system methane+decane: o, 0, experimental points, and full curves are the best least-squares fit to low-degree polynomials.

156 TABLE

3

Saturation measurements of the solubility of decane in methane T K)

y

p = 0.100 MPa 262.7 8.840x 272.4 2.245 x p = 0.20 MPa 262.0 4.691 x 273.1 1.202x p = 0.50 MPa 261.8 2.213 x 273.1 5.711 x p = 1.00 MPa 261.6 1.404 x 273.1 3.623 x p = 2.10 MPa 253.3 9.154x 263.2 1.888x 5.156x 277.3 p = 4.10 MPa 251.6 1.387x 261.9 2.539 x 272.7 4.733 x p = 6.19 MPa 251.9 3.389x 262.0 5.306x 272.5 8.095 x p = 10.76 MPa 261.8 3.376x 272.5 4.062x p = 15.10 MPa 263.0 1.512x 274.5 1.478x p = 20.10 MPa 262.3 4.618 x 274.6 4.427 x p = 25.10 MPa 262.4 1.051 x 274.9 1.031 x l

T 00

Y

T (IQ

Y

282.8 293.6

5.154x 1o-4 1.094x 10-s

302.8

2.319x 1O-3

282.8 293.6

2.609 x 1O-4 5.956 x 1O-4

302.9 312.6

1.256x 1O-3 1.996x 1O-3 *

1O-5 10-5

282.7 293.6

1.284 x 1O-4 2.815 x 1O-4

303.0

5.547x 1o-4

10-5 10K5

282.8 293.6

8.068 x 10-s 1.961 x lop4

303.1

3.371 x 10-4

10-6 10-s 1O-5

285.9 295.0 306.9

8.763 x 1O-5 1.501 x 10-4 2.641 x 1O-4 *

314.8

3.815 x 1O-4

1O-5 1O-5 10-s

282.8 293.9 304.3

8.808 x 10-s 1.615 x 1O-4 2.380x 1O-4

314.3

3.548x 1O-4

1O-5 1O-5 1O-5

285.3 294.5 305.8

1.500x 10-4 2.186x 1O-4 3.267x 1O-4

318.2

4.984 x 1O-4

1O-4 1O-4

284.5 294.2

5.123 x 1O-4 6.275 x 1O-4

304.8 314.5

8.349x 1O-4 1.077x 10-s

10-3

1O-3

283.8 294.0

1.573 x 10-s 1.744x 10-s

304.4 314.0

1.954 x 10-s 2.203 x 1O-3

1O-3 1O-3

283.5 293.7

4.591 x 10-s 4.685 x 1O-3

303.6 314.1

4.993 x 10-s 5.407 x 10-s

1o-2 10-2

283.8 294.6

1.029x lo-* 1.042x lo-*

304.2 313.7

1.073x 10-Z 1.096x lo-*

1O-5 1O-4 1O-5 10-4

l

l

l

l

Reproducibility > 2%.

perature, and therefore does not show a strong dependence on temperature. P,x,y-sections at constant temperature have been obtained by fitting the phase boundaries at constant composition by a low-degree polynomial and evaluating their functional values at the desired temperatures. In Fig. 4

157 ro p/HPa

t IO

Fig. 5. Interpolated p(n,y)-sections of the system methane + decane at constant temperature: o, T = 263.15 K, A, T = 283.15 K, 0, T = 303.15 K.

p,y-sections are included at temperatures of 263.15, 283.15 and 303.15 K. Corresponding numerical values are given in Table 4. For the sake of clarity the p,x,y-sections are also shown in Fig. 5. The p,x,y-sections nearly overlap, which implies that the solubilities in the liquid phase for this system do not show a strong temperature dependence.

260

280

Fig. 6. Interpolated

T,y-sections

320

100 -

T/K

of the system methane-t

decane at constant pressure.

158

-5 0

10

20

p/MPa

-

Fig. 7. Interpolated

p,y-sections

of the system methane+decane

at constant

temperature.

Saturation measurements

At eleven pressures, ranging from 0.1 to 25.1 MPa, solubilities in the gas phase were measured as a function of temperature (240 K < T < 315 K) in the saturation apparatus. The data points are compiled in Table 3, and included in Figs. 5 and 6. The measured isobars were fitted with low-degree polynomials, taking the temperature scale as linear and the composition scale as logarithmic. In this fashion p,y-sections were obtained by interpolating the polynomials at constant temperature. Several p,y-sections are shown in Fig. 7. Intersecting the T, log,,(y)-isobars at constant composition results in the various p,2”-sections shown in Fig. 8. Numerical values of the interpolations are also listed in Tables 4-6.

250

260

270

280 -

Fig. 8. Interpolated

290

300

310

320

T/K

p,T-sections

of the system methane+decane

at constant

composition.

159 TABLE 4 Pressure-composition X,Y T = 263.15 K 9.440x 10-5 5.201 x10-5 2.484 x lo-’ 1.582x lo-’ 1.911 x 10-5 2.736x 1O-5 5.500x 10-5 3.466x lop4 1.517x 10-3 T = 283.15 K 5.232x 1O-4 2.724 x 1O-4 1.301 x 1o-4 8.446x lo-’ 7.428x 1O-5 8.866 x 1o-5 1.336x 1O-4 4.995 x 1o-4 1.572x 1O-3 T = 303.15 K 2.298x 1O-3 1.219x 1O-3 5.580x 1O-4 3.496 x 1O-4 2.262x 1O-4 2.375 x 1O-4 3.026x 1O-4 7.955 x 1o-4 1.951 x 10-j

P

data at interpolated temperatures

@IPa)

x,y

P (MPa)

X,Y

P

0.10 0.20 0.50 1.00 2.10 4.10 6.19 10.76 15.10

4.587 x 1O-3 1.047x 10-2 0.0124 0.0247 0.0498 0.0994 0.1414 0.1986 0.2507

20.10 25.10 23.802 29.793 33.578 36.525 36.333 34.301 30.416

0.3470 0.4544 0.5241 0.5951 0.6950 0.8066 0.9008

22.778 15.762 12.086 9.288 6.027 3.425 1.596

0.10 0.20 0.50 1.00 2.10 4.10 6.19 10.76 15.10

4.524x 1O-3 1.030x lop2 0.0124 0.0247 0.0498 0.0994 0.1414 0.1986 0.2507

20.10 25.10 24.527 30.057 33.560 36.374 36.249 34.490 30.944

0.3470 0.4544 0.5241 0.5951 0.6950 0.8066 0.9008

24.068 17.390 13.614 10.585 6.926 3.927 1.833

0.10 0.20 0.50 1.00 2.10 4.10 6.19 10.76 15.10

4.983 x 1O-3 1.062x lo-* 0.0124 0.0247 0.0498 0.0994 0.1414 0.1986 0.2507

20.10 25.10 23.885 29.769 33.353 36.206 36.153 34.690 31.461

0.3470 0.4544 0.5241 0.5951 0.6950 0.8066 0.9008

25.147 18.700 14.871 11.665 7.721 4.377 2.043

(MPa)

DISCUSSION AND CONCLUSIONS

The developed saturation apparatus proved to be a welcome supplement to the static cell apparatus in the sense that the condensation behavior of dilute mixtures can now be measured. Although for the system methane + decane the experimental domains of the two types of equipment did not overlap, the results seem to combine into a uniform p,x,y phase diagram. For binary systems the two coexisting phases can be simply related by binodals at constant pressure and temperature. However, owing to the extra degrees of freedom, for systems composed of more than two components this simple relationship does not apply. This is an important limita-

160 TABLE 5 Pressure-composition sections of the saturation measurements for the system methane + decane at interpolated temperatures

T(K)

Y p (MPa) = 0.10

0.20

260.0 270.0 280.0 290.0 300.0 310.0

7.058 x 1.742x 4.057 x 8.195x 1.848x 3.615x

4.076x 9.062x 2.095 x 4.746x 9.917x 1.801 x

7-W

Y

10-s 1O-4 1o-4 1O-4 1O-3 1O-3

p (MPa) = 2.10

4.10

260.0 270.0 280.0 290.0 300.0 310.0

1.521 x 1O-5 3.141 x10-s 6.109x 1O-5 1.117x 1o-4 1.914x 10-4 3.090x 1o-4

2.099x 3.917x 7.195 x 1.265 x 2.061 x 3.034 x

T (K>

Y

260.0 270.0 280.0 290.0 300.0 310.0

p (MPa) = 15.10

20.10

1.517x 1.466 x 1.521 x 1.660 x 1.858x 2.089x

4.645 x 4.488x 4.488 x 4.624x 4.875 x 5.224x

10-3

1O-3 1O-3 10-s 1O-3 1O-3

0.50 1O-5 lo-’ 1O-4 1O-4 10-4 1O-3

1.879x 4.479 x 1.016x 2.191 x 4.496x 8.774x

1O-5 10-s 10-s 1O-4 1O-4 10-4

4.519 x 7.129x 1.127x 1.758x 2.655 x 3.819x

1.00 1O-5 10-s 1O-4 1O-4 1O-4 1O-4

1.188x 2.889 x 6.598x 1.414x 2.843 x 5.363 x

10-s 1O-5 1O-4 1O-4 1O-4 1O-4

3.214x 3.873 x 4.677x 5.741 x 7.228x 9.441 x

6.19

1O-5 1O-5 1O-5 10-4 1O-4 1O-4

10.76 1O-4 1O-5 1O-4 10-4 1O-4 10-4

25.10 1O-3 1O-3 1O-3 1O-3 1O-3 1O-3

1.054x 1.035x 1.030x 1.035x 1.054x 1.084x

10-2 lo-* 10-2 10-2 10-2 lo-*

tion in the application of our experimental set-up. However, if natural gas is assumed to be built up of pure components and binary sub-systems, measurements on systems containing more than two components can be avoided, and the advantage of a relatively simple and straightforward operation of the equipment can be exploited. The phase diagrams generated lead to some important observations. At pressures higher than about 0.5 MPa, the system starts to deviate from ideality. For the liquid phase Henry’s law no longer holds, which follows from the strong curvature of the bubble-point line in the p,x,y-sections. The dew point line also starts to deviate from the ideal situation, because the hyperbolic character disappears. This curve bends to a minimum solubility of decane (with respect to mole fraction x) in the supercritical methane, which will be reached at pressures typically between 1 and 4 MPa. At low pressures solubility is dependent on vapor pressure and

161 TABLE 6 Temperature-pressure decane at interpolated

sections of the saturation compositions

measurements

for the system methane +

T (K)

p (MPa)

y = 20 (ppm) 0.10 0.20 0.50 1.00 2.10 4.10 6.19

260.7 265.8 363.8 257.9

50

100

200

500

255.4 262.7 271.3 276.6 277.0 273.2 261.0

263.8 271.2 279.8 285.4 288.1 285.3 276.6

271.6 279.5 288.8 294.9 300.7 299.1 292.6

282.6 290.7 301.5 308.9 322.6 318.6

therefore on temperature only. However, at high pressures too the enhancement effect has to be taken into account, leading to an effective vapor pressure, primarily dictated by solvent density, which under the conditions we consider is not such a pronounced function of the temperature.

-6

-8 0

10000

20000 -

3 2/v (molm-l)

Fig. 9. Calculation of second and third cross-virial coefficients of the system methane+ decane at T = 303.15 K, according to the method proposed by Prausnitz and Keeler (1961). m3 mol-‘; z, B,,= -(387&4)~10-~ I, data-point; -9 B,,= -(366&ll)x1O-6 m3 mol-’ and C1i2 = (133 f 6)x lo-” m6 mol-‘.

162

A severe test for the consistency of the data on solubilities in the vapor phase was proposed by Prausnitz and Keeler (1961). This test involves simultaneous calculations of second and third cross-virial coefficients (B,, and Cn2, respectively) from measured isotherms. For this purpose the procedure utilized by Renon et al. (1989) was applied, resulting typically in the graph shown in Fig. 9. The resulting slope of the curve at zero pressure represents B,*, while Cl,* starts to play a role at higher pressures. The error bars represent the sum of the 2% reproducibility allowance in the saturation measurement and the error in solubility due to a 0.2 K temperature fluctuation. The dashed lines represent uncertainty limits due to the standard deviation in B,,and Cl,*. The description of the data by the virial equation turns out satisfactorily, and therefore we consider our data consistent. It is interesting to compare the experimental results with the measurements of other investigators. At a temperature of 310.85 K Reamer et al. (1942) measured a p,x,y-section by applying a sampling technique from a static cell. In Fig. 10 an interpolated p,x,y-section at T = 310.85 K is compared with the findings of Reamer et al. (1942). It can be observed that the bubble-points agree very well, while a discrepancy exists between the measured solubilities in the vapor phase. The error analysis of Reamer et al. (1942), however, reveals that the uncertainty in the measured weight

0 20

0 00

0 LO

0 60

0 80

100

DECANE

-x

METHANE

p.dF

+

+

zo-

+

o

’

+

+

t

15 -

0+ + +

IO-

,’

5_

0: 0+ 0+

0

d++, 0

METHANE

Fig. 10.

-A 0 002

-x

0 004

0 006

0 008

0 010

DECANE

Interpolated p(x,y)-section of the system methane+decane this work; +, data of Reamer et al. (1942).

at T = 310.85 K: o,

163

fraction of decane is approximately 0.003 over the whole composition range, which roughly corresponds to an uncertainty in mole fraction of 0.0004. The reproducibility of our measurements is generally better than 2%, and when the assumptions on which the experimental set-up was based hold, the accuracy will correspond to the reproducibility. This would imply that the absolute error in our experiment is much smaller than that in the experiment of Reamer et al, and that our results fall completely inside their area of uncertainty, so that in this region too our experimental results are in agreement. d’Avila et al. (1976) measured solubilities of decane in dense methane in the temperature range of 325-400 K using a saturation technique. In Fig. 11 our data are compared with the data of d’Avila et al. At approximately 6 MPa the data are in excellent agreement, but at 10 MPa a discrepancy is observed. Extending this isobar to a higher temperature would result in an absolute deviation between the two data sources of approximately 40%. We measured the highest solubility. No explanation can be given for this remarkable deviation. If it is assumed that Raoult’s law can be applied, vapor pressures of decane can be obtained from solubility data, i.e.

P*(n - C,,)

=Yb

- GdP/x(~ - clcl)

(5)

in which rc(n - C,,) can be estimated from a linear interpolation between roughly p = 0 at x(n - C,,) = 1 and p =p(x = 0.9008, T). Values of pressures, phase compositions and calculated vapor pressures are summarized for five temperatures in Table 7. In our opinion, measuring vapor pressures

250

300

350

-T/K

Fig. 11. T,y-sections of the system methane+ decane at constant pressure: o, this work; 0, data of d’Avila et al. (1976); values of pressures are shown.

164 TABLE 7 Indirect determination of the vapor pressure technique by application of Raoult’s law T (K)

p (kPa)

Y

262.7 272.4 282.8 293.6 302.8

106.0 105.4 105.5 104.4 105.2

8.840x 2.245 x 5.154 x 1.094x 2.319 x

1O-5 1O-4 10-4 10-s 1O-3

curve of decane

utilizing

the saturation

(Pa)

X

p*

0.9937 0.9942 0.9946 0.9949 0.995 1

9.431 2.381 x 5.466 x 1.148 x 2.452 x

10’ 10’ lo2 lo*

is a severe test of the performance of the saturation apparatus, because the retention time of the gas in the saturation columns is minimized. Although this effect will be somewhat compensated by an increase in diffusivity, it is to be expected that saturation is hard to achieve at low pressures. Therefore a retention time in the saturator columns of at least one minute was allowed. In Fig. 12 a comparison is given between the experimental vapor pressures determined by several authors. Excellent agreement between the recently published data of Chirico et al. (1989) and the vapor pressure data obtained in this work is shown in this figure. At low temperatures the vapor pressure of decane measured by Carruth and Kobayashi (1973) is in excellent agreement with our findings. At higher temperatures, however, the values of our vapor pressures are larger than theirs. In both experiments a saturation technique was employed. Perhaps, under these condi-

7

ln[p/Pal 6I

54-

-

lOOO/[T/Kl

Fig. 12. Experimental vapor pressures of decane: o, this work; full curve, Antoine curve from the Research Project 44 of the API (1988); 0, data of Carruth and Kobayashi (1973); W, data of Linder (1931); A, data of Chirico et al. (1989).

165

tions, saturation was not fully achieved in Carruth’s experiments. Research Project 44 of the American Petroleum Institute (1988) and data from Linder (1931), suggest somewhat larger vapor pressures of decane over the entire temperature range. This difference cannot be explained by recalling the ideal behavior assumption of the gas phase, because in that case the measured values of the vapor pressure from the saturation technique should be higher than those from the static method. Non-ideality of the liquid phase at best leads to a small correction which certainly cannot lead to an agreement between the data. Linder (1931) measured saturation pressures using a static method. Apparently discrepancies in the measurements of the vapor pressures are caused by the differences in the measuring technique. Because vapor pressures are measured directly by application of the static method one should prefer static measurements to dynamic measurements, the latter category includes the saturation technique. Overviews of measuring techniques for vapor pressures are given in the OECD Guidelines (1981) and by Spencer and Cliath (1983).

ACKNOWLEDGMENTS

The authors gratefully acknowledge the Stichting Technische Wetenschappen and Gasunie Nederland N.V. for financially supporting this project. AKZO Chemie (Hengels) freely provided the solute supporting material.

LIST OF SYMBOLS

-0 C

f A4

Am n P T S t V

x Y

calibration constants concentration refers to gas phase refers to liquid phase molar mass mass difference amount of substance pressure temperature refers to solid phase time volume mole fraction in liquid phase mole fraction in vapor phase

166

Greek symbols P

@

density flow rate

Subscripts

B C

1,2

refers to the second (heavy) component refers to the critical condition sample index

Superscripts *

refers to saturation

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