Solubility of propane in sulpholane at elevated pressures.

Schmidt, Kurt A.G. ; Jou, Fang-Yuan ; Mather, Alan E. 等

The solubility of propane in sulpholane has been determined at temperatures in the range 298-403 K at pressures up to 17.6 MPa. The experimental results were correlated by the Peng-Robinson equation of state, and binary interaction parameters have been obtained for this system. The parameters in the Krichevsky-Ilinskaya equation were calculated from these interaction parameters.

On a determine la solubilite du propane dans le sulfolane a des temperatures comprises entre 298 et 403 K et des pressions jusqu'a 17,6 MPa. Les resultats experimentaux ont ete correles par l'equation d'etat de Peng-Robinson et des parametres d'interaction binaire ont ete obtenus pour ce systeme. Les parametres dans l'equation de Krichevsky-Ilinskaya ont ete calcules a partir de ces parametres d'interaction.

Keywords: solubility, propane, sulpholane, equation of state, gas treating

Sulpholane is a polar solvent, miscible with water and a good solvent for many compounds. It is a physical solvent, in that there is no chemical reaction when gases dissolve in it. Sulpholane is used in the Sulfinol process, where it is mixed with water and an alkanolamine (Dunn et al., 1964). Originally, di-isopropanolamine was used but now N-methyldiethanolamine is more common. This solvent is used to remove the acid gases, [H.sub.2]S and C[O.sub.2], from natural gases and refinery gas mixtures. A question often posed is: what is the solubility of hydrocarbons in a physical solvent, since this quantity amounts to a loss of desirable material. An ideal solvent would remove [H.sub.2]S and C[O.sub.2] without concomitant absorption of hydrocarbons. Rivas and Prausnitz (1979) reported values of the Henry's constant of ethane in sulpholane at four temperatures in the range 303-373 K. Jou et al. (1990) measured the solubility of [H.sub.2]S, C[O.sub.2], methane and ethane in sulpholane at elevated pressures in the range of temperatures from 298-403 K. In the present work the solubility of propane in sulpholane is reported over the same temperature range.

EXPERIMENTAL

The apparatus and experimental technique that were used are similar to those described by Jou et al. (1990). The equilibrium cell was mounted in an air bath. The temperature of the contents of the cell was measured by a calibrated iron-constantan thermocouple and the pressure in the cell was measured by digital Heise gauges (0-10, 0-35 MPa). These gauges had an accuracy of [+ or -]0.1% of full scale by comparison with a dead-weight gauge. The thermocouple had an accuracy of [+ or -]0.1[degrees]C by comparison with a platinum resistance thermometer. The apparatus was checked by determination of the critical point and vapour pressure of propane, carbon dioxide, and hydrogen sulphide. Differences of [+ or -]0.1[degrees]C and 0.1% in vapour pressure were found. The sulpholane (CAS No. 126-33-0) was obtained from Aldrich and had a purity of 99%. Propane was obtained from Matheson and had a purity of 99%.

Prior to the introduction of the fluids, the cell was evacuated. About 100 [cm.sup.3] of liquid sulpholane was drawn into the cell. It was heated to 110[degrees]C and a vacuum applied to remove traces of water. The propane was added to the cell by the cylinder pressure or by means of a spindle press. Although the melting point of sulpholane is 300.6 K, data were obtained at 298.15 K when a sufficient amount of propane was added, causing a liquid phase to form. The circulation pump was started and the vapour bubbled through the solvent for at least 8 h to ensure that equilibrium was reached. A sample of the liquid phase, (2 to 20 g), depending on the solubility, was withdrawn from the cell into a 50 [cm.sup.3] sample bomb, which had previously been evacuated and weighed. The bomb contained a magnetic stirring bar to help in degassing the sample. The sample bomb was reweighed to determine the mass of the sample and then attached to a vacuum rack. The rack consisted of 6.35 mm OD stainless steel tubing connected to a calibrated Digigauge (0 to 1.0 MPa), a 50 [cm.sup.3] burette, and a 51.5 [cm.sup.3] steel reservoir. The rack was evacuated and the gas was allowed to evolve from the sample bomb into the reservoir, which was cooled by liquid nitrogen. The sample bomb was heated to about 50[degrees]C to drive out the propane. The sample bomb was then disconnected, and the apparatus allowed to warm to room temperature. The moles collected were calculated from the P-V-T data, assuming ideal gas behaviour. The correction for the residual propane left in the sample at atmospheric pressure was very small. The uncertainty in the liquid phase analyses is estimated to be [+ or -] 3%.

RESULTS

The solubility of propane in sulpholane was determined at temperatures of 298.15 K, 313.15 K, 343.15 K, 373.15 K, and 403.15 K at pressures up to 17.6 MPa. The experimental data are presented in Table 1 and plotted in Figure 1. At the lower temperatures, a sharp transition occurs between (vapour + liquid) and (liquid + liquid) equilibria. At higher pressures a liquid propane-rich phase is in equilibrium with a liquid sulpholane-rich phase.

[FIGURE 1 OMITTED]

DISCUSSION

The equilibrium data were correlated in the manner described by Jou et al. (1990). The method requires that an equation of state valid for the solvent and dilute solutions of the solute in the solvent be available. The Peng and Robinson (1976) equation of state was used in the calculations. The parameters a22 and b2 of propane were obtained from the critical constants. However, sulpholane decomposes before it reaches its critical temperature. The parameters a11 and b1 for sulpholane were therefore obtained from the vapour pressure and liquid density. The critical constants and acentric factor of the propane and the equations for the vapour pressure and density of sulpholane were taken from the compilation of Rowley et al. (2003). The resulting values of [a.sub.11] and [b.sub.1] for sulpholane, and [a.sub.22] and [b.sub.2] for propane are given in Table 2. The values of [a.sub.11] and [b.sub.1] are slightly different from those presented earlier (Jou et al., 1990) because of small differences between the data compilation used in the earlier work and that of Rowley et al. (2003). In the two-phase regions, the isothermal flash routine algorithm presented by Whitson and Brule (2000) was used. The binary interaction parameter, k12, which appears in the mixing rule of the equation of state:

[a.sub.12] = [([a.sub.11][a.sub.22]).sup.1/2] (1 - [k.sub.12]) (1)

was iteratively modified until the deviations between the calculated liquid mole fraction and the experimental value were less than the set tolerance.

Values of k12 were found to be dependent on the temperature and can be fitted by a linear relationship:

[k.sub.12] = 1.87 x [10.sup.-4]T/K - 1.87 x [10.sup.-3]

The correlation reproduces the experimental data with an overall average per cent deviation in the mole fraction of 1.6%, somewhat less than the experimental uncertainty.

The binary interaction parameter, which was fit to the two-phase data, and the pure component parameters were then used to predict a three-phase bubble point pressure. The three-phase bubble point calculations were performed with the three-phase bubble point technique described by Nutakki et al. (1988) and Shinta and Firoozabadi (1997). Based on this technique and the above mentioned parameters, the calculated three-phase point pressure and compositions are given in Table 3, together with the vapour pressure of pure propane.

The calculated mole fraction of propane in the sulpholane phase is in good agreement with the experimental values given in Table 1. The vapour phase is essentially pure propane and the calculated three-phase pressure is very close to the vapour pressure of pure propane, and is always lower than the experimental values.

Bender et al. (1984) have shown the connection between the Peng-Robinson EOS, the binary interaction parameter and the three parameters in the Krichevsky-Ilinskaya equation. This equation is discussed in the book by Prausnitz et al. (1999) and is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The three parameters are the Henry's constant, [H.sub.21], the partial molar volume at infinite dilution, and the Margules parameter, A. Recently, Schmidt (2005) has corrected the equations which relate these parameters to the binary interaction parameter in the Peng-Robinson equation of state. The equations were used to obtain the three parameters and they are given in Table 4. The Henry's constant for propane in sulpholane is plotted in Figure 2 for comparison with those for methane and ethane. The Henry's constant for methane has a maximum and is the largest, indicating that it has the lowest solubility in sulpholane of the three alkanes. Ethane is two to three times more soluble than methane, and propane is about twice as soluble as ethane. The value of the partial molar volume at infinite dilution is proportional to the "size" of the solute. The value for propane is 1.8 times that of methane and 1.3 times that of ethane.

[FIGURE 2 OMITTED]

ACKNOWLEDGEMENT

The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for the financial support of this research.

NOMENCLATURE

a parameter in the Peng-Robinson equation (Pa x [m.sup.6]/[mol.sup.2])

A Margules parameter (J/mol)

b parameter in the Peng-Robinson equation ([cm.sup.3]/mol)

[[??].sub.i] fugacity of component i in a mixture (kPa)

[H.sub.21] Henry's constant of solute 2 in solvent 1 at [P.sup.s.sub.1] (MPa)

[k.sub.ij] binary interaction parameter in the Peng-Robinson equation

[P.sup.s.sub.i] vapour pressure of component i (MPa)

P pressure (kPa)

R gas constant (J/mol x K)

T absolute temperature (K)

[[??].sup.[infinity].sub.2] partial molar volume at infinite dilution ([cm.sup.3]/mol)

[x.sub.i] mole fraction of component i in the liquid phase

[y.sub.i] mole fraction of component i in the vapour phase

Superscripts

[alpha] sulpholane-rich phase

[beta] propane-rich phase

REFERENCES

Bender, E., U. Klein, W. Ph. Schmitt and J. M. Prausnitz, "Thermodynamics of Gas Solubility: Relation Between Equation-of-State and Activity-Coefficient Models," Fluid Phase Equil. 15, 241-255 (1984).

Dunn, C. L., E. R. Freitas, J. W. Goodenbour, H. T. Henderson and M. N. Papadopoulis, "Sulfinol Process," Oil Gas J. 62 (11), 95-98 (1964).

Jou, F.-Y., R. D. Deshmukh, F. D. Otto and A. E. Mather, "Solubility of [H.sub.2]S, C[O.sub.2], CH4 and C2H6 in Sulfolane at Elevated Pressures," Fluid Phase Equil. 56, 313-324 (1990).

Nutakki, R., A. Firoozabadi, T. W. Wong and K. Aziz, "Calculation of Multiphase Equilibrium for Water-Hydrocarbon Systems at High Pressures," SPE 17390, SPE/ DOE Enhanced Oil Recovery Symposium, Tulsa, OK, U.S., April 17-20 (1988).

Peng, D.-Y. and D. B. Robinson, "A New Two-Constant Equation of State," Ind. Eng. Chem. Fundam. 15, 59-64 (1976).

Prausnitz, J. M., R. N. Lichtenthaler and E. G. de Azevedo, "Molecular Thermodynamics of Fluid-Phase Equilibria," 3rd ed., Prentice-Hall, Englewood Cliffs, NJ, U.S. (1999), p. 592.

Rivas, O. R. and J. M. Prausnitz, "Sweetening of Sour Natural Gases by Mixed-Solvent Absorption: Solubilities of Ethane, Carbon Dioxide, and Hydrogen Sulfide in Mixtures of Physical and Chemical Solvents," AIChE J. 25, 975-984 (1979).

Rowley, R. L., W. V. Wilding, J. L. Oscarson, Y. Yang, N. A. Zundel, T. E. Daubert and R. P. Danner, "DIPPR Data Compilation of Pure Compound Properties," Design Inst. Phys. Prop., AIChE, NY, U.S. (2003).

Schmidt, K. A. G., "Letter to the Editor," Fluid Phase Equil. 236, 268-269 (2005).

Shinta, A. A. and A. Firoozabadi, "Predicting Phase Behavior of Water/Reservoir-Crude Systems Using the Association Concept," SPE Reservoir Eng. 12 (2), 131-137 (1997).

Whitson, C. H. and M. R. Brule, "Phase Behavior," SPE Monograph Series 20, Soc. Petroleum Eng., Richardson, TX, U.S. (2000).

Manuscript received August 27, 2005; revised manuscript received December 27, 2005; accepted for publication January 3, 2006.

Kurt A. G. Schmidt (1), Fang-Yuan Jou (2) and Alan E. Mather (2 *)

(1.) Department of Physics and Technology, University of Bergen, Allegaten 55, N-5007 Bergen, Norway

(2.) Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G6

* Author to whom correspondence may be addressed.

E-mail address: alan.mather@ualberta.ca

Table 1. Solubility of propane (2) in sulpholane (1)

 298.15 K 313.15 K

P/MPa [x.sub.2] x P/MPa [x.sub.2] x
 [10.sup.3] [10.sup.3]

 0.267 12.9 0.113 4.68

 0.667 31.9 0.236 8.77

 0.978 (a) 45.5 0.905 34.8

 1.81 45.3 1.60 (a) 52.0

 3.10 47.1 2.16 53.7

 6.14 48.4 3.95 55.3

 9.74 48.9 7.22 54.2

13.86 50.2 9.14 56.5

17.35 51.8 13.30 59.3

 343.15 K 373.15 K

P/MPa [x.sub.2] x P/MPa [x.sub.2] x
 [10.sup.3] [10.sup.3]

 0.104 3.12 0.237 5.69

 0.211 6.00 0.662 14.9

 0.748 21.9 1.33 29.5

 1.48 41.8 3.05 62.2

 2.87 (a) 67.8 5.00 79.6

 4.29 69.1 9.84 90.7

 7.19 72.0 13.39 91.4

 9.58 74.0 17.34 99.5

11.75 75.6

13.78 77.4

17.62 79.6

 403.15 K

P/MPa [x.sub.2] x
 [10.sup.3]

 0.264 5.08

 0.732 14.6

 2.03 37.3

 3.60 61.7

 5.75 86.1

 8.22 94.9

10.49 104

13.52 114

16.93 114

(a) Three-phase point (vapour, propane-rich liquid, sulpholane-rich
liquid)

Table 2. Equation of state parameters

T/K Sulpholane (1)

 [a.sub.11]([dagger]) [b.sub.1]1([double dagger])

298.15 7.24 88.9

313.15 7.11 89.3

343.15 6.86 90.0

373.15 6.64 90.7

403.15 6.44 91.4

T/K Propane (2)

 [a.sub.22]([dagger]) [b.sub.2]([double dagger]) [k.sub.12]

298.15 1.15 56.3 0.054

313.15 1.12 56.3 0.057

343.15 1.06 56.3 0.062

373.15 1.01 56.3 0.068

403.15 0.964 56.3 0.074

([dagger]) Units of a are Pa x [m.sup.6] x [mol.sup.-2]

([double dagger]) Units of b are [cm.sup.3] x [mol.sup.-1]

Table 3. Calculated three-phase pressures and compositions

T/K P/MPa [y.sub.1] x [x.sup.[alpha].sub.2] x
 [10.sup.6] x [10.sup.3]

298.15 0.95 1.2 45

313.15 1.36 4.3 52

343.15 2.58 47 67

T/K P/MPa [x.sup.[beta].sub.2] x [P.sup.S.sub.2]/MPa
 x [10.sup.3]

298.15 0.95 3.8 0.953

313.15 1.36 4.2 1.37

343.15 2.58 4.2 2.59

Table 4. Parameters of the Krichevsky-Ilinskaya equation

T/K [H.sub.21]/MPa [??]/[cm.sup.3] A/RT
 [mol.sup.-1]

298.15 20.7 66.5 1.97

313.15 24.8 67.5 1.87

343.15 33.2 69.3 1.71

373.15 41.8 72.2 1.58

403.15 50.0 75.2 1.48