Article pubs.acs.org/jced
Solubility of Methane in Propylene Carbonate Fang-Yuan Jou and Alan E. Mather* Department of Chemical and Materials Engineering University of Alberta Edmonton, Alberta T6G 2G6 Canada
Kurt A. G. Schmidt Schlumberger-Abingdon Technology Center Abingdon, OX14 1UJ, United Kingdom ABSTRACT: The solubility of methane in propylene carbonate was measured at the temperatures (244.26, 248.14, 255.37.37, 266.48, 273.15, 298.15, 333.15, and 373.15) K. Pressures ranged from (101 to 11200) kPa. The Peng−Robinson equation of state was used to correlate the data over the full temperature and pressure range. A linearly temperature dependent binary interaction parameter was found to correlate the experimental data the best. The correlation reproduces the experimental data with an overall average percent deviation in the mole fraction of 6.9 %. The Krichevsky− Ilinskaya equation combined with the Peng−Robinson equation of state was used to obtain Henry’s constants of methane in propylene carbonate.
■
INTRODUCTION The removal of the acid gases (H2S and CO2) from gas streams is often accomplished by absorption in a liquid solvent. Two general classes of solvents are usedphysical and chemical solvents. In the latter there is a chemical reaction with the acid gases, while in the former no reaction between the solvent and the acid gases takes place. A number of organic liquids have been used as physical solvents. One of these is propylene carbonate. Propylene carbonate has two beneficial physical properties, which allow the absorption process to operate at low temperatures. In addition the amount of methane dissolved in the propylene carbonate is relatively low compared with other physical solvents. Recent applications of the propylene carbonate process have been presented by Mak et al.1 The solubility of methane dissolved in the propylene carbonate is important as it represents a loss of hydrocarbons in the process and results in hydrocarbon emissions to the atmosphere. Only four data sets for the methane−propylene carbonate binary system are extant. Rusz2 measured the solubility of methane in propylene carbonate at four temperatures (283.15, 293.15, 303.15, and 313.15) K and Shakhova and Zubchenko3 measured the solubility of methane at elevated pressures at (298.15 and 303.15) K. Lenoir et al.4 and Parcher et al.5 determined the Henry’s constant by gas chromatography.
uncertainty in the liquid phase compositional (mole fraction) analyses is estimated to be ± 3 %. Table 1. Sample Description
a
source
minimum stated purity
Aldrich Praxair
99.3 %b 99.99 %b
4-Methyl-1,3-dioxolan-2-one. bNo further purification was attempted.
■
RESULTS AND DISCUSSION The solubility of methane in propylene carbonate was measured at the temperatures of (244.26, 248.15, 255.37, 266.48, 273.15, 298.15, 333.15, and 373.15) K at pressures up to 11200 kPa. The experimental data are presented in Table 2. The equilibrium data were correlated in the manner described by Jou et al.8 The isothermal flash routine algorithm presented by Whitson and Brulé11 was used to calculate the solubility of methane at each temperature and pressure of interest. In this calculation approach the temperature and pressure are set as inputs. The Peng−Robinson9 equation (EOS) of state was used. The equation of state parameters a22 and b2 of methane (solute) were obtained from the equation of state parameters (Tc, Pc, and ω) presented in Rowley et al.10 The parameters a11 and b1 for propylene carbonate (solvent) were obtained over the complete temperature range from the vapor pressure and
■
EXPERIMENTAL SECTION The apparatus that was used is similar to that described by Jou et al.6 The experimental procedure is the same as that given by Jou and Mather.7 The provenance and purity of the methane, CAS No. 74-82-8, and the propylene carbonate (PC), CAS No. 108-32-7, samples are given in Table 1. The relative standard © 2015 American Chemical Society
chemical name propylene carbonatea methane
Received: September 14, 2014 Accepted: February 18, 2015 Published: February 26, 2015 1010
DOI: 10.1021/je500849m J. Chem. Eng. Data 2015, 60, 1010−1013
Journal of Chemical & Engineering Data
Article
was regressed from the experimental data. The objective function, in this case, was based on the deviation of the calculated liquid mole fraction from the experimental value. Values of k12 were found to have a slight dependence with the temperature and were correlated by a linear relationship:
Table 2. Solubility of Methane (2) in Propylene Carbonate (1)a P/kPa
x2·103
T/K = 244.26 10342 49.3 6895 37.0 3447 21.9
T/K = 266.48 10342 51.6 8000 41.1 6895 37.5 5450 31.5 3970 23.9 2540 16.7
T/K = 333.15 10600 54.8 7960 43.2 5600 31.8 2400 14.8 900 6.4b 400 3.0b 200 1.6b 102 0.87b
a b
P/kPa
x2·103
T/K = 248.15 10350 49.5 7600 40.0 4800 27.2 3450 22.3 2320 15.0 1880 12.2 940 6.9b 330 2.9b 330 2.5b 120 0.95b T/K = 273.15 11000 50.2 8000 41.3 5100 29.1 2400 15.1 1010 7.3b 707 5.1b 305 2.3b 120 0.95b T/K = 373.15 11200 59.8 7700 43.8 6110 36.0 4170 25.2 1850 11.9b 1850 11.8b 920 7.0b 300 2.4b 207 1.7b 101 0.84b
P/kPa
x2·103
T/K = 255.37 10342 49.9 6895 37.4 3447 21.5
k12 = 8.00·10−2 − 3.88· 10−4(T /Κ)
The Peng−Robinson equation of state, with the parameters in Table 3 and the optimal binary interaction parameter (eq 2) was able to correlate the experimental data to within an overall average percent deviation in the mole fraction of 6.9 %, somewhat greater than the experimental uncertainty. The experimental data and the correlated values from the Peng− Robinson equation of state are compared in Figure 1. The
T/K = 298.15 10500 52.0 10342 51.8 7700 40.0 6895 41.9 2500 15.1 600 4.3b 300 2.3b 105 0.83b
Figure 1. Experimental data for the propylene carbonate (1) + methane (2) system compared with correlated values using the Peng− Robinson equation of state. Experimental data: ●, 244.3 K; ○, 248.2 K; ⧫, 255.7 K; ◊, 266.5 K; ▲, 273.2 K; △, 298.2 K; ■, 333.2 K; □, 373.2 K; Peng−Robinson equation of state: solid black line, 244.3 K; round dot black line, 248.2 K; square dot black line, 255.7 K; brown solid line, 266.5 K; round dot brown line, 273.2 K; square dot brown line, 298.2 K; solid blue line, 333.2 K; round dot blue line, 373.2 K.
Standard uncertainties are u(T) = 0.1 K, ur(P) = 0.1 %, ur (x2) = 3 %. Value obtained by gas chromatography.
experimental data of Rusz2 and Shakhova and Zubchenko3 are compared with the results calculated from the Peng−Robinson equation of state in Figure 2. The calculated solubilities agree (some differences at higher pressures) with the experimental data of Shakhova and Zubchenko.3 The data of Rusz2 appear to be inconsistent with both the data and calculations obtained in this investigation and those of Shakhova and Zubchenko.3 The binary interaction parameter obtained calculates the data determined by Shakhova and Zubchenko3 to within 8.8 %, somewhat greater than the estimated error (5 %) presented in Clever and Young.12 Bender et al.13 have shown the connection between the Peng−Robinson EOS, and the Krichevsky−Ilinskaya equation. This connection allows for the calculation of the three parameters, Henry’s constant (at the vapor pressure of the solvent), H21, the partial molar volume at infinite dilution, v∞ 2̅ , and the Margules parameter, A, in the Krichevsky−Ilinskaya equation from the Peng−Robinson equation of state parameters of the solute and solvent (a22, b2, a11, and b1) and the binary interaction parameter. The Krichevsky−Ilinskaya equation is described by Prausnitz et al.14 and is
liquid density correlations presented in the compilation of Rowley et al.10 The resulting parameters a11 and b1 for propylene carbonate, and a22 and b2 for methane at each temperature of interest are presented in Table 3. The binary interaction parameter, k12, which appears in the mixing rule of the equation of state: a12 = (a11a 22)1/2 (1 − k12)
(1)
Table 3. Equation of State Parameters propylene carbonate (1)
a
(2)
methane (2)
T/K
a11a
b1b
a22a
b2b
k12
244.26 248.15 255.37 266.48 273.15 298.15 333.15 373.15
5.98 5.95 5.91 5.83 5.79 5.64 5.46 5.26
76.9 77.1 77.3 77.7 78.0 78.9 80.2 81.7
0.22 0.21 0.21 0.20 0.20 0.19 0.17 0.16
26.8 26.8 26.8 26.8 26.8 26.8 26.8 26.8
−0.015 −0.016 −0.019 −0.023 −0.026 −0.036 −0.049 −0.065
∧
ln(f2 /x 2) = ln H21 +
Units of a are Pa·m6·mol−2. bUnits of b are cm3·mol−1. 1011
v2̅ ∞(P − P1s) A 2 + (x1 − 1) RT RT
(3)
DOI: 10.1021/je500849m J. Chem. Eng. Data 2015, 60, 1010−1013
Journal of Chemical & Engineering Data
Article
al.5 than to those of Lenoir et al.4 The average absolute percent deviations between the model and the reported results are 4.1 % and 8.4 % respectively. The solubility of methane has a minimum around 333 K as evidenced by the Henry’s constant reaching a maximum value at this temperature. At lower pressures (P < 7 MPa) the solubility of methane in propylene carbonate is almost independent of temperature. At higher pressures, the solubility of methane increases with increasing temperature. Enthalpies and entropies of solution were calculated from the dependence of the Henry’s constant with temperature according to eq 4 and eq 514 and the generalized smoothing equation of Clarke and Glew.17 Figure 2. Experimental data for the propylene carbonate (1) + methane (2) system of Rusz2 and Shakhova and Zubchenko3 compared with correlated values using the Peng−Robinson equation of state. Experimental data: ▲, 298.2 K (Shakhova and Zubchenko3); △, 323.2 K, (Shakhova and Zubchenko3); ●, 283.2 K (Rusz2); ○, 303.2 K (Rusz2); ⧫ 313.2 K (Rusz2;) ◊, 293.2 K (Rusz2); Peng− Robinson equation of state: solid black line, 283.2 K; round dot black line, 293.2 K; square dot black line, 298.2 K; brown solid line, 313.2 K; round dot brown line, 323.2 K.
3 −1 v∞ 2̅ /cm mol
A/RT
244.26 248.15 255.37 266.48 273.15 298.15 333.15 373.15
135.0 135.9 137.2 139.1 139.9 142.4 143.7 142.5
33.2 33.4 33.7 34.3 34.7 36.1 38.5 41.9
0.833 0.816 0.788 0.749 0.727 0.661 0.597 0.553
⎛ ∂ ln H ⎞ Δ s2̅ ⎜ ⎟ = − ⎝ ∂ ln T ⎠ P R
(5)
Table 5. Calculated Enthalpies and Entropies of Solution of Methane in Propylene Carbonate
Table 4. Parameters of the Krichevsky−Ilinskaya Equation H21/MPa
(4)
The calculated enthalpies and entropies of solution of methane in propylene carbonate are presented in Table 5.
The equations originally presented in Bender et al.13 and Deshmukh and Mather15 were corrected by Schmidt.16 The corrected equations were used to calculate H21, v∞ 2̅ , and A at each temperature. These parameters are given in Table 4. The
T/K
⎛ ∂ ln H ⎞ Δh2̅ ⎜ ⎟ = R ⎝ ∂(1/T ) ⎠ P
T/K
Δh̅2/kJ mol−1
Δs2̅ /J mol−1K−1
244.26 248.15 255.37 266.48 273.15 298.15 333.15 373.15
−0.77 −0.74 −0.70 −0.63 −0.57 −0.37 −0.02 0.47
−63.0 −62.9 −62.7 −62.4 −62.2 −61.5 −60.4 −59.0
Table 5 shows that the dissolution of methane in propylene carbonate results in negative enthalpies and entropies of solution up to a temperature around 333 K after which the changes in enthalpy are accompanied by a positive value. The change in sign of the enthalpy of solution also indicates that the solubility of methane increases up to a temperature of about 333 K and then decreases after this temperature.
Henry’s constant for methane in propylene carbonate is plotted in Figure 3 for comparison with those obtained by Lenoir et al.4 and Parcher et al.5 As illustrated in Figure 3 the calculated Henry’s constants are nearer to those obtained by Parcher et
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for financial support of this research. Notes
The authors declare no competing financial interest.
■ Figure 3. Temperature dependence of the Henry’s law constants for methane (2) in propylene carbonate (1). ●, this investigation; ⧫, Lenoir et al.;4 ◊, Parcher et al.;5 solid line, Peng−Robinson equation of state. 1012
NOMENCLATURE a = parameter in the Peng−Robinson equation, Pa·m6/mol2 A = Margules parameter, J/mol b = parameter in the Peng−Robinson equation, cm3/mol fî = fugacity of component i in a mixture, MPa Δh21 = enthalpy of solution, J/mol H21 = Henry’s constant of solute 2 in solvent 1 at Ps1, MPa k12 = binary interaction parameter in the Peng−Robinson equation DOI: 10.1021/je500849m J. Chem. Eng. Data 2015, 60, 1010−1013
Journal of Chemical & Engineering Data
Article
Ps1 = vapor pressure of component i, MPa P = pressure, MPa Pc = critical pressure, MPa R = gas constant, J/mol·K Δs21 = entropy of solution, J/mol·K T = absolute temperature, K Tc = critical temperature, K v2̅ ∞ = partial molar volume at infinite dilution, cm3/mol xi = mole fraction of component i in the liquid phase yi = mole fraction of component i in the vapor phase ω = acentric factor
■
REFERENCES
(1) Mak, J.; Nielsen, D.; Schulte, D. An Update of the Fluor Solvent Process. Proceedings of the Laurance Reid Gas Conditioning Conference, Norman, OK, February 25−28, 2007. (2) Rusz, L. Gas Absorption Studies XX. The Decarbonatization of the Synthesis Gas with Propylene Carbonate on High Pressures. Veszp. Veg. Egy. Kőz. 1968, 11, 169−180. (3) Shakhova, S. F.; Zubchenko, Yu. P. Solubility of Methane and Argon in Organic Solvents. Khim. Prom. 1973, 49, 595−596. (4) Lenoir, J.-Y.; Renault, P.; Renon, H. Gas Chromatographic Determination of Henry’s Constants of 12 Gases in 19 Solvents. J. Chem. Eng. Data 1971, 16, 340−342. (5) Parcher, J. F.; Bell, M. L.; Lin, P. J.; Giddings, J. G. Determination of the Solubility of Gases in Liquids by Gas−Liquid Chromatography. Adv. Chromatogr. 1984, 24, 227−246. (6) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. The Solubility of Nitrous Oxide in Water at High Temperatures and Pressures. Zeit. Phys. Chem. 1992, 177, 225−239. (7) Jou, F.-Y.; Mather, A. E. Solubility of Ethane in Aqueous Solutions of 2-(2-Aminoethoxy)ethanol. J. Chem. Eng. Data 2010, 55, 5846−5847. (8) Jou, F.-Y.; Deshmukh, R. D.; Otto, F. D.; Mather, A. E. Solubility of H2S, CO2 and CH4 in n-Formyl Morpholine. J. Chem. Soc., Faraday Trans. I 1989, 85, 2675−2682. (9) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (10) Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Zundel, N. A.; Daubert, T. E.; Danner, R. P. DIPPR Data Compilation of Pure Component Properties; Design Inst. Phys. Prop.: New York, 2003. (11) Whitson, C. H.; Brulé, M. R. Phase Behavior, SPE Monograph Series 20; Soc. Petroleum Eng.: Richardson, TX, 2000. (12) Clever, H. L.; Young, C. L. Eds. Methane; IUPAC Solubility Data Series, Vol. 27/28; Pergamon Press: New York, 1987. (13) Bender, E.; Klein, U.; Schmitt, W. Ph.; Prausnitz, J. M. Thermodynamics of Gas Solubility: Relation between Equation-ofState and Activity-Coefficient Models. Fluid Phase Equilib. 1984, 15, 241−255. (14) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. “Molecular Thermodynamics of Fluid-Phase Equilibria” 3rd ed., PrenticeHall: Englewood Cliffs, NJ, 1999. (15) Deshmukh, R. D.; Mather, A. E. Letter to the Editor. Fluid Phase Equilib. 1987, 35, 313−314. (16) Schmidt, K. A. G. Letter to the Editor. Fluid Phase Equilib. 2005, 236, 268−269. (17) Clarke, E. C. W.; Glew, D. N. Evaluation of Thermodynamic Functions from Equilibrium Constants. Trans. Faraday Soc. 1966, 62, 539−545.
1013
DOI: 10.1021/je500849m J. Chem. Eng. Data 2015, 60, 1010−1013
