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PVTx measurements and partial molar volumes for water–hydrocarbon mixtures in the near-critical and supercritical conditions
Fluid Phase Equilibria 150–151 Ž1998. 537–547
PVTx measurements and partial molar volumes for water–hydrocarbon mixtures in the near-critical and supercritical conditions I.M. Abdulagatov ) , A.R. Bazaev, E.A. Bazaev, M.B. Saidakhmedova, A.E. Ramazanova Institute for Geothermal Problems of the Dagestan Scientific Center of the Russian Academy of Sciences, 367030 Makhachkala, Kalinina 39-A, Dagestan, Russian Federation
Abstract By means of a constant-volume piezometer, measurements have been made of the PVTx properties of water q hydrocarbon Ž n-heptane, n-octane, and benzene. mixtures at near-critical and supercritical conditions. The measurements cover the pressure range from 5 to 40 MPa and densities between 20 and 450 kg my3 for six compositions from 0 to 0.614 mole fraction of hydrocarbon. Tests on the piezometer and consistency tests on the measurements suggest that the results are free from significant ‘dead volume’ error. The experimental errors of the present PVTx measurements are estimated to be within "0.01 K in temperature, "0.15% in density, "2 kPa in pressure, and "0.002 mole fraction in composition. Good agreement was obtained with values reported in the literature for pure components Žwater, n-heptane, n-octane, and benzene., measured using other techniques. Values of partial molar volumes and the Krichevskii parameter have been obtained from these measurements. Analysis of the results for dilute water–hydrocarbon mixtures shows that partial molar volumes of the hydrocarbon Žsolute. near the critical point of pure water Žsolvent. exhibit remarkable anomalies. The experimental results have been interpreted in terms of modern molecular thermodynamic models for the partial molar volumes of the solute near the solvent critical point and Kirkwood–Buff fluctuation theory of solutions in terms of direct correlation function integral. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Apparent molar volume; Critical state; Density; Excess molar volume; Partial molar volume; Piezometer; Pressure; Supercritical fluid; Water
1. Introduction Water, the most important solvent in nature, has surprising properties as a reaction medium in its supercritical state. The remarkable anomalous properties of supercritical fluids, in general, as well as )
Corresponding author. N.I.S.T. Thermophysics Division 838.08, 325 Broadway, Boulder CO 80303-3328, USA. Tel.: q1-303-497-4027; fax: q1-303-497-5224; e-mail: [email protected] 0378-3812r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 8 . 0 0 3 0 0 - 8
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I.M. AbdulagatoÕ et al.r Fluid Phase Equilibria 150–151 (1998) 537–547
supercritical water, in particular, are widely used as a solvent or reaction medium for a number of technological applications w1x. Supercritical fluids are of fundamental importance in geology and mineralogy Ž for hydrothermal synthesis. , in chemistry, in the oil and gas industries Ž e.g., in tertiary oil recovery., for some new separation techniques, especially in supercritical fluid extraction, for regeneration of sorbents used in wastewater treatment, for hazardous waste decontamination of soils or equipment, and for oxidation of hazardous chemicals. Binary aqueous fluid mixtures with hydrocarbons are interesting combinations of polar and non-polar molecules. The near-critical local environment Ž microstructure. around an infinitely dilute solute can be dramatically different from the bulk average. This is associated with the divergence of the solute partial molar volume at the solvent’s critical point. The aim of this work was to use PVTx measurements of dilute water q hydrocarbon mixtures near the critical point of pure water to study the anomalous critical behavior of the partial molar volume of hydrocarbons at the critical point of pure water Ž solvent.. Very little has been published concerning the PVTx properties of water q hydrocarbon mixtures at near- and supercritical conditions due to the experimental difficulties in their measurement. In previous papers w2–4x we reported PVTx data of five water–hydrocarbon binary mixtures Ž waterq methane, –n-hexane, –n-heptane, –n-octane, –benzene. at supercritical conditions. The new PVTx data for water q n-heptane, water q n-octane, and water q benzene systems in the immediate vicinity of the solvent’s critical point provide additional information on the effects of temperature, pressure, and composition on the PVT relation in such systems, which could lead to improved understanding of the behavior near the solvent’s critical point. A number of phase equilibrium Ž PTx . studies have been made on water–n-alkane mixtures w5–7x. Most of the measurements were performed at temperatures up to the critical point of pure water.
2. Experimental Since the experimental apparatus and procedure have been reported in Refs. w2–4x, only a brief explanation is given here. Experimental methods were similar to those described in Refs. w2–4x, except that a smaller Žf 3.68 = 10y5 m3 . piezometer was used. The volume of the piezometer has been carefully calibrated by using standard fluid Ž pure water. with well known PVT properties w8x at a temperature T0 s 673 K and at a pressure P0 s 39 MPa. The volume at these conditions was VP 0,T 0 s 3.688 " 0.0003 = 10y5 m3. The main part of the apparatus consisted of an air thermostat, a piezometer, lines for filling and extracting samples, temperature control and temperature measuring devices, and pressure measuring instruments. The temperature in the air thermostat was controlled automatically to within "5 mK. The air thermostat has double walls and it has an inside volume of 0.065 m3. Guard heaters have been located between the walls of the thermostat for setting the desired temperature inside the thermostat. The regulating heater was mounted inside the thermostat to avoid thermal losses. The temperature is measured by a 10 V platinum resistance thermometer. The uncertainty in the temperature measurement, when local temperature gradients and temperature stability are taken into account, is less than "0.01 K. To minimize temperature gradients in the air thermostat, two electrically driven high-speed fans were provided. The cylindrical piezometer was made from a heat- and corrosion-resistant high-strength alloy ŽEI-437B4.. On one of the ends of the piezometer, a diaphragm-type null indicator is mounted and on
I.M. AbdulagatoÕ et al.r Fluid Phase Equilibria 150–151 (1998) 537–547
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the other end, a high pressure valve. The diaphragm Ž0.04 m in diameter and 8 = 10y5 m thick. was made from Type 321 stainless steel. The pressure measurements have an uncertainty of "2 kPa. To reach equilibrium rapidly, the electric heater was switched on and the sample was stirred with a steel ball bearing which was rotated rapidly in the sample by a mechanical rotation of the piezometer. The volume of the piezometer Ž VPT . was corrected for its variation with temperature T and pressure P. Taking into account the uncertainties in temperature, pressure and concentration measurements, the total experimental uncertainty of density, dr is not more than "0.2%.
3. Results In Tables 1–3, some of the experimental results for water q n-heptane, water q n-octane, and water q benzene binary mixtures are presented at the critical temperature of water Ž TC s 647.05 K.. Some of these measured results are also shown in Figs. 1–4. Measurements have been made at the critical temperature of water Ž TC s 647.05 K., at pressures from 5 to 40 MPa, and at six hydrocarbon mole fractions from 0 to 0.614 for each system. Fig. 3 shows the molar volume Vm of a water q hydrocarbon mixtures at the critical temperature and pressure of water Ž TC s 647.05 K and PC s 22.035 MPa. as a function of composition. The measurements of the pure components Ž water, n-heptane, n-octane, and benzene. were carried out in order to confirm the reliability of the present apparatus. In order to check the apparatus, density Table 1 Measurements of PVTx for waterqbenzene mixtures at the critical temperature of water P
r
Vm
P
r
Vm
P
r
Vm
x s 0.028 4.618 9.241 15.077 21.263 25.404 28.490 34.655
18.480 40.536 78.323 161.713 410.311 484.011 542.676
1064.954 485.505 251.271 121.699 47.964 40.661 36.265
x s 0.043 4.695 9.369 13.599 16.500 19.800 25.293 29.672 37.676
19.581 42.897 69.850 95.177 135.750 339.791 465.4007 541.279
1052.808 480.561 295.125 216.591 151.856 60.668 44.294 38.085
x s 0.063 3.508 5.424 8.593 12.890 17.537 21.282 25.352 27.185 33.646
16.037 24.380 40.564 67.143 108.301 167.917 307.127 374.552 484.691
1359.757 894.448 537.591 324.782 201.354 129.867 71.003 58.221 44.991
x s 0.075 5.424 8.593 14.235 17.537 21.610 23.105 31.127 36.787
25.086 41.801 79.324 110.502 176.650 211.529 444.505 504.305
896.808 538.195 283.611 203.590 127.354 106.355 50.612 44.610
x s 0.222 5.424 8.593 17.537 22.328 25.228 36.491
34.276 56.371 151.472 229.857 287.579 451.191
915.062 556.397 207.065 136.453 109.064 69.515
x s 0.439 5.060 9.981 17.390 22.217 28.533 35.509
46.726 104.021 223.588 313.728 406.631 471.866
950.221 426.839 198.581 141.525 109.191 94.095
P, Pressure ŽMPa.; r , Density Žkg my3 .; Vm , Molar volume Žcm3 moly1 .; x, Composition Žmole fraction of benzene.; TC s647.05 K.
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Table 2 Measurements of PVTx for waterq n-heptane mixtures at the critical temperature of water P
r
Vm
P
r
x s 0.028 4.737 13.082 18.930 21.820 24.194 28.343 38.334
19.832 66.405 123.567 180.412 279.970 421.399 524.269
1023.060 305.535 164.194 112.458 72.468 48.147 38.699
x s 0.048 4.881 12.208 17.891 21.943 25.516 30.612 37.997
22.090 64.973 117.355 178.111 296.998 419.054 492.557
992.906 337.566 186.894 123.141 73.848 52.339 44.528
x s 0.173 4.713 10.398 15.900 24.147 30.417 41.137
29.915 73.271 127.198 239.063 327.625 420.867
1076.601 439.545 253.197 134.718 98.302 76.523
x s 0.474 4.733 8.026 12.060 16.776 26.939 40.294
53.956 98.131 158.705 231.513 347.803 427.211
1055.454 580.326 358.830 245.982 163.737 133.302
Vm
P
r
Vm
x s 0.082 4.983 11.424 14.474 20.215 22.481 23.926 28.348 39.071
24.376 64.294 88.593 153.341 191.640 221.739 320.847 448.249
1016.482 385.374 279.674 161.583 129.291 111.741 77.225 55.276
x s 0.706 4.700 9.144 15.241 23.746 39.046
77.193 172.630 288.9626 377.099 454.710
984.847 440.383 263.091 201.600 167.191
P, Pressure ŽMPa.; r , Density Žkg my3 .; Vm , Molar volume Žcm3 moly1 .; x, Composition Žmole fraction of n-heptane.; TC s647.05 K.
Table 3 Measurements of PVTx for waterq n-octane mixtures at the critical temperature of water P
r
Vm
x s 0.031 4.607 7.763 11.426 17.841 21.722 23.565 26.922 28.690 38.268
19.660 35.569 54.218 107.324 176.384 244.522 368.389 410.816 507.826
1070.122 591.492 388.047 196.033 119.280 86.042 57.111 51.213 41.430
x s 0.263 5.143 9.559 15.207 20.203 36.796
43.356 87.762 149.715 224.189 402.703
998.612 493.332 289.189 193.123 107.513
P
r
Vm
P
r
Vm
x s 0.048 5.109 7.413 12.305 18.295 21.808 25.222 27.030 36.503
23.508 34.887 63.481 123.711 184.707 289.895 345.599 480.168
961.626 647.984 356.110 182.735 122.390 77.981 65.412 47.080
x s 0.078 4.603 9.854 15.993 20.470 22.717 24.142 27.232 38.257
22.642 54.347 105.487 164.622 208.561 243.363 321.304 460.100
1125.437 468.880 241.564 154.791 122.180 104.708 79.308 55.384
x s 0.425 5.154 9.463 14.991 22.375 33.562 43.211
63.473 127.773 222.786 328.275 415.971 459.470
928.248 461.118 264.462 179.479 141.641 128.231
x s 0.614 4.894 9.473 14.971 22.430 36.618
84.134 190.134 301.701 385.128 460.692
916.358 405.486 255.5406 200.184 167.350
P, Pressure ŽMPa.; r , Density Žkg my3 .; Vm , Molar volume Žcm3 moly1 .; x, Composition Žmole fraction of n-octane.; TC s647.05 K.
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Fig. 1. The pressure of the mixture waterqbenzene as a function of density at the critical temperature of water Ž647.05 K. for various compositions.
Fig. 2. Compressibility factor Ž Zs PVm r RT . as a function of pressure for waterq n-octane mixtures at the critical temperature of water Ž647.05 K. for various compositions.
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Fig. 3. Molar volume Vm as a function of composition for waterqhydrocarbon mixtures at the critical temperature and pressure of water.
Fig. 4. The pressure of the mixture waterq n-heptane as a function of composition at the critical temperature of water Ž647.05 K. for various near-critical isochores.
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Fig. 5. Test measurements of densities of benzene taken with the apparatus in comparison with experimental densities of other authors w9x.
measurements on the pure components have been carried out also on three isotherms Ž 573, 623, and 648 K.. From Fig. 5, it can be seen that the test measurements for benzene are in excellent agreement within "0.3%, with the previously measured values w9x. The excellent agreement between these measured densities may be considered as validation of these experimental results.
4. Discussion The partial molar volumes Vi , i s 1,2, are obtained from the slope of tangent Ž EVm rE x . P T w10x. The measurements of the molar volumes VmŽ P,T, x . at the critical temperature and pressure of water Ž TC s 647.05 K and PC s 22.035 MPa. have been correlated as a function of the concentration x by the equation: N yx
Vm Ž x . s V0 e
x iy g r bd
Ý Ž i y grbd . q Ž1 y x . Vmc Ž PC ,TC . q xV12 ,
Ž1.
is1
where g s 1.24, b s 0.325, and d s 4.83 are universal critical exponents; N s 2; VmcŽ PC ,TC . s 55.838 cm3 moly1 is the critical volume of pure water; and V0 and V12 are non-universal adjustable parameters. From our experimental PVTx data at the critical temperature and pressure of water, we have deduced values for V0 and V12 . Our results are: V0 s 19.385, V12 s 113.341 cm3 moly1 for water q benzene, V0 s 25.070, V12 s 189.581 cm3 moly1 for water q n-heptane, and V0 s 30.044, V12 s 230.872 cm3 moly1 for water q n-octane mixtures. From Eq. Ž 1., we derived Ž EVmrE x . P T
I.M. AbdulagatoÕ et al.r Fluid Phase Equilibria 150–151 (1998) 537–547
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which yields the partial molar volumes V1 and V2 . At the critical temperature and pressure of water in the limit x ™ 0, Ž EVmrE x . P T , diverges as xyg r bd . Consequently, V2` behaves as xy g r bd , which is in good agreement with the non-classical limiting behavior w11x. The classical Ž mean field theory. predicts the behavior of V2` as xy2r3. In Figs. 6 and 7, the partial molar volumes for hydrocarbons derived from our experimental molar volumes are shown as a function of concentration and pressure at the critical temperature of water. In the vicinity of the solvent’s critical point Ž T ™ TC ., the partial molar volume of an infinitely dilute ` . solute Ž x ™ 0. in a binary mixture is given by Ref. w12x: V2` s ry1 K T d , where d s r kT Ž1 y C12 is the infinite dilution limit of the rate of change of pressure upon solute addition at constant temperature, volume, and solvent mass. The partial molar volume of the solute V2` can be expressed ` . ` as in Ref. w12x: V2` s kTK T Ž1 y C12 , where C12 s rHc`12 Ž r .d r is the DCFI Ž solute–solvent direct ` correlation function integral. and c12 Ž r . is the direct correlation function Ž DCF. . This equation is an identity and follows from reformulating the Kirkwood–Buff fluctuation theory of solutions w13x in terms of the DCF w14x: ` C12 s1y
d r kT
,
Ž2.
Ž .yg where: d s Ž EPrE x . CV T q Ky1 T . Asymptotically near the critical point, T ™ TC , the K T A T y TC C C ™ q`, and d ™ Ž EPrE x . V T , where: Ž EPrE x . V T is the Krichevskii parameter. In terms of a long-ranged fluctuation integral, the partial molar volume of an infinitely dilute solute can be written ` as in Ref. w15x: r V2` s r kTK T y G 12 , where G 12 s rH0`Ž g 12 y 1.4p r 2 d r is the statistical excess number of solvent molecules surrounding an infinitely dilute solute molecule with respect to a
Fig. 6. Partial critical isothermal–isobaric molar volume Ž V2`. as a function of composition.
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Fig. 7. The partial molar volume Ž V2`. of the waterq n-octane mixture as a function of pressure at the critical temperature of water Ž647.05 K..
Fig. 8. The solute–solvent Žwaterq n-octane. direct correlation function integral as a function of density at the critical temperature of water Ž647.05 K..
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Table 4 The values of the Krichevskii parameter for the waterqhydrocarbon mixtures System
ŽEPrE x . CV T wMPax from PVTx measurements
ŽEPrE x . CV T wMPax from initial slopes of the critical lines Ž3.
Waterqbenzene Waterq n-heptane Waterq n-octane
52.4223 115.1093 127.4525
52.1684 230.4061 –
uniform distribution at bulk conditions. The partial molar volume at infinite dilution Ž V2` ™ "`. and cluster size G 12 ™ "` diverge strongly as K T nears the solvent’s critical point. The divergence of G 12 is the result of the long-range Ž critical. part of the distribution function g i j Ž r ., and not of the short-range solvation part. Note that G 12 can be either positive or negative. The sign of the solute’s partial molar volume V2` ™ "` and cluster size G`12 ™ "` divergences are ` determined by the value of the DCFI C12 and of d , Ž r kT y d .. Using PVTx experimental data and ` ` C12 calculated from Eq. Ž2., we obtain Ž see Fig. 8. : 0 F C12 F 1, V2` ™ q` and G 12 ™ "`. It can be seen from Fig. 8 that the water q n-octane system exhibits weakly attractive behavior in the near-critical region. The initial slopes of the critical line are related to the Krichevskii parameter as follows:
d Cs
EP
C
E PC
C
d PS
C
E TC
C
ž / ž / ž / ž /
, Ž3. E x VT E x CRL dT CXC E x CRL where: Ž EPCrE x . CRL and Ž ETCrE x . CCRL are the initial slopes of the critical lines, Ž d PSrdT . CCXC ) 0 is the slope of the solvent’s vapor-pressure curve evaluated at the critical point of the solvent Ž always positive.. The near-critical behavior of mixtures depends on the signs and the magnitudes of the derivatives Žinitial slopes of the critical lines and vapor-pressure curve at the critical point. in Eq. Ž 3. . The values of the Krichevskii parameter for the water q hydrocarbon mixtures were estimated from Eq. Ž3. using critical lines Ž TC y x, PC y x . and vapor-pressure Ž PS y TS . experimental data w16x. The results of this estimate together with values derived from our PVTx measurements are given in Table 4. s
-
5. Conclusion New measurements of the PVTx properties of water q n-heptane, water q n-octane, and water q benzene mixtures are reported. The measurements were performed by means of a constant-volume piezometer in a precision thermostat. The measurements cover the pressure range from 5 to 40 MPa and densities between 20 and 450 kg my3 for six compositions from 0 to 0.614 mole fraction of hydrocarbon. All measurements were made at the water critical temperature TC s 647.05 K. The accuracy of the present results was estimated as: molar density, "0.15%;, pressure, "2 kPa; temperature, "10 mK; and concentration, "0.002 mole fraction. For pure benzene for isotherms at 573, 623 and 648 K, it was found that the previous experimental data w9x were consistent with the present results. Using our experimental results, the partial molar volumes were determined. The non-classical anomalous critical behavior of the partial molar volume of hydrocarbons near the critical point of pure water Žsolvent. was studied.
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Acknowledgements The research was supported by the Russian Science Foundation under Grant Number 96-02-16005.
References w1x Huang, K. Daehling, T.E. Carleson, M. Abdel-Latif, P. Taylor, C. Wai, A. Propp, in: K.P. Johnson, J.M.L. Penninger ŽEds.., Supercritical Fluid Science and Technology, ACS, Washington, DC, 1989, pp. 287–298. w2x I.M. Abdulagatov, A.R. Bazaev, A.E. Ramazanova, Int. J. Thermophysics 14 Ž1993. 231–250. w3x I.M. Abdulagatov, A.R. Bazaev, A.E. Ramazanova, Ber. Bunsenges. Phys. Chem. 98 Ž1994. 1596–1600. w4x I.M. Abdulagatov, A.R. Bazaev, R.K. Gasanov, A.E. Ramazanova, J. Chem. Thermodynamics 28 Ž1996. 1037–1057. w5x Th.W. De Loos, J.H. van Dorp, R.N. Lichtenthaler, Fluid Phase Equilibria 10 Ž1983. 279–287. w6x E. Brunner, J. Chem. Thermodynamics 22 Ž1990. 335–353. w7x K. Brollos, K.H. Peter, G.M. Schneider, Ber. Bunsenges. Phys. Chem. 74 Ž1970. 682–686. w8x L. Haar, J.S. Gallagher, G.S. Kell, NBSI NRC Steam Tables, Hemisphere Publ., Washington, DC, 1984. w9x A.M. Mamedov, T.C. Akhundov, Tablizy Termodinamicheskikh Svoistv Gazov i Zhidkostei. Uglevodorody Aromaticheskogo Rayda, Moscow, GSSSD, 1978. w10x J.M.H. Levelt Sengers, in: J.F. Ely, T.J. Bruno ŽEds.., Supercritical Fluid Technology, CRC Press, Boca Raton, FL, 1991, pp. 1–56. w11x R.F. Chang, G. Morrison, J.M.H. Levelt Sengers, J. Phys. Chem. 88 Ž1984. 3389–3391. w12x I.B. Petsche, P.G. Debenedetti, J. Phys. Chem. 95 Ž1991. 386–399. w13x J.G. Kirkwood, F.P. Buff, J. Chem. Phys. 19 Ž1951. 774–777. w14x J.P. O’Connell, Mol. Phys. 20 Ž1971. 27–33. w15x P.G. Debenedetti, Chem. Eng. Sci. 42 Ž1987. 2203–2212. w16x C.P. Hicks, C.L. Young, Chem. Rev. 75 Ž1975. 119–148.
PVTx measurements and partial molar volumes for water–hydrocarbon mixtures in the near-critical and supercritical conditions I.M. Abdulagatov ) , A.R. Bazaev, E.A. Bazaev, M.B. Saidakhmedova, A.E. Ramazanova Institute for Geothermal Problems of the Dagestan Scientific Center of the Russian Academy of Sciences, 367030 Makhachkala, Kalinina 39-A, Dagestan, Russian Federation
Abstract By means of a constant-volume piezometer, measurements have been made of the PVTx properties of water q hydrocarbon Ž n-heptane, n-octane, and benzene. mixtures at near-critical and supercritical conditions. The measurements cover the pressure range from 5 to 40 MPa and densities between 20 and 450 kg my3 for six compositions from 0 to 0.614 mole fraction of hydrocarbon. Tests on the piezometer and consistency tests on the measurements suggest that the results are free from significant ‘dead volume’ error. The experimental errors of the present PVTx measurements are estimated to be within "0.01 K in temperature, "0.15% in density, "2 kPa in pressure, and "0.002 mole fraction in composition. Good agreement was obtained with values reported in the literature for pure components Žwater, n-heptane, n-octane, and benzene., measured using other techniques. Values of partial molar volumes and the Krichevskii parameter have been obtained from these measurements. Analysis of the results for dilute water–hydrocarbon mixtures shows that partial molar volumes of the hydrocarbon Žsolute. near the critical point of pure water Žsolvent. exhibit remarkable anomalies. The experimental results have been interpreted in terms of modern molecular thermodynamic models for the partial molar volumes of the solute near the solvent critical point and Kirkwood–Buff fluctuation theory of solutions in terms of direct correlation function integral. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Apparent molar volume; Critical state; Density; Excess molar volume; Partial molar volume; Piezometer; Pressure; Supercritical fluid; Water
1. Introduction Water, the most important solvent in nature, has surprising properties as a reaction medium in its supercritical state. The remarkable anomalous properties of supercritical fluids, in general, as well as )
Corresponding author. N.I.S.T. Thermophysics Division 838.08, 325 Broadway, Boulder CO 80303-3328, USA. Tel.: q1-303-497-4027; fax: q1-303-497-5224; e-mail: [email protected] 0378-3812r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 8 . 0 0 3 0 0 - 8
538
I.M. AbdulagatoÕ et al.r Fluid Phase Equilibria 150–151 (1998) 537–547
supercritical water, in particular, are widely used as a solvent or reaction medium for a number of technological applications w1x. Supercritical fluids are of fundamental importance in geology and mineralogy Ž for hydrothermal synthesis. , in chemistry, in the oil and gas industries Ž e.g., in tertiary oil recovery., for some new separation techniques, especially in supercritical fluid extraction, for regeneration of sorbents used in wastewater treatment, for hazardous waste decontamination of soils or equipment, and for oxidation of hazardous chemicals. Binary aqueous fluid mixtures with hydrocarbons are interesting combinations of polar and non-polar molecules. The near-critical local environment Ž microstructure. around an infinitely dilute solute can be dramatically different from the bulk average. This is associated with the divergence of the solute partial molar volume at the solvent’s critical point. The aim of this work was to use PVTx measurements of dilute water q hydrocarbon mixtures near the critical point of pure water to study the anomalous critical behavior of the partial molar volume of hydrocarbons at the critical point of pure water Ž solvent.. Very little has been published concerning the PVTx properties of water q hydrocarbon mixtures at near- and supercritical conditions due to the experimental difficulties in their measurement. In previous papers w2–4x we reported PVTx data of five water–hydrocarbon binary mixtures Ž waterq methane, –n-hexane, –n-heptane, –n-octane, –benzene. at supercritical conditions. The new PVTx data for water q n-heptane, water q n-octane, and water q benzene systems in the immediate vicinity of the solvent’s critical point provide additional information on the effects of temperature, pressure, and composition on the PVT relation in such systems, which could lead to improved understanding of the behavior near the solvent’s critical point. A number of phase equilibrium Ž PTx . studies have been made on water–n-alkane mixtures w5–7x. Most of the measurements were performed at temperatures up to the critical point of pure water.
2. Experimental Since the experimental apparatus and procedure have been reported in Refs. w2–4x, only a brief explanation is given here. Experimental methods were similar to those described in Refs. w2–4x, except that a smaller Žf 3.68 = 10y5 m3 . piezometer was used. The volume of the piezometer has been carefully calibrated by using standard fluid Ž pure water. with well known PVT properties w8x at a temperature T0 s 673 K and at a pressure P0 s 39 MPa. The volume at these conditions was VP 0,T 0 s 3.688 " 0.0003 = 10y5 m3. The main part of the apparatus consisted of an air thermostat, a piezometer, lines for filling and extracting samples, temperature control and temperature measuring devices, and pressure measuring instruments. The temperature in the air thermostat was controlled automatically to within "5 mK. The air thermostat has double walls and it has an inside volume of 0.065 m3. Guard heaters have been located between the walls of the thermostat for setting the desired temperature inside the thermostat. The regulating heater was mounted inside the thermostat to avoid thermal losses. The temperature is measured by a 10 V platinum resistance thermometer. The uncertainty in the temperature measurement, when local temperature gradients and temperature stability are taken into account, is less than "0.01 K. To minimize temperature gradients in the air thermostat, two electrically driven high-speed fans were provided. The cylindrical piezometer was made from a heat- and corrosion-resistant high-strength alloy ŽEI-437B4.. On one of the ends of the piezometer, a diaphragm-type null indicator is mounted and on
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the other end, a high pressure valve. The diaphragm Ž0.04 m in diameter and 8 = 10y5 m thick. was made from Type 321 stainless steel. The pressure measurements have an uncertainty of "2 kPa. To reach equilibrium rapidly, the electric heater was switched on and the sample was stirred with a steel ball bearing which was rotated rapidly in the sample by a mechanical rotation of the piezometer. The volume of the piezometer Ž VPT . was corrected for its variation with temperature T and pressure P. Taking into account the uncertainties in temperature, pressure and concentration measurements, the total experimental uncertainty of density, dr is not more than "0.2%.
3. Results In Tables 1–3, some of the experimental results for water q n-heptane, water q n-octane, and water q benzene binary mixtures are presented at the critical temperature of water Ž TC s 647.05 K.. Some of these measured results are also shown in Figs. 1–4. Measurements have been made at the critical temperature of water Ž TC s 647.05 K., at pressures from 5 to 40 MPa, and at six hydrocarbon mole fractions from 0 to 0.614 for each system. Fig. 3 shows the molar volume Vm of a water q hydrocarbon mixtures at the critical temperature and pressure of water Ž TC s 647.05 K and PC s 22.035 MPa. as a function of composition. The measurements of the pure components Ž water, n-heptane, n-octane, and benzene. were carried out in order to confirm the reliability of the present apparatus. In order to check the apparatus, density Table 1 Measurements of PVTx for waterqbenzene mixtures at the critical temperature of water P
r
Vm
P
r
Vm
P
r
Vm
x s 0.028 4.618 9.241 15.077 21.263 25.404 28.490 34.655
18.480 40.536 78.323 161.713 410.311 484.011 542.676
1064.954 485.505 251.271 121.699 47.964 40.661 36.265
x s 0.043 4.695 9.369 13.599 16.500 19.800 25.293 29.672 37.676
19.581 42.897 69.850 95.177 135.750 339.791 465.4007 541.279
1052.808 480.561 295.125 216.591 151.856 60.668 44.294 38.085
x s 0.063 3.508 5.424 8.593 12.890 17.537 21.282 25.352 27.185 33.646
16.037 24.380 40.564 67.143 108.301 167.917 307.127 374.552 484.691
1359.757 894.448 537.591 324.782 201.354 129.867 71.003 58.221 44.991
x s 0.075 5.424 8.593 14.235 17.537 21.610 23.105 31.127 36.787
25.086 41.801 79.324 110.502 176.650 211.529 444.505 504.305
896.808 538.195 283.611 203.590 127.354 106.355 50.612 44.610
x s 0.222 5.424 8.593 17.537 22.328 25.228 36.491
34.276 56.371 151.472 229.857 287.579 451.191
915.062 556.397 207.065 136.453 109.064 69.515
x s 0.439 5.060 9.981 17.390 22.217 28.533 35.509
46.726 104.021 223.588 313.728 406.631 471.866
950.221 426.839 198.581 141.525 109.191 94.095
P, Pressure ŽMPa.; r , Density Žkg my3 .; Vm , Molar volume Žcm3 moly1 .; x, Composition Žmole fraction of benzene.; TC s647.05 K.
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Table 2 Measurements of PVTx for waterq n-heptane mixtures at the critical temperature of water P
r
Vm
P
r
x s 0.028 4.737 13.082 18.930 21.820 24.194 28.343 38.334
19.832 66.405 123.567 180.412 279.970 421.399 524.269
1023.060 305.535 164.194 112.458 72.468 48.147 38.699
x s 0.048 4.881 12.208 17.891 21.943 25.516 30.612 37.997
22.090 64.973 117.355 178.111 296.998 419.054 492.557
992.906 337.566 186.894 123.141 73.848 52.339 44.528
x s 0.173 4.713 10.398 15.900 24.147 30.417 41.137
29.915 73.271 127.198 239.063 327.625 420.867
1076.601 439.545 253.197 134.718 98.302 76.523
x s 0.474 4.733 8.026 12.060 16.776 26.939 40.294
53.956 98.131 158.705 231.513 347.803 427.211
1055.454 580.326 358.830 245.982 163.737 133.302
Vm
P
r
Vm
x s 0.082 4.983 11.424 14.474 20.215 22.481 23.926 28.348 39.071
24.376 64.294 88.593 153.341 191.640 221.739 320.847 448.249
1016.482 385.374 279.674 161.583 129.291 111.741 77.225 55.276
x s 0.706 4.700 9.144 15.241 23.746 39.046
77.193 172.630 288.9626 377.099 454.710
984.847 440.383 263.091 201.600 167.191
P, Pressure ŽMPa.; r , Density Žkg my3 .; Vm , Molar volume Žcm3 moly1 .; x, Composition Žmole fraction of n-heptane.; TC s647.05 K.
Table 3 Measurements of PVTx for waterq n-octane mixtures at the critical temperature of water P
r
Vm
x s 0.031 4.607 7.763 11.426 17.841 21.722 23.565 26.922 28.690 38.268
19.660 35.569 54.218 107.324 176.384 244.522 368.389 410.816 507.826
1070.122 591.492 388.047 196.033 119.280 86.042 57.111 51.213 41.430
x s 0.263 5.143 9.559 15.207 20.203 36.796
43.356 87.762 149.715 224.189 402.703
998.612 493.332 289.189 193.123 107.513
P
r
Vm
P
r
Vm
x s 0.048 5.109 7.413 12.305 18.295 21.808 25.222 27.030 36.503
23.508 34.887 63.481 123.711 184.707 289.895 345.599 480.168
961.626 647.984 356.110 182.735 122.390 77.981 65.412 47.080
x s 0.078 4.603 9.854 15.993 20.470 22.717 24.142 27.232 38.257
22.642 54.347 105.487 164.622 208.561 243.363 321.304 460.100
1125.437 468.880 241.564 154.791 122.180 104.708 79.308 55.384
x s 0.425 5.154 9.463 14.991 22.375 33.562 43.211
63.473 127.773 222.786 328.275 415.971 459.470
928.248 461.118 264.462 179.479 141.641 128.231
x s 0.614 4.894 9.473 14.971 22.430 36.618
84.134 190.134 301.701 385.128 460.692
916.358 405.486 255.5406 200.184 167.350
P, Pressure ŽMPa.; r , Density Žkg my3 .; Vm , Molar volume Žcm3 moly1 .; x, Composition Žmole fraction of n-octane.; TC s647.05 K.
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Fig. 1. The pressure of the mixture waterqbenzene as a function of density at the critical temperature of water Ž647.05 K. for various compositions.
Fig. 2. Compressibility factor Ž Zs PVm r RT . as a function of pressure for waterq n-octane mixtures at the critical temperature of water Ž647.05 K. for various compositions.
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Fig. 3. Molar volume Vm as a function of composition for waterqhydrocarbon mixtures at the critical temperature and pressure of water.
Fig. 4. The pressure of the mixture waterq n-heptane as a function of composition at the critical temperature of water Ž647.05 K. for various near-critical isochores.
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Fig. 5. Test measurements of densities of benzene taken with the apparatus in comparison with experimental densities of other authors w9x.
measurements on the pure components have been carried out also on three isotherms Ž 573, 623, and 648 K.. From Fig. 5, it can be seen that the test measurements for benzene are in excellent agreement within "0.3%, with the previously measured values w9x. The excellent agreement between these measured densities may be considered as validation of these experimental results.
4. Discussion The partial molar volumes Vi , i s 1,2, are obtained from the slope of tangent Ž EVm rE x . P T w10x. The measurements of the molar volumes VmŽ P,T, x . at the critical temperature and pressure of water Ž TC s 647.05 K and PC s 22.035 MPa. have been correlated as a function of the concentration x by the equation: N yx
Vm Ž x . s V0 e
x iy g r bd
Ý Ž i y grbd . q Ž1 y x . Vmc Ž PC ,TC . q xV12 ,
Ž1.
is1
where g s 1.24, b s 0.325, and d s 4.83 are universal critical exponents; N s 2; VmcŽ PC ,TC . s 55.838 cm3 moly1 is the critical volume of pure water; and V0 and V12 are non-universal adjustable parameters. From our experimental PVTx data at the critical temperature and pressure of water, we have deduced values for V0 and V12 . Our results are: V0 s 19.385, V12 s 113.341 cm3 moly1 for water q benzene, V0 s 25.070, V12 s 189.581 cm3 moly1 for water q n-heptane, and V0 s 30.044, V12 s 230.872 cm3 moly1 for water q n-octane mixtures. From Eq. Ž 1., we derived Ž EVmrE x . P T
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which yields the partial molar volumes V1 and V2 . At the critical temperature and pressure of water in the limit x ™ 0, Ž EVmrE x . P T , diverges as xyg r bd . Consequently, V2` behaves as xy g r bd , which is in good agreement with the non-classical limiting behavior w11x. The classical Ž mean field theory. predicts the behavior of V2` as xy2r3. In Figs. 6 and 7, the partial molar volumes for hydrocarbons derived from our experimental molar volumes are shown as a function of concentration and pressure at the critical temperature of water. In the vicinity of the solvent’s critical point Ž T ™ TC ., the partial molar volume of an infinitely dilute ` . solute Ž x ™ 0. in a binary mixture is given by Ref. w12x: V2` s ry1 K T d , where d s r kT Ž1 y C12 is the infinite dilution limit of the rate of change of pressure upon solute addition at constant temperature, volume, and solvent mass. The partial molar volume of the solute V2` can be expressed ` . ` as in Ref. w12x: V2` s kTK T Ž1 y C12 , where C12 s rHc`12 Ž r .d r is the DCFI Ž solute–solvent direct ` correlation function integral. and c12 Ž r . is the direct correlation function Ž DCF. . This equation is an identity and follows from reformulating the Kirkwood–Buff fluctuation theory of solutions w13x in terms of the DCF w14x: ` C12 s1y
d r kT
,
Ž2.
Ž .yg where: d s Ž EPrE x . CV T q Ky1 T . Asymptotically near the critical point, T ™ TC , the K T A T y TC C C ™ q`, and d ™ Ž EPrE x . V T , where: Ž EPrE x . V T is the Krichevskii parameter. In terms of a long-ranged fluctuation integral, the partial molar volume of an infinitely dilute solute can be written ` as in Ref. w15x: r V2` s r kTK T y G 12 , where G 12 s rH0`Ž g 12 y 1.4p r 2 d r is the statistical excess number of solvent molecules surrounding an infinitely dilute solute molecule with respect to a
Fig. 6. Partial critical isothermal–isobaric molar volume Ž V2`. as a function of composition.
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Fig. 7. The partial molar volume Ž V2`. of the waterq n-octane mixture as a function of pressure at the critical temperature of water Ž647.05 K..
Fig. 8. The solute–solvent Žwaterq n-octane. direct correlation function integral as a function of density at the critical temperature of water Ž647.05 K..
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Table 4 The values of the Krichevskii parameter for the waterqhydrocarbon mixtures System
ŽEPrE x . CV T wMPax from PVTx measurements
ŽEPrE x . CV T wMPax from initial slopes of the critical lines Ž3.
Waterqbenzene Waterq n-heptane Waterq n-octane
52.4223 115.1093 127.4525
52.1684 230.4061 –
uniform distribution at bulk conditions. The partial molar volume at infinite dilution Ž V2` ™ "`. and cluster size G 12 ™ "` diverge strongly as K T nears the solvent’s critical point. The divergence of G 12 is the result of the long-range Ž critical. part of the distribution function g i j Ž r ., and not of the short-range solvation part. Note that G 12 can be either positive or negative. The sign of the solute’s partial molar volume V2` ™ "` and cluster size G`12 ™ "` divergences are ` determined by the value of the DCFI C12 and of d , Ž r kT y d .. Using PVTx experimental data and ` ` C12 calculated from Eq. Ž2., we obtain Ž see Fig. 8. : 0 F C12 F 1, V2` ™ q` and G 12 ™ "`. It can be seen from Fig. 8 that the water q n-octane system exhibits weakly attractive behavior in the near-critical region. The initial slopes of the critical line are related to the Krichevskii parameter as follows:
d Cs
EP
C
E PC
C
d PS
C
E TC
C
ž / ž / ž / ž /
, Ž3. E x VT E x CRL dT CXC E x CRL where: Ž EPCrE x . CRL and Ž ETCrE x . CCRL are the initial slopes of the critical lines, Ž d PSrdT . CCXC ) 0 is the slope of the solvent’s vapor-pressure curve evaluated at the critical point of the solvent Ž always positive.. The near-critical behavior of mixtures depends on the signs and the magnitudes of the derivatives Žinitial slopes of the critical lines and vapor-pressure curve at the critical point. in Eq. Ž 3. . The values of the Krichevskii parameter for the water q hydrocarbon mixtures were estimated from Eq. Ž3. using critical lines Ž TC y x, PC y x . and vapor-pressure Ž PS y TS . experimental data w16x. The results of this estimate together with values derived from our PVTx measurements are given in Table 4. s
-
5. Conclusion New measurements of the PVTx properties of water q n-heptane, water q n-octane, and water q benzene mixtures are reported. The measurements were performed by means of a constant-volume piezometer in a precision thermostat. The measurements cover the pressure range from 5 to 40 MPa and densities between 20 and 450 kg my3 for six compositions from 0 to 0.614 mole fraction of hydrocarbon. All measurements were made at the water critical temperature TC s 647.05 K. The accuracy of the present results was estimated as: molar density, "0.15%;, pressure, "2 kPa; temperature, "10 mK; and concentration, "0.002 mole fraction. For pure benzene for isotherms at 573, 623 and 648 K, it was found that the previous experimental data w9x were consistent with the present results. Using our experimental results, the partial molar volumes were determined. The non-classical anomalous critical behavior of the partial molar volume of hydrocarbons near the critical point of pure water Žsolvent. was studied.
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Acknowledgements The research was supported by the Russian Science Foundation under Grant Number 96-02-16005.
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