ISSN 19907931, Russian Journal of Physical Chemistry B, 2010, Vol. 4, No. 8, pp. 1178–1187. © Pleiades Publishing, Ltd., 2010 Original Russian Text © A.R. Bazaev, E.A. Bazaev, 2010, published in Sverkhkriticheskie Flyuidy: Teoriya i Praktika, 2010, Vol. 5, No. 3, pp. 15–30.
The Thermodynamic Properties of Binary Mixtures of Technologically Important Substances in the Near and Supercritical States A. R. Bazaev and E. A. Bazaev Institute of Geothermal Problems, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Russia email:
[email protected] Received December 1, 2009
Abstract—Some results of experimental studies of the p–ρ–T dependences for water–nitrogen, water– hydrocarbon, water–alcohol, and alcohol–hydrocarbon binary mixtures over the range of parameters including the critical and supercritical states are given. Earlier unknown special features of their thermody namic behavior were established; these results are of interest for the theory of solutions and are important for technological and construction calculations. The possibility of using these mixtures for increasing the effec tiveness of various technological processes was substantiated. Keywords: supercritical solvent, homogeneous gas mixtures, concentration, compressibility factor, phase transition, coexistence curve, critical parameters. DOI: 10.1134/S1990793110080026
INTRODUCTION Water, alcohols, and hydrocarbons are exten sively used in many industries as solvents and heat transfer agents (working substances) [1–4]. The data on the phase behavior and p–ρ–T dependences of these solvents in various states of aggregation, including nearcritical and supercritical states, are for instance necessary for calculations of processes and apparatus of supercritical fluid extraction, supercritical aqueous oxidation, thermodynamic cycles, power plants, etc. Water in the supercritical state is a universal ther mally stable and ecologically pure solvent. It is com pletely miscible with many organic and inorganic compounds. The high water critical parameter val ues (647.096 K, 22.064 MPa), however, limit its use as an extractant in some supercritical fluid technol ogies. The working parameters of a highboiling extractant, water, can be changed by mixing it with lowboiling solvents (that is, by creating solvent + cosolvent systems). The advantage of mixed com pared with pure solvents is the possibility of chang ing their critical parameters by the selection of com ponents (organic + organic, organic + inorganic, polar + polar, polar + nonpolar, nonpolar + nonpo lar) and composition and perform technological processes over a wide range of temperatures and pressures. In addition, the use of supercritical mix tures as extractants allows unified equipment suit
able for various supercritical fluid extraction variants to be created, which is economically justified. The use of mixtures as working substances in thermal schemes of power plants designed for the conversion of the energy of nontraditional renewable sources into electric energy also has many economical advantages compared with the use of pure working substances [5–7]. The development of ecologically friendly and economically effective supercritical fluids and super critical aqueous oxidation technologies requires the use of reliable data on phase equilibria and p–ρ–T dependences for mixtures of technologically impor tant substances over wide parameter ranges, includ ing the state near the critical point and in the super critical region. This work is not a review of data on phase equilibria and p–ρ–T dependences of mixtures. It only contains the results of our studies, which are, we believe, of obvious interest for the theory and practical applica tions of supercritical fluid extraction and supercritical aqueous oxidation. Information about studies in this field can be found, for instance, in reviews [8, 9]. We measured p–ρ–T–x dependences for the fol lowing mixtures (Table 1): water–nitrogen in homogeneous gas and supercrit ical regions;
1178
THE THERMODYNAMIC PROPERTIES OF BINARY MIXTURES
1179
Table 1. Range of changes in the parameters of the mixtures studied T, K
Mixture
p, MPa
ρ, kg/m3
Mole fraction of the second component
Water–nitrogen
523.15; 573.15; 663.15
3–70
10–500
0.20–0.80
Water–methane
523.15; 573.15; 623.15; 653.15
3–70
10–540
0.05–0.85
Water–pentane
647.1
2–40
20–600
0.03–0.70
Water–hexane
523.15; 573.15; 623.15; 643.15; 647.1; 648.15
2–40
2–600
0.03–0.90
Water–heptane
573.15; 623.15; 643.15; 647.1; 648.15; 653.15; 673.15
2–38
2–600
0.04–0.90
Water–octane
623.15; 647.1
3–36
10–480
0.03–0.80
Water–benzene
623.15; 648.15
10–580
0.03–0.90
Water–toluene
623.15; 648.15; 653.15
3–36
10–580
0.03–0.90
Water–methanol
373.15–673.15
0.2–50
50–750
0.2; 0.5; 0.8
Water–ethanol
373.15–673.15
0.2–50
50–650
0.2; 0.5; 0.8
Water–npropanol
373.15–673.15
0.2–50
50–650
0.2; 0.5; 0.8
Ethanol–npentane
373.15–623.15
0.2–40
30–500
0.5
Ethanol–nhexane
373.15–623.15
0.2–40
30–500
0.5
Ethanol–nheptane
373.15–623.15
0.2–40
50–500
0.2; 0.5; 0.8
Ethanol–noctane
373.15–623.15
0.2–40
50–500
0.2; 0.5; 0.8
water–methane in homogeneous gas and super critical regions; water–hydrocarbon (npentane, nhexane, nhep tane, noctane, benzene, and toluene) in homoge neous gas and supercritical regions; water–alcohol (methanol, ethanol, npropanol) in twophase, nearcritical, and supercritical regions; ethanol–hydrocarbon (npentane, nhexane, nheptane, and noctane) in twophase, nearcritical, and supercritical regions. EXPERIMENTAL Measurements of p–ρ–T dependences were performed along isotherms and isochores by deter mining compressibility on an experimental unit. The unit contained a constantvolume piezometer with an improved design (Fig. 1), which differed from the known analogues by the absence of ballast RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
volumes. A detailed description of the experimental unit and procedure for measurements was given in [10–12]. RESULTS The results of measurements were processes in var ious thermodynamic surface sections and are pre sented in the form of diagrams and tables. Detailed information can be found in, e.g., [11–15]. Unexpected results of p–ρ–T–x dependence mea surements were obtained for homogeneous gas mix tures of water with nitrogen and methane. A diagram of the “p, vm, x” thermodynamic surface for a water– methane mixture in the supercritical state at 653.15 K is shown in Fig. 2, and a diagram of the pressure dependence of the compressibility factor Z = pvm/RT (vm is the molar volume of the mixture and R is the universal gas constant), in Fig. 3. These data lead us to conclude that a mixture of water vapor with methane Vol. 4
No. 8
2010
1180
A.R. BAZAEV, E.A. BAZAEV
Vm, cm3/mol 300
200
100
0
20
0.2 30
0.4 40
p, MPa
50
0.8
0.6 x, mole fraction
60 1.0 Fig. 2. Surface of p, vm, x equilibrium for water–methane mixtures at 653.15 K.
Z = pVm/RT 1.4 7 1.2 6 1.0
5
0.8 0.6
4 3
0.4
2 1
0.2
0 Fig. 1. Constantvolume piezometer: 1, piezometer case; 2, differential membrane separator case; 3, shut off (control) valve; 4, ball; 5, electrical heater; 6, mem brane; 7, bolt; 8, microampermeter; 9, leadcontact; 10, ceramic tube; 11, mica; 12, disk with holes; 13, hole (pocket) for a thermocouple; 14, nipple; and 15, shell.
10
20
30
40
50
60
70 p, MPa
Fig. 3. Dependence of compressibility factor Z on pressure and water–methane mixture composition at 653.15 K; x(CH4), mole fractions: (1) 0, (2) 0.05, (3) 0.17, (4) 0.23, (5) 0.54, (6) 0.66, and (7) 1.
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
Vol. 4
No. 8
2010
THE THERMODYNAMIC PROPERTIES OF BINARY MIXTURES
1181
Z = pVm/RT 1.1
Z = pVm/RT 1.1 1 2
1.0
1 2
1.0
3 3 4
0.9
0.9 4
5
0.8
5
0.8
6
6
0.7 2
4
6
8
10 p, MPa
0.7 2
Fig. 4. Dependence of compressibility factor Z on pressure and water–methane mixture composition at 573.15 K; x(CH4), mole fractions: (1) 1, (2) 0.77, (3) 0.54, (4) 0.34, (5) 0.18, and (6) 0.
4
6
8
10 p, MPa
Fig. 5. Dependence of compressibility factor Z on pressure and water–nitrogen mixture composition at 573.15 K; x(N2), mole fractions: (1) 1, (2) 0.75, (3) 0.48, (4) 0.22, (5) 0.12, and (6) 0.
p, MPa 45
p, MPa 45 9
40
8
7
8
40 6
6
35
35 5
30
4 3 2 1
5
7
4
3 9 2
30 25 1
25 20
10
20 15 15
10
10 10 11 12
5
0
100
5
13
200
300
400
500 600 ρ, kg/m3
0
Fig. 6. “Pressure–density–composition” dependence for water–nhexane mixtures at 647.1 K; x(nC6H14), mole fractions: (1) 0, (2) 0.002, (3) 0.005, (4) 0.009, (5) 0.014, (6) 0.027, (7) 0.039, (8) 0.057, (9) 0.17, (10) 0.274, (11) 0.518, (12) 0.701, and (13) 1. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
100
200
300
400
500 600 ρ, kg/m3
Fig. 7. “Pressure–density–composition” dependence for water–benzene mixtures at 648.15 K; x(C6H6), mole fractions: (1) 0, (2) 0.028, (3) 0.043, (4) 0.063, (5) 0.075, (6) 0.222, (7) 0.439, (8) 0.522, (9) 0.871, and (10) 1. Vol. 4
No. 8
2010
1182
A.R. BAZAEV, E.A. BAZAEV
Z = pVm/RT 1.6 9 8
1.2 7
0.8
6
5
4 3 2
0.4 1
0
30
15
45 p, MPa
Fig. 8. Dependence of compressibility factor Z on pres sure and water–noctane mixture composition at 647.1 K; x(nC8H18), mole fractions: (1) 0, (2) 0.03, (3) 0.05, (4) 0.08, (5) 0.26, (6) 0.43, (7) 0.61, (8) 0.79, and (9) 1.
in the supercritical state is homogeneous over the whole composition range at pressures up to 60 MPa. The dimensionless Z value for the mixture, which characterizes the degree to which real gas properties deviate from ideal gas properties under identical con ditions, is between its values for the pure components. For a supercritical mixture of water and methane (molar ratio ~2 : 3), the Z value is close to one and almost does not depend on pressure up to 60 MPa. Water–methane and water–nitrogen gas mixtures in which the mole fraction of methane and nitrogen is ~0.75 exhibit ideal gas behavior at 573.15 K and pres sures up to 8 MPa (Figs. 4, 5). It follows that mixtures of real gases consisting of polar and nonpolar compo nents can have a thermodynamic state similar to that of an ideal (Z = 1) gas over certain ranges of composi tion and parameter changes. This does not mean that intermolecular interaction is absent in these mixtures under these conditions. Conversely, the experimental data substantiate the complex character of interac tions between polar and nonpolar molecules. The ideal gas model leads us to suggest that, at certain temperatures and compositions and independently of pressure, attraction and repulsion forces between molecules balance each other in homogeneous gas mixtures of water with nitrogen and methane. These special features of the thermodynamic behavior of gas mixtures broaden our knowledge of the mecha Z = pVm/RT
Z = pVm/RT 0.9
1.0 9 8
0.8 0.8 7
0.6 0.7
6
0.4 0.6
0.5
5
p = 10 MPa p = 15 MPa p = 20 MPa
0
0.2
0.4
4
0.6 0.8 1.0 x(М−C8H18), mole fraction
Fig. 9. Dependence of compressibility factor Z on compo sition at various pressures for water–noctane mixtures at 647.1 K.
0
3 2
0.2
1
10
20
30
40 p, MPa
Fig. 10. Dependence of compressibility factor Z on pressure and water–benzene mixture composition at 648.15 K; x(C6H6), mole fractions: (1) 0, (2) 0.03, (3) 0.04, (4) 0.06, (5) 0.08, (6) 0.22, (7) 0.52, (8) 0.87, and (9) 1.
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
Vol. 4
No. 8
2010
THE THERMODYNAMIC PROPERTIES OF BINARY MIXTURES
1183
p, MPa 31
40 35
SCL
30 25 20 15
LP 14
10 pc 5 0 370
SCG GP
395
420
445
470
495
520 T 545
570
c
1
595
620 T, K
Fig. 11. Isohores of the temperature dependence of pressure for the ethanol–nheptane system (molar ratio 1 : 1): LP is the liquid phase, GP is the gas phase, SCL is the supercritical liquidlike state, and SCG is the supercritical gaslike state (density on iso chore 1 is 50.7 kg/m3, density on isochore 14 is 251.0 kg/m3, and density on isochore 31 is 492.1 kg/m3).
nism of intermolecular interaction and are of impor tance for theoretical substantiation of potential func tion models. These experimental results are obvi ously of importance for applications, because they allow simple equations of state to be obtained for describing the properties of this class of mixtures under these conditions. The complex character of p–ρ–T–x dependences for water–hydrocarbon homogeneous gas mixtures at critical temperatures is illustrated by Figs. 6, 7. We see that the thermodynamic behavior of dilute aqueous solutions of hydrocarbons (x < 0.05, where x is the mole fraction of hydrocarbons) is determined by the thermodynamic behavior of pure water, and the behavior of mixtures with x > 0.5, by the thermody namic behavior of pure hydrocarbons. At a pressure of about 15 MPa, the Z value is almost independent of composition and is ~0.73 for the pure components and mixtures (Figs. 8, 9). Z behaves similarly in water– benzene mixtures at 648.15 K and a pressure of about 20 MPa (Fig. 10). This thermodynamic behavior of supercritical mixtures comprising polar and nonpolar components gives important information for theory and practical applications. Homogeneous water–alcohol (methanol, etha nol, and npropanol) and alcohol–hydrocarbon (n pentane, nhexane, nheptane, and noctane) solu tions (mixtures) are of special interest for supercrit ical fluid extraction, supercritical aqueous oxida tion, and nontraditional renewable energy sources. Diagrams in certain thermodynamic surface sec RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
tions for these solutions are shown in Figs. 11–13. We see that the coexistence curves of these homoge neous solutions and the corresponding pure compo nents have identical shapes. An important conclu sion can be drawn that mathematical approaches to the description of the critical state of a pure sub stance [16] can be used to estimate the critical ps, MPa 7 x=0
6
x = 0.2 x = 0.5
5 4
x = 0.8
3
x = 1.0
2 1 0
100
200
300
400 500 ρs, kg/m3
Fig. 12. Phase coexistence curves in the ps, ρs plane for the ethanol–nheptane system (x is the mole fraction of nheptane). Vol. 4
No. 8
2010
1184
A.R. BAZAEV, E.A. BAZAEV
500 ρl
300
400
290
ρs, kg/m3
280 270.0 263.5
300
K1
K3
K4
252.7 242.0 234.9
K5 K2
200
220
100
210
ρg
200
0 470
510
490
530
550
570 Ts, K
Fig. 13. Temperature dependence of the density of the liquid ρl and gas ρg phases for the ethanol–noctane mixture in the ρs, Ts plane.
pc, MPa 7
ρc, kg/m3 280
6
270
5
260
250
4
1
240 3
4
4
2
0
0.2
0.4
0.6
230
1
0
0.2
0.4
0.6
0.8 1.0 x (nalkane)
0.8 1.0 x (nalkane)
Fig. 14. Concentration dependences of mixture critical pressures: (1) ethanol–npentane, (2) ethanol–nhexane, (3) ethanol–nheptane, and (4) ethanol–noctane.
Fig. 15. Concentration dependences of mixture critical densities: (1) ethanol–npentane, (2) ethanol–nhexane, (3) ethanol–nheptane, and (4) ethanol–noctane.
parameters of water–alcohol and nalkane–alcohol mixtures [12, 17].
water–ethanol mixtures are described by the equa tions
The concentration dependences of the critical parameters of these mixtures (Figs. 14–16) can be described by polynomial equations. For instance, the composition dependences of the critical parameters of
T c = 647.10 – 239.00x + 177.76x – 71.93x ;
2
3
2
3
p c = 22.06 – 37.37x + 37.15x – 15.72x ;
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
Vol. 4
No. 8
2010
THE THERMODYNAMIC PROPERTIES OF BINARY MIXTURES
point, for the pure components and an ethanol– nheptane solution in the twophase and critical regions is shown in Fig. 17. The diagram shows that the compressibilities of the pure components at the critical point are approximately equal, and the com pressibility of solutions depends on the composition and is maximum at x = 0.5. Zc can be treated as the equation of state of a solution at the critical point. The concentration dependence of the compressibility fac tor at the critical point (Fig. 18) can be described by the equation
Tc, K 590 4
570 550
3
530 2
510
2
490
3
Z c = 0.245 – 0.447x – 0.433x . 1
470 450
1185
The critical parameter values of mixtures are listed in Table 2. 0
0.2
0.4
0.6
0.8 1.0 x (nalkane)
The special features of the thermodynamic behav ior of various classes of mixtures in the nearcritical and supercritical states were established.
Fig. 16. Concentration dependences of mixture critical temperatures: (1) ethanol–npentane, (2) ethanol–n hexane, (3) ethanol–nheptane, and (4) ethanol–n octane.
2
CONCLUSIONS
3
ρ c = 321.96 – 89.10x + 84.56x – 41.42x . The relative errors of calculations by these equa tions are 0.2% for temperature, 0.9% for pressure, and 0.06% for density. The pressure dependence of the compressibility factor Zc = pc v mc /RTc, where v mc is the molar volume of a solution with a given composition at the critical
(1) Supercritical water–methane and water–nitro gen mixtures at a certain composition (at the mole fraction of water ~40%) and pressures up to 60 MPa have a thermodynamic state similar to that of an ideal gas (Z = 1), although the properties of the pure com ponents, especially water vapor, differ from ideal gas properties under these conditions. Although the char acter of intermolecular interactions in these homoge neous gas mixtures is complex on the whole, the equation of state of an ideal gas can be used in engi neering calculations over a wide range of pressures at certain mixture compositions. For the other composi
Zc 0.4 0.5 0.8 0.2
0.3
x = 1.0 0
0.2
0.1
0
1
2
3
4
5
6
7 ps, MPa
Fig. 17. Pressure dependence of compressibility factor along the saturation curve and in the critical state for various compositions of ethanol–nheptane mixtures. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
Vol. 4
No. 8
2010
1186
A.R. BAZAEV, E.A. BAZAEV
tions, the experimental p–ρ–T–x dependences should be used [11].
Zc 0.37
(2) The compressibility factors Z of homoge neous water–hydrocarbon (nalkanes) mixtures and pure components are equal, of ~0.73, at 647.1 K and a ~15 MPa pressure. At pressures lower and higher than 15 MPa, the Z value strongly depends on compo sition. For this reason, engineering calculations should be performed using experimental p–ρ–T–x dependences [11].
0.35 0.33 0.31 0.29 0.27 0.25 0
0.2
0.4
0.6
0.8 1.0 x(nC7H16)
Fig. 18. Composition dependence of the compressibility factor of ethanol–nheptane mixtures in the critical state.
(3) The phase coexistence curves in various ther modynamic surface sections of water–aliphatic alco hol and aliphatic alcohol–nalkane mixtures and pure components have identical forms. The critical param eters of water–alcohol and nalkane–alcohol mix tures can be estimated using characteristics of the mathematical description of the critical state of pure substances [12, 17].
Table 2. Critical parameters of water–alcohol solutions Mole fraction of the second component
Tc, K
0.2 0.5 0.8 1.0
612.15 569.75 533.15 512.60
0.2 0.5 0.8 1.0
607.15 566.15 534.15 513.92
0.2 0.5 0.8 1.0
598.15 557.15 541.15 536.85
0.5
492.00
0.5
511.40
0.2 0.5 0.8 1.0
519.80 527.35 535.05 540.13
0.0 0.2 0.5 0.8 1.0
514.65 525.60 542.60 558.70 569.32
pc, MPa Water–methanol 18.0 13.5 9.9 8.1 Water–ethanol 15.8 10.9 7.8 6.1 Water–npropanol 15.1 9.5 6.5 4.99 Ethanol–npentane 5.6 Ethanol–nhexane 5.5 Ethanol–nheptane 6.1 5.4 3.9 2.7 Ethanol–noctane 6.2 6.0 5.1 3.7 2.5
ρc, kg/m3
Zc
310.0 296.0 285.3 280.0
0.238 0.241 0.228 0.204
307.3 293.5 283.4 276.0
0.241 0.253 0.250 0.240
307.1 291.0 280.0 275.0
0.261 0.275 0.265 0.244
251.4
0.324
251.9
0.340
262.5 251.8 240.8 232.0
0.303 0.356 0.327 0.263
270.0 263.5 252.7 242.0 234.9
0.247 0.312 0.361 0.328 0.257
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
Vol. 4
No. 8
2010
THE THERMODYNAMIC PROPERTIES OF BINARY MIXTURES
REFERENCES 1. I. M. Abdulagatov, Kh. S. Abdulkadyrova, and M. N. Dadashev, Teplofiz. Vys. Temp. 32 (3), 299 (1994). 2. F. M. Gumerov, A. N. Sabirzyanov, and G. I. Gumer ova, Sub and Supercritical Fluids in Processes of Poly mer Processing (Fen, Kazan, 2007) [in Russian]. 3. S. Walas, Phase Equilibria in Chemical Engineering (Butterworth, Boston, 1985; Mir, Moscow, 1989), Part 1. 4. S. Walas, Phase Equilibria in Chemical Engineering (Butterworth, Boston, 1985; Mir, Moscow, 1989), Part 2. 5. V. A. Vasil’ev, Teploenergetika, No. 5, 27 (1996). 6. A. I. Kalina, New Binary Energosystem with Binary Cycle (Calex, LLS, 2630 Carlmont Drive, Belmont, CA, USA). 7. A. R. Bazaev, in Proc. of the Conf. on Actual Problem of Developments of Renewable Energetic Resources (Makh achkala, 2008), p. 106. 8. A. M. Abdulagatov, G. V. Stepanov, and I. M. Abdula gatov, Teploenergetika, No. 8, 72 (2008).
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B
1187
9. A. M. Abdulagatov, G. V. Stepanov, and I. M. Abdula gatov, Teploenergetika, No. 9, 70 (2008). 10. A. R. Bazaev, Doctoral Dissertation in Technique (Inst. Problem Geotermii DNTs RAN, Makhachkala, 1997). 11. A. R. Bazaev and E. A. Bazaev, Teplofiz. Vys. Temp., No. 1, 48 (2004) [High Temp. 42, 41 (2004)]. 12. E. A. Bazaev, A. R. Bazaev, and A. A. Abdurashidova, Teplofiz. Vys. Temp. 47, 215 (2009) [High Temp. 47, 195 (2009)]. 13. A. R. Bazaev and V. G. Skripka, in Petroleum Industry, Referative Sci.Tech. Collection (Moscow, 1974), p. 35 [in Russian]. 14. I. M. Abdulagatov, A. R. Bazaev, and A. E. Ramaza nova, Zh. Fiz. Khim. 67, 13 (1993). 15. I. M. Abdulagatov, A. R. Bazaev, E. A. Bazaev, S. P. Khokhlachev, M. B. Saidakhmedova, and A. E. Ramazanova, J. Solut. Chem. 27, 729 (1998). 16. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford Univ., Oxford, New York 1971; Mir, Moscow, 1973). 17. E. A. Bazaev and A. R. Bazaev, in Proc. of the Intern. Conf. on Phase Transitions, Critical and Nonlinear Phe nomena in Condensed Media, Makhachkala, 7–10 Sept. (Makhachkala, 2009), p. 204.
Vol. 4
No. 8
2010