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Vapor–liquid phase behavior of the binary systems containing supercritical carbon dioxide
Chemical Engineering and Processing 43 (2004) 541–545
Vapor–liquid phase behavior of the binary systems containing supercritical carbon dioxide Li Zhiyi∗ , Wang Weili, Zhang Xiaodong, Liu Xuewu, Hu Dapeng, Xia Yuanjing R&D Institute of Liquid and Powder Engineering, Dalian University of Technology, 158 Zhongshan Rd., Xigang District, Dalian 116012, PR China Received 18 October 2002; received in revised form 9 September 2003; accepted 9 September 2003
Abstract A thermodynamic model based on the perturbation theory is investigated. The perturbed hard-sphere chain (PHSC) equation of state (EOS) is applied to calculate phase behavior of the binary systems containing supercritical carbon dioxide. A calculation program is written. The vapor–liquid phase equilibrium calculation is conducted with the binary systems and a comparison is made between the calculation results and experimental ones. It is shown that the PHSC equation of state can be reliably used for calculating the vapor–liquid phase behavior of carbon dioxide systems when the pressure is very high. © 2003 Elsevier B.V. All rights reserved. Keywords: Supercritical carbon dioxide; Perturbation theory; Phase equilibrium
1. Introduction A supercritical fluid (SCF) as a special solvent has dissolution properties like a gas and transfer properties like a liquid, It gives a new broad way to chemical engineering. Especially supercritical CO2 (SC–CO2 ) has expansively potential applications in the area of bio-chemical engineering, medicine and food industry, since it is non-toxic, environmentally acceptable, noncombustible, cheap and has a low critical temperature and a moderate critical pressure. Solubilities of all kinds of solutes in SC–CO2 are important parameters for supercritical fluid processes and they can be predicted by a proper phase equilibrium model. The common used phase equilibrium models include the Ewald equation of state and cubic equations of state. Ewald et al. [1] first tried to make a model of SCF system by Ewald equation of state. It has been realized that it is difficult to describe the mixture phase equilibrium near the critical point even though the third Ewald coefficient is used. Although the form of cubic equations of state is simple, the calculation results are not satisfactory to SC–CO2 systems because of some inherent shortcomings. ∗
Corresponding author. E-mail address: [email protected] (L. Zhiyi).
0255-2701/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2003.09.002
This paper tries to apply the perturbation theory proposed by Fermeglia et al. [2] with perturbed hard-sphere chain (PHSC) equation of state (EOS) to describe the phase behavior of binary systems containing SC–CO2 , and examines the feasibility of this model when it is used for the vapor–liquid phase equilibrium calculation.
2. Theory 2.1. PHSC EOS The equation of state considered in this paper is the PHSC EOS [3]. It takes the hard sphere chains as its reference system, in the form of Chiew equation of state [4], derived from the Percus-Yevik integral theory coupled with chain connectivity, and a van der Waals attractive term as the perturbation. The EOS in terms of pressure is the following: m
P = 1 + ρ xi xj ri rj bij gij (dij+ ) ρkT ij
−
m i
xi (ri −1)[gii (dii+ )−1]−
m
ρ xi xj ri rj aij kT ij
(1)
542
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
where P is the pressure, T the absolute temperature, ρ = N/V the number density, k the Boltzmann’s constant, dij the hard-sphere diameter, gij (dij+ ) the ij-pair distribution function of hard spheres at contact, xi = Ni /N the number fraction of molecules, ri the number of segments (hard spheres) per molecule for the ith component, aij reflects the attractive forces between two non-bonded segments, and bij is the van der Waals covolume per segment.
In Eq. (1), P and T are given, xi , xj and ρ are unknown, the other parameters can be obtained from following Eqs. (2)–(7). The Eq. (1) is an implicit five power function of density. Each pure component has three basic parameters ε, σ and r, which can be combined to give a more useful set of parameters directly related to size, shape and energetic interactions of the molecules of the fluid considered. This may be done by defining a characteristic volume V ∗ , a characteristic surface area A∗ and a characteristic “cohesive” energy E∗ . π ε Rσ 3 NA , A∗ = πrσ 3 NA , E∗ = r V∗ = Rg 6 k (2) Because of the rigorously theoretical nature of the equation of state, no mixing rules are required for the reference term, and the attractive term only requires van der Waals one-fluid mixing rules. The mixture parameters aij and bij needed for each binary pair included in the mixture are following: 2π kT kT 2π 3 3 , bij = σij εij Fa σij Fb aij = 3 εij 3 εij (3) where ε and σ are pair-potential parameters. Fa an Fb are expressed by following equations [5]: kT Fa = 1.8681 exp −0.0619 ε 3/2 kT + 0.6715 exp −1.7317 ε (4) kT Fb = 0.7303 exp −0.1649 ε 3/2 kT + 0.2697 exp −2.3793 ε No combing rule is needed for σ as a consequence of the additivity of the hard-sphere diameters, but one adjustable parameter kij is needed for energetic parameter ε. σii + σjj , 2
εij =
√ εi εj (1 − kij )
2 ξij 3 1 1 ξij + + 1 − η 2 (1 − η)2 2 (1 − η)
gij (η, ξij ) = where
(5)
m
η=
ρ x i ri b i , 4 i
2.2. Parameters determination
σij =
The required mathematical expression for gij (dij+ ) is given by the BMCS equation for hard-sphere mixtures
ξij =
bi bj bij
1/3
(6)
m
ρ 2/3 x k rk b k 4
(7)
k
If transforming Eq. (1) from molecule density basis to segment density basis, we can obtain the following equation [6] m
P = 1 + ρr φi φj bij gij (dij+ ) ρr kT ij m m 1 ρr − φi 1 − gii (dii+ ) − φi φj aij η kT i
(8)
ij
with ρr =
Nr , V
φi =
Ni r i xi ri = m , Nr j=1 xj rj
Nr =
m
N i ri
i=1
(9)
3. Numerical calculation program The numerical calculation involves solving Eq. (1) for xi , xj and ρ or ρr together with six others (Eqs. (2)–(7)). A calculation program is written for the task. Supposing the two-phase mixture containing SC–CO2 has flow rate F, composition Zi (mole fraction) and temperature T, it is pumped into equilibrium cell until a desired pressure is reached. After equilibrium has been reached, the vapor phase and liquid phase compositions are Yi and Xi (mole fraction) respectively. This calculation program consists of following modules. 3.1. Module 1: INPUT—inputting basic data In this module, the critical pressure Pc , the critical temperature Tc , the boiling point Tb , the molecular weight ME , the binary interaction parameter kij , and three molecular-based parameters V ∗ , A∗ and E ∗ are needed for input. The binary interaction parameter kij is determined by fitting binary vapor–liquid equilibrium data. The three molecular parameters V ∗ , A∗ and E ∗ can be obtained by fitting experimental data for each pure component. For pure SC–CO2 , the three molecular parameters V ∗ , A∗ and E ∗ can be fitted to vapor pressure and saturated liquid density data as functions of temperature. For other pure liquid parameters, V ∗ , A∗ and E ∗ can be regressed from pressure–volume–temperature (PVT) data.
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
3.2. Module 2: PARA—calculating three microcosmic parameters σ, r and ε The three microcosmic parameters σ, r and ε can be obtained through three macroscopic parameters V ∗ , A∗ and E ∗ with Eq. (2). 3.3. Module 3: PKIO—determining the initial value of phase equilibrium constant Ki0 (1 ≤ i ≤ m) The initial value of phase equilibrium constant can be supposed to equal to phase equilibrium constant of ideal state Ki0 (1 ≤ i ≤ m): Ps Ki0 = i P
(10)
3.4. Module 4: YNVL—determining if the mixture is in two-phase The program gives a judgment whether the mixture is in or not under given T and P. Only when both
two-phase
Ki Zi and Ki /Zi are bigger than 1, the mixture is in two-phase and the program enters the next step. 3.5. Module 5: VLP—calculating vapor and liquid phase densities The equilibrium vapor and liquid phase densities can be obtained by Eq. (1) and (8). 3.6. Module 6: CHPOT—calculating chemical potential L For each component, the chemical potential µV i and µi can be calculated with the equations given in the reference
543
[7] under corresponding temperature, pressure, vapor phase and liquid phase compositions, and vapor phase and liquid phase densities. 3.7. Module 7: ADE—adjusting phase equilibrium constant The adjustment of phase equilibrium constant can be done by the adjustment of vaporization rate. 3.8. Module 8: OUTPUT—outputting results of calculations This module can output the final vapor phase composition Yi , the liquid phase composition Xi and the phase equilibrium constant Ki of each component. The program flow is shown in Fig. 1.
4. Comparison between the calculation results and experimental ones The vapor–liquid phase equilibrium calculation has been done for the systems of SC–CO2 and octane, SC–CO2 and cyclohexane, and SC–CO2 and benzene with the calculation program. The calculation results are compared with experimental ones taken from [8,9]. The comparisons are given by Tables 1–3 where EXP means the experimental result and CAL the calculation one. From Tables 1–3, we notice that relative error of the calculation results for the liquid phase mole fraction is within 5%, and relative errors of the calculation results for the vapor phase are a slightly bigger then liquid phase, but still within 7%. The calculation results are in good agreement with experimental ones.
Table 1 VLE calculation results and experimental results for SC–CO2 + octane T (K)
P (MPa)
EXP XCO 2
CAL XCO 2
Error (%)
EXP YCO 2
CAL YCO 2
Error (%)
313.15 328.15 328.15 348.15 348.15 348.15
7.55 8.00 9.50 9.10 9.70 10.8
0.8900 0.7093 0.8815 0.6310 0.6770 0.7540
0.8648 0.7023 0.8544 0.6102 0.6519 0.7280
−2.8 −1.0 −3.1 −3.3 −3.7 −3.4
0.9920 0.9899 0.9740 0.9834 0.9786 0.9620
0.9972 0.9969 0.9946 0.9919 0.9935 0.9934
0.5 0.7 2.1 0.9 1.5 3.3
Table 2 VLE calculation results and experimental results for SC–CO2 + cyclohexane T (K)
P (MPa)
EXP XCO 2
CAL XCO 2
Error (%)
EXP YCO 2
CAL YCO 2
Error (%)
344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3
7.59 8.27 8.96 9.65 10.0 10.3 10.5 10.6 10.7
0.481 0.534 0.596 0.665 0.704 0.747 0.766 0.781 0.792
0.468 0.526 0.581 0.647 0.689 0.720 0.733 0.753 0.765
−2.7 −1.5 −2.5 −2.7 −2.1 −3.6 −4.3 −3.5 −3.4
0.947 0.949 0.946 0.940 0.935 0.927 0.923 0.920 0.916
0.989 0.988 0.988 0.991 0.989 0.980 0.979 0.978 0.976
4.4 3.9 4.4 5.4 5.7 5.7 6.1 6.3 6.6
544
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
Fig. 1. VLE calculation program flow. Table 3 VLE calculation results and experimental results for SC–CO2 + benzene T (K)
P (MPa)
EXP XCO 2
CAL XCO 2
Error (%)
EXP YCO 2
CAL YCO 2
Error (%)
344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3
7.59 8.27 8.96 9.65 10.0 10.3 10.5 10.6 10.7
0.507 0.564 0.625 0.692 0.726 0.763 0.781 0.793 0.805
0.503 0.563 0.627 0.679 0.708 0.740 0.752 0.757 0.785
−0.8 −0.2 −0.3 −1.9 −2.5 −3.0 −3.7 −4.5 −2.5
0.937 0.941 0.940 0.936 0.932 0.925 0.921 0.919 0.916
0.998 0.990 0.987 0.977 0.989 0.982 0.982 0.982 0.980
6.5 5.2 5.0 4.2 6.1 6.2 6.6 6.9 7.0
5. Conclusions High-pressure phase equilibrium calculation of supercritical fluid systems is not a well solved problem up to now. The perturbed hard-sphere chain equation of state is applied to calculate the phase behavior of supercritical CO2 systems, especially to calculate the vapor–liquid phase equilibrium of supercritical CO2 binary systems in this paper. The comparison between calculation results and experimental ones shows clearly that the perturbed
hard-sphere chain equation of state is able to describe the phase behavior of supercritical CO2 systems preferably.
Acknowledgements Financial support by the National Nature Science Foundation of China under grant NSFC 20176003 is gratefully acknowledged.
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
Appendix A. Nomenclature a A∗ b d E∗ Fa , Fb g(d+ ) k N NA P r T V V∗ x ε µ ρ σ ξ, η
attractive parameter defined by Eq. (3) characteristic surface area (m2 mol−1 ) repulsive parameter defined by Eq. (3) hard-sphere diameter (m) characteristic “cohesive” energy (j mol−1 ) parameters defined by Eq. (3) radial distribution function of hard spheres at contact Boltzmann constant number of molecules Avogadro constant pressure (Pa) number of segments per molecule temperature (K) mole volume (m3 mol−1 ) characteristic volume (m3 mol−1 ) number fraction of molecules pair-potential parameter (K) chemical potential (J mol−1 ) number density (mol m−3 ) pair-potential parameter (Å) parameters defined by Eq. (7)
Subscript i, j component of mixture
545
Superscripts cal calculation exp experiment References [1] A.H. Ewald, W.B. Jepson, J.S. Rowlinson, The solubility of solids in gases, Discuss. Faraday. Soc. 15 (1953) 238. [2] M. Fermeglia, A. Bertucco, D. Patrizio, Thermodynamic properties of pure hydrofluoro-carbons by a perturbed hard-sphere-chain equation of state, Chem. Eng. Sci. 52 (1997) 1517. [3] Y. Song, T. Hino, S.M. Lambert, J.M. Prausnitz, Liquid-liquid equilibria for polymer solutions and blends, including copolymer, Fluid Phase Equilib. 117 (1996) 69. [4] S.M. Lambert, Y. Song, J.M. Prausnitz, M. Theta, Conditions in binary and multicomponent polymer solutions using a pertured hard-sphere-chain equation of state, Macromolecules 28 (1995) 4866. [5] G.A. Mansoori, N.F. Carnahan, K.E. Starling, T.W. Leland, Equilibrium thermodynamic properties of the mixture of hard sphere, J. Chem. Phys. 54 (1971) 1523. [6] M. Fermeglia, A. Bertucco, S. Bruni, A perturbed hard sphere chain equation of state for application to hydrofluorocarbons, hydrocarbons and their mixtures, Chem. Eng. Sci. 53 (1998) 3117. [7] J.M. Mollerup, M.L. Michelsen, Calculation of thermodynamic equilibrium properties, Fluid Phase Equilib. 74 (1992) 1. [8] W.L. Weng, J. Lee, Vapor–liquid equilibrium of the octane/carbon dioxide, octane/ethane and octane/ethylene systems, J. Chem. Eng. Data 37 (1992) 213. [9] N. Nagarajan, R.L. Robinson, Equilibrium phase composition, phase densities, and interfacial tensions for CO2 + hydrocarbon systems. 3. CO2 + cyclohexane. 4. CO2 + benzene, J. Chem. Eng. Data 32 (1987) 369.
Vapor–liquid phase behavior of the binary systems containing supercritical carbon dioxide Li Zhiyi∗ , Wang Weili, Zhang Xiaodong, Liu Xuewu, Hu Dapeng, Xia Yuanjing R&D Institute of Liquid and Powder Engineering, Dalian University of Technology, 158 Zhongshan Rd., Xigang District, Dalian 116012, PR China Received 18 October 2002; received in revised form 9 September 2003; accepted 9 September 2003
Abstract A thermodynamic model based on the perturbation theory is investigated. The perturbed hard-sphere chain (PHSC) equation of state (EOS) is applied to calculate phase behavior of the binary systems containing supercritical carbon dioxide. A calculation program is written. The vapor–liquid phase equilibrium calculation is conducted with the binary systems and a comparison is made between the calculation results and experimental ones. It is shown that the PHSC equation of state can be reliably used for calculating the vapor–liquid phase behavior of carbon dioxide systems when the pressure is very high. © 2003 Elsevier B.V. All rights reserved. Keywords: Supercritical carbon dioxide; Perturbation theory; Phase equilibrium
1. Introduction A supercritical fluid (SCF) as a special solvent has dissolution properties like a gas and transfer properties like a liquid, It gives a new broad way to chemical engineering. Especially supercritical CO2 (SC–CO2 ) has expansively potential applications in the area of bio-chemical engineering, medicine and food industry, since it is non-toxic, environmentally acceptable, noncombustible, cheap and has a low critical temperature and a moderate critical pressure. Solubilities of all kinds of solutes in SC–CO2 are important parameters for supercritical fluid processes and they can be predicted by a proper phase equilibrium model. The common used phase equilibrium models include the Ewald equation of state and cubic equations of state. Ewald et al. [1] first tried to make a model of SCF system by Ewald equation of state. It has been realized that it is difficult to describe the mixture phase equilibrium near the critical point even though the third Ewald coefficient is used. Although the form of cubic equations of state is simple, the calculation results are not satisfactory to SC–CO2 systems because of some inherent shortcomings. ∗
Corresponding author. E-mail address: [email protected] (L. Zhiyi).
0255-2701/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2003.09.002
This paper tries to apply the perturbation theory proposed by Fermeglia et al. [2] with perturbed hard-sphere chain (PHSC) equation of state (EOS) to describe the phase behavior of binary systems containing SC–CO2 , and examines the feasibility of this model when it is used for the vapor–liquid phase equilibrium calculation.
2. Theory 2.1. PHSC EOS The equation of state considered in this paper is the PHSC EOS [3]. It takes the hard sphere chains as its reference system, in the form of Chiew equation of state [4], derived from the Percus-Yevik integral theory coupled with chain connectivity, and a van der Waals attractive term as the perturbation. The EOS in terms of pressure is the following: m
P = 1 + ρ xi xj ri rj bij gij (dij+ ) ρkT ij
−
m i
xi (ri −1)[gii (dii+ )−1]−
m
ρ xi xj ri rj aij kT ij
(1)
542
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
where P is the pressure, T the absolute temperature, ρ = N/V the number density, k the Boltzmann’s constant, dij the hard-sphere diameter, gij (dij+ ) the ij-pair distribution function of hard spheres at contact, xi = Ni /N the number fraction of molecules, ri the number of segments (hard spheres) per molecule for the ith component, aij reflects the attractive forces between two non-bonded segments, and bij is the van der Waals covolume per segment.
In Eq. (1), P and T are given, xi , xj and ρ are unknown, the other parameters can be obtained from following Eqs. (2)–(7). The Eq. (1) is an implicit five power function of density. Each pure component has three basic parameters ε, σ and r, which can be combined to give a more useful set of parameters directly related to size, shape and energetic interactions of the molecules of the fluid considered. This may be done by defining a characteristic volume V ∗ , a characteristic surface area A∗ and a characteristic “cohesive” energy E∗ . π ε Rσ 3 NA , A∗ = πrσ 3 NA , E∗ = r V∗ = Rg 6 k (2) Because of the rigorously theoretical nature of the equation of state, no mixing rules are required for the reference term, and the attractive term only requires van der Waals one-fluid mixing rules. The mixture parameters aij and bij needed for each binary pair included in the mixture are following: 2π kT kT 2π 3 3 , bij = σij εij Fa σij Fb aij = 3 εij 3 εij (3) where ε and σ are pair-potential parameters. Fa an Fb are expressed by following equations [5]: kT Fa = 1.8681 exp −0.0619 ε 3/2 kT + 0.6715 exp −1.7317 ε (4) kT Fb = 0.7303 exp −0.1649 ε 3/2 kT + 0.2697 exp −2.3793 ε No combing rule is needed for σ as a consequence of the additivity of the hard-sphere diameters, but one adjustable parameter kij is needed for energetic parameter ε. σii + σjj , 2
εij =
√ εi εj (1 − kij )
2 ξij 3 1 1 ξij + + 1 − η 2 (1 − η)2 2 (1 − η)
gij (η, ξij ) = where
(5)
m
η=
ρ x i ri b i , 4 i
2.2. Parameters determination
σij =
The required mathematical expression for gij (dij+ ) is given by the BMCS equation for hard-sphere mixtures
ξij =
bi bj bij
1/3
(6)
m
ρ 2/3 x k rk b k 4
(7)
k
If transforming Eq. (1) from molecule density basis to segment density basis, we can obtain the following equation [6] m
P = 1 + ρr φi φj bij gij (dij+ ) ρr kT ij m m 1 ρr − φi 1 − gii (dii+ ) − φi φj aij η kT i
(8)
ij
with ρr =
Nr , V
φi =
Ni r i xi ri = m , Nr j=1 xj rj
Nr =
m
N i ri
i=1
(9)
3. Numerical calculation program The numerical calculation involves solving Eq. (1) for xi , xj and ρ or ρr together with six others (Eqs. (2)–(7)). A calculation program is written for the task. Supposing the two-phase mixture containing SC–CO2 has flow rate F, composition Zi (mole fraction) and temperature T, it is pumped into equilibrium cell until a desired pressure is reached. After equilibrium has been reached, the vapor phase and liquid phase compositions are Yi and Xi (mole fraction) respectively. This calculation program consists of following modules. 3.1. Module 1: INPUT—inputting basic data In this module, the critical pressure Pc , the critical temperature Tc , the boiling point Tb , the molecular weight ME , the binary interaction parameter kij , and three molecular-based parameters V ∗ , A∗ and E ∗ are needed for input. The binary interaction parameter kij is determined by fitting binary vapor–liquid equilibrium data. The three molecular parameters V ∗ , A∗ and E ∗ can be obtained by fitting experimental data for each pure component. For pure SC–CO2 , the three molecular parameters V ∗ , A∗ and E ∗ can be fitted to vapor pressure and saturated liquid density data as functions of temperature. For other pure liquid parameters, V ∗ , A∗ and E ∗ can be regressed from pressure–volume–temperature (PVT) data.
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
3.2. Module 2: PARA—calculating three microcosmic parameters σ, r and ε The three microcosmic parameters σ, r and ε can be obtained through three macroscopic parameters V ∗ , A∗ and E ∗ with Eq. (2). 3.3. Module 3: PKIO—determining the initial value of phase equilibrium constant Ki0 (1 ≤ i ≤ m) The initial value of phase equilibrium constant can be supposed to equal to phase equilibrium constant of ideal state Ki0 (1 ≤ i ≤ m): Ps Ki0 = i P
(10)
3.4. Module 4: YNVL—determining if the mixture is in two-phase The program gives a judgment whether the mixture is in or not under given T and P. Only when both
two-phase
Ki Zi and Ki /Zi are bigger than 1, the mixture is in two-phase and the program enters the next step. 3.5. Module 5: VLP—calculating vapor and liquid phase densities The equilibrium vapor and liquid phase densities can be obtained by Eq. (1) and (8). 3.6. Module 6: CHPOT—calculating chemical potential L For each component, the chemical potential µV i and µi can be calculated with the equations given in the reference
543
[7] under corresponding temperature, pressure, vapor phase and liquid phase compositions, and vapor phase and liquid phase densities. 3.7. Module 7: ADE—adjusting phase equilibrium constant The adjustment of phase equilibrium constant can be done by the adjustment of vaporization rate. 3.8. Module 8: OUTPUT—outputting results of calculations This module can output the final vapor phase composition Yi , the liquid phase composition Xi and the phase equilibrium constant Ki of each component. The program flow is shown in Fig. 1.
4. Comparison between the calculation results and experimental ones The vapor–liquid phase equilibrium calculation has been done for the systems of SC–CO2 and octane, SC–CO2 and cyclohexane, and SC–CO2 and benzene with the calculation program. The calculation results are compared with experimental ones taken from [8,9]. The comparisons are given by Tables 1–3 where EXP means the experimental result and CAL the calculation one. From Tables 1–3, we notice that relative error of the calculation results for the liquid phase mole fraction is within 5%, and relative errors of the calculation results for the vapor phase are a slightly bigger then liquid phase, but still within 7%. The calculation results are in good agreement with experimental ones.
Table 1 VLE calculation results and experimental results for SC–CO2 + octane T (K)
P (MPa)
EXP XCO 2
CAL XCO 2
Error (%)
EXP YCO 2
CAL YCO 2
Error (%)
313.15 328.15 328.15 348.15 348.15 348.15
7.55 8.00 9.50 9.10 9.70 10.8
0.8900 0.7093 0.8815 0.6310 0.6770 0.7540
0.8648 0.7023 0.8544 0.6102 0.6519 0.7280
−2.8 −1.0 −3.1 −3.3 −3.7 −3.4
0.9920 0.9899 0.9740 0.9834 0.9786 0.9620
0.9972 0.9969 0.9946 0.9919 0.9935 0.9934
0.5 0.7 2.1 0.9 1.5 3.3
Table 2 VLE calculation results and experimental results for SC–CO2 + cyclohexane T (K)
P (MPa)
EXP XCO 2
CAL XCO 2
Error (%)
EXP YCO 2
CAL YCO 2
Error (%)
344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3
7.59 8.27 8.96 9.65 10.0 10.3 10.5 10.6 10.7
0.481 0.534 0.596 0.665 0.704 0.747 0.766 0.781 0.792
0.468 0.526 0.581 0.647 0.689 0.720 0.733 0.753 0.765
−2.7 −1.5 −2.5 −2.7 −2.1 −3.6 −4.3 −3.5 −3.4
0.947 0.949 0.946 0.940 0.935 0.927 0.923 0.920 0.916
0.989 0.988 0.988 0.991 0.989 0.980 0.979 0.978 0.976
4.4 3.9 4.4 5.4 5.7 5.7 6.1 6.3 6.6
544
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
Fig. 1. VLE calculation program flow. Table 3 VLE calculation results and experimental results for SC–CO2 + benzene T (K)
P (MPa)
EXP XCO 2
CAL XCO 2
Error (%)
EXP YCO 2
CAL YCO 2
Error (%)
344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3 344.3
7.59 8.27 8.96 9.65 10.0 10.3 10.5 10.6 10.7
0.507 0.564 0.625 0.692 0.726 0.763 0.781 0.793 0.805
0.503 0.563 0.627 0.679 0.708 0.740 0.752 0.757 0.785
−0.8 −0.2 −0.3 −1.9 −2.5 −3.0 −3.7 −4.5 −2.5
0.937 0.941 0.940 0.936 0.932 0.925 0.921 0.919 0.916
0.998 0.990 0.987 0.977 0.989 0.982 0.982 0.982 0.980
6.5 5.2 5.0 4.2 6.1 6.2 6.6 6.9 7.0
5. Conclusions High-pressure phase equilibrium calculation of supercritical fluid systems is not a well solved problem up to now. The perturbed hard-sphere chain equation of state is applied to calculate the phase behavior of supercritical CO2 systems, especially to calculate the vapor–liquid phase equilibrium of supercritical CO2 binary systems in this paper. The comparison between calculation results and experimental ones shows clearly that the perturbed
hard-sphere chain equation of state is able to describe the phase behavior of supercritical CO2 systems preferably.
Acknowledgements Financial support by the National Nature Science Foundation of China under grant NSFC 20176003 is gratefully acknowledged.
L. Zhiyi et al. / Chemical Engineering and Processing 43 (2004) 541–545
Appendix A. Nomenclature a A∗ b d E∗ Fa , Fb g(d+ ) k N NA P r T V V∗ x ε µ ρ σ ξ, η
attractive parameter defined by Eq. (3) characteristic surface area (m2 mol−1 ) repulsive parameter defined by Eq. (3) hard-sphere diameter (m) characteristic “cohesive” energy (j mol−1 ) parameters defined by Eq. (3) radial distribution function of hard spheres at contact Boltzmann constant number of molecules Avogadro constant pressure (Pa) number of segments per molecule temperature (K) mole volume (m3 mol−1 ) characteristic volume (m3 mol−1 ) number fraction of molecules pair-potential parameter (K) chemical potential (J mol−1 ) number density (mol m−3 ) pair-potential parameter (Å) parameters defined by Eq. (7)
Subscript i, j component of mixture
545
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