Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement
•The validity of the Kelvin equations for fluids in nanopores are rigorously tested.•The applicability of equation of state with capillary pressure model is tested.•A novel graphical method is used to obtain the vapor–liquid equilibrium in nanopores.•The limiting temperatures are established for pha...
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| Published in | Chemical engineering science Vol. 226; p. 115839 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
23.11.2020
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| Abstract | •The validity of the Kelvin equations for fluids in nanopores are rigorously tested.•The applicability of equation of state with capillary pressure model is tested.•A novel graphical method is used to obtain the vapor–liquid equilibrium in nanopores.•The limiting temperatures are established for phase transition of pure component in nanopores.
To predict phase behavior of a pure component in nanopores, various versions of Kelvin equations and equation-of-state-with-capillary-pressure (EOS–Pcap) models have been used. There has been debate on the validity of Kelvin equation, especially in sub-10-nm pores. For EOS–Pcap models, numerical iterations have been used to obtain vapor–liquid equilibrium (VLE). In slit pores with widths larger than 8 nm, the Kelvin equation agrees with (within 10%) the equilibrium vapor-phase pressures of confined propane from engineering density functional theory between 310 K and 360 K. We introduce a graphical method using pressure–volume, chemical-potential–density, and chemical-potential–pressure relations to obtain VLE using EOS–Pcap model. While the Kelvin equation takes only surface tension as an input and returns a solution for VLE up until the bulk critical point (CP), the EOS–Pcap model predicts a limiting temperature different from the bulk CP. The predictions from Kelvin equations and EOS-Pcap models can be improved by considering adsorption layer thickness. |
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| AbstractList | •The validity of the Kelvin equations for fluids in nanopores are rigorously tested.•The applicability of equation of state with capillary pressure model is tested.•A novel graphical method is used to obtain the vapor–liquid equilibrium in nanopores.•The limiting temperatures are established for phase transition of pure component in nanopores.
To predict phase behavior of a pure component in nanopores, various versions of Kelvin equations and equation-of-state-with-capillary-pressure (EOS–Pcap) models have been used. There has been debate on the validity of Kelvin equation, especially in sub-10-nm pores. For EOS–Pcap models, numerical iterations have been used to obtain vapor–liquid equilibrium (VLE). In slit pores with widths larger than 8 nm, the Kelvin equation agrees with (within 10%) the equilibrium vapor-phase pressures of confined propane from engineering density functional theory between 310 K and 360 K. We introduce a graphical method using pressure–volume, chemical-potential–density, and chemical-potential–pressure relations to obtain VLE using EOS–Pcap model. While the Kelvin equation takes only surface tension as an input and returns a solution for VLE up until the bulk critical point (CP), the EOS–Pcap model predicts a limiting temperature different from the bulk CP. The predictions from Kelvin equations and EOS-Pcap models can be improved by considering adsorption layer thickness. |
| ArticleNumber | 115839 |
| Author | Lu, Chang Shardt, Nadia Li, Huazhou Jin, Zhehui Elliott, Janet A.W. Wang, Yingnan |
| Author_xml | – sequence: 1 givenname: Yingnan surname: Wang fullname: Wang, Yingnan organization: School of Mining and Petroleum Engineering, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada – sequence: 2 givenname: Nadia surname: Shardt fullname: Shardt, Nadia organization: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada – sequence: 3 givenname: Chang surname: Lu fullname: Lu, Chang organization: School of Mining and Petroleum Engineering, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada – sequence: 4 givenname: Huazhou orcidid: 0000-0002-4541-670X surname: Li fullname: Li, Huazhou organization: School of Mining and Petroleum Engineering, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada – sequence: 5 givenname: Janet A.W. surname: Elliott fullname: Elliott, Janet A.W. organization: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada – sequence: 6 givenname: Zhehui orcidid: 0000-0001-8305-5637 surname: Jin fullname: Jin, Zhehui email: zhehui2@ualberta.ca organization: School of Mining and Petroleum Engineering, Department of Civil and Environmental Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada |
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| SubjectTerms | Adsorption Density functional theory Equation of state with capillary pressure Kelvin equations Slit graphite nanopores Vapor–liquid equilibrium |
| Title | Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement |
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