Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement

• Published in: Chemical engineering science Vol. 226; p. 115839
• Main Authors: Wang, Yingnan, Shardt, Nadia, Lu, Chang, Li, Huazhou, Elliott, Janet A.W., Jin, Zhehui
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 23.11.2020
• Subjects: Adsorption; Density functional theory; Equation of state with capillary pressure; Kelvin equations; Slit graphite nanopores; Vapor–liquid equilibrium; Density functional theory; Kelvin equations; Slit graphite nanopores; Vapor–liquid equilibrium; Adsorption; Equation of state with capillary pressure
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2020.115839

•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.