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

Abstract

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.