Study on interfacial tension in confined spaces using the extended Patel-Teja equation of state

In confined spaces, the molecule-wall interactions and the strong confinement effect in nanopores lead to a significant deviation in the interfacial tension of confined fluids from that of unconfined fluids. This makes it difficult for classical equations of state to achieve accurate predictions. To address this issue, this study modified the classical cubic Patel-Teja equation of state (EOS) and established an extended Patel-Teja EOS suitable for confined spaces. Firstly, a new pressure term was introduced to characterize the influence of molecule-wall interactions. Secondly, based on experimental and molecular simulation data, a dimensionless correlation for critical property shifts was derived to describe the shift of critical properties in confined spaces. Finally, the capillary pressure effect in confined spaces was considered in the calculation of interfacial tension. Comparison with experimental data or literature data verifies that the extended Patel-Teja EOS exhibits high accuracy when calculating the interfacial tension in confined spaces. It can be used to analyze the influence of temperature, pressure and nanopore size on the interfacial tension of pure substances and binary mixtures. In the CO₂-CH₄ system, with the increase of pore radius, the growth rate of interfacial tension is 2.25 % in the range of 5 nm to 100 nm. From 100 nm to 1000 nm, the growth rate of interfacial tension is only 0.01 %, and finally it gradually approaches the interfacial tension in unconfined spaces. The study can provide theoretical support for the fluid interfacial behavior in processes such as oil and gas exploitation.