Critical temperature shift modeling of confined fluids using pore-size-dependent energy parameter of potential function

The behavior and critical properties of fluids confined in nanoscale porous media differ from those of bulk fluids. This is well known as critical shift phenomenon or pore proximity effect among researchers. Fundamentals of critical shift modeling commenced with developing equations of state (EOS) based on the Lennard–Jones (L–J) potential function. Although these methods have provided somewhat passable predictions of pore critical properties, none represented a breakthrough in basic modeling. In this study, a cubic EOS is derived in the presence of adsorption for Kihara fluids, whose attractive term is a function of temperature. Accordingly, the critical temperature shift is modeled, and a new adjustment method is established in which, despite previous works, the bulk critical conditions of fluids are reliably met with a thermodynamic basis and not based on simplistic manipulations. Then, based on the fact that the macroscopic and microscopic theories of corresponding states are related, an innovative idea is developed in which the energy parameter of the potential function varies with regard to changes in pore size, and is not taken as a constant. Based on 94 available data points of critical shift reports, it is observed that despite L–J, the Kihara potential has sufficient flexibility to properly fit the variable energy parameters, and provide valid predictions of phase behavior and critical properties of fluids. Finally, the application of the proposed model is examined by predicting the vapor–liquid equilibrium properties of a ternary system that reduced the error of the L–J model by more than 6%.