Analytical Investigation of the Confinement Effect on Capillary Condensation Pressure of Fluids in Nanopores

Abstract

Abstract Phase behavior in nanopores, because of its widespread industrial applications, has attracted great attention from numerous researchers in recent years. However, there are still several aspects that are not fully understood in this area, such as the confinement effect on saturation pressure, critical properties, and phase boundary. In this work, real gas effect is firstly incorporated into the original Kelvin equation, along with the pore size effect on surface tension, the multilayer adsorption, and the molecule-wall interaction potential to improve the accuracy of the capillary condensation pressure calculation. Firstly, the validity of the original Kelvin equation is examined by calculating the capillary condensation pressure of pure fluids at different pore sizes. Subsequently, the compressibility factor is computed with a modified Peng-Robinson equation of state and the molecule-wall interaction potential is correlated with the number of adsorption layers in nanopores, both of which are coupled into the original Kelvin equation. Consequently, the modified Kelvin equation is validated with collected experimental data from the literature. It is found that the capillary condensation pressure computed by the original Kelvin equation manifest a significant deviation from those measured from experiments at pore size smaller than 15 nm. At pore size of 2 nm, the capillary condesantion pressure calculated with the original Kelvin equation is 627.5% and 407.8% higher than the experimental data for nitrogen and argon, respectively. Among the four factors which are incorporated into the original Kelvin equation for modification, molecule-wall interaction potential has the most significant contribution with a ratio of 72%, while the pore size effect on surface tension has the least to none contribution. The modified Kelvin equation is satisfactory to calculate the suppressed capillary condensation pressure of fluids in nanopores with pore size down to 2 nm. The overall relative devation for 3 data points of nitrogen at 77 K and 5 data points for argon at 87 K is 6.5% and 6.7%, respectively. This work provides a quantitative understanding of the confinement effect on capillary condensation pressure of fluids, which can help to investigate the phase behavior of reservoir fluids in nano-sized pores more accurately. The newly developed explicitly analytical model can be easily introduced into various simulators to provide a reliable instruction for the development of shale reservoirs.