Compressibility of a Simple Fluid in Cylindrical Confinement: Molecular Simulation and Equation of State Modeling

Abstract

Fluids confined in nanoporous materials exhibit thermodynamic properties that differ from the same fluid in bulk. Recent experiments and molecular simulations suggested that the isothermal compressibility is among these properties. The compressibility determines the elastic response of a fluid to mechanical impact, and in particular, the speed of acoustic wave propagation through it. Knowledge of the compressibility of fluids confined in nanopores is needed for understanding the elastic wave propagation in fluid-saturated nanoporous media, such as hydrocarbon-bearing shales. Molecular simulations allow for the prediction of the elastic properties of a confined fluid but require computationally expensive calculations for each system and pore size. Therefore, there is interest for a more straightforward model that can predict the elastic properties of a confined fluid as a function of the external pressure and confining pore size. Such models can be based on an equation of state (EOS) for a confined system. Here, we explore a possibility for a generalized van der Waals EOS for confined fluids to predict the compressibility. We also calculate the elastic properties of argon confined in silica nanopores from grand canonical Monte Carlo simulations. We obtain comparable adsorption isotherm predictions of the EOS and simulations at various pore sizes and temperatures without changing any other parameters. We then see how the predictions of the elastic properties from simulations compare to the EOS and find reasonable agreement. Additionally, we vary the solid–fluid interaction parameters in both the EOS and molecular simulations to represent solids other than silica and see how the elastic moduli depend on the other properties of confining pores related to the interaction strength. This work is a step toward a quantitative description of wave propagation in fluid-saturated nanoporous media.

Elastic properties of confined fluids from molecular modeling to ultrasonic experiments on porous solids

“…In the last two decades, numerous works published in the literature presented several attempts to develop equations of state for confined fluids. While typically those were not employed to predict compressibility, a recent work has demonstrated that it is feasible and showed that one of these equations [75] qualitatively predicts compressibility of confined fluids [81]. Therefore, another open challenge is to adapt an existing equation of state, or develop a new one, which can provide quantitative predictions for compressibility of confined fluids.…”

“…However, none of those works have been developed for the elastic properties. Dobrzanski et al explored the possibility of an EOS for confined fluids to predict the compressibility of the fluid [81]. They used the generalized van der Waals (vdW) EOS developed by Travalloni et al [75,76] for squarewell fluid confined in a cylindrical pore:…”

“…7. Notably, even though the equation is rather simple, having only two fitting parameters, it is able to capture the behavior of the elastic properties seen in simulations across various pore sizes and temperatures [81].…”

“…A series of publications by Schappert and Pelster reported ultrasonic experiments on Vycor glass saturated with liquid argon [33, 49, 102, 113-115, 138, 159-161], which is an excellent system for molecular modeling because interactions of argon atoms with each other and with glass surfaces can be readily modeled by simple Lennard-Jones potentials. Their work stimulated Gor and co-workers to focus on DFT and MC simulations for this system [22,23,30,62,81,162], and to make a step towards the comparison of simulations to ultrasonic data [108,109].…”

Distinct Enhancement of the Longitudinal Modulus of Liquid Nitrogen in Nanoporous Vycor Glass

“…For the identification of the influencing factors and their contribution to the elasticity, current research focuses on simple model systems. In recent years several experimental and theoretical studies on the elasticity of adsorbates in nanopores were published. ,− Previous research revealed different factors that influence the elastic properties of adsorbates. ,,− The elastic moduli of adsorbates in nanoconfinement are changed as a result of the so-called solvation pressure (or adsorption stress), , which is also the cause for the well-known effect of sorption-induced deformation. ,− Thus, a variation of the Laplace pressure (that contributes to the solvation pressure) during the sorption process causes a change of the adsorbate’s longitudinal modulus, β ads . ,, But also for fully saturated pores at the saturation vapor pressure p 0 , the solvation pressure results in a deviation of β ads from bulk values. ,, Indeed, simulations and DFT calculations by Gor and his group showed that there is a linear relation between the adsorbate’s elasticity and the inverse pore size. , …”