Statistical Mechanical Model for Adsorption Coupled with SAFT-VR Mie Equation of State

Abstract

We extend the SAFT-VR Mie equation of state to calculate adsorption isotherms by considering explicitly the residual energy due to the confinement effect. Assuming a square-well potential for the fluid-solid interactions, the structure imposed by the fluid-solid interface is calculated using two different approaches: an empirical expression proposed by Travalloni et al. ( Chem. Eng. Sci. 65 , 3088 - 3099 , 2010 ), and a new theoretical expression derived by applying the mean value theorem. Adopting the SAFT-VR Mie ( Lafitte et al. J. Chem. Phys. , 139 , 154504 , 2013 ) equation of state to describe the fluid-fluid interactions, and solving the phase equilibrium criteria, we calculate adsorption isotherms for light hydrocarbons adsorbed in a carbon molecular sieve and for carbon dioxide, nitrogen, and water adsorbed in a zeolite. Good results are obtained from the model using either approach. Nonetheless, the theoretical expression seems to correlate better the experimental data than the empirical one, possibly implying that a more reliable way to describe the structure ensures a better description of the thermodynamic behavior.

Random surface statistical associating fluid theory: Adsorption of n-alkanes on rough surface

“…In these publications [5,8] Radial Distribution Function (RDF) was calculated from result [9] where analytical expression was obtained, however this form of RDF does not provide correct expression for density derivative which is needed in DFT calculations. Alternative way was developed in work [10] where mean-value theorem was applied in order to calculate confinement term in Helmholtz free energy. This approach contains an assumption of a square-well potential for the fluid-solid interactions.…”

How does the shape and surface energy of pores affect the adsorption of nanoconfined fluids?

“…Theoretical and semiempirical models used to predict the adsorption isotherms of gases require assumptions to be made on the pore geometry and the topology of the existing pore network. The most common workhorse models are based on simplified scenarios, typically either cylindrical [12][13][14][15][16][17] or slit-like [18][19][20][21][22][23] pore geometries. In contrast with these idealized conformations, a detailed analysis of porous materials (e.g., montmorillonite, silica, carbons, clays, etc.)…”

Derivative Properties Data for Hydrogen–Ethylene Supercritical Mixtures Using a SAFT EoS and a SAFT Force Field

“…Based on Wertheim’s thermodynamic perturbation theory, − Chapman et al introduced the statistical associating fluid theory (SAFT), a successful family of models that inspired the development of countless equations of state for a broad range of different applications, including confined fluids, − electrolytes, polymers, and liquid crystals . PC-SAFT and SAFT-VR Mie are very accurate and versatile modern variants of SAFT that are already present in commercial process simulators.…”