An Equation of State for Pore-Confined Fluids

The prediction of properties in porous materials is of continuing interest in the fields of chemical and materials engineering. Application areas include, among others: (1) the use of supercritical fluids to modify porous materials, (2) physical adsorption of trace components from gaseous effluents, (3) gas storage using microporous materials, and (4) chemical separations using inorganic membranes. The confinement of a fluid in a porous matrix changes its properties relative to its bulk state and this may be important in engineering applications. As such, a number of researchers have worked in this area while attempting to advance knowledge in the field. For instance, the interplay between fluid-wall and fluid–fluid interactions, and the effects of confinement and pore geometry in mesoscopic porous materials has been studied theoretically and using computer simulation by Findenegg and collaborators. The effect of confinement on the criticality of fluids in controlled-pore materials with narrow-size distribution has also been studied, indicating a shift of the gasliquid critical point of the fluid in the porous material to lower temperature. However, the situation is different in amorphous mesoporous materials such as silica aerogel; due to the wide pore-size distribution and ill-defined pore geometry, it has not been possible to establish a quantitative description of the critical point shift. Given this situation, there has been substantial effort over the years devoted to developing equations of state suitable for thermodynamic property predictions in fluids confined in porous media, nevertheless, tractable, physically based models have remained elusive. An important class of these equations of state are of the mean field type, which are of interest because they are often analytic, and, therefore, amenable for use in process engineering calculations. Two important questions arise in the context of such equations of state: how accurate are they for real fluids and can the required number of adjustable parameters for their use be kept to a minimum and have some physical meaning? Our purpose in this article is to investigate both of these points with respect to the model and approach described here. For pure fluids, the proposed equation of state only requires the pure fluid critical properties. As a result, we believe that a fair comparison can be made between the proposed model and other equations of state that require similar knowledge, such as the Peng-Robinson (PR) equation of state, one of the most successful engineering cubic equations of state. Our model, however, has an important advantage over the PR equation of state, in that it can be theoretically and rationally extended for calculating thermodynamic properties of pore-confined fluids. We now describe the theoretical underpinnings of the model followed by calculations illustrating its use for both bulk and confined fluid situations.