A New State Equation for Sorptives in Near-Critical and Overcritical Temperature Regions

Abstract

This paper proposes a theoretical approach aimed at evaluation of fluid compression factor, activity, and cohesion energy at near-critical and overcritical temperatures, for the fluid molar volumes ranging from 40% of the critical value. Such data are necessary in the theoretical description of sorption processes, developed in our previous papers. The approach is based on separate analysis of fluid entropy and cohesion energy. A theoretical model is used, which makes possible to derive a formula for the athermal compression factor of hard sphere fluids. It involves using a correction for the fluid accentric factor. Also applicability of other expressions is discussed. In turn, the mathematical model for the fluid cohesion energy was obtained by high accuracy approximation of universal compression factor data, with critical point conditions being taken into account. It is recommended to complete the compression data with empirical orthobaric compression factors. The coefficients of the model are expressed as functions of the fluid accentric factor. As the result, a state equation applicable for fluids of accentric factor less than 0.45 and reduced molar volume larger than 0.5 is proposed. For methane and carbon dioxide, the equations of better accuracy are proposed, with coefficients adjusted individually by nonlinear optimization. They are applicable for the reduced volume ranging from 0.4.

Complementary study of microporous adsorbents with DFT and LBET

“…In spite of this, the monolayer coverage Table 1 Spherical molecular diameter D and relative fugacity f/f s,max for adsorptives at a bulk reference state of packing ratio h (see Ref. [16]), corresponding to molar volumes V s used/found with LBET Fig. 3 for explanations).…”

“…Otherwise, e.g. for H 2 at 77 and 87 K, we apply an original equation of state [16] developed for highly compressed fluids (in adsorption systems Fig. 1.…”

High-Accuracy PVT Relationships for Compressed Fluids and Their Application to BET-like Modelling of CO2 and CH4 Adsorption

“…A number of recommendations have been made in the literature suggesting ways of overcoming this problem by extrapolating the vapour-liquid equilibrium data up to the studied temperature [see, for example, Wakasugi et al (1981)]. However, mathematical models of sorption processes developed by our team, referred to as LBET formulae (Milewska- Duda and Duda 1997;Milewska-Duda et al 2000a;Milewska-Duda 2002, 2005) also require the evaluation of the variation of the cohesion energy relative to the molar volumes of the sorptives in the reference state, a process that can only be undertaken using an adequate equation of state for the fluid. The classical van der Waals formula cannot be used for this purpose.…”

“…Although more than 2000 improved equations of state derived for different purposes can be found in the literature (Reid et al 1987;Kenonic Controls Ltd. 1999), not one provides relationships between the molar volume and the fluid cohesive energy. Hence, we have proposed (Milewska-Duda et al 2000b) a method for deriving PVT relationships which is sufficiently accurate to be used for the evaluation of all the physical properties of gaseous/vaporous sorptives necessary for the BET-like mathematical description of sorption processes.…”

Comparative analysis of sorption of small molecule hydrocarbons and polar substances in polish hard coals

“…8) is calculated as a ratio of the pore radius to sorbate molecule radius. Molecule size is calculated using the state equation dedicated to this model (Milewska-Duda et al 2000a). The whole sorption system is divided on an a priori basis into eleven subsystems with different dominant pore sizes.…”