(481b) A New Pure-Component Equation of State Designed for Accurate Reproduction of Phase-Equilibrium, Caloric and Volumetric Properties with Emphasis on Supercritical-Property Prediction

Numerous modifications to the Van der Waals model have been presented over the years with the aim of representing with increasing accuracy the thermodynamics of complex systems. As a matter of facts, the most of those do not incorporate a substantial difference in the functional combination of attractive and repulsive forces, with respect to the original formulation introduced by Van der Waals.

From the Van der Waals proposal, even the most successful engineering two-parameters cubic equations of state (EoS) still express their attractive and repulsive term by introducing a parameter a, which is a measure of the attractive forces (â??energy parameterâ?) between molecules, and the parameter b, which is a measure of the size (â??intrinsic volumeâ? or â??co-volumeâ?) of the molecules. The pure-component a energy parameter is directly proportional to the temperature-dependent alpha function α(T) which is a measure of how the a parameter deviates from its critical value.

A wide variety of α-functions has been proposed over the past years. Those contain parameters which are adjusted according to different criteria: either over a whole set of components or for each specie (â??generalizedâ? versus â??component-specificâ? α-function); either considering the whole temperature domain or specifically in the subcritical or supercritical regions (â??overallâ? versus â??domain-specificâ? α-function). Furthermore, among the mostly applied formulations, two different functional forms are identifiable: polynomial and exponential forms.

 In this work, the popular component-specific Twu (1991) alpha function (denoted Twu91), which exhibits an exponential form has been selected to model Vapour-Liquid Equilibrium (VLE) behaviour of mixtures containing supercritical components.

A key outcome of our work is that the use of the Twu91 α-function together with some sets of component-dependent parameters has resulted in the inaccurate VLE modelling of such mixtures, in spite of the use of advanced EoS/g^E mixing rules. A detailed examination of this issue has shown that the application of such sets of parameters entails the generation of abnormal deviations of the α-functions, when extrapolating at supercritical conditions. In parallel, the use of the simple generalized and polynomial Soave alpha function incorporated in the same advanced EoS/g^Emixing rules as previous, has led to very accurate results.

On the basis of these counterintuitive results, it was attempted to understand how the use of an EoS coupled with a generalized alpha function (with no adjustable parameter) could induce better modelling results than an EoS coupled with a more flexible alpha function involving 3 adjustable parameters. It has been shown that the calibration of α-functions requires the imposition of constraints to the parameters under regression in order to guarantee consistent predictions of the derived thermodynamic properties (residual enthalpy, entropy, heat capacity �) at all temperatures (sub- or super-critical).

Starting from these conclusions, the Twu91 alpha-function has been re-parameterized for a large series of pure components (1,000) and for the Redlick-Kwong (RK) and Peng-Robinson (PR) EoS. In the light of the newly regressed parameters, a generalized Twu-type α function, performing better than Soaveâ??s α function, has been proposed. The use of this new generalized Twu alpha function has been used to model the VLE data of binary systems containing a supercritical component and has led to improved modelling results with respect to the use of the simple Soave alpha-function.

Furthermore, a third parameter (called volumetric translationand denoted c) was added to the RK and PR EoS in order to improve the reproduction of volumetric properties. The parameter was estimated for the same large series of pure components (~1,000) and general correlations making it possible to estimate c from the mere knowledge of the acentric factor were proposed.

At the end, a new 3-parameter (a,b,c) PR-based EoS is proposed with the aim to ensure accurate predictions of phase-equilibrium, caloric and volumetric properties of pure components in both the sub- and super-critical regions. Complete EoS-parameter databases are provided for ~1,000 pure components and for all the other compounds, general correlations are proposed making it possible to estimate EoS parameters from a limited amound of experimental information (generally, the acentric factor).