A consistency test for α-functions of cubic equations of state

Abstract

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Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of volumetric, energetic and saturation properties of pure compounds in the sub- and super-critical domains

“…Development of the translated-consistent tc-PR and tc-RK cubic equations of state for a safe and accurate prediction of pure-compound densities and other thermodynamic properties -4 -by Le Guennec et al [1] also tested whether 12 α-functions, generally available in process simulation software programs, were or not able to pass the proposed consistency test. They concluded that eight over twelve of these well-known α-functions (Soave 1972 [5], Soave 1984 [6], Gibbons-Laughton [7], Stryjek-Vera [8], Boston-Mathias [9], Mathias-Copeman [10], Mathias [11], Twu 1995 [12,13]) failed the proposed consistency test whatever the values of the parameters are.…”

“…(4). As explained by Le Guennec et al [1], the set of (L, M, N) parameters can be labeled consistent if the resulting α-function satisfies the constraints defined by Eq. (3).…”

“…The reason is that a vapor pressure calculation only involves the α-function itself whereas enthalpy and heat-capacity calculations involve also the first and second derivatives of the α-function respectively. In addition, it has been showed [1] that the use of sat P , vap H ∆ and sat P,L c data to determine α-function parameters dramatically improves the extrapolability of the EoS in the supercritical domain.…”

“…As recalled in one of our recent papers [1], numerous modifications to the Van der Waals cubic equation of state (CEoS) [2] have been presented over the years with the aim of representing with increasingly accuracy the properties of complex systems. Despite these modifications, the attractive and repulsive terms of CEoS are still expressed by introducing a parameter a which is a measure of the attractive forces between molecules and a parameter b…”

“…to express the attractive term as the product of its value at the critical temperature ( c a ) by the so-called alpha function. The paper by Le Guennec et al [1] highlights that such α- …”