Vapor–liquid critical properties of multi-component fluid mixture

Cai, Jun; Qiu, Deling; Zhang, Luning; Hu, Ying

doi:10.1016/j.fluid.2005.11.003

Cited by 12 publications

(12 citation statements)

References 43 publications

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“…The parameterizing functions c D , c Θ , c Σ , and c Ω determine the precise form of the implicit dependence of D, Θ, Σ, and Ω defined by (12). Two of the parameterizing functions may be chosen fairly freely and determine the coordinate transformation; the remaining ones are then fixed by the relation (18) and the universal EOS.…”

Section: Order Parameter and Generalized Polar Coordinatesmentioning

confidence: 99%

“…Ignoring these, as often done in these formulations, therefore requires additional approximations which may result in artifacts very close to the critical point (Kiselev & Friend [36]). Other papers (e.g., [11,12]) implement the renormalization group approach more directly, resulting in an iterative definition of an equation of state that in the limit of infinitely many iterations satisfies the correct scaling laws. A thorough discussion of many practically relevant issues is given in the surveys by Anisimov & Sengers [3] and Behnejad et al [6].…”

Section: Phenomenological Scaling Models For Fluid Mixturesmentioning

confidence: 99%

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Analytic Representation of Critical Equations of State

Neumaier

2014

J Stat Phys

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A new form is proposed for equations of state (EOS) of thermodynamic systems in the 3-dimensional Ising universality class. The new EOS guarantees the correct universality and scaling behavior close to critical points and is formulated in terms of the scaling fields only -unlike the traditional Schofield representation, which uses a parametric form.Close to a critical point, the new EOS expresses the square of the strong scaling field Σ as an explicit function Σ 2 = D 2e −1 W (D −e 0 Θ) of the thermal scaling field Θ and the dependent scaling field D > 0, with a smooth, universal function W and the universal exponents e −1 = δ/(δ + 1), e 0 = 1/(2 − α). A numerical expression for W is derived, valid close to critical points.As a consequence of the construction it is shown that the dependent scaling field can be written as an explicit function of the relevant scaling fields without causing strongly singular behavior of the thermodynamic potential in the one-phase region.Augmented by additional scaling correction fields, the new EOS also describes the state space further away from critical points. It is indicated how to use the new EOS to model multiphase fluid mixtures, in particular for vapor-liquid-liquid equilibrium (VLLE) where the traditional revised scaling approach fails.A thermodynamic field is a function of pressure P , absolute temperature T , and the chemical potential µ i of each pure component i in the mixture. For a fluid with C components, the physically realizable thermodynamic states form a (C +1)-dimensional 1 As a result, much of the statistical mechanics literature on critical scaling is written in a "magnetic" terminology. Most of this language is inappropriate in a fluid mixture context. Hence we choose here an independent notation and indicate at times alternative traditional notation in footnotes.2 For a recent verification in case of the Lennard-Jones fluid see Watanabe et al. [58].

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Section: Order Parameter and Generalized Polar Coordinatesmentioning

confidence: 99%

Section: Phenomenological Scaling Models For Fluid Mixturesmentioning

confidence: 99%

Analytic Representation of Critical Equations of State

Neumaier

2014

J Stat Phys

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“…. , ρ C ) as a function of reduced temperature and densities, one must solve the nonlinear system of equations (8). Often, ( 8) is uniquely solvable for the ρ i , but if there are multiple solutions, the solution with largest reduced Helmholtz free energy f is the correct one.…”

Section: Free Energiesmentioning

confidence: 99%

A multi-phase, multi-component critical equation of state

Neumaier¹

2013

Preprint

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Realistic equations of state valid in the whole state space of a multi-component mixture should satisfy at least three important constraints: (i) The Gibbs phase rule holds. (ii) At low densities, one can deduce a virial equation of state with the correct multicomponent structure. (iii) Close to critical points, plait points, and consolute points, the correct universality and scaling behavior is guaranteed. This paper discusses semiempirical equations of state for mixtures that express the pressure as an explicit function of temperature and the chemical potentials. In the first part, expressions are derived for the most important thermodynamic quantities. The main result of the second part is the construction of a large family of equations of state with the properties (i)-(iii).

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“…Thus far, many authors have applied this method using different mean-field theories (e.g. Mean-Spherical Approximation (MSA) [26], equation of state for chain-like molecules [29,30], the SAFT equation and its variants [31,32,33,34,35,36,37,38,39,40], cubic equations [41,42,43,44,45,46,47,48], and others [49,50]), obtaining similarly good results. However, some aspects in the method are still unclear, including parameter estimation procedures and approximations in the renormalization equations.…”

Section: Introductionmentioning

confidence: 99%

“…The renormalization-group theory such as introduced by White and co-workers [23,24,25] and further developed by Lue and Prausnitz [26,27] is based on a transformation of the grand canonical partition function into a functional integral. In the present work, we used the derivation provided by White and co-workers [23,24,25] and applied successfully by other authors for cubic equations of state [46,43,42,41]. Details of the method can be found in the cited references.…”

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confidence: 99%

Renormalization Group Theory Applied to the CPA Equation of State: Impacts on Phase Equilibrium and Derivative Properties

Silva

Abreu

Tavares

2019

Preprint

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Calculation of thermodynamic properties such as vapor-liquid phase behavior with equations of state is largely and successfully employed in chemical engineering applications.<br>However, in the proximities of the critical point, the different density-fluctuation scales inherent to critical phenomena introduce significant changes in these thermodynamic properties, with which the classical equations of state are not prepared to deal.<br>Aiming at correcting this failure, we apply a renormalization-group methodology to the CPA equation of state in order to improve the thermodynamic description in the vicinity of critical points.<br>We use this approach to compute vapor-liquid equilibrium of pure components and binary mixtures, as well as derivative properties such as speed of sound and heat capacity.<br>Our results show that this methodology is able to provide an equation of state with the correct non-classical behavior, thus bringing it in consonance with experimental observation of vapor-liquid equilibrium and derivative properties in near-critical conditions.

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Vapor–liquid critical properties of multi-component fluid mixture

Cited by 12 publications

References 43 publications

Analytic Representation of Critical Equations of State

Analytic Representation of Critical Equations of State

A multi-phase, multi-component critical equation of state

Renormalization Group Theory Applied to the CPA Equation of State: Impacts on Phase Equilibrium and Derivative Properties

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