Phase equilibria for mixtures containing very many components. Development and application of continuous thermodynamics for chemical process design

Cotterman, Ronald L.; Bender, R.; Prausnitz, John M.

doi:10.1021/i200028a033

Cited by 224 publications

(130 citation statements)

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“…The common feature of all these recent models is the utilization of continuous thermodynamics (CT), a theory developed by Gal-Or, Cullinan & Galli (1975) and by Cotterman, Bender & Prausnitz (1985). In CT, the chemical potential for a mixture containing numerous components is appropriately represented, and the Gibbs function is derived through molecular thermodynamic methods in terms of the probability distribution function (PDF) describing the mixture composition.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Clercq

Bellan

2005

J. Fluid Mech.

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A representation of multicomponent-liquid (MC-liquid) composition as a linear combination of two single-Gamma probability distribution functions (PDFs) is used to describe a large number of MC-liquid drops evaporating in a gas flow. The PDF, called the double-Gamma PDF, depends on the molar mass. The gas-phase conservation equations are written in an Eulerian frame and the drops are described in a Lagrangian frame. Gas conservation equations for mass, momentum, species and energy are combined with differential conservation equations for the first four moments of the gascomposition PDF and coupled to the perfect gas equation of state. Source terms in all conservation equations account for the gas/drop interaction. The drop governing equations encompass differential conservation statements for position, mass, momentum, energy and four moments of the liquid-composition PDF. Simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops colder than the surrounding gas. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. During the layer evolution, the drops heat and evaporate. The results address the layer evolution, and the state of the gas and drops when layers reach a momentum-thickness maximum past the double vortex pairing. Of interest is the influence of the liquid composition on the development of the vortical features of the flow, on the vortical state reached after the second pairing, and on the gas temperature and composition. The MC-liquid simulations are initiated with a single-Gamma PDF composition so as to explore the development of the double-Gamma PDF. Examination of equivalent simulations with n-decane, diesel and three kerosenes as the liquid, permits assessment of the single-species versus the MC-liquid aspect, and of mixture composition specific effects. Global layer growth and global rotational characteristics are unaffected by liquid specificity; however, the global mixing is highly liquid-specific. Also liquidspecific is the evolution of the ensemble-averaged drop characteristics and of the volumetric averages representing the gas composition. Visualized rotational characteristics show that the small-scale vortical activity increases with increased fuel volatility, which is confirmed by analysis of the vorticity budgets. Homogeneous-planeaverage budgets of the vorticity and vorticity-magnitude equations indicate that the stretching and tilting, and momentum-source terms are responsible for the difference among simulations. For all MC liquids, the gas displays a high level of composition heterogeneity, which can directly be traced to the original PDF representing the MC-liquid composition. Under most conditions, the single-Gamma PDF develops into a double-Gamma PDF; however, the extent of this transformation, indicative of vapour condensation onto drops, is not readily parametrized by the liquid volatility, initial carrier-gas temperature or trace vapour in the initial ...

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Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Clercq

Bellan

2005

J. Fluid Mech.

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“…Symbol o stands for the functional derivative operator [8,10]. A similar relation holds for the fugacity in the supercritical phase.…”

Section: Introductionmentioning

confidence: 93%

“…For binary interaction parameter ars• we use (8) From experimental vapor-liquid equilibrium (VLE) data, we obtain for propaneparaffins,…”

Section: Hydrocarbonsmentioning

confidence: 99%

“…In this work we discuss application to supercritical-fluid extraction of recent work [8,9] on the framework of continuous thermodynamics (i.e. thermodynamics of mixtures with very many components).…”

Section: Introductionmentioning

confidence: 99%

“…Suppose that we have a liquid phase (L) and a supercritical phase (SF) at equilibrium; as discussed elsewhere [8], the conditions for equilibrium for the case of a semi-continuous mixture are for every discrete component i and for every continuous component…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Supercritical‐Fluid Extraction Calculations for High‐Boiling Petroleum Fractions Using Propane. Application of Continuous Thermodynamics

Cotterman

Dimitrelis

Prausnitz

1984

Ber Bunsenges Phys Chem

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Supercritical‐fluid extraction is a useful process for upgrading heavy multicomponent mixtures such as high‐boiling petroleum fractions. Design‐oriented calculations are reported for an extraction process using propane to extract intermediate components from a petroleum fraction with molecular weights in the range 150‐−500. The composition of the heavy‐hydrocarbon mixture is described by two continuous distribution functions of molecular weight, one for paraffinic and one for aromatic components. Process calculations are based on a recently developed thermodynamic framework for mixtures with very many components, coupled with an equation of state of the van der Waals form. Particular attention is given to multicomponent phase equilibria in the retrograde region where solvent recovery is favorable. Quantitative results are given for solvent capacity and selectivity as a function of operating conditions.

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A continuous polydisperse thermodynamic algorithm for a modified flory-Huggins model: The (polystyrene + nitroethane) example

Sousa¹,

Rebelo²

2000

J. Polym. Sci. B Polym. Phys.

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Phase equilibria for mixtures containing very many components. Development and application of continuous thermodynamics for chemical process design

Cited by 224 publications

References 4 publications

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects

Supercritical‐Fluid Extraction Calculations for High‐Boiling Petroleum Fractions Using Propane. Application of Continuous Thermodynamics

A continuous polydisperse thermodynamic algorithm for a modified flory-Huggins model: The (polystyrene + nitroethane) example

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