Phase Equilibria in Binary and Multicomponent Systems. Modified van Laar-Type Equation

Black, Cline

doi:10.1021/ie50579a042

Cited by 34 publications

(21 citation statements)

References 24 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A suit able method for this purpose has already been discussed (5). It is applied here to calculate completely all phase equilibria involved in the usual azeotropic distillation process.…”

Section: Phase Equilibriamentioning

confidence: 99%

“…For this calculation a trace of pentane 1 Χ 10" 5 and a small fraction of ethanol 9 Χ 10" 5 The sample calculation is shown as Table I These last five pages of computer output provide a tray-to-tray summary of heat and material flows and detailed quantities for the phase equilibria, also a summary of the three-phase condenser and accumulator results and the water product out. The last output page shows the fraction of the aqueous phase that satisfies the water balance.…”

Section: Azeotropic Distillation Program Adp/adpllementioning

confidence: 99%

See 1 more Smart Citation

Azeotropic Distillation Results from Automatic Computer Calculations

Black

Golding

Ditsler

1974

Advances in Chemistry

Self Cite

View full text Add to dashboard Cite

In azeotropic distillation the added component, or entrainer, is taken overhead with one of two or more components being separated in a distillation column. If a second liquid phase forms upon condensing the overhead vapors, the entrainer-rich phase is refluxed or recycled back to the col umn. The other liquid phase is discarded, recycled to some suitable point in the plant, or processed further to recover dissolved components before being discarded. Methods pre sented earlier by one of the authors are applied to calculate two and three phase equilibria required in a computer pro gram for calculating azeotropic distillations. A brief descrip tion of the program is given; a sample output is listed and described. Calculated results for dehydrating aqueous etha nol mixtures are compared for the entrainers, n-pentane, benzene, and diethyl ether. Column flows, heat loads, and stage requirements are lowest for n-pentane. The entrain ers are rated in decreasing order of suitability: n-pentane, benzene, and diethyl ether.T^Vistribution of components between separable phases is the basis for **** most commonly used separation methods. Regardless of the type of separation step, its design depends on accurate distribution coefficients for the components between the contacting phases. These are given in compositions or more fundamental properties of the equilibrium phases.In distillation the components are distributed between separable vapor and liquid phases. The distribution coefficients or Κ values are the ratios of the vapor-liquid compositions in the equilibrium phases.They are expressed as the liquid phase activity coefficients, γ/s, the vapor 64 Downloaded by GEORGETOWN UNIV on August 25, 2015 |

show abstract

“…A suit able method for this purpose has already been discussed (5). It is applied here to calculate completely all phase equilibria involved in the usual azeotropic distillation process.…”

Section: Phase Equilibriamentioning

confidence: 99%

Section: Azeotropic Distillation Program Adp/adpllementioning

confidence: 99%

Azeotropic Distillation Results from Automatic Computer Calculations

Black

Golding

Ditsler

1974

Advances in Chemistry

Self Cite

View full text Add to dashboard Cite

show abstract

“…Renon and Prausnitz ( 1968a) have derived equations from fundamental considerations of molecular forces. Black ( 1958) Both Renon (1968a) and Black (1959) have presented the multicomponent forms of their equations. Expression of Black's empirical addition is not simple and has been the subject of much conjecture.…”

Section: Activity Coefficient Equationsmentioning

confidence: 99%

“…Prausnitz et al (1967) have recommended a procedure where the total solution vapor pressure is calculated with the activity coefficient equation and fitted to the experimental pressure data. Black (1958) gives three graphical procedures for calculating the three constants for his equation from vaporliquid data. Although his procedures can be computerized, they are still rather complicated and the more direct regression fit has been used in this work.…”

Section: Activity Coefficient Equationsmentioning

confidence: 99%

Calculation of multicomponent liquid‐liquid equilibrium with Renon's and Black's activity equations

Guffey¹,

Wehe²

1972

AIChE Journal

View full text Add to dashboard Cite

The combination of optimization theory and thermodynamics was used to develop a fast, reliable computerized procedure for predicting or representing multicomponent liquid‐liquid phase equilibrium. Both the Renon and Black activity coefficient equations were compared with experimental data using the procedure. Experimental data for three quarternary systems from the literature were examined. Prediction of ternary data from binary data is not very reliable, although ternary data can nearly always be represented by adjustment of the predicted binary constants. Quarternary data can be predicted from accurate ternary representations of similar species provided the additional compound is from the same family group. The Renon equation is recommended rather than the Black equation.

show abstract

“…While there have been a number of attempts, for examples, such as those made by White [9], Wohl [10], Black [11], and Chien and Null [12], to extend the original van Laar equations to multicomponent systems, none of these attempts could be considered satisfactory and truly representing an extension of the original van Laar equations. In this study, we have rectified the excess Gibbs free energy equation developed by van Laar and extended the reformulated equations to multicomponent systems.…”

Section: Introductionmentioning

confidence: 99%

Extending the Van Laar Model to Multicomponent Systems

Peng¹

2010

TOTHERJ

View full text Add to dashboard Cite

Abstract:The original van Laar equation for representing the excess Gibbs free energies of liquid mixtures contains certain deficiencies that have prevented the equation from being applied to multicomponent systems. We have analyzed the temperature dependency of the energy parameter in modern cubic equations of state and modified the original van Laar equation with a view to extending the equation to multicomponent systems. It is found that the consideration of the temperature dependency of the energy parameter has lead to a modified van Laar equation involving additional terms. These extra terms serve to provide some physical significance that can be attached to the van Laar equation to allow it to unambiguously represent the behavior of the excess Gibbs free energy and activity coefficients of nonideal solutions. The final form of the modified van Laar equation for multicomponent mixtures involves two size parameters and an interaction parameter for each of the constituent binary pairs; the latter parameter replaces a term consisting of a combination of the two energy parameters and two size parameters for the components in a binary mixture. For mixtures involving only hydrocarbons the size parameters can be readily calculated from the critical properties by means of any of the cubic equations of state of the van der Waals type.

show abstract

Phase Equilibria in Binary and Multicomponent Systems. Modified van Laar-Type Equation

Cited by 34 publications

References 24 publications

Azeotropic Distillation Results from Automatic Computer Calculations

Azeotropic Distillation Results from Automatic Computer Calculations

Calculation of multicomponent liquid‐liquid equilibrium with Renon's and Black's activity equations

Extending the Van Laar Model to Multicomponent Systems

Contact Info

Product

Resources

About