Dispersion activity coefficient models. Part 1: cubic equations of state

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Abstract

An explicit expression for dispersion in activity coefficient models can be derived from cubic equations of state (cEoS). Here we show that all the two-parameter cEoS deliver a van Laar type of equation. The difference between these equations can be characterized by a single parameter K, which can be computed directly from the cEoS characteristic parameters. The theoretical values for K are always higher than experimental activity coefficient data of alkane mixtures indicate. We show that mixtures of linear and branched alkanes require K=4.13 and K=3.04, respectively, while the lowest theoretical value, K=9, is given by the van der Waals equation. This mismatch in results is caused by the assumptions, which are made in the derivation of the van der Waals equation of state and which remain present in later developed cEoS. One of these is that all molecules are spherical, which leads to the inconsistency that the ratio of the covolume and the van der Waals volume is always 4, while this ratio for linear alkanes decreases rapidly to nearly 2 with increasing chain length. Another assumption is that all molecules experience the same number of external interactions, which neglects the fact that polyatomic molecules have less intermolecular interactions per spherical segment due to presence of covalent bonds and the occurrence of intramolecular interaction. Therefore, the van Laar type of activity coefficient equations are limited in their use as predictive model for dispersion. Perturbed hard-sphere chain equation of state will be discussed in part 2.

Original languageEnglish
Article number112275
Number of pages13
JournalFluid Phase Equilibria
Volume501
DOIs
Publication statusPublished - 1 Dec 2019

Fingerprint

cubic equations
Activity coefficients
Equations of state
equations of state
Alkanes
coefficients
Paraffins
alkanes
trucks
Molecules
Covalent bonds
polyatomic molecules
covalent bonds
interactions
Chain length
molecules
derivation
occurrences

Keywords

  • Activity model
  • Cubic equation of state
  • Dispersion
  • Van Laar

Cite this

@article{12b28552695f4d6289457968b14ea30e,
title = "Dispersion activity coefficient models. Part 1: cubic equations of state",
abstract = "An explicit expression for dispersion in activity coefficient models can be derived from cubic equations of state (cEoS). Here we show that all the two-parameter cEoS deliver a van Laar type of equation. The difference between these equations can be characterized by a single parameter K, which can be computed directly from the cEoS characteristic parameters. The theoretical values for K are always higher than experimental activity coefficient data of alkane mixtures indicate. We show that mixtures of linear and branched alkanes require K=4.13 and K=3.04, respectively, while the lowest theoretical value, K=9, is given by the van der Waals equation. This mismatch in results is caused by the assumptions, which are made in the derivation of the van der Waals equation of state and which remain present in later developed cEoS. One of these is that all molecules are spherical, which leads to the inconsistency that the ratio of the covolume and the van der Waals volume is always 4, while this ratio for linear alkanes decreases rapidly to nearly 2 with increasing chain length. Another assumption is that all molecules experience the same number of external interactions, which neglects the fact that polyatomic molecules have less intermolecular interactions per spherical segment due to presence of covalent bonds and the occurrence of intramolecular interaction. Therefore, the van Laar type of activity coefficient equations are limited in their use as predictive model for dispersion. Perturbed hard-sphere chain equation of state will be discussed in part 2.",
keywords = "Activity model, Cubic equation of state, Dispersion, Van Laar",
author = "Krooshof, {Gerard J.P.} and Remco Tuinier and {de With}, Gijsbertus",
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Dispersion activity coefficient models. Part 1 : cubic equations of state. / Krooshof, Gerard J.P. (Corresponding author); Tuinier, Remco; de With, Gijsbertus.

In: Fluid Phase Equilibria, Vol. 501, 112275, 01.12.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - An explicit expression for dispersion in activity coefficient models can be derived from cubic equations of state (cEoS). Here we show that all the two-parameter cEoS deliver a van Laar type of equation. The difference between these equations can be characterized by a single parameter K, which can be computed directly from the cEoS characteristic parameters. The theoretical values for K are always higher than experimental activity coefficient data of alkane mixtures indicate. We show that mixtures of linear and branched alkanes require K=4.13 and K=3.04, respectively, while the lowest theoretical value, K=9, is given by the van der Waals equation. This mismatch in results is caused by the assumptions, which are made in the derivation of the van der Waals equation of state and which remain present in later developed cEoS. One of these is that all molecules are spherical, which leads to the inconsistency that the ratio of the covolume and the van der Waals volume is always 4, while this ratio for linear alkanes decreases rapidly to nearly 2 with increasing chain length. Another assumption is that all molecules experience the same number of external interactions, which neglects the fact that polyatomic molecules have less intermolecular interactions per spherical segment due to presence of covalent bonds and the occurrence of intramolecular interaction. Therefore, the van Laar type of activity coefficient equations are limited in their use as predictive model for dispersion. Perturbed hard-sphere chain equation of state will be discussed in part 2.

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