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

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

1 Citaat (Scopus)

Uittreksel

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.

TaalEngels
Artikelnummer112275
Aantal pagina's13
TijdschriftFluid Phase Equilibria
Volume501
DOI's
StatusGepubliceerd - 1 dec 2019

Vingerafdruk

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

Trefwoorden

    Citeer dit

    @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",
    year = "2019",
    month = "12",
    day = "1",
    doi = "10.1016/j.fluid.2019.112275",
    language = "English",
    volume = "501",
    journal = "Fluid Phase Equilibria",
    issn = "0378-3812",
    publisher = "Elsevier",

    }

    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.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    TY - JOUR

    T1 - Dispersion activity coefficient models. Part 1

    T2 - Fluid Phase Equilibria

    AU - Krooshof,Gerard J.P.

    AU - Tuinier,Remco

    AU - de With,Gijsbertus

    PY - 2019/12/1

    Y1 - 2019/12/1

    N2 - 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.

    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.

    KW - Activity model

    KW - Cubic equation of state

    KW - Dispersion

    KW - Van Laar

    UR - http://www.scopus.com/inward/record.url?scp=85070880802&partnerID=8YFLogxK

    U2 - 10.1016/j.fluid.2019.112275

    DO - 10.1016/j.fluid.2019.112275

    M3 - Article

    VL - 501

    JO - Fluid Phase Equilibria

    JF - Fluid Phase Equilibria

    SN - 0378-3812

    M1 - 112275

    ER -