Modeling of the Interfacial Behavior of Carbon Dioxide + Methyl Myristate, Carbon Dioxide + Palmitate, and Carbon Dioxide + Methyl Myristate + Methyl Palmitate Mixtures Using CPA-EOS and Gradient Theory

Abstract

This work presents the vapor–liquid equilibrium and the interfacial behavior modeling of binary and ternary CO\(_2\) + ester mixtures, with the cubic plus association equation of state (CPA-EOS) combined with the density gradient theory. The binary mixtures, CO\(_2\) + methyl myristate and CO\(_2\) + methyl palmitate, were studied at temperatures from 313.15 K to 333.15 K, considering the ester molecules as non-associating and the carbon dioxide as non-associating or self-associating (2B scheme) molecule. Phase behavior was predicted with binary interaction parameters adjusted from binary mixture phase equilibrium experimental data. Results show than there are some points better represented by the associating scheme, but the overall trend shows that the CPA-EOS with the non-associating scheme for all the molecules is the best option for describing the phase equilibrium and calculating the interfacial tension for the CO\(_2\) + ester binary mixtures. For this reason, the CO\(_2\) + methyl myristate + methyl palmitate mixture at 313.15 K was modeled only with non-associating fluids. The AAD% for the calculated interfacial tensions, considering non-associating molecules in the mixture is 9.7 % for the CO\(_2\) + methyl myristate mixture, 15.1 % for the CO\(_2\) + methyl palmitate mixture, and 7.9 % for the CO\(_2\) + methyl myristate + methyl palmitate mixture.

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Abbreviations

\(\kappa\) :

Influence parameter

A :

Adjustable parameter of the influence parameter

a :

Attractive parameter in CPA-EOS

\(a_0\) :

Adjustable parameter of the CPA-EOS

AAD :

Statistical deviation

B :

Adjustable parameter of the influence parameter

b :

Covolume parameter in the CPA-EOS

\(c_1\) :

Adjustable parameter of the CPA-EOS

\(f_0\) :

Helmholtz energy density

g :

The radial distribution function

\(k_{ij}\) :

Interaction parameter in the CPA-EOS

n :

Number of points

\(n_c\) :

Number of components

P :

Absolute pressure

R :

Universal gas constant

T :

Absolute temperature

x :

Liquid mole fraction

\(X_{A_i}\) :

The mole fraction of the molecule i not bonded at site A

y :

Vapor mole fraction

z :

Position in the interface

\(\beta ^{A_i B_i}\) :

Association volume

\(\beta ^{A_i B_j}\) :

Cross-association volume

\(\Delta ^{A_i B_j}\) :

The association strength

\(\epsilon ^{A_i B_i}\) :

Association energy

\(\epsilon ^{A_i B_j}\) :

Cross-association energy

\(\eta\) :

Reduced density

\(\gamma\) :

Interfacial tension

\(\kappa _{ij}\) :

Cross-influence parameter

\(\mu\) :

Chemical potential

\(\Omega\) :

Grand thermodynamic potential

\(\rho\) :

Mole density

c :

Critical condition

ijs :

Species

0:

Equilibrium condition

exp :

Experimental

L :

Liquid phase

theo :

Theoretical

V :

Vapor phase

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Acknowledgements

A.H acknowledges the economic support given by the UCSC.

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Hernández, A., Zabala, D. Modeling of the Interfacial Behavior of Carbon Dioxide + Methyl Myristate, Carbon Dioxide + Palmitate, and Carbon Dioxide + Methyl Myristate + Methyl Palmitate Mixtures Using CPA-EOS and Gradient Theory. Int J Thermophys 42, 31 (2021). https://doi.org/10.1007/s10765-020-02788-4

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Keywords

  • CPA-EOS
  • Gradient theory
  • Interfacial behavior
  • Vapor-liquid equilibrium