Analysis of Thermodynamic Consistency Behavior of CO2 Solubility in Some Associating Solvents

  • Milad Mashayekhi
  • Hossein SakhaeiniaEmail author
  • Mohammad Shokouhi


The thermodynamic consistency analysis of ten mixtures of CO2/associating solvents with total of 160 isothermal data sets was investigated. For this purpose, the area test based on the generalized Gibbs–Duhem equations was applied and the Peng and Robinson/Stryjek and Vera equation of state with Panagiotopoulos–Reid combining rule (PRSV/PR EoS) was employed to correlate the isothermal PTx data. The binary adjustable constants in PRSV/PR EoS were figured out by optimization of errors on pressure and defined area simultaneously as an objective function in bubble pressure algorithm. The results turn out that among 160 isotherms meaningfully investigated, 29 data sets were found to be thermodynamically consistent, 72 data sets were found to be not fully consistent, 55 data sets were found to be thermodynamically inconsistent, and 4 data sets were found to be tried with other models.


Carbon dioxide Equation of state Gibbs–Duhem equation Thermodynamic consistency Thermodynamics modeling 

List of symbols



Characteristic pure compound parameter in PRSV EoS


Universal gas constant

kij and kji

First and second binary interaction parameters


Third adjustable parameter


Molar volume


Residual molar volume


Residual molar enthalpy


Residual molar Gibbs energy


Reduced temperature


The critical temperature


The critical pressure


Interaction parameter in PRSV EoS

\(\alpha \left( T \right)\)

Temperature-dependent parameter in cubic equation of state


Co-volume constant in cubic equation of state


Compressibility factors

x1 and x2

Liquid phase mole fraction of components 1 and 2

φ1 and φ2

Fugacity coefficients of components 1 and 2


Molecular weight


Acentric factor


Number of data point


Integral for point x2i to x2i+1 using Px experimental data


Integral for point x2i to x2i+1 using thermodynamic model


Individual deviation in the system pressure for each point


Average deviation in the system pressure


Maximum deviation in the system pressure

% ∆Ai

Individual relative percent area deviation



Peng–Robinson–Stryjek–Vera equation of state


Thermodynamically consistent


Thermodynamically inconsistent


Not fully consistent


1,2-Propylene glycol


Ethylene glycol


Diethylene glycol


Triethylene glycol


Objective function


Weighting factor in objective function



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Authors and Affiliations

  1. 1.Department of Chemical Engineering, Central Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.Gas Science Department, Gas Research Division, Research Institute of Petroleum Industry (RIPI)National Iranian Oil Company (NIOC)TehranIran

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