# Models and theories The CPA equation of

Models and theories
The CPA equation of state is composed predominantly of two parts: physical item and the association item based on the thermodynamic perturbation theory [21], [22], [26], [27]. The physical item is used to represent intermolecular physical interaction, usually representing the SRK cubic equation of state or PR cubic equation of state. The association item is used to highlight the association of molecular hydrogen bonds. As for non-association complexes, the CPA equation of state can be simplified into the SRK equation of state [28].

Model parameters
The CPA equation of state contains five pure compositional parameters [34], including three non-association complex parameters (α0, b, c1) and two association complex parameters (, ). Generally, the five pure compositional parameters can be determined through the fitting of experimental vapour pressures and saturated liquid density data. The three non-association complex parameters can be determined either through the fitting of experimental data, or through calculation of critical pressure, critical temperature and eccentric factor by using conventional techniques.
Of energy parameters in the CPA equation of state, α is a function relevant to temperature, whereas b is a function irrelevant to temperature.
In the application of CPA equation of state in multi-component mixtures, energy and volume parameters of the physical item can be calculated by using the conventional van der Waals one-fluid (vdW1f) mixing rules.
In which,
In which,where, Tr is the reference temperature; k and l are intermolecular interaction parameters of molecules i–j, respectively.

Results and discussions

Conclusions
In this study, the applicability and accuracy of the four equations of state in determining the thermodynamic properties of polar compound water were discussed. All these equations of state can produce satisfactory saturated vapor pressure results of water, but they have different performances in calculating the density and enthalpy of water.

Introduction
Alkanolamines (such as MDEA) are widely employed for Tylosin tartrate structure gas removal in gas treatment processes because of their ability to act as a weak base for reaction with the acidic gases [1].
Up to now, a notable number of experimental works have been accomplished to measure acid gas solubility in MDEA aqueous solutions and therefore many of VLE experimental data have been generated. These data can be utilized to design and simulate gas treatment units through a precise thermodynamic modeling process [2].
In recent years, a category of models, so-called φ–φ approach, have been highlighted because they are capable to describe both liquid and vapor phases through a specified EoS [2]. According to a useful theory known as the “Perturbation Theory”, deviation of a system with respect to the ideal state can be expressed using additional terms in the model. This capability makes us able to develop the suitable model for a specific system through add or removal of some terms. Based on the Perturbation Theory, recently, a class of EoSs, so-called association models, have attracted attention because of their ability to explicitly take hydrogen bonding into account [2]. Such models are especially suitable for highly-polar and strongly-association compounds such as alkanolamines, acids and water [3]. SAFT EoS variants are best-known families of such models in which Wertheim\'s contribution is responsible for the association part of the model. Because of the complexity in analyzing and implementing such models, so far, few works have been performed on these models. A review of the applications of these association models for acid gas sequestration using alkanolamines is explained in the following.
Najafloo et al. [4] applied eSAFT-HR EoS to correlate the CO2 solubility in MDEA aqueous solutions in various conditions. In this work, 413 VLE data from different authors were utilized to model H2O + MDEA + CO2 system so that the overall overage absolute deviation (AAD) achieved was equal to 11.2. In a similar work, Pahlavanzadeh and Fakouri-Baygi [5], predicted the absorption of CO2 by MDEA aqueous solutions using the Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) equation of state considering different association schemes for the components. The achieved results show good predictability of the model.