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# In previous works Wang et al the PR

In previous works (Wang et al. [4,5]), the PR-CPA EoS has been applied to describe the solubilities of hydrocarbons (including methane, ethane, propane, n-butane, n-pentane, n-hexane, benzene, toluene, and ethyl-benzene) and mercaptans (including methyl mercaptan and ethyl mercaptan) in aqueous MDEA, DEA and MEA solutions in Vapor Liquid Equilibrium (VLE), Liquid Liquid Equilibrium (LLE), and Vapor Liquid Liquid Equilibrium (VLLE) conditions. Parameters of associating compounds were determined by regression from experimental data. With optimized parameters, hydrocarbons and mercaptans solubilities in aqueous alkanolamine solutions were successfully represented by the model; the ARDs (Average relative deviation) are under 10% for alkanes, 18% for aromatics and 20% for mercaptans.
In this work, we focus on the solubility of ITE gases in aqueous alkanolamines solutions. Unlike hydrocarbons, aromatics and mercaptans, the chemical reactions between CO2/H2S – alkanolamine - water and the formation of electrolyte species must be considered. The thermodynamic models used to resolve this problem can be grouped into three categories. The first and the simplest are the empirical models. Thanks to their simplicity, they are quite popular for early phase studies. These models utilize simple mathematical correlations for phase equilibria and fitted chemical equilibrium constants (Posey et al. [6]). The Kent–Eisenberg model [7] is an example of such a model. This kind of model is unsuitable for estimating the speciation and rigorous energy balances. For the other two categories of more rigorous models, two approaches can be considered: asymmetric approaches (excess Gibbs energy model for the liquid phase and EoS for the vapour phase) and symmetric approaches (equation of state-based models). For the asymmetric approach, the Desmukh–Mather model [8] has been widely used. This model utilizes the extended Debye–Hückel expression to estimate the activity coefficients of electrolyte species for long-range interactions. Dicko et al. [9] have applied this model for the modelling of equilibrium properties of CO2 –H2S-MDEA-water system. This model uses empirical terms to represent short-range interactions. The electrolyte-NRTL [10] and UNIQUAC [11] models, which are rather more complex activity based models, can also be used. For the symmetric approach, the Fürst and Renon [12] EoS is one of the most widely used approaches. In this work, a new symmetric approach for accounting for the chemical reaction is developed and it is combined with the PR-CPA EoS.

Thermodynamic model
Due to their simplicity, accuracy and computational efficiency, classical Cubic EoS are widely used in the petroleum and chemical industries. In the beginning of 1980s, Wertheim [13] has developed a theory for chain and associating molecules. This theory is implemented in the Statistical Associating Fluid Theory EoS [14], which is based on perturbation theory and includes the hard sphere model as reference.
In 1996, Kontogeorgis et al. [15] have proposed to combine Wertheim's theory with an adapted radial distribution function and SRK EoS. This model is called Cubic Plus Association EoS (CPA EoS), expressed by Equation (1):
The cubic term can be any cubic EoS e.g. SRK or PR. As these two EoS are both widely used cubic EoS, and as a continuity of the previous work [16], the PR-CPA EoS has been applied in this work, expressed by Equation (2):
The CPA model is presented in detail in Appendix A.
While the PR EoS accounts for the physical interaction contribution between the species, the association term takes into account the specific site-site interaction due to hydrogen bonding. Therefore, it is suitable for describing systems where water and alkanolamines molecules form hydrogen bonds (including self- and cross-interactions as well as solvation/induced association effects). Moreover, Dowell et al. [17] have successfully developed a simplified approach which allows treating chemical reactions with the Wertheim theory. In this approach, the chemical reactions between alkanolamine and CO2 have been treated as pseudo-cross association between them.