https://doi.org/10.3389/fenrg.2021.785039
“Physical dissolution and chemical absorption happen in the process of CO2 captured by amine solution, so physical equilibrium and chemical equilibrium need to be considered. There are a variety of intermolecular interactions in the loaded solution, including the interactions between molecules, between molecules and ions, and between ions, making the solution deviate from the ideal state. It is necessary to introduce an activity coefficient model for correction. The relative theories of physical equilibrium, chemical equilibrium, and activity coefficient that need to be considered in establishing a thermodynamic model are introduced in this section.
Physical Equilibrium
In a vapor–liquid equilibrium system, the activity of the components during the liquid phase is the same as the fugacity during the gas phase. For the components of amines and water, which use pure substances as the reference state, the formula of equilibrium can be expressed as
For the component CO2 using the infinite dilution state as the reference state, which is amine and CO2, the equilibrium formula is as follows:
where yiyi represents the mole fraction of component ii at the gas phase, ∅i∅i represents the fugacity coefficient of component ii at the gas stage, PP represents the total pressure at the system temperature, PsiPis represents the vapor pressure of component ii at the system temperature, xixi represents the mole fraction of component ii at the liquid stage, γ∗iγi∗ represents the asymmetric activity coefficient of ii in water, and HiHi represents Henry’s constant of ii in water at the system temperature and vapor pressure of water.
The dependence of the Henry constant on temperature can be expressed as
The Redlich–Kwong (RK) equation of the state model was used to describe the gas phase. The Henry constant of CO2 in water was taken from the study by Chen et al. (1979).
Chemical Absorption
Chemical absorption reaction equations in the loaded HEPZ solution are as follows:
All the reaction equilibrium constants of the reactions mentioned above can be obtained from the standard-state Gibbs free energies of the equations’ chemicals. The calculation equation is as follows:
where KjKj represents the chemical equilibrium constant of reaction jj, RR represents the universal gas constant, TT represents the temperature, and ΔG0jΔGj0 represents the reference state Gibbs energy change of reaction jj. Knowing the standard Gibbs free energy, the standard enthalpy of each component’s formation, and the heat capacity in the reference state in the reaction equilibrium equation, the equilibrium constant of each reaction can be calculated. For reactions four to six, the equilibrium constants from the previous studies were usually consistent with the concentrations based on the molality. However, in this study, the model is on the basis of the mole fraction. Therefore, the equilibrium constants were converted by the method mentioned in the study by Li et al. (2014a).
Protonation reactions 7 and 8 produced new ions HEPZH+HEPZH+ and HEPZH2+2HEPZH22+ in solution, which are absent in the ion database of Aspen. Therefore, the standard-state thermodynamic properties of HEPZH+HEPZH+ and HEPZH2+2HEPZH22+ are lacked in Aspen and need to be manually adjusted to fit the pKapKa values from the study by Hamborg and Versteeg (2009). For HEPZCOO−HEPZCOO− and HEPZCOOHHEPZCOOH, the standard-state thermodynamic properties are regressed from CO2CO2 solubility data obtained in this study. Using the thermodynamic properties of the products and the reactants, the equilibrium constants of all reactions can be obtained.
Activity Coefficient
Referring to 3.2, a series of reactions will take place in the loaded HEPZ solution, and multiple ions were produced in the process. The interaction between ions causes the liquid system to gradually deviate from the ideal state. It needs to introduce a coefficient model with accurate activity for calculations and simulation. In this study, the activity coefficients for binary interactions in the unloaded amine solution were calculated by the NRTL model, but those for the molecule–molecule binary, molecule–ion pair binary, and ion pair–ion pair binary in the loaded amine solution were calculated by the ENRTL model. The dependence of binary parameters on the temperature can be expressed as
where ijij can be molecule–molecule, molecule–ion pair, ion–molecule pair, or ion pair–ion pair. Meanwhile, the binary parameter aijaij is 0.3 for the molecule–molecule interaction, 0.2 for the molecular–ion pair interaction, and 0 for the ion pair–ion pair interaction, and the default values for both ion pair–ion pair and molecule–molecule binary parameters are 0. The default value of the molecule–ion pair binary parameters aijaij is (8, −4) when the molecule is H2O; otherwise, the default values are set at 8 and −15. The default values for bijbij are 0.”