Methodologies of heat of absorption calculation

https://doi.org/10.1039/C9RA00164F

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It is difficult to experimentally determine each individual reaction’s contribution to the overall heat of CO₂ absorption. Thermodynamic analysis is proved to be a useful and powerful method to study the absorption process and absorption heat in CO₂ capture systems.^27–29 Two models that are commonly used in thermodynamics studies of CO₂ capture process: (1) the extended UNIQUAC model developed by Thomsen and Rasmussen³³ and (2) the e-NRTL model proposed by Chen et al.³⁴ Gudjonsdottir et al.³⁵ reported that, if the interaction parameters better fit the experimental data in the NH₃–CO₂–H₂O system, the e-NRTL model covers a wider range of conditions than the extended UNIQUAC model. Jilvero et al.³¹ also demonstrated that the e-NRTL model is more accurate for the prediction of CO₂ partial pressure at low temperatures (10–40 °C).

There are two commonly ways for calculating absorption heat. The van’t Hoff equation based on equilibrium constant (eqn (3))^27,28 and a thermodynamic relation based on VLE data (eqn (6)).^36,37 The van’t Hoff equation (eqn (3)) is derived directly from the general form of Gibbs–Helmholtz equation (G–H equation),³⁷ and the general form of G–H equation is:³⁸(1)

Further, the relationship between the equilibrium constant and Gibbs free energy is:ΔG = −RT ln K(2)

Eqn (2) can be substituted into eqn (1) and we can obtain the van’t Hoff equation:(3)

For the thermodynamic relation based on VLE data (eqn (6)), Sherwood and Prausnitz (1962) gave a detailed description in their paper. The general expression for calculating the absorption heat is:³⁹(4)where, ϕ is vapor phase fugacity coefficient, y is mole fraction in vapor phase, γ is liquid phase activity coefficient and x is mole fraction in liquid phase, subscripts 1 is lighter component.

Eqn (4) is perfectly general, as no simplifying physical assumptions have been made. However its application in this form requires extensive data in the single-phase vapor and liquid regions. Sherwood and Prausnitz point out that eqn (4) can be simplified to eqn (5) after some simplifying physical assumptions.³⁹(5)

For simplification at ambient pressures, CO₂ partial pressures are always used instead of CO₂ solubility in eqn (5) that the absorption heat can be obtained simply from VLE data.^36,37(6)

The comparison of difference between the absorption heat calculated by the above two methods and the experimental data reported by Liu et al.²⁰ is illustrated in Fig. 1. It clearly shows that the values for CO₂ absorption heat calculated by van’t Hoff equation based on equilibrium constant (eqn (3)) agree better with experimental data than that by thermodynamic relation based on VLE data (eqn (6)). The main reason is that van’t Hoff equation based on equilibrium constant (eqn (3)) is derived directly from the general form of G–H equation, as no assumptions have been made; however, the use of thermodynamic relation based on VLE data (eqn (6)) implies inherent assumptions,^37,39,40 which reduces the accuracy of eqn (6). Additionally, thermodynamic relation based on VLE data (eqn (6)) can only give us the overall absorption heat, but the current study mainly focuses on the endothermic/exothermic condition of each individual reaction. Therefore, in this paper, the van’t Hoff equation based on equilibrium constant is selected to calculate the heat of each reaction.

According to the above description, in this study e-NRTL model integrated in Aspen Plus is used to describe the liquid phase activity coefficients. The van’t Hoff equation based on equilibrium constant is selected to calculate the heat of each reaction. The flash module in Aspen Plus (V7.2) is chosen to calculate the chemical equilibrium and solution speciation. Then the heat of CO₂ absorption can be obtained from the solution speciation and chemical equilibrium constants.

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