Mass Diffusivity in Water-Lean Solvents

In eq 14, the diffusivity D_A⁰ in a certain unloaded solvent (α = 0) can be obtained as a function of the molar volume of the solute at normal boiling point V_A (V_A = 34.0 cm³·mol^–1 for CO₂), the solvent’s molecular weight M and viscosity η, its association parameter χ, and the process temperature T. The association parameter is related to how clustered together the solvent molecules are in a real solution, meaning χ = 1.0 for ordinary nonassociated solvents and χ = 2.6 for a highly associated solvent such as water, which forms hydrogen bonds. Some organic liquids, such as methanol (χ = 1.9) and ethanol (χ = 1.5), have their association parameters reported in the original article by Wilke and Chang. (30) For other solvents, it is usually simpler and safer to assume that χ = 1.0.

The Wilke–Chang correlation can be used for preliminary evaluation of the CO₂ diffusivity in water-lean solvents containing novel organic diluents. More than that, it gives an idea of how the diffusivity should decrease with viscosity for a fixed solvent, i.e., by the power of 1. In other words, a consequence of the Wilke–Chang correlation is that eq 14 can be used to calculate the CO₂ diffusivity in a loaded solution (α > 0) D_A by considering how the viscosity of this solution increases with loading and fixing z = 1.

More recently, the decrease of CO₂ diffusivity with viscosity in liquid solvents has been reported to follow the power of z = 0.8 by Versteeg and van Swaaij (31) and z = 0.72 by Dugas and Rochelle. (32) Regarding specifically the case of water-lean solvents, the value of z = 0.524 was obtained by Yuan and Rochelle (9) for N-methyl-2-pyrrolidone (NMP) + MEA low-aqueous mixtures, who have proposed that CO₂ can diffuse between molecular clusters despite increasing solvent viscosities at higher loadings.

The takeaway is that there is great uncertainty regarding how CO₂ diffusivity depends on viscosity. From the pragmatic point of view, the values of z = 0.8 or 0.72 are more firmly established in the literature, and the latter will be used for evaluating how D_A varies with η (and consequently with α).

Meanwhile, we have adopted the approach suggested by Park et al. (33) and Hwang et al. (34) for calculating the amine diffusivity D_B⁰ in unloaded water-lean solvents. This approach consists of adapting the amine diffusivity from aqueous to water-lean based on how CO₂ diffusivity shifts between these two classes of solvents, as seen in eq 15. In eq 15, D_A^0* is the CO₂ diffusivity and D_B^0* is the amine diffusivity, both measured experimentally in an aqueous solvent, whereas D_A⁰ can be either obtained experimentally or evaluated by the Wilke–Chang correlation.