Mass Diffusivity in Water-Lean Solvents

“Both CO2 diffusivity and amine diffusivity are known to decrease with an increase in viscosity. In the case of CO2, a simple way of representing this is by the famous Wilke–Chang correlation, (30) which is expressed by the following equation:

In eq 14, the diffusivity DA0 in a certain unloaded solvent (α = 0) can be obtained as a function of the molar volume of the solute at normal boiling point VA (VA = 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) DA 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 DA 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 DB0 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 15DA0* is the CO2 diffusivity and DB0* is the amine diffusivity, both measured experimentally in an aqueous solvent, whereas DA0 can be either obtained experimentally or evaluated by the Wilke–Chang correlation.


The amine diffusivity also decreases with viscosity, and less controversially so, as both Versteeg and van Swaaij (31) and Snijder et al. (35) have verified in practice that such a decrease follows the power of z = 0.6, as expressed in eq 16.


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