Viscous fingering in supercritical fluid extraction: Polydispersity and mass transfer

The linear stability of miscible displacement in supercritical fluid extraction (SFE) from polydisperse packed beds—composed of two dominating fractions of distinct particle sizes a0a1—is investigated in the limit of large Pe number. The process involves the convective transport of solute coupled with heterogeneous interfacial mass transfer, described on the basis of shrinking core approach. The base state exhibits the moving extraction front with inherent discontinuities related to particle depletion. The governing stability equations for three-dimensional perturbations in a cylindrical geometry are derived in the quasi-steady-state approximation using a normal mode analysis. The model identifies controlling dimensionless parameters: the log mobility ratio R, the dimensionless time τ, the size ratio a0 of particle sizes of two fractions, the volume fraction α of the smallest (dust) particles, and an effective wave number. Results show that the system remains unconditionally stable in the limit of small viscosity variation when R≪1. However, the onset of instability is predicted with increasing extraction time and extent of the extractor volume affected by extraction. As predicted, packed beds with a high volume fraction of small particles, α0.7, are particularly prone to instability at SFE conditions even for moderate viscosity contrasts, R∼0.3. The study is relevant for the design and scale-up of SFE processes.