Optimization of supercritical fluid extraction: Polydisperse packed beds and variable flow rates

• Shrinking core model is employed to simulate SFE kinetics.
• Different ways of particle ensemble packing and variable flow rates are considered as optimization parameters.
• Locally monodisperse stratified (LMS) packed bed is shown to be the optimal packing.
• Optimal domains of overall particle-size distribution functions are defined.
• Necessary conditions of complete extraction are deduced.

This theoretical study examines variable-in-time flow rates v(t) and different ways of packing polydisperse ensemble of ground particles as controls in supercritical fluid extraction (SFE) to maximize the extraction yield. The so-called packing function χ is introduced to describe the local particle-size distribution in the pack along the extraction vessel. The research is based on the modified shrinking-core (SC) model for the mass transfer inside particles and assumes the pseudo-steady solvent flow in the SFE vessel. It is rigorously proven that for any variable flow rate v(t) and overall particle-size distribution F, the corresponding locally-monodisperse stratified (LMS) packing χ0 maximizes the current amount of extracted solute, while the appropriate filtration policy extends the domain of efficient particle-size distributions. Sufficient conditions that guarantee a certain extraction degree at a fixed time are deduced and formulated in terms of F-distribution. Being of obvious practical significance for finely ground substrates, optimization is shown to be rather limited for relatively big particles (commonly used in laboratory experiments), and only longer extraction times, higher oil solubility and diffusion rates allow noticeable increase in the extraction yield in this case.

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