Mathematical modeling of supercritical extraction of sage oil

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Abstract
Modeling of supercritical CO2 extraction of essential oils from leaves was studied using sage at 90 bar (9 MPa) and 50°C. The fractional separation of the extracts enabled essential oil to be obtained. Four mean sage particle sizes ranging from 0.25 to 3.10 mm were tested. The model proposed was based on differential mass balances performed along the extraction bed. Experimental data suggest that the internal mass transfer was the controlling stage for the extraction process. Different hypotheses were tested on vegetable matter geometry, and their incidence on the model performance was evaluated. The particle shape proved to be a key factor in fitting experimental results, which were fairly good when the conventional spherical geometry was replaced by a realistic slab geometry. Diffusivity of the solute in the solid matrix was used as the only adjustable parameter of the model; its best fit value was 6.0 × 10−13 m2/s. The effect of the introduction of particle‐size distribution into calculations was also tested. To verify if the external mass‐transfer mechanisms influence the extraction process, experiments at two different CO2 flow rates were also performed. Simplified models were also considered, and the extent of approximations was evaluated.