Logistic Kinetic Modeling and Interpretation of Mass Transfer in Supercritical CO₂ Extraction in Oregano, Chamomile and Moringa

The supercritical CO₂ extraction of essential oils from Origanum vulgare L., Matricaria chamomilla L., and Moringa oleifera Lam. was kinetically interpreted using a logistic mass transfer approach under different combinations of pressure and temperature. Extractions were performed in a fixed-bed SFE system operated for 210 min using high-purity CO₂ under pressures ranging from 100 to 500 bar and temperatures between 30 and 60 °C, depending on the vegetable matrix. The logistic model was parameterized through the total extractable mass (m_t), the characteristic time associated with the maximum extraction rate (t_m), and the kinetic slope parameter b. The highest extraction yields were obtained at 300 bar and 45 °C for oregano (2.807 g), 100 bar and 40 °C for chamomile (5.006 g), and 500 bar and 60 °C for moringa (5.433 g). Simultaneously, increasing pressure and temperature systematically reduced, decreasing from 16.737 to 8.75 min in oregano and from 15.01 to 9.73 min in moringa, indicating an intensification of convective-diffusional transport mechanisms. The model adequately reproduced the experimental extraction curves, particularly in Oregon, where SSD values remained below 0.03 under all evaluated conditions. Unlike highly parameterized phenomenological approaches, the proposed logistic formulation represented the extraction dynamics using kinetically interpretable parameters without requiring experimentally inaccessible internal coefficients. The results demonstrate that logistic modeling constitutes a mathematically simplified but kinetically robust alternative for the comparative analysis and preliminary optimization of supercritical extraction systems applied to aromatic and medicinal plant matrices.