SFEModeling.jl
Kinetic model fitting for supercritical fluid extraction.
Overview
SFEModeling.jl fits kinetic models for supercritical fluid extraction (SFE) to one or more experimental extraction curves. The package:
- Accepts experimental data and operating conditions in laboratory units (g, cm, min).
- Supports 6 kinetic models, from rigorous PDE/physical models to simple empirical correlations.
- Fits model parameters using global optimization from BlackBoxOptim.jl — no manual multi-start needed.
- Provides a graphical interface accessible via desktop shortcut or
sfegui().
Supported models
| Model | Parameters | Description |
|---|---|---|
| Sovová (1994) | kya, kxa, xk/x0 | PDE — broken & intact cells; multi-curve with shared xk/x0 |
| Shrinking Core — Moreno-Pulido et al. (2026) | Tm, tau_g | Physical — diffusion-limited leaching |
| Esquível (1999) | k1 | Empirical — single exponential |
| Zekovic (2003) | k1, k2 | Empirical — accessible fraction × exponential |
| PKM — Maksimovic (2012) | k1, k2, k3 | Parallel-reaction kinetics |
| Spline — Rodrigues (2003) | k1–k4 | Piecewise-linear CER/FER/DC |
See the Models page for the equations.
References
Martínez, J.; Martínez, J.M. (2008). Fitting the Sovová's supercritical fluid extraction model by means of a global optimization tool. Computers & Chemical Engineering, 32(8), 1735–1745. https://doi.org/10.1016/j.compchemeng.2007.08.016
Martínez, J.; Monteiro, A.R.; Rosa, P.T.V.; Marques, M.O.M.; Meireles, M.A.A. (2003). Multicomponent model to describe extraction of ginger oleoresin with supercritical carbon dioxide. Industrial & Engineering Chemistry Research, 42(5), 1057–1063. https://doi.org/10.1021/ie020694f
References for models
Sovová, H. (1994). Rate of the vegetable oil extraction with supercritical CO₂ — I. Modelling of extraction curves. Chemical Engineering Science, 49(3), 409–414. https://doi.org/10.1016/0009-2509(94)87012-8
Moreno-Pulido, C.; Olwande, R.; Myers, T.; Font, F. (2026). Approximate solutions to the shrinking core model and their interpretation. Applied Mathematical Modelling, 154, 116715. https://doi.org/10.1016/j.apm.2025.116715
Esquível, M.M.; Bernardo-Gil, M.G.; King, M.B. (1999). Mathematical models for supercritical extraction of olive husk oil. Journal of Supercritical Fluids, 16(1), 43–58. https://doi.org/10.1016/S0896-8446(99)00014-5
Zeković, Z.P.; Lepojević, Ž.D.; Milošević, S.G.; Tolić, A.Š. (2003). Modeling of the thyme: liquid carbon dioxide extraction system. Acta Periodica Technologica, 34, 125–133. https://doi.org/10.2298/APT0334125Z
Maksimović, S.; Ivanović, J.; Skala, D. (2012). Supercritical extraction of essential oil from Mentha and mathematical modelling. Procedia Engineering, 42, 1767–1777. https://doi.org/10.1016/j.proeng.2012.07.571
Rodrigues, V.M.; Rosa, P.T.V.; Marques, M.O.M.; Petenate, A.J.; Meireles, M.A.A. (2003). Supercritical extraction of essential oil from aniseed using CO₂: Solubility, kinetics, and composition data. Journal of Agricultural and Food Chemistry, 51(6), 1518–1523. https://doi.org/10.1021/jf0257493