Thanachai Obchoei1,2 and Wiroj Limtrakarn1,2This email address is being protected from spambots. You need JavaScript enabled to view it.
1Department of Mechanical Engineering, Faculty of Engineering, Thammasat University, Pathum Thani, Thailand, 12120
2Thammasat University Center of Excellence in Computational Mechanics and Medical Engineering, Thammasat University, Pathum Thani, Thailand
Received: August 20, 2025 Accepted: November 16, 2025 Publication Date: December 27, 2025
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
Sovová’s Broken and Intact Cell (BIC) model predicts a linear curve in the fast extraction zone. However, the extraction behavior during the initial phase is commonly nonlinear, exhibiting a decreasing trend rather than the linear response predicted by the original model. This study proposes a mathematical model that uses a power law (PL) function of the form e = axb to describe the fast extraction phase. It is then coupled with a PDE/ODE system to model the slow extraction phase. The proposed model integrates key elements from both Sovová’s BIC model and the Reverchon model, replicating Sovová’s approach during the fast extraction phase while following Reverchon’s formulation for the slow extraction phase. The model was validated through supercritical CO2 extraction experiments of argan kernel oil under varying pressures (300-400 bar) and temperatures (40−60◦C ). The two non-constant power law parameters, a and b, were determined using response surface methodology (RSM) based on experimental data and were used to develop predictive equations correlating these parameters with pressure and temperature. This approach improves the predictive accuracy for both Type A and Type B extractions. The proposed model provides a more accurate representation of extraction kinetics and can be extended to other BIC types, thereby enhancing its applicability across a wide range of plant matrices in supercritical fluid extraction processes.
Keywords: BICmodel, Argan kernel oil, Supercritical CO2 fast extraction phase, Response surface methodology, PL-RSM model
[1] H.Park, J.-S. Kim, S. Kim, E.-S. Ha, M.-S. Kim, and S.-J. Hwang, (2021) “Pharmaceutical Applications of Supercritical Fluid Extraction of Emulsions for Micro /Nanoparticle Formation" Pharmaceutics 13: 1928. DOI: 10.3390/pharmaceutics13111928.
[2] A.I. Artemiev, K. M. Demkin, I. V. Kazeev, and N. V. Menshutina, (2024) “Search for New Active Substances for the Development of Pharmaceuticals Using Supercritical Fluid Extraction" Biochemistry (Moscow), Sup plement Series B: Biomedical Chemistry 18: 323–330. DOI: 10.1134/S1990750824600511.
[3] M. Oman, M. Škerget, and Z. Knez, (2013) “Appli cation of supercritical fluid extraction for separation of nutraceuticals and other phytochemicals from plant mate rial" Macedonian Journal of Chemistry and Chemical Engineering 32: 183. DOI: 10.20450/mjcce.2013.443.
[4] L. Li, M. Chen, Y. Zeng, and G. Liu, (2022) “Application and Perspectives of Supercritical Fluid Technology in the Nutraceutical Industry" Advanced Sustainable Systems 6: DOI: 10.1002/adsu.202200055.
[5] A. A. Khalil, M. M. Rahman, A. Rauf, M. R. Islam, S. J. Manna, A. A. Khan, S. Ullah, M. N. Akhtar, A. S. M. Aljohani, W. A. Abdulmonem, and J. Simal-Gandara, (2024) “Oleuropein: Chemistry, extraction techniques and nutraceutical perspectives-An update" Critical Reviews in Food Science and Nutrition 64: 9933–9954. DOI: 10.1080/10408398.2023.2218495.
[6] H. Sovová, (1994) “Rate of the vegetable oil extraction with supercritical CO2—I. Modelling of extraction curves" Chemical Engineering Science 49: 409–414. DOI: 10.1016/0009-2509(94)87012-8.
[7] H. Sovová, J. Kuˇcera, and J. Jež, (1994) “Rate of the vegetable oil extraction with supercritical CO2—II. Ex traction of grape oil" Chemical Engineering Science 49: 415–420. DOI: 10.1016/0009-2509(94)87013-6.
[8] A. Mouahid, M. Claeys-Bruno, and S. Clercq, (2024) “A New Methodology Based on Experimental Design and Sovová’s Broken and Intact Cells Model for the Prediction of Supercritical CO2 Extraction Kinetics" Processes 12: DOI: 10.3390/pr12091865.
[9] E. Reverchon, (1996) “Mathematical modeling of super critical extraction of sage oil" AIChE Journal 42: 1765–1771. DOI: 10.1002/aic.690420627.
[10] T. Obchoei and W. Limtrakarn, (2024) “Axisymmetric f low model of cannabis oil extraction of supercritical fluid extraction CO2 process" International Journal of Thermofluids 22: 100682. DOI: 10.1016/j.ijft.2024.100682.
[11] A. Mouahid, C. Rébufa, and Y. L. Dréau, (2024) “Supercritical CO2 extraction of Walnut (Juglans regia L.) oil: Extraction kinetics and solubility determination" The Journal of Supercritical Fluids 211: 106313. DOI: 10. 1016/j.supflu.2024.106313.
[12] M. H. Zuknik, N. N. Norulaini, W. W. N. Dalila, N. R. Ali, and A. M. Omar, (2016) “Solubility of vir gin coconut oil in supercritical carbon dioxide" Journal of Food Engineering 168: 240–244. DOI: 10.1016/j. jfoodeng.2015.08.004.
[13] J. M. del Valle, J. C. de la Fuente, and E. Uquiche, (2012) “A refined equation for predicting the solubility of vegetable oils in high-pressure CO2" The Journal of Supercritical Fluids 67: 60–70. DOI: 10.1016/j.supflu.2012.02.004.
[14] K. Tomita, S. Machmudah, A. T. Quitain, M. Sasaki, R. Fukuzato, and M. Goto, (2013) “Extraction and solubility evaluation of functional seed oil in supercritical carbon dioxide" The Journal of Supercritical Fluids 79: 109–113. DOI: 10.1016/j.supflu.2013.02.011.
[15] E.Reverchon, G. Donsi, and L. S. Osseo, (1993) “Modeling of supercritical fluid extraction from herbaceous matrices" Industrial & Engineering Chemistry Re search 32: 2721–2726. DOI: 10.1021/ie00023a039.
[16] R.Hartono,G.Mansoori,andA.Suwono,(2001)“Pre diction of solubility of biomolecules in supercritical sol vents" Chemical Engineering Science 56: 6949–6958. DOI: 10.1016/S0009-2509(01)00327-X.
[17] Z. Vatani, S. R. Bajgiran, G. Amini, and S. Tayyebi, (2020) “Solubility modeling of supercritical fluid ex traction in a wide range compounds: comparison be tween fuzzy-genetic and new empirical models" Energy Sources, Part A: Recovery, Utilization, and Environ mental Effects 42: 365–374. DOI: 10.1080/15567036. 2019.1587083.
[18] G. Sodeifian and M. M. B. Usefi, (2023) “Solubility, Extraction, and Nanoparticles Production in Supercritical Carbon Dioxide: A Mini-Review" Chem Bio Eng Re views 10: 133–166. DOI: 10.1002/cben.202200020.
[19] E. Torres-Ramón, C. García-Rodríguez, K. Estévez Sánchez, I. Ruiz-López, G. Rodríguez-Jimenes, G. R. de la Vega, and M. García-Alvarado, (2021) “Opti mization of a coconut oil extraction process with supercrit ical CO2 considering economical and thermal variables" The Journal of Supercritical Fluids 170: 105160. DOI: 10.1016/j.supflu.2020.105160.
[20] A. Promraksa, C. Siripatana, N. Rakmak, and N. Chusri, (2020) “Modeling of Supercritical CO2 Extraction of Palm Oil and Tocopherols Based on Volumetric Axial Dispersion" The Journal of Supercritical Fluids 166: 105021. DOI: 10.1016/j.supflu.2020.105021.
[21] I. Zaidul, N. N. Norulaini, A. M. Omar, and R. Smith, (2007) “Supercritical carbon dioxide (SC-CO2) extraction of palm kernel oil from palm kernel" Journal of Food Engineering 79: 1007–1014. DOI: 10.1016/j.jfoodeng. 2006.03.021.
[22] T. Obchoei and W. Limtrakarn, (2023) “Numerical model of supercritical fluid extraction CO 2 technique for cannabis extraction" Eur. Chem. Bull 12: 7354–7364. DOI: https: //doi.org/10.31838/ecb/2023.12.si6.654.
[23] A. Mouahid, I. Bombarda, M. Claeys-Bruno, S. Amat, E. Myotte, J.-P. Nisteron, C. Crampon, and E. Badens, (2021) “Supercritical CO2 extraction of Moroccan argan (Argania spinosa L.) oil: Extraction kinetics and solubility determination" Journal of CO2 Utilization 46: 101458. DOI: 10.1016/j.jcou.2021.101458.
[24] G. Sodeifian, M. Markom, J. M. Ali, M. Z. M. Salleh, and R. Derakhsheshpour, (2025) “Solubility of gemcitabine (an anticancer drug) in supercritical carbondiox ide green solvent: Experimental measurement and thermodynamic modeling" Scientific Reports 15: 4451. DOI: 10.1038/s41598-025-88817-4.
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