Skip to main content
Log in

Evaluation of Supercritical Fluid Extraction Model Parameters by Monte-Carlo Methods

  • Published:
Theoretical Foundations of Chemical Engineering Aims and scope Submit manuscript

Abstract

The problem of evaluation of model parameters for supercritical fluid extraction of oil from ground plant materials with high initial oil contents was studied. The information content of laboratory experimental data was analyzed by the Markov chain Monte Carlo method. The accuracy of evaluation of the main effective parameters of the model was determined for the apparent diffusion coefficient, saturation concentration of oil in the solvent, and the total content of target compounds in the raw material. Various parameterizations of the inverse problem were considered. Given the initial oil content, the diffusion coefficient can be evaluated from the individual overall extraction curve corresponding to coarse grinding. At the same time, simultaneous evaluation of all the three parameters is possible only with combined analysis of at least two curves corresponding to fine and coarse grinding. The experiment with fine grinding allows identification of only the total content of the target compounds and the saturation concentration, but cannot be used to evaluate the apparent diffusion coefficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. Gumerov, F.M., Sverkhkriticheskie flyuidnye tekhnologii. Ekonomicheskaya tselesoobraznost’ (Supercritical Fluid Technologies: Economic Feasibility), Kazan: Akad. Nauk Resp. Tatar., 2019.

  2. Gumerov, F.M., Khairutdinov, V.F., and Zaripov, Z.I., An additional condition of efficiency of the supercritical fluid extraction process, Theor. Found. Chem. Eng., 2021, vol. 55, pp. 348–358. https://doi.org/10.1134/S0040579521030076

    Article  CAS  Google Scholar 

  3. Kas’yanov, G.I., Tekhnologicheskie osnovy CO 2 -obrabotki rastitel’nogo syr’ya (Technological Fundamentals of CO2 Processing of Vegetable Raw Materials), Moscow: Rossel’khozakademiya, 1994.

  4. Meyer, F., Stamenic, M., Zizovic, I., and Eggers, R., Fixed bed property changes during scCO2 extraction of natural materials – Experiments and modeling, J. Supercrit. Fluids, 2012, vol. 72, pp. 140–149. https://doi.org/10.1016/j.supflu.2012.08.022

    Article  CAS  Google Scholar 

  5. Fiori, L., Grape seed oil supercritical extraction kinetic and solubility data: Critical approach and modeling, J. Supercrit. Fluids, 2007, vol. 43, p. 43.

    Article  CAS  Google Scholar 

  6. Fiori, L., Supercritical extraction of sunflower seed oil: Experimental data and model validation, J. Supercrit. Fluids, 2009, vol. 50, p. 218.

    Article  CAS  Google Scholar 

  7. Özkal, S.G., Yener, M.E., and Bayındırlı, L., Mass transfer modeling of apricot kernel oil extraction with supercritical carbon dioxide, J. Supercrit. Fluids, 2005, vol. 35, p. 119.

    Article  Google Scholar 

  8. Özkal, S.G., Salgin, U., and Yener, M.E., Supercritical carbon dioxide extraction of hazelnut oil, J. Food Eng., 2005, vol. 69, p. 217.

    Article  Google Scholar 

  9. Salgin, U. and Korkmaz, H., A green separation process for recovery of healthy oil from pumpkin seed, J. Supercrit. Fluids, 2011, vol. 58, p. 239.

    Article  CAS  Google Scholar 

  10. Salgin, U. and Salgin, S., Effect of main process parameters on extraction of pine kernel lipid using supercritical green solvents: Solubility models and lipid profiles, J. Supercrit. Fluids, 2013, vol. 73, p. 18.

    Article  CAS  Google Scholar 

  11. Salgin, S. and Salgin, U., Supercritical fluid extraction of walnut kernel oil, Eur. J. Lipid Sci. Technol., 2006, vol. 108, p. 577.

    Article  CAS  Google Scholar 

  12. Romero-Guzmán, M.J., Vardaka, E., Boom, R.M., and Nikiforidis, C.V., Influence of soaking time on the mechanical properties of rapeseed and their effect on oleosome extraction, Food Bioprod. Process., 2020, vol. 121, p. 230.

    Article  Google Scholar 

  13. Egorov, A.G., Mazo, A.B., and Maksudov, R.N., Extraction from a polydisperse granular layer of milled oilseeds with supercritical carbon dioxide, Theor. Found. Chem. Eng., 2010, vol. 44, pp. 642–650. https://doi.org/10.1134/S0040579510050027

    Article  CAS  Google Scholar 

  14. Maksudov, R.N., Egorov, A.G., Mazo, A.B., Aljaev, V.A., and Abdullin, I.S., Mathematical model of oil-bearing crop seeds extraction by supercritical carbon dioxide, Sverkhkrit. Flyuidy: Teor. Prakt., 2008, vol. 3, p. 20.

    Google Scholar 

  15. Kas’yanov, G.I., Results of scientific research on carbon dioxide processing of vegetable and animal raw materials, Izv. Vyssh. Uchebn. Zaved., Pishch. Tekhnol., 2007, vol. 298, p. 79.

    Google Scholar 

  16. Rai, A., Mohanty, B., and Bhargava, R., Fitting of broken and intact cell model to supercritical fluid extraction (SFE) of sunflower oil, Innovative Food Sci. Emerging Technol., 2016, vol. 38, p. 32.

    Article  CAS  Google Scholar 

  17. Sovová, H., Broken-and-intact cell model for supercritical fluid extraction: Its origin and limits, J. Supercrit. Fluids, 2017, vol. 129, p. 3.

    Article  Google Scholar 

  18. Salamatin, A.A., Supercritical fluid extraction of the seed fatty oil: Sensitivity to the solute axial dispersion, Ind. Eng. Chem. Res., 2020, vol. 59, p. 18126.

    Article  CAS  Google Scholar 

  19. Koltsov, N.I., Quasi-invariants of chemical reactions in the ideal displacement reactor, Theor. Found. Chem. Eng., 2020, vol. 54, pp. 913–918. https://doi.org/10.1134/S004057952004020X

    Article  CAS  Google Scholar 

  20. Fiori, L., Basso, D., and Costa, P., Seed oil supercritical extraction: Particle size distribution of the milled seeds and modeling, J. Supercrit. Fluids, 2008, vol. 47, p. 174.

    Article  CAS  Google Scholar 

  21. Egorov, A.G. and Salamatin, A.A., Bidisperse shrinking core model for supercritical fluid extraction, Chem. Eng. Technol., 2015, vol. 38, p. 1203.

    Article  CAS  Google Scholar 

  22. Goto, M., Roy, B.C., and Hirose, T., Shrinking-core leaching model for supercritical-fluid extraction, J. Supercrit. Fluids, 1996, vol. 9, p. 128.

    Article  CAS  Google Scholar 

  23. Egorov, A.G., Salamatin, A.A., and Maksudov, R.N., Forward and inverse problems of supercritical extraction of oil from polydisperse packed bed of ground plant material, Theor. Found. Chem. Eng., 2014, vol. 48, pp. 39–47. https://doi.org/10.1134/S0040579514010011

    Article  CAS  Google Scholar 

  24. Salamatin, A.A., Theoretical study of the regimes of supercritical fluid extraction in a polydisperse bed of vegetable raw materials, Cand. Sci. (Phys.-Math.) Dissertation, Kazan: Kazan. Fed. Univ., 2017.

  25. Akhmadiev, F.G. and Gizzyatov, R.F., Stochastic simulation of the process of size separation of granular materials on sieve classifiers, Theor. Found. Chem. Eng., 2020, vol. 54, pp. 828–837. https://doi.org/10.1134/S0040579520050279

    Article  CAS  Google Scholar 

  26. Khaliullina, A.S., Khaziev, R.Sh., and Salamatin, A.A., Quantitative determination of diterpene acids in garden sage leaves, J. Anal. Chem., 2017, vol. 72, p. 810.

    Article  CAS  Google Scholar 

  27. Salamatin, A.A., Egorov, A.G., Maksudov, R.N., and Alyaev, V.A., Interpretation of yield curves for the components being recovered in supercritical fluid extraction, Vestn. Kazan. Tekhnol. Univ., 2013, vol. 16, p. 74.

    CAS  Google Scholar 

  28. Kol’tsov, N.I., A method for solving the inverse problem of chemical kinetics for a nonisothermal gradientless reactor based on steady-state data, Theor. Found. Chem. Eng., 2020, vol. 54, pp. 863–871. https://doi.org/10.1134/S004057952005036X

    Article  Google Scholar 

  29. Orazbayev, B.B., Shangitova, Zh.Ye., Orazbayeva, K.N., Serimbetov, B.A., and Shagayeva, A.B., Studying the dependence of the performance efficiency of a Claus reactor on technological factors with the quality evaluation of sulfur on the basis of fuzzy information, Theor. Found. Chem. Eng., 2020, vol. 54, pp. 1235–1241. https://doi.org/10.1134/S0040579520060093

    Article  CAS  Google Scholar 

  30. Vrugt, J.A. and Ter Braak, C.J.F., DREAM(D): An adaptive Markov chain Monte Carlo simulation algorithm to solve discrete, noncontinuous, and combinatorial posterior parameter estimation problems, Hydrol. Earth Syst. Sci., 2011, vol. 15, pp. 3701–3713. https://doi.org/10.5194/hess-15-3701-2011

    Article  Google Scholar 

  31. Vrugt, J.A., Ter Braak, C.J.F., Diks, C.G.H., Robinson, B.A., Hyman, J.M., and Higdon, D., Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling, Int. J. Nonlinear Sci. Numer. Simul., 2009, vol. 10, p. 273.

    Article  Google Scholar 

  32. Ter Braak, C.J.F., A Markov chain Monte Carlo version of the genetic algorithm differential evolution: Easy Bayesian computing for real parameter spaces, Stat. Comput., 2006, vol. 16, pp. 239–249. https://doi.org/10.1007/s11222-006-8769-1

    Article  Google Scholar 

  33. Mosegaard, K., Resolution analysis of general inverse problems through inverse Monte Carlo sampling, Inverse Probl., 1998, vol. 14, p. 405.

    Article  Google Scholar 

  34. Cordua, K.S., Hansen, T.M., and Mosegaard, K., Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information, Geophysics, 2012, vol. 77, p. H19.

    Article  Google Scholar 

  35. Ganin, P.G., Markova, A.V., Moshinskii, A.I., Rubtsova, L.N., and Sorokin, V.V., Calculating the extraction of a substance from a porous system with a variable diffusion coefficient, Theor. Found. Chem. Eng., 2020, vol. 54, p. 838.

    Article  CAS  Google Scholar 

  36. Kheifets, L.I. and Neimark, A.V., Mnogofaznye protsessy v poristykh sredakh (Multiphase Processes in Porous Media), Moscow: Khimiya, 1982.

  37. Salamatin, A.A., Numerical scheme for non-linear model of supercritical fluid extraction from polydisperse ground plant material: Single transport system, IOP Conf. Ser.: Mater. Sci. Eng., 2016, vol. 158, article no. 012081.

  38. Salamatin, A.A., Detection of microscale mass-transport regimes in supercritical fluid extraction, Chem. Eng. Technol., 2017, vol. 40, p. 829.

    Article  CAS  Google Scholar 

  39. Sovová, H., Kučera, J., and Jež, J., Rate of the vegetable oil extraction with supercritical CO2—II. Extraction of grape oil, Chem. Eng. Sci., 1994, vol. 49, p. 415.

    Article  Google Scholar 

  40. Sovová, H., Rate of the vegetable oil extraction with supercritical CO2—I. Modelling of extraction curves, Chem. Eng. Sci., 1994, vol. 49, p. 409.

    Article  Google Scholar 

  41. Salamatin, A.A. and Egorov, A.G., Optimization of supercritical fluid extraction: Polydisperse packed beds and variable flow rates, J. Supercrit. Fluids, 2015, vol. 105, p. 35.

    Article  CAS  Google Scholar 

  42. del Valle, J.M., Extraction of natural compounds using supercritical CO2: Going from the laboratory to the industrial application, J. Supercrit. Fluids, 2015, vol. 96, p. 180.

    Article  CAS  Google Scholar 

  43. Eikani, M.H., Khandan, N., Feyzi, E., and Ebrahimi, I.M., A shrinking core model for Nannochloropsis salina oil extraction using subcritical water, Renewable Energy, 2019, vol. 131, pp. 660–666. https://doi.org/10.1016/j.renene.2018.07.091

    Article  CAS  Google Scholar 

  44. Oliveira, E.L.G., Silvestre, A.J.D., and Silva, C.M., Review of kinetic models for supercritical fluid extraction, Chem. Eng. Res. Des., 2011, vol. 89, no. 7, pp. 1104–1117. https://doi.org/10.1016/j.cherd.2010.10.025

    Article  CAS  Google Scholar 

  45. del Valle, J.M., Carrasco, C.V., Toledo, F.R., and Núñez, G.A., Particle size distribution and stratification of pelletized oilseeds affects cumulative supercritical CO2 extraction plots, J. Supercrit. Fluids, 2019, vol. 146, p. 189.

    Article  CAS  Google Scholar 

  46. Mosegaard, K. and Sambridge, M., Monte Carlo analysis of inverse problems, Inverse Probl., 2002, vol. 18, p. R29.

    Article  Google Scholar 

  47. del Valle, J.M. and Aguilera, J.M., An improved equation for predicting the solubility of vegetable oils in supercritical CO2, Ind. Eng. Chem. Res., 1988, vol. 27, p. 1551.

    Article  CAS  Google Scholar 

  48. del Valle, J.M., de la Fuente, J.C., and Uquiche, E., A refined equation for predicting the solubility of vegetable oils in high-pressure CO2, J. Supercrit. Fluids, 2012, vol. 67, pp. 60–70. https://doi.org/10.1016/j.supflu.2012.02.004

    Article  CAS  Google Scholar 

  49. Salamatin, A.A., Khaliullina, A.S., and Khaziev, R.S., Extraction of aromatic abietane diterpenoids from Salvia officinalis leaves by petroleum ether: Data resolution analysis, Ind. Crops Prod., 2020, vol. 143, article no. 111909.

    Article  CAS  Google Scholar 

  50. Bowman, A.W. and Azzalini, A., Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations, Oxford Statistical Science Series, vol. 18, Oxford: Clarendon, 1997.

    Google Scholar 

Download references

ACKNOWLEDGMENTS

We are grateful to A.A. Zaikin, associate professor, Mathematical Statistics Department, Kazan State University, for useful discussions during the preparation of this article.

Funding

This study was financially supported by the Russian Foundation for Basic Research (grant nos. 19-31-60013 and 18-41-160001 (creation of an algorithm for constructing a distribution sample and its verification)) and partially by the Program for Strategic Academic Leadership at Kazan (Volga) Federal University.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Salamatin.

Additional information

Translated by L. Smolina

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salamatin, A.A., Khaliullina, A.S. Evaluation of Supercritical Fluid Extraction Model Parameters by Monte-Carlo Methods. Theor Found Chem Eng 56, 69–83 (2022). https://doi.org/10.1134/S0040579521060117

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040579521060117

Keywords:

Navigation