Skip to main content
SpringerLink
Log in

Stochastic Simulation of the Process of Size Separation of Granular Materials on Sieve Classifiers

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

Abstract

The process of separation of granular materials into specific size fractions on sieve classifiers based on Poisson processes that relate to discontinuous Markov processes with discrete states is studied. The residence of particles of a certain size fraction on the surface of the sieves is defined as certain states, and a transition point from one state to another state (sieving) is defined as a random process. To determine the probabilities of states, a system of stochastic differential equations is constructed, the coefficients of which are calculated as dependent on the probability of sifting the particles into sieve cells. The solutions allow one to calculate the extraction rate and evaluate the separation efficiency. A computational experiment is conducted to study the main characteristics of the process.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

Similar content being viewed by others

REFERENCES

  1. Vaisberg, L.A., Ivanov, K.S., and Mel’nikov, A.E., Improvement of approaches to the mathematical modeling of vibrational screening processes, Obogashch. Rud, 2013, no. 2, p. 21.

  2. Gortinskii, V.V., Demskii, A.B., and Boriskin, M.A., Protsessy separirovaniya na zernopererabatyvayushchikh predpriyatiyakh (Separation in Grain Processing Plants), Moscow: Kolos, 1973.

  3. Akhmadiev, F.G. and Gizzyatov, R.F., Modeling of separation of granular materials on multiple-deck classifiers using the theory of stochastic processes, Theor. Found. Chem. Eng., 2018, vol. 52, no. 3, pp. 360–370. https://doi.org/10.1134/S0040579518030028

    Article  CAS  Google Scholar 

  4. Nepomnyashchii, E.A., Kinetics of the processing of disperse materials, Teor. Osn. Khim. Tekhnol., 1973, vol. 7, no. 5, p. 754.

    Google Scholar 

  5. Akhmadiev, F.G., Gizzyatov, R.F., and Nazipov, I.T., Hydrogasdynamics and kinetics of separation of disperse media on sieve classifiers, J. Eng. Phys. Thermophys., 2017, vol. 90, no. 5, pp. 1077–1086. https://doi.org/10.1007/s10891-017-1659-x

    Article  CAS  Google Scholar 

  6. Ogurtsov, V.A., Fedosov, S.V., and Mizonov, V.E., Modeling of the kinetics of vibrational screening based on the theory of Markov chains, Stroit. Mater., 2008, no. 5, p. 33.

  7. Dolgunin, V.N., Ukolov, A.A., and Ivanov, O.O., Segregation kinetics in the rapid gravity flow of granular materials, Theor. Found. Chem. Eng., 2006, vol. 40, no. 4, pp. 393–404. https://doi.org/10.1134/S0040579506040099

    Article  CAS  Google Scholar 

  8. Nadutyi, V.P. and Lapshin, E.S., Kinetics of screening with variable vibrational excitation along the length of the screening surface, Khim., Khim. Tekhnol. Ekol., 2008, no. 38, p. 11.

  9. Beeckmans, J., Jutan, A., and Can, J., Monte Carlo simulation of a probability screen, Can. J. Chem. Eng., 1989, vol. 67, no. 2, p. 329.

    Article  CAS  Google Scholar 

  10. Pascoe, R.D., Fitzpatrick, R., and Garratt, J.R., Prediction of automated sorter performance utilizing a Monte Carlo simulation of feed characteristics, Miner. Eng., 2015, vol. 72, p. 101.

    Article  CAS  Google Scholar 

  11. Akhmadiev, F.G., Gizzyatov, R.F., and Kiyamov, Kh.G., Mathematical modeling of thin-layer separation of granular materials on sieve classifiers, Theor. Found. Chem. Eng., 2013, vol. 47, no. 3, pp. 254–261. https://doi.org/10.1134/S0040579513030019

    Article  CAS  Google Scholar 

  12. Generalov, M.B., Mekhanika tverdykh dispersnykh sred v protsessakh khimicheskoi tekhnologii (Mechanics of Solid Disperse Media in Chemical Engineering Processes), Kaluga: Izd. Bochkarevoi, 2002.

  13. Rozenbaum, R.B., Resistance forces for the motion of solids in a fluidized bed and the possibility of applying the concept of the effective viscosity of the bed, Teor. Osn. Khim. Tekhnol., 1979, vol. 13, no. 4, p. 570.

    CAS  Google Scholar 

  14. Ryzhkov, A.F. and Tolmachev, E.M., On the selection of the optimal height of a vibrofluidized bed, Teor. Osn. Khim. Tekhnol., 1983, vol. 17, no. 2, p. 206.

    CAS  Google Scholar 

  15. Blekhman, I.I. and Dzhanelidze, G.Yu., Vibratsionnoe peremeshchenie (Vibrational Movement), Moscow: Nauka, 1964.

  16. Nigmatulin, R.I., Osnovy mekhaniki geterogennykh sred (Fundamentals of the Mechanics of Heterogeneous Media), Moscow: Nauka, 1978.

  17. Akhmadiev, F.G., Gizzyatov, R.F., and Nazipov, I.T., Mathematical modeling of the classification of granular materials using screens, Sovrem. Naukoemk. Tekhnol., 2019, no. 12-1, p. 30.

  18. Barskii, M.D., Optimizatsiya protsessov razdeleniya zernistykh materialov (Optimization of the Separation of Granular Materials), Moscow: Nedra, 1978.

  19. Akhmadiev, F.G., Some problems of multicriteria process optimization, Theor. Found. Chem. Eng., 2014, vol. 48, no. 5, pp. 574–582. https://doi.org/10.1134/S0040579514050145

    Article  CAS  Google Scholar 

  20. Bharucha-Reid, A.T., Elements of the Theory of Markov Processes and Their Applications, New York: McGraw-Hill, 1960.

    Google Scholar 

  21. Kazakov, V.A., Vvedenie v teoriyu markovskikh protsessov i nekotorye radiotekhnicheskie zadachi (An Introduction to the Theory of Markov Processes and Some Radio Engineering Problems), Moscow: Sovetskoe Radio, 1973.

  22. Tikhonov, V.I. and Mironov, M.A., Markovskie protsessy (Markov Processes), Moscow: Sovetskoe Radio, 1977.

  23. Feller, W., An Introduction to Probability Theory and Its Applications, 2 vols., New York: Wiley, 1957, vol. 1, 2nd ed.

    Google Scholar 

  24. Karpenko, A.P., Sovremennye algoritmy poiskovoi optimizatsii. Algoritmy, vdokhnovlennye prirodoi (Modern Algorithms for Search Optimization: Algorithms Inspired by Nature), Moscow: Mosk. Gos. Tekh. Univ. im. N. E. Baumana, 2014.

  25. Akhmadiev, F.G., Gizzyatov, R.F., and Nazipov, I.T., Computer simulation and optimization of the kinetics of the processing of heterogeneous media, Certificate of the State Registration of a Computer Program no. 2016661926 RU, 2016.

Download references

Author information

Authors and Affiliations

  1. Kazan State University of Architecture and Civil Engineering, Kazan, Russia

    F. G. Akhmadiev & R. F. Gizzyatov

Authors
  1. F. G. Akhmadiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. F. Gizzyatov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. G. Akhmadiev.

Additional information

Translated by O. Kadkin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akhmadiev, F.G., Gizzyatov, R.F. Stochastic Simulation of the Process of Size Separation of Granular Materials on Sieve Classifiers. Theor Found Chem Eng 54, 828–837 (2020). https://doi.org/10.1134/S0040579520050279

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040579520050279

Keywords:

Search

Navigation