IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p994-d774893.html
   My bibliography  Save this article

Mathematical Modeling of Changes in the Dispersed Composition of Solid Phase Particles in Technological Apparatuses of Periodic and Continuous Action

Author

Listed:
  • Oleg M. Flisyuk

    (Department of Processes and Apparatus, Saint Petersburg State Institute of Technology, Technical University, Moskovsky Avenue 26, 109013 Saint Petersburg, Russia)

  • Nicolay A. Martsulevich

    (Department of Processes and Apparatus, Saint Petersburg State Institute of Technology, Technical University, Moskovsky Avenue 26, 109013 Saint Petersburg, Russia)

  • Valery P. Meshalkin

    (Department of Processes and Apparatus, Saint Petersburg State Institute of Technology, Technical University, Moskovsky Avenue 26, 109013 Saint Petersburg, Russia)

  • Alexandr V. Garabadzhiu

    (Department of Processes and Apparatus, Saint Petersburg State Institute of Technology, Technical University, Moskovsky Avenue 26, 109013 Saint Petersburg, Russia)

Abstract

This article presents a methodological approach to modeling the processes of changing the dispersed composition of solid phase particles, such as granulation, crystallization, pyrolysis, and others. Granulation is considered as a complex process consisting of simpler (elementary) processes such as continuous particle growth, agglomeration, crushing and abrasion. All these elementary processes, which are also complex in themselves, usually participate in the formation of the dispersed composition of particles and proceed simultaneously with the predominance of one process or another, depending on the method of its organization and the physicochemical properties of substances. A quantitative description of the evolution of the dispersed composition of the solid phase in technological processes in which the particle size does not remain constant is proposed. Considering the stochastic nature of elementary mass transfer events in individual particles, the methods of the theory of probability are applied. The analysis of the change in the dispersed composition is based on the balanced equation of the particle mass distribution function. The equation accounts for all possible physical mechanisms that effect changes in particle size during chemical and technological processes. Examples of solutions to this equation for specific processes of practical importance are provided. The obtained analytical solutions are of independent interest and are in good agreement with the experimental data, which indicates the adequacy of the proposed approach. These solutions can also be used to analyze similar processes. The effectiveness has been confirmed during the analysis and calculation of the processes of granulation of various solutions and disposal of oil-containing waste to obtain a granular mineral additive.

Suggested Citation

  • Oleg M. Flisyuk & Nicolay A. Martsulevich & Valery P. Meshalkin & Alexandr V. Garabadzhiu, 2022. "Mathematical Modeling of Changes in the Dispersed Composition of Solid Phase Particles in Technological Apparatuses of Periodic and Continuous Action," Mathematics, MDPI, vol. 10(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:994-:d:774893
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/994/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/6/994/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    2. Singh, Mehakpreet & Singh, Randhir & Singh, Sukhjit & Singh, Gagandeep & Walker, Gavin, 2020. "Finite volume approximation of multidimensional aggregation population balance equation on triangular grid," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 191-212.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francesco Bartaloni, 2021. "Existence of the Optimum in Shallow Lake Type Models with Hysteresis Effect," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 358-392, August.
    2. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    3. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.
    4. Alessandro Calvia & Gianluca Cappa & Fausto Gozzi & Enrico Priola, 2023. "HJB Equations and Stochastic Control on Half-Spaces of Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 710-744, August.
    5. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    6. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2018. "Geographic Environmental Kuznets Curves: The Optimal Growth Linear-Quadratic Case," AMSE Working Papers 1813, Aix-Marseille School of Economics, France.
    7. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    8. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    9. Fabbri, Giorgio & Gozzi, Fausto & Zanco, Giovanni, 2021. "Verification results for age-structured models of economic–epidemics dynamics," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    10. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    11. Dario Debowicz & Alex Dickson & Ian A. MacKenzie & Petros G. Sekeris, 2023. "Income and the (eventual) rise of democracy," Discussion Papers Series 661, School of Economics, University of Queensland, Australia.
    12. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    13. Carmen Camacho & Alexandre Cornet, 2021. "Diffusion of soil pollution in an agricultural economy. The emergence of regions, frontiers and spatial patterns," PSE Working Papers halshs-02652191, HAL.
    14. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," AMSE Working Papers 2003, Aix-Marseille School of Economics, France.
    15. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "A Spatiotemporal Framework for the Analytical Study of Optimal Growth Under Transboundary Pollution," Department of Economics University of Siena 813, Department of Economics, University of Siena.
    16. Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2023. "Growth Models with Externalities on Networks," Working Papers 2023: 23, Department of Economics, University of Venice "Ca' Foscari".
    17. Giorgio Fabbri & Francesco Russo, 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," LIDAM Discussion Papers IRES 2017003, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    18. Cristiano Ricci, 2023. "A non-invariance result for the spatial AK model," Papers 2311.06811, arXiv.org.
    19. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    20. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:994-:d:774893. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.