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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">energy</journal-id><journal-title-group><journal-title xml:lang="ru">Энергетика. Известия высших учебных заведений и энергетических объединений СНГ</journal-title><trans-title-group xml:lang="en"><trans-title>ENERGETIKA. Proceedings of CIS higher education institutions and power engineering associations</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1029-7448</issn><issn pub-type="epub">2414-0341</issn><publisher><publisher-name>BNTU</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21122/1029-7448-2024-67-4-332-344</article-id><article-id custom-type="elpub" pub-id-type="custom">energy-2390</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ТЕПЛОЭНЕРГЕТИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>НEAT POWER ENGINEERING</subject></subj-group></article-categories><title-group><article-title>Расчетно-экспериментальное исследование закономерностей формирования кипящего слоя инертного керамзитового материала</article-title><trans-title-group xml:lang="en"><trans-title>Computational and Experimental Study of the Patterns of Formation of a Fluidized Bed  of Inert Haydite Particles Material</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Митрофанов</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Mitrofanov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Павлодар</p></bio><bio xml:lang="en"><p>Pavlodar</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Василевич</surname><given-names>С. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Vasilevich</surname><given-names>S. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Адрес для переписки:Василевич Сергей Владимирович -Белорусская государственная академия авиации,ул. Уборевича, 77,220096, г. Минск, Республика Беларусь/Тел.: +375 17 249-97-65svasilevich@yandex.ru</p></bio><bio xml:lang="en"><p>Address for correspondence:Vasilevich Siarhei V. - Belarusian State Academy of Aviation,77, Uborevich str.,220096, Minsk, Republic of Belarus.Tel.: +375 17 249-97-65svasilevich@yandex.ru</p></bio><email xlink:type="simple">svasilevich@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Стойко</surname><given-names>С. О.</given-names></name><name name-style="western" xml:lang="en"><surname>Stojko</surname><given-names>S. O.</given-names></name></name-alternatives><bio xml:lang="ru"><p>г. Минск</p></bio><bio xml:lang="en"><p>Minsk</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Торайгыров университет</institution><country>Казахстан</country></aff><aff xml:lang="en"><institution>Toraighyrov University</institution><country>Kazakhstan</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Белорусская государственная академия авиации</institution><country>Беларусь</country></aff><aff xml:lang="en"><institution>Belarusian State Academy of Aviation</institution><country>Belarus</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>12</day><month>08</month><year>2024</year></pub-date><volume>67</volume><issue>4</issue><fpage>332</fpage><lpage>344</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Митрофанов А.В., Василевич С.В., Стойко С.О., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Митрофанов А.В., Василевич С.В., Стойко С.О.</copyright-holder><copyright-holder xml:lang="en">Mitrofanov A.V., Vasilevich S.V., Stojko S.O.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://energy.bntu.by/jour/article/view/2390">https://energy.bntu.by/jour/article/view/2390</self-uri><abstract><p>В настоящее время актуальной тенденцией развития топливно-энергетических комплексов ряда стран является диверсификация генерации за счет вовлечения местных видов твердого топлива. При этом термохимическая переработка топлива часто реализуется в псевдоожиженном состоянии. Существенная доля дисперсных видов топлива не может быть переведена в состояние стабильного псевдоожижения. Выходом в таких случаях является создание псевдоожиженного слоя инертного носителя, в который затем вводят частицы целевого топливного компонента. В настоящей работе предпринято расчетно-экспериментальное исследование псевдоожижения инертного сыпучего материала (гранул керамзита). Целью настоящей работы является разработка математической модели формирования псевдоожиженного слоя, позволяющей вести расчет процесса по его локальным характеристикам, а также идентификация параметров модели и ее проверка по данным натурного эксперимента. В ходе исследования решены задачи разработки численного метода расчета распределения скоростей и концентраций по высоте аппарата, выполнена параметрическая идентификация предложенной математической модели, эмпирическая проверка результатов моделирования. В качестве математической основы построения модели использован математический аппарат теории цепей Маркова. Для идентификации параметров модели и ее верификации использованы данные собственного натурного эксперимента. Сравнение расчетных и экспериментальных данных показало высокую прогностическую эффективность модели для известного гранулометрического состава ожижаемого продукта. Результаты натурных экспериментов показали также значительную эволюцию гранулометрического состава частиц керамзита при их длительном пребывании в псевдоожиженном слое, что требует отдельного исследования, а также введения соответствующих поправок в математическую модель для ее дальнейшего совершенствования.</p></abstract><trans-abstract xml:lang="en"><p>At present, an actual trend in the development of fuel and energy complexes in a number of countries is the diversification of generation via the involvement of local types of solid fuel. In this case, thermochemical processing of fuel is often carried out in a fluidized state. A significant proportion of dispersed fuels cannot be transferred to a state of stable fluidization. The solution in such cases is to create a fluidized bed of inert carrier, into which particles of the target fuel component are then introduced. In this work, a computational and experimental study of the fluidization of inert bulk material (haydite granules) was carried out. The key purpose of the work was to develop a mathematical model for the formation of a fluidized bed, which makes it possible to calculate the process based on its local characteristics, as well as to identify the model parameters and test it using experiment data. During the study the problems of developing a numerical method for calculating the distribution of velocities and concentrations along the height of the apparatus were solved, parametric identification of the proposed mathematical model was carried out, and empirical verification of the modeling results was carried out. The mathematical apparatus of the theory of Markov chains was used as the mathematical basis for constructing the model. The data from our own laboratory full-scale experiment were used to identify the parameters of the model and verify it. A comparison of calculated and experimental data showed the high predictive efficiency of the model for the given granulometric composition of the fluidizing product. The results of the laboratory full-scale experiments also showed a significant evolution of the granulometric composition of haydite granules during their long-term stay in a fluidized bed, which requires a separate study, as well as the introduction of appropriate amendments to the mathematical model for its further improvement.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>: псевдоожиженный слой</kwd><kwd>численное моделирование</kwd><kwd>цепи Маркова</kwd><kwd>профиль скорости газа</kwd><kwd>частицы керамзита</kwd></kwd-group><kwd-group xml:lang="en"><kwd>fluidized bed</kwd><kwd>numerical simulation</kwd><kwd>Markov chains</kwd><kwd>gas velocity profile</kwd><kwd>haydite particles</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Fortov V. E., Popel’ O. S. (2014) The Current Status of the Development of Renewable Energy Sources Worldwide and in Russia. Thermal Engineering, 61 (6), 389–398. https://doi.org/10.1134/s0040601514060020.</mixed-citation><mixed-citation xml:lang="en">Fortov V. E., Popel’ O. S. (2014) The Current Status of the Development of Renewable Energy Sources Worldwide and in Russia. Thermal Engineering, 61 (6), 389–398. https://doi.org/ 10.1134/s0040601514060020.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Karpunin I. I., Kuzmich V. V., Balabanova T. (2011) Usage of Vegetal Wastes for Energy Production Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’e-dinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, (6), 72–75 (in Russian).</mixed-citation><mixed-citation xml:lang="en">Karpunin I. I., Kuzmich V. V., Balabanova T. (2011) Usage of Vegetal Wastes for Energy Production Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’e-dinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, (6), 72–75 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Korsak E. P. (2019) Formation of the System of Threats to Energy Security of the Republic of Belarus. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 62 (4), 388–398. https://doi.org/10.21122/1029-7448-2019-62-4-388-398 (in Russian).</mixed-citation><mixed-citation xml:lang="en">Korsak E. P. (2019) Formation of the System of Threats to Energy Security of the Republic of Belarus. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 62 (4), 388–398. https://doi.org/10.21122/1029-7448-2019-62-4-388-398 (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Pode R. (2016) Potential Applications of Rice Husk Ash Waste From Rice Husk Biomass Power Plant. Renewable and Sustainable Energy Reviews, 53, 1468–1485. https://doi.org/10.1016/j.rser.2015.09.051.</mixed-citation><mixed-citation xml:lang="en">Pode R. (2016) Potential Applications of Rice Husk Ash Waste From Rice Husk Biomass Power Plant. Renewable and Sustainable Energy Reviews, 53, 1468–1485. https://doi.org/10.1016/ j.rser.2015.09.051.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Pysmenna U. Yе., Trypolska G. S. (2020) Sustainable Energy Transitions: Overcoming Negative Externalities. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 63 (4), 312–327. https://doi.org/10.21122/1029-7448-2020-63-4-312-327.</mixed-citation><mixed-citation xml:lang="en">Pysmenna U. Yе., Trypolska G. S. (2020) Sustainable Energy Transitions: Overcoming Negative Externalities. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 63 (4), 312–327. https://doi.org/10.21122/1029-7448-2020-63-4-312-327.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Grammelis P. (ed.) (2011) Solid Biofuels for Energy. London, Springer London. https://doi.org/10.1007/978-1-84996-393-0.</mixed-citation><mixed-citation xml:lang="en">Grammelis P. (ed.) (2011) Solid Biofuels for Energy. London, Springer London. https://doi. org/10.1007/978-1-84996-393-0.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Yates J. G., Lettieri P. (2016) Fluidized-Bed Reactors: Processes and Operating Conditions. Cham, Springer International Publishing. https://link.springer.com/book/10.1007/978-3-319-39593-7.</mixed-citation><mixed-citation xml:lang="en">Yates J. G., Lettieri P. (2016) Fluidized-Bed Reactors: Processes and Operating Conditions. Cham, Springer International Publishing. https://link.springer.com/book/10.1007/978-3-319-39593-7.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Perry’s Chemical Engineers’ Handbook. (1998). Choice Reviews Online, 35 (06), 35-3079-35-3079. https://doi.org/10.5860/choice.35-3079.</mixed-citation><mixed-citation xml:lang="en">Perry’s Chemical Engineers’ Handbook. (1998). Choice Reviews Online, 35 (06), 35-3079-35-3079. https://doi.org/10.5860/choice.35-3079.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Arromdee P., Kuprianov V. I. (2012) A Comparative Study on Combustion of Sunflower Shells in Bubbling and Swirling Fluidized-Bed Combustors with a Cone-Shaped Bed. Chemical Engineering and Processing: Process Intensification, 62, 26–38. https://doi.org/10.1016/j.cep.2012.10.002.</mixed-citation><mixed-citation xml:lang="en">Arromdee P., Kuprianov V. I. (2012) A Comparative Study on Combustion of Sunflower Shells in Bubbling and Swirling Fluidized-Bed Combustors with a Cone-Shaped Bed. Chemical Engineering and Processing: Process Intensification, 62, 26–38. https://doi.org/10.1016/j.cep.2012.10.002.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Kaewklum R., Kuprianov V. I. (2010) Experimental Studies on a Novel Swirling Fluidized-Bed Combustor Using an Annular Spiral Air Distributor. Fuel, 89 (1), 43–52. https://doi.org/10.1016/j.fuel.2009.07.027.</mixed-citation><mixed-citation xml:lang="en">Kaewklum R., Kuprianov V. I. (2010) Experimental Studies on a Novel Swirling Fluidized-Bed Combustor Using an Annular Spiral Air Distributor. Fuel, 89 (1), 43–52. https://doi.org/ 10.1016/j.fuel.2009.07.027.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Madhiyanon T., Lapirattanakun A., Sathitruangsak P., Soponronnarit S. (2006) A Novel Cyclonic Fluidized-Bed Combustor (ψ-FBC): Combustion and Thermal Efficiency, Temperature Distributions, Combustion Intensity, and Emission of Pollutants. Combustion and Flame, 146 (1–2), 232–245. https://doi.org/10.1016/j.combustflame.2006.03.008.</mixed-citation><mixed-citation xml:lang="en">Madhiyanon T., Lapirattanakun A., Sathitruangsak P., Soponronnarit S. (2006) A Novel Cyclonic Fluidized-Bed Combustor (ψ-FBC): Combustion and Thermal Efficiency, Temperature Distributions, Combustion Intensity, and Emission of Pollutants. Combustion and Flame, 146 (1–2), 232–245. https://doi.org/10.1016/j.combustflame.2006.03.008.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Wu X., Li K., Song F., Zhu X. (2017) Fluidization Behavior of Biomass Particles and its Improvement in a Cold Visualized Fluidized Bed. BioResources, 12 (2), 3546–3559. https://doi.org/10.15376/biores.12.2.3546-3559.</mixed-citation><mixed-citation xml:lang="en">Wu X., Li K., Song F., Zhu X. (2017) Fluidization Behavior of Biomass Particles and its Improvement in a Cold Visualized Fluidized Bed. BioResources, 12 (2), 3546–3559. https://doi.org/10.15376/biores.12.2.3546-3559.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Zhong W., Jin B., Zhang Y., Wang X., Xiao R. (2008) Fluidization of Biomass Particles in a Gas−Solid Fluidized Bed. Energy Fuels, 22 (6), 4170–4176. https://doi.org/10.1021/ef800495u.</mixed-citation><mixed-citation xml:lang="en">Zhong W., Jin B., Zhang Y., Wang X., Xiao R. (2008) Fluidization of Biomass Particles in a Gas−Solid Fluidized Bed. Energy Fuels, 22 (6), 4170–4176. https://doi.org/10.1021/ef800495u.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Bannon D., Deza M., Masoumi M., Estejab B. (2023) Assessment of Irregular Biomass Particles Fluidization in Bubbling Fluidized Beds. Energies, 16 (4), 2051. https://doi.org/10.3390/en16042051.</mixed-citation><mixed-citation xml:lang="en">Bannon D., Deza M., Masoumi M., Estejab B. (2023) Assessment of Irregular Biomass Particles Fluidization in Bubbling Fluidized Beds. Energies, 16 (4), 2051. https://doi.org/10. 3390/en16042051.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Deza M., Franka N. P., Heindel T. J., Battaglia F. (2009) CFD Modeling and X-Ray Imaging of Biomass in a Fluidized Bed. Journal of Fluids Engineering, 131 (11), 111303. https://doi.org/10.1115/1.4000257.</mixed-citation><mixed-citation xml:lang="en">Deza M., Franka N. P., Heindel T. J., Battaglia F. (2009) CFD Modeling and X-Ray Imaging of Biomass in a Fluidized Bed. Journal of Fluids Engineering, 131 (11), 111303. https://doi. org/10.1115/1.4000257.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Leon M. A., Dutta A. (2010) Fluidization Characteristics of Rice Husk in a Bubbling Fluidized Bed. The Canadian Journal of Chemical Engineering, 88 (1), 18–22. https://doi.org/10.1002/cjce.20245.</mixed-citation><mixed-citation xml:lang="en">Leon M. A., Dutta A. (2010) Fluidization Characteristics of Rice Husk in a Bubbling Fluidized Bed. The Canadian Journal of Chemical Engineering, 88 (1), 18–22. https://doi.org/10.1002/ cjce.20245.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Armesto L., Bahillo A., Veijonen K., Cabanillas A., Otero J. (2002) Combustion Behaviour of Rice Husk in a Bubbling Fluidised Bed. Biomass and Bioenergy, 23 (3), 171–179. https://doi.org/10.1016/s0961-9534(02)00046-6.</mixed-citation><mixed-citation xml:lang="en">Armesto L., Bahillo A., Veijonen K., Cabanillas A., Otero J. (2002) Combustion Behaviour of Rice Husk in a Bubbling Fluidised Bed. Biomass and Bioenergy, 23 (3), 171–179. https://doi.org/10.1016/s0961-9534(02)00046-6.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Minimum and Complete Fluidization Velocity for Sand-Palm Shell Mixtures, Part I: Fluidization Behavior and Characteristic Velocities (2010). American Journal of Applied Sciences, 7 (6), 763–772. https://doi.org/10.3844/ajassp.2010.763.772.</mixed-citation><mixed-citation xml:lang="en">Minimum and Complete Fluidization Velocity for Sand-Palm Shell Mixtures, Part I: Fluidization Behavior and Characteristic Velocities (2010). American Journal of Applied Sciences, 7 (6), 763–772. https://doi.org/10.3844/ajassp.2010.763.772.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Oliveira T. J. P., Cardoso C. R., Ataíde C. H. (2013) Bubbling Fluidization of Biomass and Sand Binary Mixtures: Minimum Fluidization Velocity and Particle Segregation. Chemical Engineering and Processing: Process Intensification, 72, 113–121. https://doi.org/10.1016/j.cep.2013.06.010.</mixed-citation><mixed-citation xml:lang="en">Oliveira T. J. P., Cardoso C. R., Ataíde C. H. (2013) Bubbling Fluidization of Biomass and Sand Binary Mixtures: Minimum Fluidization Velocity and Particle Segregation. Chemical Engineering and Processing: Process Intensification, 72, 113–121. https://doi.org/10.1016/j.cep.2013.06.010.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Toschi F., Zambon M. T., Sandoval J., Reyes-Urrutia A., Mazza G. D. (2020) Fluidization of Forest Biomass-Sand Mixtures: Experimental Evaluation of Minimum Fluidization Velocity and CFD Modeling. Particulate Science and Technology, 39 (5), 549–561. https://doi.org/10. 1080/02726351.2020.1786202.</mixed-citation><mixed-citation xml:lang="en">Toschi F., Zambon M. T., Sandoval J., Reyes-Urrutia A., Mazza G. D. (2020) Fluidization of Forest Biomass-Sand Mixtures: Experimental Evaluation of Minimum Fluidization Velocity and CFD Modeling. Particulate Science and Technology, 39 (5), 549–561. https://doi.org/10. 1080/02726351.2020.1786202.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Clarke K. L., Pugsley T., Hill G. A. (2005) Fluidization of Moist Sawdust in Binary Particle Systems in a Gas–Solid Fluidized Bed. Chemical Engineering Science, 60 (24), 6909–6918. https://doi.org/10.1016/j.ces.2005.06.004.</mixed-citation><mixed-citation xml:lang="en">Clarke K. L., Pugsley T., Hill G. A. (2005) Fluidization of Moist Sawdust in Binary Particle Systems in a Gas–Solid Fluidized Bed. Chemical Engineering Science, 60 (24), 6909–6918. https://doi.org/10.1016/j.ces.2005.06.004.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Pérez N. P., Pedroso D. T., Machin E. B., Antunes J. S., Verdú Ramos R. A., Silveira J. L. (2017) Fluid Dynamic Study of Mixtures of Sugarcane Bagasse and Sand Particles: Minimum fluidization Velocity. Biomass and Bioenergy, 107, 135–149. https://doi.org/10.1016/j.biombioe. 2017.08.015.</mixed-citation><mixed-citation xml:lang="en">Pérez N. P., Pedroso D. T., Machin E. B., Antunes J. S., Verdú Ramos R. A., Silveira J. L. (2017) Fluid Dynamic Study of Mixtures of Sugarcane Bagasse and Sand Particles: Minimum fluidization Velocity. Biomass and Bioenergy, 107, 135–149. https://doi.org/10.1016/j.biombioe. 2017.08.015.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Chen T., Ku X., Lin J., Ström H. (2020) CFD-DEM Simulation of Biomass Pyrolysis in Fluidized-Bed Reactor with a Multistep Kinetic Scheme. Energies, 13 (20), 5358. https://doi.org/10.3390/en13205358.</mixed-citation><mixed-citation xml:lang="en">Chen T., Ku X., Lin J., Ström H. (2020) CFD-DEM Simulation of Biomass Pyrolysis in Fluidized-Bed Reactor with a Multistep Kinetic Scheme. Energies, 13 (20), 5358. https://doi.org/ 10.3390/en13205358.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Deen N. G., Van Sint Annaland M., Van der Hoef M. A., Kuipers J. A. M. (2007) Review of Discrete Particle Modeling of Fluidized Beds. Chemical Engineering Science, 62 (1), 28–44. https://doi.org/10.1016/j.ces.2006.08.014.</mixed-citation><mixed-citation xml:lang="en">Deen N. G., Van Sint Annaland M., Van der Hoef M. A., Kuipers J. A. M. (2007) Review of Discrete Particle Modeling of Fluidized Beds. Chemical Engineering Science, 62 (1), 28–44. https://doi.org/10.1016/j.ces.2006.08.014.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Sommerfeld M., Cui Y., Schmalfuß S. (2019) Potential and Constraints for the Application of CFD Combined with Lagrangian Particle Tracking to Dry Powder Inhalers. European Journal of Pharmaceutical Sciences, 128, 299–324. https://doi.org/10.1016/j.ejps.2018.12.008.</mixed-citation><mixed-citation xml:lang="en">Sommerfeld M., Cui Y., Schmalfuß S. (2019) Potential and Constraints for the Application of CFD Combined with Lagrangian Particle Tracking to Dry Powder Inhalers. European Journal of Pharmaceutical Sciences, 128, 299–324. https://doi.org/10.1016/j.ejps.2018.12.008.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Wang T., Zhang F., Furtney J., Damjanac B. (2022) A Review of Methods, Applications and Limitations for Incorporating Fluid Flow in the Discrete Element Method. Journal of Rock Mechanics and Geotechnical Engineering, 14 (3), 1005–1024. https://doi.org/10.1016/j.jrmge.2021.10.015.</mixed-citation><mixed-citation xml:lang="en">Wang T., Zhang F., Furtney J., Damjanac B. (2022) A Review of Methods, Applications and Limitations for Incorporating Fluid Flow in the Discrete Element Method. Journal of Rock Mechanics and Geotechnical Engineering, 14 (3), 1005–1024. https://doi.org/10.1016/j.jrmge.2021.10.015.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Ma H., Zhao Y. (2018) CFD-DEM Investigation of the Fluidization of Binary Mixtures Containing Rod-Like Particles and Spherical Particles in a Fluidized Bed. Powder Technology, 336, 533–545. https://doi.org/10.1016/j.powtec.2018.06.034.</mixed-citation><mixed-citation xml:lang="en">Ma H., Zhao Y. (2018) CFD-DEM Investigation of the Fluidization of Binary Mixtures Containing Rod-Like Particles and Spherical Particles in a Fluidized Bed. Powder Technology, 336, 533–545. https://doi.org/10.1016/j.powtec.2018.06.034.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Ma H., Xu L., Zhao Y. (2017) CFD-DEM Simulation of Fluidization of Rod-Like Particles in a Fluidized Bed. Powder Technology, 314, 355–366. https://doi.org/10.1016/j.powtec.2016.12.008.</mixed-citation><mixed-citation xml:lang="en">Ma H., Xu L., Zhao Y. (2017) CFD-DEM Simulation of Fluidization of Rod-Like Particles in a Fluidized Bed. Powder Technology, 314, 355–366. https://doi.org/10.1016/j.powtec.2016.12.008.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Feng Y. Q., Xu B. H., Zhang S. J., Yu A. B., Zulli P. (2004) Discrete Particle Simulation of Gas Fluidization of Particle Mixtures. AIChE Journal, 50 (8), 1713–1728. https://doi.org/10.1002/aic.10169.</mixed-citation><mixed-citation xml:lang="en">Feng Y. Q., Xu B. H., Zhang S. J., Yu A. B., Zulli P. (2004) Discrete Particle Simulation of Gas Fluidization of Particle Mixtures. AIChE Journal, 50 (8), 1713–1728. https://doi.org/ 10.1002/aic.10169.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Xiong Q., Choi H. S., Lan X., Wang S. (2022). Editorial: Recent Advances in Multiscale CFD Simulation of Pyrolysis. Journal of Analytical and Applied Pyrolysis, 165, 105569.</mixed-citation><mixed-citation xml:lang="en">Xiong Q., Choi H. S., Lan X., Wang S. (2022). Editorial: Recent Advances in Multiscale CFD Simulation of Pyrolysis. Journal of Analytical and Applied Pyrolysis, 165, 105569.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">de Munck M. J. A., Peters E. A. J. F., Kuipers J. A. M. (2023) Fluidized Bed Gas-Solid Heat Transfer Using a CFD-DEM Coarse-Graining Technique. Chemical Engineering Science, 280, 119048. https://doi.org/10.1016/j.ces.2023.119048</mixed-citation><mixed-citation xml:lang="en">de Munck M. J. A., Peters E. A. J. F., Kuipers J. A. M. (2023) Fluidized Bed Gas-Solid Heat Transfer Using a CFD-DEM Coarse-Graining Technique. Chemical Engineering Science, 280, 119048. https://doi.org/10.1016/j.ces.2023.119048</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Berthiaux H., Mizonov V., Zhukov V. (2005) Application of the Theory of Markov Chains to Model Different Processes in Particle Technology. Powder Technology, 157 (1–3), 128–137. https://doi.org/10.1016/j.powtec.2005.05.019.</mixed-citation><mixed-citation xml:lang="en">Berthiaux H., Mizonov V., Zhukov V. (2005) Application of the Theory of Markov Chains to Model Different Processes in Particle Technology. Powder Technology, 157 (1–3), 128–137. https://doi.org/10.1016/j.powtec.2005.05.019.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Dehling H. G., Hoffmann A. C., Stuut H. W. (1999) Stochastic Models for Transport in a Fluidized Bed. SIAM Journal on Applied Mathematics, 60 (1), 337–358. https://doi.org/10.1137/s0036139996306316.</mixed-citation><mixed-citation xml:lang="en">Dehling H. G., Hoffmann A. C., Stuut H. W. (1999) Stochastic Models for Transport in a Fluidized Bed. SIAM Journal on Applied Mathematics, 60 (1), 337–358. https://doi.org/10.1137/ s0036139996306316.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Berthiaux H., Mizonov V. (2008) Applications of Markov Chains in Particulate Process Engineering: A Review. The Canadian Journal of Chemical Engineering, 82 (6), 1143–1168. https://doi.org/10.1002/cjce.5450820602.</mixed-citation><mixed-citation xml:lang="en">Berthiaux H., Mizonov V. (2008) Applications of Markov Chains in Particulate Process Engineering: A Review. The Canadian Journal of Chemical Engineering, 82 (6), 1143–1168. https://doi.org/10.1002/cjce.5450820602.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Catak M., Baş N., Cronin K., Tellez-Medina D., Byrne E. P., Fitzpatrick J. J. (2010) Markov Chain Modelling of Fluidised Bed Granulation. Chemical Engineering Journal, 164 (2–3), 403–409. https://doi.org/10.1016/j.cej.2010.02.022.</mixed-citation><mixed-citation xml:lang="en">Catak M., Baş N., Cronin K., Tellez-Medina D., Byrne E. P., Fitzpatrick J. J. (2010) Markov Chain Modelling of Fluidised Bed Granulation. Chemical Engineering Journal, 164 (2–3), 403–409. https://doi.org/10.1016/j.cej.2010.02.022.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Mitrofanov A., Mizonov V., Tannous K., Ovchinnikov L. (2016) A Markov Chain Model to Describe Fluidization of Particles with Time-Varying Properties. Particulate Science and Technology, 36 (2), 244–253. https://doi.org/10.1080/02726351.2016.1243180.</mixed-citation><mixed-citation xml:lang="en">Mitrofanov A., Mizonov V., Tannous K., Ovchinnikov L. (2016) A Markov Chain Model to Describe Fluidization of Particles with Time-Varying Properties. Particulate Science and Technology, 36 (2), 244–253. https://doi.org/10.1080/02726351.2016.1243180.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Zhuang Y., Chen X., Liu D. (2016) Stochastic Bubble Developing Model Combined with Markov Process of Particles for Bubbling Fluidized Beds. Chemical Engineering Journal, 291, 206–214. https://doi.org/10.1016/j.cej.2016.01.095.</mixed-citation><mixed-citation xml:lang="en">Zhuang Y., Chen X., Liu D. (2016) Stochastic Bubble Developing Model Combined with Markov Process of Particles for Bubbling Fluidized Beds. Chemical Engineering Journal, 291, 206–214. https://doi.org/10.1016/j.cej.2016.01.095.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Mizonov V., Mitrofanov A. (2020) Application of the Theory of Markov Chains to Model Different Processes in Particle Technology. Advances in Engineering Research. Nova Science Publishers. New-York, 2020. Vol. 33. P. 1–74. https://doi.org/10.1016/j.powtec.2005.05.019.</mixed-citation><mixed-citation xml:lang="en">Mizonov V., Mitrofanov A. (2020) Application of the Theory of Markov Chains to Model Different Processes in Particle Technology. Advances in Engineering Research. Nova Science Publishers. New-York, 2020. Vol. 33. P. 1–74. https://doi.org/10.1016/j.powtec.2005.05.019.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Mitrofanov A. V., Mizonov V. E., Shpeynova N. S., Vasilevich S. V., Kasatkina N. K. (2021) Experimental and Theoretical Study of the Axial Distribution of Solid Phase Particles in a Fluidized Bed. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 64 (4), 349–362 (in Russian). https://doi.org/10.21122/1029-7448-2021-64-4-349-362.</mixed-citation><mixed-citation xml:lang="en">Mitrofanov A. V., Mizonov V. E., Shpeynova N. S., Vasilevich S. V., Kasatkina N. K. (2021) Experimental and Theoretical Study of the Axial Distribution of Solid Phase Particles in a Fluidized Bed. Energetika. Izvestiya Vysshikh Uchebnykh Zavedenii i Energeticheskikh Ob’edinenii SNG = Energetika. Proceedings of CIS Higher Education Institutions and Power Engineering Associations, 64 (4), 349–362 (in Russian). https://doi.org/10.21122/1029-7448-2021-64-4-349-362.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Tamir A. (1998) Applications of Markov Chains in Chemical Processes. Applications of Markov Chains in Chemical Engineering. Elsevier, 498–589. https://doi.org/10.1016/B978-044482356-4/50007-9.</mixed-citation><mixed-citation xml:lang="en">Tamir A. (1998) Applications of Markov Chains in Chemical Processes. Applications of Markov Chains in Chemical Engineering. Elsevier, 498–589. https://doi.org/10.1016/B978-044482356-4/50007-9.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Mizonov V., Mitrofanov A., Ogurtzov A., Tannous K. (2014) Modeling of Particle Concentration Distribution in a Fluidized Bed by Means of the Theory of Markov Chains. Particulate Science and Technology, 32 (2), 171–178. https://doi.org/10.1080/02726351.2013.839016.</mixed-citation><mixed-citation xml:lang="en">Mizonov V., Mitrofanov A., Ogurtzov A., Tannous K. (2014) Modeling of Particle Concentration Distribution in a Fluidized Bed by Means of the Theory of Markov Chains. Particulate Science and Technology, 32 (2), 171–178. https://doi.org/10.1080/02726351.2013.839016.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Esin A., Altun M. (1984) Correlation of Axial Mixing of Solids in Fluidized Beds by a Dispersion Coefficient. Powder Technology, 39 (2), 241–244. https://doi.org/10.1016/0032-5910(84)85041-x.</mixed-citation><mixed-citation xml:lang="en">Esin A., Altun M. (1984) Correlation of Axial Mixing of Solids in Fluidized Beds by a Dispersion Coefficient. Powder Technology, 39 (2), 241–244. https://doi.org/10.1016/0032-5910(84)85041-x.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Khan A. R., Richardson J. F. The Resistance to Motion of a Solid Sphere in a Fluid. Chemical Engineering Communications, 62 (1–6), 135–150. https://doi.org/10.1080/00986448708912056.</mixed-citation><mixed-citation xml:lang="en">Khan A. R., Richardson J. F. The Resistance to Motion of a Solid Sphere in a Fluid. Chemical Engineering Communications, 62 (1–6), 135–150. https://doi.org/10.1080/00986448708912056.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Nawaz Z., Xiaoping T., Wei X., Wei F. (2010) Attrition Behavior of Fine Particles in a Fluidized Bed with Bimodal Particles: Influence of Particle Density and Size Ratio. Korean Journal of Chemical Engineering, 27 (5), 1606–1612. https://doi.org/10.1007/s11814-010-0240-5.</mixed-citation><mixed-citation xml:lang="en">Nawaz Z., Xiaoping T., Wei X., Wei F. (2010) Attrition Behavior of Fine Particles in a Fluidized Bed with Bimodal Particles: Influence of Particle Density and Size Ratio. Korean Journal of Chemical Engineering, 27 (5), 1606–1612. https://doi.org/10.1007/s11814-010-0240-5.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Wu D., Gu Z., Li Y. (2015) Attrition of Catalyst Particles in a Laboratory-Scale Fluidized-Bed Reactor. Chemical Engineering Science, 135. P. 431–440. https://doi.org/10.1016/j.ces.2015.01.005.</mixed-citation><mixed-citation xml:lang="en">Wu D., Gu Z., Li Y. (2015) Attrition of Catalyst Particles in a Laboratory-Scale Fluidized-Bed Reactor. Chemical Engineering Science, 135. P. 431–440. https://doi.org/10.1016/j.ces. 2015.01.005.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">Ghods N., Golshan S., Zarghami R., Sotudeh-Gharebagh R. (2019) CFD-DEM Modelling of Particles Attrition in Jet-In-Fluidized Beds. Chemical Engineering Research and Design, 148, 336–348. https://doi.org/10.1016/j.cherd.2019.06.015.</mixed-citation><mixed-citation xml:lang="en">Ghods N., Golshan S., Zarghami R., Sotudeh-Gharebagh R. (2019)  CFD-DEM Modelling of Particles Attrition in Jet-In-Fluidized Beds. Chemical Engineering Research and Design, 148, 336–348. https://doi.org/10.1016/j.cherd.2019.06.015.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">Alonso M., Arias B., Fernández J. R., Bughin O., Abanades C. (2018) Measuring Attrition Properties of Calcium Looping Materials in a 30 kW Pilot Plant. Powder Technology, 336, 273–281. https://doi.org/10.1016/j.powtec.2018.06.011.</mixed-citation><mixed-citation xml:lang="en">Alonso M., Arias B., Fernández J. R., Bughin O., Abanades C. (2018) Measuring Attrition Properties of Calcium Looping Materials in a 30 kW Pilot Plant. Powder Technology, 336, 273–281. https://doi.org/10.1016/j.powtec.2018.06.011.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">Mitrofanov A., Mizonov V., Camelo A., Tannous K. (2019) Application of the Theory of Markov Chains to Theoretical Study of Processes in a Circulating Fluidized Bed. Particulate Science and Technology, 37 (8), 1032–1037. https://doi.org/10.1080/02726351.2018.1525459.</mixed-citation><mixed-citation xml:lang="en">Mitrofanov A., Mizonov V., Camelo A., Tannous K. (2019) Application of the Theory of Markov Chains to Theoretical Study of Processes in a Circulating Fluidized Bed. Particulate Science and Technology, 37 (8), 1032–1037. https://doi.org/10.1080/02726351.2018.1525459.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
