Vol. 337 No. 5 (2026)

DOI https://doi.org/10.18799/24131830/2026/5/5139

Porous particle effective thermal conductivity under torrefaction conditions

Relevance. Currently, the technology of low-temperature pyrolysis of biomass, including waste from woodworking and logging (wood pellets), is being developed. In this relation the mathematical models of the carbon-containing particles torrefaction in a gas stream are being developed and investigated. One of the tasks that arise in mathematical modeling is the choice of a method for calculating the thermal conductivity of porous wood pellets subjected to thermochemical processing in a gas stream at temperatures from 300 to 1000 K. A significant number of studies are devoted to the investigation and development of methods for calculating heat transfer in porous bodies. Many models of thermal conductivity of porous bodies have been proposed, based on five main models: parallel model, sequential model, two variants of the Maxwell–Aiken model, and efficient medium model. The following formulas are used in the Russian scientific community: G.N. Dulnev, N.Y. Taits, L.A. Brovkin, V.I. Odelevsky. Aim. To perform a comparative analysis of formulas for calculating the coefficient of effective thermal conductivity of porous bodies under conditions of wood pellets torrefaction, taking into account the effect of radiative heat transfer in the pores, to develop the recommendations on the choice of formulas. Object. Torrefied wood pellets. Methods. Mathematical modeling, comparative analysis. Results and conclusions. The basis for choosing the formula for calculating the effective thermal conductivity coefficient should be experimental data on the porosity of bodies and pore sizes, as well as on the thermal conductivity of porous bodies in the temperature range corresponding to the process under study. In the absence of such data, it is recommended to use the equation corresponding to the parallel model of a porous body, adjusted for radiative heat transfer according to L.A. Brovkin method.

Popov S.K., Valineeva A.A., Borissova N.G. Porous particle effective thermal conductivity under torrefaction conditions. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 2026, vol. 337, no. 5, pp. 63-73. https://doi.org/10.18799/24131830/2026/5/5139

Keywords:

Wood pellets, torrefaction, low-temperature pyrolysis, effective thermal conductivity, porous materials

Authors:

Stanislav K. Popov

Anna A. Valineeva

Nina G. Borissova

References:

1. Bergman P.C A., Kiel J.H.A. Torrefaction for biomass upgrading. Proceedings of the 14th European Biomass Conference and Exhibition. Paris, France, 17–21 October 2005. Available at: https://www.researchgate.net/publication/228699171_Torrefaction_for_biomass_upgrading#fullTextFileContent (date of request: 14 April 2025).

2. Panwar N.L., Divyangkumar N. An overview of recent advancements in biomass torrefaction. Environ Dev Sustain, 2024. DOI: 10.1007/s10668-024-05623-0

3. Valineeva A.A. Improving the efficiency of granular biofuel torrefaction plants based on the study of its low-temperature pyrolysis. Cand. Diss. Moscow, 2024. 20 p. (In Russ.)

4. Zaichenko V.M. Thermal effects during the torrefaction of plant biomass. Experiment and mathematical modeling. Thermal Power Engineering, 2023, no. 5, pp. 31–39. (In Russ.)

5. Astafyev A.V. Substantiation of the conditions for the implementation of autothermal pyrolysis of organic biomass in relation to heat technology equipment. Cand. Diss. Tomsk, 2021. 179 p. (In Russ.) Available at: https://portal.tpu.ru/portal/pls/portal/!app_ds.ds_view_bknd.download_doc?fileid=8554 (accessed: 14 April 2025).

6. Wardach-Swiecicka I., Kardaś D. Modelling thermal behaviour of a single solid particle pyrolysing in a hot gas flow. Energy, 2021, 221, 119802. DOI: 10.1016/j.energy.2021.119802

7. Assoumani N., Simon-Wagner M., Kidani-Sahban F., Tagne Tagne A., El Marouani M., Obounou Akong M.B., Rogaume Y., Girods P., Zoulalian A. Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool. Sustainability, 2021, vol. 13, 13892. DOI: 10.3390/su132413892

8. Popov S.K., Valineeva A.A., Serikov E.A. A model of heat and mass transfer during pyrolysis of a carbon-containing particle in a gas stream. Industrial Power engineering, 2023, no. 5, pp. 2–9. (In Russ.) DOI: 10.34831/EP.2023.20.83.001

9. Valineeva A.A., Popov S.K. Thermal engineering and chemical kinetics of the torrefaction process of wood pellets. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 2024, vol. 335, no. 10, pp. 87–100. (In Russ.) DOI: 10.18799/24131830/2024/10/4498

10. Hersel P., Orhon A., Jóźwik M., Kardaś D. 2D model of a biomass single particle pyrolysis – analysis of the influence of fiber orientation on the thermal decomposition process. Sustainability, 2025, vol. 17, 279. DOI: 10.3390/su17010279

11. Odelevsky V.I. Calculation of generalized conductivity of heterogeneous systems. Journal of Technical Physics, 1951, vol. 21, no. 6, pp. 667–677. (In Russ.)

12. Dulnev G.N., Zarichnyak Yu.P. Thermal conductivity of mixtures and composite materials. Leningrad, Energiya Publ.,1974. 264 p. (In Russ.)

13. Taits N.Y. Steel heating technology. Moscow, Metallurgizdat Publ., 1962. 568 p. (In Russ.)

14. Brovkin L.A. Temperature fields of bodies during heating and melting in industrial furnaces. Ivanovo, IEI Publ., 1973. 364 p. (In Russ.)

15. Jianfeng W., James K.C., Mike F.N., Donald J.C. A new approach to modelling the effective thermal conductivity of heterogeneous materials. International Journal of Heat and Mass Transfer, 2006, vol. 49, pp. 3075–3083. DOI: 10.1016/j.ijheatmasstransfer.2006.02.007

16. Brailsford A.D., Major K.G. The thermal conductivity of aggregates of several phases including porous materials. British Journal of Applied Physics, 1964, vol. 15, pp. 313–319. DOI: 10.1088/0508-3443/15/3/311

17. Zimmerman R.W. Thermal conductivity of fluid-saturated rocks. Journal Petroleum Science and Engineering, 1989, no. 3, pp. 219–227. DOI: 10.1016/0920-4105(89)90019-3

18. Del Rio J.A., Zimmerman R.W., Dawe R.A. Formula for the conductivity of a two-component material based on the reciprocity theorem. Solid State Communications, 1998, vol. 106, no. 4, pp. 183–186. DOI: 10.1016/s0038-1098(98)00051-9

19. Hashin Z., Shtrikman S. A variational approach to the theory of the effective magnetic permeability of multiphase materials. Journal of Applied Physics, 1962, vol. 33, no. 10, pp. 3125–3131. DOI: 10.1063/1.1728579

20. Danilov V.A. Modeling of thermal processes in porous materials and studies of their thermal and hydrodynamic characteristics. Cand. Diss. Kazan, 2012. 16 p. (In Russ.)

21. Kirsanov Yu.A. Modeling of thermophysical processes. St Petersburg, Polytechnic Publ., 2022. 229 p. (In Russ.) DOI: 10.25960/7325-1192-5

22. Krylova O.B. Improving the operating modes of thermal furnaces for heating bulk tanks. Cand. Diss. Leningrad, 1988. 16 p. (In Russ.)

23. Gusenkova N.P. Improvement of heating modes of bulk tanks in thermal furnaces. Cand. Diss. Ivanovo, 2000. 23 p. (In Russ.)

24. Shen Du, Dawson Li, Meng-Jie Li, Ya-Ling He. Numerical study on the effective thermal conductivity and thermal tortuosity of porous media with different morphologies. Science China Technological Sciences, 2024, vol. 67 (6). DOI: 10.1007/s11431-023-2481-4

25. Wang M., Pan N. Modeling and prediction of the effective thermal conductivity of random open-cell porous foams. International Journal of Heat and Mass Transfer, 2008, vol. 51, pp. 1325–1331. DOI: 10.1016/j.ijheatmasstransfer.2007.11.031

26. Fiedler T., Pesetskaya E., Öchsner A., Grácio J. Calculations of the thermal conductivity of porous materials. Materials Science Forum, 2006, vol. 514–516, pp. 754–758. DOI: 10.4028/www.scientific.net/msf.514-516.754

27. Perevezentsev G.A. Improving the energy efficiency of heating furnaces when heating bulk tanks. Cand. Diss. Ivanovo, 2022. 20 p. (In Russ.)

28. Miller R.S., Bellan J. A generalized biomass pyrolysis model based on superimposed cellulose, hemicellulosic and lignin kinetics. Combust Sci Technol, 1997, vol. 126, pp. 97–137. DOI: 10.1080/00102209708935670

29. Glazov V.S., Abdulkerimov S.A., Purdin M.S., Aliev K.B. Determination of thermophysical properties of porous translucent bodies. Collection of materials of the Ninth International School of Thermophysics. Thermophysical research and measurements in quality control of substances, materials and products. Dushanbe, October 6–11, 2014. Dushanbe, Khoji Hassan LLC Publ., 2014. pp. 88–97. (In Russ.)

30. Glazov V.S., Gorelov M.V., Yurkina M.Yu. Determination of the thermophysical properties of a translucent porous plate when heated by radiation. Actual problems of drying and thermal moisture treatment of materials in various industries and the agro-industrial complex. Collection of scientific articles of the First International Lykov Scientific Readings. Moscow, September 22–23, 2015. Kursk, CJSC "University Book" Publ., 2015. pp. 466–469. (In Russ.)

31. Wu S.K. Improving the efficiency of a high-temperature heat technology installation by means of vortex heat exchange intensifiers in the channels of an external fence. Cand. Diss. Moscow, 2021. 19 p. (In Russ.)

32. Dulnev G.N. Heat transfer through solid disperse systems. J. Eng. Phys. Thermophys, 1965, vol. 9, no. 3, pp. 275–279.

33. Suleymanov M.G., Bukhmirov V.V. Investigation of the effect of porosity and container type on the temperature field of heated cages. Bulletin of IGEU, 2017, no. 5, pp. 5–10. (In Russ.) DOI: 10.17588/2072-2672.2017.5.005-010