Nonlinear Analysis of Integrated Kinetics and Heat Transfer Models of Slow Pyrolysis of Biomass Particles using Differential Transformation Method
AbstractThe inherent nonlinearities in the kinetics and heat transfer models of biomass pyrolysis have led to the applications of various numerical methods in solving the nonlinear problems. However, in order to have physical insights into the phenomena and to show the direct relationships between the parameters of the models, analytical solutions are required. In this work, approximate analytical solutions for the nonlinear integrated kinetics and heat transfer of pyrolysis of biomass particle under isothermal and non-isothermal heating conditions are presented using differential transformation method. Also, the results of the analytical solutions are compared with the numerical and experimental results in literature. Good agreements are established between the present results and the past works. Thereafter, parametric studies are carried out on the effects of heating conditions, heating rates, thermo-geometric parameters, boundary conditions, particles shape and size on the pyrolysis kinetics and thermal decomposition of biomass particles. It is therefore expected that this study will enhance the understanding of the pyrolysis by giving physical insights into the various factors and the parameters affecting the thermochemical process.
 Pyle, D. L., and Zaror, C. A., "Heat Transfer and Kinetics in the Low Temperature Pyrolysis of Solids", Chemical Engineering Science, Vol. 39, pp. 147–158, (1984). Bamford, C. H., Crank, J., and Malan, D. H., "The Combustion of Wood Part I", Proceedings of the Cambridge Philosophical Society, Vol. 42, pp. 166–182, (1946). Roberts, A. F., and Clough, G., "Thermal Degradation of Wood in an Inert Atmosphere", In: Proceedings of the Ninth Symposium (International) on Combustion, the Combustion Institute, Pittsburgh, pp. 158–167, (1963). Weatherford, W. D., and Sheppard, D. M., "10th int. Symposium on Combustion", the Combustion Institute, Pitts, pp. 897, (1965). Tinney, E. R., "The Combustion of Wood Dowels in Heated Air", In: Proceedings of the 10th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 925–930, (1965). Matsumoto, T., Fujiwara T., and Kondo, J., "12th int. Symposium on Combustion, the Combustion Institute, Pitts, pp. 515, (1969). Roberts, A. F., "13th Int. Symposium on Combustion, the Combustion Institute, Pitts, pp. 893, (1971). Kung, H. C., "A Mathematical Model of Wood Pyrolysis", Combustion and Flame, Vol. 18, pp. 185–195, (1972), Maa, P. S., and Bailie, R. C., "Combustion Science and Technology", Vol. 7, pp. 257, (1973). Kansa, E. J., Perlee H. E., and Chaiken, R., "Mathematical Model of Wood Pyrolysis Including Internal Forced Convection, Combustion and Flame, Vol. 29, pp. 311–324, (1977), Chan, W. R., Kelbon, M., and Krieger, B. B., "Modeling and Experimental Verification of Physical and Chemical Processes during Pyrolysis of Large Biomass Particle", Fuel 64, pp. 1505–1513, (1985), Koufopanos, C. A., Papayannakos, N., Maschio, G., and Lucchesi, A., "Modelling of the Pyrolysis of Biomass Particles, Studies on Kinetics, Thermal and Heat Transfer e4ects, the Canadian Journal of Chemical Engineering, Vol. 69, pp. 907–915, (1991), Lee, C. K., Chaiken, R. F., and Singer, J. M., "Charring Pyrolysis of Wood in 0res by Laser Simulation", In: Proceedings of the 16th Symposium (International) on Combustion, the Combustion Institute, Pittsburgh, pp. 1459–1470, (1976). Miyanami, K., Fan, L. S., Fan L. T., and Walawender, W. P., "A Mathematical Model for Pyrolysis of a Solid Particle Effects of the Heat of Reaction", the Canadian Journal of Chemical Engineering, Vol. 55, pp. 317–325, (1977). Fan, L. T., Fan, L. S., Miyanami, K., Chen, T. Y., and Walawender. W. P., "A mathematical Model for Pyrolysis of a Solid Particle Effects of the Lewis Number", the Canadian Journal of Chemical Engineering, Vol. 55, pp. 47–53, (1977). Simmons, G. M., and Gentry, M., "Particle Size Limitations Due to Heat Transfer in Determining Pyrolysis Kinetics of Biomass", J. Anal. and Appl. Pyrolysis, Vol. 10, pp. 117-127, (1986). Villermaux, J., Antoine, B., Lede, J., and Soulignac, F., "A New Model for Thermal Volatilization of Solid Particles undergoing Fast Pyrolysis", Chemical Engineering Science, Vol. 41, pp. 151–157, (1986). Di Blasi, C., "Analysis of Convection and Secondary Reaction Effects within Porous Solid Fuels undergoing Pyrolysis", Combustion Science and Technology, Vol. 90, pp. 315–340. (1993). Melaaen, M. C., and Gronli, M. G., "Modeling and Simulation of Moist Wood Drying and Pyrolysis", In: Bridgwater, A.V., Boocock, D.B.G. (Eds.), Developments in Thermochemical Biomass Conversion, Blackie, London, pp. 132–146, (1997). Jalan, R. K., and Srivastava, V. K., "Studies on Pyrolysis of a Single Biomass Cylindrical Pellet–kinetic and Heat Transfer Effects", Energy Conversion and Management, Vol. 40, pp. 467–494, (1999). Ravi, M. R., Jhalani, A., Sinha, S., and Ray, A., "Development of a Semi-empirical Model for Pyrolysis of an Annular Sawdust Bed", Journal of Analytical and Applied Pyrolysis, Vol. 71, pp. 353-374, (2004). Babu, B. V., and Chaurasia, A. S., "Modeling for Pyrolysis of Solid Particle: Kinetics and Heat Transfer Effects", Energy Conversion and Management, Vol. 44, pp. 2251–2275, (2003), Sheth, P. N., and Babu, B. V., "Kinetic Modeling of the Pyrolysis of Biomass National Conference on Environmental Conservation, Pilani, India, pp. 453-458, (2006). Yang, Y. B., Phan, A. N., Ryu, C., Sharifi, V., and Swithenbank, J., "Mathematical Modelling of Slow Pyrolysis of Segregated Solid Wastes in a Packed-bed Pyrolyser Elsevier Journal of Fuel, (2006). Mandl, C., Obernberger, I., and Biedermann, F., "Updraft fixed-bed Gasification of Softwood Pellets: Mathematical Modelling and Comparison with Experimental Data In: Proceedings of the 17, European Biomass Conference & Exhibition Hamburg, Italy, (2009). Weerachanchai, P., Tangsathitkulchai, C., and Tangsathitkulchai, M., "Comparison of Pyrolysis Kinetic Model for Thermogravimetric Analysis of Biomass", Suranree Journal of Tecnologies, Vol. 17, No. 4, pp. 387-400, (2010). Slopiecka, K., Bartocci, P., and Fantozzi, F., "Thermogravimetric Analysis and Kinetic Study of Poplar Wood Pyrolysis", 3rd International Conference on Applied Energy, Perugia, Italy, pp. 1687-1698, (2011). Gauthier, G., Melkior, T., Salvador, S., Corbetta, M., Frassoldati, A., Pierucci, S., Ranzi, E., Bennadji, H., and Fisher, E.M., "Pyrolysis of Thick Biomass Particles: Experimental and Kinetic Modelling", Chemical Engineering Transactions, Vol. 32, (2013). Suriapparao, D. V., and Vinu, R., "Effects of Biomass Particle Size on Slow Pyrolysis Kinetics and Fast Pyrolysis Product Distribution", Waste Biomass Valorization, (2017). Bennadji, H., "Low-Temperature Pyrolysis of Woody Biomass in the Thermally Thick Regime", Energy & Fuels, Vol. 27, No. 3, pp. 1453-1459, (2013). Ranzi, E., "Comprehensive and Detailed Kinetic Model of a Traveling Grate Combustor of Biomass", Energy and Fuels, Vol. 25, No. 9, pp. 4195-4205, (2011). Park, W.C., Atreya, A., and Baum, H.R., "Experimental and Theoretical Investigation of Heat and Mass Transfer Processes during Wood Pyrolysis", Combustion and Flame, Vol. 157, No. 3, pp. 481-494, (2010). Norinaga, K., et al. "Detailed Chemical Kinetic Modelling of Vapour-phase Cracking of Multi-component Molecular Mixtures Derived from the Fast Pyrolysis of Cellulose", Fuel, Vol. 103, pp. 141-150, (2013). Ranzi, E., "Hierarchical and Comparative Kinetic Modeling of Laminar Flame Speeds of Hydrocarbon and Oxygenated Fuels", Progress in Energy and Combustion Science, Vol. 38, No. 4, pp. 568-501, (2012). Gentile, G., Eduardo, P., Debiagi, A., Cuoci, A., Frassoldati, E., Ranzi, T., and Faravelli, A., "Computational Framework for the Pyrolysis of Anisotropic Biomass Particles", Chemical Engineering Journal, Article in Press, (2017). Anca-Couce, A., "Reaction Mechanisms and Multi-scale Modelling of Lignocellulosic Biomass Pyrolysis", Progress in Energy and Combustion Science, Vol. 53, pp. 41-79, (2016). Mettler, M.S., Vlachos, D.G., and Dauenhauer, P.J., "Top Ten Fundamental Challenges of Biomass Pyrolysis for Biofuels", Energy & Environmental Science 5, pp. 7797-7809, (2012). Cuoci, A., Frassoldati, T., Faravelli, E., and Ranzi, A., "Computational Tool for the Detailed Kinetic Modeling of Laminar Flames: Application to C2H4/CH4 Coflow Flames", Combustion and Flame, Vol. 160, pp. 870-886, (2013). Cuoci, A., Frassoldati, T., Faravelli, E., and Ranzi, "Open SMOKE++: An Object-oriented Framework for the Numerical Modeling of Reactive Systems with Detailed Kinetic Mechanisms", Computer Physics Communications, Vol. 192, pp. 237-264, (2015). Maffei, T., Gentile, G., Rebughini, S., Bracconi, M., Manelli, F., Lipp, S., Cuoci, A., and Maestri, M., "A Multiregion Operator-splitting CFD Approach for Coupling Microkinetic Modeling with Internal Porous Transport in Heterogeneous Catalytic Reactors", Chemical Engineering Journal, Vol. 283, pp. 1392-1404, (2016). Blondeau, J., and Jeanmart, H., "Biomass Pyrolysis at High Temperatures: Prediction of Gaseous Species Yields from an Anisotropic Particle", Biomass and Bioenergy, Vol. 41, pp. 107-121, (2012). Gronli, M., "A Theoretical and Experimental Study of the Thermal Conversion of Biomass", PhD Thesis, NTNU, Trondheim, (1996). Bennadji, H., Smith, K., Shabangu, S., and Fisher, E.M., "Low-temperature Pyrolysis of Woody Biomass in the Thermally Thick Regime, Energy & Fuels, Vol. 27, pp. 1453-1459, (2013). Corbetta, M., Frassoldati, A., Bennadji, H., Smith, K., Serapiglia, M.J., Gauthier, G., Melkior, T., Ranzi, E., and Fisher, E.M., "Pyrolysis of Centimeter-scale Woody Biomass Particles: Kinetic Modeling and Experimental Validation, Energy & Fuels, Vol. 28, pp. 3884-3898, (2014). Gauthier, G., "Syntesis of Second Generation Biofuels: Study of Pyrolysis of Centimeter-scale Wood Particles at High Temperature", Univerisite de Toulouse, (2013). Gauthier, G., Melkior, T., Grateau, M., Thiery, S., and Salvador, S., "Pyrolysis of Centimetre-scale Wood Particles: New Experimental Developments and Results", Journal of Analytical and Applied Pyrolysis, Vol. 104, pp. 521-530, (2013). Paulsen, A.D., Hough, B.R., Williams, C.L., Teixeira, A.R., Schwartz, D.T., Pfaendtner, J., and Dauenhauer, P.J., "Fast Pyrolysis of Wood for Biofuels: Spatiotemporally Resolved Diffuse Reflectance in Situ Spectroscopy of Particles", ChemSusChem, Vol. 7, pp. 765-776, (2014). Ranzi, E., Cuoci, A., Faravelli, T., Frassoldati, A., Migliavacca, G., Pierucci, S., and Sommariva, S., "Chemical Kinetics of Biomass Pyrolysis", Energy & Fuels, Vol. 22, pp. 4292-4300, (2008). Debiagi, P.E.A., Pecchi, C., Gentile, G., Frassoldati, A., Cuoci, A., Faravelli, T., and Ranzi, E., "Extractives Extend the Applicability of Multistep Kinetic Scheme of Biomass Pyrolysis", Energy & Fuels, Vol. 29, pp. 6544-6555, (2015). Debiagi, P.E.A., Gentile, G., Pelucchi, M., Frassoldati, A., Cuoci, A., Faravelli, T., and Ranzi, E., "Detailed Kinetic Mechanism of Gas-phase Reactions of Volatiles Released from Biomass Pyrolysis", Biomass and Bioenergy, Vol. 93, pp. 60-71, (2016). Zaror, C. A., "Studies of the Pyrolysis of Wood at Low Temperatures", PhD. Dissertation, University of London", (1982). Ojolo, S. J., Osheku, C. A., and Sobamow, M. G., "Analytical Investigations of Kinetic and Heat Transfer in Slow Pyrolysis of a Biomass Particle", Int. Journal of Renewable Energy Development, Vol. 2, No. 2, pp. 105-115, (2013). Sobamowo, M.G., Ojolo, S. J., Osheku, C. A., and Kehinde, A. J., "Heat Transfer Analysis in Pyrolysis of Different Shapes Biomass Particles Subjected to Different Boundary Conditions", Integral Transform Methods,Journal of Heat and Mass Transfer Research, Article in Press. Bidabadi, M., Mostafavi, S. A., Dizaji, F. F., and Dizaji. B. H., "An Analytical Model for Flame Propagation through Moist Lycopodium Particles with Non-unity Lewis Number [J]. International Journal of Engineering, Vol. 27, No. 5, pp. 793−802, (2014). Dizaji, B. H., and Bidabadi, M., "Analytical Study about the Kinetics of Different Processes in Pyrolysis of Lycopodium Dust [J]. Journal of Fuel and Combustion, Vol. 6, No. 2, pp. 13−20, (2014), (in Persian) Lédé,, J., and Authier, O., "Temperature and Heating rate of Solid Particles undergoing a Thermal Decomposition", which Criteria for Characterizing Fast Pyrolysis Journal of Analytical and Applied Pyrolysis, Vol. 113, pp. 1-14, (2015). Font, R., Marcilla, A., Verdu, E., and Devesa, J., "Kinetics of the Pyrolysis of Almond Shells and Almond Shells Impregnated with COCl2 in a Fluidized Bed Reactor and in a Pyroprobe 100, Industrial and Engineering Chemistry Research, Vol. 29, pp. 1846–1855, (1990). Shafizadeh, F., and Chin, P.P.S., "Thermal Deterioration of Wood", ACS Symposium Series Vol. 43, pp. 57–81, (1977). Thurner, F., and Mann, U., "Kinetic Investigation of Wood Pyrolysis", Industrial and Engineering Chemical Process Design and Development, Vol. 20, pp. 482–488, (1981). Janse, A.M.C., Westerhout, A.M.C., and Prins, W., "Modelling of Flash Pyrolysis of a Single Wood Particle", Chemical Engineering and Processing, Vol. 39, pp. 239-252, (2000). Srivastava, V. K., Sushil and Jalan, R. K., "Prediction of Concentration in the Pyrolysis of Biomass Materials-II", Energy Conversion and Management, Vol. 37, No. 4, pp. 473-483, (1996). Liden, C. K., Berruti, F., and Scott, D. S., "A Kinetic Model for the Production of Liquids from the Flash Pyrolysis of Biomass", Chem. Eng. Commun, Vol. 65, pp. 207–221, (1988). Prakash, N., and Karunanithi, T., "Kinetic Modelling in Biomass Pyrolysis a Review", Journal of Applied Sciences Research, Vol. 4, No. 12, pp. 1627-1636, (2008), Branca, C., and Di Blasi, C., "Kinetics of the Isothermal Degradation of Wood in the Temperature Range, 528-708 K. Journal of Analytical and Applied Pyrolysis, Vol. 67, pp. 207-219, (2003), Holman, J. P., "Heat Transfer", Sixth Edition, McGraw-Hill Book Company, (1986). Zhou, J.K., "Differential Transformation and its Applications for Electrical Circuits", Huazhong University Press, Wuhan, China, (1986). (in Chinese). Sobamowo, M. G., "Nonlinear Analysis of Flow-induced Vibration in Fluid-conveying Structures using Differential Transformation Method with Cosine-after Treatment Technique", Transaction of Iranian Society of Mechanical Engineers, Vol. 18, No. 1, pp. 43-63, Publication of Iranian Society of Mechanical Engineers, (2018), Sobamowo, M. G., Jayesimi, L. O., and Waheed, M. A., "Axisymmetric Magneto hydrodynamic Squeezing Flow of Nanofluid in a Porous Medium under the Influence of Slip Boundary Conditions Transport Phenomena in Nano and Micro Scales", Vol. 6, No. 2, pp. 122-132, Publication of University of Sistan and Baluchestan, Iranian Society of Mechanical Engineers, Iran, (2018), Sobamowo, M. G., "Nonlinear Thermal and Flow-induced Vibration Analysis of Fluid-Conveying Carbon Nanotube Resting on Winkler and Pasternak Foundations", Thermal Science and Engineering Progress, Elsevier, Vol. 4, pp. 113-149, (2017). Sobamowo, M. G., "Singular Perturbation and Differential Transform Methods to Two-dimensional Flow of Nanofluid in a Porous Channel with Expanding/contracting Walls Subjected to a Uniform Tranverse Magnetic Field", Thermal Science and Engineering Progress, Vol. 4, pp. 71-84, Elsevier, (2017), Sobamowo, M. G., Ojolo, S. J., and Osheku, C. A., "Analysis of Pyrolysis Kinetics of Biomass Particle under Isothermal and Non-isothermal Heating Conditions using Differential Transformation Method", Global Journal of Research in Engineering, Vol. 17, No. 6, pp. 1-21, Global Journal Inc. USA, (2017). Sobamowo, M. G., Jayesimi, L. O., and Waheed, M. A., "On the Squeezing Flow of Nanofluid through a Porous Medium with Slip Boundary and Magnetic Field: A Comparative Study of Three Approximate Analytical Methods", Global Journal In. USA, Vol. 17, No. 6, pp. 61-67, (2017). Adeleye, O. A., Olawale, O. L., and Sobamowo, M. G., "Prediction of Phagocyte Transmission for Foreign Body Responses to Subcutaneous Biomaterial Implantations using Differential Transform Method", Journal of Biomimetrics, Biomaterials and Biomedical Engineering, Vol. 32, pp. 98-114, Trans Tech Publications, Switzerland, (2017). Holman, J. P., "Heat Transfer", Sixth Edition, McGraw-Hill Book Company, (1986).