The Semenov formulation of the biological self-heating process in compost piles

Thiansiri Luangwilai, Havinder Sidhu, Mark Nelson, Dong Chen


We formulate and investigate a uniformly distributed mathematical model (based upon Semenov's theory for thermal explosions) for the thermal response of cellulosic materials in compost piles. The model consists of a mass balance equation for oxygen, a heat balance equation, and incorporates the heat release due to biological activity within the pile. Biological heat generation is known to be present in most industrial processes handling large volumes of bulk organic materials. We utilise singularity theory to investigate the generic properties of the model, as well as to determine the locus of different singularities, namely the cusp, isola and double limit point. Singularity theory provides a useful tool to systematically analyse this system. We investigate the conditions where biological activity results in the initiation of an elevated temperature branch within the compost pile.

  • V. Balakotaiah and D. Luss, Global analysis of the multiplicity features of multi-reaction lumped-parameter systems, Chemical Engineering Science, 39, 865--881, 1984.
  • P. C. Bowes, Self-heating: Evaluating and Controlling the Hazards, Elsevier Press, Amsterdam, The Netherlands, 1984.
  • X. D. Chen and D. A. Mitchell, Start-up strategies for self-heating and efficient growth in stirred bioreactors for solid state fermentation, CHEMECA '96, 24th Australian and New Zealand Chemical Engineering Conference, Weiss, G.(ed.), 4(The Institution of Engineering), 111--116, 1996.
  • D. A. Frank--Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, 2nd edition, Plenum Press, New York, USA, 1969.
  • M. Golubitsky and D. Schaeffer, The classification theorem, in Singularities and Groups in Bifurcation Theory, 1st Edition, Vol. 1, Chap. IV, (Springer, Berlin, Germany), 196--202, 1985.
  • W. Hogland, T. Bramryd and I. Persson Physical, biolocical and chemical effects of unsorted fractions of industrial solid waste fuel storage, Waste Management and Research, 32, 21--98, 1996.
  • P. F. Hudak, Spontaneous combustion f shale spoils at sanitary landfill, Waste Management, 22, 687--688, 2001.
  • M. Khanahmadi, R. Roostaazad, A. Safekordi, R. Bozorgmehri and D. A. Mitchell, Investigating the use of cooling surfaces in solid-state fermentation tray bioreactors: modelling and experimentation, Journal of Chemical Techonology and Biotechnology, 79, 1228--1242, 2004.
  • H. Kubler, Heat generating processes as cause of spontaneous ignition in forest products, Forest Products Abstracts, 10, 6299--327, 1987.
  • E. Liwarska-Bizukojc, M. Bizukojc and S. Ledakowicz, Kinetic model for the process of aerobic biodegradation of organic fraction of municipal solid waste, Bioprocess and Biosystems Engineering, 24, 195--202, 2001.
  • T. Luangwilai, H. S. Sidhu, M. I. Nelson and X. D. Chen, Using Singularity Theory to Analyse a Spatially Uniform Model of Self-Heating in Compost Piles, Submitted to East-West Journal of Mathematics, Khon Kaen University, Thailand, 2009.
  • M. I. Nelson , E. Balakrishnan and X. D. Chen, A Semenov model of self-heating in compost piles, Transaction of IChemE Part B: Process Safety and Environmental Protection, 81, 375--383, 2003.
  • M. I. Nelson , H. S. Sidhu and X. D. Chen, A Spatially Uniform Model of Oxidative Self-Heating in Compost Piles, In proceedings of the 35th Australian Chemical Engineering Conference, CHEMECA 2007, 1673--1683, 2007.
  • M. I. Nelson , T. R. Marchant, G. C. Wake, E. Balakrishnan and X. D. Chen, Self-heating in compost piles due to biological effects, Chemical Engineering Science, 62(17), 4612--4619, 2007. doi:10.1016/j.ces.2007.05.018
  • R. Rynk, Fires at composting facilities, BioCycle Magazine, 41(1), 54--58, 2000.
  • N. N. Semenov, Zur theorie des verbrennungsprozesses, Zeitschrift Fur Physik, 48, 571--582, 1928.
  • H. S. Sidhu, M. I. Nelson and X. D. Chen, A simple spatial model for self-heating compost piles, ANZIAM J., 48(CTAC2006), C135--C150, 2007.

Full Text:



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.