A Process-Based Mathematical Model on Methane Production with Emission Indices for Control
In this paper, a process-based mathematical model is developed for the production of methane through biodegradation. It is a three-dimensional model given by ordinary differential equations. The results of the analysis of the model are interpreted through three emission indices, which are introduced for the first time. The estimation of either one or all of them can interpret the feasibility of the equilibrium and the long-term emission tendency of methane. The vulnerability of the methane production process with respect to soil temperature effects in methanogenic phase has been discussed and a feasible condition within a specified temperature range has defined for the nonvulnerability of the methane production process and also it has shown that under the same condition, zero-emission process of methane will be nonvulnerable with respect to the soil temperature effects in methanogenic phase. Lastly, condition for zero emission of methane is also obtained and it is interpreted through the emission indices.
KeywordsStability Basin of attraction Methanogenesis Nonvulnerability Monod type-2 kinetics Liapunov function
Unable to display preview. Download preview PDF.
- AGU—American Geophysical Union, 2002. Control Of Methane Emission Would Reduce Both Global Warming and Pollution, Researchers Find. News Oct.9.http://www.agu.org/sci_soc/prrl/prrl023.html.
- Balch, W.E., Fox, G.E., Magrum, L.J., Woese, C.R., Wolfe, R.S., 1979. Methanogenesis: Reevaluation of a unique biological group. Microbiol. Rev. 43, 260–296.Google Scholar
- Berthouex, P.M., Brown, L.C., 1994. Statistics for Environmental Engineers. Lewis, Boca Raton, FL.Google Scholar
- Chakraborty, A., Bhattacharaya, D.K., 2005. A process based model on methane emission with its oxidation process from rice fields and corresponding control indices, J. Environ. Model. Assess (in revision).Google Scholar
- Dlugokencky, E.J., Masarie, K.A., Lang, P.M., Tans, P.P., 1998. Continuing decline in the growth rate of the atmospheric methane burden. Nature 393 (6684), 447–450.Google Scholar
- Down To Earth, 1995. A Lot of Gas Produced From Paddy Fields. Science and Technology Editorial Report, February 28, India.Google Scholar
- Endo, G., Noike, T., Matsumoto, J., 1983. Effect of temperature and pH on acidogenic phase in anaerobic digestion. Proc. Jpn. Soc. Civil Eng. 330, 49–57.Google Scholar
- EPA, 1999. Inventory of Greenhouse Gas Emissions and Sinks 1990–1997. Office of Policy, Planning and Evaluation, U.S. Environmental Protection Agency, Washington, DC, http://www.epa.gov/globalwarming/inventory/index.html.
- Goh, B.S., 1977. Global stability in many species systems. Emerg. Nat. III, 135–143.Google Scholar
- Goh, B.S., 1980. Management and Analysis of Biological populations. Elsevier Scientific, New York.Google Scholar
- IPCC—Intergovernmental Panel On Climate Change, 1996. XII. Summary for policymakers. In: Houghton, J.T., Meira- Filho, L.G., Chancellor, B.A., Kattenberg, A., Maskell, K. (Eds.), Climate Change 1995: The Scientific Basis of Climate Change. Cambridge University Press, Cambridge, UK, 572 pp.Google Scholar
- Keisuke, H., Tastsuya, N., Matsumoto, J., 1985. Mathematical Modeling of The Anaerobic Digestion Process: Mathematical Models in Biological Waste Water Treatment: Develpments in Environmental Modeling, vol. 7. Elesevier, New York, pp. 583–634.Google Scholar
- Kropff, M.J., Matthews, R.B., VanLaar, H.H., TenBerge, H.F.M., 1995. The rice model ORYZAI and its testing. In: Matthews, R.B., Kropff, M.J., Bachelet, D., VanLaar, H.H. (Eds.), Modeling the Impact of Climate Change on Rice-Production in Asia. CAB International, Oxon, UK, pp. 27–50.Google Scholar
- Lawrence, A.W., McCarty, P.L., 1969. Kinetics of methane fermentation in anaerobic treatement. J. Water Pollut. Control Fed. 41, R1–R17.Google Scholar
- Nagumo, N., 1942. Uber die Lage der Integrakurven gewonlicher Differantialgleichungen. Proc. Phys. Math. Soc. Jpn. 24, 551.Google Scholar
- Neue, H.U., Roger, P.A., 1993. Rice agriculture factors controlling emissions. In: Khalil, M.A.K. (Ed.), Atmospheric Methane: Sources, Sinks, and Role in Global Change, NATO ASI Series. Springer-Verlag, Berlin, pp. 254–298.Google Scholar
- O'Rourke, J.T., 1968. Kinetics of anaerobic treatment at reduced temperatures. Thesis presented to Stanford University in partial fulfillment of the requirement for the degree of Doctor of Philosophy: Cited by Lawrence A. W. 1971. Application of process kinetics to design of anaerobic processes. Adv. Chem. Ser. 105, 163–189.Google Scholar
- Speece, R.E., McCarty, P.L., 1962. Nutrient requirement and biological solids accumulation in anaerobic digestion. Proc. First Int. Conf. Water Pollut. Res. 2, 305–322.Google Scholar
- Toerien, D.F., Hattingh, W.H.J., 1969. Anaerobic digestion-I. The microbiology of anaerobic digestion. Water Res. 3, 385–416.Google Scholar
- Wackett, L., Jian Ma, 2000. Methanogenesis Pathway Map, University of Minnesota, USA, http://umbbd:ahc.umn.edu/C1cyc/C1cyc_map.html.
- Wang, B., 1995. Effects of Rice Cultivars on Dial and Seasonal Methane Emission, PhD thesis, University of the Philippines, Los Banos, Philippines, 130 pp.Google Scholar
- Yuexin, L., 1996. Modeling the Emissions of Nitrous Oxide (N2O) and Methane (CH4) From the Terrestrial Biosphere to the Atmosphere, PhD thesis, Department Of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA.Google Scholar
- Zeikus, J.G., 1977. The biology of methanogenic bacteria. Bacteriol. Rev. 41, 514–541.Google Scholar