Numerical modelling of anaerobic digestion reactor dynamics with a delay

Khan, Ashfaq A ; Shepherd, John J ; Stacey, Andrew J

ANZIAM Journal, Tome 56 (2016), / Harvested from Australian Mathematical Society

Résumé

Anaerobic digestion of municipal and animal wastes provides a potentially important means of producing energy sustainably. The reliable production of methane from anaerobic digestion requires that bacteria metabolise municipal and agricultural wastes to produce mainly carbon dioxide and methane. Our model uses Monod based kinetics and is complex since the biomass concentration growth is inhibited with the increase in substrate. The production of methane depends on the number of methanogenic bacteria; there is evidence from previous chemostats experiments that there is a time delay in population number of these cells to respond to changes in substrate concentrations. In this article we focus on determining the dynamical response of the methane production rate under different dynamics of feed conditions and temperatures. Since there is a delay in the methane bacteria mass response, we include the effects of the delay on the dynamics of the system based on modification of kinetics in a simple fermentation anaerobic model. We compare the dynamics of the system with and without delay to show the contribution of delay to the overall stability of the system. References O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer. Dynamical model development and parameter identification for an anaerobic wastewater treament process. Biotechnol. Bioeng. 75:424–438, 2001. doi:10.1002/bit.10036 T. F. Thingstad and T. I. Langeland. Dynamics of chemostat culture: The effect of a delay in cell response. J. Theor. Biol., 48:149–159, 1974. doi:10.1016/0022-5193(74)90186-6 J. R. Beddington and R. M. May. Time delays are not nessarily destabilizing. Math. Biosci. 27:109–119, 1975. doi:10.1016/0025-5564(75)90028-0 K. Y. San and G. Stephanopoulos. The effect of growth rate delays in substrate-inhibited kinetics on the optimal profile of fed-batch reactors. J. Theor. Biol. 28:356–361, 1986. doi:10.1002/bit.260280308 G. Stephanopoulos and K. Y. San. Studies on-line bioreactor identification. I. Theory. Biotechnol. Bioeng. 26:1176–1188, 1984. doi:10.1002/bit.260261006 A. A. Khan, A. J. Stacey and J. J. Shepherd. Optimization of methane output for an anaerobic waste digester. ANZIAM J. 54:C523–C539, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6322 J. F. Andrews. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng. 10:707–723, 1968. doi:10.1002/bit.260100602 D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzzhni, S. G. Pavlostathis, A. Rozzi, W. T. M. Sanders, H. Siegrist, and V. A. Vavilin. Anaerobic digestion model No. 1 (ADM1). Water Sci. Technol. 45(10):65–73, 2002 http://wst.iwaponline.com/content/45/10/65 K. J. Beers. Numerical methods for chemical engineering: Applications in Matlab. Cambridge, New York, USA, 2007. http://www.cambridge.org/us/academic/subjects/engineering/chemical-engineering/numerical-methods-chemical-engineering-applications-matlab J. F. Andrews. The development of a dynamic model and control strategies for the anaerobic digestion process. In Mathematical Models in Water Pollution Control, A. James (ed). Wiley, 1978. A. W. Bush and A. E. Cook. The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater J. Theor. Biol. 63:385–395, 1976. doi:10.1016/0022-5193(76)90041-2 L. F. Shampine, I. Gladwell and S. Thompson. Solving ODEs with Matlab. Cambridge, New York, USA, 2003. http://www.cambridge.org/us/academic/subjects/mathematics/numerical-analysis/solving-odes-matlab?format=PB

Détail

Publié le : 2016-01-01
DOI : https://doi.org/10.21914/anziamj.v57i0.10474