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Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model

  • Received: 27 May 2020 Accepted: 31 July 2020 Published: 13 August 2020
  • This paper deals with a mathematical analysis of two-steps model of anaerobic digestion process, including dynamics of soluble microbial products (SMP). We propose to investigate effects of the new variable SMP on qualitative properties of the process in different generic cases. Equilibria of the model are graphically established considering qualitative properties of the kinetics and, their stability are proved theoretically and/or verified by numerical simulations. It will shown that the model has a rich qualitative behavior as equilibria bifurcation and multi-stability according to the considered bifurcation parameter.

    Citation: Boumediene Benyahia, Tewfik Sari. Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5504-5533. doi: 10.3934/mbe.2020296

    Related Papers:

  • This paper deals with a mathematical analysis of two-steps model of anaerobic digestion process, including dynamics of soluble microbial products (SMP). We propose to investigate effects of the new variable SMP on qualitative properties of the process in different generic cases. Equilibria of the model are graphically established considering qualitative properties of the kinetics and, their stability are proved theoretically and/or verified by numerical simulations. It will shown that the model has a rich qualitative behavior as equilibria bifurcation and multi-stability according to the considered bifurcation parameter.


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    [1] M. J. Wade, J. Harmand, B. Benyahia, T. Bouchez, S. Chaillou, B. Cloez, et al., Perspectives in mathematical modelling for microbial ecology, Ecol. Model., 321 (2016), 64-74.
    [2] S. Di, A. Yang, Analysis of productivity and stability of synthetic microbial communities, J. R. Soc. Interface, 16 (2019), 20180859.
    [3] T. Sari, M. El Hajji, J. Harmand, The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat, Math. Biosci. Eng., 9 (2012), 627-645.
    [4] M. El Hajji, F. Mazenc, J. Harmand, A mathematical study of a syntrophic relationship of a model of anaerobic digestion process, Math. Biosci. Eng., 7 (2010), 641-656.
    [5] D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzhnyi, S. G. Pavlostathis, A. Rozzi, et al., The IWA Anaerobic Digestion Model No 1 (ADM1), Water Sci. Technol., 45 (2002), 65-73.
    [6] Z. Khedim, B. Benyahia, B. Cherki, T. Sari, J. Harmand, Effect of control parameters on biogas production during the anaerobic digestion of protein-rich substrates, Appl. Math. Model., 61 (2018), 351-376.
    [7] T. Sari, J. Harmand, A model of a syntrophic relationship between two microbial species in a chemostat including maintenance, Math. Biosci., 275 (2016), 1-9.
    [8] T. Sari, M. J. Wade, Generalised approach to modelling a three-tiered microbial food-web, Math. Biosci., 291 (2017), 21-37.
    [9] M. J. Wade, Not Just Numbers: Mathematical Modelling and Its Contribution to Anaerobic Digestion Processes, Processes, 8 (2020), 888.
    [10] D. J. Batstone, D. Puyol, X. Flores-Alsina, R. Jorge, Mathematical modelling of anaerobic digestion processes: applications and future needs, Rev. Environ. Sci. Biotechnol., 14 (2015), 595-613.
    [11] O. Bernard, Z. Hadj-Sadock, D. Dochain, A. Genovesi, J. P. Steyer, Dynamical model development and parameter identification for an anareobic wastewater treatment process, Biotechnol. Bioeng., 75 (2001), 424-438.
    [12] O. Bernard, G. Bastin, On the estimation of the pseudo-stoichiometric matrix for macroscopic mass balance modelling of biotechnological processes, Math. Biosci., 193 (2005), 51-77.
    [13] J. A. Arzate, M. Kirstein, F. C. Ertem, E. Kielhorn, H. R. Malule, P. Neubauer, et al., Anaerobic Digestion Model (AM2) for the Description of Biogas Processes at Dynamic Feedstock Loading Rates, Chem. Ing. Tech., 89 (2017), 686-695.
    [14] V. Alcaraz-González, J. Harmand, A. Rapaport, J. P. Steyer, V. González-Alvarez, C. Pelayo-Ortiz, Software sensors for highly uncertain WWTPs: a new approach based on interval observers, Water Res., 36 (2002), 2515-2524.
    [15] V. Alcaraz-González, J. P. Steyer, J. Harmand, A. Rapaport, V. González-Alvarez, C. Pelayo-Ortiz, Application of a Robust Interval Observer to an Anaerobic Digestion Process, Dev. Chem. Eng. Miner. Process., 13 (2008), 267-278.
    [16] B. Benyahia, T. Sari, B. Cherki, J. Harmand, Bifurcation and stability analysis of a two step model for monitoring anaerobic digestion processes, J. Process Control, 22 (2012), 1008-1019.
    [17] T. Sari, B. Benyahia, The operating diagram for a two-step anaerobic digestion model, preprint, https://hal.inrae.fr/hal-02557464, (2020).
    [18] M. Sbarciog, M. Loccufier, E. Noldus, Determination of appropriate operating strategies for anaerobic digestion systems, Biochem. Eng. J., 51 (2010), 180-188.
    [19] J. Hess, O. Bernard, Design and study of a risk management criterion for an unstable anaerobic wastewater treatment process, J. Process Control, 18 (2008), 71-79.
    [20] N. Dimitrova, M. Krastanov, Nonlinear stabilizing control of an uncertain bioprocess model, Int. J. Appl. Math. Comput. Sci., 19 (2009), 441-454.
    [21] A. Donoso-Bravo, P. Gajardo, M. Sebbah, D. Vicencio, Comparison of performance in an anaerobic digestion process: one-reactor vs two-reactor configurations, Math. Biosci. Eng., 16 (2019), 2447-2465.
    [22] M. Weedermann, Analysis of a model for the effects of an external toxin on anaerobic digestion, Math. Biosci. Eng., 9 (2012), 445-459.
    [23] O. H. Abdelkader, A. H. Abdelkader, Modeling Anaerobic Digestion Using Stochastic Approaches, Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer International Publishing, 99 (2019), 373-396.
    [24] S. Hassam, E. Ficara, A. Leva, J. Harmand, A generic and systematic procedure to derive a simplified model from the Anaerobic Digestion Model No. 1 (ADM1), Biochem. Eng. J., 99 (2015), 193-203.
    [25] B. Benyahia, T. Sari, B. Cherki, J. Harmand, Anaerobic membrane bioreactor modeling in the presence of Soluble Microbial Products (SMP) - the Anaerobic Model AM2b, Chem. Eng. J., 228 (2013), 1011-1022.
    [26] A. Charfi, N. Thongmak, B. Benyahia, M. Aslam, J. Harmand, N. Ben Amar, et al., A modelling approach to study the fouling of an anaerobic membrane bioreactor for industrial wastewater treatment, Bioresour. Technol., 245 (2017), 207-215.
    [27] B. Benyahia, A. Charfi, M. Heran, B. Cherki, N. Kalboussi, J. Harmand, Coupling a simple and generic membrane fouling model with biological dynamics: application to the modeling of an Anaerobic Membrane BioReactor (AnMBR), preprint, https://hal.inrae.fr/hal-02558408, (2020).
    [28] A. Charfi, E. Parka, M. Aslam, J. Kim, Particle-sparged anaerobic membrane bioreactor with fluidized polyethylene terephthalate beads for domestic wastewater treatment: Modelling approach and fouling control, Bioresour. Technol., 258 (2018), 263-269.
    [29] Á. Robles, M. V. Ruano, A. Charfi, G. Lesage, M. Heran, J. Harmand, et al., A review on anaerobic membrane bioreactors (AnMBRs) focused on modelling and control aspects, Bioresour. Technol., 270 (2018), 612-626.
    [30] F. Campillo, M. Chebbi, S. Toumi, Stochastic modeling for biotechnologies: Anaerobic model AM2b, Math. Biol. Environ., 28 (2019), 13-23.
    [31] O. Hadj Abdelkader, Méthodes stochastiques pour la modélisation et l'identification des bioprocédés de digestion anáerobie, Ph.D Thesis, Tlemcen University, 2019.
    [32] G. Bastin, D. Dochain, On-line Estimation and Adaptive Control of Bioreactors, Elsevier, 1990.
    [33] B. Benyahia, Modélisation et Observation des Bioprocédés à Membranes: Application à la digestion anáerobie, Ph.D Thesis, Tlemcen University, 2012.
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