This work proposes a mathematical model on partial nitritation/anammox (PN/A) granular bioreactors, with a particular interest in the start-up phase. The formation and growth of granular biofilms is modelled by a spherical free boundary problem with radial symmetry and vanishing initial value. Hyperbolic PDEs describe the advective transport and growth of sessile species inhabiting the granules. Parabolic PDEs describe the diffusive transport and conversion of soluble substrates, and the invasion process mediated by planktonic species. Attachment and detachment phenomena are modelled as continuous and deterministic fluxes at the biofilm-bulk liquid interface. The dynamics of planktonic species and substrates within the bulk liquid are modelled through ODEs. A simulation study is performed to describe the start-up process of PN/A granular systems and the development of anammox granules. The aim is to investigate the role that the invasion process of anaerobic ammonia-oxidizing (anammox) bacteria plays in the formation of anammox granules and explore how it affects the microbial species distribution of anaerobic ammonia-oxidizing, aerobic ammonia-oxidizing, nitrite-oxidizing and heterotrophic bacteria. Moreover, the model is used to study the role of two key parameters in the start-up process: the anammox inoculum size and the inoculum addition time. Numerical results confirm that the model can be used to simulate the start-up process of PN/A granular systems and to predict the evolution of anammox granular biofilms, including the ecology and the microbial composition. In conclusion, after being calibrated, the proposed model could provide quantitatively reliable results and support the start-up procedures of full-scale PN/A granular reactors.
Citation: Fabiana Russo, Alberto Tenore, Maria Rosaria Mattei, Luigi Frunzo. Multiscale modelling of the start-up process of anammox-based granular reactors[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10374-10406. doi: 10.3934/mbe.2022486
This work proposes a mathematical model on partial nitritation/anammox (PN/A) granular bioreactors, with a particular interest in the start-up phase. The formation and growth of granular biofilms is modelled by a spherical free boundary problem with radial symmetry and vanishing initial value. Hyperbolic PDEs describe the advective transport and growth of sessile species inhabiting the granules. Parabolic PDEs describe the diffusive transport and conversion of soluble substrates, and the invasion process mediated by planktonic species. Attachment and detachment phenomena are modelled as continuous and deterministic fluxes at the biofilm-bulk liquid interface. The dynamics of planktonic species and substrates within the bulk liquid are modelled through ODEs. A simulation study is performed to describe the start-up process of PN/A granular systems and the development of anammox granules. The aim is to investigate the role that the invasion process of anaerobic ammonia-oxidizing (anammox) bacteria plays in the formation of anammox granules and explore how it affects the microbial species distribution of anaerobic ammonia-oxidizing, aerobic ammonia-oxidizing, nitrite-oxidizing and heterotrophic bacteria. Moreover, the model is used to study the role of two key parameters in the start-up process: the anammox inoculum size and the inoculum addition time. Numerical results confirm that the model can be used to simulate the start-up process of PN/A granular systems and to predict the evolution of anammox granular biofilms, including the ecology and the microbial composition. In conclusion, after being calibrated, the proposed model could provide quantitatively reliable results and support the start-up procedures of full-scale PN/A granular reactors.
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Fabiana Russo, Alberto Tenore, Maria Rosaria Mattei, Luigi Frunzo. Multiscale modelling of the start-up process of anammox-based granular reactors[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10374-10406. doi: 10.3934/mbe.2022486
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