This study develops a two-dimensional, multi-species biofilm model to investigate the influence of environmental factors, specifically temperature and concentrations of oxygen, acetate, and ammonium on nitrogen removal in membrane aerated biofilm reactors (MABRs). The resulting model is a highly nonlinear reaction-diffusion system, explored through computer simulations, and captures microbial interactions, substrate transport, and nitrogen transformations within a biofilm, incorporating the counter-diffusion mechanism. Three nitrogen removal pathways have been examined in this study: nitritation-denitritation (ND), partial nitrification-anammox (PN/A), and conventional nitrification-denitrification (CND). The simulation results show that temperature and concentrations of oxygen and acetate significantly affect nitrogen removal rates and contributions of each pathway. ND dominates under most conditions, while PN/A prevails in oxygen-limited scenarios ($ O_{\infty} = 0.25-0.5\; gm^{-3} $) and co-dominates with ND at moderate oxygen levels ($ O_{\infty} = 0.5-1\; gm^{-3} $). CND is significant only at higher oxygen concentrations ($ O_{\infty} = 5\; gm^{-3} $) with low ammonium ($ N_{1\infty} = 5-15\; gm^{-3} $) and acetate levels ($ A_{\infty} = 6\; gm^{-3} $). Moreover, it has been shown that temperature enhances nitrogen removal primarily by increasing the contribution of anammox. Effective removal rates ($ > 0.1\; g/m^2/d $) occur at $ O_{\infty}\geq 1\; gm^{-3} $ with low to moderate acetate levels ($ A_{\infty} = 6\; gm^{-3} $ to $ < 100\; gm^{-3} $). The simulations further indicate that MABRs can achieve a stable ND nitrogen removal efficiency with biofilm thickness exceeding approximately $ 0.8\; mm $. In this scenario, ammonium-oxidizing bacteria (AOB) and ND denitrifiers outcompete aerobic heterotrophs and nitrite-oxidizing bacteria, resulting in a biofilm structure predominantly composed of AOB and ND denitrifiers. The findings of this study provide valuable insights for optimizing MABR design and operation to achieve energy efficient nitrogen removal.
Citation: Maryam Ghasemi, Sheng Chang. Modeling nitrogen removal in membrane aerated biofilm reactors: the role of nitritation, denitritation, and anammox nitrogen removal[J]. Mathematics in Engineering, 2025, 7(3): 350-383. doi: 10.3934/mine.2025015
This study develops a two-dimensional, multi-species biofilm model to investigate the influence of environmental factors, specifically temperature and concentrations of oxygen, acetate, and ammonium on nitrogen removal in membrane aerated biofilm reactors (MABRs). The resulting model is a highly nonlinear reaction-diffusion system, explored through computer simulations, and captures microbial interactions, substrate transport, and nitrogen transformations within a biofilm, incorporating the counter-diffusion mechanism. Three nitrogen removal pathways have been examined in this study: nitritation-denitritation (ND), partial nitrification-anammox (PN/A), and conventional nitrification-denitrification (CND). The simulation results show that temperature and concentrations of oxygen and acetate significantly affect nitrogen removal rates and contributions of each pathway. ND dominates under most conditions, while PN/A prevails in oxygen-limited scenarios ($ O_{\infty} = 0.25-0.5\; gm^{-3} $) and co-dominates with ND at moderate oxygen levels ($ O_{\infty} = 0.5-1\; gm^{-3} $). CND is significant only at higher oxygen concentrations ($ O_{\infty} = 5\; gm^{-3} $) with low ammonium ($ N_{1\infty} = 5-15\; gm^{-3} $) and acetate levels ($ A_{\infty} = 6\; gm^{-3} $). Moreover, it has been shown that temperature enhances nitrogen removal primarily by increasing the contribution of anammox. Effective removal rates ($ > 0.1\; g/m^2/d $) occur at $ O_{\infty}\geq 1\; gm^{-3} $ with low to moderate acetate levels ($ A_{\infty} = 6\; gm^{-3} $ to $ < 100\; gm^{-3} $). The simulations further indicate that MABRs can achieve a stable ND nitrogen removal efficiency with biofilm thickness exceeding approximately $ 0.8\; mm $. In this scenario, ammonium-oxidizing bacteria (AOB) and ND denitrifiers outcompete aerobic heterotrophs and nitrite-oxidizing bacteria, resulting in a biofilm structure predominantly composed of AOB and ND denitrifiers. The findings of this study provide valuable insights for optimizing MABR design and operation to achieve energy efficient nitrogen removal.
| [1] |
M. Ali, S. Okabe, Anammox-based technologies for nitrogen removal: advances in process start-up and remaining issues, Chemosphere, 141 (2015), 144–153. https://doi.org/10.1016/j.chemosphere.2015.06.094 doi: 10.1016/j.chemosphere.2015.06.094
|
| [2] |
H. E. Al-Hazmi, D. Grubba, J. Majtacz, A. Ziembińska-Buczyńska, J. Zhai, J. Mąkinia, Combined partial denitrification/anammox process for nitrogen removal in wastewater treatment, J. Environ. Chem. Eng., 11 (2023), 108978. https://doi.org/10.1016/j.jece.2022.108978 doi: 10.1016/j.jece.2022.108978
|
| [3] |
S. Jenni, S. E. Vlaeminck, E. Morgenroth, K. M. Udert, Successful application of nitritation/anammox to wastewater with elevated organic carbon to ammonia ratios, Water Res., 49 (2014), 316–326. https://doi.org/10.1016/j.watres.2013.10.073 doi: 10.1016/j.watres.2013.10.073
|
| [4] |
J. G. Kuenen, Anammox bacteria: from discovery to application, Nat. Rev. Microbiol., 6 (2008), 320–326. https://doi.org/10.1038/nrmicro1857 doi: 10.1038/nrmicro1857
|
| [5] |
H. Siegrist, D. Salzgeber, J. Eugster, A. Joss, Anammox brings WWTP closer to energy autarky due to increased biogas production and reduced aeration energy for N-removal, Water Sci. Technol., 57 (2008), 383–388. https://doi.org/10.2166/wst.2008.048 doi: 10.2166/wst.2008.048
|
| [6] |
Y. J. Feng, S. K. Tseng, T. H. Hsia, C. M. Ho, W. P. Chou, Partial nitrification of ammonium-rich wastewater as pretreatment for anaerobic ammonium oxidation (anammox) using membrane aeration Bioreactor, J. Biosci. Bioeng., 104 (2007), 182–187. https://doi.org/10.1263/jbb.104.182 doi: 10.1263/jbb.104.182
|
| [7] |
S. Lackner, H. Horn, Comparing the performance and operation stability of an SBR and MBBR for single-stage nitritation-anammox treating wastewater with high organic load, Environ. Technol., 34 (2013), 1319–1328. https://doi.org/10.1080/09593330.2012.746735 doi: 10.1080/09593330.2012.746735
|
| [8] |
M. Kornaros, S. N. Dokianakis, G. Lyberatos, Partial nitrification/denitrification can be attributed to the slow response of nitrite oxidizing bacteria to periodic anoxic disturbances, Environ. Sci. Technol., 44 (2010), 7245–7253. https://doi.org/10.1021/es100564j doi: 10.1021/es100564j
|
| [9] |
J. Li, M. Feng, S. Zheng, W. Zhao, X. Xu, X. Yu, The membrane aerated biofilm reactor for nitrogen removal of wastewater treatment: Principles, performances, and nitrous oxide emissions, Chem. Eng. J., 460 (2023), 141693. https://doi.org/10.1016/j.cej.2023.141693 doi: 10.1016/j.cej.2023.141693
|
| [10] |
M. Lan, P. Yang, L. Xie, Y. Li, J. Liu, P. Zhang, et al., Start-up and synergistic nitrogen removal of partial nitrification and anoxic/aerobic denitrification in membrane aerated biofilm reactor, Environ. Res., 214 (2022), 113901. https://doi.org/10.1016/j.envres.2022.113901 doi: 10.1016/j.envres.2022.113901
|
| [11] |
M. Li, C. Du, J. Liu, X. Quan, M. Lan, B. Li, Mathematical modeling on the nitrogen removal inside the membrane-aerated biofilm dominated by ammonia-oxidizing archaea (AOA): effects of temperature, aeration pressure and COD/N ratio, Chem. Eng. J., 338 (2018), 680–687. https://doi.org/10.1016/j.cej.2018.01.040 doi: 10.1016/j.cej.2018.01.040
|
| [12] |
S. Matsumoto, A. Terada, S. Tsuneda, Modeling of membrane-aerated biofilm: effects of C/N ratio, biofilm thickness and surface loading of oxygen on feasibility of simultaneous nitrification and denitrification, Biochem. Eng. J., 37 (2007), 98–107. https://doi.org/10.1016/j.bej.2007.03.013 doi: 10.1016/j.bej.2007.03.013
|
| [13] |
B. J. Ni, A. Joss, Z. Yuan, Modeling nitrogen removal with partial nitritation and anammox in one floc-based sequencing batch reactor, Water Res., 67 (2014), 321–329. https://doi.org/10.1016/j.watres.2014.09.028 doi: 10.1016/j.watres.2014.09.028
|
| [14] |
O. Wanner, H. H. Eberl, M. C. M. Van Loosdrecht, E. Morgenroth, D. R. Noguera, C. Picioreanu, et al., Mathematical modelling of biofilms, IWA Publishing, 2006. https://doi.org/10.2166/9781780402482 doi: 10.2166/9781780402482
|
| [15] |
A. G. Dorofeev, Yu. A. Nikolaev, M. N. Kozlov, M. V. Kevbrina, A. M. Agarev, A. Yu. Kallistova, et al., Modeling of anammox process with the biowin software suite, Appl. Biochem. Microbiol., 53 (2017), 78–84. https://doi.org/10.1134/S0003683817010100 doi: 10.1134/S0003683817010100
|
| [16] |
X. D. Hao, J. J. Heijnen, M. C. M. van Loosdrecht, Model-based evaluation of temperature and inflow variations on a partial nitrification–ANAMMOX biofilm process, Water Res., 36 (2002), 4839–4849. https://doi.org/10.1016/S0043-1354(02)00219-1 doi: 10.1016/S0043-1354(02)00219-1
|
| [17] |
Y. Liu, J. Sun, L. Peng, D. Wang, X. Dai, B. J. Ni, Assessment of heterotrophic growth supported by soluble microbial products in anammox biofilm using multidimensional modeling, Sci. Rep., 6 (2016), 27576. https://doi.org/10.1038/srep27576 doi: 10.1038/srep27576
|
| [18] |
T. Liu, J. Guo, S. Hu, Z. Yuan, Model-based investigation of membrane biofilm reactors coupling anammox with nitrite/nitrate-dependent anaerobic methane oxidation, Environ. Int., 137 (2020), 105501. https://doi.org/10.1016/j.envint.2020.105501 doi: 10.1016/j.envint.2020.105501
|
| [19] |
F. Russo, A. Tenore, M. R. Mattei, L. Frunzo, Multiscale modelling of the start-up process of anammox-based granular reactors, Math. Biosci. Eng., 19 (2022), 10374–10406. https://doi.org/10.3934/mbe.2022486 doi: 10.3934/mbe.2022486
|
| [20] |
H. J. Eberl, D. F. Parker, C. M. Van Loosdrecht, A new deterministic spatio-temporal continuum model for biofilm development, J. Theor. Med., 3 (2001), 161–175. https://doi.org/10.1080/10273660108833072 doi: 10.1080/10273660108833072
|
| [21] |
B. Emerenini, B. A. Hense, C. Kuttler, H. J. Eberl, A mathematical model of quorum sensing induced biofilm detachment, PlosOne, 10 (2015), e0132385. https://doi.org/10.1371/journal.pone.0132385 doi: 10.1371/journal.pone.0132385
|
| [22] |
M. Ghasemi, H. J. Eberl, Time adaptive numerical solution of a highly degenerate diffusion-reaction biofilm model based on regularisation, J. Sci. Comput., 74 (2018), 1060–1090. https://doi.org/10.1007/s10915-017-0483-y doi: 10.1007/s10915-017-0483-y
|
| [23] |
C. Pellicer-Nácher, B. F. Smets, Structure, composition, and strength of nitrifying membrane-aerated biofilms, Water Res., 57 (2014), 151–161. https://doi.org/10.1016/j.watres.2014.03.026 doi: 10.1016/j.watres.2014.03.026
|
| [24] |
I. Klapper, B. Szomolay, An exclusion principle and the importance of mobility for a class of biofilm models, Bull. Math. Biol., 73 (2011), 2213–2230. https://doi.org/10.1007/s11538-010-9621-5 doi: 10.1007/s11538-010-9621-5
|
| [25] |
M. Ghasemi, S. Chang, S. Sivaloganathan, Exploring aeration strategies for enhanced simultaneous nitrification and denitrification in membrane aerated bioreactors: a computational approach, Bull. Math. Biol., 86 (2024), 117. https://doi.org/10.1007/s11538-024-01343-8 doi: 10.1007/s11538-024-01343-8
|
| [26] |
M. Ghasemi, S. Chang, H. J. Eberl, S. Sivaloganathan, Simulation of composition and mass transfer behaviour of a membrane biofilm reactor using a two dimensional multi-species counter-diffusion model, J. Mem. Sci., 618 (2021), 118636. https://doi.org/10.1016/j.memsci.2020.118636 doi: 10.1016/j.memsci.2020.118636
|
| [27] |
H. J. Eberl, R. Sudarsan, Exposure of biofilms to slow flow fields: the convective contribution to growth and disinfection, J. Theor. Biol., 253 (2008), 788–807. https://doi.org/10.1016/j.jtbi.2008.04.013 doi: 10.1016/j.jtbi.2008.04.013
|
| [28] |
M. R. Frederick, C. Kuttler, B. A. Hense, H. J. Eberl, A mathematical model of quorum sensing regulated EPS production in biofilm communities, Theor. Biol. Med. Mod., 8 (2011), 8. https://doi.org/10.1186/1742-4682-8-8 doi: 10.1186/1742-4682-8-8
|
| [29] |
M. Ghasemi, S. Sonner, H. J. Eberl, Time adaptive numerical solution of a highly non-linear degenerate cross-diffusion system arising in multi-species biofilm modelling, Eur. J. Appl. Math., 29 (2018), 1035–1061. https://doi.org/10.1017/S0956792518000554 doi: 10.1017/S0956792518000554
|
| [30] |
M. A. Efendiev, S. Zelik, H. J. Eberl, Existence and longtime behavior of a biofilm model, Commun. Pure Appl. Anal., 8 (2009), 509–531. https://doi.org/10.3934/cpaa.2009.8.509 doi: 10.3934/cpaa.2009.8.509
|
| [31] | H. J. Eberl, L. Demaret, A finite difference scheme for a degenerated diffusion equation arising in microbial ecology, Electron. J. Differ. Equ., 15 (2007), 77–95. |
| [32] |
H. J. Eberl, H. Khassehkhan, L. Demaret, A mixed-culture model of a probiotic biofilm control system, Comput. Math. Meth. Med., 11 (2010), 99–118. https://doi.org/10.1080/17486700902789355 doi: 10.1080/17486700902789355
|
| [33] |
H. J. Eberl, M. S. Collinson, A modeling and simulation study of siderophore mediated antagonism in dual-species biofilms, Theor. Biol. Med. Model., 6 (2009), 30. https://doi.org/10.1186/1742-4682-6-30 doi: 10.1186/1742-4682-6-30
|
| [34] |
J. Rang, Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs, J. Comput. Appl. Math., 286 (2015), 128–144. https://doi.org/10.1016/j.cam.2015.03.010 doi: 10.1016/j.cam.2015.03.010
|
| [35] |
M. Ghasemi, H. J. Eberl, Extension of a regularization based time-adaptive numerical method for a degenerate diffusion-reaction biofilm growth model to systems involving quorum sensing, Proc. Comput. Sci., 108 (2017), 1893–1902. https://doi.org/10.1016/j.procs.2017.05.089 doi: 10.1016/j.procs.2017.05.089
|
| [36] |
M. Ghasemi, S. Chang, S. Sivaloganathan, Modeling and simulation study of simultaneous nitrification-denitrification in membrane aerated bioreactor, J. Member. Sci., 668 (2023), 121210. https://doi.org/10.1016/j.memsci.2022.121210 doi: 10.1016/j.memsci.2022.121210
|
| [37] |
M. Ghasemi, S. Chang, S. Sivaloganathan, Unraveling the role of inert biomass in membrane aerated biofilm reactors for simultaneous nitrification and denitrification, Math. Appl. Sci. Eng., 5 (2024), 120–148. https://doi.org/10.5206/mase/17134 doi: 10.5206/mase/17134
|
| [38] |
C. S. Laspidou, B. E. Rittmann, Modeling the development of biofilm density including active bacteria, inert biomass, and extracellular polymeric substances, Water Res., 38 (2004), 3349–3361. https://doi.org/10.1016/j.watres.2004.04.037 doi: 10.1016/j.watres.2004.04.037
|
| [39] |
M. Seifi, M. H. Fazaelipoor, Modeling simultaneous nitrification and denitrification (SND) in a fluidized bed biofilm reactor, Appl. Math. Model., 36 (2012), 5603–5613. https://doi.org/10.1016/j.apm.2012.01.004 doi: 10.1016/j.apm.2012.01.004
|
| [40] |
M. González-Brambilaa, O. Monroya, F. López-Isunzab, Experimental and theoretical study of membrane-aerated biofilm reactor behavior under different modes of oxygen supply for the treatment of synthetic wastewater, Chem. Eng. Sci., 61 (2005), 5268–5281. https://doi.org/10.1016/j.ces.2006.03.049 doi: 10.1016/j.ces.2006.03.049
|
| [41] |
Y. Liu, T. Zhu, S. Ren, T. Zhao, H. Chai, Y. Xu, et al., Contribution of nitrification and denitrification to nitrous oxide turnovers in membrane-aerated biofilm reactors (MABR): a model-based evaluation, Sci. Total Environ., 806 (2022), 151321. https://doi.org/10.1016/j.scitotenv.2021.151321 doi: 10.1016/j.scitotenv.2021.151321
|
| [42] |
J. Majtacz, D. Grubba, K. Czerwionka, Application of the anammox process for treatment of liquid phase digestate, Water, 12 (2020), 2965. https://doi.org/10.3390/w12112965 doi: 10.3390/w12112965
|
| [43] |
W. Lauterborn, H. Bolle, Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary, J. Fluid Mech., 72 (1975), 391–399. https://doi.org/10.1017/S0022112075003448 doi: 10.1017/S0022112075003448
|
| [44] |
D. Lu, H. Bai, F. Kong, S. N. Liss, B. Liao, Recent advances in membrane aerated biofilm reactors, Crit. Rev. Environ. Sci. Technol., 51 (2020), 649–703. https://doi.org/10.1080/10643389.2020.1734432 doi: 10.1080/10643389.2020.1734432
|
| [45] |
E. Syron, H. Kelly, E. Casey, Studies on the effect of concentration of a self-inhibitory substrate on biofilm reaction rate under co-diffusion and counter-diffusion configurations, J. Member. Sci., 335 (2009), 76–82. https://doi.org/10.1016/j.memsci.2009.02.038 doi: 10.1016/j.memsci.2009.02.038
|
| [46] |
J. Drewnowski, A. Remiszewska-Skwarek, S. Duda, G. Łagód, Aeration process in bioreactors as the main energy consumer in a wastewater treatment plant. Review of solutions and methods of process optimization, Processes, 7 (2019), 311. https://doi.org/10.3390/pr7050311 doi: 10.3390/pr7050311
|
| [47] |
L. Zhang, Y. Narita, L. Gao, M. Ali, M. Oshiki, S. Okabe, Maximum specific growth rate of anammox bacteria revisited, Water Res., 116 (2017), 296–303. https://doi.org/10.1016/j.watres.2017.03.027 doi: 10.1016/j.watres.2017.03.027
|
| [48] | J. Peeters, J. Moran, ZeeLung MABR simple, low-energy process intensification, Intensification of Resource Recovery ($IR^2$), Water Environment Federation (WEF), Manhattan College, New York, 2017. |