This study presents an innovative 2D spatio-temporal model that sheds light on the intricate formation of biofilms, incorporating two essential biomass decay pathways: cell lysis and endogenous respiration. The model encompasses heterotrophic bacteria (HB), anaerobic heterotrophic bacteria (AHB), and autotrophic bacteria (AB), offering a comprehensive understanding of multi-species biofilm development. Through meticulous simulations, we explore the primary mechanisms behind inert biomass formation in biofilms, revealing the key roles played by the lysis of HB, AHB, and AB, as well as the endogenous respiration of HB. Moreover, the simulations reveal how species of higher abundance contribute significantly to inert biomass generation, reshaping our understanding of biofilm dynamics. Crucially, this study highlights the indispensability of considering biofilm inert biomass when modeling the nitrification and denitrification behaviors of a membrane aerated biofilm reactor (MABR). The distribution of oxygen and acetate across biofilm thickness is remarkably different when inert biomass is factored in, underscoring the necessity for a more holistic approach to modeling biofilm behavior. With the introduction of the inert biomass inclusive biofilm model, our simulations explore the interactive effects of key process conditions - bulk concentrations of oxygen ($O_{\infty}$), ammonium nitrogen ($N_{1\infty}$), acetate ($A_{\infty}$), and biofilm thickness - on the nitrification and denitrification performance of MABR. A compelling correlation emerges between higher bulk concentrations of oxygen and ammonium nitrogen and optimal nitrification rates, achieving an impressive range of 0.3 to 1.1 g ammonium/$m^{2}/d. Delving into denitrification, we observe that high $O_{\infty}$, low $N_{1\infty}$, and either high or low $A_{\infty}$ levels impede AHB formation and consequently hinder denitrification. Our findings provide a roadmap for achieving simultaneous nitrification and denitrification, contingent on specific conditions: $10[gm^{-3}] < O_{\infty} < 15[gm^{-3}]$, $12[gm^{-3}] < N_{1\infty} < 20[gm^{-3}]$, $A_{\infty}$ ranging from $3[gm^{-3}]$ to $12[gm^{-3}]$, and a biofilm thickness $> 1.4[mm]$. While our study reveals promising avenues for simultaneous nitrification and denitrification, denitrification rates still lag behind nitrification rates under the same conditions. As a result, we advocate for further investigations to devise strategies that can enhance denitrification in MABR systems. In conclusion, this study advances our knowledge of biofilm dynamics by introducing a comprehensive model and illuminating the key factors driving nitrification and denitrification performance in MABRs. These findings pave the way for improved biofilm engineering and wastewater treatment strategies, opening new horizons for sustainable environmental practices.
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