Cette thèse s'intéresse à l'application d'un modèle mathématique unidimensionnel de formation et de croissance de biofilms multi-espèces. Le modèle se compose d'un système d'équations non linéaires aux dérivées partielles hyperboliques, décrivant la croissance d'espèces microbiennes dans le biofilm, et un système d'équations semi-linéaires aux dérivées partielles paraboliques, qui régit la diffusion de substrat de la phase aqueuse vers la matrice du biofilm. L'ensemble conduit à un problème de valeur limite libre, essentiellement hyperbolique. Dans une première étude, l'analyse et la simulation de la phase initiale de croissance du biofilm ont été examinées. Le problème mathématique résultant a été discuté en utilisant la méthode des caractéristiques et le théorème du point fixe a été utilisé pour déterminer l'existence et l'unicité des solutions mathématiques. Un deuxième aspect de la thèse porte sur l'analyse et la prévision de la dynamique des populations microbienne dans plusieurs types biofilms pour le traitement des eaux usées. Le modèle a été appliqué pour simuler la compétition bactérienne et évaluer l'influence de la diffusion du substrat sur la stratification microbienne des biofilms multi-espèces, en incluant les bactéries nitrifiantes, Anammox et bactéries sulfato-réductrices. Dans les deux cas, la méthode des caractéristiques a été utilisée à des fins numériques et l'équation de conservation de masse joue un rôle crucial pour vérifier l'exactitude des simulations. Les résultats des simulations montrent que le modèle est en mesure d'évaluer correctement les effets des conditions limites qui s'exercent sur la concurrence bactérienne. Enfin, ce modèle a été étendu pour inclure le phénomène de colonisation microbienne. Le nouveau modèle est capable de prendre en compte l'invasion de nouvelles espèces en se basant sur un ensemble d'équations non linéaires aux dérivées partielles hyperboliques pour ce qui concerne le processus de croissance. De plus, le processus d'invasion biologique d'espèces nouvelles dans le biofilm a été modélisé par un système d'équations non linéaires aux dérivées partielles paraboliques. Ce modèle d'invasion a été appliqué avec succès pour simuler l'invasion des bactéries hétérotrophes dans les biofilms autotrophes / This dissertation relates to the applications of a one-dimensional mathematical model for multispecies biofilm formation and growth. The model consists of a system of nonlinear hyperbolic partial differential equations, describing the growth of microbial species in biofilms, and a system of semilinear parabolic partial differential equations, which governs substrate diffusion from the surrounding aqueous phase into the biofilm. Overall, this leads to a free boundary value problem, essentially hyperbolic. In a first study, the analysis and simulations of the initial phase of biofilm growth have been addressed. The resulting mathematical problem has been discussed by using the method of characteristics and the fixed-point theorem has been used to obtain existence, uniqueness and properties of solutions. A second aspect of the thesis deals with the analysis and prediction of population dynamics in multispecies biofilms for wastewater treatment. The model has been applied to simulate the bacterial competition and to evaluate the influence of substrate diffusion on microbial stratification for a nitrifying multispecies biofilm including Anammox bacteria and a sulfate-reducing biofilm. In both cases, the method of characteristics has been used for numerical purposes and the mass conservation equation plays a crucial role in checking the accuracy of simulations. The simulation results reveal that the model is able to evaluate properly the effects that boundary conditions exert on bacterial competition. Finally, the biofilm model has been extended to include the colonization phenomenon. The new model is able to take into account the invasion of new species diffusing from bulk liquid to biofilm, still based on a set of nonlinear hyperbolic partial differential equations for what concerns growth process. Indeed, the biological invasion process of new species into the biofilm has been modeled by a system of nonlinear parabolic partial differential equations. The invasion model has been successfully applied to simulate the invasion of heterotrophic bacteria in a constituted autotrophic biofilm and viceversa

The nitrification process, the biologically mediated process of ammonia treatment in water resources recovery facilities (WRRF), remains the most common treatment process to mitigate the adverse effects of effluent ammonia discharges in surface water. However, it is well established that the temperature-sensitive process of nitrification remains hindered at low temperatures in conventional suspended growth technologies; specifically, passive treatment systems such as the lagoons, representing over 50% of Canadian treatment facilities in operation. As such, nitrification in lagoon facilities remains unreliable during the cold seasons with no nitrification occurring at 1°C. In contrast to suspended growth systems, attached growth technologies such as the moving bed biofilm reactors (MBBR) have recently been proven capable of achieving significant nitrification rates at temperatures as low as 1°C and are proposed as suitable upgrade systems to the common lagoon facility to reach year-long ammonia treatment targets. As such, the main objective of this research is to investigate and expand the current knowledge by investigating the key research questions lacking in the current literature on post-carbon, low temperature nitrifying MBBR systems. With this aim, a temperature-controlled study of attached growth nitrification kinetics was conducted to isolate the effects of low temperatures on nitrifying MBBR system performance down to 1°C. A removal rate of 98.44 ± 4.69 gN/m³d is identified as the 1°C intrinsic removal rate and the design removal rate for nitrifying MBBR systems at low temperatures. Considering this intrinsic rate at 1°C, an assessment of reactor efficiency at elevated TAN concentrations typical of non-combined sewer systems indicates that a two reactor in-series MBBR system configuration is recommended for retrofitting lagoon facilities connected to sanitary sewers. The study of the reactor performance to temperatures as low as 1°C demonstrates a non-linear decline in removal efficiency between 10°C and 1°C, with the existence of a kinetic threshold temperature delineated between 4°C and 2°C. As such, this delineated temperature range accounts for a significant decline in the performance of low carbon nitrifying MBBR systems during the onset of the cold seasons. This research identifies new recommended Arrhenius correction coefficient values taking into account this kinetic threshold temperature, with a coefficient of 1.049 being recommended above the kinetic threshold (≥4°C) and 1.149 below the threshold temperature at 1°C. Moreover, since the elapsed time to low temperature was identified as a key factor of attached growth nitrification kinetics, a modified theta model accounting for temperature and time is proposed in this research to accurately model the rate of nitrifying MBBR systems between 4°C and 1°C. Finally, with the severe adverse effects of sudden decreases in temperature, or cold shocks, on nitrification kinetics being previously demonstrated but not well understood, this research compares acclimatized and cold shocked MBBR reactors down to 1°C. The findings indicate 21% lower kinetics in the cold shocked reactor with reactor efficiencies never reaching those of the acclimatized reactor despite extended operation at 1°C. Thus, the research delineates the potentially lasting effects of extreme weather events such as cold air outbreaks and snowmelt periods on nitrifying MBBR system performance. On the other hand, these same findings demonstrate the resiliency of nitrifying MBBR reactors as nitrification was maintained within these systems despite being cold-shocked down from 10°C and 1°C. This study of attached growth kinetics was coupled with an investigation of the nitrifying biofilms, biomass, and microbiome responses to low temperatures and cold shock down to 1°C to provide an understanding of the changes occurring in these systems down to the cellular level. Comparisons of acclimatized and cold shocked nitrifying biofilms responses down to 1°C were characterized by increases in biofilm thickness, increases in biomass viability; and, greater shifts in microbiome communities occurring above 4°C in the acclimatized biofilm. Considering these observations, results also indicated a significant increase in nitrifiers per carrier above 4°C. As such, these findings suggested that the bulk of nitrifying biofilm adaptation to cold temperatures occurs above 4°C, a crucial adaptation phase in acclimatized systems. This adaptation phase is shown to be lacking in cold-shocked systems, with the cold shocked biofilm and microbiome demonstrating significant differences with the acclimatized systems’ biofilm and microbiome. This research was performed to answer the critical research questions relating to the design and operation of the post-carbon, low temperature nitrifying MBBR systems, with the first low temperature MBBR systems being scheduled to begin operation in the fall of 2020. This research expands the current knowledge on low temperature attached growth nitrification kinetics as well as cold shocked attached growth nitrification kinetics in MBBR systems down to 1°C. In addition, this research delineates the effects of low temperatures and cold shocks on the nitrifying MBBR system’s biofilms and their embedded cells.

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With the rise in global energy prices, as well as energy consumption being the largest source of greenhouse gas emissions, biofilm-based systems utilized for wastewater treatment, such as moving bed biofilm reactors (MBBRs), have grown in popularity for their lower energy consumption compared to conventional activated sludge processes. However, this technology requires large amounts of energy to constantly distribute and suspend its biofilm carrier within the reactor by either aerators or mechanical mixers. Many studies have been done on optimizing the aeration systems, but limited research has been focused on the mechanical mixing systems. This master’s thesis project aims to narrow the research and data gaps in MBBR mechanical mixing by conducting scaled-down experiments to study the influence of different mixer configurations on carrier’s flow fields in a reactor tank. The main objective is to determine the conditions for good carrier mixing and their energy use efficiency. Other objectives include determining the effects of scaling on carrier flow fields and whether the experimental results can be used to help develop and validate MBBR computational fluid dynamics (CFD) models. The results showed that good carrier mixing occurred in conditions where (1) mixer height was 3 cm from the bottom of the tank, had no inclinations and positioned along a long wall; (2) mixer flows could maintain their momentum; (3) sufficient length was given for mixer jet streams to develop and widen; (4) there was a dual presence of vertical flow loops and horizontal bulk flow loops; (5) 2 mixers did not result in counter- rotating flows; and (6) 2 mixers were not positioned in one corner of the tank. The effects of scaling did not impact the carrier flow fields and was determine by comparing the experimental results from this study with the results from a previous experiment that utilized a smaller tank. The results from this study could qualitatively match with the results of the CFD model. Limitations that occurred during the study when trying to define “good mixing” were also discussed. Lastly, the thesis ends with stating future work and recommendations. / Med stigande globala energipriser och en energiförbrukning som är den största källan till utsläpp av växthusgaser, har biofilmbaserade system för avloppsvattenrening, t.ex. biofilmsreaktorer med rörlig bädd (MBBR), ökat i popularitet tack vare sin lägre energiförbrukning jämfört med konventionella processer med aktivt slam. Denna teknik kräver dock stora mängder energi för att ständigt distribuera och suspendera biofilmbäraren i reaktorn med hjälp av antingen luftare eller mekaniska blandare. Många studier har gjorts för att optimera luftningssystemen, men begränsad forskning har fokuserats på de mekaniska blandningssystemen. Detta examensarbete syftar till att minska forsknings- och dataluckorna inom mekanisk blandning i MBBR genom att genomföra nedskalade experiment för att studera hur olika blandarkonfigurationer påverkar bärarens flödesfält i en reaktortank.Huvudsyftet är att fastställa villkoren för god blandning av bärare och deras energianvändningseffektivitet. Andra mål är att fastställa effekterna av skalning på bärarnas flödesfält och om de experimentella resultaten kan användas för att utveckla och validera CFD-modeller (Computational Fluid Dynamics) för MBBR. Resultaten visade att god bärarblandning inträffade under förhållanden där (1) blandarhöjden var 3 cm från tankens botten, utan lutningar och placerad längs en lång vägg; (2) blandarflöden kunde behålla sitt momentum; (3) tillräcklig längd gavs för blandarjetströmmar att utvecklas och breddas; (4) det fanns en dubbel närvaro av vertikala flödesslingor och horisontella bulkflödesslingor; (5) 2 blandare inte resulterade i motroterande flöden; och (6) 2 blandare inte placerades i ett hörn av tanken. Effekterna av skalning påverkade inte bärarens flödesfält och fastställdes genom att jämföra de experimentella resultaten från denna studie med resultaten från ett tidigare experiment som använde en mindre tank. Resultaten från denna studie kunde kvalitativt matchas med resultaten från CFD-modellen. Begränsningar som uppstod under studien när man försökte definiera "bra blandning" diskuterades också. Slutligen avslutas avhandlingen med att ange framtida arbete och rekommendationer.