Mathematical modelling of an intermittent anoxic/aerobic MBBR: Estimation of nitrification rates and energy savings.

This study aimed at modelling the performance of a novel MBBR configuration, named A/O-MBBR, comprised of a pre-anoxic reactor, with an HRT of 4.5 h, coupled with an intermittent anoxic/aerobic MBBR (HRT = 6.8 h). The lab-scale system was fed with municipal wastewater with an average influent Total Ammonia Nitrogen (TAN) and total COD (TCOD) concentrations of 46 mg of TAN-N L-1 and 310 mg TCOD L-1. During the whole experimental period, TAN removal efficiency was always higher than 96%; denitrification was also very effective, achieving nitrate and nitrite concentrations in the effluent both lower than 5 mg NOx-N L-1 on average. Moreover, TCOD average removal efficiency was equal to 85%. Modelling was performed to investigate the nitrification efficacy enhancement; to this aim, a biofilm model was developed, adopting the equations for mixed-culture biofilms and the Activated Model Sludge n°1 (ASM1) for the biological processes rates. The model allowed to determine the maximum uptake rate for autotrophic growth (µA was 2.5 d-1) and the semisaturation constant (KOA was 0.2 mg O2 L-1), suggesting that the nitrification process was 3-fold faster than average and very effective at low oxygen concentrations. The model estimated that about 85% of TAN was removed by the biofilm and only the remaining part by suspended biomass in the bulk liquid. Finally, it was assessed that the A/O-MBBR configuration allowed for a 45-60% savings of the energy requirement compared to a Benchmark WWTP layout.

Multiscale Modelling of De Novo Anaerobic Granulation.

A multiscale mathematical model is presented to describe de novo granulation, and the evolution of multispecies granular biofilms, in a continuously fed bioreactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation governing the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass as well as exchange fluxes with the bulk liquid. Starting from a vanishing initial value, the expansion of the free boundary is initiated by the attachment process, which depends on the microbial species concentrations within the bulk liquid and their specific attachment velocity. Nonlinear hyperbolic PDEs model the growth of the sessile microbial species, while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species within the granular biofilm. Nonlinear ODEs govern the evolution of soluble substrates and planktonic biomass within the bulk liquid. The model is applied to an anaerobic, granular-based bioreactor system, and solved numerically to test its qualitative behaviour and explore the main aspects of de novo anaerobic granulation: ecology, biomass distribution, relative abundance, dimensional evolution of the granules and soluble substrates, and planktonic biomass dynamics within the bioreactor. The numerical results confirm that the model accurately describes the ecology and the concentrically layered structure of anaerobic granules observed experimentally, and that it can predict the effects on the process of significant factors, such as influent wastewater composition; granulation properties of planktonic biomass; biomass density; detachment intensity; and number of granules.

ADM1-based mechanistic model for the role of trace elements in anaerobic digestion processes.

An original mechanistic model able to describe the fate of trace elements (TE) in anaerobic digestion systems has been synthetized from mass balance equations. The model takes into account the main biochemical and physico-chemical processes affecting TE bioavailability and it is aimed at evaluating the effect that the combination of such processes exerts on the system performance. Five main modules have been introduced: biochemistry, physico-chemistry, sorption, complexation and precipitation. The model is based on mass conservation principles and is formulated as a set of ordinary differential equations for the soluble and particulate components constituting the system. Model applications of two illustrative cases are provided. The first case is based on experimental results and examines the effect of TE depletion in an AD process of food waste (FW). The second case shows the effects of different metal supplements on methane production and biogas composition. The simulation results confirm that the model can fairly be used to predict the effect of TE dynamics and bioavailability, by considering biological, chemical and physicochemical processes in AD environments.

Mathematical modeling of dispersal phenomenon in biofilms.

A mathematical model for dispersal phenomenon in multispecies biofilm based on a continuum approach and mass conservation principles is presented. The formation of dispersed cells is modeled by considering a mass balance for the bulk liquid and the biofilm. Diffusion of these cells within the biofilm and in the bulk liquid is described using a diffusion-reaction equation. Diffusion supposes a random character of mobility. Notably, biofilm growth is modeled by a hyperbolic partial differential equation while the diffusion process of dispersed cells by a parabolic partial differential equation. The two are mutually connected but governed by different equations that are coupled by two growth rate terms. Three biological processes are discussed. The first is related to experimental observations on starvation induced dispersal [1]. The second considers diffusion of a non-lethal antibiofilm agent which induces dispersal of free cells. The third example considers dispersal induced by a self-produced biocide agent.

Sensitivity analysis for an elemental sulfur-based two-step denitrification model.

A local sensitivity analysis was performed for a chemically synthesized elemental sulfur (S0)-based two-step denitrification model, accounting for nitrite (NO2 -) accumulation, biomass growth and S0 hydrolysis. The sensitivity analysis was aimed at verifying the model stability, understanding the model structure and individuating the model parameters to be further optimized. The mass specific area of the sulfur particles (a*) and hydrolysis kinetic constant (k1) were identified as the dominant parameters on the model outputs, i.e. nitrate (NO3 -), NO2 - and sulfate (SO4 2-) concentrations, confirming that the microbially catalyzed S0 hydrolysis is the rate-limiting step during S0-driven denitrification. Additionally, the maximum growth rates of the denitrifying biomass on NO3 - and NO2 - were detected as the most sensitive kinetic parameters.

Continuum and discrete approach in modeling biofilm development and structure: a review.

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Modeling multispecies biofilms including new bacterial species invasion.

A mathematical model for multispecies biofilm evolution based on continuum approach and mass conservation principles is presented. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, attachment, and detachment, and, in particular, is able to predict the biological process of colonization of new species and transport from bulk liquid to biofilm (or vice-versa). From a mathematical point of view, a significant feature is the boundary condition related to biofilm species concentrations on the biofilm free boundary. These data, either for new or for already existing species, are not required by this model, but rather can be predicted as results. Numerical solutions for representative examples are obtained by the method of characteristics. Results indicate that colonizing bacteria diffuse into biofilm and grow only where favorable environmental conditions exist for their development.