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.

Surrogate based Global Sensitivity Analysis of ADM1-based Anaerobic Digestion Model.

In order to calibrate the model parameters, Sensitivity Analysis routines are mandatory to rank the parameters by their relevance and fix to nominal values the least influential factors. Despite the high number of works based on ADM1, very few are related to sensitivity analysis. In this study Global Sensitivity Analysis (GSA) and Uncertainty Quantification (UQ) for an ADM1-based Anaerobic Digestion Model have been performed. The modified version of ADM-based model selected in this study was presented by Esposito and co-authors in 2013. Unlike the first version of ADM1, focused on sewage sludge degradation, the model of Esposito is focused on organic fraction of municipal solid waste digestion. It his recalled that in many applications the hydrolysis is considered the bottleneck of the overall anaerobic digestion process when the input substrate is constituted of complex organic matter. In Esposito's model a surfaced based kinetic approach for the disintegration of complex organic matter is introduced. This approach allows to better model the disintegration step taking into account the effect of particle size distribution on the digestion process. This model needs thus GSA and UQ to pave the way for further improvements and reach a deep understanding of the main processes and leading input factors. Due to the large number of parameters to be analyzed a first preliminary screening analysis, with the Morris' Method, has been conducted. Since two quantities of interest (QoI) have been considered, the initial screening has been performed twice, obtaining two set of parameters containing the most influential factors in determining the value of each QoI. A surrogate of ADM1 model has been defined making use of the two defined quantities of interest. The output results from the surrogate model have been analyzed with Sobol' indices for the quantitative GSA. Finally, uncertainty quantification has been performed. By adopting kernel smoothing techniques, the Probability Density Functions of each quantity of interest have been defined.

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.

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.

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.

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.

Mathematical modelling of disintegration-limited co-digestion of OFMSW and sewage sludge.

This paper presents a mathematical model able to simulate under dynamic conditions the physical, chemical and biological processes prevailing in a OFMSW and sewage sludge anaerobic digestion system. The model proposed is based on differential mass balance equations for substrates, products and bacterial groups involved in the co-digestion process and includes the biochemical reactions of the substrate conversion and the kinetics of microbial growth and decay. The main peculiarity of the model is the surface based kinetic description of the OFMSW disintegration process, whereas the pH determination is based on a nine-order polynomial equation derived by acid-base equilibria. The model can be applied to simulate the co-digestion process for several purposes, such as the evaluation of the optimal process conditions in terms of OFMSW/sewage sludge ratio, temperature, OFMSW particle size, solid mixture retention time, reactor stirring rate, etc. Biogas production and composition can also be evaluated to estimate the potential energy production under different process conditions. In particular, model simulations reported in this paper show the model capability to predict the OFMSW amount which can be treated in the digester of an existing MWWTP and to assess the OFMSW particle size diminution pre-treatment required to increase the rate of the disintegration process, which otherwise can highly limit the co-digestion system.

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.

Fate of Trace Metals in Anaerobic Digestion.

A challenging, and largely uncharted, area of research in the field of anaerobic digestion science and technology is in understanding the roles of trace metals in enabling biogas production. This is a major knowledge gap and a multifaceted problem involving metal chemistry; physical interactions of metal and solids; microbiology; and technology optimization. Moreover, the fate of trace metals, and the chemical speciation and transport of trace metals in environments--often agricultural lands receiving discharge waters from anaerobic digestion processes--simultaneously represents challenges for environmental protection and opportunities to close process loops in anaerobic digestion.

Model calibration and validation for OFMSW and sewage sludge co-digestion reactors.

A mathematical model has recently been proposed by the authors to simulate the biochemical processes that prevail in a co-digestion reactor fed with sewage sludge and the organic fraction of municipal solid waste. This model is based on the Anaerobic Digestion Model no. 1 of the International Water Association, which has been extended to include the co-digestion processes, using surface-based kinetics to model the organic waste disintegration and conversion to carbohydrates, proteins and lipids. When organic waste solids are present in the reactor influent, the disintegration process is the rate-limiting step of the overall co-digestion process. The main advantage of the proposed modeling approach is that the kinetic constant of such a process does not depend on the waste particle size distribution (PSD) and rather depends only on the nature and composition of the waste particles. The model calibration aimed to assess the kinetic constant of the disintegration process can therefore be conducted using organic waste samples of any PSD, and the resulting value will be suitable for all the organic wastes of the same nature as the investigated samples, independently of their PSD. This assumption was proven in this study by biomethane potential experiments that were conducted on organic waste samples with different particle sizes. The results of these experiments were used to calibrate and validate the mathematical model, resulting in a good agreement between the simulated and observed data for any investigated particle size of the solid waste. This study confirms the strength of the proposed model and calibration procedure, which can thus be used to assess the treatment efficiency and predict the methane production of full-scale digesters.