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Microfiltration technology is a widely used engineering strategy for fresh water production and water treatment. The major concern in many applications is the formation of a biological fouling layer leading to increased hydraulic resistance and flux decline during membrane operations. The growth of bacteria constituting such a biological layer implicates the formation of a multispecies biofilm and the consequent increase of operational costs for reactor management and cleaning procedures. To predict the biofilm growth and evolution during the filtration process, a one-dimensional continuous model has been developed by considering a free boundary value problem describing biofilm dynamics and EPS production in different operational phases of microfiltration systems. The growth of microbial species and EPS is governed by a system of hyperbolic PDEs. Substrates dynamics are modeled thorough parabolic equations accounting for diffusive and advective fluxes generated during the filtration process. The free boundary evolution depends on both microbial growth and detachment processes. The proposed model has been solved numerically to simulate biofilm evolution during biologically relevant conditions, and to investigate the hydraulic behavior of the membrane. The model has been calibrated and validated using lab scale experimental data. In all cases, numerical results accurately predicted the membrane pressure drop occurring in the microfiltration system., Comment: 18 pages, 8 figures, preprint version

Increasing anthropogenic activity has contributed to local imbalances in the natural sulfur cycle, leading to serious environmental problems. Industrial wastewater containing sulfate has contributed to this sulfur imbalance. Biological sulfate reducing processes that involve a bacterial biomass attached to media (biofilm), represent an attractive solution to the problem. The advantage of bacteria disposing in a biofilm is very important in an environmental industrial application, as the bacteria in the biofilm, different from suspended bacteria, cannot be washed out with the water flow. This allows to retain the biomass within the reactor and therefore to operate at shorter hydraulic retention time (HRT),and higher biomass concentration . Biological sulfate reduction in anaerobic fixed growth reactors has been investigated extensively at lab-scale. Under anaerobic conditions dissimilatory sulfate reducing bacteria use sulfate as a terminal electron acceptor for the degradation of organic compounds. In this anaerobic process, sulfate is reduced to sulfide by the action of sulfate reducing bacteria (SRB), which have the ability of coupling the oxidation of organic matter (electron donor) to the reduction of sulfate (electron acceptor) and depend on hydrolytic and fermentative bacteria that degrade complex organic matter. A major problem of sulfate-reducing fixed-growth reactors is the formation of undesired bacteria species which compete for space and substrate in the biofilm with SRB. This work presents a mathematical model able to simulate the physical, chemical and biological processes prevailing in a sulfate reducing biofilm under dynamic conditions. The proposed model includes sulfate reduction by complete and incomplete SRB; COD (lactate) removal by sulfate reduction and by acetogenic bacteria; acetate consumption via methanogenesis. The method of characteristics is used for the numerical resolution of the model equations. In particular the effect of the COD/SO42- ratio and the effect of different simulation times on the reactor performances in terms of bacterial species distribution and substrate diffusion trends in the biofilm have been assessed.

The work presents a mathematical modelling approach to study dynamic competition during the attachment phenomena in the initial phase of biolm growth. Biofilm development is described by a set nonlinear hyperbolic partial dierential equations. Diffusion of substrates through biolm is modeled by a set of semilinear parabolic partial differential equations. The two sets of equations are mutually connected. The resulting mathematical problem is a free boundary value problem, which is essentially hyperpolic. A characteristic-like method is introduced to convert differential equations to integral equations. Fixed-point theorem is used to obtain existence, uniqueness and properties of solutions. The model has been applied to the biological competition of heterotrophic-autotrophic bacteria in a multi-specie biolm. The eects of dierent attachment rates on the biolm dynamic performances predicting biolm thickness, volume fractions of bacterial species and substrate concentration trends have been investigated. The simulations show that the dierent attachment rates infuence biolm thickness, of course. However, the volume fractions of bacterial species mainly depend on biolm internal dynamics and substrate concentration trends. The bulk concentrations of microbial species play a relative important role only in the outermost layers of biolm.

This paper presents a mathematical model able to simulate the physical, chemical and biological processes prevailing in a multispecies biofilm including ANAMMOX bacteria under dynamic conditions. A mathematical modeling approach for microbial growth and decay is proposed. The model can simulate the activities of heterotrophs and autotrophs living in a biofilm and evaluate the interactions between the related processes: COD oxidation, denitrification, nitrification and ANAMMOX. The model takes into account all the possible microbial interactions characterizing a multispecies biofilm and is aimed at evaluating the optimal conditions for the development of ANAMMOX bacteria. The model has been applied to simulate the anammox competition in a multispecies biofilm in several conditions. The method of characteristics has been used for the numerical process. The simulations have been performed to evaluate the dynamical response of biofilm in terms of volume fractions of bacteria and concentration trends of substrates. The results show that the model is capable to reveal the microbial stratification in biofilm, evaluating the effect of substrate diffusion on biomass growth.

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.

In this work, an original mathematical model for metals leaching from electronic waste in a dark fermentation process is proposed. The kinetic model consists of a system of non-linear ordinary differential equations, accounting for the main biological, chemical, and physical processes occurring in the fermentation of soluble biodegradable substrates and in the dissolution process of metals. Ad-hoc experimental activities were carried out for model calibration purposes, and all experimental data were derived from specific lab-scale tests. The calibration was achieved by varying kinetic and stoichiometric parameters to match the simulation results to experimental data. Cumulative hydrogen production, glucose, organic acids, and leached metal concentrations were obtained from analytical procedures and used for the calibration. The results confirmed the high accuracy of the model in describing biohydrogen production, organic acids accumulation, and metals leaching during the biological degradation process. Thus, the mathematical model represents a useful and reliable tool for the design of strategies for valuable metals recovery from waste or mineral materials. Moreover, further numerical simulations were carried out to analyze the interactions between the fermentation and the leaching processes and to maximize the efficiency of metals recovery due to the fermentation by-products.

A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation which governs the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass and the 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 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 reactor. The numerical results confirm that the model accurately describes the ecology and the concentrically-layered structure of anaerobic granules observed experimentally, and is able to predict the effects of some significant factors, such as influent wastewater composition, granulation properties of planktonic biomass, biomass density and hydrodynamic and shear stress conditions, on the process performance., Comment: 41 pages, 21 figures, preprint version

The dynamics of biofilm lifecycle are deeply influenced by the surrounding environment and the interactions between sessile and planktonic phenotypes. Bacterial biofilms typically develop in three distinct stages: attachment of cells to a surface, growth of cells into colonies, and detachment of cells from the colony into the surrounding medium. The attachment of planktonic cells plays a prominent role in the initial phase of biofilm lifecycle as it initiates the colony formation. During the maturation stage, biofilms harbor numerous microenvironments which lead to metabolic heterogeneity. Such microniches provide conditions suitable for the growth of new species, which are present in the bulk liquid as planktonic cells and can penetrate the porous biofilm matrix. We present a 1D continuum model on the interaction of sessile and planktonic phenotypes in biofilm lifestyle which considers both the initial attachment and colonization phenomena. The model is formulated as a hyperbolic-elliptic free boundary value problem with vanishing initial value. Hyperbolic equations reproduce the transport and growth of sessile species, while elliptic equations model the diffusion and conversion of planktonic cells and dissolved substrates. The attachment is modelled as a continuous, deterministic process which depends on the concentrations of the attaching species. The growth of new species is modelled through a reaction term in the hyperbolic equations which depends on the concentration of planktonic species within the biofilm. Existence and uniqueness of solutions are discussed and proved for the attachment regime. Finally, some numerical examples show that the proposed model correctly reproduces the growth of new species within the biofilm and overcomes the ecological restrictions characterizing the Wanner-Gujer type models., Comment: 17 pages, 9 figures, preprint version

In this work, we present a probabilistic analysis of a detailed one-dimensional biofilm model that explicitly accounts for planktonic bacterial invasion in a multi-species biofilm. The objective is (1) to quantify and understand how the uncertainty in the parameters of the invasion submodel impacts the biofilm model predictions (here the microbial species volume fractions); and (2) to spot which parameters are the most important factors enhancing the biofilm model response. An emulator (or “surrogate”) of the biofilm model is trained using a limited experimental design of size N=216 and corresponding to a Halton’s low-discrepancy sequence in order to optimally cover the uncertain space of dimension d=3 (corresponding to the three scalar parameters newly introduced in the invasion submodel). A comparison of different types of emulator (generalized Polynomial Chaos expansion – gPC, Gaussian process model – GP) is carried out; results show that the best performance (measured in terms of the Q2 predictive coefficient) is obtained using a Least-Angle Regression (LAR) gPC-type expansion, where a sparse polynomial basis is constructed to reduce the problem size and where the basis coordinates are computed using a regularized least-square minimization. The resulting LAR gPC-expansion is found to capture the growth in complexity of the biofilm structure due to niche formation. Sobol’ sensitivity indices show the relative prevalence of the maximum colonization rate of autotrophic bacteria on biofilm composition in the invasion submodel. They provide guidelines for orienting future sensitivity analysis including more sources of variability, as well as further biofilm model developments., BERC 2014-2017 (Basque Government); BCAM Severo Ochoa accreditation SEV-2013-0323 (Spanish Ministry of Economy and Competitiveness MINECO); PhD Grant "La Caixa 2014" (La Caixa Foundation).

A mathematical model for anaerobic digestion in plug-flow reactors is proposed on the basis of mass balance considerations. The model consists of a system of parabolic partial differential equations for the variables representing the concentrations of the bio-components constituting the waste matrix and takes into account convective and diffusive phenomena. The plug-flow reactor is modelled as a one-dimensional domain; the waste matrix moves in the direction of the reactor axis and undergoes diffusive phenomena which reproduce the movement of the bio-components along the reactor axis due to a gradient in concentration. The velocity characterizing the convection of the waste matrix is not fixed a priori but it is considered as an additional unknown of the mathematical problem. The variation in the convective velocity allows to account the mass variation occurring along a plug-flow reactor due to the conversion of solids. The equation governing the convective velocity is derived by considering the density of the waste matrix within the reactor constant over time and the sum of the volume fractions of the bio-components constituting the waste matrix constrained to unity. The waste matrix undergoes biochemical transformations catalysed by anaerobic microbial species which lead to the production of gaseous methane, the final product of the anaerobic digestion process. Biochemical processes are modelled using a simplified scheme and a differential equation is used to describe the dynamics of the produced gaseous methane. A finite difference scheme is used for the numerical integration. Model consistency is showed through numerical simulations which investigate the effect of the variation of some operating parameters on process performance. The model is then applied to a real case scenario of engineering interest. Simulations produce results in good agreement with experimental observations., 25 pages, 11 figures, preprint version

A surface-based kinetic model for the anaerobic digestion of potato waste was proposed. The model was calibrated and validated, and a local sensitivity analysis was performed to investigate the most sensitive parameters. The model consisted of a modified Anaerobic Digestion Model n.1 where the disintegration process was defined through a surface-based approach able to account for the influence of the particle size on the process development. Ad-hoc experiments were carried out to calibrate and validate the model at a laboratory scale. The calibration and validation procedures accounted for the methane production and organic acid concentrations observed during experimental tests. The quality of model fitting with lab-scale data was evaluated by the Modeling Efficiency, the Index of Agreement, and the Root Mean Square Error methods. Results confirmed the high accuracy of the model for the bio-methane and organic by-products prediction during the anaerobic conversion of potato waste.

A mathematical model describing the microbial interactions in phototrophic-heterotrophic biofilms is presented. The main phenomena and factors involved in the model include: biomass growth and decay, substrates production, diffusion and consumption, biological invasion of planktonic species and detachment. In particular, non linear hyperbolic PDEs describe the growth of the microbial species while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species. The whole system of PDEs is considered in a free boundary domain. The following syntrophic interactions are also modelled: the exchange of dissolved oxygen, organic carbon and inorganic carbon produced and released by phototrophs and heterotrophs, respectively. The positive effect of heterotrophic pioneers on the phototrophic growth is modelled by introducing a phototrophic colonization rate depending on the EPS fraction in the biofilm. Numerical simulations are performed to test model accuracy. Simulation results reproduce the main symbiotic mechanisms between phototrophs and heterotrophs reported in literature, such as the positive effect of heterotrophic pioneers and their EPS production on phototrophic growth and the effects of phototrophic organic carbon release on the invasion and growth of heterotrophic bacteria. Furthermore, model results highlight the role played by heterotrophic species under photoinhibition conditions, which provide a positive shading contribution to phototrophic growth. Light is confirmed as the most significant factor in the ecology of phototrophic-heterotrophic biofilms. Such results confirm the accuracy of the model that correctly predicts the evolution of a phototrophic-heterotrophic biofilm and the main phenomena involved, and can be seen as an auxiliary tool in different industrial applications, such as wastewater treatment and bioenergy production.

Due to the multiplicity of biogeochemical processes taking place in anaerobic digestion (AD) systems and limitations of the available analytical techniques, assessing the bioavailability of trace elements (TEs) is challenging. Determination of TE speciation can be facilitated by developing a mathematical model able to consider the physicochemical processes affecting TEs dynamics. A modeling framework based on anaerobic digestion model no 1 (ADM1) has been proposed to predict the biogeochemical fate TEs in AD environments. In particular, the model considers the TE adsorption–desorption reactions with biomass, inerts and mineral precipitates, as well as TE precipitation/dissolution, complexation reactions and biodegradation processes. The developed model was integrated numerically, and numerical simulations have been run to investigate the model behavior. The simulation scenarios predicted the effect of (i) organic matter concentration, (ii) initial TEs concentrations, (iii) initial Ca–Mg concentrations, (iv) initial EDTA concentration, and (v) change in TE binding site density, on cumulative methane production and TE speciation. Finally, experimental data from a real case continuous AD system have been compared to the model predictions. The results prove that this modelling framework can be applied to various AD operations and may also serve as a basis to develop a model-predictive TE dosing strategy.

In this work, a free boundary problem is presented for the attachment process in the initial phase of multispecies biofilm formation. The free boundary is represented by the biofilm thickness and it is assumed to be initially zero. The growth of attached species is governed by nonlinear hyperbolic PDEs. The free boundary evolution is governed by a first-order differential equation depending on the attachment, detachment, biomass velocity and substrates. The quasi-static diffusion of substrates is modelled by a system of semi-linear elliptic PDEs. The qualitative analysis of solutions leads to prove existence, uniqueness and some properties of solutions. We highlight that the free boundary velocity is greater than the characteristic velocity during the first instants of biofilm formation and the free boundary is a space-like line. It is proved that the attachment function depends linearly on the concentrations of all the attaching species. The first phase of biofilm growth is shown to be completely determined by environmental conditions and characterized by a specific mathematical inequality. The opposite inequality describes the further phase where the bulk liquid stops to directly affect the biofilm life. The mentioned inequalities could be assumed as rigorous definitions of non-mature and mature biofilms, respectively. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.

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., This work has been developed in the framework of the COST Action 1302 (“European Network on Ecological Roles of Trace Metals in Anaerobic Biotechnologies”) supported by COST (European Cooperation in Science and Technology). L. Frunzo and M.R. Mattei acknowledge the support from the Progetto Giovani G.N.F.M. 2017 >Analisi di Sistemi Biologici Complessi>. L. Frunzo also acknowledges the support from the project VOLAC - Valorization of OLive oil wastes for sustainable production of biocide-free Antibiofilm Compounds, funded by CARIPLO foundation.

A mathematical model able to simulate the physical, chemical and biological interactions prevailing in multispecies biofilms in the presence of a toxic heavy metal is presented. The free boundary value problem related to biofilm growth and evolution is governed by a nonlinear ordinary differential equation. The problem requires the integration of a system of nonlinear hyperbolic partial differential equations describing the biofilm components evolution, and a systems of semilinear parabolic partial differential equations accounting for substrates diffusion and reaction within the biofilm. In addition, a semilinear parabolic partial differential equation is introduced to describe heavy metal diffusion and sorption. The biosoption process modeling is completed by the definition and integration of other two systems of nonlinear hyperbolic partial differential equations describing the free and occupied binding sites evolution, respectively. Numerical simulations of the heterotrophic-autotrophic interaction occurring in biofilm reactors devoted to wastewater treatment are presented. The high biosorption ability of bacteria living in a mature biofilm is highlighted, as well as the toxicity effect of heavy metals on autotrophic bacteria, whose growth directly affects the nitrification performance of bioreactors.

A continuum approach to mathematical modeling of multispecies biofilm formation and growth is presented. The equations governing the biological process are derived from mass balance principles in the general 3D situation. The 1D equations are inferred as special cases. A system of n nonlinear hyperbolic partial differential equations (PDEs) for the n bacterial species forming the biofilm, m semilinear parabolic (or elliptic) PDEs for the m substrates present in the biofilm, and an ordinary differential equation (ODE) for the motion of the biofilm boundary are obtained. In addition, a further system of parabolic PDEs is added in some situations, such as the invasion of new bacterial species and colonization into an already constituted biofilm. All equations mentioned are mutually connected and must be solved simultaneously in a domain that is a further unknown within the mathematical problem. Transforming the problem to characteristic coordinates yields positive answers about model consistency (uniqueness, existence, positiveness of solutions). The invasion problem is illustrated with some simulations based on the method of characteristics. The biofilm-reactor model is also discussed.

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

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. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.

A 1-D mathematical model for analysis and prediction of microbial colonization of anaerobic multispecies biofilms for methane production is presented. The model combines the related processes of hydrolysis, acidogenesis, acetogenesis, methanogenesis and takes into account phenomena of substrate reaction and diffusion, biomass growth, detachment and, in particular, the colonization of new species from bulk liquid to biofilm. The colonization phenomenon is initiated by planktonic cells, present in the bulk liquid but not initially in the biofilm, which thanks to the characteristic porous structure of biofilm matrix, may enter the channels and establish where they find favorable growth conditions. The model consists of a free boundary value problem where the biofilm growth process is governed by nonlinear hyperbolic PDEs and substrate dynamics are dominated by semilinear parabolic PDEs. The transport of colonizing bacteria from the bulk liquid to the biofilm is modelled by using a diffusionreaction equation, where the reaction term represents the loss of planktonic bacteria due to their establishment within the biofilm. The method of characteristics is used for numerical purposes. The model is based on the biological framework of ADM1 and has been applied to simulate microbial competition and evaluate the influence of substrate diffusion on microbial stratification. Specific scenarios have been simulated describing the effect of colonization of motile bacteria into an established anaerobic biofilm.

The biofilm matrix is a complex of secreted polymers, absorbed nutrients and metabolites, cell lysis products, and even particulate material. Being polyanionic in nature, this matrix plays a crucial role in the biosorption of metal cations. In this work, the adsorption process of heavy metals in biofilms is modeled in one space dimension. The mathematical model is a free-boundary value problem for nonlinear hyperbolic and parabolic partial differential equations. Biomass and extracellular polymeric substances (EPS) growth is governed by hyperbolic equations, and substrate evolution by parabolic equations. All equations are mutually connected. The model is general and can work for any number of microbial species, EPS, and substrates. In numerical analysis, heterotrophic-autotrophic competition for space with oxygen as common substrate is considered. The model can describe biofilm growth dynamics including spatial distribution of microbial species, substrate concentrations, EPS formation, and, in particular, is able to simulate heavy metal diffusion and adsorption into biofilm. Numerical simulations for representative examples are obtained by the method of characteristics. Results indicate that model is able to capture the main features of heavy metal adsorption process on EPS.

This work presents an integrated mathematical model able to simulate the physical, chemical, and biological processes prevailing in a sulfate-reducing biofilm under dynamic conditions. The model includes sulfate reduction by complete and incomplete sulfate-reducing bacteria (SRB); lactate removal by sulfate reduction and by acetogenic bacteria and acetate consumption via methanogenesis. Numerical integration based on the method of characteristics has been developed. The major problem of sulfate-reducing fixed-growth reactors is the formation of undesired bacterial species, which compete for space and substrate within the biofilm with SRB. The effect of COD/ratio on the reactor performances in terms of bacterial species distribution and substrate diffusion trends in the biofilm has been assessed. The simulation results reveal a stratification of microbial activities in biofilm reflecting the different ecological niches created by substrate gradients.

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 (SO42−) 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.