Invasion moving boundary problem for a biofilm reactor model

The work presents the analysis of the free boundary value problem related to the invasion model of new species in biofilm reactors. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species growth and a system of semi-linear elliptic partial differential equations describing the substrate trends. The model is completed with a system of elliptic partial differential equations governing the diffusion and reaction of planktonic cells, which are able to switch their mode of growth from planktonic to sessile when specific environmental conditions are found. Two systems of nonlinear differential equations for the substrate and planktonic cells mass balance within the bulk liquid are also considered. The free boundary evolution is governed by a differential equation that accounts for detachment. The qualitative analysis is performed and a uniqueness and existence result is discussed. Furthermore, two special models of biological and engineering interest are discussed numerically. The invasion of Anammox bacteria in a constituted biofilm inhabiting the deammonification units of the wastewater treatment plants is simulated. Numerical simulations are run to evaluate the influence of the colonization process on biofilm structure and activity.Comment: 20 pages, 11 figures, original pape

Modeling sorption of emerging contaminants in biofilms

A mathematical model for emerging contaminants sorption in multispecies biofilms, based on a continuum approach and mass conservation principles is presented. Diffusion of contaminants within the biofilm is described using a diffusion-reaction equation. Binding sites formation and occupation are modeled by two systems of hyperbolic partial differential equations are mutually connected through the two growth rate terms. The model is completed with a system of hyperbolic equations governing the microbial species growth within the biofilm; a system of parabolic equations for substrates diffusion and reaction and a nonlinear ordinary differential equation describing the free boundary evolution. Two real special cases are modelled. The first one describes the dynamics of a free sorbent component diffusing and reacting in a multispecies biofilm. In the second illustrative case, the fate of two different contaminants has been modelled

Moving boundary problem for the detachment in multispecies biofilms

The work presents the qualitative analysis of the free boundary value problem related to the detachment process in multispecies biofilms. In the framework of continuum approach to one-dimensional mathematical modelling of multispecies biofilm growth, we consider the system of nonlinear hyperbolic partial differential equations governing the microbial species growth, the differential equation for the biomass velocity, the differential equation that governs the free boundary evolution and also accounts for detachment, and the elliptic system for substrate dynamics. The characteristics are used to convert the original moving boundary equation into a suitable differential equation useful to solve the mathematical problem. We also provide another form of the same equation that could be used in numerical applications. Several properties of the solutions to the free boundary problem are shown, such as positiveness of the functions that describe the microbial concentrations and estimates on the characteristic functions. Uniqueness and existence of solutions are proved by introducing a suitable system of Volterra integral equations and using the fixed point theorem

On a free boundary problem for biosorption in biofilms

The work presents the qualitative analysis of the free boundary value problem related to the biosorption process in multispecies biofilms. In the framework of continuum biofilm modeling, the mathematical problem consists of a system of nonlinear hyperbolic partial differential equations for microbial species growth and spreading, a system of semilinear parabolic partial differential equations describing the substrate trends and a system of semilinear parabolic partial differential equations accounting for the diffusion, reaction and biosorption of different agents on the various biofilm constituents. Two systems of nonlinear hyperbolic partial differential equations have been considered as well for modeling the dynamics of the free and bounded sorption sites. The free boundary evolution is regulated by a nonlinear ordinary differential equation. Overall, this leads to a free boundary value problem essentially hyperbolic. The main result is the existence and uniqueness of the solutions to the stated free boundary value problem, which have been derived by converting the partial differential equations to Volterra integral equations and then using the fixed point theorem. Moreover, the work is completed with numerical simulations for a real case examining the growth of a heterotrophic–autotrophic biofilm devoted to wastewater treatment and acting as a sorbing material for heavy metal biosorption. Keywords: Biosorption; Multispecies biofilms; Hyperbolic free boundary value problem; Method of characteristic

A mechanistic mathematical model for photo fermentative hydrogen and polyhydroxybutyrate production

An original mathematical model describing the photo fermentation process is proposed. The model represents the first attempt to describe the photo fermentative hydrogen production and polyhydroxybutyrate accumulation, simultaneously. The mathematical model is derived from mass balance principles and consists of a system of ordinary differential equations describing the biomass growth, the nitrogen and the substrate degradation, the hydrogen and other catabolites production, and the polyhydroxybutyrate accumulation in photo fermentation systems. Moreover, the model takes into account important inhibiting phenomena, such as the self-shading and the substrate inhibition, which can occur during the evolution of the process. The calibration was performed using a real experimental data set and it was supported by the results of a sensitivity analysis study. The results showed that the most sensitive parameters for both hydrogen and PHB production were the hydrogen yield on substrate, the catabolites yield on substrate, and the biomass yield. Successively, a different experimental data set was used to validate the model. Performance indicators showed that the model could efficiently be used to simulate the photo fermentative hydrogen and polyhydroxybutyrate production by Rhodopseudomonas palustris. For instance, the index of agreement of 0.95 was observed for the validated hydrogen production trend. Moreover, the model well predicted the maximum PHB accumulation in bacterial cells. Indeed, the predicted and observed accumulated PHB were 4.5 and 4.8%, respectively. Further numerical simulations demonstrated the model consistency in describing process inhibiting phenomena. Numerical simulations showed that the acetate and nitrogen inhibition phenomena take place when concentrations are higher than 12.44 g L-1 and lower than 4.76 mg L-1, respectively. Finally, the potential long term hydrogen production from accumulated polyhydroxybutyrate in bacterial cells was studied via a fast-slow analysis technique

Modelling the effect of SMP production and external carbon addition on S-driven autotrophic denitrification

The aim of this study was to develop a mathematical model to assess the effect of soluble microbial products production and external carbon source addition on the performance of a sulfur-driven autotrophic denitrification (SdAD) process. During SdAD, the growth of autotrophic biomass (AUT) was accompanied by the proliferation of heterotrophic biomass mainly consisting of heterotrophic denitrifiers (HD) and sulfate-reducing bacteria (SRB), which are able to grow on both the SMP derived from the microbial activities and on an external carbon source. The process was supposed to occur in a sequencing batch reactor to investigate the effects of the COD injection on both heterotrophic species and to enhance the production and consumption of SMP. The mathematical model was built on mass balance considerations and consists of a system of nonlinear impulsive differential equations, which have been solved numerically. Different simulation scenarios have been investigated by varying the main operational parameters: cycle duration, day of COD injection and quantity of COD injected. For cycle durations of more than 15 days and a COD injection after the half-cycle duration, SdAD represents the prevailing process and the SRB represent the main heterotrophic family. For shorter cycle duration and COD injections earlier than the middle of the cycle, the same performance can be achieved increasing the quantity of COD added, which results in an increased activity of HD. In all the performed simulation even in the case of COD addition, AUT remain the prevailing microbial family in the reactor

Production of biohythane from food waste via an integrated system of continuously stirred tank and anaerobic fixed bed reactors

The continuous production of biohythane (mixture of biohydrogen and methane) from food waste using an integrated system of a continuously stirred tank reactor (CSTR) and anaerobic fixed bed reactor (AFBR) was carried out in this study. The system performance was evaluated for an operation period of 200 days, by stepwise shortening the hydraulic retention time (HRT). An increasing trend of biohydrogen in the CSTR and methane production rate in the AFBR was observed regardless of the HRT shortening. The highest biohydrogen yield in the CSTR and methane yield in the AFBR were 115.2 (±5.3) L H2/kgVSadded and 334.7 (±18.6) L CH4/kgCODadded, respectively. The AFBR presented a stable operation and excellent performance, indicated by the increased methane production rate at each shortened HRT. Besides, recirculation of the AFBR effluent to the CSTR was effective in providing alkalinity, maintaining the pH in optimal ranges (5.0–5.3) for the hydrogen producing bacteria

Photofermentative production of hydrogen and poly-β-hydroxybutyrate from dark fermentation products

The aim of this work is to investigate the hydrogen and poly-β-hydroxybutyrate (PHB) production during the photofermentative treatment of the effluent from a dark fermentation reactor fed with the organic fraction of municipal solid waste. Two different inocula, an adapted culture of Rhodobacter sphaeroides AV1b and a mixed consortium of purple non sulphur bacteria have been investigated under the same operational conditions. Different hydrogen productivities of 364 and 559NmL H2 L(-1) were observed for the Rhodobacter sphaeroides and the mixed culture consortium tests, respectively: the consortium of PNSB resulted 1.5-fold more productive than the pure culture. On the other hand, Rhodobacter sphaeroides culture showed a higher PHB productivity (155mg PHB g COD(-1)) than the mixed culture (55mg PHB g COD(-1)). In all the tests, the concomitant H2 and PHB production was associated to a dissolved COD removal higher than 80%

Mass loss controlled thermal pretreatment system to assess the effects of pretreatment temperature on organic matter solubilization and methane yield from food waste.

HIGHLIGHTS Direct correlation between substrate composition and TP effect was identified. The new experimental TP set-up minimized organic compound loss during TP of FW. The solubilization of carbohydrate and protein determined the optimal temperature of FW TP. Low temperature (80°C) TP attained the highest carbohydrate solubilization and methane yield. The effects of thermal pretreatment (TP) on the main characteristics of food waste (FW) and its biochemical methane potential (BMP) and distribution of volatile fatty acids (VFAs) under mesophilic condition (35°C) were investigated. The TP experiments were carried out at 80, 100, 120°C for 2 h and 140°C for 1 h. The designed TP set-up was able to minimize the organic matter loss during the course of the pretreatment. Soluble organic fractions evaluated in terms of chemical oxygen demand (COD) and soluble protein increased linearly with pretreatment temperature. In contrast, the carbohydrate solubilization was more enhanced (30% higher solubilization) by the TP at lower temperature (80°C). A slight increment of soluble phenols was found, particularly for temperatures exceeding 100°C. Thermally pretreated FW under all conditions exhibited an improved methane yield compared to the untreated FW, due to the increased organic matter solubilization. The highest cumulative methane yield of 442 (±8.6) mL/gVSadded, corresponding to a 28.1% enhancement compared to the untreated FW, was obtained with a TP at 80°C. No significant variation in the VFAs trends were observed during the BMP tests under all investigated conditions

A sensitivity analysis for sulfur-driven two-step denitrification model

A local sensitivity analysis was performed for a S0-driven two-step denitrification model, accounting for NO2 - accumulation, biomass growth and S0 solubilization. The model sensitivity was aimed at verifying the model stability, understanding the identifiability of the model structure and evaluating the model parameters to be further optimized. The sensitivity analysis identified the mass specific area of the sulfur particles (a*) and hydrolysis kinetic constant (k1) as the dominant parameters. Additionally, the maximum growth rate of the denitrifying biomass on NO3 - (μmax 2,3) and NO2 - (μmax 2,4) were detected as the most sensitive kinetic parameters. Further calibration would be performed for the sensitive model parameters to optimize the quality of the model