The continuum heterogeneous biofilm model with multiple limiting substrate Monod kinetics

Net growth rate of continuum heterogeneous biofilms with inhibition kinetics

Biofilm systems can be modeled using a variety of analytical and numerical approaches, usually by making simplifying assumptions regarding biofilm heterogeneity and activity as well as effective diffusivity. Inhibition kinetics, albeit common in experimental systems, are rarely considered and analytical approaches are either lacking or consider effective diffusivity of the substrate and the biofilm density to remain constant. To address this obvious knowledge gap an analytical procedure to estimate the effectiveness factor (dimensionless substrate mass flux at the biofilm-fluid interface) was developed for a continuum heterogeneous biofilm with multiple limiting-substrate Monod kinetics to different types of inhibition kinetics. The simple perturbation technique, previously validated to quantify biofilm activity, was applied to systems where either the substrate or the inhibitor is the limiting component, and cases where the inhibitor is a reaction product or the substrate also acts as the inhibitor. Explicit analytical equations are presented for the effectiveness factor estimation and, therefore, the calculation of biomass growth rate or limiting substrate/inhibitor consumption rate, for a given biofilm thickness. The robustness of the new biofilm model was tested using kinetic parameters experimentally determined for the growth of Pseudomonas putida CCRC 14365 on phenol. Several additional cases have been analyzed, including examples where the effectiveness factor can reach values greater than unity, characteristic of systems with inhibition kinetics. Criteria to establish when the effectiveness factor can reach values greater than unity in each of the cases studied are also presented.

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.

Dual substrate limitation modeling and implications for mainstream deammonification

Substrate limitation occurs frequently in wastewater treatment and knowledge about microbial behavior at limiting conditions is essential for the use of biokinetic models in system design and optimization. Monod kinetics are well-accepted for modeling growth rates when a single substrate is limiting, but several models exist for treating two or more limiting substrates simultaneously. In this study three dual limitation models (multiplicative, minimum, and Bertolazzi) were compared based on experiments using nitrite-oxidizing bacteria (limited by dissolved oxygen and nitrite) and ANaerobic AMMonia-OXidizing bacteria or Aanammox (limited by ammonium and nitrite) within mixed liquor from deammonification pilots. A deterministic likelihood-based parameter estimation followed by Bayesian inference was used to estimate model-specific parameters. The minimum model outperformed the other two by a slight margin in three separate analyses. 1) Parameters estimated using the minimum model were closest to parameters estimated from single limitation batch tests. 2) Among simulations based on each model's own estimated parameters, the minimum model best described the experimental observations. 3) Among simulations based on parameters estimated from single limitation, the minimum model best described the experimental observations. The dual substrate model selected among the three studied can effect a 75% process performance variation based on simulations of a full-scale mainstream deammonification system.

Resource recovery using whey permeate to cultivate Phellinus linteus mycelium: Solid-state and submerged liquid fermentation

The growth characteristics of Phellinus linteus mycelium were assessed and compared under solid-state fermentation (SSF) and submerged liquid fermentation (SLF) systems on whey permeate medium. Response surface methodology was used to investigate the growth rates of mycelia under various conditions of operating temperature (TO), initial pH, and substrate concentration ([S]). The optimal growth conditions of P. linteus mycelium were determined to be 26.1°C, pH 4.6, and 60.3g of lactose/L in the SSF system, and 29.0°C, pH 5.0, and 65.3g of lactose/L in the SLF system. The maximum growth rates were predicted to be 1.92 ± 0.01 mm/d in SSF and 192.1 ± 0.0mg/L per day in SLF. Random trials were conducted to experimentally validate the evaluated optimal conditions. The differences between the modeled and observed values were only 5.3% in the SSF system and 6.1% in the SLF system. Significant engineering factors differed between the fermentation techniques; TO was significant in both cultivation systems, whereas initial pH was significant in SSF but [S] was significant in SLF. Our findings can be used to guide the operation of the bioconversion process for cultivating P. linteus mycelium using whey permeate wastewater.