Abstract
In this work, we consider a model of the biodenitrification process taking place in a spatially-distributed bioreactor, and we take into account the limitation of the kinetics by both the carbon source and the oxidized nitrogen. This model concerns a single type of bacteria growing on nitrate, which splits into adherent bacteria or free bacteria in the liquid, taking all interactions into account. The system obtained consists of four diffusion-convection-reaction equations for which we show the existence and uniqueness of a global solution. The system is approximated by a standard finite element method that satisfies an optimal a priori error estimate. We compare the results obtained for three forms of the growth function: single substrate limiting, “multiplicative” form, and “minimum” form. We highlight the limitation of the ‘ single substrate limiting model”, where the dependency of the bacterial growth on the nitrate is neglected, and find that the “minimum” model gives numerical results closer to the experimental results.
Highlights
The biodenitrification process is realized by heterotrophic microbial ecosystems
Most standard models of microbial growth in laboratory bioreactors, such as the chemostat or the piston flow reactor, take into account the tendency of bacteria to adhere to surfaces and form biofilm; such models neglect the possible diffusion of attached biomass
Earlier, we considered a model of the biodenitrification process taking place in a spatially-distributed bioreactor with a single type of bacteria growing on nitrate and that splits into adherent and free bacteria in the liquid, taking all Processes 2020, 8, 890; doi:10.3390/pr8080890
Summary
The biodenitrification process (degradation of nitrite and nitrate into gaseous nitrogen) is realized by heterotrophic microbial ecosystems. Nitrates are the best acceptor of electrons that can replace oxygen so that they should be considered in the modeling as a limiting compound. In the case of the existence of two limiting substrates, the growth function μ(·) can take various forms (see [6]). H.A. et al [8] (2017) compared three dual limitation models (multiplicative, minimum, and Bertolazzi) based on experiments considering two bacteria types, where the growth of the first one is limited by dissolved oxygen and nitrite, whereas the growth of the second by ammonium and nitrite. We will first study the limit of the model with μ(·) given by (1), by comparing it to the case where nitrates are considered as a limiting substrate; it emerges that this first model remains valid up to a threshold beyond which the results are no longer valid. Some numerical tests are presented where the advantage of the growth function (3) is highlighted by comparisons with previous simulations obtained with (1) and (2)
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