title: From the affinity constant to the half-saturation index: understanding conventional modeling concepts in novel wastewater treatment processes.
abstract: The "affinity constant" (KS) concept is applied in wastewater treatment models to incorporate the effect of substrate limitation on process performance. As an increasing number of wastewater treatment processes rely on low substrate concentrations, a proper understanding of these so-called constants is critical in order to soundly model and evaluate emerging treatment systems. In this paper, an in-depth analysis of the KS concept has been carried out, focusing on the different physical and biological phenomena that affect its observed value. By structuring the factors influencing half-saturation indices (newly proposed nomenclature) into advectional, diffusional and biological, light has been shed onto some of the apparent inconsistencies present in the literature. Particularly, the importance of non-ideal mixing as a source of variability between observed KS values in different systems has been illustrated. Additionally, discussion on the differences existent between substrates that affect half-saturation indices has been carried out; it has been shown that the observed KS for some substrates will reflect transport or biological limitations more than others. Finally, potential modeling strategies that could alleviate the shortcomings of the KS concept have been provided. These could be of special importance when considering the evaluation and design of emerging wastewater treatment processes.
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium; Acciona Agua S.A., R&D Department, Av. De les Garrigues 22, 08820 El Prat del Llobregat, Barcelona, Spain.
authors.forename: Marina
authors.initials: M
authors.lastname: Arnaldos
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium.
authors.forename: Youri
authors.initials: Y
authors.lastname: Amerlinck
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium.
authors.forename: Usman
authors.initials: U
authors.lastname: Rehman
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium.
authors.forename: Thomas
authors.initials: T
authors.lastname: Maere
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium.
authors.forename: Stijn
authors.initials: S
authors.lastname: Van Hoey
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium.
authors.forename: Wouter
authors.initials: W
authors.lastname: Naessens
authors.affiliation: BIOMATH, Department of Mathematical Modelling, Statistics and Bio-informatics, Coupure Links 653, 9000 Gent, Belgium. Electronic address: Ingmar.Nopens@ugent.be.
authors.forename: Ingmar
authors.initials: I
authors.lastname: Nopens
mesh_terms: D007700:Kinetics; D008962:Models, Theoretical; D012722:Sewage / Q000032:analysis*; D014865:Waste Disposal, Fluid; D062065:Wastewater / Q000032:analysis*; D014874:Water Pollutants, Chemical / Q000032:analysis*
chemical_list: D012722:Sewage; D062065:Wastewater; D014874:Water Pollutants, Chemical
keywords: Activated sludge modeling; Half-saturation constant; Kinetic constants; Monod function; Novel modeling frameworks; Switching function