Role of the diffusion coefficient in one-dimensional convection – diffusion models for sedimentation/thickening in secondary settling tanks

Mathematical Modelling and Computer Simulation of Activated Sludge Systems

“…As a result, a discrete solids profile is obtained rather than a settling curve. A limited number of studies were conducted to estimate n clar which is required to obtain mesh-independent results (Verdickt et al 2006). Wett (2002) proposed a conceptual three-layer model which differentiates clarification, hindered settling and compression zones.…”

“…In theory, as the number of layers increases, a model should resolve the detailed behaviour of the settling process and improve the accuracy of the predicted settling curve (Jeppsson and Diehl 1996;Ekama et al 1997;Vanderhasselt and Vanrolleghem 2000). Verdickt et al (2006) proposed the following exponential function to describe the observed relationship between n clar,min and E z : For example, Takacs et al (1991) originally modelled the clarifier as consisting of 10 layers.…”

“…In addition to the E z value, the results presented by Verdickt et al (2006) indicated that the operational status of the clarifier strongly influenced the required number of layers. Therefore, the authors emphasized that caution should be taken when using values for n clar,min under different conditions than those for which they were derived.…”

“…Hamilton et al (1992) included the dispersion term in their model and suggested the spatially constant value 0.54 m 2 /h for E z . Verdickt et al (2006) investigated in depth the role of the E z coefficient in modelling sedimentation/thickening processes in secondary clarifiers. This is an advantage for the identification process, but causes certain dangers in terms of physical interpretation.…”

Steady-state, control, and capacity calculations for flocculated suspensions in clarifier–thickeners

“…In other words, the entropy condition judges those profiles to be admissible that are produced by vanishing hydrodynamic diffusion (in the context of other models, this is also called vanishing viscosity solution). Let us mention that hydrodynamic diffusion with a constant ε N 0 is part of some clarifier-thickener models including those of Lev et al (1986) and Verdickt et al (2006). The omission of hydrodynamic diffusion, which nevertheless is implicitly present through the entropy condition, is justified by practical limitations, theoretical considerations, computational comparisons, and experimental results, see Section 7.4 of Berres et al (2003) for details.…”