PBM and activated sludge flocculation: From experimental data to calibrated model

Abstract

(vol % and D[4, 3]

Analysis of the aggregation–fragmentation population balance equation with application to coagulation

“…(6)] with the initial condition given by Eq. (14). The integration was terminated when dρ/dτ 10 −6 which was found to be a sufficient condition for the steady state to be reached.…”

“…Interactions of the clusters [12], heterogeneity and anisotropy of the flow field and the associated uncertainty in the estimation of ε can however lead to significantly smaller values of α. In particular, Waldner et al [13] report α ≈ 0.2 for the coagulation of fully destabilized polystyrene particles in a stirred tank, and Nopens et al [14] report α ≈ 0.01 for the flocculation of activated sludge. Further, it is assumed that the two aggregation mechanism superimpose which provides to be suitable for particles with negligible repulsive interactions in a turbulent flow [15].…”

“…The same model was applied by Chung et al [7] to interpret the coagulation of a polymer latex at high solid volume fraction (φ = 0.15-0.20) in a stirred vessel and by Rahmani et al [28] to interpret the flocculation of asphaltenes in a Taylor-Couette flow device. Further, Nopens et al [14] used this model to investigate the flocculation of activated sludge, while Sommer at al. [29] introduced a different fragment distribution (however still a homogeneous one, cf.…”

A methodological approach for direct quantification of the activated sludge floc size distribution by using different techniques

“…In spite of its practical importance, the mechanisms and mathematical modeling of activated sludge flocculation have not been well established, mainly due to the limitations in correct measurement and evaluation of floc size (Nopens et al 2005). Due to the floc's biological nature, the very complex and fragile structure and heterogeneous doi: 10.2166/wst.2009.535 composition, the size measurement procedure itself often influences the experimental outcome and affects the interpretation of the activated sludge floc size distribution (FSD), leading to contradictory results.…”

The inverse problem in granulation modeling—Two different statistical approaches

“…[27][28][29] A more fundamental algorithmic development for the sensitivity of coagulation only processes has been presented by Man et al 30 and Bailleul et al 31 In more general terms, the inverse problem for population balance models has been the subject of research for many years, for instance for the determination of rate constants in agglomeration problems, 32 crystallization 33 and sludge flocculation. 34 More recently, the parameter estimation for a three-dimensional population balance model framework was reported by Ramachandran and Barton. 35 They developed a framework that addresses the numerical stability of the optimization, being challenged by the solving of the discretized population balance model.…”