Investigating kernel structures for Ca-induced activated sludge aggregation using an inverse problem methodology

In certain biological systems, enhancing agents such as calcium (Ca) are applied to improve flocculation. However, the whereabouts of the mechanism is poorly understood which hampers the process optimisation in terms of efficiency and cost. Three different experimental data sets of Ca induced flocculation (resp. 8, 16 and 32 meq Ca2+.l−1) are examined. A Population Balance Model (PBM) is applied to model the aggregation process. As traditional literature expressions for collision frequency and efficiency can not describe the data, an inverse problem solution methodology to recover the aggregation kernel structures from the experimental data is followed. Prior to this, a similarity analysis is performed in order to transform the data and simplify the solution of the inverse problem. Multiple sequential similarity regions are observed suggesting different flocculation mechanisms occurring in time. For every similarity distribution, its own kernel is recovered through the inverse solution methodology. The use of multiple kernels results in improved model predictions. Furthermore, a methodology is proposed to compare the retrieved kernel with literature kernels in order to identify their flaws. This comparison indicates that Ca-addition not only enhances the growth of flocs but also lowers their fractal dimension. Finally, a hypothesis is presented as to how the aggregation kinetics change with increasing amounts of added calcium.

► Inverse problems are solved for experimental datasets of Ca-induced flocculation.
► Multiple similarity regions occur suggesting different kernels are valid in time.
► PBMs with recovered kernels are able to accurately describe the experimental data.
► A method to evaluate and improve existing literature kernels is proposed.
► Kernels should adopt a time dependent fractal dimension.