The activated sludge process is widely used for wastewater treatment. Before discharging the cleaned water to the receiving water body, the sludge needs to be separated from the sludge. This is traditionally done gravitationally, exploiting the higher density of the sludge. However, the flocculation state of the sludge plays an important role in this settling process. Modeling of activated sludge flocculation using a PBM framework with existing kernels from literature has proven to be a tedious task (Nopens et al., 2005). An alternative way of retrieving the kernels based on experimental data is to solve the inverse problem hereby exploiting self-similarity present in the data (Wright and Ramkrishna, 1992; Sathyagal et al., 1995).

We present here the application of the inverse problem approach to extract the aggregation kernel for the flocculation process. The computational intricacies associated with the inverse problem of interest are discussed. The quality of the inversion was adjudged through the comparison of the forward solution to the population balance equation with the experimental data. Results showed good description for the entire distribution dynamics, including the peaks and tails. The inverse problem approach results in an empirical equation for the aggregation kernel, which hardly conveys any physical significance. This limits the applicability range of the model to optimize and control the process in general. To overcome this, the empirical kernel can be confronted with mechanistic kernels. In the activated sludge flocculation application under study, these kernels might correspond to the shear aggregation, differential settling, charge effects, etc. The objective of the presentation is to discuss the formulation of the effective aggregation kernel that considers two or more concurrent and /or competitive mechanisms in the flocculation process.

References

Nopens, I., Koegst, T., Mahieu, K., Vanrolleghem, P., 2005. Population balance model and activated sludge flocculation: from experimental data to a calibrated model. AIChE J. 51 (5), 1548–1557.

Sathyagal, A., Ramkrishna, D., Narsimhan, G., 1995. Solution of inverse problems in population balances — ii particle break-up. Comp. Chem. Eng. 19 (4), 437–451.

Wright, H., Ramkrishna, D., 1992. Solutions of inverse problems in population balances — i aggregation kinetics. Comp. Chem. Eng. 16 (12), 1019–1038.