Flocculation modelling of differential sedimentation based on fundamental physics of settling particles and fractal theory

Abstract

Sedimentation is a fundamental operation in wastewater treatment works. A rational design of sedimentation tanks is currently achieved by plotting iso-percentile (iso-percentage) concentration removal profiles from flocculent settling data. A major drawback of the graphical iso-percentage method is that the iso-percentile lines are often manually interpolated and are mere hand drawn estimations. This is because the settling behaviour of sludge particles is highly non-linear. The manual analytical process is therefore very tedious, inaccurate and subjective. Hence, an optimised design of sedimentation tanks is necessary in order to eliminate the errors incurred during data analysis. In this study, a mechanistic iso-percentile flocculent model (referred to as the velocity flocculation model) is developed to simulate the behaviour of flocculating colloidal particles in turbid water. This model is based on the physical meanings of flocculent settling particles and on fractal theory. It is formulated to produce automated iso-percentile curves which are fundamental in the design of sedimentation tanks. The iso-percentile model was vertically integrated into a velocity model to produce a model expressing the velocity of particles as a function of removal rate. The velocity model has an obvious advantage over the iso-percentile model in that it is easy to contextualize. It can be reverted back to the iso-percentile trajectory analysis eliminating the need for extensive data interpolation and may in future eliminate the need for settling column analysis altogether. In the current study, the integrated velocity form is used to predict instantaneous flocculent settling velocity of fine suspended particles under near quiescent conditions. This is vital since it is difficult to obtain velocity values in-situ or directly from sedimentation tanks. Model validity and competency was tested by a direct comparison with existing literature models, such as Ozer’s model and Ramatsoma and Chirwa’s model. Model comparison was based on the goodness of fit, the least sum of square errors and mathematical consistency with known flocculent settling behaviour. The newly developed iso-percentile model achieved a more accurate simulation of physical experimental data, did not violate any of the mathematical constraints and yielded lower sum of square errors than originally achieved by Ozer and Ramatsoma and Chirwa. Notably, the proposed velocity model offers a distinctive advantage over conventional interpolated-iso-percentile based models which are prone to numerical errors during interpolation. Its performance (velocity model) was compared against Je and Chang’s velocity model. Higher velocity values were observed for the new model than for Je and Chang’s model implying that empirically based models would tend to under-predict the velocity values. The model developed in this study brings us one step closer to achieving full automation of the settling tank and clarifier design.