Mathematical modeling of water flocculation process with high turbidity: studies and comparative analysis between methods and models

Abstract

The quality of water used by a population is directly proportional to the efficiency of its treatment. Mathematical modeling appears in this context as a tool for optimizing processes in order to make them more efficient, economical and sustainable. This work analyzed and compared the effectiveness of phenomenological mathematical models used in flocculation kinetics in water treatment. The results were obtained by comparing the Argaman and Kaufman Model with the Bratby Method; the Aggregation and Rupture Equation Method - MEAR; and the Method of the First Partial Derivative in Relation to the Velocity Gradient in Flocculation - MPDPG and a model that includes a new term (K_C) that contemplates a supposed process of irreversibility of floc. The mathematical modeling was validated and compared with experimental data. The coefficients of the models and methods were obtained using the Excel® solver® tool using spreadsheets from the same application. It was possible to identify that the Bratby Method, which obtained an average deviation of the order of 30%, was the least efficient, while the MEAR and MPDPG Methods, which obtained about 18% of average deviation and the Kc Model with a deviation of the order of 19%, proved to be efficient in describing the experimental data used.

Keywords: flocculation, mathematical modeling, water treatments.