Mathematical modeling and analysis of the flocculation process in chambers in series

In this study, the flocculation process in continuous systems with chambers in series was analyzed using the classical kinetic model of aggregation and break-up proposed by Argaman and Kaufman, which incorporates two main parameters: K _a and K _b. Typical values for these parameters were used, i. e., K _a = 3.68 × 10^?5–1.83 × 10^?4 and K _b = 1.83 × 10^?7–2.30 × 10^?7 s^?1. The analysis consisted of performing simulations of system behavior under different operating conditions, including variations in the number of chambers used and the utilization of fixed or scaled velocity gradients in the units. The response variable analyzed in all simulations was the total retention time necessary to achieve a given flocculation efficiency, which was determined by means of conventional solution methods of nonlinear algebraic equations, corresponding to the material balances on the system. Values for the number of chambers ranging from 1 to 5, velocity gradients of 20–60 s^?1 and flocculation efficiencies of 50–90 % were adopted.