Abstract
A dynamic model of the settling process in the secondary settler of a wastewater treatment plant is given by a nonlinear scalar conservation law for the sludge concentration under the form of a partial differential equation (PDE). A numerical algorithm is given, which also includes a mathematical model of the aeration tank. Theoretical and numerical simulations are then compared with real data. The evolution of the shock corresponding to the rising of a sludge blanket is described by an ordinary differential equation (ODE). Consequently, regulation strategies of the rising of a sludge blanket in case of important water admission to the plant are proposed. We end briefly with two possible extensions. A model with two classes of particles in interaction is introduced to take into account the particle size change, as well as a model giving the distribution of residence times to take into account its effect on the velocity.
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