ANALYSIS OF A CONSERVATION PDE WITH DISCONTINUOUS FLUX - A MODEL OF SETTLER

A dynamic model of the settling process in the secondary settler of a wastewater treatment plant is given by a nonlinear scalar conservation law c(t) + psi(x,c)x = 0 for the sludge concentration c(t,x), where t he flux function psi(x,c) presents discontinuities. The authors analyz e this partial differential equation (PDE) with emphasis both on the e xistence of stationary solutions and on the evolution of the shock cor responding to the rising of a sludge blanket. Theoretical and numerica l simulations are compared with real data. A model with two classes of particles in interaction is introduced to take into account the thick ening process, which appears to improve the fit with the data. Further more, regulation strategies of the rising of a sludge blanket in case of important water admission to the plant are proposed.