Representation of a Continuous Settling Tank by Hybrid Partial Differential Non Linear Equations for Control Design. Issue 2 (2020) - Valentin, C.; Dochain, D.; Jallut, C.; Santos Martins, V. Dos
Abstract: The representation of the main physical phenomena of continuous sedimentation within a settling tank (hydrodynamics of two-phase suspensions) is essential for the further control design of the quality of the solid-liquid separation. The model is still made of non-linear partial differential equations after simplifying assumptions and considering a one dimensional settler. It comes from both mass and momentum balance equations and includes effective solid stress appearing when the solid particles concentration is above a given threshold which depends on the quality of the sludge. Then a mobile interface appears between two different behaviours. The settler is divided into two zones to represent this discrete phenomenon. Our goal is to develop a model that can be used for a further control design of the water quality at the top outlet of the settling tank. A hybrid state space representation is provided with the different dynamics in each of the two zones, the constitutive equations and the boundary conditions. The steady state profile is calculated. A simplified version of a settling tank model is simulated.