Dynamic Modeling of a Batch Sludge Settling Column by Partial Differential Non Linear Equations with a Moving Interface

C. Valentin (1) , Couenne F. (1) , C. Jallut (1) , J.M. Choubert (2) , M. Tayakout-Fayolle (1)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

The further goal of the model presented in this paper is to propose a new digital tool to predict the behaviour of a main equipment of the water resource recovery facilities, the secondary settling tank. Most of the time, models of this liquid/solid two-phase system are based on a dynamic solid phase mass balance and a settling velocity constitutive expression stemming from the Kynch'assumption. The new model presented here is based on both dynamic mass and dynamic momentum balance equations and on an explicit representation of the sludge blanket depth. Therefore, it stands for a wider range of operating conditions. It includes effective solid stress appearing when the solid particles concentration is above a given threshold and a moving interface above which there is no solid particles: the sludge blanket. A study of the main physical phenomena into a batch sludge sedimentation column (hydrodynamics of two-phase suspensions) is usually carried out before a faithful representation of continuous sedimentation within a continuous settling tank is deduced. The batch settler is divided into three zones (clarification, thickening and compression) by the moving interface, the sludge blanket, and by the thickening/compression concentration threshold. A one dimensional implicit hybrid partial differential non linear equations (Hybrid NL-PDE's) state space representation is proposed based on the different dynamics in each of the three zones as well as the constitutive equations and the boundary conditions. Some simulations are given and compared with sludge blanket height measurements in a column.

Mots clés: Model; Partial Differential Equations (PDE's); Non linear system; Mobile interface; Constitutive equations; Boundary Conditions; Batch sludge settling column; simulations

Domaines: Génie des procédés; Génie chimique; Automatique; Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Automatique / Robotique

C. Valentin, Couenne F., C. Jallut, J.M. Choubert, M. Tayakout-Fayolle. Dynamic Modeling of a Batch Sludge Settling Column by Partial Differential Non Linear Equations with a Moving Interface. ADCHEM 2021 11th IFAC SYMPOSIUM on Advanced Control of Chemical Processes, Jun 2021, Venise (virtual), Italy. 6 p. ⟨hal-03026811⟩