Centrifugal Settling of Flocculated Suspensions: A Sensitivity Analysis of Parametric Model Functions

Abstract

The centrifugal settling of a flocculated suspension in a rotating tube can be modeled by a strongly degenerate parabolic partial differential equation whose coefficients depend on two material-specific model functions, namely, the hindered settling function and the effective solid stress function. These model functions are usually given by certain nonlinear algebraic expressions that involve a small number of parameters. The present work is related to the problem of determining these parameters for a given material. This problem of parameter identification consists in minimizing the distance between observed and simulated concentration profiles by successively varying the parameters employed for the simulation, starting from an initial guess. The feasibility and robustness of this procedure, which does not necessarily lead to a unique solution, decisively depends on the sensitivity of the solution of the direct problem to the different scalar parameters. These sensitivities are evaluated by a series of numerical experiments. It turns out that the model is extremely sensitive to the choice of the so-called critical concentration marking the transition between hindered settling and compression. Moreover, the robustness of the parameter identification method depends significantly on whether intermediate (i.e., transient) or stationary concentration profiles are used for identification.

Keywords:

• Centrifugation
• Flocculated suspension
• Numerical simulation
• Parameter identification
• Sedimentation
• Sensitivity analysis

ACKNOWLEDGMENTS

SB and RG acknowledge support by Conicyt (Chile) through Fondecyt project 11080253. RB and RG acknowledge support by Conicyt (Chile) through Fondecyt project 1090456. In addition, RB acknowledges support by Fondap in Applied Mathematics, project 15000001, and BASAL project CMM, Universidad de Chile and Centro de Investigación en Ingeniería Matemática (CI²MA), Universidad de Concepción, and project AMIRA P996/INNOVA 08CM01-17 “Instrumentación y Control de Espesadores.”