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Advanced methods of flux identification for clarifier–thickener simulation models

Betancourt, Fernando; Bürger, Raimund; Diehl, Stefan LU and Mejías, Camilo (2014) In Minerals Engineering 63(August 2014). p.2-15
Abstract
Mathematical models for the simulation of batch settling and continuous clarifier-thickeners can usually be expressed as a convection-diffusion partial differential equation (PDE). Reliable numerical methods require that the nonlinear flux function of this PDE has been identified for a given material. This contribution summarizes, and applies to experimental data, a recent approach [Bürger, R., Diehl, S., 2013. Inverse Problems 29, 045008] for the flux identification in the case of a suspension that shows no compressive behavior. The experimental Kynch test and the Diehl test, which are based on an initially homogenous suspension either filling the whole settling column or being initially located above clear liquid, respectively, provide... (More)
Mathematical models for the simulation of batch settling and continuous clarifier-thickeners can usually be expressed as a convection-diffusion partial differential equation (PDE). Reliable numerical methods require that the nonlinear flux function of this PDE has been identified for a given material. This contribution summarizes, and applies to experimental data, a recent approach [Bürger, R., Diehl, S., 2013. Inverse Problems 29, 045008] for the flux identification in the case of a suspension that shows no compressive behavior. The experimental Kynch test and the Diehl test, which are based on an initially homogenous suspension either filling the whole settling column or being initially located above clear liquid, respectively, provide data points that represent a convex and concave, respectively, suspension-supernate interface. A provably convex (concave) smooth approximation of this interface is obtained by solving a constrained least-squares minimization problem. The interface-approximating function can be converted uniquely into an explicit formula for a convex (concave) part of the flux function. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Batch sedimentation, Flux identification, Mathematical model, Solid-liquid separation, Thickener simulation
in
Minerals Engineering
volume
63
issue
August 2014
pages
2 - 15
publisher
Pergamon
external identifiers
  • wos:000337880500002
  • scopus:84901596913
ISSN
0892-6875
DOI
10.1016/j.mineng.2013.09.012
language
English
LU publication?
yes
id
85e0cd99-7f25-4713-b225-200bd1bb2c06 (old id 4450794)
alternative location
http://www.sciencedirect.com/science/article/pii/S0892687513002859
date added to LUP
2014-07-02 17:08:36
date last changed
2017-06-25 03:17:05
@article{85e0cd99-7f25-4713-b225-200bd1bb2c06,
  abstract     = {Mathematical models for the simulation of batch settling and continuous clarifier-thickeners can usually be expressed as a convection-diffusion partial differential equation (PDE). Reliable numerical methods require that the nonlinear flux function of this PDE has been identified for a given material. This contribution summarizes, and applies to experimental data, a recent approach [Bürger, R., Diehl, S., 2013. Inverse Problems 29, 045008] for the flux identification in the case of a suspension that shows no compressive behavior. The experimental Kynch test and the Diehl test, which are based on an initially homogenous suspension either filling the whole settling column or being initially located above clear liquid, respectively, provide data points that represent a convex and concave, respectively, suspension-supernate interface. A provably convex (concave) smooth approximation of this interface is obtained by solving a constrained least-squares minimization problem. The interface-approximating function can be converted uniquely into an explicit formula for a convex (concave) part of the flux function.},
  author       = {Betancourt, Fernando and Bürger, Raimund and Diehl, Stefan and Mejías, Camilo},
  issn         = {0892-6875},
  keyword      = {Batch sedimentation,Flux identification,Mathematical model,Solid-liquid separation,Thickener simulation},
  language     = {eng},
  number       = {August 2014},
  pages        = {2--15},
  publisher    = {Pergamon},
  series       = {Minerals Engineering},
  title        = {Advanced methods of flux identification for clarifier–thickener simulation models},
  url          = {http://dx.doi.org/10.1016/j.mineng.2013.09.012},
  volume       = {63},
  year         = {2014},
}