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Conservation law with multiply discontinuous flux modelling a flotation column

Bürger, Raimund ; Diehl, Stefan LU and Martí, María Carmen (2018) In Networks and Heterogeneous Media 13(2). p.339-371
Abstract

Flotation is a unit operation extensively used in the recovery of valuable minerals in mineral processing and related applications. Essential insight to the hydrodynamics of a otation column can be obtained by studying just two phases: gas and uid. To this end, the approach based on the drift-flx theory, proposed in similar form by several authors, is reformulated as a one-dimensional non-linear conservation law with a multiply discontinuous flux. The unknown is the gas volume fraction as a function of height and time, and the flux function depends discontinuously on spatial position due to several feed inlets. The resulting model is similar, but not equivalent, to previously studied clarifier-thickener models for solid-liquid... (More)

Flotation is a unit operation extensively used in the recovery of valuable minerals in mineral processing and related applications. Essential insight to the hydrodynamics of a otation column can be obtained by studying just two phases: gas and uid. To this end, the approach based on the drift-flx theory, proposed in similar form by several authors, is reformulated as a one-dimensional non-linear conservation law with a multiply discontinuous flux. The unknown is the gas volume fraction as a function of height and time, and the flux function depends discontinuously on spatial position due to several feed inlets. The resulting model is similar, but not equivalent, to previously studied clarifier-thickener models for solid-liquid separation and therefore adds a new real-world application to the field of conservation laws with discontinuous flux. Steady-state solutions are studied in detail, including their construction by applying an appropriate entropy condition across each flux discontinuity. This analysis leads to operating charts and tables collecting all possible steady states along with some necessary conditions for their feasibility in each case. Numerical experiments show that the transient model recovers the steady states, depending on the feed rates of the different inlets.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Conservation law, Discontinuous flux, Kinematic flow models, Otation, Steady state
in
Networks and Heterogeneous Media
volume
13
issue
2
pages
33 pages
publisher
American Institute of Mathematical Sciences
external identifiers
  • scopus:85047067153
ISSN
1556-1801
DOI
10.3934/nhm.2018015
language
English
LU publication?
yes
id
3e1183e6-1d62-4691-9de7-92f05e996b14
date added to LUP
2018-05-29 15:03:08
date last changed
2021-09-15 03:17:33
@article{3e1183e6-1d62-4691-9de7-92f05e996b14,
  abstract     = {<p>Flotation is a unit operation extensively used in the recovery of valuable minerals in mineral processing and related applications. Essential insight to the hydrodynamics of a otation column can be obtained by studying just two phases: gas and uid. To this end, the approach based on the drift-flx theory, proposed in similar form by several authors, is reformulated as a one-dimensional non-linear conservation law with a multiply discontinuous flux. The unknown is the gas volume fraction as a function of height and time, and the flux function depends discontinuously on spatial position due to several feed inlets. The resulting model is similar, but not equivalent, to previously studied clarifier-thickener models for solid-liquid separation and therefore adds a new real-world application to the field of conservation laws with discontinuous flux. Steady-state solutions are studied in detail, including their construction by applying an appropriate entropy condition across each flux discontinuity. This analysis leads to operating charts and tables collecting all possible steady states along with some necessary conditions for their feasibility in each case. Numerical experiments show that the transient model recovers the steady states, depending on the feed rates of the different inlets.</p>},
  author       = {Bürger, Raimund and Diehl, Stefan and Martí, María Carmen},
  issn         = {1556-1801},
  language     = {eng},
  month        = {06},
  number       = {2},
  pages        = {339--371},
  publisher    = {American Institute of Mathematical Sciences},
  series       = {Networks and Heterogeneous Media},
  title        = {Conservation law with multiply discontinuous flux modelling a flotation column},
  url          = {http://dx.doi.org/10.3934/nhm.2018015},
  doi          = {10.3934/nhm.2018015},
  volume       = {13},
  year         = {2018},
}