ENCYCLOPÉDIE DE LA RECHERCHE SUR L’ALUMINIUM AU QUÉBEC 2013 | Page 71

DÉVELOPPEMENT, OPTIMISATION ET INTÉGRATION DES PROCÉDÉS DE FABRICATION ET DE CONCEPTION
DEVELOPMENT, OPTIMIZATION AND PROCESS INTEGRATION OF MANUFACTURING AND DESIGN

Modeling the injection of
alumina MODÉLISATION DE LA DISPERSION D’ALUMINE

69

MODELING THE DISPERSION OF ALUMINA
Csilla Kaszás 1, László I. Kiss 1, Jean-François Bilodeau2, Sébastien Guérard2
2

1 Université du Québec à Chicoutimi, Saguenay
Centre de recherche et développement Arvida, Rio Tinto Alcan, Saguenay

For the undisturbed operation of the Hall-Héroult cell, the dissolution and distribution of the alumina in the electrolyte is essential.
Equilibrium of alumina concentration in the cell is never achieved as it is continuously consumed by the process, and added
periodically by the injection system. Even in experimental cells, being much smaller than the industrial ones, the alumina
concentration cannot be considered constant; it changes in space as well as in time. Though concentration can be measured by
electro-analytical methods or by chemical analysis of samples1, a single, discrete value does not provide sufficient information
about the distribution of alumina.

agglomerates not included
in this model, but may be
found in another project
of UQAC2

alumina
injection

calumina(space, time) = ?

Schematic illustration of the objective

The behavior of solutions (steady laminar flow, incompressible fluid, no sources or sinks, isothermal,
no external forces) is described by the following equation.3

where c: concentration of the added material, t: time, v: velocity and D: diffusion coefficient, the
latter is considered constant.
With MATLAB PDE solver, the initialboundary value problems of the above partial
differential equation may be solved in one
space variable and time. One space variable
means that the model could represent a slab,
a cylindre or a spherical geometry.

dimensionless
parameters;
cmax=1

The alumina injection is represented by the
initial condition.
Second type boundary condition was applied
indicating a closed system.

x=0 : center
x=1 : edge

The following simplified study is focusing only on the dispersion of the alumina by diffusion and convection, examining the effect
of the movement of the medium. The kinetics of alumina injection in a real cell is more complex, it depends on the properties of
the alumina and electrolyte as well as on the operating conditions.

v = const
ρ ≠ const

far from the case of
a point feeder

ρ = const
v ~ 1/x or 1/x2
v → ∞ (x=0)

PRIX // AWARD

rapid dispersion

Pe = vX/D

entrainment by the fluid
removes some alumina

For the same concentration, the
injected mass is different for the
3 geometries

Although the cylindrical and the spherical geometry is closer to the reality, the simple radial flow pattern does not correspond to
the real conditions
In the slab geometry, the homogeneous velocity field corresponds to a part of the liquid layer that fills the ACD (anode-cathode
space).

Csilla Kaszás
László I. Kiss
Université du Québec
à Chicoutimi
Jean-François Bilodeau
Sébastien Guérard
Centre de Recherche et
Développement Arvida,
Rio Tinto Alcan

The authors would like to express their gratitude to Rio
Tinto Alcan and the Natural Sciences and Engineering
Research Council of Canada for their financial
support.

1.

2.

ACD

3.

The model could be completed with another spatial variable and a more realistic velocity field can applied.

Journée des étudiants – REGAL

O. Kobbeltvedt, S. Rolseth, J.
Thonstad:
The
dissolution
behaviour of alumina in cryolite
bath on a laboratory scale and in
point fed industrial cells, SINTEF
Materials Technology 1995 p127135
V. Dassylva et al.: Étude de la
formation et de l’ évolution
d’agrégats, Encyclopédie de la
recherche sur l’aluminium au
Québec – edition 2012, Journée
des etudiants du REGAL
V. G. Levich: Physicochemical
Hydrodinamics, Prentice-Hall, Inc
1962

For the stable operation of the Hall-Heroult cell, the dissolution and distribution
La dissolution et la distribution de l’alumine dans l’électrolyte est un facteur essentiel
au bon fonctionnement du procédé Hall-Héroult. La concentration d’alumine est
of the alumina in the electrolyte is an essential factor. There are only discrete
mesurée ponctuellement dans la Palais des congrès de Montréal, QC, Canada, 22 octobre 2013
cuve; ceci ne fournit pas d’information sur la
measurement data available of the concentration of alumina in the reduction
dispersion de l’alumine dans le bain. Le modèle présenté se concentre sur la
pot that do not provide information about the dynamics of the dissolution and
dispersion de l’alumine par diffusion et convection et étudie l’effet de la vitesse
dispersion. The model presented here focuses on the dispersion of the alumina
du milieu, en ignorant le processus complexe de formation d’agrégats d’alumine.
by diffusion and convection, examining the effect of the velocity of the medium,
L’équation de conservation de la masse aux dérivées partielles a été résolue
ignoring the complex process of agglomerate formation of alumina. The relevant
pour une dimension à l’aide du logiciel MATLAB®. Le modèle permet d’obtenir la
partial differential equation was solved in one dimension in MATLAB®. The results
concentration d’alumine