Note: Descriptions are shown in the official language in which they were submitted.
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Method for estimating dynamic state variables in an electrolytic cell suitable
for the
Hall-Fleroult electrolysis process
Technical field of the invention
The invention relates to the field of fused salt electrolysis, and more
precisely to the
monitoring of Hall-Heroult process for making aluminium by fused salt
electrolysis. In
particular, the invention relates to a novel method of monitoring aluminium
smelting
process. This method is based on a particular approach of anode current
measurement
using digital communication for easy wiring, installation and maintenance, and
applies a
Kalman filter type state observer to a dynamic model of the process for the
estimation of
unmeasured process variables.
Prior art
The Hall-Heroult process is the only continuous industrial process for
producing metallic
.. aluminium from aluminium oxide. Aluminium oxide (A1203) is dissolved in
molten cryolite
(Na3AIF6), and the resulting mixture (typically at a temperature comprised
between 940 C
and 970 C) acts as a liquid electrolyte in an electrolytic cell. An
electrolytic cell (also called
"pot") used for the Hall-Heroult process typically comprises a steel shell, a
lining usually
made from refractory bricks, a cathode usually covering the whole bottom of
the pot (and
which is usually made from graphite, anthracite or a mixture of both), and a
plurality of
anodes (usually made from carbon) that plunge into the liquid electrolyte.
Anodes and
cathodes are connected to external busbars. An electrical current is passed
through the
cell (typically at a voltage between 3.7 V to 5 V) which splits the aluminium
oxide in
aluminium ions and oxygen ions. The oxide ions are reduced to oxygen at the
anode, said
oxygen reacting with the carbon of the anode. The aluminium ions move to the
cathode
where they accept electrons supplied by the cathode; the resulting metallic
aluminium is
not miscible with the liquid electrolyte, has a higher density than the liquid
electrolyte and
will thus accumulate as a liquid metal pad on the cathode surface from where
it needs to
be removed from time to time, usually by suction.
In order to decrease the capital cost per ton of production capacity of
aluminum, the size
of aluminium reduction cells, as well as the number of anodes per cell, tends
to increase.
Thus, keeping the cell in a balanced state has become increasingly important.
One of the
crucial process variables is the alumina content and its uniformity in the
cell. The
concentration of dissolved alumina needs to be regulated in a limited range to
prevent
anode effect and the formation of sludge, and its distribution affects the
balance of the
cell. As alumina is consumed during the electrolysis process, it must be added
regularly,
through so-called feeders. Feeders are most often associated with crust-
breakers that
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provide a hole into the crust of solidified liquid bath (containing a mixture
of cryolite and
alumina) that forms on the top of the electrolyte layer; the feeder then dumps
alumina
powder through that hole into the liquid bath.
However, the concentration of dissolved alumina in the electrolyte of an
electrolytic cell
does not lend itself to direct or continuous measurement during operation: a
sample for
chemical analysis is usually taken several times per weeks but not necessarily
each day ¨
this would be totally insufficient to identify for instance a drift of alumina
concentration due
to faulty equipment, such as malfunctioning of the crust breaker or feeder, or
a leak of the
feeder. What can be measured directly and continuously is cell resistance: the
currently
available control strategies of the process, such as the ones described in US
4,654,129
and US 4,766,552, are largely dependent on the cell resistance. The cell
resistance
represents a combination of the average anode-cathode distance (ACD), global
bath
composition and bath properties in the cell, which is not able to reflect the
spatial
variations in the cell. As a consequence, approaches based on cell resistance
would leave
localised abnormalities undetected until they become severe and apparent on
the cell
resistance.
In order to improve the cell control, and, in particular, to identify
defective feeders or crust
breakers early, it would be desirable to gain localized information on
operating parameters
within an electrolysis cell. As an example, it is known (see K. Rye et al.,
"Current
redistribution among individual anode carbons in a Hall-Heroult prebake cell
at low
alumina concentration", TMS Light Metals 1998, p. 241-246) that anodes located
in areas
where the concentration of dissolved alumina is low take less current than
anodes in
areas where the alumina concentration is higher. Various methods and devices
for
measurement of the current through each individual anode have been proposed.
These
methods include the calculation of the anode currents from voltage drop
measurement
across a length of conductor (see US 4,786,379 and WO 94/002859), and the use
of Hall
Effect sensors (see J.W. Evans and N. Urata ("Wireless and Non-Contacting
Measurement of Individual Anode Currents in Hal-Heroult Pots; Experience and
Benefits",
Light Metals 2012, TMS, p. 939-942).
The measurement of anode current distribution in a cell provides a general
guide to the
cell conditions in the vicinity of each anode, but a quantitative analysis
allowing to obtain
localized information on the electrolysis process in a Hall-Heroult cell is
very difficult. This
is because the variation and interactions of anode currents are complicated,
for example,
through a number of ways as follows:
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(i) While the anode current affects local cell conditions, it is also affected
by these
conditions.
(ii) Variation in one anode current will affect others due to the controlled
line current.
(iii) Anode current represents a combination of localized variables. As they
are coupled,
the separation of one variable from others is not easy.
(iv) There are mass and energy transfers within the cell that will cause
spatial variations,
which, in turn, can alter the anode current distribution.
Therefore, anode current needs to be treated as part of a dynamic system,
where the
variations of process variables are taken into account.
State observer is a mathematical tool in system science that is used to
estimate the
internal states of a dynamic system based on the measured inputs and outputs
of the
system. It provides the basic structure to the process monitoring and control
methods in a
wide range of industrial applications.
Kalman filter-type state observer has been disclosed in a number of
publications, such as
US 4,814,050 and WO 2009/067019. In these approaches, the state estimation is
based
on the whole cell, thus the spatial variations are not accounted for. The use
of Kalman
filter-type state observer with anode currents in Hall-Heroult cells has been
discussed in a
certain number of papers: Jakobsen et.al., "Estimating alumina concentration
distribution
in aluminium electrolysis cells", Proc. 10th IFAC Symposium on Automation in
Mining,
Mineral and Metal Processing, p.253-258 (2001); K. Hestetun, M. Hovd,
"Dectecting
abnormal feed rate in aluminium electrolysis using extended Kalman filter", I
FAC World
Congress, Praha 2005; and K. Hestetun, M. Hovd, "Detection of abnormal alumina
feed
rate in aluminium electrolysis cells using state and parameter estimation",
16th European
Symposium on Computer Aided Process Engineering and 9th International
Symposium on
Process Systems Engineering, Elsevier 2006, p.1557-1562. These papers
attempted to
estimate local cell conditions using the measured individual anode current.
However, as
pointed out by the authors, the ACD change cannot be accommodated in these
methods.
In fact, the initial conditions need to be carefully chosen in the mentioned
papers, and are
assumed to be constant, which deviates the purpose of state estimation.
The problem that the present invention endeavors to resolve is therefore to
propose an
improved method for monitoring of aluminium reduction cells which can deal
with the
interactions between spatial process variables and interaction between current
in different
anodes. Moreover, the invention wishes to provide such a method, which allows
for
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different initial estimation of states and can be used effectively online. And
eventually, the
method for monitoring aluminium reduction cells should be simple, reliable and
robust in
view of its use in an industrial environment.
Object of the invention
The present invention is devoted to the estimation of spatial alumina
concentration and
local ACD using a multi-stage state observer. In each stage, the cell is
discretized
successively into subsystems, with each containing a number of anodes. The
states in
each subsystem are estimated based on a dynamic model using the measurement of
anode currents associated with the subsystem, measurement of cell voltage,
feeding
information and the estimation from the previous stage.
The dynamic model used in each stage of the state observer has the following
features:
1. It includes the dynamics of alumina addition, dissolution and consumption.
The addition
of the alumina is referred to the dumps from the feeders. The dissolution of
the alumina
follows a specific rate equation and the consumption of the dissolved alumina
can be
obtained from Faraday's equation. In addition, the model also deals with the
mass transfer
between subsystems due to the induced bath flow.
2. It includes the dynamics of ACD variation, which is associated with the
consumption of
carbon anodes, the beam movement, and the accumulation of liquid aluminium at
the
cathode.
3. It calculates cell voltage from a semi-empirical equation, which is a
function of anode
current, alumina concentration, ACD and other parameters. Cell voltage
equations are
known by a person skilled in the art and can be found in the standard textbook
of
Grjotheim, K. & Kvande, H. 1993, "Introduction to aluminium electrolysis:
understanding
the Hall-Hero ult process", Aluminium-Verlag, Dusseldorf, or in Haupin's
paper,
"Interpreting the components of cell voltage", TMS Light Metals 1998, p. 531-
537.
The model can be represented as the following discrete-time state-space form:
N +1
cun = fl(Cun,kun, feedN ,M
N+1 r N =N AA-
Cd = 2 (Cd , mun,/ , (42 )
ACDN+1 = f3(ACDN ,BAIN )
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vN = h(S/,ACDN,iN,O)
(equation 1)
where N represents the time step, cõ is the concentration of the undissolved
alumina, kõ
is the effective rate constant for the dissolution of alumina, cd is the
concentration of the
5
dissolved alumina, M is the mass of bath in the subsystem, BM is the variation
in beam
movement, i is the total anode current flowing into the subsystem impacting
the
consumption of dissolved alumina and the rate of change of ACD, d1 and d2
represent the
mass transfer between relevant subsystems, v is the cell voltage, h represents
the voltage
equation, e represents the relevant process parameters.
The estimation of spatial alumina concentration and ACD is achieved by a state
observer.
In an advantageous embodiment the observer is of Kalman filter type, which
estimates the
state variables as well as their uncertainties, and sequentially updates the
estimation
when the next measurement is available, based on a weighted average. According
to an
essential feature of the present invention, the estimation result from one
stage is used an
input in the next stage.
A first object of the invention is a method of producing aluminium in an
electrolytic cell
using the Hall-Heroult electrolysis process, said cell comprising
- a cathode forming the bottom of said electrolytic cell and comprising a
plurality
of parallel cathode blocks, each cathode block carrying at least one current
collector bar and two electrical connections points,
- a lateral lining defining together with the cathode a volume containing
the liquid
electrolyte and the liquid metal resulting from the Hall-Heroult electrolysis
process,
said cathode and lateral lining being contained in an outer metallic shell,
- a plurality of anode assemblies suspended above the cathode, each anode
assembly comprising at least one anode and a metallic anode rod connected to
an anode busbar (so-called "anode beam"),
- a plurality of alumina feeders by which alumina powder is fed into the
liquid
bath,
said method comprising the following steps:
- dividing said cell into at least n subsystems,
- for each subsystem, estimating the local value of at least one target or
output
parameter on the basis of the value of the measurement of at least one input
parameter,
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- modifying at least one of said input parameters in the cell by exerting a
physical
action upon the cell, if at least one estimated value of said output
parameter, for
at least one subsystem, is substantially different from another estimated
value
of said output parameter for another subsystem.
Said output parameter is the local alumina concentration in the subsystem
and/or the
alumina dissolution rate and/or the local anode-cathode distance in the
subsystem.
Said input parameter is selected from the group formed by: currents of anodes
in the
subsystem, anode beam movement in the subsystem, cell voltage in the
subsystem,
alumina dumps in the subsystem, ACD change rate, and/or said input parameter
is the
output of a previous estimate of one or more of said local variables.
In an advantageous embodiment said input parameter is the individual anode
current
determined for each anode in the subsystem.
The number of subsystems (n) is advantageously chosen between 2 and 16, and is
preferably equal to 4. Said subsystems correspond to sectors of substantially
same
length, divided along the main dimension of the cell.
In an advantageous embodiment said output parameter is the local concentration
of
alumina in the bath, and said physical action comprises increasing or
decreasing the
alumina dump in the subsystem in which the estimated concentration of alumina
in the
bath is inferior or superior, respectively, to a predetermined target value.
In another advantageous embodiment, which can be combined with the previous
one,
said output parameter is the anode ¨ cathode distance, and said physical
action
comprises increasing or decreasing the anode ¨ cathode distance, when the
estimated
anode ¨ cathode distance is inferior or superior, respectively, to a
predetermined target
value.
Said method can comprise the following steps,
- measuring at least one value, called here "level 1 measured value", of said
input
parameter for the whole cell,
- obtaining at least one value, called here "level 1 estimated value", of said
output
parameter, on the basis of said level 1 measured value, using a mathematical
observer;
- dividing said cell into at least two subsystems called "level 2 subsystems",
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- for each level 2 subsystem, measuring at least one value, called "level 2
measured
value", of said input parameter,
- for each level 2 subsystem, obtaining at least one value, called "level 2
estimated
value", of said output parameter, on the basis both of said level 2 measured
value
and of said level 1 estimated value, using said mathematical observer.
It can further comprise the following steps, carried out in a recursive
(cascaded) way:
- dividing said cell into at least 2n subsystems of level n,
- for each subsystem of level n: measuring at least one value, called
"level n
measured value", of said input parameter
- for each subsystem of level n: obtaining at least one value, called
"level n
estimated value", of said output parameter, on the basis both of said level n
measured value and of said level (n-1) estimated value, using said
mathematical
observer.
In an advantageous embodiment said mathematical observer is of the Kalman
filter-type.
Another object of the invention is an electrolytic cell suitable for the Hall-
Heroult
electrolysis process, said cell comprising
- a cathode forming the bottom of said electrolytic cell and comprising a
plurality of
parallel cathode blocks, each cathode block carrying at least one current
collector
bar and two electrical connections points,
- a lateral lining defining together with the cathode a volume containing
the liquid
electrolyte and the liquid metal resulting from the Hall-Heroult electrolysis
process,
said cathode and lateral lining being contained in an outer metallic shell,
- a plurality of anode assemblies suspended above the cathode, each anode
assembly comprising at least one anode and a metallic anode rod connected to
an
anode busbar (so-called "anode beam"),
- a plurality of alumina feeders by which alumina powder is fed into the
liquid bath,
and said electrolytic cell being characterized in that it comprises specific
means for
carrying out a method according to the invention.
Said specific means comprise a specifically programmed microprocessor.
In an advantageous embodiment said cell comprises means to determine
individual
anode currents for each anode.
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The method according to the present invention has several advantages in view
of prior art,
amongst which:
1. The observer produces quantitative spatial estimation of state variables
based on a
dynamic model, which provides a more systematic way of utilizing anode current
measurements.
2. The observer has a flexible structure. The exact discretization of the cell
can depend on
the level of details required and the area of interests.
3. The multi-stage configuration ensures system observability (without which
the system is
not observable, which means that all the state variables cannot be estimated)
and
reduces modelling errors and uncertainties as estimations from the previous
stage are
served as additional information as well as constraints.
4. The observer is tuned properly so that it produces converging results at
different
starting conditions of reasonable ranges.
Figures
Figure 1 is a schematic view, showing an electrolytic cell for carrying a
monitoring process
according to the invention.
Figure 2 is a schematic diagram of the multi-stage state observer.
Figure 3 shows the estimated spatial alumina concentration during a time when
a feeder
is blocked on purpose.
Figure 4 shows estimated spatial alumina concentration during a time when a
feeder or
crust breaker problem has occurred.
Description
1. General presentation
An aluminium smelter plant comprises a plurality of electrolytic cells
arranged the one
behind the other (and side by side), typically along two parallel lines. These
cells are
electrically connected in series by means of conductors, so that electrolysis
current
passes from one cell to the next. The number of cells in a series is typically
comprised
between 50 and over 400, but this figure is not substantial for the present
invention. The
cells are arranged transversally in reference of main direction of the line
they constitute. In
other words the main dimension, or length, of each cell is substantially
orthogonal to the
main direction of a respective line, i.e. the circulation direction of
current.
Referring to figure 1, a Hall-Heroult electrolytic cell 1, the general
structure of which is
known per se, first comprises a cathode 2 forming the bottom of said
electrolytic cell and
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comprising a plurality of parallel cathode blocks, each cathode block being
provided with
at least one current collector bar and two electrical connection ends. A
lateral lining 3
defines together with the cathode a volume V containing the liquid electrolyte
8 and the
liquid metal 9 resulting from the Hall-Heroult electrolysis process, said
cathode and lateral
lining being contained in an outer metallic potshell 4. Said electrolytic cell
further
comprises a plurality of anode assemblies suspended above the cathode, each
anode
assembly comprising at least one anode 11-18 and a metallic anode rod 6
connected to
an anode busbar 7 (so-called anode beam). In the shown example, there are two
rows of
eight anodes 11-18, only one row being illustrated. Moreover, the cell
includes four
aluminium feeders 21-24 (linked to an outside alumina supply, not shown on the
figure)
regularly provided along the main dimension of the cell, between its tap end T
and its duct
end D.
The Hall-Heroult process as such, the way to operate the latter, as well as
the cell
arrangement are known to a person skilled in the art and will not be described
here in
more detail. It is sufficient to explain that the current is fed into the
anode beam 7, flows
from the anode beam 7 to the plurality of anode rods 6 and to the anodes 11-18
in contact
with the liquid electrolyte 8 where the electrolytic reaction takes place.
Then the current
crosses the liquid metal pad 9 resulting from the process and eventually will
be collected
.. at the cathode blocks forming the cathode 2. In the present description,
the terms "upper"
and "lower" refer to mechanical elements in use, with respect to a horizontal
ground
surface. Moreover, unless otherwise specifically mentioned, "conductive" means
"electrically conductive".
In the present invention embodiment, attempt is made to estimate the local
alumina
concentration, alumina dissolution rate and average anode cathode distance
(ACD),
which are referred to as "state variables", in the above mentioned
electrolyte. This
estimation is carried out on the basis of the determination of four
parameters, i.e.
P1: anode currents, P2: alumina dumps,
P3: anode beam movement, P4: cell voltage
In view of this determination, the cell is provided with four series of
sensors or actuators,
each being relative to one respective of the above listed parameters:
S11 to S18: means to sensors determine anode current. In the framework of this
invention
anode currents can be determined using any method. In an advantageous
embodiment
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the number of these sensors is equal to the number of anode rods and they can
be
positioned on the beam between two adjacent anode rods.
A21 to A24: alumina dumps actuators. Each of these actuators is positioned at
the outlet
of its respective feeder 21-24, and is controlling the opening and closing of
said feeder.
5 Each opening of the outlet is releasing a fixed volume of powdered
alumina into the
electrolytic bath, and the quantity of alumina fed through each feeder is
calculated from
said fixed volume and the density of alumina. We will refer here to a
"measurement" in
relation with the determination of the number of alumina dumps, although in
practice it is
usually not the mass of dumped alumina that is measured but the number alumina
dumps
10 of a volume of powder predetermined by the volume of the feeder is
counted by the
actuator.
S3: one single beam movement sensor for the whole cell.
S4: one single cell voltage sensor for the whole cell.
The method according to the invention does not depend upon the means and
methods
used for the determination of the input parameters, provided that said means
are capable
of determining said input parameters.
All the sensors and actuators are connected to a central unit U; this
connection is
symbolized as dotted lines on figure 1. Said central unit U is provided in
particular with a
calculator configured to use an extended Kalman Filter. On figure 1 the
voltage beam
sensor (measuring the anode beam height) and voltage beam actuator (modifying
the
abode beam height) is symbolized by the letter B, and the sensor measuring the
cell
voltage by the letter Z.
We describe here an embodiment of the method according to the invention, in
relation
with figure 2, where:
U
N i u s the input to the j-th observer in the i-th stage at time step N,
X
N i u s the estimation result from the j-th observer in the i-th stage at time
step N.
Time step 0
In step 0 the system is initialised. The number of stages in the cascaded
state observer is
decided. Reasonable initial estimations of the global (average) state
variables and
estimation of error covariance are made.
Time step 1
- Stage 1
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The four input parameters (line current, ACD change rate (determined from
anode
consumption rate and aluminium accumulation rate), beam movement, alumina
dumps)
are determined (measured) for the whole cell. More precisely, one global value
is used for
each parameter, even if more than one value is measured; this means, for
example, that
the alumina dumps for the four feeders are summed up to become one global
value, and
the current value used here is the line current, which is the summation of all
individual
anode currents. These values serve as u111 to the observer. The estimation of
states at
time step 1 (x111) is produced using the standard extended Kalman filter
algorithm with the
initial estimation of states and error covariance. x111 contains the
estimation of average
alumina concentration in the bath, alumina dissolution rate and average ACD at
time
step 1.
In step 0, initial estimations of these variables are made, they are used to
calculate an
estimated cell voltage using equation (1). The difference between this
estimated cell
voltage and the measured cell voltage is then used to adjust the estimated
variables. After
some time (normally one feeding cycle), the estimated variables will be within
reasonable
range of the real variables.
- Stage 2
At this stage, the cell is divided into two identical subsystems, i.e. SUB1 1
and SUB1 2
(shown on figure 1).
The four input parameters are determined for the each subsystem SUB1 1 and
SUB1 2,
plus cell voltage and possibly outputs from previous state estimation stages.
ACD change
rate (determined from anode consumption rate and aluminium accumulation rate)
and
beam movement are determined (measured) for the whole cell. Local variables
(i.e.
variables that are determined for each subsystem SUB1 1 and SUB12) that are
used are
anode current and alumina dumps. More precisely, one global value is used for
each
subsystem, even if more than one value is measured. As a consequence, anode
current
in stage 2 means the summation of all individual anode current in the
subsystem, and
alumina dump in stage 2 means the summation of alumina dumps in each
subsystem.
At this stage, the filter receives two types of input data, i.e. measured
parameters of
stage 2 (u121 and u122), as well as estimated parameters of stage 1 (x111).
u121 contains the respective anode currents, cell voltage, beam movement and
alumina
dumps measured in the first subsystem, while u122 contains the respective
anode currents,
cell voltage, beam movement and alumina dumps measured in the second
subsystem.
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The estimation of states in the two subsystems is obtained using the standard
extended
Kalman filter, subject to the constraint that the average of x121 and x122 is
x111, the
estimated parameters of stage 1. x121 and x122 contain the estimated alumina
concentration, alumina dissolution, rate and ACD in the two subsystems; these
are the
outputs.
It should be noted that the operation of this filter at stage 2 is different
from the one at
stage 1.
- Stage 3 and beyond
The cell is divided into further subsystems (SUB21 to SUB24 on figure 1). The
cell is
subsequently divided into subsystems and the estimation results in the
previous stage are
used in the current stage. The estimation stops when the desired number of
stages has
been reached. As in step 2, local variables that are used in each subsystem
are anode
current and alumina dumps.
Time step 2 and beyond
The standard Kalman filter recursion is applied in each stage, using the
estimation results
from previous time step as the new starting point.
In the outlined method, the estimated alumina concentration and ACD are
produced after
nth stage state observer at each time step. It is an approach which provides
online
monitoring of spatial variables of a smelter cell.
Upon the basis of the estimated values, for each parameter, appropriate
regulation of the
electrolytic cell can be carried out.
Thus, let us consider that the estimated value of alumina concentration is
lower in
subsystem SUB21 than in the other subsystems. The operator will then increase
the flow
rate of alumina (or the number of dumps of a predetermined volume of alumina
powder),
delivered by feeder 21.
Let us consider that the estimated value of anode cathode distance is lower in
subsystem
SUB21 than in the other subsystems. The operator will then adjust the anode-
cathode
distance of the anodes in the said subsystem by raising or lowering the anode
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Examples
These examples present results obtained through the method according to the
invention.
Example 1
The cell has been divided into four subsystems, where zone 1 is at the tap
end, zone 2 is
in between zone 1 and zone 3, zone 4 is at the duct end and adjacent to zone
3. In this
example, a feeder in zone 2 is blocked on purpose while the total alumina feed
rate to the
cell is maintained as usual, i.e. the other feeders dump more to compensate
the blocked
feeder. The goal was to estimate the spatial variables in the four subsystems.
The cascaded state observer therefore contained three stages. Following the
procedure
described above, the spatial distribution of alumina concentration in the four
zones was
estimated and figure 3 depicts the estimated values of spatial alumina
concentration in
response to the blocked feeder. As can be seen, following the feeder blocking,
there is a
significant difference in the spatial alumina concentration in the four zones
depending on
the location. The estimated alumina concentrations in zone 1 and zone 2
decrease, while
the concentrations in zone 3 and zone 4 increase. The concentration in zone 2
is the
lowest since the feeder in this area is blocked, but due to the flow of
electrolyte, the
concentration in zone 1 is also relatively low. The same applies to the
concentration in
zone 3. As for zone 4, it is the furthest away from zone 2 and therefore it is
the least
affected by the depletion of alumina in zone 2. It causes the alumina content
in this zone
to increase, and to become the highest in the cell.
It should be noted that apart from the blocked feeder, the alumina addition
rate in the
other feeders was the same in this example. Even so, the cascaded state
observer is able
to produce the reasonable and logical estimation of spatial variables based on
the
information available.
Example 2:
In this example, the configuration of the discretised cell was the same as
that in Example
1. Figure 4 shows the estimated spatial alumina concentration in the four
zones with an
unexpected feeder or crust breaker problem, which was later discovered to be
in zone 2.
Similar to what is shown in Example 1, there is a significant difference in
the spatial
alumina concentration in the four zones towards the end of the period. The
estimated
alumina concentrations in zone 1 and zone 2 are relatively lower than the
concentrations
in zone 3 and zone 4. It indicates that there is a depletion of alumina
concentration in
zone 1 and zone 2, which may be due to the feeder/breaker problem.
CA 03012166 2018-07-20
WO 2017/141134 PCT/IB2017/050661
14
It should be noted that in this example, the cascaded state observer does not
know the
feeder/breaker problem a priori, instead it assumes the regular alumina
addition rate.
Even so, the estimation of spatial variables is able to pinpoint the
problematic area in the
cell. This allows the quick identification of the defective feeder or crust
breaker device,
and eventually speeds up the work of the maintenance team in the plant.
