Mei C., Zhou J., Peng X. Simulation and Optimization of Furnaces and Kilns for Nonferrous Metallurgical Engineering
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4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
optimal output of cobalt enriched matte and slag could be decided according to
furnace state and decisions mentioned above. That is, by optimizing the weight of
input materials and load current and its duration time, electric consumption would
be reduced, slag constitution would be improved, separation condition for matte
and slag would be improved, valuable metals’ loss in slag would be decreased,
thus, integrated index of production process would be optimized, and the goal of
energy saving and consumption reducing would be achieved. To realize these, an
optimization decision-making model is necessary.
Slag cleaning process is a complex system with characteristics of multi-variable,
nonlinear and long time delay (Peng,1998;Peng and Su et al.,1996;Peng and Mei
et al.,1996). It is difficult to build a precise mathematical model based on
smelting mechanism. Further more, because the optimal samples collected in real
production process are relatively insufficient, it is difficult to build an
optimization decision-making model using the fuzzy control model identification
algorithm and adaptive optimization algorithm introduced in Section 4.3 for a
slag cleaning process. Therefore, it is proposed to build an optimization
decision-making model using fuzzy neural network adaptive modeling methods
of multi-variable system introduced in Section 4.4.1.
4.4.2.1
Objective function and learning samples
The wastage functions of the slag cleaning process is defined as
p
Ni Ni Co Co
pbz
z
()yzd zd
Qdw
x
+
=+
•• •
•
(4.43)
where
b
d is the price of electric energy (yuan / kW• h);
z
w is the electric
energy consumption per ton of converter slag (kW
• h/t);
p
y is the output of the
cleaned slag (t/shift);
Ni
z is the percentage content of nickel in slag (%);
Ni
d
is the price of nickel (yuan/t);
Co
z is the percentage content of cobalt in slag
(%);
Co
d is the price of cobalt (yuan/t);
z
x is the weight of the converter slag
inputted per shift (t / shift).
The value of Q
p
reflects synthetically the value of energy consumed and
valuable metal lost is the slag cleaning process. Taking it as objective function,
data with small value Q
p
are selected as learning samples from lots of real
production data. The fuzzy neural network model trained by these samples is
fuzzy neural network optimization decision making model.
4.4.2.2
Fuzzy neural network decision-making model for slag cleaning process
According to the mechanism analysis of slag cleaning process, considering of
operation and control experience of spot technicians, and through stepwise
regression analyzing the huge amount of real production data accumulated in
production practice, the following relation functions can be obtained:
Xiaoqi Peng and Yanpo Song
a) Input of converter slag at time k:
zzz s l g g
( ) [ ( 1), ( 1), ( 1), ( 1), ( 1),xkFxkxkxkxkyk=−−−−−
pW W T T
hphp
(1), (1), (1),(1),(1)]yk x k x k x k x k−−−−− (4.44)
b) Input of sulphide at time k:
),1(),1(),1(),1(),([)(
pglzzll
−−−−= kykykxkxkxFkx
)]1(),1(),1(),1(
phph
TTWW
−−−− kxkxkxkx (4.45)
c) Input of quartz sand at time k:
),1(),1(),1(),(),1(),([)(
psllzzss
−−−−= kykxkxkxkxkxFkx
)]1(),1(),1(),1(),1(
phph
TTWWg
−−−−− kxkxkxkxky (4.46)
d) Input of coke powder at time k:
)](),([)(
lzcc
kxkxFkx =
(4.47)
e) Load current in the smelting stage of the kth shift:
),1(),1(),(),(),([)(
psslzhW
h
−−= kykxkxkxkxFkx
)]1(),1(),1(
pp
TWg
−−− kxkxky (4.48)
f) Duration time of the smelting stage of the kth shift:
),1(),1(),(),(),([)(
psslzTT
hh
−−= kykxkxkxkxFkx
)]1(),1(),1(
pp
TWg
−−− kxkxky (4.49)
g) Load current in the cleaning stage of the kth shift:
),(),(),(),(),([)(
hp
WsslzpW
kxkxkxkxkxFkx = )]1(),1(),(
gpT
h
−− kykykx (4.50)
h) Duration time of the cleaning stage of the kth shift:
),(),(),(),(),([)(
hpp
WsslzTT
kxkxkxkxkxFkx = )]1(),1(),(
gpT
h
−− kykykx (4.51)
i) Output of cobalt enriched matte at time k:
),1(),(),1(),(),1(),([)(
gsllzzgg
−−−= kykxkxkxkxkxFky
)()](),(),(),(
gTWTW
pphh
kykxkxkxkx Δ+ (4.52)
j) Output of cleaned slag at time k:
ggzz ll ss
( ) [ ( ), ( 1), ( ), ( 1), ( ), ( 1),yk Fxkxk xkxk xkxk=−−−
)()](),(),(),(),1(
pTWTWp
pphh
kykxkxkxkxky Δ+− (4.53)
where,
hl h
gh
ll l
()/()
Δ () 0 ( )
()/()
l
LL k LL
y
kLLL
LL k LL
−
⎧
⎪
=<<
⎨
⎪
−
⎩
(4.54)
hz h
p
lh
lz l
()/( )
() 0 ( )
()/()
ZZ k Z Z
y
kZZZ
ZZ k ZZ
−
⎧
⎪
Δ= <<
⎨
⎪
−
⎩
(4.55)
where L is the height of liquid matte surface at instant k
−1; L
h
is the max
allowable height of liquid matte surface; k
l
is correction coefficient for the height
ı
İ
ı
İ
4 Thermal Engineering Processes Simulation Based on Artificial Intelligence
of liquid matte surface; L
l
is the minimum allowable height of liquid matte
surface; Z is the height of liquid slag surface at instant k
−1; Z
h
is the max
allowable height of liquid slag surface; k
z
is correction coefficient for the height
of liquid slag surface; Z
l
is the minimum allowable height of liquid slag surface;
)(
g
kyΔ is called matte surface height correction coefficient; )(
p
kyΔ is called
slag surface height correction coefficient.
According to Eq. 4.44 through Eq. 4.53 and the method introduced in Section 4.4.1,
the fuzzy neural network decision making model for a slag cleaning process can be
built, the process of decision making based on this model can be shown as Fig. 4.7:
Fig. 4.7 Fuzzy neural network decision-making process of cleaning slag furnace
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Beijing
Hologram Simulation of Aluminum
Reduction Cells
Naijun Zhou
The “hologram simulation” concept is put forward to replace the traditional
“Three-fields” (including magnetic field, thermal field and force field) notion in
simulating aluminum reduction cells. The core of the hologram simulation is to
simulate microstructures of the cells’ parameters distribution under various
structural and operating conditions. In hologram simulation, the effect of various
input information can no longer be treated as single or independent variables,
because of the interacting they have with each other. The hologram simulation
approach can be used for both static and dynamic analysis of the cells, and it as
more suitable to describe the detail working of the cells. In this chapter, the
models for several main physical fields including the current field, magnetic field,
thermal field, and the molten metal flow field are respectively discussed;
moreover, the dynamic simulation method and several calculation models of the
current efficiency for aluminum reduction cells also are introduced.
5.1
Introduction
As aluminum is widely used in industries, the need to maintain sufficient supply,
therefore that the development of aluminum has very bright future. In 2006, the
annual production of primary aluminum worldwide is about 23,869,000 t, of
which the annual production of China is about 9,349,000 t, according to
International Aluminum Institute. This makes China the first ranked producer in
the world and it has an annual growth rate of 19.8% (Huang, 2007; Guo, 2007).
Since its invention in 1886, the Hall-Heroult process has been the only method
Naijun Zhou
used in the aluminum industry. The aluminum production is a significant consumer of
electricity. In China, the annual electricity consumption of aluminum production is
13.7
× 10
10
kW·h, which accounts for 4.8% of the total industry consumption(Yang,
2007), and the expense in electricity is about 45% of the aluminum manufacturing
cost. Therefore, to reduce the energy consumption and increase the current efficiency
has being an important subject for researchers in aluminum industry. With the
development and improvement of aluminum electrolytic technology, especially the
application of computer technology in the design and operating of cells, the mean
energy consumption per ton aluminum has greatly decreased from 41,900kW·h/t(Al)
at the beginning of last century to present 12,900 kW·h /t(Al) in advanced aluminium
reduction cells, the current efficiency has been improved to 95%, and the average cell
life has been improved to more than 5 years.
There are two main types of aluminum reduction cells: the self-baking anode
cells and the prebaked anode cells. The self-baking anode cells are normally
associated with small cell capacity, low current intensity which usually does not
exceed 80kA, low current efficiency and bad production conditions. Hence, it is
being gradually replaced by prebaked anode cells. Comparatively, the all
production quota of the prebaked anode cells are better than that of self-baking
anode cells. For example, the current intensity of modern large-size prebaked cells
reaches 500kA, and annual potline output is about 390,000t (Vanvoren et al.,2001).
Moreover, adopting the automatic point feeder, and production environment are
better than that of the self-baking cells. At present in China, the productivity of the
self-baking anode cells accounts for 3.5% of total production of aluminum
(Huang,2007); while the prebaked cells are mainly in sizes of 200kA and 240kA,
large-size cells such as 350kA and 400kA are in the development. Fig. 5.1 is a schematic
Fig. 5.1 Cross section sketch of a prebaked anode aluminium reduction cell
5 Hologram Simulation of Aluminum Reduction Cells
of the cross section of a prebaked anode aluminum reduction cell.
With development and application of many new technologies in the last decade,
great progress has been achieved on technical parameters of prebaked cells in
China. For example, the recent successful application of the fuzzy intelligent
control technology in 160kA and 180kA aluminum reduction cells have
respectively resulted in current efficiencies of 93.57% and 93.74%, and direct
current power consumptions of 13,372 kWgh/t(Al) and 13,049 kW·h·/t(Al), which
are close to the advanced level in the world(Fcrioncuot,1997). However, the
aluminum electrolysis technology level in China is still behind that of the
developed countries. For instance, the mean current efficiency in China is only
92%, and average DC power consumption is over 13,500 kW·h/t(Al), which
indicates great potentials for technological progress.
The three-fields technology plays an important role in the improvement of
aluminum electrolysis technical and economic index. In China, the origin of the
three-field technology can be tracked back to late 1970s, when 160kA central
charging prebaked cells made by Japan Light-Metal Company were entirely
imported to China. As the technical package consisted of three computer software,
i.e. calculation programs for magnetic field, heat analysis of cathode and anode, and
stress distribution of shell, it was called “three-fields technology” for short (refer to
the magnetic field, thermal field and stress field) in the course of digestion and
development of the software. Since 1980s, the three-fields analytic technique has
been widely applied to the design of aluminum reduction cells, and made great
contribution to the technical progress. It has also been applied to the design and
rebuild of aluminum reduction cells as virtual methods in China since 1990s.
It is now well known that there are various physical parameter fields in and
around aluminum cells having considerable effect on the operation of cells, which
include the current field, magnetic field, thermal field (temperature field), velocity
field, concentration field, stress field and so on. Since the physical parameter
fields inter-couple with each other (refer to Fig. 5.2), the analysis of any sole field
becomes more and more difficult because it has to be relied on excess assumption
which causes deviations between the predicted results and practical situations.
As the traditional three-field technologies can hardly contain all the physical
parameter fields and their interrelations, the authors are to use the concept of
“hologram simulation” to replace the three-fields notion. The core of the hologram
simulation is to simulate microstructures of parameters distribution with various
structural parameters and operate conditions of the cells. The simulation process
consists of four stages: model development, model solving, results output and test
validation. Apparently, the traditional three-field technologies are still an
important part of the hologram simulation. However, what makes them different is
that in hologram simulation, effect of various input information on every physical
Naijun Zhou
Fig. 5.2 Relation of various physical parameter fields in aluminum reduction cells
parameters and the parameters themselves can no longer be treated as
independent or separated information. In fact, they are a unity inter-relating and
interacting with each other. Therefore, compared to the three-field analysis
technology, the hologram simulation technology is more suitable to describe the
essence of the aluminum cell’s work. It can be used for both static analysis and
dynamic action simulation for the cells, of which the latter is beyond the capability
of the traditional three-field analysis technology. This is to be discussed in details
in the Section 5.5. The principle of the hologram simulation technology for
aluminum reduction cells is illustrated in Fig. 5.3.
The keys to hologram simulation are:
a) Comprehensive observation and analysis of cells’ working process, trying to
find out the qualitative influence regularities among various information and
influence of information on the results;
b) Development of appropriate mathematical and physical model;
c) Determination of solving conditions and algorithm;
d) Test and modification of the simulation results.
In this chapter, the first four sections are to discuss development of the models
of several main physical parameter fields. The fifth section is to introduce an