ISSN 1067-8212, Russian Journal of Non-Ferrous Metals, 2008, Vol. 49, No. 5, pp. 336339. Allerton Press, Inc., 2008.Original Russian Text M.I. Alkatsev, E.E. Mamontova, D.V. Mamontov, 2008, published in Izvestiya VUZ. Tsvetnaya Metallurgiya, 2008, No. 5, pp. 1821.

336

1. INTRODUCTIONOxygen-flash autogenous smelting is a type of sul-

fide concentrate smelting in a weighed state. Accordingto [1], a furnace for sintering sulfide copper concen-trates in a weighed state existed as early as 1848 inNorth America. There are several types of weighedautogenous smelting, including the oxygen-flash smelt-ing used at the Almalyk copper smelter since 1968 [2].

The purpose of this work is to simulate the thermaloperation of autogenous smelting furnaces of coppersulfide charges. According to [3], the energy length ofthe torch is 4 m. The charge components in the torchovercome this distance for

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AN INVESTIGATION OF CERTAIN REGULARITIES 337

tion concentrate are established via the constructionand solution of the set of equations obtained from thefollowing material balances: copper in oxygenflashsmelting, copper in flotation, converting, and silica inconverting.

2.2. Thermal Balances

Equations of temperature dependences of the aver-age heat capacity of charge components and productsof oxygen-flash smelting, as well as the enthalpies ofthermolysis and oxidation reactions of sulfides neces-sary for calculations, were preliminarily determined ina computational manner and introduced into a block ofthe thermal balance of the computer program. The ther-modynamic data are taken from [5].

In order to form a mathematical model combiningthe melting point of products with independent vari-ables, a simulation (computer) fractional linear facto-rial experiment with a

N

k

2

= 16 number of experi-ments, where

k

= 6 is the number of independent vari-ables, was realized. We used

X

5

X

1

X

2

X

3

X

4

and X

6

X

1

X

3

(1)as generating relationships.

In a general form, the dependence of the slag tem-perature on some factors can be expressed by the fol-lowing function:

(2)Here,

P

is the consumption coefficient of the charge;Cu

c

, S

c

is the content of copper and sulfur in the matte,respectively, %; Cu

m

is the amount of copper in thematte, %; O

2

is the oxygen content in the blast, vol %;

W

is wetting of the matte, %; and

t

sl

is the slag temper-ature,

C.Boundary conditions, in the context of which the

regression equations were obtained, are presented inthe table.

In the table, the quantities

X

i

are the independentvariables in a dimensionless scale:

tsl f P Cuc Sc Cum O2 W, , , , ,( ).=

X1P 1.025

0.025-----------------------, X2Cuc 21.0

3.0-------------------------,= =

As a result of processing the simulation experimentsby the least-squares method, we obtained the followinglinear dependences of regression.

X3Sc 34.0

2.0---------------------, X4Cum 50.0

10.0--------------------------,= =

X5O2 93.0

2.0----------------------, X6W 0.4

0.2------------------.= =

Start

Introduction of starting data:1. Charge composition

Calculation of material balances

Calculation of the thermal balance

Planning of the imitation experiment

Identification of the mathematical model

End

2. Cu

m

, %3. O

2

blast, %4. Humidity

of smelting, conversion, and flotation

of oxygen-flash smelting and temperatureof smelting products

and formation of the mathematicalmodel

t

=

f

(Cu

m

, S

sl

, O

2

, H

2

O)

Fig. 2.

Skeleton algorithm of imitation simulation of oxy-gen-flash smelting.

Boundary conditions of independent variables

Levels

P

(

X

1

) Cu

c

(

X

2

) S

c

(

X

3

) Cu

m

(

X

4

) O

2

(

X

5

)

W

(

X

6

)

Main level (0) 1.025 21.0 34.0 50.0 93.0 0.4Range of varying 0.025 3.0 2.0 10.0 2.0 0.2

Lower level (1) 1.000 18.0 32.0 40.0 91.0 0.2Upper level (+1) 1.050 24.0 36.0 60.0 95.0 0.6

338

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No. 5

2008

ALKATSEV et al.

In the dimensionless scale:

(3)

in the dimensional scale:

(4)

where

F

calc

is the calculated value of

F

statistics,

F

0.05;

N

1;

N

k

1

is the tabulated value of the Fischer cri-terion

F

, and is the adequacy variance.

Since

F

calc

>

F

0.05;

N

1;

N

k

1

, regression equations (3)and (4) are accepted to be equal to the results of com-puter calculation.

The approximation error is

S

ad

= = =

30.9, which equals 2.4% of the average slag tempera-ture in the furnace.

Since Eq. (3) is reliable, independent variables (indimensionless scale) can be arranged by the force oftheir effect on the slag temperature according to theirabsolute values as follows:

X

4

(Cu

m

),

X

2

(Cu

s

),

X

3

(S

s

),

X

1

(

P

),

X

6

(

W

), and

X

5

(O

2

).

tsl 1285.0 24.938X1 64.938X2 64.188X3+ +=+ 141.313X4 4.313X5 5.188X6,+

tsl 957.5P 21.646Cuc 32.094Sc 14.131Cum+ +=+ 2.156O2 25.937W 1230.0,

Fcalc 33.00, F0.05; N 1; N k 1 3.00,= =

Sad2 952.23,=

Sad2

Sad2 952.23

In other words, the copper content in the matteexerts the strongest effect on the slag temperature.Other factors, in the order from strongest to weakest,are the copper and sulfur content in the charge, furnaceproductivity, and, to a smaller extent (in the context ofaccepted limitations), charge humidity and oxygenamount in the blast.

The partial dependences of the slag temperature onvarious factors according to Eq. (3) are presented inFig. 3.

Partial graphs are plotted by the following equa-tions:

Autogeneity conditio5ns of smelting, where smelt-ing will proceed autogeneously at the specified furnacetemperature, are the functions of many variables andcan be calculated by formulas (3) and (4).

Identification of the obtained mathematical modelwas performed in two stages:

(i) The adequacy of the model to the data obtainedby computer model calculations. This method of iden-tification is correct itself since it is based on fundamen-tal thermodynamic laws and reliable experimental data(Kirchhoffs law, equations of the temperature depen-dence of the heat capacity of substances, etc.). The ade-quacy of the models was substantiated above.

(ii) The evaluation of the convergence of the calcu-lated data with industrial data is carried out. We usedpublications of materials on operation of the Almalykcopper smelter [2, 6]. The calculated slag temperaturesdeviated by (2030)C from production temperatures,and the relative error was 24%.

CONCLUSIONS(i) Based on the developed software, an adequate

mathematical model is obtained that relates the temper-ature of smelting products to furnace productivity, cop-per and sulfur content in the charge, copper in thematte, oxygen in the blast, and charge humidity.

(ii) The program is written using a modern algorith-mic high-level language Visual BASIC.Net and allowsone to plan computer experiments and form adequatemathematical models of oxygen-flash smelting.

REFERENCES1. Metallurgicheskaya obrabotka rud vo vsveshennom sos-

toyanii. Sbornik statei (Metallurgical Processing of Oresin a Weighed State. Collected Articles), Volskii, A.N.,Ed., Moscow: ONTI, 1936.

t1 1285 23.938X1, t2+ 1285 64.938X2,= =

t3 1285 64.188X3, t4+ 1285 141.313X4,+= =

t5 1285= 4.313X5, t6+ 1285 5.188X6.=

1.00.500.51.0Xi

1450

1400

1350

1300

1250

1200

1150

1100

t, C

1

2

3

4

56

Fig. 3. Partial dependences of the average slag temperatureon X1, the productivity coefficient of the furnace of thecharge (1); X2, copper content in the charge (2); X3, sulfurcontent in the charge (3); X4, copper amount in the matte(4); X5, oxygen content in the blast (5); and X6, chargehumidity (6). Independent variables Xi are presented in thedimensionless scale.

RUSSIAN JOURNAL OF NON-FERROUS METALS Vol. 49 No. 5 2008

AN INVESTIGATION OF CERTAIN REGULARITIES 339

2. Kupryakov, Yu.P., Avtogennaya plavka mednykh kon-tsentratov vo vzveshennom sostoyanii (AutogenousSmelting of Copper Concentrates in the Weighed State),Moscow: Metallurgiya, 1979.

3. Skuratov, A.P., Paretskii, V.M., and Skuratova, S.D.,Tsvetn. Met. (Moscow), 1989, no. 4, p. 27.

4. Alkatsev, M.I., Mamontov, D.V., and Mamontova, E.V.,Calculation of the Process of Oxygen-Flash Smelting 1.0Svidetelstvo ob ofitsialnoi registratsii programmy dlya

EVM No. 2007611391 (Rossiya) (RF Certificate of theComputer Program No. 2007611391), 2007.

5. Kubaschewski, O. and Alcock, C.B., MetallurgicalThermochemistry, Oxford: Pergamon, 1979.

6. Bochkarev, L.M., Bykhovskii, Yu.A., Makarov, D.M.et al., Metallurgiya tsvetnykh metallov: Sbornik nauch-nykh trudov No. 29 Gintsvetmet (Metallurgy of Nonfer-rous Metals: Collected Articles No. 29 of Gintsvetmet),Moscow: Metallurgiya, 1969, p. 5.

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