Use of statistical analyze for calculation of specific slag heat of "Trepca" shaft furnace.

Terziqi, Avni ; Rizaj, Musa ; Kamberaj, Naim 等

Abstract: In shaft furnace of metallurgic complex in "Trepca", during the agglomerate melting, gained slag consist plenty of components as are: Pb, ZnO, CaO, Fe, Si[O.sub.2], S etc. Values of content components have impacts in values of specific heat of slag. Handling of this problematic requires one statistical approach, using data from 465 laboratory measurements annually. According to the proper statistical model are made calculation of statistical distribution and dispersion characteristics of spreading for components of slag that are used for calculation of specific heats of slag components. Gained results are important data for thermal calculation of shaft furnace, pre-furnace or electric furnace for using of slag components from technologic process.

Key words: furnace, slag, model, specific heat.

1. INTRODUCTION

Lead slag introduce one complicated system of different oxide alloys, with basic components ([F.sub.e]O, [C.sub.a]O, [S.sub.i][O.sub.2], [Z.sub.n]O, S), which consist about 90% of slag compound. Slags that are coming from furnace with high temperature, together with heat introduce the irreversible lost from metallurgical and thermal aspect. From 465 observations the measurements result of the slag compound, for annually production, it's observed that is existing one pronounced variation of value of slag components and this variation is of not determinate character with normal dispersion ore lognormal. Therefore, for research of dispersion percentage of slag components it's requested one statistical approach (Hubler 1996). Using calculated values from statistical model, with one correct approximation can calculate the specific heat of the slag from shaft-furnace in industrial complex Trepca. The specific heat values can be used for calculation of the thermal balances of shaft furnace, pre-furnace ore electrical furnace with aim to use secondary resource.

2. STATISTICAL ANALYSIS OF SLAG CONSIST

For regulation of data from measured results of quantity in percentage of slag components, it's done statistical model. In this statistical model, with commune statistics it implied the commune consist value of the components in the slag during 465 measurements. Case operand (Variable) xi is components consist in percentage with their corresponding density. For illustration are given distributions characteristics, dispersion and statistical interpolation of the slag in table 1. The average value of the slag components are given by histogram in figure 1.

For calculate parameters a [sigma], [mu], [theta], [lambda] and [delta] (ek. 1, 2) of interpolated curves for slag components are used equation between empiric moments and theoretic moments (Girone 2003). Interpolated lognormal curves are valid for distribution of Pb and S distribution, while interpolated normal curves for ZnO, CaO, FeO and Si[O.sub.2] components.

F(x) = N/[sigma][square root of 2[pi]]exp[-[(x--[mup]).sup.2]/2[[sigma].sup.2]] (1)

F(x) = N[sigma]/[square root of 2[pi](x--[theta])]exp{-1/2[[lambda] + [[delta] log(x--[theta])].sup.2]} (2)

3. SPECIFIC HEATS OF SLAG

Specific heat introduces necessary energy for growing temperature of slag unit for temperature unit. For calculation of specific heat of the slag first we calculate the specific heat of the components (lead, copper, zinc, iron, calcium, silicon dioxide, sulphide) in slag per kJ/kgK according to equation (Michael, J.; Howard, N. 2004):

[C.sub.Ki] (T) = [a.sub.i] + [b.sub.i]T--[c.sub.i][T.sup.-2] (3)

When the values the specific heat coefficients of the slag components a, b and c is known, then are determinate by following equations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

Since in slag compound are quantity of M components, for whose we don't know consist off, therefore the specific heat of the slag is calculated by following equation (Gordon 1993):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

Where [bar.[X.sub.i]] shows the average values of slag consist components assigned according by the statistical measurement and analysis (tab. 1).

For average temperature of the slag [T.sub.b]=1423 K, for normal work of the furnace, according to equation (4) till (12), approximate calculation of specific heat of slag component is done. Gained results are given in histogram introduced in fig. 2. From the diagram is visible that slag components Si[O.sub.2] and CaO have the specific heat with high value, then other components with lower value.

Meanwhile the introduced diagram in fig.3 it's shown the specific heat of components and of slag in function of the slag temperature in the actual limits from 1373 up to 1473 K. From this diagram it's visible that with grow of the slag temperature are grown also the values of the specific heat of the slag components.

After assessment of the average value for specific heat we can determine quantity of consisted heat of slag in shaft furnaces of the Trepca.

[Q.sub.b] = [C.sub.b] [G.sub.b]([T.sub.b]--273) (13)

Where for the normal working conditions of the furnace the quantity of the slag that is going out of the furnace is [G.sub.b]=4.1667 kg/s while the calculated quantity of heat is Qb=5131 kw.

[FIGURE 3 OMITTED]

4. CONCLUSION

Unregulated work of the shaft furnace in Trepca is manifested by the lost of the link of the lead with slag, with unexpected breaks of the furnace and other complications of the work regime. These complications are influent in variation of the percentage values of the slag components. This confirms also the asymmetry and abnormality of slag components distribution. For slag components distribution can be conclude that the interpolated curve of distribution for Pb and S is approximately lognormal while for other components ZnO, CaO, FeO and Si[O.sub.2] is approximately normal.

In case of normal work of the furnace with average temperature of the slag [T.sub.b]=1423 K, slag components Si[O.sub.2] and CaO have the specific heat with higher value, then other components with lower value. Gained results for the specific heat of the slag are based in statistical analysis of the data from laboratory measurements of the slag consist. Those values can be used with enough accurately for thermal calculation for use of the slag heat, for assignment of the pre-furnace with aim to separate the lead and other metals in the future moderations in industrial complex Trepca.

5. REFERENCES

Michael, J.; Howard, N. (2004). Fundamentals of Engineering Thermodynamics, John Wiley, ISBN 0-471-27471-2, Hoboken.

Hubler. J. (1996). Statistics for economy (Statistiques por l'economie), Breal, ISBN 2 85394 914 1, Paris.

Girone, G. (2003). Statistical reading (Lezioni di Statistika), Dudaj-Foundations SOROS, ISBN 99927-50-51-0, Tirana.

Gordon, M. (1993). Thermal calculation of metallurgical furnace, Metallurgy, ISBN5-229-00711-7, Moskva.

Table 1. Statistical parameters

 Slag components

 Pb ZnO CaO SiO2 FeO S

VQ 4.70 9.80 15.50 21.50 33.00 2.35
Me 1.38 9.65 18.63 23.30 32.80 1.34
[mu] 1.56 9.63 18.62 23.43 32.82 1.40
V(x) 0.79 2.33 4.98 7.57 7.48 0.24
[sigma](x) 0.89 1.53 2.23 2.75 2.74 0.49
[delta] 1.20 2.39
[lambda] 0.57 -0.04
[theta] 0.68 0.29

Fig. 1. Slag components

Pb 1.56
ZnO 9.63
CaO 18.62
SiO2 23.43
FeO 32.82
S 1.40
M 12.54

Note: Table made from pie chart.

Fig. 2. Calculated average vales of the specific heat of
components and slag Tb=1423 K.

cPb 0.175
cCu 0.497
cZnO 0.688
cFeO 0.859
cCaO 0.995
cSiO2 1.615
cS 1.627
cb 1.071

Note: Table made from bar graph.