Model for analysis of material and thermal balance parameters of pre-furnace on Trepca shaft furnace.

Terziqi, Avni ; Kamberaj, Naim ; Bajraktari, Bekim 等

1. INTRODUCTION

Slag of Trepca Shaft Furnace, except of fundamental components FeO, Cao, SiO2 and ZnO who makes up to approx 90% of its mass, contains other useful elements such as Pb, Ag and Au. If Pb, Ag, Au are not separated from slag therefore announced huge losses (Agolli, 1985). Setting of the pre-furnace enables splitting of about 50% of lead from the total amount of lead linked with slag. Process that works in pre-furnace (PF) can be considered as purely mechanical process that must come off in the temperature range 1100-1200 [degrees]C burning of combustibles. Assessment of the amounts of separated lead, combustion of combustibles and of thermal parameter analysis is in the interest for trial about establishment of PF) on Trepca Shaft Furnace.

[FIGURE 1 OMITTED]

2. COMBUSTION PROCESS IN PF

For heating of slag in the pre-furnace (PF) the combustible fuel is used with the elementary composition: C, H, O, N, S, A (ash) and W (moisture). Minimum amount of oxygen for burning the combustibles (Gordon, 1993) is [m.sup.3]/kg:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Veritable amount of air needed for combustibles burning is m3/kg:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Wherein: [alpha] = 1-1.3 and k = [N.sub.2]/[O.sub.2].

Specific volumes of combustible products: [V.sub.CO2] = 1.867C/100, [V.sub.H2O] = (11.2H+1.244W)/100, [V.sub.SO2] = 0.7S/100, [V.sub.O2] = ([alpha]-1)[V.sub.O2],

[V.sub.N2] = (0.8N+[alpha]k[V.sub.O2])/100, [V.sub.a] = [V.sub.CO2] + [V.sub.H2O] + [V.sub.SO2] + [V.sub.O2] + [V.sub.N2].

Density of products designated by the formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The amount of heat released during combustion, kJ/kg:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Specific heat of combustibles, kJ/kg:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

The volume of air for burning a kilogram of combustibles on the air temperature ([t.sub.a] = 25 [degrees]C), [m.sup.3]/kg:

L = [L.sub.a] ([t.sub.a] + 273) / 273 (6)

3. MATERIAL AND THERMAL BALANCE OF PF

The heat amount obtained from burning of combustibles,

kW:

[Q.sub.1] = [Q.sub.ld] B (7)

The physical heat amount possessed by the combustibles, kW:

[Q.sub.2] = [C.sub.ld] [t.sub.ld] B (8)

Where is: [t.sub.ld] -temperature of combustibles, [degrees]C. The amount of heat that possessed by the air, kW:

[Q.sub.3] = L[C.sub.a][t.sub.a] B (9)

The amount of physical heat that possessed by the slag, kW:

[Q.sub.4] = [C.sub.b][G.sub.b] ([T.sub.b] - 273) (10)

Where is: [T.sub.b]-temperature of slag, K.

The total amount of heat at the entrance to the pre-furnace, kW:

[Q.sub.h] = [Q.sub.1] + [Q.sub.2] + [Q.sub.3] + [Q.sub.4] (11)

The amount of slag of physical heat at outlet of the PF, kW.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

Slag amount of (PF) at the outlet, kg /s.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

Amount of heat that possessing lead at the outlet of PF, kW:

[Q'.sub.2=] [C.sub.Pb] ([T.sub.pb] - 273)[G.sub.Pb] (14)

Mass of the lead at the outlet of (PF), kg/s:

[G.sub.Pb] = [G.sub.b][r.sub.Pb][r.sub.Pbm][r.sub.Pbmsh] (15)

Wherein is: [r.sub.Pbm] -- part of lead in slag, %; [r.sub.Pbm]--part of the lead connected mechanically with slag, %; [r.sub.Pbmsh]- the separated share of the lead connected mechanically with slag, %. The amount of outgoing heat with combustion products:

[Q'.sub.3] = [V.sub.a][C.sub.g] ([T.sub.g] - 273)B (16)

Specific heat of combustion products, kJ/kg:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

The amount of heat from incomplete chemical burning of combustibles:

[Q'.sub.4] = [V.sub.a] [a.sub.p][b.sub.p] B (18)

Where are: bp= 12,142 -- heat of 1% CO and 1/2% [H.sub.2] in kJ/[m.sup.3], [a.sub.p] = 2% of the heat released.

Amount of the heat from mechanical incomplete burning of combustibles for 1% in kW:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Total currents of the heat through the pre-furnace walls (Sacadura, 1993) in kJ:

[Q.sub.6] = [n.summation over (i-1)]{([T.sub.b] - [T.sub.i])/[[m.summation over (j=1)]([[delta].sub.ij]/[[lambda].sub.ij] + 1/[alpha]]}[S.sub.i] (20)

Wherein are: i = a-side walls, f-base and k-cover of PF: j = 1, 2 m, wall layers of PF; [[lambda].sub.ij] and [[delta].sub.ij] are coefficients of thermal conductivity and thickness for material layers of PF walls; [alpha]- coefficient of heat conductivity from surfaces of the walls toward environment [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The amount of heat lost by the radiation in PF, kJ:

[Q'.sub.7] = [C.sub.O] [(T/100).sup.4] [([pi]/4)([d.sup.2.sub.f] + [b.sup.2.sub.b]) + [a.sub.1][b.sub.1]][phi][phi] (21)

Wherein: [C.sub.o]-coefficient of radiation to the absolute black body. The total amount of heat at the outlet of PF taking into consideration about 2% of uncounted losses:

[Q.sub.d] = ([Q'.sub.1] + [Q'.sub.2] + [Q'.sub.3] + [Q'.sub.4] + [Q'.sub.5] + [Q'.sub.6] + [Q'.sub.7])0.02 (22)

By the principle of thermal balance [Q.sub.h]=[Q.sub.d], and system of equations from (1) to (22) is gained the expression for determining the needed amount of combustibles for maintaining temperature in the PF, kg/s.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Real amount of air needed for combustibles burning kg/s:

[G.sub.L] = L [[rho].sub.L] B (23)

Amount of gases, kg/s:

[G.sub.a] = [V.sub.a] [rho] B (24)

Amount of the components at the entrance, kg/s:

[G.sub.h] = [G.sub.b] + B + [G.sub.L] (25)

Amount of components at the outlet, kg /s:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

4. ACCOUNTS AND ANALYSIS OF MATERIAL AND THERMAL BALANCE PARAMETERS OF PF

The PFSH program is compiled for needed calculations on Pascal programming language. The data entry program is:

[G.sub.b]=4.1667kg/s; [r.sub.Pb]=0.0155%; [r.sub.Pbm]=0.5%; [r.sub.Pbmsh]=0.6% (Girone, 2003); [L.sub.P]=3.392m; [L.sub.P1]=1.196m; [B.sub.P]=2.192m; [H.sub.1]=1.646m; [H.sub.2]=2.066 m; [H.sub.B]=0.624 m; [a.sub.p]=2.0; [d.sub.b]=0.3m; [d.sub.f]=0.35m; [a.sub.1]=0.2m; [b.sub.1]=0.124m; [[delta].sub.a1]= [[delta].sub.a2]= [[delta].sub.f1]= [[delta].sub.f2]= [[delta].sub.k2]=250m; [[delta].sub.a3]=[[delta].sub.f3]=[[delta].sub.k3]=0.020m; [[delta].sub.a4]=[[delta].sub.f4]=[[delta].sub.k4]=0.016m; [[delta].sub.k1]=0; [[lambda].sub.1]=2.5 W/(m K); [[lambda].sub.2]=0.48W/(m K); [[lambda].sub.3]=0.054 W/(m K); [[lambda].sub.4]=45W/(m K); [alpha]=17 W/([m.sup.2]K); C=85.5; H=11%; O=0.3%; N=0.6%; A=0.1%; W=2.0%; S=0.5%; [O.sub.2]=21%; [N.sub.2]=79%; [alpha]=1.2; [t.sub.ld]=110[degrees]C; [t.sub.a]=25[degrees]C; [c.sub.a]=1.302 kJ/kgK; [T.sub.b]=1423K; [T.sub.Pb]=973K; [T.sub.g]=1473K; [C.sub.o]=5.67; [PHI]=0.7; [phi]=1.0; [r.sub.L]=1.184; [c.sub.b]=1.071 kJ/kgK.

[FIGURE 2 OMITTED]

In Fig.2 is presented the amount spent of combustibles in the PF in function of [T.sub.b] for [G.sub.b]=4.1667 kg / s and in Fig.3. The lead separation amount of PF in function to the [r.sub.Pb] for [G.sub.b]=4.1667 kg/s and [r.sub.Pbmsh]. In Fig. 4 is presented the material balance for [T.sub.b]=1423 K, [G.sub.b]=4.1667 kg/s while in Fig. 5. Thermal balance for [T.sub.b]=1423 K, [G.sub.b]=4.1667 kg/s and B=0.01066 kg/s.

[FIGURE 3 OMITTED]

5. CONCLUSION

The amount of lead separated in PF ([G.sub.Pbyear]) is depended on Gb), [r.sub.Pb], [r.sub.Pbm], and [r.sub.Pbmsh]. For average values of these factors ([G.sub.b]=4.1667 kg / s,([r.sub.Pb]=1.55, [r.sub.Pbmsh]=0.5 and [r.sub.Pbm]=0.5%), the average value of separated lead amount is [G.sub.Pbyear]=418.5 t/year. The combustible amount spent of in PF to normal working conditions for [T.sub.b]=1423 K and [G.sub.b]=4.1667 kg/s is B=0.01066 kg/s.

Results obtained for lead division and combustibles consumption in PF, are of interest for economic work analysis of PF.

6. REFERENCES

Agolli, F., (1985). Metalurgjia e metaleve me ngjyra (Metallurgy and metal color), Faculty of mining and metallurgy, Mitrovice

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

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

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

Sacadura, J. (1993). Knowledge for thermal transfer (Initiation aux transferts thermiques, TEC&DOC, ISBN 2-85206-618-1, Paris

Fig 4. Material balance for [T.sub.b]=1423 K, [G.sub.b]=4.1667 kg/s

Gb 4.1667
B 0.0108
GL 0.1744
Gh 4.3517
GPb 0.0195
Ga 0.1844
Gd 4,3454
Gbd 4,1418

Note: Table made from bar graph.

Fig 5. Material balance for [T.sub.b]=1423 K, [G.sub.b]=4.1667 kg/s
and B=0.01066 kg/s

Q1 430.365
Q2 2.363
Q3 4.791
Q4 5131.025
Qh 5568.543
Q1' 5100.239
Q2' 2.122
Q3' 264.307
Q4' 34.423
Q5' 4.304
Q6' 38.428
Q7' 15.534
Q8' 109.187
Qd 5568.543

Note: Table made from bar graph.