IL32295A - Blast furnace operation - Google Patents

Description

IMPROVT5 3HTS If OR RELATING TO BLAST PORHACS OPERATION MBTALLU OICAL PROCESSES LIMITED and IMPERIAL SMELTING CORPORATION (JJ.S.C,) LIMITED carrying on business together in the Bahamas under the name and style of METALLURGICAL DEVKLOPMEHT COHPAHY 599 This invention relates to a method of improving the operating efficiency of a zinc-lead "blast furnace, into which are charged carbonaceous fuel and a sinter containing zinc oxide and lead oxide, preheated oxygen-containing gas "being "blown in through tuyeres near the bottom of the furnace, while "below these tuyeres molten lead and slag are run off, usually at intervals but possibly continuously, the zinc oxide in the charge being mostly reduced to zinc vapour, which, together with the permanent gases generated (consisting mostly of carbon monoxide, carbon dioxide and nitrogen), is conducted through an offtake (or offtakes) above the furnace stock-line to a condenser (or condensers) , where it is condensed, usually by being brought into contact with a shower of molten lead.

The improved operating efficiency of a zinc-lead blast furnace is attained, according to the invention, by an improved method of controlling the relative amounts and temperatures of the charge materials and oxygen-containing gas introduced into the furnace, the control measures taken involving the inter-pretation of the current furnace performance in the light of a model representing the important underlying physico-chemical factors. One feature of the invention is that, although any complete description of the chemical reactions occurring in the shaft must be very complex, our physico-chemical studies have determined which of these are important and what are their important characteristics. By this means we have developed a model that is adequate for representing furnace performance and that can be translated into mathematical form suitable for handling in a computer.

The important reactions occurring in the furnace shaft are as follows. Firstly, combustion of carbonaceous fuel at the tuyeres yields mostly carbon monoxide together with some carbon dioxide by the exothermic reactions: C + 02 = CO (A) CO + 102 = C02 (B) Some of the carbon monoxide reduces zinc oxide to produce zinc vapour by the endothermic reactions: ZnO + CO = Zn + C02 (C) Somewhat higher up in the shaft some of the carbon dioxide generated in reactions (B) and (C) reacts with carbon in coke to form carbon monoxide, by the endothermic reaction: C + C02 = 2C0 (D) Partly in the zone where reaction (D) occurs, but mostly in the top zone of the furnace, where the sinter (which is normally charged cold when taken from store but which may be at a higher temperature when conveyed direct from the sinter plant) and the coke (normally charged at about 800°C) become heated by the upcoming gases, some zinc oxide is regenerated on the surface of the descending charge by the exothermic reversal of reaction (C) : Zn + C02 = ZnO + CO (E) Also near the top of the furnace charge, lead oxide is reduced by carbon monoxide: PbO + CO = Pb + C02 (F) One feature of the physico-chemical model is that the furnace operation is basically dependent on rates of heat and mass transfer and on the rate of reaction (D) , the other reactions (the reactions (C), (E) and (F) ) being so rapid that their rates are essentially determined by rates of mass transfer. As a consequence there is an equilibrium zone in the furnace where the gas and solid are at substantially the same temperature and where there is chemical equilibrium between gas and solid with respect to reaction (C) and (E).

This invention consists in a method of operating a zinc/ lead blast furnace, comprising continually monitoring the values of (i) the zinc/carbon ratio in the charge (ii) the pre-heat temperature of the blast (iii) the ratio of slag-forming materials to carbon in the charge (iiii) the composition of the product gases from the furnace (v) the zinc content of the slag and (vi) the temperature of the molten slag leaving the furnace and adjusting the ratio of zinc to carbon in the charge and the pre-heat temperature of the blast so as to maximize the zinc elimination according to the relationship; SZP (b1 + bQD + b2p + b$PTp + b^p2 + b5Tp) Θ (R2) = V - » (a0 + &1Τρ + a≥D + a^2 + a^D2 + a^ D) where Rz = zinc elimination V = a constant Sz = Weight of slag-forming material in charge/ weight of zinc in charge F = I D = Izinc/carbon ratio in charge K* - a constant p + 1 = the number of moles of carbon burnt per atom of oxygen in blast Tp = pre-heat temperature of blast and bQ to bj- and to a^ are polynomial coefficients .

The invention will be further described with reference to the accompanying drawings, in which: Figure 1 is a diagrammatic cross-section of a blast furnace according to the invention, Figure 2 is a computer flow diagram, Figure 3 is a flow diagram of computer calculations.

The fundamental purpose behind the equations to be developed, is to be able to predict the effect on zinc elimination at future points in time, of changes in operating conditions. This model will first be developed in a static form and then adapted to give the dynamic response of the plant.

The output of the shaft can be measured by a combination of any two of the following functions :- (a) The rate of input of zinc to the furnace, (b) The rate of output of zinc in gas, (c) The rate of output of zinc in slag.

The performance is measured entirely in terms of zinc smelting; this is because the level of lead used has little effect on the performance of the furnace as a zinc smelter.

Normally, the amount of lead fed to the furnace is between 1/3 and 1/2 the zinc feed, on a weight for weight basis.

Of the three functions named above, the rate of output of zinc in gas is extremely difficult to measure on a short term basis and hence output will be measured in terms of zinc input and zinc loss.

FORMULATION OF THE STATIC MODEL The operation of the I.S.F. shaft is basically dependent on thermodynamic considerations, rates of heat and mass transfer and the rate of reaction D a¾ove. The rates of the other reactions are sufficiently rapid to be considered as instantaneous. It has been shown, that, over a considerable length of the furnace, the gas and solid are at thermal and chemical equilibrium (Zone II. Figure 1), The chemical equilibrium for zinc reduction is defined by:- [P.CO2] [P.Zn] where P refers to partial pressures, = and K is a function of temperature.

[P. CO] aZnOs The activity of zinc oxide solid (aZn0_) will be assumed to be unity.

Within the equilibrium zone, the endothermic reaction of carbon with carbon dioxide occurs (reaction D) and the equilibrium is maintained by rapid oxidation of zinc by csrbon dioxide which is an exothermic reaction. Above the equilibrium zone preheating of the charge, to equilibrium temperature, takes place by a combination of gas cooling and zinc reoxidation, the proportion of each being governed by the relative rates of heat and mass transfer. This preheating zone is shown as Zone I in Figure 1. It is assumed that the relationship between the rate of heat and mass transfer is governed by the Chilton Colburn Analogy and that radiant heat can be neglected. As some of the charge preheating is performed by cooling of the gas, the gas leaves the charge in a non-equilibrium condition, and, to prevent excessive deposition of zinc oxide in the gas offtakes, the gas is reheated by adding air above the charge. This reacts exothermically with carbon monoxide in the gas.

In view of the presence of the equilibrium zone, it is convenient to divide the furnace at the top of the equilibrium zone and treat the two sections separately. (a) The Equilibrium and Smelting Zone (Zones II and III, Figure 1) The inputs to this zone are:- (i) Air at preheat temperature T^ (ii) Charge at equilibrium temperature The outputs are: (i) Gas at equilibrium temperature T (ii) Slag at temperature Τ_Ί If the zone is considered as "black box" , the overall reaction in the zone can be written as:- RN2 + (l+p)C + >2 + zZnO zZn +(z-p) C02+(l+2p-z)C0+ RN2 where z is the number of mols of zinc smelted per atom of oxygen in blast and (p + 1) is the number of mols of carbon burnt per atom of oxygen in blast and R is the value of inerts to oxygen in the blast gas assumed to be 1-881 in the following calculations, i.e. the value for air. Assuming the activity of zinc oxide is unity the equilibrium is defined by:- K = [z(z-p)3 / [(l+2p-z) (2.881+p+z)] (1) where the equilibrium constant is related to the equilibrium temperature (T ) by the equation Tk InK = - 7,34-5 + Tk (51.23 - 2.92 lnTfc) (2) where ¾· = Te + 273.3.

Equation 2 contains the value of the free energy, at temperature T-^, for the reaction ZnO + CO — Zn + C0,->.

A further equation can be formed from a heat balance over the whole zone. Inserting the appropriate heats of reaction at temperature T , the sensible heat terms for heating blast from temperature T^ to e and the solid sinter slag from Tg to Ts]_¾ together with the latent heat of melting of slag, gives the equation: z(42, 110+10.17Te- 13.02Tsl) = 21, 50+1.37Te-p(4-2,370-2.0?Ce) -Z(13.02T -, - 13.13ΤΩ+4-322)-S(0.24A0 n - 0.2607ΤΛ + 126.4) -^Te ~ ^ 16· 75 + 0„00121 (Τθ + Τρ) ) (3) where Ζ = mols of zinc oxide entering the equilibrium zone per atom of oxygen in blast.

S = lbs of slag material entering the equilibrium zone per lb atom of oxygen in blast.

This equation assumes a heat loss of - kilocalories per lb atom of oxygen in blast.

Equations 1, 2 and 3 can be solved for z and T if the values of Z, S, p, T, and Tg^ are known. This calculation was carried out on an Elliot 503 computer and the computer flow diagram is shown in Figure 2.

For calculating the new value of T , equation (2) is re-arranged in the form: Te(new) = 47 , 34-5/[ 51.23-Rlnk - 2, 9 ln(Te(old) +273.3) ] W This calculation was found to be rapidly convergent, four iterations being sufficient under all conditions. If the process is reversed, i.e. equation 3 used to calculate Te and equations 1 and 2 to calculate z, the method is divergent.

The value of T lies between 950°C and 1150°C and its value depends mainly on the levels of and p. (b) The Charge Preheating Zone. (5) and (10) The equations for this zone are as follows :-dTg/dx = -h(Tg - Ts) (5) dPl/dx - hDi In [(l-P1)/(l-p1)] (6) Hs(dTg/dx) = Hg(dTg/dx) + Ht dy/dx (7) ¾ = (z-y)/( 2.881 + p + z - y) (8) P2 = (l+2p-z+y)/(2.881 + p + z - y) (9) P3 = (z-p-y)/(2,881 + p + z - y) (10) [(ι-ρ1)/(ΐ-ρ1)]0·81 - [(Ι-Ρ3)/(Ι-Ρ3)]0*81 - [(Ι+Ρ2)/(Ι+Ρ2)] (ID Κ = P^Pj/Pg ^12) where ^, ρ2 and ρ^ are the partial pressures of zinc, carbon monoxide and carbon dioxide in the bulk of the gas phase and P^, ?2 and P^ are the same partial pressures at the solid surface, T is the gas temperature, T is the solid temperature, x is the distance measured up the furnace from the top of the equilibrium zone, y is the number of lb moles of zinc oxidised per lb atom of oxygen in blast, from x = 0 to x = x and is the relative diffusivity of zinc where is given by Di = 0.81/[0.81(p1 + p3) + 1.0(p2 + pN )] (13) Equations 5 and 6 give the rates of heat and mass transfer respectively in the zone; the connecting constant (h) between the two equations involves the Chilton Colburn Analogy. (This assumes the Lewis No is unity and the partial pressure of inert gas remains sensibly constant). Equation 7 defines a heat balance over the length dx where Ησ is the heat capacity of the charge, Hg is the heat capacity of the gas and is the heat of the reaction, at temperature Ts , of the reaction Zn + CO—^ ZnO + CO. Equation 11 is a mass balance for the gas constituents at the solid surface and, like equation 15, it assumes that the diffusivities of zinc vapour and carbon dioxide are approximately 0.81 times the diffusivities of carbon monoxide and nitrogen. Since the reaction between zinc and ce,rbon dioxide is fast the gas at the surface of the solid will be at equilibrium; this is shown in equation 12 where: R(Ts+273.3)lnK = -47,3 5+(Ts+173.5) (51.23-2.92 ln(Ts+273.3)) . This assumes that the oxidation reaction takes place on the solid surface only (i.e. the reaction is heteropolar) .

Differentiating equation 8 and re-arranging equations 5» 6 and 7 gives :-dy/dTs. = CHS-Hg (dTg/dTg)] /HT (14) dy/dTs = Hs/[¾-(Hg(2.881+p)(Tg-Ys)/(DiU(2.881+P+z-y)2) )] (15) where U = In [ (l-P1)/(l-p1) ] is given by the solution of the equation [ (2.881+p+z-y)-eu(2.881+p) ] [ (2.881+p+z-y)-eu(2.881+2p) ] = K [(3.881+3 )e°*81u-(2.381+p+z-y)] [2.881+p+z-y] (16) These differential equations have the following boundary conditions Tg = Ts = Te ,' y° = 0 initial T = T„ final S f where f is the solid temperature at the top of the charge.

The total amount of zinc reoxidised over the whole zone (n) is given by n = (dy/dT3) dTS moIs per atom oxygen in blast. s e For computer solution of the equations, it was found convenient to re-write equation 16 in the form: U = In C2 dU/d C2 = [1/C2] (17) dC2/d K = -[(3.881+3p)C20,81 -01] / [01(5.762+3ρ) - 02(5.762 + p) (2.881+p) + 0.81 G102"°*19(3.881+3p) ] (18) where 01 = 2,881 + p + z - y. dK/d = Kf(23851.V(Ta + 273)2 + 1. 71/(T_ + 273.3)"' (19) Since the initial value of Ts = e the initial value of will be that calculated for the equilibrium zone. 02 (initial) = 1, and U (initial) - 0.

The final solid temperature is the mean temperature of sinter at 15°G and coke at 800°C. However, the combustion of top Sir above the charge gives rise to radiation from the gas above the charge on to the top of charge thus altering the value of T^* In the calculation carried out it was decided to ignore this radiation. It was felt that this would not affect the form of the polynomial though it might give rise to errors in the coefficients calculated theoretically (when the model is used to control the furnace, only the form of the polynomial obtained from theoretical considerations will be used, the coefficients being obtained by regression of plant data) .

Equations 14-, 15, 171 18 and 19 were solved by a simple iterative process. The solid temperature range (T — T^.) was divided into a number of steps ^T and, starting with Tg = Tg and knowing the value p,z and K (initial) values of /\ , . C2, A.U, Alg and were calculated and hence new values of Tgn To) v» K5 u and 02 obtained. This is repeated until is then halved and a second iteration carried out to find a new value of n. Further iterations were then carried out (halving ATs each time) until n remains constant to within + 1.0 x 10""^. The method 'is fairly rapidly convergent, the number of iterations varying between 2 and 5 depending on the initial values of z and p.

The initial number of steps was 16 in each case, i.e.

(T - Tf)/16 for the first iteration. (c) The Model of the Whole Furnace Shaft.

The two sections of the model can now be combined to provide an overall relationship for the shaft. The inputs to the model are D, ' Sr,' Tp ,7 p^ and Ts1. where D is the ratio of zinc to carbon in the charge (wt/wt) and Sr the ratio of slag forming material to carbon in the charge (wt/wt). The output to be predicted, for elimination calculations, is the zinc loss in slag. From D and Sr the values of Z and S which are inputs to the equilibrium and smelting zone model can be calculated using the formulae Z = 12.01D (p + l)/65.38 + n (20) S = 12.01 Sr (p + 1) (21) Because of the dependence of Z on n, a further iterative process, for the model as a whole, must be used. The flow diagram of the computer calculations is shown in Figure 3· This calculation is rapidly convergent, requiring only 3 or 4- iterations to obtain z and n to the required degree of accuracy. From z and n, the value of the zinc losses in slag per unit of carbon charged (wt/wt), L, can be calculated using the formula L = D - 5.W (z - n)/(p + 1) (22) -4- with z and n accurate to 2.0 x 10 , the value of L is accurate to + 0.001, Using an Elliot 503 computer, programmed in Algol, each determination of L takes approximately 5 seconds.

As the model equations are too complex to transcribe into polynomial form by analytical means, values for L for a factorial design of p, and D, at 3 levels of Sr and 2 levels of T , , were calculated and regression analysis used to determine the form of the polynomial which fits the results.

Gropho of somo- of t s calculated values of L are ohown in The best fit polynomial was found to be of the form L = aQ + a1 p + a2 Tp + a^ D + a p Tp + a^p2 (23) If ZW is the loss of zinc in slag per unit of zinc input, as a weight percentage, the equation for ZW is of the form ZW = aQ + F(a1p + a≥Tp + a^ + ^pTp + a^p2) where F = 1/D (24) Typical values for the constants, at Sr = 0.80 and Q?sl = 1300°C are given in equation 25 below ZW = 125.5 + F(263.8p - 1.721 x 10"½ + 2.370 x 10"1 TpP - 908.3P2 - 54.32) (25) With L accurate to + 0.001, ZW is accurate to approximately 0.1% absolute. (d) The Carbon Burping Rate The variable p, in the above equations for ZW, is not in itself an independent but is representative of the carbon burning rate p.er unit of air. This is dependent on the factors :- (a) The proportion of CO and CO^ produced in the combustion and smelting zone (zone I) (b) The amount of carbon gasification reaction in the equilibrium zone (zone II).

At our present state of knowledge, exact mathematical equations for the first condition cannot be formulated.

However, equations for the rate of carbon gasification are known and values are available for the kinetic constants.

For the case where the carbonaceous fuel is metallurgical coke, it has been shown that the rate of the reaction C + C02 2C0 can be expressed by the general equation R = ΚχΡ C02/ [1 + K2P CO + K5PC02] (26) where R is the rate, in lb mols per minute per atmosphere per lb of carbon. It has been shown that the rate is independent of gas velocity (over a certain maximum velocity) and that the rate equation can be simplified, with little loss of accuracy, to R = Κ Έ002/ [1 + K2PC0] (27) where the values of and K2 are given by: Κχ = 3.56 x 105 exp (- .2 x 10 /R k (28) K2 - 3.35 10"8 exp (4.68 x lO^/ ^. (29) where T^ is the absolute temperature.

These values are for powdered coke, the value of K-^ for lump being approximately half this value, i.e. log K = 3.250 - 0.921 x 10 (l/¾) (30) log K2 = 7.475 + 1.036 x lO (!/¾.) (3D These values of and K2 were obtained from the experimental data.

In a slice of equilibrium zone thickness dx ft. and area A sq. ft., the weight of carbon is 100A dx/(2.222 D + 3.4-44) lbs and hence, for a blast rate of V c.f.m. , the differential equation for p is given by dp/dx = -(2.48 x 10^ R.A)/( (1 + 0.645D)V) (32) where R is given by equation 26 and x is measured down the furnace.

As p decreases down the furnace the values of z and T must also change to maintain chemical and thermal equilibrium. To maintain thermal equilibrium the following equation must hold (dp/dx)^ + (dz/dx) H2 + (d Te/dx) (Hg + Hs) = 0 (33) where H-^ is the heat of the reaction C + C02 —> 2 CO = +42.367 - 2.09 Tg H2 is the heat of the reaction ZnO + CO — Zn + C02 = +46.54-2 - 2.96 Te and Hg and Hs are the heat capxacities of the gΰas and solid (per atom oxygen in blast).

To maintain chemical equilibrium equations (1) and (2) must hold. Differentiation and substitution gives (dTe/dx) (2385.4/(Te + 273.3)2 - 1.471/(Te + 273.3)) = (dz/dx) (l/z+l/(z-p) + l/(l+2p-z)-l/(2.881+p+z)) - dp/dx (l/(z-p) + l/(2.881+p+z) + 2/(l+2p-z)) (3^) To maintain a mass balance for zinc, with counter current flow, the following relationship must exist dz/dx = dZ/dx (35) Using equations 33» 34- ancL 35 values of dz/dx, d T /dx and dZ/dx can "be calculated from dp/dx.

The initial conditions, for these differential equations are the values T , p, z, Z and S at the top of the equilibrium zone which are those calculated in the determination of zw.

The final condition is x = Le where Le is the leng°th of the equilibrium zone. For positive values of p, a method similar to that used for the charge preheating zone is adequate for solution of these differential equations. However, for negative values of p, the rate of convergence is very slow and a great improvement was found if, for each step in x (delta x) , the equations were solved using Gills adaption of the Runge-Kutta equations. To be consistent this method was used throughout.

Since it is the value of p at the top of the equilibrium zone (pT) which is the variable to be predicted, values of pT were chosen to give a factorial design of p at the bottom of the equilibrium zone (pB) . For each value of pB, values of pT were obtained for a factorial design of T^ and D. This obviously-required a certain amount of trial and error since, although pT was the initial condition for the solution, pB was the variable which was being set to a target value. This was particularly difficult at negative values of pT when small changes in pT made large changes in pB. The relationship between pT and D was similar to that between pT and T^ except that the change of pT with D is too small to show up clearly on a graph.

It can be seen that the form of the relationship between pT and pB is asymptotic, i.e. as pB —? as pT — pB and as pB -0.5 pT tends to a constant dependent on Tp and D(-0.5 is the minimum possible value of pB and corresponds to combustion to pure 002)· The curves are best fitted by polynomials containing terms of the form T , D, pB and l/(pB + 0.5) and regression analysis showed that a good fit was obtained with an equation of the form: pT = aQ+a1pB+a2/(pB+ 0.5) +a^Tp +¾pB2 +a^/(pB + 0.5)2 + a6TppB + a?Tp/(pB + 0.5) + agD (36) Typical values of these constants are given by the equation: pT + 0.248 + 0.629ΡΒ - 0.156/(pB + 0.5) + 2.21*" 10"^ + 2.78pB2 + 1.31* 10" /(pB + 0.5)2 - 9.32* 10~ TppB - 5.9 * 10"5/(pB + 0.5) - 2.03* 10"¾ (37) These constants are for L = 14 ft, A/V = 0.0165 min.ft"1, Sr = 1.00, Tsl = 1100°C. The relationship between pT, Tp and D is of the form: pT = aQ + ¾1Τρ + a2D (38) and it will be assumed that the relationship between pB, Tp and D is also of this form. Substituting this relationship into equation 35 and expanding by the binomial expansion gives the equation: pT = b0+b1Tp+b2(l/F) + b5T + b^(l/F)2 + b5Tp(l/F) (39) where D = 1/F and pT is equivalent to p in equation 23.

(The equation for predicting zinc loss in slag), MAXIMISED ELIMINATION The function to be used is a gross function based on raw material inputs and product outputs. It does not include charges for overheads, wages, power and engineering services. it is only concerned with the two major products, i.e. zinc and lead, though it may "be necessary, at a later date, to refine the function to include minor constituents such as copper, cadmium and the precious metals. Full derivation of this function will not be given only the final form, which where : Rz is the zinc elimination V: constant -^Q Remaining symbols: as defined in the text.

Optimisation is carried by predicting, in the future, values for various levels of F and T using equations 23 and 38, Jr in which the coefficients are constantly updated using plant data (1).

A hill climbing technique is used to determine the levels of D and Tp which give the maximum value to the average of four values of the function predicted at different times in the future. This optimisation is subject to certain constraints on both the levels of the independent variables and the zinc loss in slag.

MAKING THE MODEL DYNAMIC For accurate prediction of the performance of the furnace, the predicting equations must include terms which allow for the dynamic behaviour of the plant. Including all the individual past values of the plant variables would lead to a very large computing system, so weighted averages of independent variable terms are used. In predicting the value of a dependent, previous values of that dependent are not explicitly used, i.e. actual values are predicted, not changes in value. Although, in some 0 cases, prediction of change can give greater accuracy, it results in the need for greatly increased computer syste predict and optimise in the future.

Claims (3)

CLAIMS . A method of operating a zinc/lead blast furnace , comprising continually monitoring the values of (i) the zinc/carbon ratio in the charge (ii) the pre-heat temperature of the blast (iii) the ratio of slag-forming materials to carbon in the charge (iiii) the composition of the product gases from the furnace (v) the zinc content of the slag and (vi) the temperature of the molten slag leaving the furnace and adjusting the ratio of zinc to carbon in the charge and the pre-heat temperature of the blast so as to maximize the zinc elimination according to the relationship; SZF + bQD + b2p + b3pTp + b^p + b5Tp ) Θ (Rz) = V , K (aQ + &1Tp + a2D + a^2 + a^D + a^Tp D) zinc elimination a constant weight of slag-forming material in charge/ zinc in charge

1. "zinc/carbon ratio in chari K = a constant p + 1 = the number of moles of carbon burnt per atom of oxygen in blast Tp = pre-heat temperature of blast and bQ to b^ and aQ to a^ are polynomial coefficients.

2. A method as claimed in claim 1 in which future values of Θ (Rz) are predicted for various levels of F and using equations (23) and (38) herein, in which equations the coefficients are constantly updated using monitored plant data, and levels of D and are determined which give a maximum value to an average of a number of values of the function Θ (Rz).

3. A method of operating a zinc "blast furnace substantially as hereinbefore described, with reference to the accompanying drawings . For the App!icsncs SH/PAK. PAK/SH.