Reduction of Iron Ore Fines with Coal Fines by Statistical Design of Experiments* By S. MOOKHERJEE, * * A. M UKHERJEE, * * * B. K. DHINDA W * * * and H. S. RAY*** Synopsis A study of simultaneous effects of the major processing variables on the extent of reduction of a column of iron ore fine surrounded by coal fines in an externally heated shaft reactor is reported. The variables studied are ore particle size, coal particle size, coal/ore ratio, time, and temperature. Statistically planned series of isothermal experiments have been carried out to quantitatively assess the effects of each of these variables and of their interaction the extent o f reduction. Within the range of the variables studied, use o f computational methods to find the values of each of the variables to obtain the maximum extent of reduction have also been discussed. I. Introduction Various features of some natural gas based direct reduction processes and some noncoking coal based direct reduction processes have been reviewed in the literature.1 3) In view of the fact that large amounts of ore fines and coal fines are available,4~ direct reduction processes utilizing fines are also of interest in India. Several such processes have been reported in the literature. For example, the Hoganas process,2t which has been in use in Sweden for many years, uses iron ore fines and coke fines packed in alternate layers or concentric rings in ceramic saggers. These saggers are heated in a tunnel kiln at a temperature of around 1 200 C. The sponge iron is crushed and used for either production of iron powder or as replacement of high quality scrap for producing special steels. The Bardin Institute of Moscow has developed a process5~ in which a vertical column of iron ore fines is reduced by an annular column of coal fines in an externally heated shaft reactor. The ore and coal fines are charged from the top and a highly metallized and sintered rod of sponge iron is continuously withdrawn from the bottom. In either of these processes the reaction is between unmixed layers of ore and coal. Such a reaction is the theme of the present study. This paper presents a statistically planned series of isothermal experiments to study the effect of process variables like time, temperature, ore particle size, coal particle size, and coal/ore ratio on the extent of reduction of a column of iron ore fines surrounded by an annular layer of coal fines in an externally heated shaft reactor. II. Statistical Design of Experiments Use of statistical design of experiments in the area of iron ore reduction has been very limited so far. Morrison el al."~ have studied the effects of time, temperature and carbon/iron ratio on the extent of reduction and on pellet properties for iron oxide reduction using char in a laboratory rotary kiln. Their major conclusions were: (a,) all the three factors have a strong influence on the extent of reduction, (b) optimum reduction occurs between the temperature range 1 040-1 100 C, (c) the greater the extent of reduction, the better are the physical properties, (d) high C/Fe ratio gives high compression strength and resistance to abrasion, and (e) swelling decreases with time and with increasing temperature. The design matrix used by these authors for exploring their system was complex and time consuming. For routine optimization of systems it may be worthwhile to try design matrices which involve less number of experiments and yet give more useful information. In the present investigation, it was decided to use a relatively simple design. The simplest way of designing an experiment to obtain a linear model is to make the factors vary on two levels. The formula used for this purpose is: N = 2h...(1) where, k : number of variables or factors N: number of trials. This is known as a factorial experiment and all possible combinations of the factor levels will have to be executed during experimentation. The present study has been carried out in two parts. In the first part, the variables considered are temperature, iron ore particle size, coal particle size, and coal/ore ratio, while in the second part the variables studied are temperature, time, ore particle size, and coal particle size. Since the number of variables in each series are four and each is to be varied between two levels, the number of trials or experiments required for each series is 16. To reduce the number of trials, partial factorial design has been selected. A one-half replication of a 24 factorial experiment requires 241=8 number of trials. It should be noted that when fractional replications are used, the linear effects are confounded with the interaction effects. This is thought to be of not much significance as the study has been carried out to find the effects of various factors on the extent of reduction and to get an insight into the possible mechanism of reaction. * ** *** Manuscript received on April 23, 1985; accepted in the final form on September 13, 1985. Regional Research Laboratory, Bhubaneswar-751 013, India. Department ol' Metallurgical Engineering, Indian Institute of Technology, Kharagpur-721 0 1986 ISIJ 302,.India.. Technical Report (101)
(102 ) Transactions ISIJ, Vol. 26, 1986 For the present study, it should be noted that of the four variables, the coefficients of the first three variables indicate the effect of these variables on the yield while that of the fourth variable is confounded with an interaction term. In reality a4x4=a4x4+ axix2x3. But in practice the coefficient of the ternary interaction is found to be negligibly small. Hence, although the coefficient of x4, the fourth variable is a confounded one, it can be used to get an idea of the effect of this variable on the yield. Apart from it the present design matrix gives the coefficients for three interactions also viz. x1x2, x2x3, x1x3, independently. The factor levels are in effect the boundaries of the area to be searched for a given process variable. If xj denotes the variables (factors), then, and x0 xjmax+xjmiii ( ) jr 2... 2 xj max-xj miri dxj = 2...(3) The point with co-ordinates x, x2i x3,..., etc. is called the centre point of the design or the base level and 4xj is the change interval or unit on the x; axis. It is customary to convert the xj co-ordinates to a new dimensionless system of co-ordinates X j by the coding equation. III. Experimental Condition and Procedure The ore used for this study was Noamundi ore and the material was sieved into two size fractions, namely, -250 pm+ 180 tm and -150 pm+90 rim. Each of these size fractions were analysed for their chemical constituents. The results for the two size fractions were similar and the analysis is shown in Table 3. The coal used in this study was a non-coking coal from the Hutar Colliery of Daltangunj field. The coal fines were sieved and two size fractions, namely, -1000 pm + 710 pm and -600 pm + 250 ~cm were used in the experiments. The proximate analysis of the two size fractions of the coal are shown in Table 4. The ore and the coal fines were charged into a mild steel crucible of 32 mm internal diameter and 50 mm height. A glass tube was placed in the centre of the crucible and iron ore of a fixed weight was poured into this tube. The annular space between the glass tube and the mild steel tube was filled with Table 3. Chemical analysis of hematite ore (dry basis). x./=x (4) 4x ; Thus the upper level of X; becomes + 1 and the lower level -1 in the coded form. The actual (natural scale) and coded (dimensionless scale) values of the factors for the two series of experiments are shown in Tables 1 and 2, respectively. Table 1. Actual and coded values of the variables for first series of experiments. Table 2. Actual and coded values of the variables for second series of experiments.
Transactions ISI1, Vol. 26, 1986 (103) a fixed weight of coal fines. The crucible was lightly tapped three times and the glass tube was then slowly withdrawn from the crucible. No other load was applied on the ore and coal particles. The crucible and its contents was then isothermally heated in muffle furnace for a fixed length of time. At the end of the heating period, the crucible was withdrawn from the furnace and quenched with a jet of water on its sides. Care was taken to see that no water came in contact with the reacted mass. After cooling, the sample was crushed to -150,eem and then chemically analysed for total iron. This total iron value was used to obtain the degree of reduction by the equation of Chernyshev et a1.7' given below: where, K %FeT-%Fe1,.100 L %FeT'%FeT a : degree of reduction K: ratio of weight of iron ore to that of oxygen in the ore % Fed : percentage of total iron in the initiall ore % Fey, : percentage of total iron in the reduced mass. The bulk density of the loosely filled ore and coal beds are given in Table 5. Table 6 gives the weights of raw materials used and diameter of the iron ore column for different weight ratios of coal to iron ore. The values were selected to maintain an approximate bed height of 40 mm for both ore and coal. For the first part of experiments, the coal to ore ratio was varied between 0.9: 1 (lower level) and 1.5: 1 (upper level). For all the experiments in this part, the reaction was carried out for 2 hr. For the second part of experiments the coal to ore ratio was kept at 1.2: 1 for all the experiments while reaction time was varied between 120 min (lower level) and 180 min (upper level). To avoid systematic errors, the sequence of each trial was selected from a table Table 5. Bulk density of ore and coal beds. of random numbers. Thus for both the parts the experiments were carried out in the sequence, namely 2, 3, 7, 8, 1, 4, 5, 6 where each of these numbers indicate trial numbers as given in the design matrix. Iv. Results and Discussion 1. Results of First Part of Experiments The design matrix and results are shown in Table 7. Here X1=temperature, X2=ore size, X3=coal/ore ratio, X4 = X1X2X3 = coal size, and Y1= degree of reduction (%) X1, X2, X3, X4 being in the coded form. With the help of this matrix the coefficients of their regression equation were solved. The regression equation to which the experimental data is fitted is of the type Y = a0+~ a.1x.1+~ a,,1(x, X.1)...(5) The regression coefficients are estimated by a0=-. a ~X,,,Y,, 1= N, a ( X,,1)Y'",,; _ ~ '~~', and so on N where, N: number of trials. The regression equation considered inn the present study is given as Y = a0+a1xl+a2x2+a3x3+a4x4+a5x1x2 +a6x 1X3+a7X 2X3...(5) The final regression equation is Y1= 77.10+2.37X1+1.44X2+0.01X3-1.88X4.50X1X2+0.02X1X3-0.91 X2X3...(6) where, X1, X2, X3, X4: in the coded form, i.e., in dimensionless scale. The relationships between the coded values (X;) and actual values (x;) are given as X l = (x1-1000)/50, x2 = (x2-164.16)/47.97, x3 = (x3-1.2)/0.3, and x4 = (x4-614.96)/227.65. Table 7. Design matrix and results of Part-1 experiments. Table 6. Weights of ore and coal and ore colum for different weight to ore. diameter of ratios of coal
(104 ) Transactions ISIJ, Vol. 26, 1986 Using these relationships the regression equation (Eq. (6)) can be converted to the uncoded form. Random experiments were carried out to test the regression equation thus developed for their validity. The conditions for the random experiments are : x1=1000 C, x2=164.32 ~Cm, x3=1.2, and x4=595.82 pm. Three identical trials were conducted separately and all the three trials gave identical degree of reduction, namely, Y1=77.62 %. By substituting the values of X1... X4 in Eq. (6) one gets Y1= 77.27 %. From this observation it was concluded that as standard deviation is nearly zero, all the coefficients are significant. Also, since the experimental and calculated values of the random experiment, namely, 77.62 % and 77.27 %, are in good agreement with each other it was concluded that the model developed is valid over the range of variation studied. The effect of each of the variables individually and in combination can be estimated from the above regression equation (Eq. (6)). It can be seen that within the range of variables selected for the experiments, the extent of reduction increases with increase in temperature, ore particle size and decrease in coal particle size. The effect of coal/ore ratio is seen to be quite small. The coefficients of the interaction terms XiX2 and X2X3 are, however, negative. This shows that the mechanism of the process is quite complicated. The combined effect of increase of temperature and ore size (XiX2) is negative and this indicates the possibility of sintering playing an important role in affecting the rate of reaction. With simultaneous increase in ore size and coal/ore ratio (X2X3) the yield decreases. The non-coking coal used liberates volatile matter on heating. The volatile matter helps in some initial reduction as it contains some amount of hydrogen. On the other hand, the volatile matter also contains other substances like tar etc. which may help to block the pores of the ore bed. With increase in ore particle size and coal/ore ratio, the porosity of the iron ore bed increases and also the amount of volatile matter increases. Thus a greater amount of volatile matter flows through the ore bed and hence there is a possibility that larger number of pores will get blocked by tar present in the volatile matter. This blockage of pores of the partially reduced bed of iron ore grains decreases the reducibility of the grains. This negative effect is, however, not present for the increase of temperature and coal/ore ratio (X1X3). As the temperature of reaction is increased, the volatile matter is liberated at a much faster rate and hence its residence time in the ore bed decreases with increase in temperature. Thus the overall effect on the progress of reduction is a positive one. The effect of change of one of the variables, namely, ore particle size was tested separately. Keeping the other three variables fixed at values selected for the random experiments, the ore particle size was varied and the results are shown in Table 8. Thus it is shown experimentally that the prediction by the model is correct as far as ore particle size is considered. This helps to further confirm that the model is adequate. Although Eq. (6) indicates negligible effect of coal/ore ratio, it is known from the results of several authors that gasification of carbon plays an important part in the reduction of iron oxides by solid reducing agents. The reason for the small coefficient for this factor could be that for the range selected, the amount of coal is quite in excess. To find the effect of coal/ore ratio in the reduction rate, separate experiments were carried out with the ratio varied from 1.2: 1 to 0.6: 1. The values of other factors selected were : Ore size =-500 pm+250 pm, coal size=-710 pm+500 pm, temperature= 1000 C and holding time= 120 min. The results are given in Table 9. It is thus seen that upto a coal/ore ratio of 1: 1, the degree of reduction increases with increase in the amount of coal. With further increase in the amount of coal the effect is no longer prevalent. It should, however, be noted that in industrial practice excess coal is used. The excess char at the end of a run is recycled. A computer programme was developed based on the random search technique to find the conditions for which the extent of reduction will be maximum. Each of the variables were varied from their lower level to upper level, namely, -1 to + 1 in steps of 0.2. Some of the results are shown in Table 10 where the values of the variables are in their coded forms. The programme was run on a HP-1000 system. 2. Results of Second Part of Experiments The design matrix and results are shown in Table 11. Here X1=temperature, X2=ore size, X3=time, X4 = X1X2X3 = coal size, and Y2 = degree of reduction, (%). X1, x2, X3, X4 are all in the coded forms. With the help of this matrix, the coefficients of the regression equation were evaluated as explained earlier and the equation is given as, Table 8. Effects of change reduction. of ore size on extent of Table 9. Effect of coal/ore ratio on extent of reduction. Technical Report
Transactions 'SIT, Vol. 26, 1986 (105) Y2 = 80.07+4.38X1+ 1.16X2+3.45X3+0.72X4 +0.21 X1X2+ 1.53X1X3+0.23X2X3... (7) where X1, X2, X3, X4 are in the coded forms. The relationship between the coded values (X;) and actual values (x1) are given as X1= (x1-1000)/50, x2 = (x2-164.16)/47.97, x3 = (x3-150)/30, and x4 = (x4-614.96)/227.65. Using these relationships the regression equation can be converted into the uncoded form. Random experiments were carried out for the conditions: x1=1 000 C, x2= 164.32 pm, x3= 150 min, and X4=595.82 jim. For the three trials carried out separately, identical values of 79.5 % were obtained for the degree of reduction. By substituting the values of X1, X2, X3, X4 in Eq. (7) one gets Y2= 80.13 %. Hence it was concluded that all the coefficients are significant and that the model is valid over the range of variation studied. It is seen in Eq. (7) that all the variables excepting coal particle size have a positive effect on the degree of reduction. In other words, for an increase of the first three variables from their base level value to the upper level value, the degree of reduction increases, where as, the extent of reduction decreases with Table 10. Calculated tion from values the model. of the extent of reduc- increase in coal particle size. In contrast to the model developed in the first series, the coefficients of all the interaction terms in this model are positive. The combined effect of temperature and ore particle size (X1X2) being positive indicate that the negative effect of sintering of the reduced ore particles decreases with increasing reaction time. This is to be expected as the rate of sintering is maximum initially and decreases with progress of reaction. The increase in the degree of reduction with simultaneous increase of temperature and time (X1X3) and also with increase of ore particle size and holding time (X2X3) as indicated by the model is also quite justified. It can also be seen that the increase of temperature and time has the maximum influence on the extent of reduction considered individually, and that increase of temperature has a greater effect than increase of time. This agrees fairly well with established laws of chemical kinetics. Using the computer programme conditions for maximum extent of reduction were calculated. This and some other calculations of degree of reduction from the model are shown in Table 12. V. Conclusions The application of statistical design of experiments in the present work to study the effect of various process variables, namely, temperature, time, coal/ore ratio, ore and coal particle sizes on the extent of reduction of a column of iron ore fines surrounded by coal fines in externally heated crucibles have been found to be quite useful. It gives a large amount of information with less expenditure of time. The interaction coefficients in the regression equation developed have been exploited to have better understanding of the reaction involved in the reduction of iron ore by coal. Other than the obvious positive effect of temperature and time on the extent of reduction, the porosity of the iron ore column (which depends on the ore particle size) is found to play an important role in the reduction process. The models predict that decrease in coal particle size Table 12. Calculated tion from values of the model. the extent of reduc- Table 11. Design matrix and results of Part-2 ex- periments.
(106 ) Transactions ISIJ, Vol. 26, 1986 increases the extent of reduction indicating that the gasification of carbon also plays an important role in the reduction process. This is further asserted by the fact that the reduction rate increases with increase in the coal/ore ratio. The regression equations developed for the two series of experiments are found to be adequate within the ranges selected for the various variables. These equations, therefore, can be used to predict the value of the degree of reduction for various values (within the range) of the factors. The maximum extent of reduction within the range of the study have been evaluated with the help of a computer. It should be noted that for this purpose no constraints were used. However, constraints like cost, productivity, etc. can be incorporated in these models to get optimum values for extent of reduction. Nomenclature x : base level 4x1: range of variation of the factor x,i 11a x : upper level of the factor ximm 11: lower level of the factor X.i: factor in coded form X : base level of the factor in coded form (0) 4X, : range of variation of the factor in coded form (+1 to -1) Yz : response variable ao : value of the response variable when all the variable factors are at the base level a; : coefficient of the primary variable in the regression equation a7z; : coefficient of the binary interaction effect of the variables Xl, : primary variable X?l,, : interaction effects N: total number of experiments in the design matrix REFERENCES 1) R. L. Stephenson : Direct Reduced Iron; Technology and Economics of Production and Use, Iron Steel Soc. RIME, Penn., (1980). 2) Direct Reduction of Iron Ore-A Bibliographical Survey, Metals Soc., London, (1979). 3) L, von Bogdandy and H. J. Engell: The Direct Reduction of Iron Ores, Springer-Verlag, Berlin, (1971). 4) S. Mookherjee and A. Mukherjee: Trans. Ind. Inst. Metals. 35 (1982), Special Number, 21. 5) V. F. Knyazev: Alternate Routes to Steel, ISI, London, (1971), 76. 6) A. L. Morrison, J. K. Wright and K. MeG. Bowling: Ironmaking Steelmaking, (1978), No. 1, 32. 7) A. M. Chernyshev, N. K. Kornilova and Yu V. Tarasenko: Izv. VUZav Cher. Met., 3 (1977), 21. (Steel in USSR, 7 (1977), No. 3, 133).