Numerical prediction is performed on the reduction of wüstite under simulated blast furnace conditions using factorial design approach. Wüstite sinter samples with different basicity (0.5, 1.0, and 2.0) are reduced with a gas mixture consisting of 30% CO, 10% H2, 5% CO2, and 55% N2 at 950–1100°C. In all cases, the reduction degree of wüstite increased with basicity and temperature. A 23 factorial design is applied to derive a regression model based on the experimental data of acidic (CaO/SiO2 = 0.5) and basic (CaO/SiO2 = 2.0) wüstite which is reduced at 950°C and 1100°C for 5 and 35 min. The developed mathematical model is applied to predict the reduction degree of wüstite at different basicity (0.5, 1.0, and 2.0), interval of time (5–35 min), and temperatures (950, 1000, 1050°C, and 1100°C). In general, the results of the driven models are found to be in good agreement with the experimental data of reduction of wüstite in many cases. The MATLAB program is used to carry out the required calculations.
The use of mathematical models in the experimental analysis has increased over the years due to its efficiency in explaining, predicting, and controlling the processes [
The previous survey summarized some studies that have been carried out experimentally to elucidate the effect of some factors on the reduction rate of wüstite. However, the effective magnitude of these factors either individually or collectively on the reduction rate of wüstite sinter is still not clear. This can be carried out by the application of statistical factorial design approach which has several advantages in highlighting the effect of individual variables and their relative importance on the reduction process [
In the current study, pure chemical Fe2O3, CaO, and SiO2 were used to eliminate the effect of other impurities which normally exist in the iron ore and affect the reduction process. Pure sinter mixtures with different basicity (CaO/SiO2: 0.5, 1.0, and 2.0) are prepared. The acidic mixture with basicity equal to 0.5 consisted of 85% Fe2O3, 5% CaO, and 10% SiO2. The neutral mixture with basicity equal to 1.0 is composed of 85% Fe2O3, 7.5% CaO, and 7.5% SiO2. The basic mixture with basicity equal to 2.0 consists of 85% Fe2O3, 10% CaO, and 5% SiO2. The oxide powders were mixed well in a ball-mill to guarantee the complete homogeneity of the mixtures. Equal weights of ~2.0 g of each mixture were pressed in a cylindrical mould of ~1.0 cm inner diameter at 10 kN using a hydraulic press. Under these conditions equal size compacts (diameter = 0.99 cm and height = 1.0 cm) have been prepared. The compacts were dried at 100°C for 24 hours, then fired in a muffle furnace up to 1300°C with heating rate 10 K/min, and kept at this temperature for 1.0 h to ensure the complete reactions between different oxides (Fe2O3, CaO, and SiO2). The prepared sinters (acidic, neutral, and basic) were fast cooled down in air to room temperature and then kept in a desiccator for subsequent reduction experiments.
The reduction experiments have been carried out in a vertical tube furnace as shown in Figure
Schematic diagram of reduction system.
The sinter samples which prereduced to wüstite with 20% CO, 20% CO2, 5% H2, and 55% N2 at 900°C were subsequently reduced with 30% CO, 5% CO2, 10% H2, and 55% N2 at 950–1100°C. The reduction curves of wüstite sinters at 950°C, 1000°C, 1050°C, and 1100°C are given in Figures
Conditions of experiments and reduction degree of wüstite sinter.
Trail number | Basicity | Time, min | Temperature, °C | Reduction degree, %; 1st | Reduction degree, %; 2nd | Reduction degree, %; average |
---|---|---|---|---|---|---|
1 | 0.5 | 5 | 950 | 37.1135 | 36.9957 | 37.0546 |
2 | 2.0 | 5 | 950 | 47.8015 | 47.6659 | 47.7337 |
3 | 0.5 | 35 | 950 | 64.0251 | 63.8383 | 63.9317 |
4 | 2.0 | 35 | 950 | 89.3165 | 89.1381 | 89.2273 |
5 | 0.5 | 5 | 1100 | 47.8021 | 47.6653 | 47.7337 |
6 | 2.0 | 5 | 1100 | 72.1252 | 71.7068 | 71.9160 |
7 | 0.5 | 35 | 1100 | 83.0875 | 82.7623 | 82.9249 |
8 | 2.0 | 35 | 1100 | 99.7213 | 99.4791 | 99.6002 |
Comparison between the reduction curves of different basis sinter reduced at (a) 950°C, (b) 1000°C, (c) 1050°C, and (d) 1100°C.
The controlling parameters which are considered in the current applied 23 factorial design are including the effect of basicity (CaO/SiO2), reduction time, and temperature on reduction process of wüstite sinter.
By convention, the effect of a factor was denoted by a capital Latin letter. Thus “
The average effect of any factor can be defined as the change in response produced by a change in the level of that factor averaged over the levels of the other factors. The symbols
Mathematical formulations are used to estimate the effect of different parameters on the reduction degree of wüstite sinter. The effect of
Table
Algebraic signs for calculating effects in the 23 design.
Treatment combination | Factorial effect | |||||||
---|---|---|---|---|---|---|---|---|
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(1) | + | − | − | + | − | + | + | − |
|
+ | + | − | − | − | − | + | + |
|
+ | − | + | − | − | + | − | + |
|
+ | + | + | + | − | − | − | − |
|
+ | − | − | + | + | − | − | + |
|
+ | + | − | − | + | + | − | − |
|
+ | − | + | − | + | − | + | − |
|
+ | + | + | + | + | + | + | + |
Sum of squares for the effects in the 23 design with
Analysis of variances.
Source of variance | Average effect | Sum of square (SS) | Degree of freedom | Mean of square (MS) |
|
---|---|---|---|---|---|
|
21.0075275 | 1765.264847 | 1 | 1765.26485 | 41728.19065 |
|
58.7255825 | 13794.77616 | 1 | 13794.7762 | 326087.6410 |
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17.0467075 | 1162.360946 | 1 | 1162.360946 | 27476.45446 |
|
6.5728625 | 172.8100858 | 1 | 172.8100858 | 4084.969017 |
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2.6150975 | 27.35493974 | 1 | 27.35493974 | 646.6293955 |
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4.2312625 | 71.61432938 | 1 | 71.61432938 | 1692.854415 |
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−4.2479775 | 72.18125136 | 1 | 72.18125136 | 1706.255593 |
Error | 0.338431131 | 8 | 0.04230389 | ||
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|||||
Total | 17066.70099 | 15 |
From the data given in Table
The contrast coefficients which are used to estimate the effects are summarized in Table
Contrast coefficients of effects.
Effects | (1) |
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−1 | +1 | −1 | +1 | −1 | +1 | −1 | +1 |
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−1 | −1 | +1 | +1 | −1 | −1 | +1 | +1 |
|
+1 | −1 | −1 | +1 | +1 | −1 | −1 | +1 |
|
−1 | −1 | −1 | −1 | +1 | +1 | +1 | +1 |
|
+1 | −1 | +1 | −1 | −1 | +1 | −1 | +1 |
|
+1 | +1 | −1 | −1 | −1 | −1 | +1 | +1 |
|
−1 | +1 | +1 | −1 | +1 | −1 | −1 | +1 |
The results of the experiment can be expressed in terms of regression model. The regression model is given in the following:
Actual and predicted reduction degree at different conditions (variables).
Variable | Predicted RD, % | Actual RD, % | Residence ( |
The residence variation | ||
---|---|---|---|---|---|---|
1st | 2nd | 1st | 2nd | |||
(1) | 8.024465 | 7.14062 | 6.9957 | +0.072 | −0.072 | ±0.072 |
|
15.58829 | 14.5836 | 14.6959 | −0.056 | +0.056 | ±0.056 |
|
51.679715 | 50.67498 | 50.8083 | −0.067 | +0.067 | ±0.067 |
|
80.89079 | 80.27172 | 79.6381 | +0.32 | −0.320 | ±0.32 |
|
13.97009 | 12.87576 | 13.1653 | −0.145 | +0.145 | ±0.145 |
|
35.25779 | 34.40974 | 34.2268 | +0.091 | −0.091 | ±0.091 |
|
74.57909 | 73.54268 | 73.7623 | −0.11 | +0.11 | ±0.11 |
|
100.02429 | 99.7209 | 99.4791 | 0.12 | −0.12 | ±0.12 |
The relation between the natural variable and the coded variable can be given as follows: the coded variable is equal to [(natural variable − 1/2(variable at high level + variable at low level))/1/2(variable at high level − variable at low level)]. Based on this, the RD can be predicted in terms of basicity, time, and temperature as given in the full regression model formulation in (
This full regression formulation indicates that the reduction degree of wüstite sinter is not only affected by the individual parameter (basicity, time, or temperature) but also by the mutual interactions among all of these parameters.
In order to examine the validity and the efficiency of the current regression model the derived equation is used to estimate the reduction degree of wüstite at different basicity (0.5, 1.0, and 2.0), reduction time (5, 10, 15, 20, 25, 30, and 35 min), and temperatures (950°C, 1000°C, 1050°C, and 1100°C). The results are compared to that obtained from the experimental reduction trails as can be seen in Figure
Experimental and predicted reduction degree of wüstite with different basicity at (a) 950°C, (b) 1000°C, (c) 1050°C, and (d) 1100°C.
In the current study, wüstite sinter with different basicity (CaO/SiO2 = 0.5, 1.0, and 2.0) was prepared and reduced with 30% CO, 5% CO2, 10% H2, and 55% N2 at 950–1100°C. A 23 factorial design is built on the experimetal data of reduction at lowest and highest basicity and reduction tempeartures. The main findings can be summarized in the following points. The higest reduction degree was exhibited by the basic wüstite sinter (CaO/SiO2 = 2.0) which followed neutral wustite (CaO/SiO2 = 1.0) and the lowest by acidic wüstite sinter (CaO/SiO2 = 0.5). A full regression formulation was develpoed to calculate the reduction degree (RD) of wüstite based on basicity ( The highest positive effect on the reduction degree was exhibited by the interval of time followed by basicity and then the applied temperature. In the binary interaction, the basicity with time exhibited the highest positive effect on the reduction of wüstite followed by time with temperature and then basicity with temperature. The ternary interaction between the basicity, time, and temperature showed a negative effect on the reduction degree of wüstite. The validation of the regression model exhibited a good agreement with the experimental results at relatively low temperature (≤1000°C). A significant deviation was obtained at high temperature (≥1050°C) which was attributed to the formation of highly reducible calcium ferrite phase.
The author declares that there is no conflict of interests regarding the publication of this paper.