Assessment of Nonuniform Batch Distribution in Blast Furnace

In industry, nonuniform distribution of the material and energy resources significantly affects the stability of production processes and impairs product quality. In particular, in blast furnaces, nonuniform distribution of the batch components and the gas temperature significantly affects furnace performance. A literature review shows that the nonuniformity is usually assessed by means of various coefficients taking account of the variability in the material and energy resources in the course of production. The variation coefficient introduced by Pearson in 1895 is most commonly used. The relation between the square of the variation coefficient V² and X² = [n(N–1)/N]V² is established. According to this relation, the random quantity V² has a χ²_k distribution with k degrees of freedom: k = N–1. Here n = n₁ + n₂ + … + n_N; n_i is the ith measurement (\(i = \overline {1,N} \)); and N is the total number of measurements. The proposed method of assessing the nonuniformity is based on the statistics χ²_k and X², as proposed by Pearson in 1901 and 1904, respectively. Here X₀ is intended for verification of hypothesis H₀: that the empirical and statistical distributions agree. The azimuthal nonuniformity of the distribution of materials and gases in the blast furnace is based on the consistency of the Pearson statistics χ²_k and X². The quantile factor q is employed if the calculations of X² do not employ the frequency of the measured quantities but, by analogy, the magnitudes of the physical quantities. In this method, after correction, X² is used to assess the deviation p from a uniform distribution (the nonuniformity factor): p = p(χ²_k), p ∈ (0; 1–α); χ²_k= X²_co-qX². If X² and χ²_k are to be consistent for measurements of physical quantities (the temperature or pressure) or of materials (friable materials, gases), X² must be corrected so that qX²_max ≈ χ²_k(α), X²_max ⊂ (X²₁, …,X²_M), where M is the number of experiments for which X² is determined; χ²_k(α) is the upper α quantile of χ²_k; q is the quantile factor introduced for correction of X²; X²_max is the limiting value of X²_max permissible in determining the nonuniformity measure. The method is tested in estimating the relative nonuniformity of the batch components and the distribution of the azimuthal temperature for 2014- and 1370-m³ blast furnaces at OAO Magnitogorskii Metallurgicheskii Kombinat. The influence of the sequence in which the batch components are selected in the bunker of the nonconical furnace-charging system on the azimuthal nonuniformity of the materials and the smelting characteristics is analyzed.