Evaluation of uneven distribution of charge materials at blast furnace

In various industries, the uneven distribution of material and  energy resources significantly affects stability of the technological  process and reduces the quality of products. In particular, in the blastfurnace production, the uneven distribution of charge materials and  the temperature of gases significantly affect technical and economic  performance of the furnace. The analysis of bibliographic sources  has shown that for the estimation of unevenness various coefficients  were generally used, taking into account the variability of material and  ener gy resources in the production process, the coefficient of variation  introduced by K. Pierson in 1895 was the most widespread. It was determined the relation between the square of the coefficient of variation of V² and the value  X²= (n(N-1))/N*V² according to which the random  variable V² has  X²_k a distribution with k degrees of freedom, k  =  N  –  1,  where n  =  n₁ + n₂ + … + n_N , n_i is the value of the i-th measurement,  i = 1, N – is the number of measurements. The proposed method  for estimating the unevenness is based on statistics  X²_k,  and X² also  introduced by K. Pearson in 1901 and 1904, respectively. The latter  was intended to test the H₀-correspondence of the empirical and statistical distribution. The method for determining the circumferential  irregularity in the distribution of materials and gases in a blast furnace  is based on the consistency of X²_k and X² of Pearson statistics, using  the so-called quantile factor q, if in calculations of X² the valu es   of the ,physical quantities themselves are used, by analogy, not the frequency  of the measured quantities. In this method, X²-statistic after correction  was used to determine the measure of deviation  (p) from the uniform  distribution, i.e. the unevenness coefficientp = p(X²/^k), p  є  (0; 1 – α),   X²_k =  X²_max= qX² was calculated. In order to reconcile X² and  X²_k statistics with the measurements of the physical quantities (temperature,  pressure) or materials (granular, gaseous), the X²-statistic must be adjusted so that  qX²_max ≈ X²_k (α), X²_max с(X²₁,..., Х²_M )where M – is the  number of experiments for which the values   of X²-statics were determined,  X²_k (α) – the upper α-quantile of  X²_k  statistic, q – the quantile multiplier, introduced for the correction of the X²-statistic values,  X²_max–  the maximum value of X²-statistic is admissible for determining the  measure of non-uniformity.The method was tested to evaluate the relative non-uniformity of the loaded charge components and the distribution of peripheral temperature at blast furnaces of OJSC “MMK” with  volume of 2014 and 1370 m³. The influence of the sequence of a set of  charge components in the hopper of a bell-less charging device of the  furnace on the coefficient of circumferential unevenness (p) and the  technical and economic parameters of melting was revealed.

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