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*V2according to which the random  variable V2 has  X2k a distribution with k degrees of freedom, k  =  N  –  1,  where n  =  n1 + n2 + … + nN, ni 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  X2k,  and X2also  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 X2k 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),   X2k =  X2max= qX2 was calculated. In order to reconcile X2 and  X2k statistics with the measurements of the physical quantities (temperature,  pressure) or materials (granular, gaseous), the X2-statistic must be adjusted so that  qX2max≈ X2k(α), X2max с(X21,..., Х2M )where M – is the  number of experiments for which the values   of X2-statics were determined,  X2k(α) – the upper α-quantile of  X2k statistic, q – the quantile multiplier, introduced for the correction of the X2-statistic values,  X2max–  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.