Evaluation of uneven distribution of charge materials at blast furnace

Abstract

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.