Multidimensional Analysis of Coal Separation Processes
The purpose of the separation processes in coal processing is obtaining products of certain ash contents. In the most of cases it is assumed that the separation process is described by one, selected parameter, which usually is grain size or material density. The separation may be described by means of statistical distributions of random variables, what allows forecasting the separation results of certain enrichment method. There are very well known the applications of approximations of Tromp separation curves or distribution functions of Erasmus, Meloy or Weihull. It is necessary to say that if the fitness of the approximation more suitable, then the characteristics of the process itself is also better. In purpose of obtaining more appropriate results, these methods were modified by application the mathematical functions, as i.e. hyperbolic tangens function. Furthermore, on the basis of empirical data, so-called interpolations may be performed in purpose of getting more appropriate results of approximation. One of the most known techniques of interpolation is Hughes method.This method for interpolating standard data involves breaking down each interval into a number of smaller sub-intervals. The results of such one-dimensional approach not always contain the full information of the searched distribution. It happens because such interpretation of the problem is not completely correct. In practice, the separation process depends not only on the one parameter (i.e.grain size), but also on many other features characterizing certain material (i.e. its density). It seems then that in some cases the application of multidimensional grain characteristics distributions will be more appropriate. In this paper, the technique of joining the distributions of grain size and density by means of so-called Morgenstern distributions is shown. The general form of these distributions is as following:F(x, y)= F1 (x)F2(y)1 +μ(1- F1 (x))(1- F2 (y))where μ∈<-1,1> is distribution parameter, F1(x) and F2(y) are the marginal distribution functions of two selected features describing material (i.e. particles size distribution and material density).The paper contains the presentation of multidimensional approach to separation processes by application the various statistical distribution functions and interpolation techniques. The presented method will refer to the coal separation processes.
Multidimensional analysis Morgenstern distribution functions Particle size Particle density
T.Tumidajski T. Niedoba
University of Science and Technology AGH, Faculty of Mining and Geoengineering,Department of Mineral Processing and Environmental Protection, Poland
国际会议
XXIV International Mineral Processing Congress(第24届国际矿物加工大会)
北京
英文
2357-2364
2008-09-24（万方平台首次上网日期，不代表论文的发表时间）