Journal Article

Methodological Elements of Applying Two- and Multi-Dimensional Distributions of Grained Materials Properties to Coal Beneficiation

Niedoba, Tomasz

2013

Overview

Processes of beneficiation are a primary component of mineral processing operations. The efficiency of the process and potential beneficiation of the material are evaluated by means of beneficiation curves. There are many varieties of beneficiation curves, among which one of the most often applied is a group called Henry's beneficiation curves. Of these, the basic curve for ash content in feed is the most often used. This paper presents the methods of ash content curve approximation. This paper is divided into two parts. Part one contains the approximation of the basic Henry's beneficiation curve λ = λ(γ) for energetic coal of type 31 (data from one of the Upper Silesian coal mines were applied for this purpose) conducted by means of two varying methods. The first method was based on a determination of the functional relation between ash content and density λ = λ[0](ρ) as well as between yield and density γ = F(ρ). Then, by determination of the reverse function ρ = F[-1](γ) and its combination with the first function, the searched relation for λ(γ) was obtained. The second method was based on approximation of the function γ = Φ(λ) by means of combining two logistical functions (the combining point was determined by means of the ordinary kriging method). Then, using the reverse function, the searched function λ(γ) was obtained. The adequacy of approximation was evaluated by comparison of the ash content both in individual fractions and throughout the whole material. The second part of the paper proposes ways of determining the surface λ = λ(d,ρ) by means of regression of the first type by applying two- and three-dimensional Morgenstern distribution functions and by means of regression of the second type by applying known two-dimensional distribution functions or two-dimensional kernel approximation. The latter function is the nonparametric statistical method increasingly used. Furthermore, the paper provides formulas for mean ash content as a component of the whole investigated material.

• Publisher: Polish Academy of Sciences
• Subject: Approximation / Coal mining / Materials science / Normal distribution / Process engineering / Studies