Performance Analysis of Coal Cleaning Operations: Relationship Between Probable Error in Separation and Organic Efficiency Performance Analysis of Coal Cleaning Operations: Relationship Between Probable Error in Separation and Organic Efficiency

Separation efficiency of coal cleaning equipment is typically assessed by Probable Error in Separation (Ep) and Organic Efficiency (Eorg). The first one is determined on the basis of precise cut point density of separation and implies that for ideal separation the error is zero. The second one is calculated on the basis of yield of clean coal/ middling at the target ash and implies that for ideal separation the efficiency is 100%. Plant operators worldwide being accountable for the tonnage of the clean coal and middling produced regularly monitor Eorg with some application in plant design in India. Ep is universally used as an equipment selection criterion from among the vendors, in commercial contracts and sometimes for performance analysis of coal cleaning equipment carried out at the plants. Since both are performance measures there should possibly be a relationship between the two for specific cleaning equipment or for a particular type of density separators. Such relationships are however rarely observed. Moreover there are many instances where high to very high Eorg does not translate into low to very low Ep. Therefore, is there a dichotomy between the two performance measures?

QMC integration errors and quasi-asymptotics

A crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.