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160                          Advances in Productive, Safe, and Responsible Coal Mining

         matter content, which is a function of specific gravity. Hence, the ash content of dif-
         ferent gravity fractions can be regressed against the average specific gravity as deter-
         mined using the traditional approach. The resultant regression equation can then be
         used to calculate a corrected average specific gravity of the fraction based on its
         ash content. This approach has been shown to be very reliable, particularly when
         the regression is applied to samples from one location [8]. Another advantage of this
         approach is its ability to correct errors in washability analysis, which are relatively
         frequent when working with fine size fractions.

         9.2.5 Sample analysis

         Each of the specific gravity fractions collected in the above fashion was rinsed, dried,
         weighed, and analyzed for ash, sulfur, and 51 trace elements. The ash analysis was
         conducted according to ASTM standards in a muffle furnace at a university labora-
         tory. Trace element analyses, which included analysis for sulfur, were conducted at
         a commercial laboratory using aqua regia digestion followed by inductively coupled
         plasma mass spectrometry (ICP-MS) and inductively coupled plasma atomic emission
         spectroscopy (ICP-AES).


         9.2.6 Modeling gravity separation partition curves
         A density cut point of 1.9 was simulated on ROM material with a corresponding
         probable error (E p ) value of 0.057. With this information, partition numbers were
         calculated using Whiten’s classification function [9], which is as follows:

                                             1
             Partition Number ¼ 100⨯                                     (9.1)
                                          ln3 SG SG 50 Þ
                                             ð
                                  1 + exp
                                               E p
         This partition number represents the percentage of the density fraction “SG” reporting
         to product when a density cut of “SG 50 ” is made. Comparing actual yield predicted by
         partition curve modeling with theoretical yield predicted by the washability analysis
         provides an estimation of organic efficiency, which is a measure of achievable product
         quantity and quality.


         9.2.7 Modeling cost impacts of dilution
         OSD’s impact on the overall operating cost of a coal mine was examined by separating
         it into four components.

         9.2.7.1 Mining costs
         The mining cost component is separated into extraction costs and material handling
         costs. The extraction cost impact is a result of the fact that OSD material has no value
         to the customer and is expected to be discarded in the coal preparation process. Mining
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