A generalization of distribution data for characterizing the performance of float-sink coal cleaning devices

The performance of float-sink coal cleaning devices customarily is characterized by a distribution curve, in which the percent of feed reporting to clean coal is plotted against specific gravity. For a given vessel and a given feed a family of distribution curves can be obtained, each having its own specific gravity of separation. This paper presents a method for combining these distribution curves at different specific gravities of separation, for a given coal cleaning vessel and a given feed, into a single, generalized distribution curve which is independent of the specific gravity of separation. This curve can be expressed in tabular form or it can be represented mathematically by an exponential type equation, known as a Weibull function. A different generalized distribution curve will be obtained for each of several different size fractions. A method is presented for utilizing these curves with feeds which encompass a broad spectrum of sizes. The well-known concepts of error area and probable error are extended to the generalized distribution curve. It is shown that the conventional probable error, and — under certain conditions — the conventional error area, are directly proportional to the specific gravity of separation for a given vessel and a given feed size.