Self-similarity of upgrading parameters used for evaluation of separation results

A proper characterization of upgrading results requires two material balance parameters, usually plotted as upgrading curves. It was presented in the paper that such pairs of separation result parameters have a certain degree of self-similarity defined as an extent to which one parameters is a part of the other. Some pairs of upgrading parameters have a significant degree of self-similarity. Upgrading curves based on such parameters are unsuitable for a simple statistical evaluation of separation results, especially when the determination coefficient R2 is used for this purpose. This is so because the R2 value can be as high as almost 1, even for highly scattered original data points. It results from comparison of nearly two identical parameters. It was shown in the paper that, for example, the upgrading curve relating the content of the considered component in concentrate less the content of the considered component in tailing and the content of the considered component in concentrate have the self-similarity approaching 99% on a 0 to 100% scale proposed in the paper. Other upgrading curves used in mineral processing have medium (between 50 and 60%) self-similarity, while the Fuerstenau plot, relating recovery of the useful component in concentrate and recovery of the remaining components in the tailing, has a relatively low self-similarity which changes with recovery from 0 to about 50%.

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► Parameters of upgrading results (quality vs. quantity) plots have a certain degree of self-similarity.
► Upgrading curves parameters having high degree of self-similarity are unsuitable for statistical evaluation.
► The recovery-recovery plot has much smaller self-similarity than yield-grade, grade-grade, and grade-recovery curves.