Reproducible Nomogram-Based Tools for Rapid Analysis and Design of Mineral Processing Operations

Abstract

Abstract

Nomograms once provided efficient solutions to engineering calculations, but their use declined with digital computing. This study presents a reproducible set of nomograms for classical mineral processing relationships—Bond’s law, the modified Hogg and Fuerstenau mill power model, Azzaroni’s make-up ball size equation, closed-circuit circulating load and two-product recovery—complemented by auxiliary charts for mill speed, apparent charge density and slurry properties. The charts are generated with the open-source tools PyNomo and Nomogen, and all scripts, software versions and verification code are publicly available. Accuracy was assessed by separating construction error, obtained by reproducing the isopleth geometry numerically for 2000 random cases per chart, from reading error, simulated with a 0.25 mm placement uncertainty at native print size. The maximum construction error observed in the tested samples was below 0.13%, and the median simulated reading error is 0.04%–1.4%, except for the circulating load chart (3.4%), where it reflects the intrinsic sensitivity of the percent-solids method. A chained ball mill sizing example reproduces the analytical solution and agrees with Moly-Cop Tools™; because both implement the same equations, this verifies the graphical procedure rather than validating the models, which were not compared with industrial data. The nomograms are intended as transparent first-pass tools for education, preliminary design and operational screening.