Mining Engineering cheat sheet

Bond work index: W = 10·Wi·(1/√P80 − 1/√F80), where W is specific energy in kWh/short ton and P80, F80 are 80% passing sizes in µm; Wi is determined by locked-cycle Bond ball mill test.

Comminution energy split rule: crushing is efficient for coarse reduction (feed > ~25 mm), rod mills for 10–25 mm, ball mills for fine grinding; Bond third theory assumes energy proportional to new surface area via 1/√d.

Liberation size: grind only to the size where the target mineral is liberated; overgrinding raises energy and slimes losses. Assess with mineral liberation analysis or optical grain-size counting.

Flotation: collectors render sulfide surfaces hydrophobic (xanthates for galena, sphalerite, chalcopyrite); frothers stabilize bubble size; depressants (cyanide, zinc sulfate) and activators (copper sulfate for sphalerite) control selectivity; pH governs xanthate adsorption.

Gravity separation: jigging for coarse (mm–cm) coal and ore; shaking tables for 0.05–2 mm; spirals for 0.075–1 mm; heavy-medium (DMS) uses magnetite suspensions, typically 1.3–1.8 SG for coal and up to 2.9 SG for ore.

Magnetic separation: low-intensity (LIM) for strongly magnetic magnetite; high-intensity (WHIMS) for weakly magnetic hematite and ilmenite; high-gradient (HGMS) for paramagnetic fines.

Cyanide leaching (gold): Elsner equation 4Au + 8CN⁻ + O₂ + 2H₂O → 4[Au(CN)₂]⁻ + 4OH⁻; kinetics depend on dissolved O₂, pH ~10–11 to limit HCN, and cyanide concentration.

Mass balance: recovery R = C·c/(F·f) and concentrate grade relation; two-product formula gives concentrate grade from feed, concentrate and tailings assays: c = f·(F/T ratios) - always check assays by weight balance.

Coal preparation: washability curves (float-sink tests) set the separation density; DMS cyclones and dense-medium baths achieve organic efficiency; moisture and ash determine product value.

Sampling: Gy's theory of sampling - sample mass must scale with particle size and heterogeneity; correct sampling (all particles have equal chance of selection) avoids bias; never sample from a stream edge.

Grinding circuits: closed circuit with hydrocyclone or classifier returns coarse to mill; circulating load typically 200–350% for ball mills; use trommel/screen to limit overgrinding.

Leaching alternatives: heap leach (low grade, long cycle, 60–90 days), agitated tank leach (fast, high grade), and pressure oxidation/biooxidation for refractory sulfide gold ores.

Dewatering: thickening (flocculant-assisted settling) followed by filtration (pressure/vacuum) or drying; tailings management includes paste and dry stacking.

Comminution circuit design: SAG mill plus ball mill (SAB) or SABC with pebble crusher; power draw scales with mill volume and charge; charge ~30–45% of mill volume.

Grade control: blast-hole sampling, grade-shell modeling, ore/waste cut-off grade determined by break-even calculation including mining, processing and refining costs.

Environmental: acid rock drainage risk from sulfide waste; neutralization by lime; tailings dam design uses factor of safety and freeboard criteria.