Mineral Processing, Mass Balancing & Hydrocyclone Classification Handbook

In modern mineral processing plants, accurate mass balancing is the fundamental prerequisite for metallurgical accounting, circuit optimization, and plant control. Whether sizing a primary SAG mill, calculating circulating load ratios in closed-circuit ball milling, or assessing flotation recovery performance, deterministic mass balance equations allow process engineers to reconcile sampling data and pinpoint recovery bottlenecks.

When a feed stream (F) with metal grade (f) is separated into a concentrate product (C) with grade (c) and a tailings waste stream (T) with grade (t), the total mass and metal balance equations are expressed as: F = C + T F × f = C × c + T × t Solving these equations simultaneously yields the mass yield (Y) and valuable metal recovery (R): Mass Yield Y (%) = (C / F) × 100% = [ (f - t) / (c - t) ] × 100% Recovery R (%) = (C × c) / (F × f) × 100% = [ (c / f) × (f - t) / (c - t) ] × 100%

Hydrocyclones separate fine particles from coarse mineral particles using centrifugal force. The d50 cut-point represents the particle size with an equal 50% probability of reporting to overflow or underflow. Plitt Model: d50 (μm) = [ 50.5 × Dc^0.46 × Di^0.6 × Do^0.68 ] / [ Du^0.56 × P^0.24 × (ρs - ρf)^0.5 ] × exp(0.06 × Cv)