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MINERAL PROCESSING & EXTRACTIVE METALLURGY
2 min reference note
Mineral Processing, Mass Balancing & Hydrocyclone Classification Handbook
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1. Executive Summary & Plant Relevance
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.
2. Two-Product Mass Balance Mathematics
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 Γ f = C Γ c + T Γ t
Solving these equations simultaneously yields the mass yield (Y) and valuable metal recovery (R):
Mass Yield Y (%) = (C / F) Γ 100% = [ (f - t) / (c - t) ] Γ 100%
Recovery R (%) = (C Γ c) / (F Γ f) Γ 100% = [ (c / f) Γ (f - t) / (c - t) ] Γ 100%
3. Hydrocyclone Classification & Plitt Cut-Point Model
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 (ΞΌm) = [ 50.5 Γ Dc^0.46 Γ Di^0.6 Γ Do^0.68 ] / [ Du^0.56 Γ P^0.24 Γ (Οs - Οf)^0.5 ] Γ exp(0.06 Γ Cv)
PEER-REVIEWED TEXTBOOK & JOURNAL CITATIONS
Wills, B. A., & Finch, J. A. (2015). Wills' Mineral Processing Technology (8th ed.). Butterworth-Heinemann. [Access Reference]