🎓 Lesson 1
D1
Getting Started with Separation Process Engineering
Separation process engineering is the science of splitting mixtures—like ore and waste rock—into useful parts using physical or chemical methods.
🎯 Learning Objectives
- ✓ Explain the role of separation processes in the mining value chain from blasting to concentrate production
- ✓ Analyze particle size distribution data to select appropriate separation technology
- ✓ Calculate mass balance for a simple gravity separation circuit
- ✓ Apply Stokes’ law to estimate settling velocity of ore particles in water
- ✓ Compare energy consumption across common separation methods (e.g., screening vs. hydrocycloning)
📖 Why This Matters
Every ton of copper, gold, or lithium starts as raw rock containing <1% valuable mineral. Separation process engineering transforms that rock into marketable concentrate—removing 90–99% of waste while preserving metal recovery. Without precise separation, mines face lower revenues, higher tailings volumes, regulatory penalties, and unsustainable water/energy use. In fact, separation accounts for ~65% of total processing energy in hard-rock mining—making it the largest controllable cost center after blasting and hauling.
📘 Core Principles
Separation relies on exploiting differences in physical or chemical properties between components: size (screening, crushing), density (jigging, dense-medium separation), surface chemistry (flotation), magnetism (low/high-intensity magnetic separation), or solubility (leaching, solvent extraction). The process begins with liberation—breaking rock to expose target minerals—and ends with concentration—enriching valuable phases. Efficiency depends on three pillars: (1) degree of liberation (governed by comminution), (2) selectivity (how well one property discriminates components), and (3) throughput capacity (equipment sizing and residence time). Real-world systems are rarely single-unit; they’re integrated circuits where output from one stage becomes input to the next—requiring rigorous mass and assay balancing.
📐 Stokes’ Law for Terminal Settling Velocity
Stokes’ law predicts how fast spherical particles settle in laminar flow—a foundational model for gravity separation, sedimentation, and hydrocyclone design. It applies when Reynolds number < 1 (typically fine particles < 0.1 mm in water). Deviations require correction factors (e.g., Wallis or turbulent drag corrections) for industrial-scale equipment.
Stokes’ Settling Velocity
v_t = \frac{d^2 (\rho_p - \rho_f) g}{18\mu}Calculates terminal settling velocity of a rigid spherical particle in laminar flow.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| v_t | Terminal settling velocity | m/s | Constant velocity reached when drag force equals net gravitational force |
| d | Particle diameter | m | Equivalent spherical diameter of the particle |
| \rho_p | Particle density | kg/m³ | True density of the solid particle |
| \rho_f | Fluid density | kg/m³ | Density of the continuous phase (e.g., water, dense medium) |
| g | Gravitational acceleration | m/s² | Standard acceleration due to gravity (9.81 m/s²) |
| \mu | Dynamic viscosity | Pa·s | Resistance to flow of the fluid medium |
Typical Ranges:
Fine galena in water (75 µm): 0.01 – 0.03 m/s
Quartz sand in water (500 µm): 0.05 – 0.15 m/s
💡 Worked Example
Problem: Calculate the terminal settling velocity of a spherical galena (PbS) particle (ρ_p = 7.5 g/cm³) with diameter 75 µm in water at 20°C (ρ_f = 0.998 g/cm³, μ = 1.002 cP).
1.
Step 1: Convert units: d = 75 µm = 7.5 × 10⁻⁵ m; ρ_p = 7500 kg/m³; ρ_f = 998 kg/m³; μ = 1.002 × 10⁻³ Pa·s
2.
Step 2: Apply Stokes’ law: v_t = [d² (ρ_p − ρ_f) g] / (18μ) = [(7.5e−5)² × (7500 − 998) × 9.81] / (18 × 1.002e−3)
3.
Step 3: Compute numerator = (5.625e−9) × 6502 × 9.81 ≈ 3.59e−4; denominator = 0.018036 → v_t ≈ 0.0199 m/s
4.
Step 4: Verify Re = (ρ_f v_t d)/μ = (998 × 0.0199 × 7.5e−5)/1.002e−3 ≈ 1.48 → slightly above Re=1; thus, result is approximate but acceptable for preliminary design.
Answer:
The settling velocity is 0.0199 m/s (≈ 72 mm/s), which falls within the typical range of 10–100 mm/s for fine heavy minerals in water-based separators.
🏗️ Real-World Application
At the Olympic Dam copper-uranium-gold operation (BHP, South Australia), a multi-stage separation circuit processes 40 Mt/year of ore. Primary crushing is followed by SAG/ball milling to P80 ≈ 106 µm. Liberation analysis confirmed >90% chalcopyrite exposure at this grind size. A dense-medium cyclone (DMS) separates high-density sulfide-rich particles (SG > 3.2) from low-density silicates (SG < 2.8) — achieving 92% Cu recovery in the DMS concentrate. That concentrate then feeds flotation, where reagent-controlled surface chemistry further upgrades Cu grade from 2.1% to 28%. Mass balance closure across the circuit is maintained within ±0.5% via online gamma-ray analyzers and calibrated slurry density meters.
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