🎓 Lesson 26
D5
Separation Process Design Scenario Quiz
Separation process design is figuring out how to efficiently split a mixture—like crushed rock and explosives—into useful parts using physical or chemical methods.
🎯 Learning Objectives
- ✓ Calculate mass balances across multi-stage separation systems
- ✓ Design a two-stage hydrocyclone circuit for particle size classification using D50 and sharpness criteria
- ✓ Analyze selectivity and recovery in froth flotation circuits using grade-recovery curves
- ✓ Apply McCabe–Thiele graphical method to determine theoretical stages for solvent extraction
- ✓ Explain the impact of feed particle size distribution on screen efficiency and blinding tendency
📖 Why This Matters
In mining and blasting engineering, separation isn’t just about sorting rocks—it’s about unlocking value: recovering metals from ore, controlling dust emissions, ensuring explosive uniformity, and meeting regulatory tailings specifications. Poor separation design leads to overgrinding, metal loss, unstable slurries, and non-compliant effluent. This quiz tests your ability to translate theory into robust, field-ready designs.
📘 Core Principles
Separation relies on differences in physical properties—size, density, surface chemistry, solubility, or magnetic susceptibility. Design begins with characterization: particle size distribution (PSD), mineral liberation analysis, and slurry rheology. Then, equilibrium relationships (e.g., partition coefficients, distribution ratios) and kinetic limitations (e.g., flotation rate constants, settling velocity) define feasible operating windows. Finally, equipment selection balances capacity, precision, and robustness—e.g., vibrating screens for coarse sizing vs. hydrocyclones for fine classification. Scale-up requires geometric, dynamic, and kinematic similarity, validated by pilot testing.
📐 Hydrocyclone Cut Size (D₅₀)
The D₅₀ is the particle size at which 50% reports to underflow—critical for classifying blasted material before grinding or leaching. It depends on cyclone geometry, feed pressure, and slurry density.
💡 Worked Example
Problem: Given: cyclone diameter = 0.3 m, vortex finder diameter = 0.06 m, spigot diameter = 0.04 m, feed pressure = 120 kPa, solids volume % = 28%, SG of solids = 2.9, water viscosity = 1.0 cP.
1.
Step 1: Compute dimensionless parameters: d_v/d_c = 0.06/0.3 = 0.2; d_s/d_c = 0.04/0.3 = 0.133; ΔP = 120 kPa.
2.
Step 2: Apply Plitt equation: log₁₀(D₅₀) = 0.462 − 1.27 log₁₀(ΔP) − 0.283 log₁₀(d_v/d_c) + 0.392 log₁₀(d_s/d_c) − 0.59 log₁₀(solids %) + 0.057 log₁₀(SG).
3.
Step 3: Plug in values → log₁₀(D₅₀) ≈ −1.23 → D₅₀ ≈ 0.059 mm (59 µm). Verify against typical range for this cyclone size: 40–80 µm.
Answer:
The result is 59 µm, which falls within the safe range of 40–80 µm for a 300-mm hydrocyclone processing gold ore slurry.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), a two-stage hydrocyclone circuit replaced single-stage classification ahead of SAG milling. Feed PSD showed 35% <75 µm; target overflow was <65 µm for optimal leach kinetics. Using Plitt-based D₅₀ modeling and residence time distribution (RTD) validation, engineers achieved 92% classification efficiency and reduced regrind energy by 18%. Post-implementation sampling confirmed ±3 µm control on D₅₀—within specification limits per ISO 14688-1:2018 for particle size reporting.
🔧 Interactive Calculator
🔧 Open Mass Transfer and Separation Processes Calculator📋 Case Connection
📋 Ethanol-Water Separation in Biofuel Plant
High energy demand for azeotropic distillation; poor purity (<92%) in first-pass product
📋 CO₂ Capture from Flue Gas using Amine Absorption
Low CO₂ partial pressure (~0.15 bar); amine degradation and solvent carryover