🎓 Lesson 12
D5
Fluidization Regimes and Minimum Fluidization Velocity Calculation
Fluidization is when a bed of solid particles behaves like a fluid when gas or liquid flows upward through it at just the right speed.
🎯 Learning Objectives
- ✓ Calculate minimum fluidization velocity (Uₘf) using Ergun- and Wen & Yu-based correlations
- ✓ Analyze fluidization regimes (fixed, bubbling, turbulent, slugging, fast) using Archimedes and Reynolds numbers
- ✓ Explain how particle size distribution, density, and voidage affect Uₘf and bed stability
- ✓ Apply dimensionless criteria to diagnose fluidization behavior in heap leaching or ore roasting systems
- ✓ Design a lab-scale fluidized bed reactor for metal recovery by selecting appropriate gas velocity and particle size
📖 Why This Matters
In mining, fluidization enables efficient heat/mass transfer in processes like fluidized-bed roasting of sulfide ores (e.g., zinc concentrates), in-situ uranium leaching, and catalyst regeneration in hydrometallurgical reactors. Misjudging Uₘf leads to catastrophic failures: too low → channeling and poor extraction; too high → elutriation, particle loss, and equipment erosion. Understanding fluidization ensures optimal reagent contact, energy efficiency, and environmental compliance—making it indispensable for sustainable mineral processing.
📘 Core Principles
Fluidization begins when upward fluid drag equals particle buoyant weight. As velocity increases, the bed transitions through distinct regimes: fixed bed → incipient fluidization → bubbling → turbulent → fast fluidization → pneumatic transport. Regime identification depends on two key dimensionless numbers: Archimedes number (Ar), which compares gravitational to viscous forces, and minimum fluidization Reynolds number (Reₘf). Particle sphericity, size distribution (span < 1.5 ideal), and bed voidage (εₘf ≈ 0.4–0.45 for monodisperse spheres) critically influence stability. In complex geometries—such as irregular ore fragments in heap leaching—the effective particle diameter must be corrected using Sauter mean diameter (d₃₂) or equivalent spherical diameter derived from sieve analysis.
📐 Key Calculation
The minimum fluidization velocity (Uₘf) is most reliably estimated using the Ergun equation solved at incipient fluidization conditions—or empirically via the Wen & Yu correlation for gas-fluidized beds. The latter is preferred for mining applications involving air or SO₂-laden gases due to its validation across wide particle size ranges (50–2000 μm) and densities (1500–7800 kg/m³).
💡 Worked Example
Problem: Calculate Uₘf for crushed chalcopyrite ore (ρₛ = 4200 kg/m³, dₚ = 350 μm, sphericity ϕ = 0.68) fluidized with ambient air (ρ = 1.2 kg/m³, μ = 1.8×10⁻⁵ Pa·s) at 25°C.
1.
Step 1: Compute Archimedes number: Ar = (ρ_f (ρ_s − ρ_f) g d_p³) / μ² = (1.2 × (4200−1.2) × 9.81 × (350×10⁻⁶)³) / (1.8×10⁻⁵)² ≈ 1.12×10⁴
2.
Step 2: Apply Wen & Yu: Reₘf = (33.7)² + 0.0408 Ar − 33.7 = √(1135.69 + 0.0408×11200) − 33.7 ≈ √(1135.69 + 457.0) − 33.7 ≈ √1592.7 − 33.7 ≈ 39.9 − 33.7 = 6.2
3.
Step 3: Solve for Uₘf: Uₘf = (Reₘf × μ) / (ρ_f × d_p) = (6.2 × 1.8×10⁻⁵) / (1.2 × 350×10⁻⁶) = (1.116×10⁻⁴) / (4.2×10⁻⁴) ≈ 0.266 m/s
Answer:
The result is 0.266 m/s, which falls within the safe range of 0.2–0.4 m/s for coarse sulfide concentrates in industrial roasters.
🏗️ Real-World Application
At the Red Dog Mine (Alaska), fluidized-bed roasters process 2,500 t/d of zinc-lead concentrate. Engineers used Uₘf calculations—calibrated with pilot-scale cold-flow tests—to set primary air velocity at 0.32 m/s (15% above calculated Uₘf) to ensure stable bubbling regime while preventing attrition of 250–500 μm particles. Real-time pressure drop monitoring across the bed confirmed uniform fluidization; deviations >±8% triggered automatic air-flow adjustment—reducing off-gas SO₂ spikes by 22% and extending refractory life by 30%.
🔧 Interactive Calculator
🔧 Open Fluid Flow and Transport Phenomena Calculator📋 Case Connection
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