🎓 Lesson 9
D5
Modeling Dispersion and Segregation in Real Reactors
Real reactors don’t mix perfectly—this topic explains how chemicals spread out and separate as they flow through industrial equipment like blast holes or leach pads, affecting efficiency and safety.
🎯 Learning Objectives
- ✓ Calculate axial dispersion coefficient (Dₐ) from RTD data using pulse input experiments
- ✓ Analyze segregation potential in fragmented muck piles using particle size–density–velocity relationships
- ✓ Explain how non-ideal flow patterns (e.g., channeling, dead zones) alter effective residence time distribution in blast-induced heap leach reactors
- ✓ Apply segregation indices (e.g., Coefficient of Variation for fragment size) to assess blast fragmentation quality
- ✓ Design sampling protocols for post-blast muck piles that account for spatial segregation bias
📖 Why This Matters
In mining, a blast doesn’t just break rock—it creates a heterogeneous pile where fine, reactive material may segregate at the toe while coarse, low-grade fragments roll uphill. If your heap leach pad receives segregated feed, acid percolation becomes uneven, recovery drops by 5–15%, and cyanide consumption spikes. Understanding dispersion and segregation helps you predict *where* gold dissolves—and where it hides.
📘 Core Principles
Dispersion arises from two mechanisms: molecular diffusion (dominant at low Re) and turbulent eddy mixing (dominant in high-Re flows like slurry transport or airblast). It’s quantified by the axial dispersion coefficient Dₐ, which links to the Péclet number (Pe = uL/Dₐ). Segregation, meanwhile, follows Stokes’ law and terminal velocity sorting: particles with similar size but different density (e.g., sulfides vs. gangue) separate during free fall or conveyor transfer; those with similar density but different size (e.g., 10 mm vs. 100 mm fragments) separate during vibration or slope movement. In blast engineering, both phenomena begin *during detonation* (fragment ejection trajectories) and continue *post-blast* (muck pile formation, shovel loading, haulage, and stacking).
📐 Axial Dispersion Coefficient from RTD
The axial dispersion coefficient Dₐ is derived from the variance σ²_θ of the residence time distribution (RTD) curve obtained via tracer testing in a reactor (e.g., leach column or simulated blast crater flow path). For a long cylindrical reactor under laminar or transitional flow, Dₐ relates to σ²_θ and mean residence time θ̄ via the dispersion model solution.
💡 Worked Example
Problem: A tracer test on a 3.2-m-tall pilot-scale leach column (diameter = 0.3 m) yields θ̄ = 42 min and σ²_θ = 289 min². Superficial velocity u = 1.8 × 10⁻⁴ m/s. Estimate Dₐ and Pe.
1.
Step 1: Convert θ̄ and σ²_θ to seconds: θ̄ = 42 × 60 = 2520 s; σ²_θ = 289 × 3600 = 1,040,400 s²
2.
Step 2: Use the analytical relation for a dispersion model: σ²_θ / θ̄² = 2/Pe − 2/Pe² ≈ 2/Pe (for Pe > 10), so Pe ≈ 2 × θ̄² / σ²_θ = 2 × (2520)² / 1,040,400 ≈ 12.2
3.
Step 3: Compute Dₐ = uL / Pe = (1.8 × 10⁻⁴ m/s)(3.2 m) / 12.2 ≈ 4.72 × 10⁻⁵ m²/s
Answer:
Dₐ = 4.7 × 10⁻⁵ m²/s, Pe = 12.2 — indicating transitional flow with moderate dispersion (typical for fractured ore columns).
🏗️ Real-World Application
At Newmont’s Boddington Mine (WA), post-blast muck pile segregation led to 18% lower gold recovery in the upper third of the heap. Core sampling revealed fines (<10 mm) concentrated at the toe (62% of total fines) while +50 mm fragments dominated the crest. Engineers used DEM (Discrete Element Modeling) calibrated with high-speed blast video and fragment tracking to redesign initiation sequence and burden spacing—reducing size segregation index (CV_size) from 0.91 to 0.43 and improving overall recovery by 9.2%.