🎓 Lesson 10
D5
Building 3D Geometallurgical Block Models
A 3D geometallurgical block model is a digital map of a mine that shows not just where rock is located, but also its metallurgical properties—like how easily it crushes or how much metal it contains—broken down into small 3D blocks.
🎯 Learning Objectives
- ✓ Construct a 3D block model by integrating drill-hole assay, lithology, and metallurgical test data using geostatistical estimation
- ✓ Analyze spatial continuity and uncertainty of metallurgical parameters using variogram modeling and cross-validation
- ✓ Design optimal block support sizes and estimation strategies based on domain-specific anisotropy and data density
- ✓ Apply conditional simulation to quantify risk in downstream process performance (e.g., flotation recovery variability)
- ✓ Explain the impact of grade-metallurgical property correlations on mill feed planning and blending strategies
📖 Why This Matters
In modern integrated mining operations, knowing *where* the ore is no longer enough—you must know *how it will behave* in the plant. A poorly constructed geometallurgical model can lead to unexpected throughput bottlenecks, reagent overconsumption, or suboptimal recoveries—even when grade targets are met. At Newmont’s Boddington Mine, implementing a validated 3D geometallurgical model reduced grinding circuit energy use by 8% and improved gold recovery predictability by ±1.2% (vs. ±4.7% pre-model). This lesson equips you to build models that bridge geology and metallurgy—not just visually, but functionally.
📘 Core Principles
Geometallurgical modeling rests on three interlocking pillars: (1) *Metallurgical domain definition*, where lithological, structural, and alteration units are classified by their consistent processing behavior; (2) *Spatial characterization*, requiring rigorous geostatistical treatment—including non-stationary trend modeling and co-kriging of correlated variables (e.g., Cu grade vs. Bond Work Index); and (3) *Model validation*, which goes beyond cross-validation residuals to include metallurgical response testing (e.g., predicting SAG mill throughput from modeled Wi and hardness). Unlike resource models focused on grade, geometallurgical models prioritize *functional attributes*: variables must be measurable, process-relevant, and scalable from lab test to full-scale operation. Critical attention must be paid to support effects—lab tests on 2 kg samples cannot reliably represent bulk behavior without upscaling protocols grounded in fragmentation and liberation physics.
📐 Block Model Support Correction for Bond Work Index
Lab-scale Bond Work Index (Wi) values require support correction to represent full-blasthole or bench-scale material. The correction accounts for scale-dependent fracture density and grain boundary exposure. The standard empirical upscaling uses the 'size–scale factor' derived from field calibration datasets.
Wi Upscaling Correction
Wi_field = Wi_lab × (P80_lab / P80_field)^γCorrects laboratory-scale Bond Work Index to represent full-scale blast fragmentation conditions.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| Wi_field | Field-scale Bond Work Index | kWh/tonne | Estimated work index representing bench-scale material behavior |
| Wi_lab | Laboratory-scale Bond Work Index | kWh/tonne | Measured Wi on prepared sub-sample (typically 2–5 kg) |
| P80_lab | Laboratory P80 size | mm | 80% passing size of lab test feed |
| P80_field | Field P80 size | mm | 80% passing size of actual fragmented muck pile (from image analysis or sieving) |
| γ | Scaling exponent | dimensionless | Empirically calibrated exponent (0.18–0.25); 0.22 recommended for hard rock systems per AMIRA P970B |
Typical Ranges:
Hard rock copper-gold porphyry: 7.0 – 12.5 kWh/t
Banded iron formation (BIF): 10.0 – 18.0 kWh/t
💡 Worked Example
Problem: Given: Lab Wi = 14.2 kWh/t (measured on 2 kg composite, 100% <6.35 mm); blasthole diameter = 250 mm; bench height = 15 m; average fragment size (P80) post-blast = 420 mm.
1.
Step 1: Compute representative fragment size ratio: R = P80_lab / P80_field = 6.35 mm / 420 mm = 0.0151
2.
Step 2: Apply scaling exponent (γ = 0.22, per AMIRA P970B calibration): Wi_field = Wi_lab × R^γ = 14.2 × (0.0151)^0.22
3.
Step 3: Calculate: (0.0151)^0.22 ≈ 0.621 → Wi_field = 14.2 × 0.621 = 8.82 kWh/t
Answer:
The upscaled Wi is 8.8 kWh/t, which falls within the typical range of 7–12 kWh/t for weathered porphyry ores at bench scale.
🏗️ Real-World Application
At Rio Tinto’s Pilbara Iron Ore operations, a 3D geometallurgical model was built integrating 2,400+ drill holes with 12,000+ laboratory metallurgical tests (crushing, grinding, magnetic separation response). Litho-geometallurgical domains were defined using hierarchical cluster analysis of combined geochemical (SiO₂, Al₂O₃, P) and mechanical (UCS, Wi) data. The resulting 10×10×5 m block model drove dynamic ROM pad blending—reducing magnetite concentrate silica variability from ±1.8% to ±0.4%, enabling consistent sinter feed specification without offline quality control delays. Model validation used blind 3-month mill feed predictions, achieving R² = 0.89 for grind size (P80) and 0.76 for Fe recovery.