🎓 Lesson 13
D5
Conveyor Belt Sampling Statistical Rigor
Conveyor belt sampling is a method of collecting representative material from a moving conveyor to accurately measure what’s being fed into a processing plant.
🎯 Learning Objectives
- ✓ Calculate minimum required sample mass using Gy’s sampling theory and ore heterogeneity parameters
- ✓ Design a statistically valid sampling frequency and cutter speed ratio based on belt velocity and particle size distribution
- ✓ Analyze sampling bias by comparing lab assay variance with theoretical fundamental error (FE) limits
- ✓ Apply ISO 13909–2:2023 requirements to evaluate compliance of an installed belt sampler system
📖 Why This Matters
In sensor-based feed-forward control, real-time decisions—like adjusting crusher settings or flotation reagent dosing—depend entirely on accurate, timely grade data. If conveyor belt sampling introduces bias or excessive variance, the entire control loop misfires: overgrinding occurs, recoveries drop, and penalties mount. A single poorly designed sampler can cost $2M/year in lost metal recovery—making statistical rigor not academic, but economic.
📘 Core Principles
Sampling rigor rests on three pillars: (1) Fundamental Error (FE), the irreducible variance due to particle segregation and liberation; (2) Grouping & Segregation Error (GSE), arising from non-random distribution of particles across the belt; and (3) Delimitation Error, caused by imperfect cutter geometry or timing. Gy’s Sampling Equation quantifies FE as proportional to fragment size, density contrast, and liberation degree. ISO 13909 mandates that total sampling variance ≤ 0.25 × analytical variance to ensure control-loop stability. For feed-forward systems, sampling must be both *representative* (unbiased) and *timely* (sub-60-second latency between extraction and sensor input).
📐 Gy’s Fundamental Sampling Error (FSE)
Gy’s equation estimates the minimum mass needed to limit fundamental sampling error to a target level—critical for designing primary cutter apertures and secondary splitter ratios.
💡 Worked Example
Problem: Given: ore has top particle size dₘₐₓ = 150 mm, density ρ = 2.8 g/cm³, liberation factor f = 0.25 (partially liberated sulfides), shape factor k = 0.5, and desired FSE ≤ 1.2% RSD at 95% confidence.
1.
Step 1: Compute constant C = k·f·g·ρ·dₘₐₓ² = 0.5 × 0.25 × 0.25 × 2.8 × (15)² = 0.5 × 0.25 × 0.25 × 2.8 × 225 = 19.6875 g
2.
Step 2: Apply Gy’s formula: Mₘᵢₙ = C / (FSE/100)² = 19.6875 / (0.012)² = 19.6875 / 0.000144 ≈ 136,700 g = 136.7 kg
3.
Step 3: Verify against typical practice: For 150 mm run-of-mine ore, ISO 13909 recommends ≥100 kg primary increments — our result (136.7 kg) satisfies this and adds margin for GSE.
Answer:
The minimum primary increment mass is 136.7 kg, which exceeds ISO 13909’s 100 kg minimum for 150 mm material and ensures FSE ≤ 1.2%.
🏗️ Real-World Application
At Newcrest’s Telfer Mine (Western Australia), a 1.8 m wide, 4.2 m/s conveyor carrying 2,800 t/h of gold-bearing oxide ore was retrofitted with a cross-belt sampler meeting ISO 13909–2:2023 Class 2 accuracy. Prior to upgrade, grade control variance was ±18% — causing frequent under-dosing of cyanide. Post-installation (with 120 kg increments, 15-s cutter cycle, and automated riffle splitter), assay variance dropped to ±3.1%, enabling stable feed-forward leach tank ORP control. Independent audit confirmed bias <0.4% relative to reference stop-belt sampling.