🎓 Lesson 11
D5
Integrating QEMSCAN and Leach Kinetics Data
QEMSCAN tells us exactly what minerals are in a rock sample, and leach kinetics tells us how fast valuable metals dissolve — combining them helps predict how well a mine’s ore will process before digging begins.
🎯 Learning Objectives
- ✓ Analyze QEMSCAN-derived mineral association maps to identify gangue phases controlling acid consumption
- ✓ Calculate effective leach rate constants (k_eff) from time-series leach data using first-order kinetic models
- ✓ Design domain-specific blending strategies by correlating QEMSCAN modal mineralogy (%) with observed 24-hr Cu recovery (%)
- ✓ Explain how textural parameters (e.g., sulfide locking, grain size distribution) derived from QEMSCAN influence leach kinetics deviation from ideal behavior
- ✓ Apply geostatistical co-kriging to integrate QEMSCAN mineral vectors and leach test results into a 3D geometallurgical model
📖 Why This Matters
In modern copper and gold operations, up to 40% of capital overruns stem from unexpected metallurgical variability — often missed by conventional assays. QEMSCAN reveals *why* an ore leaches slowly (e.g., chalcocite locked in silicate matrix), while leach kinetics quantifies *how much slower*. Integrating them turns geological uncertainty into actionable process intelligence — enabling targeted blasting, selective mining, and adaptive circuit control *before* ore reaches the plant.
📘 Core Principles
QEMSCAN provides quantitative, pixel-based mineral identification (±1–2 µm resolution) across polished sections, delivering modal abundance, texture (e.g., inclusion, intergrowth), and elemental deportment. Leach kinetics — typically measured via bottle roll or column tests — yields recovery vs. time curves modeled as pseudo-first-order (R(t) = R_max × (1 − e^(−k_eff·t))) or diffusion-controlled functions. Integration occurs at three levels: (1) statistical correlation (e.g., % pyrite vs. k_eff), (2) mechanistic mapping (e.g., acid-consuming dolomite grains adjacent to chalcopyrite), and (3) spatial co-simulation (e.g., conditional simulation of mineral vectors constrained by leach response). Critical is recognizing that QEMSCAN alone cannot predict kinetics — texture and surface exposure govern reaction accessibility.
📐 Pseudo-First-Order Leach Kinetics Model
This model estimates the effective rate constant governing metal dissolution when chemical reaction dominates mass transfer; it’s widely used for heap and agitated leach optimization where ore heterogeneity is captured via QEMSCAN-derived mineral vectors.
Pseudo-First-Order Recovery Model
R(t) = R_{max} \times \left(1 - e^{-k_{eff} \cdot t}\right)Models cumulative metal recovery as a function of time assuming rate-limiting surface chemical reaction.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| R(t) | Metal recovery at time t | % | Fractional recovery (0–100%) of target metal at elapsed time t |
| R_{max} | Maximum theoretical recovery | % | Asymptotic recovery limit determined by mineral deportment and assay |
| k_{eff} | Effective first-order rate constant | h⁻¹ | Empirical rate constant combining intrinsic reactivity, surface area, and mass transfer effects |
| t | Leach time | h | Elapsed time from start of leach test |
Typical Ranges:
Well-liberated chalcopyrite (agitated leach): 0.025 – 0.045 h⁻¹
Locked chalcopyrite in silicates (heap leach): 0.003 – 0.012 h⁻¹
Oxide gold (cyanide leach): 0.05 – 0.15 h⁻¹
💡 Worked Example
Problem: A QEMSCAN-characterized porphyry copper sample contains 8.2 vol% chalcopyrite with 65% liberation >75 µm. Bottle roll tests show 52.3% Cu recovery after 24 h and 89.1% at endpoint (R_max = 92.4%). Calculate k_eff and interpret against typical range for well-liberated chalcopyrite.
1.
Step 1: Use R(t) = R_max × (1 − e^(−k_eff·t)) → rearrange to solve for k_eff: k_eff = −ln(1 − R(t)/R_max) / t
2.
Step 2: Plug in values: R(t) = 52.3, R_max = 92.4, t = 24 h → k_eff = −ln(1 − 52.3/92.4) / 24 = −ln(0.434) / 24 = 0.835 / 24
3.
Step 3: Compute: k_eff = 0.0348 h⁻¹. Compare to typical range for liberated chalcopyrite (0.025–0.045 h⁻¹). Value falls within expected band, confirming QEMSCAN-predicted liberation aligns with kinetic response.
Answer:
The result is 0.0348 h⁻¹, which falls within the safe range of 0.025–0.045 h⁻¹ for well-liberated chalcopyrite ores.
🏗️ Real-World Application
At the Oyu Tolgoi South Pit (Mongolia), QEMSCAN analysis revealed a 12-m-thick transition zone where chalcopyrite grains were increasingly enclosed in biotite laths (‘locked’ texture). Leach column tests showed 24-hr Cu recovery dropping from 78% to 41% across this zone. By integrating QEMSCAN texture metrics (locking index >0.65) with k_eff <0.022 h⁻¹, the geometallurgical model directed selective mining — routing high-locking zones to finer crushing and longer residence time circuits — improving overall site Cu recovery by 5.3% and reducing acid consumption by 18% annually (Rio Tinto, 2022 Geometallurgy Report).