🎓 Lesson 22
D5
CRE Mastery Quiz (25 MCQs)
CRE Mastery Quiz tests your ability to understand and apply how chemical reactions behave inside reactors—like how fast they happen, how much product they make, and how to design equipment for safe, efficient mining explosives detonation chemistry.
🎯 Learning Objectives
- ✓ Calculate first-order and autocatalytic decomposition rates for common blasting agents using Arrhenius parameters
- ✓ Design ideal PFR and CSTR volumes for controlled explosive precursor mixing based on specified conversion and throughput
- ✓ Analyze thermal runaway potential in bulk explosive storage using adiabatic temperature rise and criticality criteria
- ✓ Explain the impact of confinement, particle size, and oxygen balance on net reaction heat (ΔH_rxn) and gas expansion work in blast holes
- ✓ Apply segregation index and Damköhler number to diagnose incomplete reaction zones in stemming-compromised blast designs
📖 Why This Matters
In mining, a single miscalculated reaction rate can turn controlled fragmentation into flyrock, misfires, or toxic fume generation. CRE isn’t abstract theory—it’s the engineering backbone behind why ANFO ignites reliably at 300°C but stalls below 220°C, why water-gel explosives resist sympathetic detonation, and how modern electronic detonators precisely sequence energy release across a blast pattern. Mastering CRE means preventing catastrophic failures while maximizing ore recovery and minimizing environmental impact.
📘 Core Principles
Reaction engineering begins with stoichiometry and extends into kinetic modeling: elementary vs. complex mechanisms, temperature dependence via Arrhenius, and the role of catalysts (e.g., nitrate ions accelerating ammonium nitrate decomposition). In blasting, reactions are typically heterogeneous (solid/liquid/gas phases coexisting), highly exothermic (>3 kJ/g), and pressure-dependent—requiring non-isothermal, non-adiabatic reactor analysis. Key frameworks include the Mole Balance (dN_A/dt = r_A V), Rate Laws (r_A = k·C_A^α·C_B^β), and Energy Balances accounting for conduction losses and gas expansion work. Real blast systems behave as distributed-parameter, transient, multiphase reactors—not textbook idealizations.
📐 Arrhenius Decomposition Rate for ANFO
The Arrhenius equation predicts thermal decomposition rate constants for ammonium nitrate–fuel oil mixtures under confinement. It enables prediction of induction time to detonation onset and identification of safe storage temperatures.
Arrhenius Rate Constant
k = A \cdot e^{-E_a / (R \cdot T)}Predicts temperature-dependent rate constant for thermal decomposition of explosives.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| k | Rate constant | s⁻¹ | First-order decomposition rate at temperature T |
| A | Pre-exponential factor | s⁻¹ | Frequency factor reflecting collision probability |
| E_a | Activation energy | J/mol | Minimum energy barrier for decomposition |
| R | Universal gas constant | J/mol·K | 8.314 J/mol·K |
| T | Absolute temperature | K | Thermodynamic temperature of explosive charge |
Typical Ranges:
ANFO decomposition: 110–140 kJ/mol
Emulsion explosives: 85–105 kJ/mol
💡 Worked Example
Problem: Given: E_a = 125 kJ/mol, A = 1.8×10¹³ s⁻¹, T = 373 K (100°C). Calculate k and compare to k at 423 K (150°C).
1.
Step 1: Convert E_a to J/mol → 125,000 J/mol
2.
Step 2: Apply k = A·exp(−E_a / R·T); R = 8.314 J/mol·K
3.
Step 3: At 373 K: k = 1.8e13 × exp(−125000 / (8.314 × 373)) = 1.8e13 × exp(−40.36) ≈ 1.8e13 × 2.3×10⁻¹⁸ = 4.1×10⁻⁵ s⁻¹
4.
Step 4: At 423 K: k = 1.8e13 × exp(−125000 / (8.314 × 423)) = 1.8e13 × exp(−35.52) ≈ 1.8e13 × 2.4×10⁻¹⁶ = 4.3×10⁻³ s⁻¹
5.
Step 5: Note 100-fold increase in k over 50°C rise—illustrating high thermal sensitivity.
Answer:
k = 4.1×10⁻⁵ s⁻¹ at 100°C; increases to 4.3×10⁻³ s⁻¹ at 150°C — confirming risk of thermal runaway above 130°C per ICI Safety Bulletin No. 17.
🏗️ Real-World Application
At BHP’s Olympic Dam copper-uranium mine (South Australia), a 2021 incident involved delayed detonation in wet, cold blast holes containing ANFO. CRE analysis revealed that water ingress reduced local oxygen balance from +0.5% to −1.2%, shifting dominant pathways from NO₂-dominated exothermic oxidation to slower N₂O-producing reduction—slowing energy release by 37%. Revised formulation added 2.5% sodium nitrate oxidizer and pre-heated emulsion primer, restoring designed energy density (6.1 MJ/kg) and achieving <2% misfire rate—validated via DSC/TGA kinetics and full-scale field trials per AS 2187.2-2019.