🎓 Lesson 10
D5
Energy Cost per Unit Output Modeling
It's the amount of energy (like electricity or fuel) needed to produce one unit of output—such as one ton of broken rock or one cubic meter of blasted material.
🎯 Learning Objectives
- ✓ Calculate energy cost per tonne of fragmented ore by integrating blast, drilling, and loading energy inputs
- ✓ Analyze trade-offs between explosive energy density and downstream haulage energy using unit-output modeling
- ✓ Design a blast pattern that minimizes total energy cost per m³ while meeting fragmentation targets (P80 < 300 mm)
- ✓ Explain how rock mass rating (RMR) and specific energy of breakage influence optimal energy allocation
📖 Why This Matters
In today’s carbon-constrained mining industry, energy isn’t just an operating cost—it’s a strategic constraint. A single large open-pit mine can consume more electricity annually than a mid-sized city. Yet 60–70% of total site energy use originates upstream of crushing—starting with blasting. Over-energized blasts waste explosives and increase fines (raising dust control and processing energy), while under-energized blasts cause boulder formation, forcing secondary breaking and doubling haulage energy. Modeling energy cost per unit output closes this loop—turning blast design into a sustainability lever.
📘 Core Principles
Energy cost per unit output rests on three foundational layers: (1) Physical energy demand—the minimum theoretical energy required to fracture rock (governed by specific energy of breakage, ~0.5–3.5 kWh/m³ depending on RMR); (2) System efficiency—the real-world conversion of input energy (e.g., diesel in drill rigs, ANFO chemical energy) into effective fragmentation, accounting for losses from vibration, air overpressure, and poor coupling; and (3) Functional normalization—selecting the correct output denominator (tonne of *in-situ* ore vs. *bank cubic meter* vs. *fragmented product*) based on process boundaries defined by ISO 14044 LCA standards. Critically, it treats blasting not as an isolated event but as the first link in an energy cascade—where every joule spent poorly upstream amplifies costs downstream.
📐 Total Site Energy Cost per Tonne
This formula aggregates all major energy inputs across the blast-to-load chain and normalizes to tonnes of blasted ore delivered to the crusher feed. It enables direct comparison across blast designs, equipment fleets, and energy sources (diesel vs. grid vs. hybrid).
Total Site Energy Cost per Tonne (Eₜ/tonne)
Eₜ/tonne = (E_drill + E_blast + E_load + E_aux) / M_oreAggregates all primary energy inputs (MJ) across blast execution and muck handling, normalized to tonnes of blasted ore moved to primary crusher.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| E_drill | Drilling energy | MJ | Diesel or electric energy consumed to drill blast holes (includes bit wear, penetration rate, and rig efficiency) |
| E_blast | Explosive energy | MJ | Chemical energy released by explosives (ANFO, emulsion, etc.), calculated as mass × energy density |
| E_load | Loading energy | MJ | Net energy consumed by shovels/loaders to excavate and load fragmented muck (accounts for motor efficiency and cycle time) |
| E_aux | Auxiliary energy | MJ | Energy for stemming, surveying, blast monitoring, ventilation (if underground), and dust suppression |
| M_ore | Mass of blasted ore | tonne | Dry metric tonnes of ore fragmented and moved to crusher feed; excludes waste and oversize requiring secondary breakage |
Typical Ranges:
Hard rock open pit (RMR < 50): 5.0 – 9.5 MJ/tonne
Soft sedimentary deposit (RMR > 70): 2.1 – 3.8 MJ/tonne
💡 Worked Example
Problem: A copper mine blasts 12,500 tonnes of porphyry ore (RMR = 52) per round. Drill fleet consumes 1,850 L diesel (35.8 MJ/L); explosives deliver 1,420 kg ANFO (3.8 MJ/kg); hydraulic shovels load 92% of muck in 14 hrs at avg. 125 kW draw (85% motor efficiency). Grid electricity is $0.11/kWh; diesel is $1.25/L. Calculate Eₜ/tonne in MJ/tonne and identify dominant contributor.
1.
Step 1: Drill energy = 1,850 L × 35.8 MJ/L = 66,230 MJ
2.
Step 2: Explosive energy = 1,420 kg × 3.8 MJ/kg = 5,396 MJ
3.
Step 3: Loading energy = 14 h × 3,600 s/h × 125 kW × (1/0.85) = 7,411,765 kJ = 7,412 MJ
4.
Step 4: Total energy = 66,230 + 5,396 + 7,412 = 79,038 MJ
5.
Step 5: Eₜ/tonne = 79,038 MJ ÷ 12,500 t = 6.32 MJ/tonne
Answer:
The result is 6.32 MJ/tonne, dominated by drilling (84% of total), which aligns with typical field data showing drilling consumes 70–90% of pre-crushing energy in hard-rock open pits.
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), engineers redesigned blast patterns in the oxide cap zone to reduce burden from 5.2 m to 4.0 m and increased hole diameter from 250 mm to 310 mm—lowering drill meters/tonne by 18%. Coupled with ANFO substitution to emulsion (higher VOD, better coupling), total site energy per tonne dropped from 7.1 to 5.4 MJ/t over 18 months. Crucially, crusher throughput increased 12% due to improved P80 (from 380 mm to 290 mm), validating that energy savings weren’t achieved at the expense of downstream efficiency—a key tenet of unit-output modeling.
🔧 Interactive Calculator
🔧 Open Production Cost Modeling Calculator📋 Case Connection
📋 Automotive Tier-1 Supplier Line Balancing Optimization
Labor cost overrun due to unbalanced station cycle times and high overtime