🎓 Lesson 9
D5
Calculating Space Cost Using Thermal Load Weighting
Space cost using thermal load weighting is a way to fairly divide overhead costs (like electricity and cooling) among different mining equipment based on how much heat each machine generates during operation.
🎯 Learning Objectives
- ✓ Calculate thermal load weight for a given piece of mining equipment using nameplate power, duty cycle, and efficiency data
- ✓ Apply thermal load weighting to allocate overhead costs across multiple equipment types in a blast-hole drilling fleet
- ✓ Analyze and compare space cost allocations using thermal load weighting versus traditional machine-hour rate methods
- ✓ Explain why thermal load weighting improves cost recovery for ventilation and cooling infrastructure in high-heat mining environments
📖 Why This Matters
In modern mining—especially in deep, hot, or confined underground operations—the cost of removing waste heat often exceeds the cost of the electricity powering the equipment itself. Traditional overhead allocation methods (e.g., allocating cooling costs equally per machine hour) misattribute these costs: a 1,200 kW diesel-hydraulic drill rig running at 75% load generates vastly more heat than a 45 kW control panel operating continuously. Thermal load weighting fixes this mismatch—ensuring that capital and operational expenditures for ventilation fans, refrigeration plants, and heat exchangers are fairly recovered from the equipment actually driving thermal demand. Getting this right impacts equipment lifecycle costing, fleet optimization decisions, and regulatory compliance with occupational heat stress standards.
📘 Core Principles
Thermal load weighting rests on three foundational principles: (1) Waste heat generation is proportional to electrical/mechanical energy input minus useful work output; (2) In mining machinery, >85% of input energy typically converts to heat (via friction, inefficiency, and exhaust), not mechanical work; (3) Facility-level thermal management systems (e.g., mine-wide refrigeration) have finite capacity—and cost—directly tied to total heat rejection requirements. The method therefore treats thermal load—not just runtime—as the causal driver of overhead cost. It integrates engineering thermodynamics (first law), equipment performance data (nameplate ratings, duty cycles, efficiency curves), and facility infrastructure constraints. Crucially, it distinguishes between *instantaneous* heat generation (kW) and *integrated* thermal burden (kWh/day), requiring time-weighted averaging for realistic allocation.
📐 Key Calculation
The thermal load weight (TLW) for a piece of equipment is calculated as the ratio of its normalized thermal energy contribution to the sum of all equipment contributions. Normalization accounts for both power draw and operational time, adjusted for conversion efficiency and ambient heat gain factors. This weight is then applied to allocate space-related overhead (e.g., refrigeration cost per kWh of cooling) proportionally.
Thermal Load Weight (TLW)
TLW_i = (P_i × DC_i × (1 − η_i) × AF_i) / Σ(P_j × DC_j × (1 − η_j) × AF_j)Computes the proportional share of thermal management overhead assigned to equipment i based on its relative waste heat contribution.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| P_i | Rated electrical or mechanical power input | kW | Nameplate or validated maximum continuous power rating of equipment i |
| DC_i | Average duty cycle | decimal (0–1) | Fraction of time equipment operates at rated load over representative period (e.g., monthly SCADA average) |
| η_i | Overall energy conversion efficiency | decimal (0–1) | Measured or manufacturer-specified efficiency converting input energy to useful work (includes motor, gearbox, hydraulic, and drive losses) |
| AF_i | Auxiliary heat gain factor | dimensionless | Empirically derived multiplier capturing additional heat from exhaust, coolant, hydraulics, or battery systems beyond motor losses |
Typical Ranges:
Diesel LHD in hot climate: 1.20 – 1.35
Electric conveyor drive: 1.02 – 1.08
Ventilation fan motor: 1.00 – 1.03
💡 Worked Example
Problem: A copper mine’s underground workshop houses three assets: (1) A Sandvik DD422 drill rig (rated 1,100 kW, average duty cycle 65%, motor efficiency 92%, auxiliary heat gain factor 1.15); (2) A FLSmidth 300 kW crusher drive (duty cycle 85%, efficiency 94%, aux factor 1.05); (3) A Siemens 75 kW control cabinet (duty cycle 100%, efficiency 96%, aux factor 1.02). Calculate TLW for each asset to allocate $285,000/year refrigeration cost.
1.
Step 1: Compute thermal load per asset = Rated Power × Duty Cycle × (1 − Efficiency) × Auxiliary Factor
2.
Step 2: Drill rig: 1100 × 0.65 × (1−0.92) × 1.15 = 65.78 kW thermal; Crusher: 300 × 0.85 × (1−0.94) × 1.05 = 16.07 kW; Cabinet: 75 × 1.00 × (1−0.96) × 1.02 = 3.06 kW
3.
Step 3: Sum total thermal load = 65.78 + 16.07 + 3.06 = 84.91 kW → TLW_drill = 65.78/84.91 = 0.775; TLW_crusher = 0.189; TLW_cabinet = 0.036
4.
Step 4: Allocate refrigeration cost: Drill = 0.775 × $285,000 = $220,875; Crusher = $53,865; Cabinet = $10,260
Answer:
The drill rig bears 77.5% of refrigeration overhead—consistent with industry observation that mobile equipment dominates thermal load. This allocation is 3.2× higher than a naive machine-hour method would assign (which would likely weight drill rig at ~45% due to lower uptime).
🏗️ Real-World Application
At Newmont’s Boddington Gold Mine (Western Australia), thermal load weighting was implemented in 2021 to reallocate $4.2M/year in chilled water infrastructure costs across 14 underground production zones. Prior machine-hour allocation caused under-recovery from high-power LHDs and over-recovery from low-load monitoring systems—distorting maintenance budgeting and delaying critical cooling upgrades. After switching to thermal load weighting (using OEM power curves, SCADA duty logs, and measured motor temperatures), zone-level cost allocations shifted by up to 28%. This revealed two zones with 3× higher thermal load/kW installed than design assumptions—prompting targeted installation of localized heat exchangers and reducing overall refrigeration plant runtime by 11%. The change also improved alignment with ISO 8573-1 air quality compliance reporting for heat-stress risk assessments.
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