🎓 Lesson 6
D4
Gas Dispersion Modeling: Gaussian vs. CFD Approaches
Gas dispersion modeling predicts how toxic or flammable gases spread in air after a release, helping engineers design safer mines and plants.
🎯 Learning Objectives
- ✓ Explain the physical assumptions and limitations of Gaussian versus CFD dispersion models
- ✓ Apply Pasquill-Gifford stability classes to estimate atmospheric dispersion coefficients for mining ventilation scenarios
- ✓ Analyze CFD simulation outputs to identify high-concentration zones near blast initiation points or ventilation intakes
- ✓ Calculate downwind concentration using the Gaussian plume equation for a point source under neutral atmospheric conditions
- ✓ Design a tiered consequence modeling strategy—selecting Gaussian for initial risk screening and CFD for detailed hazard zone mapping around critical infrastructure
📖 Why This Matters
In underground and open-pit mines, gas releases—from blasting fumes (NO₂, CO), diesel emissions, or natural gas seepage—can rapidly reach hazardous concentrations. A 2019 incident at a South African platinum mine resulted in 7 fatalities due to undetected CO accumulation in a dead-end drift; post-incident analysis showed Gaussian modeling overpredicted dilution by 40% because it ignored recirculation. Choosing the right dispersion model isn’t academic—it’s lifesaving. This lesson equips you to select, apply, and critically evaluate tools that directly inform ventilation design, emergency response planning, and ALARP (As Low As Reasonably Practicable) risk decisions.
📘 Core Principles
Gaussian models treat the plume as a symmetrical, bell-shaped distribution governed by empirical turbulence parameters—ideal for flat terrain, steady wind, and distances >100 m from the source. They assume constant wind speed, no chemical reaction, and no terrain interaction. CFD, in contrast, numerically solves conservation equations for mass, momentum, and species transport on a 3D mesh, capturing vortex shedding behind haul trucks, channeling through adits, and density-driven flows (e.g., heavier-than-air H₂S pooling in sumps). For mining, CFD becomes essential when modeling: (1) confined or semi-confined spaces (shafts, stopes), (2) complex topography (pit walls, spoil heaps), and (3) buoyant or dense-gas releases—where Gaussian assumptions break down completely.
📐 Gaussian Plume Concentration
The standard Gaussian plume equation estimates ground-level concentration at distance x downwind and y,z crosswind/vertical offsets. It’s used for rapid screening of worst-case releases (e.g., diesel exhaust during equipment maintenance in a blind heading). Accuracy degrades within the 'near-field' (<50 m) and under unstable or very stable atmospheric conditions.
💡 Worked Example
Problem: A blast ventilation fan releases 0.8 kg/s of NO₂ at height H = 2.5 m above floor level in a tunnel. Wind speed u = 3.2 m/s, atmospheric stability class is D (neutral), and receptor is at x = 150 m, y = 0 m, z = 0 m (ground centerline). Calculate C(x,0,0) using σy = 12.5 m and σz = 8.1 m.
1.
Step 1: Identify knowns — Q = 0.8 kg/s, u = 3.2 m/s, H = 2.5 m, x = 150 m, y = 0, z = 0, σy = 12.5 m, σz = 8.1 m
2.
Step 2: Apply Gaussian equation: C = (Q / (2π·u·σy·σz)) × exp[−0.5·(y/σy)²] × {exp[−0.5·((z−H)/σz)²] + exp[−0.5·((z+H)/σz)²]} → Since y=0 and z=0, exp terms reduce to exp[−0.5·(−H/σz)²] + exp[−0.5·(H/σz)²] = 2·exp[−0.5·(H/σz)²]
3.
Step 3: Compute exponent: (2.5 / 8.1)² = 0.0956 → −0.5 × 0.0956 = −0.0478 → exp(−0.0478) = 0.953 → factor = 2 × 0.953 = 1.906. Denominator = 2π × 3.2 × 12.5 × 8.1 = 2035.7. So C = (0.8 / 2035.7) × 1.906 = 0.000749 kg/m³ = 749 mg/m³.
Answer:
C = 749 mg/m³ — exceeds OEL (Occupational Exposure Limit) for NO₂ (950 µg/m³ 8-hr TWA), indicating immediate hazard requiring engineering controls. This falls within typical range for unmitigated releases at 150 m in neutral conditions (100–2000 mg/m³).
🏗️ Real-World Application
At Newmont’s Boddington Gold Mine (Western Australia), CFD modeling (using ANSYS Fluent) was deployed to assess H₂S dispersion from a sulfide ore stockpile adjacent to the crusher plant. Gaussian screening predicted safe concentrations (>1 ppm threshold) beyond 300 m—but CFD revealed persistent eddies trapping H₂S at <5 ppm within 80 m of the east-facing wall due to diurnal katabatic winds. This insight drove relocation of the air intake duct and installation of real-time H₂S sensors—reducing exceedance events by 92% in 12 months. The project followed AIChE’s CCPS Guidelines and was validated against tracer gas (SF₆) field tests per AS/NZS 62276:2021.
📋 Case Connection
📋 Ammonia Refrigeration System HAZOP & LOPA Integration at Midwest Food Processing Plant
Unplanned releases during maintenance due to undocumented isolation points and missing P&IDs
📋 Grain Elevator Dust Explosion Mitigation Using ASTM E1226-Based Risk Model
Historic dust explosions (3 incidents since 1995); inadequate housekeeping and venting