1. Why Gaussian plume for H₂S
Hydrogen sulfide is one of the few oilfield toxics whose ERPG-2 (30 ppm, 1-hour) sits in the same range as plausible accidental releases from sour separators, flare KO drums, and gas lift lines. Operators need a defensible way to set buffer distances from quarters and roads — the Pasquill-Gifford Gaussian plume gives a closed-form, peer-reviewed estimate that satisfies EPA RMP §68 worst-case analysis and is faster than running a CFD model for every scenario.
The Gaussian plume is steady-state, neutrally buoyant, and assumes flat terrain. Those assumptions are deliberately conservative for H₂S because the gas (MW 34) is only slightly heavier than air (MW 29) — heavy-gas effects (DEGADIS, SLAB) typically matter only for refrigerated leaks (cryogenic propane, LNG) where the cold vapor is much denser than ambient.
2. The Gaussian centerline equation
For a continuous point source of mass release rate Q at height H, the centerline ground-level concentration at downwind distance x is:
where u is the wind speed at release height and σ_y, σ_z are the cross-wind and vertical Gaussian dispersion coefficients (both functions of x and stability class). For a ground-level release (H = 0) the exponential term equals 1 and C decays as roughly 1/x for the Briggs power-law σ's.
Converting to volumetric ppm via ideal gas at receiver T, P:
3. Briggs σ coefficients
Briggs (1973) gave compact power-law fits to the Pasquill-Gifford σ_y, σ_z charts. The forms used here:
| Class | Rural σy (m) | Rural σz (m) |
|---|---|---|
| A (very unstable) | 0.22·x·(1+10⁻⁴·x)−0.5 | 0.20·x |
| B | 0.16·x·(1+10⁻⁴·x)−0.5 | 0.12·x |
| C | 0.11·x·(1+10⁻⁴·x)−0.5 | 0.08·x·(1+2·10⁻⁴·x)−0.5 |
| D (neutral) | 0.08·x·(1+10⁻⁴·x)−0.5 | 0.06·x·(1+1.5·10⁻³·x)−0.5 |
| E | 0.06·x·(1+10⁻⁴·x)−0.5 | 0.03·x·(1+3·10⁻⁴·x)−1 |
| F (stable) | 0.04·x·(1+10⁻⁴·x)−0.5 | 0.016·x·(1+3·10⁻⁴·x)−1 |
Use urban coefficients when the receiver is within an industrial complex or town; the mechanical turbulence from buildings increases σ for the same x. Class D (neutral) with u = 3–5 m/s is the default screening case in API RP 55 and most operator HSE manuals.
4. ERPG / IDLH thresholds for H₂S
| Threshold | Concentration | Meaning |
|---|---|---|
| ERPG-1 | 0.1 ppm | Detection / mild odor; no impairment. |
| ERPG-2 | 30 ppm | Boundary at which escape may be impaired after 1-hr exposure. EPA RMP toxic endpoint. |
| ERPG-3 / IDLH | 100 ppm | Life-threatening after 1-hr exposure (NIOSH IDLH). |
| OSHA PEL (ceiling) | 20 ppm (ceiling; 50 ppm 10-min peak) | Occupational ceiling — not for dispersion endpoint. |
Note: olfactory fatigue sets in above ~100 ppm — workers cannot smell the gas, which is one of the reasons fixed H₂S detectors are mandatory wherever a release scenario can reach IDLH within the response time.
5. Model limits
- Near field (x < 100 m). Briggs σ are calibrated to ≥100 m. Inside that zone use CFD or jet-source models (e.g., AFTOX).
- Calm wind (u < 1 m/s). The continuous-plume assumption breaks down — use a puff model (INPUFF) or DEGADIS for stagnant conditions.
- Heavy gas. H₂S vapor density is close to air, so the neutrally-buoyant Gaussian is acceptable. For two-phase / cryogenic releases (refrigerated LPG, NH₃, Cl₂) use DEGADIS or SLAB instead.
- Terrain & obstacles. Gaussian assumes flat featureless terrain. In river valleys or near tall structures the plume can be channelled or deflected — verify with on-site met data.
- Buoyancy. A hot release from a flare or vent has an effective stack height greater than the physical height (Briggs plume rise). The calculator uses H_physical only — apply your own plume-rise correction if needed.
6. References
- Pasquill, F. (1961). "The estimation of the dispersion of windborne material." Meteorological Magazine 90, 33–49.
- Briggs, G.A. (1973). Diffusion Estimation for Small Emissions. ATDL Contribution No. 79, NOAA.
- AIHA ERPG/WEEL Committee, 2026 Handbook — Hydrogen Sulfide.
- NIOSH (1994). Documentation for IDLHs — Hydrogen Sulfide. NIOSH/CDC.
- EPA 40 CFR §68 (RMP) Appendix A — toxic endpoints.
- API RP 55 — Oilfield H₂S Safe Operations.
Ready to map a plume?
→ Launch Calculator