Atmospheric Dispersion Modeling for Midstream Facilities

1. Overview & Applications

Atmospheric dispersion modeling predicts how airborne pollutants travel and dilute after being released from a source. For midstream oil and gas facilities, dispersion analysis is essential for stack height design, permit applications, emergency response planning, and demonstrating compliance with ambient air quality standards.

Common Midstream Applications

Why Dispersion Modeling Matters

Dispersion modeling serves several critical purposes in midstream engineering:

• Stack height determination: Ensures pollutant concentrations at ground level do not exceed ambient standards
• Facility siting: Establishes safe distances between emission sources and receptors (residences, workplaces, public areas)
• Permit compliance: Demonstrates that facility emissions will not cause or contribute to NAAQS violations
• Emergency planning: Predicts toxic gas concentrations during accidental releases (H2S, SO2) for evacuation zone planning
• Equipment design: Sizes stacks, selects flare heights, and determines the need for emission controls

2. The Gaussian Plume Model

The Gaussian plume model is the most widely used method for estimating pollutant concentrations from point sources. Developed from work by Sutton (1932), Pasquill (1961), and Gifford (1961), it assumes that the concentration distribution in both the crosswind (y) and vertical (z) directions follows a Gaussian (bell-curve) distribution.

The General Equation

The steady-state Gaussian plume equation for a continuous point source with ground reflection is:

Key Assumptions

• Steady-state conditions: Emission rate, wind speed, and atmospheric stability are constant over the period of interest
• Uniform wind: Wind direction and speed do not vary with height within the plume layer
• Conservation of mass: No chemical transformation, deposition, or decay of pollutant during transport
• Flat terrain: Ground is assumed flat with complete reflection (no absorption)
• Gaussian distribution: Concentration profiles follow normal distributions in y and z directions
• Continuous emission: Source emits continuously from a single point at constant rate

Understanding the Terms

Maximum Ground-Level Concentration

The maximum ground-level concentration (GLC) occurs at the downwind distance where the vertical dispersion coefficient σz equals the effective stack height divided by the square root of 2:

This relationship shows that the maximum ground-level concentration is inversely proportional to the square of the effective stack height. Doubling the effective height reduces the maximum GLC by approximately 75%, making stack height one of the most effective controls for reducing ground-level impacts.

3. Atmospheric Stability (Pasquill-Gifford)

Atmospheric stability determines how rapidly a plume spreads as it travels downwind. The Pasquill-Gifford classification system divides atmospheric conditions into six stability classes, from very unstable (A) to very stable (F), based on wind speed, solar radiation, and cloud cover.

Stability Class Definitions

Determining Stability Class

The Pasquill-Gifford stability class is determined by surface wind speed and the degree of insolation (daytime) or cloud cover (nighttime):

Dispersion Coefficients

The dispersion coefficients σy and σz are empirical functions of downwind distance and stability class, derived from tracer experiments. They represent the standard deviation of the concentration distribution in the lateral and vertical directions.

Typical Dispersion Coefficient Values

Values are approximate; actual coefficients vary by parameterization (Turner, ISC3, Briggs).

Effect of Stability on Plume Behavior

• Unstable (A, B): Strong vertical mixing creates a wide, short plume. Maximum concentrations occur close to the source and can be very high but dissipate rapidly. These conditions occur during sunny afternoons with light winds.
• Neutral (D): Moderate dispersion in all directions. This is the default assumption for overcast conditions and is often used as a reasonable average for long-term assessments.
• Stable (E, F): Suppressed vertical mixing creates a narrow, elevated plume that travels long distances before reaching the ground. Maximum concentrations are lower but occur at greater distances. These conditions occur during clear nights with light winds. Stable conditions are typically the worst case for elevated sources because the plume remains concentrated over longer distances.

4. Plume Rise (Briggs Equations)

Plume rise is the additional elevation gained by the exhaust gas after leaving the stack tip, caused by the gas being hotter and/or faster-moving than the surrounding atmosphere. The effective stack height equals the physical stack height plus the plume rise, and it is the effective height that determines ground-level concentrations.

Components of Plume Rise

Two mechanisms contribute to plume rise:

• Buoyancy rise: Hot exhaust gas is less dense than ambient air and rises due to thermal buoyancy. This is typically the dominant mechanism for industrial sources with high exhaust temperatures.
• Momentum rise: The vertical velocity of the gas exiting the stack carries the plume upward. This is significant for sources with high exit velocities but small temperature differences.

Briggs Buoyancy Flux

Briggs Final Plume Rise Equations

The final plume rise depends on both the flux parameters and the atmospheric stability:

Typical Plume Rise Values

5. Stack Height Determination & GEP

Stack height is one of the most critical design parameters for controlling ground-level pollutant concentrations. The taller the stack, the greater the dilution before the plume reaches ground level. However, regulatory constraints prevent using excessively tall stacks as a substitute for emission controls.

Good Engineering Practice (GEP) Stack Height

EPA regulations at 40 CFR 51.100 define Good Engineering Practice stack height as the maximum creditable stack height for dispersion modeling purposes. Emissions credit cannot be taken for stack heights exceeding the GEP value.

Stack Height Selection Guidelines

6. Building Downwash Effects

When a stack is located near a building, the aerodynamic wake created by the building can pull the plume down to ground level, dramatically increasing concentrations near the source. This phenomenon, called building downwash, is one of the most important considerations in stack design for midstream facilities where stacks are often located on or near compressor buildings, process buildings, or equipment skids.

Downwash Mechanisms

• Cavity region: The immediate lee of the building creates a recirculation zone where concentrations can be very high. The cavity extends approximately 1.5L downwind of the building.
• Wake region: Beyond the cavity, enhanced turbulence from the building wake increases dispersion rates for 5–10 building heights downwind.
• Stack tip downwash: When exit velocity is less than 1.5 times the wind speed, the plume bends down behind the stack tip, reducing the effective emission height.

Stack Tip Downwash Correction

Huber-Snyder Building Downwash

When a stack is shorter than the GEP height, the Huber-Snyder method reduces the effective stack height to account for building wake effects. The reduction depends on the building dimensions relative to the stack height.

7. Terrain & Urban Effects

Terrain Classification

The terrain surrounding a facility significantly affects dispersion patterns. EPA categorizes terrain into three types for modeling purposes:

Urban vs. Rural Dispersion

The urban heat island effect and increased surface roughness in urban areas enhance mechanical and thermal turbulence, causing greater plume dispersion. EPA accounts for this by shifting the stability classification toward neutral in urban areas:

8. Regulatory Context

National Ambient Air Quality Standards (NAAQS)

Dispersion modeling is used to demonstrate that facility emissions will not cause or contribute to violations of the NAAQS established under 40 CFR 50:

H2S Ambient Standards

There is no federal NAAQS for hydrogen sulfide (H2S), but many states have established ambient air quality standards or guidelines. Common state standards include:

Key Regulatory Programs

9. EPA Modeling Tiers

EPA's Guideline on Air Quality Models (40 CFR Part 51, Appendix W) establishes a tiered approach to dispersion modeling, from simple screening models to sophisticated refined models:

Tier 1: Screening Models

Tier 2: Refined Models

When to Use Each Tier

• Screening (Tier 1): Initial feasibility studies, minor source permits, preliminary stack height design, emergency planning estimates. If the screening result shows compliance with a margin, no further analysis is needed.
• Refined (Tier 2): Required when screening analysis shows potential exceedances, for PSD/major NSR permits, when site-specific meteorology is available, or when terrain or building effects are complex.

References

• Pasquill, F. (1961). The estimation of the dispersion of windborne material. The Meteorological Magazine, 90, 33–49.
• Gifford, F.A. (1961). Use of routine meteorological observations for estimating atmospheric dispersion. Nuclear Safety, 2, 47–51.
• Briggs, G.A. (1969). Plume Rise. USAEC Critical Review Series, TID-25075.
• Briggs, G.A. (1971). Some recent analyses of plume rise observations. Proceedings, Second International Clean Air Congress.
• Briggs, G.A. (1975). Plume rise predictions. Lectures on Air Pollution and Environmental Impact Analysis, AMS, Boston.
• Turner, D.B. (1970). Workbook of Atmospheric Dispersion Estimates. EPA AP-26.
• EPA (1995). SCREEN3 Model User's Guide. EPA-454/B-95-004.
• EPA (2004). AERMOD: Description of Model Formulation. EPA-454/R-03-004.
• 40 CFR Part 50 — National Primary and Secondary Ambient Air Quality Standards.
• 40 CFR Part 51 — Requirements for Preparation, Adoption, and Submittal of Implementation Plans.
• 40 CFR 51.100 — Good Engineering Practice Stack Height.
• 40 CFR Part 51, Appendix W — Guideline on Air Quality Models.