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Modeling of Buoyant Plumes of Flammable Natural Gas

John Hargreaves

Analyst

Safety Basis Technical Services Group

LA-UR-12-21161

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Calculation of Natural Gas (NG) Hazards

•Analysis of natural gas (NG) explosions are required in support of safe nuclear operations

•This presentation will be based on work done analyzing NG hazards near LANL’s anticipated construction of a new TRU waste facility (TWF)

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Analysis of the NG Hazard

Analysis of an NG hazard requires:

• Identification of suitable simplifying assumptions and the geometry of the problem

• Selection of an analytical method or model

• Determination of an NG source term

• Characterization of a trajectory and flammable content of NG plume

• Calculation of the hazard potential of deflagration or detonation of the NG plume

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Assumptions and Limitations

• The analysis of an NG hazard requires assumptions to define the problem:

• Modeling of natural gas

• Definition of the NG source term

• Modeling of plume, plume rise, and atmospheric conditions

• Limitations of modeling an NG plume

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Modeling Natural Gas

Natural Gas can be modeled as pure methane

• NG is primarily methane (80 per cent or higher). The natural gas used at LANL averages between 96 and 97 percent methane. Higher fractions, e.g., butane, ethane, and propane, are separated by the vendor prior to delivery. Other constituents such as carbon dioxide, hydrogen sulfide, and nitrogen are also often removed, but may remain in trace quantities.

• Comparatively small molecule allows use of the ideal gas law [pv = nRT]

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Definition of NG Source Term

• Source can be a pipeline or a storage tank

• Pipeline flow may be treated as compressible and friction-limited

• Pipeline diameter, pipeline length, pressure, pipe roughness, and Fanning friction factor.

• Assumption on ambient pipeline temperature required.

• Determine conditions of flow, exit temperature, Mach number, flow density, total mass flux and volumetric flow

Existing NG Pipeline Adjacent to TWF

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Definition of NG Source Term

•Solve for Mach number and exit pressure of flow numerically

•Determine flow condition; i.e., choked or unchoked

•Determine density of exit flow; this indicates buoyancy

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Modeling a Buoyant Plume

• Plumes can be modeled as Gaussian, Top-Hat, or Non-Gaussian

• A Gaussian model assumes plume properties follow a Gaussian distribution over the plume cross section

• A Top-Hat model assumes properties are constant over the cross section

• Models are based on equations for conservation of fuel mass, total mass, and momentum

• Comparisons of these show top-hat and Gaussian models give very similar results

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Modeling a Buoyant Plume

•Briggs and Hanna developed theory for vertical and bent-over plumes

•Plume rise divides into momentum- and buoyancy-dominated flow

•Based on initial momentum flux and buoyancy flux

•Plume rise is usually dominated early (up to 5 to 10 seconds) by momentum

•If advecting wind velocity is 1 m/s or less, plume assumed to be vertical

•Vertical rise and bent-plume trajectories determined by the formulae:

where u is the advecting wind

velocity

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Limitations Modeling a Buoyant Plume

• Calculation of an exit velocity of the plume is geometry or “constant” dependent

• Terrain surface roughness can not be taken into account

• Gaussian distributions may not be accurate, especially in low wind velocities

• Building wake effects are ignored

• Localized air turbulence, aerosolization, gaseous depolymerization, water vapor reactions forming new products, or significant evaporation or condensation

• These last effects are more typical of heavier species of gas and not natural gas (methane)

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Plume Trajectory Plots30 m Standoff; 3-Inch Line

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3-D Plume Trajectory Plot (50 m)

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Tying Together Pasquill Stability, Turner Air Concentrations and Slade Power Law Approximations

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Plotting Concentration, Wind Speed, and Pasquill Stability Class Together (30 m)

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30 m Standoff Distance a Problem

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Plotting Concentration, Wind Speed, and Pasquill Stability Class Together (50 m)

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Determining Conservative Values for Explosive Overpressures

•Overpressure can be calculated using the TNT-equivalent method

•Assume a cylindrical plume and assume a 9 v/o air/methane mix

•Very conservative approach, but has value in possibly bounding the analysis

•New theory by Epstein and Fauske allows more precise calculation of total mass of flammable gas released in a vertical plume