Modeling of Buoyant Plumes of Flammable Natural Gas

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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 LANLs 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