explosions, expulsion rate, dispersion and ignition

Explosions, Expulsion Rate, Dispersion and Ignition of Released Fuels: A Review

David G. Lilley* Lilley & Associates, 7221 Idlewild Acres, Stillwater, Oklahoma 74074

A review of pertinent information on fire dynamics of explosions is undertaken. The very real possibility of a deliberate or accidental failure in storage or supply lines carrying fuel is considered. A review of pertinent information on fire dynamics of explosions is undertaken. Topics include: fundamentals, characterization, vapor cloud explosions, blast damage due to over-pressurization, procedure for estimating the over-pressure, blast fragment missile damage, and energy of mechanical explosions. The emphasis is on understanding and applying the technical ideas in real-world situations. In the source release of material, the evolution and dispersion of liquids and gases being released under pressure is considered. They can be toxic or flammable or explosive in nature, and this is extremely dangerous. If the ensuing cloud comes in contact with an ignition source, and the fuel-air ratio is within flammability bounds, the resulting explosion and fire can often be devastating.

Many of the effects of explosions, release and dispersion of material are presented in

empirical equations, and programmed into the Visual Basic for Applications VBA codes, behind the Excel spreadsheet, and results are automatically tabulated with 2-D and 3-D graphic illustrations. In the dispersion of the released material, in particular, the mass fraction, volumetric fraction and parts per million at locations further downstream and to the side are calculated, and related to the possible ignition. A multitude of parameters affecting the situation can be changed to illustrate their influence on the calculations. Depending on the atmospheric stability conditions, wind speed, amount of material released, the concentration levels of the released material at specific locations may or may not provide potential ignition from a competent ignition source.

I. Introduction Explosions, and the evolution, dispersion and possible ignition of flammable fuel release into the atmosphere

is an important safety topic in fire protection engineering, see Combustion Institute (1979), NFPA (2008), AGA (1988), ASME (1973), SFPE (2008) and Lilley (1990a and b). Lilley (1995 and 1996) lists some of the basic properties of flammable liquids, gases and solids. In the release and dispersion of flammable material, either particles of solids, liquid droplets of various sizes, or a vapor cloud is formed which spreads and disperses as the released material mixes and is carried downstream in the atmosphere. See ASME (1973) and other references given in the extensive reference list. Solid and liquid droplet trajectories are discussed in detail by Lilley (2010).

If the initial breakage does not produce an immediate explosion and fire, the main problem of the released material is that it is important to know if a potential ignition source is located where the fuel concentration is within the flammable or explosive limits, these being the percentage (usually by volume) of a substance in air that will burn once ignited. Most substances have both an upper (rich) and a lower (lean) flammable (explosive) limit, called the UEL and LEL, respectively. Either too much or too little fuel in the vapor-air mixture can prevent burning. There is a wide range of fuels with different flammable limits. Higher temperatures and/or higher pressures generally increase the range over which a given fuel-air mixture is capable of being ignited and burned. Lilley (2008) discusses the entire “fire dynamics” problem from ignition to investigation and beyond. _________________________________ * Professor, Fellow AIAA Copyright © 2011 by David G. Lilley. All rights reserved. Published by AIAA with permission.

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49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4 - 7 January 2011, Orlando, Florida

AIAA 2011-525

Copyright © 2011 by David G. Lilley. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

Chemical engineering problems of release and dispersion of toxic substances is discussed in detailed in

Wark (1998), Crowl and Louvar (1990), Hanna (1987), DeNevers (1995), Kletz (1994), LaGrega (1994), Lees(1980) and EPA (1992). Cote and Linville (1990) describe many of the manufacturing processes used in industry, identify the fire hazards associated with those processes, and detail the methods used to control and eliminate them. Litigation aspects associated with the reasons for the occurrence of fires - origin, cause and responsibility - is addressed in several texts, including Berry (1989), Kennedy (1985 and 1990) and Patton (1994). Lilley (1990, 1995 through 1999, 2003, 2004 and 2008) lists some of the basic properties of flammable liquids, gases and solids.

The present contribution is concerned with:

1. Explosions, blast damage and fragment missile damage 2. Mathematical simulations of release, and plume and puff dispersion models 3. Effects of stability conditions, wind speed and exit mass flow rate conditions 4. Presentation of the relevant effects have been implemented in the Excel/VBA platform. 5. The computer codes include dynamic 2-D and 3-D graphic displays 6. Ground level release is considered in both plume and puff dispersion models for simplicity

II. Explosions

A. Basics

An "explosion" is generally considered to be the process of rapid release of energy involving spontaneous and vigorous reactions with rapid production of very large volumes of gases and heat fluxes, having destructive effects on nearby surroundings. NFPA 921 (2004) simply and generally defines explosion as:

Explosion -- "The sudden conversion of potential energy (chemical or mechanical) into kinetic energy with the

production and release of gases under pressure, or the release of gas under pressure. These high-pressure gases then do mechanical work such as moving, changing, or shattering nearby materials."

Explosions are mostly classified into diffuse and concentrated type of explosions, low yield and high yield

explosives, and it is assumed that the reader is familiar with elementary concepts of fires and explosions, including:

1. Diffuse and concentrated explosions 2. Deflagration and detonation explosions 3. Pressure vessel ruptures 4. Steam explosions 5. Concentrated or high yield explosives 6. Lower and upper explosive limits 7. Effect of initial temperature and pressure 8. Stoichiometric concentration 9. Minimum Oxygen Concentration (MOC) and inerting 10. Ignition energy 11. Autoignition and auto-oxidation 12. Adiabatic compression 13. Sprays and mists 14. Deflagration Indices 15. Consequences of an Explosion in a Confined Space 16. Characteristics of Vapor Cloud Explosions VCEs 17. Boiling Liquid Expanding Vapor Explosions (BLEVE)

Further information about fires and explosions are given in short courses by Lilley (2003 and 2004) and a handbook chapter, see Lilley (2008). Typical explosion characteristics are given in Table 1.

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B. Explosion Characterization

Explosions are either detonations or deflagrations; the difference depends on the speed of the shock wave emanating from the explosion. It is known that the maximum pressure achieved and the maximum rate of pressure increase are important in characterizing the effect of an explosion. Experimental data gives rise to modeling simulation about the characteristics of explosions. The limits of flammability or explosivity are used to determine the safe concentrations for operation or the quantity of inert required to control the concentration within safe regions. The maximum rate of pressure rise is indicative of the robustness of an explosion. Thus, the explosive behavior of different materials can be compared on a relative basis.

Parameters that significantly affect the behavior of explosions are: 1. Ambient temperature 2. Ambient pressure 3. Composition of explosive material 4. Physical properties of explosive material 5. Nature of ignition source: type, energy, and duration 6. Geometry of surroundings: confined or unconfined 7. Amount of combustible material 8. Turbulence of combustible material 9. Time before ignition 10. Rate at which combustible is released

A plot of the log of the maximum pressure slope versus the log of the vessel volume frequently produces a

straight line of slope –1/3. This relationship is called the "Cubic Law" with

g31

max K ttanconsVdtdP

St31

max KVdtdP

where Kg and Kst are called the deflagration indices for gas and dust respectively. As the robustness of an explosion increases, the deflagration indices Kg and KSt increase. Several values are now given.

Average Kg Values for Selected Gases

Gas Kg (bar m/s) Methane 55 Propane 75 Hydrogen 550

Average Kst Values for Selected Dusts

Dust Pmax (bar) KSt

(bar m/s) PVC 6.7 - 8.5 27-98 Milk Powder 8.1 - 9.7 58-130 Polyethylene 7.4 - 8.8 54-131 Sugar 8.2 - 9.4 59-165 Resin Dust 7.8 - 8.9 108-174 Brown Coal 8.1 - 10.0 93-176 Wood Dusts 7.7 - 10.5 83-211 Cellulose 8.0 - 9.8 56-229 Pigments 6.5 - 10.7 28-344 Aluminum 5.4 - 12.9 16-750

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St Classes for Dusts Deflagration

Index, KSt St Class

0 St-0 1 - 200 St-1

200 - 300 St-2 > 300 St-3

Consequences of an explosion in a confined space lead to

erimentalexp

31

maxvesselin

31

maxV

dtdPV

dtdP

The subscript "in vessel" is for the reactor or building. The subscript "experimental" applies to data

determined in the laboratory using either the vapor or dust explosion apparatus. The equation allows the experimental results from the dust and vapor explosion apparatus to be applied to determining the explosive behavior of materials in buildings and process vessels. The constants Kg and KSt are not physical properties of the material because they are dependent on the composition of the mixture, the mixing within the vessel, the shape of the reaction vessel, and the energy of the ignition source. It is, therefore, necessary to run the experiments as close as possible to the actual conditions under consideration. Experimental studies indicate that the maximum explosion pressure is usually not affected by changes in volume and the maximum pressure and the maximum pressure rate are linearly dependent upon the initial pressure. As the initial pressure is increased, a point is reached where the deflagration turns into a detonation.

C. Vapor Cloud Explosions

The most dangerous and destructive explosions in the chemical process industries are vapor cloud explosions (VCEs). These explosions occur by a sequence of steps. There is a sudden release of a large quantity of flammable vapor. Typically this occurs when a vessel, containing a superheated and/or pressurized liquid, ruptures, especially if the liquid being released changes to vapor form as the reduced external pressure presents itself. Then, dispersion of the vapor throughout an area occurs while the cloud mixes with air. Finally, ignition of the resulting vapor cloud occurs when a suitable ignition source presents itself. Some of the parameters that affect VCE behavior are:

1. Quantity of material released. 2. Fraction of material vaporized. 3. Probability of ignition of the cloud. 4. Distance traveled by the cloud prior to ignition. 5. Time delay before ignition of the cloud. 6. Probability of explosion rather than fire. 7. Existence of a threshold quantity of material. 8. Efficiency of explosion. 9. Location of ignition source with respect to release.

D. Blast Damage due to Over-Pressurization

The explosion of a dust or gas (either as a deflagration or detonation) results in a reaction front moving outwards from the ignition source preceded by a shock wave or pressure front. After the combustible material is consumed, the reaction front terminates, but the pressure wave continues its outward movement. A blast wave is composed of the pressure wave and subsequent wind. It is the blast wave that causes most of the damage.

Peak overpressure resulting from the pressure wave impacting on a structure is a function of the rate of pressure rise. Good estimates of blast damage, however, are obtained using just the peak overpressure, and on the basis of the equivalent mass of TNT, see Tables 2 and 3 for human injury and property damage criteria versus overpressure.

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The procedure is as follows:

1. Denote the equivalent mass of TNT by mTNT, and using r for the distance away from ground zero of the

explosion, the empirically derived scaling law is

31TNT

em

rz

where ze is a scaled distance, units of ft/lb1/3 or m/kg1/3. This correlation has been found to be good for

determining the over-pressure produced by an explosion at a particular distance away from the explosion. 2. The equivalent energy of TNT is 1120 cal/gm (= 4.69 MJ/kg) and this is used in the conversion into the TNT

equivalent energy.

E. Procedure for Estimating the Overpressure at any Given Distance The procedure for estimating the overpressure p at any distance, r, due to the explosion of a mass of material is as follows:

1. Compute the energy of the explosion using established thermodynamic procedures, 2. Convert the energy to an equivalent amount of TNT, 3. Use the scaling law and the correlations (Figures 1 and 2 or fitted equations, see below) to estimate the

overpressure, and 4. Use Tables 2 and 3 to estimate the human and property damage.

The relationship between overpressure and scaled distance away, Figures 1 and 2, from the explosion is

almost a linear one when plotted on log-log paper. Hence the relationship between the variables can be found by the method of least squares for a straight line of the transformed variables, and in terms of the original variables the relationship is of the form

y = x

where and are best-fit constants.

English Engineering units. When y is equal to p (the overpressure in lbf/in2) and ze is the scaled distance in units of ft/lb1/3 then, using five points for the curve fit:

= 29.579 and = -1.054

Thus

p = 29.6 ze -1.054

SI Units. When y is equal to p (the overpressure in kPa) and ze is the scaled distance in units of m/kg1/3 then, using five points for the curve fit:

= 572.678 and = -1.685

Thus

p = 573 ze -1.685 Example re Overpressure at a Given Distance A mass of 2 kg of TNT is exploded. Compute the overpressure at a distance of 20 m from the explosion.

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Solution

The value of the scaling parameter is determined as:

31TNT

em

rz

31

31e kgm8.15kg2

m20z

Hence, from Figure 2, the overpressure is estimated to be about 6 kPa = 0.9 psi. According to Table 3, this is almost enough to get partial demolition of houses, certainly shattering glass windows.

F. Blast Fragment Missile Damage

An explosion occurring in a confined structure can rupture the structure resulting in the projection of debris over a wide area. This debris, or missiles, can cause appreciable injury to people and damage to structures and process equipment. Unconfined explosions also create missiles by blast wave impact and subsequent translation of structures. The mass of explosive and the maximum horizontal range of the fragments can be estimated from first expressing the mass as an equivalent mass of TNT, and then using the figure to estimate the maximum horizontal range of fragments. The relationship between distance x away from the explosion and the equivalent mass m of TNT explosive, see Figure 3, is almost a linear one when plotted on log-log paper. Hence the relationship between the variables can be found by the method of least squares for a straight line of the transformed variables, and in terms of the original variables the relationship is of the form

y = x

where and are best-fit constants.

English Engineering units. When y is equal to x (the maximum distance away in ft that a fragment will go) and m is the equivalent mass of TNT in lbm, then, using five points for the curve fit:

= 797.680 and = 0.221

Thus

x = 798 m 0.221 This relationship is useful during accident investigations for calculating the energy level required to project fragments to an observed distance from the location of the explosion. Example re Blast Damage A reactor contains the equivalent of 5,000 lb of TNT. If it explodes, estimate the injury to people and the damage to structures 300 ft away. Solution

The scaled distance is:

313131

TNTe lbft5.17

lb000,5ft300

mrz

Then the overpressure is about 2 psi using Figure 1. This indicates Table 2 that serious wounds could well occur and from Table 3 that houses will be severely damaged at this location.

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III. Evolution of Flammable Material

A. Basics Explosive breakages in fuel-carrying conduits and tanks will result in the release of flammable material. This topic falls within the science of chemical process safety, health and loss prevention, topics addressed in SFPE (2008), NFPA (2008), Lees (1980), Crowl and Louvar (1990) and AIChE (1990). These and other authors discuss the many principles, guidelines, and calculations that are necessary for safe design and operation, and analysis of failures, including: fires and explosions, vessel overpressure protection, hazards identification and risk assessment, source models, and dispersion modeling. For example, material may be released from holes and cracks in tanks and pipes, from leaks in flanges, pumps, and valves, and a large variety of other sources. When an accidental or deliberate fracture occurs in a fuel line or storage tank, the source models represents the material release process. The relevant model will provide useful information for determining the consequences of the pressurized release, including the rate of material release, the total quantity released, and the physical state of the material. Source models are constructed from fundamental or empirical equations representing the physico-chemical processes occurring during the release of materials. Several basic source models are available, each applicable to the particular release scenario:

1. Flow of liquids through a hole 2. Flow of liquids through a hole in a tank 3. Flow of liquids through pipes 4. Flow of vapor through holes 5. Flow of vapor through pipes 6. Flashing liquids 7. Liquid pool evaporation or boiling

and problem parameters come into play in determining the amount of release or rate of release. The purpose of the source model is to determine: the form of material released (solid, liquid or vapor), the total quantity of material released, and the rate at which it is released.

B. Energy Balance Equation Source releases are driven by pressure differences, and resulting velocities depend upon the density of the fluid (liquid or gas), whether or not the fluid is compressible, and whether or not choking (maximum flow) conditions occur. The volume flow rate (m3/s or ft3/s) and mass flow rate (kg/s or lbm/s) may be determined via introduction of the flow passage cross-sectional area and density of the flowing material. A correction factor is introduced to cater for the flow being less than ideal, via multiplication by Co (called the discharge coefficient, a number less than one). A mechanical energy balance describes the various energy forms associated with flowing fluids,

dP V

ggg

z Fc c

2

20

where P = the pressure (N/m2 = Pa or lbf/ft2) = the fluid density (kg/m3 or lbm/ft3) V = the average instantaneous velocity of the fluid (m/s or ft/s) gc = the conversion factor constant (= 1 kg-m/N-s2 or 32.2 lbm ft/lbf-s2) = the unitless velocity profile correction factor with the following values, = 0.5 for laminar flow = 1.0 for turbulent flow with almost a flat velocity profile g = the acceleration due to gravity (= 9.81 m/s2 or 32.2 ft/s2) z = the height above some datum (m or ft) F = the net frictional loss term (J/kg or ft lbf/lbm) For incompressible liquids the density is constant and the first term in the equation is replaced by P/P.

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C. Flow of Liquid Through a Hole Since there is no altitude change, only the pressure and kinetic energy (by virtue of the square of the velocity) terms remain. There is a trade-off between pressure energy and velocity produced. That is, high pressure and zero velocity inside the container, with the resulting liquid escaping into zero gage pressure at a high velocity. In practice the driving pressure gives a lower exit velocity than the idealized equation gives, because of losses associated with the flow going through the area reduction. This is taken into account by multiplying the ideal answer by a number less than unity, this number being called the discharge coefficient Co. The resulting equation for the velocity (m/s or ft/s) of fluid exiting the leak is

V = gco

Pg2C

and the mass flow rate Qm (in kg/s or lbm/s) due to a hole of area A (m2 or ft2) is given by Qm = VA = ACo gc Pg2

The total mass of liquid spilled is dependent on the total time the leak is active. In these equations gc is the familiar conversion factor (= 32.2 lbm-ft/lbf-s2 in US customary units and = 1 kg-m/N-s2 in SI units) and Pg is the gage pressure pushing the fluid through the hole to an ambient zero gage pressure. The discharge coefficient Co is a complicated function of the Reynolds number of the fluid escaping through the leak, the contour of approach to the exit, and the diameter of the hole. The following guidelines are suggested.

1. For sharp-edged orifices and for Reynolds numbers greater than 30,000, Co approaches the value 0.61. For these conditions, the exit velocity of the fluid is independent of the size of the hole.

2. For a well-rounded nozzle the discharge coefficient approaches unity. 3. For short sections of pipe attached to a vessel (with a length-diameter ratio not less than 3), the discharge

coefficient is approximately 0.81. 4. For cases where the discharge coefficient is unknown or uncertain, use a value of 1.0 to maximize the

computed flows.

D. Flow of Liquid Through a Hole in a Tank When the hole in a tank is below the liquid surface level, there is an additional hydrostatic pressure due to depth acting as well as the pressure in the region just above the liquid surface level. The resulting equation for the instantaneous velocity (m/s or ft/s) of fluid exiting the leak is

V = Lgc

o ghPg

2C

where hL (m or ft) is the liquid surface height above the leak. The instantaneous mass flow rate Qm (in kg/s or lbm/s) due to a hole of area A (m2 or ft2) is given by

Qm = VA = A Lgc

o ghPg

2C

As the tank empties, the liquid height decreases and the velocity and mass flow rate will decrease.

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E. Flow of Vapor Through Holes Free expansion leaks for gas (vapor) through holes differs from that of liquid flow because of the very much lower density of the fluid and the fact that it is compressible and pressure, temperature and density all change as the gas escapes and its velocity increases as it goes through the exit. The gas obeys the ideal gas law P = R T/M where P = the absolute pressure (N/m2 = Pa or lbf/ft2) = the fluid density (kg/m3 or lbm/ft3) R = the universal gas constant (= 8314 J/kg-mole K or 1545 ft-lbf/lbm-mole R) T = the absolute temperature (degrees K or R) M = the molecular weight of the gas (kg/kg-mole or lbm/lbm-mole) For the isentropic (no heat transfer and no mechanical losses) expansion of the gas P/ = constant where is the ratio of the heat capacities, = Cp/Cv. In general is the specific heat ratio of the gas emerging, which is equal to 1.67, 1.40 and 1.32 according to whether the gas is monotomic, diatomic (or air) and triatomic, respectively. Introducing the discharge coefficient and keeping absolute pressures yields the equation for mass flow rate (in kg/s or lbm/s) as

1

o

2

oo

coom P

PPP

1TRMg2APCQ

where P is the absolute pressure of the external surroundings, Po is the absolute pressure of the source (both in N/m2 or lbf/ft2), and R stands for the universal gas constant. The above equation holds only for flows which are not choked, that is flows with upstream absolute pressure less than about twice the downstream absolute pressure (which is usually the atmosphere). For high pressure ratios (with upstream absolute pressure greater than about twice the downstream absolute pressure) the flow becomes sonic at the hole. Then the flow rate depends only on the upstream driving absolute pressure Po and the mass flow rate (in kg/s or lbm/s) is given by

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o

coom 1

2TRMgAPCchokedQ

where M is the molecular weight of the escaping vapor or gas, To is the absolute temperature of the source, and R is the universal gas constant. For sharp-edged orifices with Reynolds numbers greater than 30,000 (and not choked), a constant discharge coefficient Co of 0.61 is indicated. However, for choked flows, the discharge coefficient increases as the downstream pressure decreases. For these flows and for situations where Co is uncertain, a conservative value of 1.0 is recommended when the maximum (worst) possible scenario is being estimated.

IV. Dispersion and Possible Ignition of Released Material Dispersion models describe the airborne transport of materials away from the accident site. After a release, the airborne material (small solid particles, small liquid droplets, and/or vapor) is carried away by the wind in a characteristic plume or a puff. Larger particles and larger drops of liquid fuel form trajectories with air resistance and the flight paths are affected by local wind conditions, see Lilley (2010). In plume and puff releases, the

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maximum concentration occurs at the release point (which may or may not be a ground level). For simplicity only ground level releases are considered in this paper. Concentrations downwind are less, due to turbulent mixing and dispersion of the substance with air. A wide variety of parameters affect atmospheric dispersion of toxic materials:

1. Wind speed 2. Atmospheric stability 3. Ground conditions, buildings, water, trees 4. Height of the release above ground level 5. Momentum and buoyancy of the initial material released

Two types of vapor cloud dispersion models are commonly used: the plume and puff models, collectively known as the Pasquill-Gifford model using dispersion coefficients that empirically specify the rates of spread of the dispersing material. The plume model describes the steady-state concentration of material released from a continuous source. The puff model describes the temporal concentration of material from a single release of a fixed amount of material. Models are available that permit concentration (kg/m3) and volumetric concentration percent (%) to be calculated at location (x,y,z) as a function of time (t) after initial release. It is important to determine if the mixture is within the flammability limits at a nearby ignition source, in the case of fuel release. Useful references include AIChE (1990), ASME (1973), Crowl and Louvar (1990), EPA, NOAA and NSC (1992), and Hanna and Drivas (1987). Further recommendation for possible modification of the basic diffusion equation results are given in DeNevers (1995) and LaGrega et al. (1994). Sprays of liquid droplets and particles may be handled via computation of particle trajectories, including air resistance and wind effects, as outlined by Chow (1979) and Lilley (1992 and 2010).

A. Plume Model

It is common to utilize the dispersion coefficients, x, y, and z. These represent the standard deviations of the concentration in the downwind, crosswind, and vertical (x,y,z) directions, respectively. The dispersion coefficients are a function of atmospheric conditions and the distance downwind from the release. The atmospheric conditions are classified according to six different stability classes. The stability classes depend on wind speed and quantity of sunlight. During the day, increased wind speed results in greater atmospheric stability, while at night the reverse is true. This is due to a change in vertical temperature profiles from day to night. Stability classes are given in Table 3. The dispersion coefficients, y and z for a continuous source were developed by Gifford and are given in figures and tables. Values for y are not provided since it is reasonable to assume x = y. Table 4 gives equations for these "plume" release coefficients as functions of downstream distance x. For a plume with continuous steady state source of constant mass release rate Qm (kg/s) and a wind velocity u (m/s) in the x-direction, the ground concentration is given at z = 0 by , see Wark et al (1998)

C(x, y, 0) = Qu

ym

y z yexp

12

2

where C represents concentration (kg/m3). This can also be transferred to volumetric concentration, and to parts per million (ppm). The concentration along the centerline of the plume directly downwind is given at y = z = 0 by

C(x, 0, 0) = Qu

m

y z

For continuous ground level release the maximum concentration occurs at the release point. For a plume with continuous steady state source of constant mass release rate and wind velocity in x-direction, the concentrated equation for elevated source (smoke releases) with reflection can be found in Wark et al (1998).

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B. Puff Model As with the plume model, dispersion coefficients x, y, and z are utilized as identified for puff releases in figures and tables. Table 4 gives equations for these "puff" release coefficients as functions of downstream distance x. The downstream concentrations on the ground (z = 0) for a puff of mass release Q (kg) with a wind velocity u (m/s) in the x-direction as shown in Wark et al (1998) is given by

m*

C(x, y, 0, t) = 2y

22

xzyx2/3

*m yutx

21exp

2Q

The ground level concentration along the x-axis is given at y = z = 0 via

C(x, 0, 0, t) = 2

xzyx2/3

*m utx

21exp

2Q

The center of the cloud is found at coordinates (ut, 0, 0). The concentration at the center of this moving cloud is given by

C (ut, 0, 0, t) = zyx

2/3

*m

2Q

C. Possible Ignition of Released Material

Ignition of the released material occurs if the volume concentration of the leaked substance falls between the flammable limits and a suitable ignition source is present. Flammable limits apply generally to vapors and are defined as the volume concentration range in which a flammable substance can produce a fire or explosion when an ignition source such as a spark or open flame is present. The concentration is generally expressed as percent fuel by volume in air. Information regarding the combustion properties of common flammable gases can be obtained from Lilley (2004 and 2008).

Above the upper flammable limit (UFL) the mixture of substance and air is too rich in fuel (deficient in oxygen) to burn. This is sometimes called the upper explosive limit (UEL). Below the lower flammable limit (LFL) the mixture of substance and air lacks sufficient fuel (substance) to burn. This is sometimes called the lower explosive limit (LEL). Any concentration between these limits can ignite or explode. Flammability ranges of specific materials can be obtained from Lilley (2004 and 2008). Being above the upper limit is not particularly safe, either. If a confined space is above the upper flammable limit and is then ventilated or opened to an air source, the vapor will be diluted and the concentration will drop into the flammable limit range in many locations.

V. Plume Distribution A. Sample Validation Problem On an overcast day, an emission of 10 kg/s (22 lbm/s) of butane occurs continuously from a ground level release point. The wind speed is 3 m/s (10 ft/s). Calculate the mean concentration (in volume percent) of butane at 20 meters (66 feet) downwind and 4 meters (13 feet) to the side. Assume the gas is neutrally buoyant and omit consideration of the dense gas situation. If a small pilot flame is located at that point, is ignition likely to occur or not? Discuss. (This problem is taken from Lilley (1997c) and it is solved for the purpose of verification of the code being developed and used to illustrate parameter effects. The agreement is precise.)

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Solution Let us take stability class C. Plume equations give x = y = 0.195 x 0.90 = 2.89 m z = 0.112 x 0.91 = 1.71 m

C(x, y, z) = Qu

ym

y z yexp

12

2

(a) At x = 20 m, y = 0 m, u = 3 m/s, exp [ ] = 1

C (20, 0, 0) = 102 89 171 3( . )( . )( )

= 0.215 kg/m3

Air has 1.2 kg/m3 so volume concentration percent is

= 0 215 5812 29. /. /

x 100 = 9.0%

(b) At x = 20 m, y = 4 m, u = 3 m/s

C (20, 4, 0) = C(20, 0, 0) exp 12

42 89

2

.

= (0.215) (0.384) = 0.0825 kg/m3

Volume concentration percent is

= 0 0825 5812 29. /

. / = 3.4%

B. Parameter Effects

Figure 4 (a) through (c) shows how the volume concentrations vary with lateral distance. Volume concentrations are expressed in percentages on y axis and lateral distance is measured in meters on x axis. In the figure, stability classes are varied by keeping the mass flow rate Q (10 kg/s) of gas released and velocity of wind (6 m/s) constant. Stability classes considered are A, C and E, respectively, representing unstable, neutrally stable and stable atmospheric conditions. As we can see from the figure, volume concentrations are higher for the more stable stability classes. Here, volume concentrations for stability class E are more than the volume concentrations for stability class C, and these are more than those of stability class A. These results are consistent with the plume model equations. For a constant wind speed, the dispersion will be less for a higher stability class than for a lower stability class. Hence, one sees that the volume concentrations are high for stability class E of stable atmospheric conditions.

Similar figures may also be generated for other wind speeds, other than the speed of 6 m/s as in Figure 4. For example, a summary of the centerline concentration with the unstable atmospheric conditions of stability class A, is given in Figures 5, with Parts (a) through (c) showing how volume concentration changes with lateral distances, with a wind velocity of 3, 6 and 9 m/s respectively. It is observed that the corresponding volume concentrations for which the wind velocity is 3 m/s are more than the volume concentration at higher wind speeds. Hence, the higher the velocity of the wind, the lesser is the volume concentration at a specified downstream location.

Perspective views with dynamic graphic are also generated automatically with the Excel/VBA codes. For example, Figure 6 Parts (a) and (b) present the perspective and plan views of volumetric concentration, with the continuous plume model with 10 kg/s release into a 3 m/s wind of a neutrally stable atmosphere of stability class C.

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VI. Puff Distribution A. Sample Validation Problem

A bottle of liquid SO2 is burst at ground level and instantaneously releases 80 pounds of SO2 (36.24 kg). What is the approximate maximum concentration that will be observed by a person who is 1000 m directly downwind under worst-case meteorological conditions. (This problem is taken from Wark et al (1998) and it is solved for the purpose of verification of the code being developed and used to illustrate parameter effects. The agreement is precise.) Solution For ground level sources, the worst-case meteorological conditions occur with C stability at a wind speed of 1 m/s. (This is the lowest value of u generally recommended in the continuous release Gaussian dispersion models). Based on the equations in Table 3, and using a stability condition of very stable, the y and z values at 1000 m downwind are calculated to be 9.4 m and 3.4 m, respectively. The value of x is assumed to be equal to y. Substituting the values into the equation for Puff release and setting the exponential term equal to unity, the centerline mass concentration at x = 1000 m becomes

32/3 m/kg0153.0)0.1(

)4.3)(4.9)(4.9()2()24.36)(2()0,0,1000(CC

This agrees precisely with Wark, et al (1998) when the dispersion coefficients are equal to 9.4 m with stable meteorological conditions. In the general computer program, the formulas (for dispersion coefficients from fitted curves through limited data) would actually give x = y =9.35 and z =3.38, thereby giving slight discrepancy versus the other calculations. Results from the sample validation can be verified for lateral distributions also at 1000 m downstream, and other downstream locations. At this distance, the concentration is about 0.015 kg/m3 on the centerline. At x = 500 m it is 0.0815 kg/m3

. B. Parameter Effects

Figures 7 Parts (a) (b) and (c) shows how the volume concentrations vary with lateral distance. Volume concentrations are expressed in percentages on the y axis versus the lateral distance in meters at several downstream x locations. The stability classes are unstable, neutrally stable and stable, respectively, called stability class A, B and C in the three parts of the figure. In all cases the mass released Q* is 10 kg into a wind of speed 3 m/s. As we can see from these figure, volume concentrations are higher for more stable atmospheric conditions. Hence, it is seen that the volume concentrations are higher for the most stable class considered, stability class E. Similar graphs can be developed for other wind speed conditions. Figures 8 and 9 represent plan views and perspective views, respectively, for a 10 kg sudden puff release with a wind velocity of 4 m/s in an unstable atmosphere with stability class A. In each figure, Parts (a), (b) and (c) represent views at time 5, 10 and 15 seconds, respectively. These graphics are automatically generated with the Excel/VBA code as calculations are accomplished for a specific case.

VII. Conclusions

The very real possibility of a deliberate or accidental failure in a supply line carrying fuel to a power plant has been considered. Explosions and/or the release of toxic, flammable and explosive materials which may subsequently ignite and explode. The resulting explosion and fire can often be devastating. A review was undertaken of pertinent information related to these industrial problems, with release rates, and vapor clouds with plume and puff release of material, and its potential ignition. Any concentration of fuel between the limits UFL and LFL can ignite or explode. Being above the upper limit is not safe, since as the cloud approaches a potential ignition source, a range of fuel-air ratios passes the location. Information related to the release, dispersion and possible ignition of released materials has been given, and the Excel/VBA platform was used to effect calculations.

13

References AGA (1988). “Fundamentals of Gas Appliances.” American Gas Association, Arlington, VA, 1988. AIChE (1990). "Safety, Health and Loss Prevention in Chemical Processes.” AIChE, NY, 1990. ASME (1973). "Prediction of the Dispersion of Airborne Effluents." ASME, NY, 1973. Berry, D. J. (1989). "Fire Litigation Handbook." 2nd Printing, NFPA, Quincy, MA, 1989. Carroll, J. R. (1979). "Physical and Technical Aspects of Fire and Arson Investigation." Thomas, Springifeld, IL,

1979. Chow, C-Y (1979). "Computational Fluid Mechanics." Wiley, NY, 1979. Combustion Institute (1979). "Colloquium on Fire and Explosion." 17th Symposium on Combustion, The

Combustion Institute, Pittsburgh, PA, 1979. Cote, A. E. and Linville, J. L. (Editors) (1990). "Industrial Fire Hazards Handbook." NFPA, Quincy, MA, 1990. Crowl, D. A. and Louvar, J. F. (1990). "Chemical Process Safety: Fundamentals with Applications." Prentice Hall,

Englewood Cliffs, NJ, 1990. DeNevers, N. (1995). "Air Pollution Control Engineering." McGraw-Hill, New York, 1995. EPA, NOAA and NSC (1992). "CAMEO, ALOHA and MARPLOT." EPA, NOAA and NSC, 1992. Hanna, S. R. and Drivas, P. J. (1987). "Vapor Cloud Dispersion Models." AICHE, NY, 1987. John, J. E. A. (1984). “Gas Dynamics.” 2nd Edition, Prentice Hall, Englewood Cliffs, New Jersey, 1984. Kennedy, J. and Kennedy, P. M. (1985). "Fires and Explosions: Determining Cause and Origin." Investigations

Institute, Chicago, 1985. Kennedy, J. and Kennedy, P. M. (1990). "Explosion Investigation and Analysis – Kennedy on Explosions."

Investigations Institute, Chicago, 1990. Kletz, T. (1994). “What Went Wrong? Case Histories of Process Plant Disasters.” 3rd Edition, Gulf Pub. Co.,

Houston, TX, 1994.

LaGrega, M. D., Buckingham, P. L. and Evans, J. C. (1994). "Hazardous Waste Management." McGraw-Hill, New York, 1994

Lees, F. P. (1980). “Loss Prevention in the Process Industries.” Butterworths, London, 1980. Lilley, D. G. (1990a). “Fuels, Flammability, Fires and Flames." Applied Engineering, Stillwater, OK 1990. Lilley, D. G. (1990b) "Fire Investigation Technical Information." Applied Engineering, Stillwater, OK 1990. Lilley, D. G. (1992). "Computational Fluid Dynamics: Course Notes." Applied Engineering, Stillwater, OK, 1992. Lilley, D. G. (1995a). "Fire Dynamics." Short Course, 1995. Lilley, D.G. (1995b). “Fire Dynamics”. Paper AIAA-95-0894, 33rd Aerospace Sciences Meeting, Reno, NV, Jan.

9-12, 1995. Lilley, D. G. (1996a). “Fire Hazards of Flammable Fuel Release.” Paper AIAA 96-0405, 34th Aerospace Sciences

Meeting, Reno, NV, Jan. 15-18, 1996.

14

Lilley, D. G. (1996b). “Flammable Fuel Release.” Forum on Industrial & Environment Applications of Fluid

Dynamics, ASME Fluids Engineering Conference, San Diego, CA, Jul. 7-11, 1996. Lilley, D.G. (1997a). “Structural Fire Development”. Paper AIAA-97-0265, 35th Aerospace Sciences Meeting,

Reno, NV, Jan. 6-10, 1997. Lilley, D.G. (1997b). “Estimating Fire Growth and Temperatures in Structural Fires”. Paper AIAA-97-0266, 35th

Aerospace Sciences Meeting, Reno, NV, Jan. 6-10, 1997. Lilley, D.G. (1997c). “Evolution, Dispersion and Ignition of Flammable Fuel Release”. ASME 17th International

Computers in Engineering Conference, Sacramento, CA, Sep. 14-17, 1997.

Lilley, D.G. (1998a). “Fuel Release and Ignition Calculations.” Paper AIAA-98-0262, 36th Aerospace Sciences Meeting, Reno, NV, Jan. 12-15, 1998.

Lilley, D.G. (1998b). “Fire Development Calculations.” Paper AIAA-98-0267, 36th Aerospace Sciences Meeting,

Reno, NV, Jan. 12-15, 1998. Lilley, D.G. (1999). “Release and Ignition of Flammable Material.” International Joint Power Generation

Conference, San Francisco, CA, Jul. 25-28, 1999. Lilley, D.G. (2003). “Explosions: Technical Aspects of Fuel Gas Explosions.” Short Course, repeated and updated

annually, Lilley & Associates, Stillwater, OK, 2003. Lilley, D. G. (2004). "Fire Dynamics," Short Course, 2nd Edition, repeated and updated annually, Lilley &

Associates Course, Technical Manual, Calculation Manual, Case Studies, and Review Problems, Stillwater, OK, 2004.

Lilley, D.G. (2005). “Explosions: Some Fundamentals for Investigators.” Paper AIAA-2005-0379, 43rd Aerospace

Sciences Meeting, Reno, NV, Jan. 10-13, 2005. Lilley, D. G. (2008). "Fire Dynamics," Chapter in Safety Professionals Handbook (Joel M. Haight, Ed.), American

Society of Safety Engineers, 2008, pp. 427-473. Lilley, D.G. (2010). “Trajectories of Projectiles in 3-D Space with an Excel/VBA Code.” Paper AIAA-20-1359,

48th Aerospace Sciences Meeting, Orlando, FL, Jan. 4-7, 2010. NFPA (2008). “Fire Protection Handbook”, 20th Edition (Cote, A. E. ed.), National Fire Protection Association,

Quincy, MA. NFPA 921 (2004). "Guide for Fire and Explosion Investigations." NFPA, Quincy, MA, 2004. Patton, A. J. (1994). "Fire Litigation Sourcebook." 2nd Edition, Wiley, NY, 1994. SFPE (2008). “Handbook of Fire Protection Engineering” 4rd ed. Boston, MA: National Fire Protection Association

and Society of Fire Protection Engineers.

Wark, K., Warner, C. F. and Davis, W. T. (1998). “Air Pollution: Its Origin and Control.” 3rd Edition, Addison Wesley Longman, Inc., Menlo Park, CA, 1998.

15

TABLE 1. Typical Explosion Characteristics

Typical Characteristics

Lighter-than-Air

Gases

Heavier-than-Air

Gases Liquid Vapors Dusts Explosives Backdrafts BLEVEs

Low-order damage 3 4 4 2 2 5 2

High-order damage 2 1 1 2 3 0 2

Secondary explosion 3 3 2 4 0 1 0

Gas/vapor/dust pocketing 3 2 2 2 0 0 0

Deflagrationa 4 4 4 4 1 5 4b

Detonation 1 1 1 1 4 0 1b

Underground migration 2 2 2 0 0 0 0

BLEVEs 2 3 5 0 0 0 5

Post-explosion fires 3 3 4 3 1 5 3

Pre-explosion fires 2 2 2 3 2 5 4

Seated explosions 0c 0c 0c 0 4d 0 2

Minimum ignition energy (mJ)e

0.17-0.25 0.17-0.25 0.25 10 - 40 e f

Note: 0 = never, 1 = seldom, 2 = sometimes, 3 = often, 4 = nearly always, 5 = always a Deflagrations may transition into detonations under certain conditions. b The strength of the confining vessel may allow the pressure wave at failure to be supersonic. c Gases and vapors may produce seats if confined in small vessels, and if the materials on which they explode can be sufficiently compressed or shattered. d All high explosives and some low explosives will produce seated explosions if the materials on which they explode can be sufficiently compressed or shattered. e Ignition energies vary widely. Most modern high explosives are designed to be insensitive to ignition. Energies for detonations are nine orders of magnitude larger than the minimum ignition energies. f BLEVEs are not combustion explosions and do not require ignitions.

16

TABLE 2. Human Injury Criteria (includes injury from flying glass and direct overpressure effects)

Overpressure (psi) Injury Comments Source

0.6 Threshold for injury from flying glass* Based on studies using sheep and dogs a

1.0-2.0 Threshold for skin laceration from flying glass Based on U.S. Army data b

1.5 Threshold for multiple skin penetrations from flying glass (bare skin)*

Based on studies using sheep and dogs a

2.0-3.0 Threshold for serious wounds from flying glass Based on U.S. Army data b

2.4 Threshold for eardrum rupture Conflicting data on eardrum rupture b

2.8 10% probability of eardrum rupture Conflicting data on eardrum rupture b

3.0 Overpressure will hurl a person to the ground One source suggested an overpressure of 1.0 psi for this effect

c

3.4 1% eardrum rupture Not a serious lesion d

4.0-5.0 Serious wounds from flying glass near 50% probability

Based on U.S. Army data b

5.8 Threshold for body-wall penetration from flying glass (bare skin)*

Based on studies using sheep and dogs a

6.3 50% probability of eardrum rupture Conflicting data on eardrum rupture b

7.0-8.0 Serious wounds from flying glass near 100% probability

Based on U.S. Army data b

10.0 Threshold lung hemorrhage Not a serious lesion [applies to a blast of long duration (over 50 m/s)]; 20-30 psi required for 3 m/s duration waves

d

14.5 Fatality threshold for direct blast effects Fatality primarily from lung hemorrhage b

16.0 50% eardrum rupture Some of the ear injuries would be severe d

17.5 10% probability of fatality from direct blast effects

Conflicting data on mortality b





27.0 1% mortality A high incidence of severe lung injuries [applies to a blast of long duration (over 50 m/s)]; 60-70 psi required for 3 m/s duration waves

d



Note: For SI units, 1 psi = 6.9 kPa. *Interpretation of tables of data presented in reference. a Fletcher, Richmond, and Yelverron, 1980. b Loss Prevention in the Process Industries. c Brasie and Simpson, 1968. d U.S. Department of Transportation, 1988.

17

TABLE 3. Property Damage Criteria

Overpressure (psi) Damage Source

0.03 Occasional breaking of large glass windows already under strain a

0.04 Loud noise (143 dB). Sonic boom glass failure a

0.10 Breakage of small windows, under strain a

0.15 Typical pressure for glass failure a

0.30 “Safe distance” (probability 0.95 no serious damage beyond this value) Missile limit Some damage to house ceilings 10% window glass broken

a

0.4 Minor structural damage a, c

0.5-1.0 Shattering of glass windows, occasional damage to window frames. One source reported glass failure at 0.147 psi (1 kPa).

a, c, d, e

0.7 Minor damage to house structures a

1.0 Partial demolition of houses, made inhabitable a

1.0-2.0 Shattering of corrugated asbestos siding Failure of corrugated aluminum-steel paneling Failure of wood siding panels (standard housing construction)

a, b, d, e

1.3 Steel frame of clad building slightly distorted a

2.0 Partial collapse of walls and roofs of houses a

2.0-3.0 Shattering of nonreinforced concrete or cinder block wall panels [1.5 psi (10.3 kPa) according to another source

a, b, c, d

2.3 Lower limit of serious structural damage a

2.5 50% destruction of brickwork of house a

3.0 Steel frame building distorted and pulled away from foundations a

3.0-4.10 Collapse of self-framing steel panel buildings Rupture of oil storage tanks Snapping failure – wooden utility tanks

a, b, c

4.0 Cladding of light industrial buildings ruptured a

4.8 Failure of reinforced concrete structures e

5.0 Snapping failure – wooden utility poles a, b

5.0-7.0 Nearly complete destruction of houses a

7.0 Loaded train wagons overturned a, b, c, d

7.0-8.0 Shearing/flexure failure of brick wall panels [8 in. to 12 in. (20.3 cm to 30.5 cm) thick, not reinforced] Sides of steel frame buildings blown in

d

Note: For SI units, 1 psi = 6.9 kPa. *Interpretation of tables of data presented in reference. a Fletcher, Richmond, and Yelverron, 1980. b Loss Prevention in the Process Industries. c Brasie and Simpson, 1968. d U.S. Department of Transportation, 1988.

18

TABLE 4. Atmospheric Stability Classes for Use with the Pasquill-Gifford Dispersion Model, see Crowl and Louvar (1990)

Wind Speed

Day radiation intensity

Night cloud cover

(m/s) strong Medium slight cloudy Calm & clear <2 A A-B B 2-3 A-B B C E F 3-5 B B-C C D E 5-6 C C-D D D D >6 C D D D D

Stability classes for Plume model: A, B: unstable C, D: neutral E, F: stable

TABLE 5. Equations and Data for Pasquill-Gifford Dispersion Coefficients,

see Crowl and Louvar (1990)

EQUATION FOR CONTINUOUS PLUMES

Stability class

Horizontal y = x (m)

A y = 0.493x0.88 B y = 0.337x0.88 C y = 0.195x0.90 D y = 0.128x0.90 E y = 0.091x0.91 F y = 0.067x0.90

TABLE 5. Equations and Data for Pasquill-Gifford Dispersion Coefficients (con't)

Stability class

x (m)

Vertical z (m)

100 - 300 z = 0.087x1.10 A 300 - 3000 log10 z = 1.67 + 0.902 log10x + 0.181(log10x)2 100 - 500 z = 0.135x0.95 B

500 - 2 x 104 log10 z = -1.25 + 1.09 log10x + 0.0018(log10x)2 C 100 - 105 z = 0.112x0.91

100 - 500 z = 0.093x0.85 D 500 - 105 log10 z = -1.22 + 1.08 log10x - 0.06(log10x)2 100 - 500 z = 0.082x0.82 E 500 - 105 log10 z = -1.19 + 1.04 log10x - 0.070(log10x)2 100 - 500 z = 0.057x0.80 F 500 - 104 log10 z = -1.91 + 1.37 log10x - 0.119(log10x)2

19

TABLE 6. Data for Puff Releases, see Crowl and Louvar (1990)

Stability condition

Horizontal y = x

(m) Vertical z

(m) Unstable y = 0.14x0.92 z = 0.53x0.73 Neutral y = 0.06x0.92 z = 0.15x0.70 Very stable y = 0.02x0.89 z = 0.05x0.61

x = 100 m x = 4000 m

Stability condition

y (m)

z (m)

y (m)

z (m)

Unstable 10 15 300 220 Neutral 4 3.8 120 50 Very stable 1.3 0.75 35 7

Stability classes for Puff model: A: unstable B: neutral C: stable

20

Figure 1 Correlation between overpressure and scaled distance, English engineering units

Figure 2 Correlation between overpressure and scaled distance, SI units

Figure 3 Maximum horizontal range of blast fragments, English engineering units

21

Volume Concentration vs Lateral Distance x = 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 m

0

1

2

3

4

5

6

-10 -5 0 5 10Lateral Distance (m)

Volu

me

Con

cent

ratio

n %

12345678910

(a) Atmosphere Unstable, Stability Class A

Volume Concentration vs Lateral Distance

x = 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 m

0

2

4

6

8

10

12

14

16

18

-10 -5 0 5 10

Lateral Distance (m)

Volu

me

Con

cent

ratio

n % 1

2345678910

(b) Atmosphere Neutral, Stability Class C

Volume Concentration vs Lateral Distance

x = 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , 100 m

0

10

20

30

40

50

60

-10 -5 0 5 10

Lateral Distance (m)

Volu

me

Con

cent

ratio

n % 1

2345678910

(c) Atmosphere Stable, Stability Class E

Figure 4 Volume Concentration vs Lateral Distance at Various Downstream Distances x in meters, for a 10 kg/s

Continuous Plume Release into a 6 m/s wind.

22

Volume Concentration vs Downstream Distance

0

5

10

15

20

0 50 100Downstream distance (m)

Volu

me

Conc

entra

tion

%150

(a) Wind Speed 3 m/s

Volume Concentration vs Downstream Distance

0

5

10

15

20


Vol

ume

Conc

entra

tion

%

150

(b) Wind Speed 6 m/s

Volume Concentration vs Downstream

Distance

0

5

10

15

20


Volu

me

Conc

entra

tion

%

150

(b) Wind Speed 9 m/s

Figure 5 Volume Concentration vs Downstream Distance, for a 10 kg/s Continuous

Plume Release in to an unstable atmosphere with stability class A

23

113 25 37 49 61 73 85 97

S1

S350123456789

10

Upstream Distance Y (m)

Downstream Distance X (m)

Perspective View

9-108-97-86-75-64-53-42-31-20-1

(a) Downstream Distance and Upstream Distance vs Volume concentration

1 10 19 28 37 46 55 64 73 82 91 100S1

S10

S19

S28

S37


Lateral Distance Y (m)

Plan View

9-108-97-86-75-64-53-42-31-20-1

(a) Downstream Distace and Lateral Distance vs Volume concentration

Figure 6 Perspective View and Plan View for a 10 kg/s Continuous Plume Model with wind velocity 3 m/s in a

neutral atmosphere with a stability class C.

24


0

10

20

30

40

50

60

70

80


Volu

me

Con

cent

ratio

n %

12345678910

(a) Atmosphere Unstable, Stability Class A


0

20

40

60

80

100

120


Volu

me

Con

cent

ratio

n % 1

2345678910

(b) Atmosphere Neutral, Stability Class B


0

20

40

60

80

100

120


Volu

me

Con

cent

ratio

n %

12345678910

(a) Atmosphere Stable, Stability Class C

Figure 7 Volume Concentration vs Lateral Distance at Various Downstream Distances, x in meters, for a 10 kg Puff

release into a 3 m/s wind.

25

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

S1

S7

S13

S19

S25

S31

S37



Plan View

4.5-54-4.53.5-43-3.52.5-32-2.51.5-21-1.50.5-10-0.5

(a) Downstream Distance and Lateral Distance vs Volume Concentration at time 5 s.

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

S1

S7

S13

S19

S25

S31

S37



Plan View

4.5-54-4.53.5-43-3.52.5-32-2.51.5-21-1.50.5-10-0.5

(b) Downstream Distance and Lateral Distance vs Volume Concentration at time 10 s.

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

S1

S7

S13

S19

S25

S31

S37



Plan View

4.5-54-4.53.5-43-3.52.5-32-2.51.5-21-1.50.5-10-0.5

(c) Downstream Distance and Lateral Distance vs Volume Concentration at time 15 s.

Figure 8 Plan View of a 10 kg Puff Release with a wind velocity of 4 m/s in an unstable atmosphere with

stability class A.

26

114 27 40 53 66 79 92

S1S360

0.51

1.52

2.53

3.54

4.55



Perspective View

4.5-54-4.53.5-43-3.52.5-32-2.51.5-21-1.50.5-10-0.5

(a) Downstream Distance and Lateral Distance vs Volume Concentration at time 5 s.

114 27 40 53 66 79 92

S1S360

0.51

1.52

2.53

3.54

4.55



Perspective View

4.5-54-4.53.5-43-3.52.5-32-2.51.5-21-1.50.5-10-0.5

(b) Downstream Distance and Lateral Distance vs Volume Concentration at time 10 s.

114 27 40 53 66 79 92

S1S360

0.51

1.52

2.53

3.54

4.55



Perspective View

4.5-54-4.53.5-43-3.52.5-32-2.51.5-21-1.50.5-10-0.5

(c) Downstream Distance and Lateral Distance vs Volume Concentration at time 15 s.

Figure 9 Perspective View of a 10 kg Puff Release with a wind velocity of 4 m/s in an unstable atmosphere

with stability class A.

27