NUREG/CR-0075

ACCIDENTAL VAPOR PHASE EXPLOSIONS

ON TRANSPORTATION ROUTES

NEAR NUCLEAR POWER PLANTS

Final Report

January - April 1977

T. V. Eichler H. S. Napadensky

lIT Research Institute

Prepared for

U. S. Nuclear Regulatory Commission
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NUREG/CR-0075

R5

ACCIDENTAL VAPOR PHASE EXPLOSIONS

ON TRANSPORTATION ROUTES

NEAR NUCLEAR POWER PLANTS

Final Report

January - April 1977

T. V. Eichler H. S. Napadensky

Manuscript Completed: December 1977

Date Published: May 1978

I IT Research Institute

10 West 35th Street

Chicago, IL 60616

Prepared for

Division of Engineering Standards

Office of Standards Development

U. S. Nuclear Regulatory Commission

Under FIN No. A 20057
FOREWORD

Final report J6405 is the result of a research study conducted for Argonne National Laboratory by the lIT Research

Institute under Contract 31-109-38-3776. This report is entitled

"Accidental Vapor Phase Explosions on Transportation Routes Near

Nuclear Plants", and covers the contract period January 26, 1977

to April 25, 1977.

This study was performed under the supervision of

Dr. J. Costello, Nuclear Regulatory Commission, and Dr. C. A. Kot

and-Dr. R. A. Valentin, Argonne NationalLaboratory. Their contributions and those of A. H. Wiedermann, IITRI, are gratefully appreciated. We wish to pay special thanks to Mr. Wiedermann and

Dr. Costello for their technical review of this report.

Respectfully submitted,

TIstitute

Thomas V. Eichler

Project Engineer

Fire and Safety Research

Enginiering Research Division

Approved by:

Dr. K.

Director of Research

Engineering Research Division

ii
ABSTRACT

This report presents the results of a study of the potential

blast effectiveness of vapor cloud explosions for hydrocarbons

released under accident conditions associated with transportation

routes near nuclear plants. The objective is to provide a methodology for estimating TNT equivalency of accidents of this type

in order that safe standoff distances for nuclear plants can be

evaluated.

Results are presented that establish the maximum blast effectiveness that can be attributed to fuel-air explosions on the

basis of thermodynamics and experimental data. A review of accidental vapor cloud explosions is included and comparisons are

made to determine a realistic basis for evaluating an accident's

potential destructiveness. It is hoped that this study contributes

toward the resolution of the many inconsistencies that appear on

this subject.

iii
CONTENTS

ACCIDENTAL VAPOR PHASE EXPLOSIONS

ON TRANSPORTATION ROUTES NEAR NUCLEAR PLANTS

Page

INTRODUCTION 1

1.1 Background 1

1.2 Accident Conditions 2

1.2.1 Material Involvement 3

1.2.2 Ignition-Explosion Process 6

1.2.3 Topographical and Meteorological

Conditions 9

1.3 Approach 12

2 CRITERIA AND METHODOLOGY OF TNT EQUIVALENCY 14

2.1 Definition and General Criteria 14

2.2 Asymmetric Model 16

3 TNT EQUIVALENCY OF CONTROLLED VAPOR PHASE

EXPLOSIONS 20

3.1 Detonation Experiments 20

3.2 Empirical Calculation of TNT Equivalency 24

3.3 General Considerations of Vapor Phase

Detonations 28

3.4 Deflagration Explosions 37

3.5 Summary of Controlled Experimental Results 40

4 TNT EQUIVALENCY OF ACCIDENTAL VAPOR CLOUD

EXPLOSIONS 42

4.1 History 42

4.2 Flixborough, England Industrial Process

Accident 43

4.3 Franklin County, Missouri PipelineRupture 47

4.4 East St. Louis, Illinois Rail Tank Car

Accident 47

4.5 Decatur, Illinois Rail Tank Car Accident 51

4.6 Houston, Texas Rail Tank Car Accident 53

4.7 Summary of.Accident Analysis Results 53

5 CONCLUSIONS AND RECOMMENDATIONS 55

5.1 Conclusions 55

'5.2 Recommendations 57

REFERENCES 59

iv
LIST OF FIGURES

1 Pressure-quality curve for propane showing ideal

and actual expansions 4

2 Momentum release per pound of fuel and tank dump

time versus temperature 4

3 Loading response curves for a reactor building

wall element as a function of peak overpressure

and impulse 13

4 Asymmetric isodamage (.APs=constant) curve 19

5 Half surface-space blast asymmetry model 19

6 Peak overpressure-energy scaled distance for vapor

phase and TNT detonations 26

7 Energy scaled static impulse-distance for Kogarko

vapor phase and TNT detonations 29

8 Theoretical energy partitioning of fuel-oxygen

explosions (methane) 32

9 Overpressure-distance of fuel-oxygen hemisphere

detonations scaled by mass Of blast equivalent

stoichiometric mixture 36

10 Spherical blast effects of deflagrations in fueloxygen mixtures 38

11 Deflagration kinematics for Woolfolk and Ablow

combustion tests 39

12 Flixborough damage data points 44

13 Flixborough data points and range of TNT energy

equivalency on log-log plot 44

14 Explosion area at East St. Louis accident 49

15 East St. Louis isodamage map 50

16 NTSB Report NTSB-RAR-75-4 damage to Lake View

School, Decatur, Illinois 52

17 Explosion area of Houston accident 54

18 Estimated standoff distance of nuclear plant as

function of potential combustible material involvement for 1 psi blast overpressure 58-

v
LIST OF TABLES

Page

1 Heat of Combustion of Combustible Gases Involved

in Vapor Cloud Accidents 17

2 Spherical Detonations of Methane-Oxygen 22

3 Hemispherical Detonation of Propane-Oxygen 23

4 Spherical Detonations of Hydrogen-Oxygen-Nitrogen 25

5 Hemispherical Detonations of Propane-Oxygen 35

vi
IITRI Final Report J6405

ACCIDENTAL VAPOR PHASE EXPLOSIONS

ON TRANSPORTATION ROUTES NEAR NUCLEAR PLANTS

1. INTRODUCTION

Vapor clouds consisting of a hydrocarbon-air mixture have

formed and exploded following accidents in the transportation

of potentially explosive cargo. In order to determine safe

standoff distances so nuclear power plants are not endangered

by this type of accident, it is necessary to estimate their

potential blast effects realistically and with confidence.

This can be accomplished in an efficient manner if the concept of TNT equivalency can be shown to be relevant and a proper

methodology developed. It is the objective of the present study

to examine the nature of accidental vapor cloud explosions,

develop a properly defined concept of TNT equivalency, calibrate

it from the available controlled test data, and evaluate its

significance against accidental blast damage data.

1.1 Background

Vapor cloud explosions are violent deflagrations or detonations that release their energy of chemical reaction to the surroundings in a manner that generates substantial overpressure

and causes blast damage. This type of explosion involves incredibly complex phenomena ranging from the chemical kinetics

of the energy release and turbulent flame propagation to the air

mixing dynamics of two-phase flows and atmospheric dispersion.

The accident environment ensures that a very large number of

variables will be involved such that, if it were desired to experimentally test accident scenarios to develop an adequate statistical

base, the number of experiments required would be impossibly large.

Thus, the very existence of accidental vapor cloud explosions represents their significance as a major hazard.

The probability of a vapor cloud explosion on a transportation route near any particular site is, however, very small.

Davenport (1) in a recently completed compilation of confirmed

1
vapor cloud explosions lists seven rail tank car and three tanker

truck incidents in which significant overpressures were created.

Documentation by the National Transportation Safety board exists

for the last three tank car incidents occurring in 1972 and 1974.

Numerous other vapor cloud incidents have been documented

for spills from pipelines, storage tanks, and, mostly, industrial

process vessels or equipment. Vessel failure accounts for nearly

two-thirds of transportation releases compared with only about

one-third overall, the remainder being mostly piping, valve, or

fittings failures. Davenport (1) lists 33 such confirmed explosions and 17 vapor cloud incidents in which overpressures were

not created. Strehlow (2) lists 69 explosions out of 108 vapor

cloud ignitions of combustible material.

Accident analysis of vapor phase blast effects has been pioneered by Brasie and Simpson, Burgess, Strehlow, Brinkley and

others. In spite of their excellent work, however, there exist

substantial inconsistencies and false impressions with regard to

vapor cloud explosions. For example, Brasie and Simpson (3) used

the overpressure-distance curve for a nuclear energy release as

their reference damage relation. This inconsistency results in

TNT equivalence values almost 100% larger than those corresponding

to the TNT curve.

Thus, a rational basis for evaluating the damage potential

of accidental vapor phase explosions must be established in order

to apply the existing knowledge to a successful regulatory process.

This basis must also provide a quantitative understanding of

inherent limitations and margins of error.

1.2 Accident Conditions

The ultimate goal of the accident hazard evaluation is to

estimate the probability of occurrence of a vapor cloud explosion having given blast effects at a given site. Thus,

P(specific blast effects at specific site)

P(specific blast effects/vapor cloud explosion

at specific site)

x P(vapor cloud explosion at specific site)

2
The last probability is extremely low whereas the conditional

probability relates to the nature of vapor cloud explosions and

is of concern in the present study.

The probability of achieving specific blast effects is essentially one of determining the nature of the energy coupling to the

mechanisms that produce these specific effects, both symmetric

and asymmetric. The primary accident conditions controlling the

explosive energy release and blast energy coupling are

" material involvement

" ignition-explosion process

" topographical and meteorological conditions

1.2.1 Material Involvement

Only the material released to the atmosphere prior to an

explosion event can be potentially involved in the energy release.

The spill rate depends on the tank conditions, material properties,

ambient temperature, and rupture size. For a pressurized liquid,

flash vaporization rates and the initial momentum of the spill

can be readily estimated. Hardee and Lee (4)* show for a specific

case that flash vaporization of liquid propane results in 30% of

the total mass in a vapor phase after isentropic expansion; this

is compared in Figure I with an experimental release having a

final quality of 27% vapor phase.

Initial momentum releases for several pressurized liquids

are shown in Figure 2. This momentum is released very rapidly,

in about a quarter of a second for propane. it should be noted

that liquid propane at 70°F generates an initial spill velocity

of about 400 miles per hour. Applying continuity and momentum

requirements to the expansion process gives the tank dump time

in terms of the contents and rupture size.

td= (a W (1.1)

d Ptank P atm )Ar

* Their calculations for cloud growth contain several apparent

inconsistencies; therefore, only the information presented

here is used from their report.

3
0.3

4IJ

0

4 1

0

(.0

4-3

4ýJ

01

0.2

0.1

0

0

Figure

20

1

40 60 80 100 120

Pressure (psi)

Pressure-quality curve for propane

showing ideal and actual expansions (4)

1000

4-4

4.J

.005 '3

a) o0 4 -4

4-1

.003 $

.002

.001 2 -

E-4

500

0 L

-50 0 50 100 150

Temperature (0 F)

Figure 2 Momentum release per pound of fuel

and tank dump time versus temperature (4)

4
where W = tank contents (ibs)

Ptank tank pressure (psi)

= momentum release per pound of fuel (ft-lb/sec/lb)

td = tank dump time (sec)

A = rupture area (ft 2 )

Normalized tank dump times for several materials are given

in Figure 2. As an example, assume a tank car cargo of 150,000

pounds (30,900 gallons) of liquid propane at relatively warm temperatures. The tank dump time as a function of rupture area is,

from data in Figure 2, given as

td = 180/Ar (1.2)

Thus, the contents would be completely released in 10 minutes for

a 7k inch diameter puncture hole, corresponding to a spill rate

of 3090 gallons per minute, and in just 1 minute for a 231⁄2 inch

hole"* The release of pressurized propane can, therefore, be

very rapid and about 25% to 30% of the spill appears almost

immediately in the undiluted vapor phase. The remaining 70%-75%/

exists as a fine spray of liquid droplets.**

As this two-phase mixture is turbulently mixed with entrained

air, liquid droplets are heated and vaporize.*** It requires the

heat capacity of about 9 pounds of ambient air to vaporize 1 pound

of liquid propane at its boiling point, -42°C. Thus, 1 pound of

pressurized propane will give a vapor phase-air mixture of roughly

13%/ by weight, 97, by volume, propane at -42*C. This mixture is

about one-third denser than surrounding ambient air at 68°F.

• Using the formula given by Brasie (5) for the combined weight

flux of vapor and liquid yields a release rate for propane

over twice the values computed from equation 1.2.

*** This spray is apparently ignored by Jungclaus (15) as contributing to the vapor cloud material involvement.

•.** Not all of the liquid droplets will, of course, form vapor

or spray; Kletz (6) suggests using an amount equal to the

adiabatic flash, but thi.s is a nonsupported estimate.

5
The major conclusions to be inferred are that, for hydrocarbon materials having a high vapor pressure and low boiling

point and'stored under pressure, the spill mechanism tends to

" promote rapid mixing of large portions of the

available fuel,

" produce fuel-air mixtures in the vapor phase close

to the upper explosive limit,

* generate a negatively buoyant vapor cloud due to

the low temperature of the fuel-air mixture and

the weight of the hydrocarbon molecules which

strongly influences its subsequent convective

dilution.

1.2.2 Ignition-Explosion Process

Ignition in an accident environment can be expected to occur

near the cloud boundary by the first source encountered by gases

within the flammability limits. The proximity of the ignition

source, therefore, controls the size of the vapor cloud and influences the magnitude of the explosion.

Although accident and tank puncture mechanisms can be expected

to produce ignition sources near the spill source, and immediate

combustion has been observed in many accidents, the close-in rich

mixture concentration, high flow velocity;, and low temperature

provide favorable conditions for vapor cloud growth. If no ignition source is found, the vapor will ultimately disperse harmlessly

into the atmosphere. A study of rail tank car accidents (see

Section 4.1) indicates that ignition is more likely to occur than

no ignition.

Since the cloud seeks an ignition source as it expands, ignition is very site-specific with the probability of ignition-increasing and probability of continued material involvement decreasing

as the cloud grows. It can also be expected to be significant with

respect to asymmetrical blast effects, but results are not available to determine the relationship.

The blast effects of a vapor cloud explosion are highly

dependent on the mode of combustion. Whereas Geiger (7) states

6
that the probability of the detonation mode occurring is very

low, Davenport (1) lists twice as many vapor cloud ignitions

creating significant overpressures as those that did not. Also,

Strehlow's (.2) data can be similarly interpreted. Thus, either

detonation or overpressure producing deflagration appear to have

the highest probability of occurrence. The quality of available

accident data unfortunately does not allow us to establish the

exact nature of the energy release and blast coupling mechanism.

The transition from slow combustion to rapid deflagration or

detonation is a likely vapor cloud explosion scenario. It is

interesting to note here the following description from the NTSB

report (8) on the 1972 East St. Louis, Illinois incident.

"Flames were first observed at or near an unoccupied

caboose standing on Track No. 19. The flames progressed westward toward Track No. 25 and eastward

toward Track No. 15. An orange flame then spread

upward, and a larger vapor cloud flared with explosive force. Estimate of the time lapse between these

occurrences range from 2 to 30 seconds. Almost immediately thereafter a second, more severe explosion

was reported".

This almost certainly describes just such a transition. A

very elongated vapor cloud formed, since the spill source was

moving, which most probably accounts for the apparent double explosion (it is easy to visualize a concentration discontinuity in

this type'of cloud geometry). If the two explosions occurred soon

enough together, their blast waves would have Coalesced!

A detonation wave represents a stable state of combustion

characterized by a subsonic flame propagation relative to the

precompressed unreacted gas equal to the detonation velocity relative to the ambient gas. A minimum amount of hydrodynamic energy

must be available to support its propagation. Similarly, the

propagation of any combustion wave requires hydrodynamic energy

to support it, and this energy can only come from the ignition

source or the chemical reaction.

7
Flame acceleration is readily observed in all detonable fueloxygen mixtures; however, Kogarko (9) using centrally ignited

balloons reports no discernible flame accelerations in air mixtures

of acetylene, propane, and methane. Therefore, it is important

to consider what conditions in the accidental vapor cloud environment are capable of generating flame accelerations.

Lee (10) formulated a criterion for self-initiation which

illustrates the relative ease with which mixtures can attain the

autoignition limit corresponding to detonation. Taking the chemical energy release per unit mass as 2 to 1 for hydrocarbon-oxygen

to hydrocarbon-air mixtures, the turbulent flame speed for selfinitiation of the air mixtures is about 755 fps compared with 215

fps for the oxygen mixtures. Therefore, an amplification factor,

the ratio of the critical turbulent flame speed to the characteristic laminar flame speed, is 460 for air mixtures and 6 for oxygen

mixtures using typical laminar speeds of about 1.6 fps for fuel-air

and 32.8 fps for fuel-oxygen. For acetylene and hydrogen-air

mixtures, the amplification required is about 150.

Thus, not only are self-accelerating mechanisms present in

fuel-oxygen mixtures as a result of their energy density, but the

transition to detonation occurs with relative ease due to their

low critical turbulent flame speed. Just the opposite is true

for fuel-air mixtures, however, and very large flame accelerations.

must take place. It should be noted that even if transition to

detonation does'not take place, the very high flame speeds permissible in fuel-air mixtures greatly increase the rate of energy

release and, therefore, the propensity to generate blast effects

in the surroundings.

In the absence of a strong ignition source, the only mechanism

for making hydrodynamic energy available for an accelerating flame

propagation is through the boundary conditions. Boundary effects

are extremely complex, involving wave interactions and turbulent

flame structures, and only the gross effects of simple boundary

geometries have been successfully investigated.

8
Several general observations can be made on the effectiveness

of the boundary conditions in providing hydrodynamic energy to an

accelerating deflagration wave. The compression wave interactions

are strongly influenced by boundary geometry. Coalescence of

these reflections with the deflagration accelerates it, producing

stronger pressure pulses which are again reflected, and so on.

As the deflagration accelerates it becomes turbulent, and as the

intensity of the turbulence increases, larger amounts of hydrodynamic energy become available at the deflagration. In general,

the rate of acceleration is slow at the lower velocities and

extremely rapid just prior to detonation.

It is possible for some of the energy released by the early

deflagration to be coupled to the blast wave by the following

mechanism. As the detonation moves through the unreacted but

energetic gas, its strength increases above the normal detonation

level thereby recapturing and making available some of the early

energy release.

In the accident environment complex boundary effects are

provided by structures and the ground. Thus, not only are complex wave interactions and turbulent deflagrations likely, but

local volumetric explosions induced by radiative or shock focusing

are a distinct possibility. Locally confined combustion can induce a

detonation wave in the cloud provided that a propagating detonation wave is

established during the partial confinement.

1.2.3 Topographical and Meteorological Conditions

Site specific factors of terrain and atmospheric conditions

have a variety of effects on a vapor cloud explosion. Thus, the

universal observation is made that if a particular accident had

occurred at a different place, or different time, it could have

been either much worse or not as bad.

In addition to the boundary effects on the combustion process,

the local terrain influences the vapor cloud formation since the

cloud is heavier than air and tends to hug the ground. In the

9
case of the £970 Franklin County, Missouri (11) pipeline rupture,

the propane vapor cloud flowed downhill into a shallow valley

and slowly filled it. The valley in effect formed a huge container

for the vapor cloud although ignition was delayed 24 minutes until

a source 1500 ft from the rupture was reached.

Atmospheric conditions have a profound influence on both the

nature of the vapor cloud explosion and the resulting blast effects.

Unfortunately, quantitative evaluation of the phenomena involved

is subject to extremely large error at the present time. Burgess,

et al (12) points out three basic difficulties in applying simple

air pollution type dispersion models:

" Measurements of statistical correlation coefficients

are made at low concentrations and far from the source.

" Dispersion models relate average concentrations over

extended time periods.

" Vapor clouds are heavier than air thereby suppressing

the vertical dispersion.

Other more general difficulties are:

" Gaussian type diffusion models are essentially spacetime averaged curve-fitting techniques that do not

account for the relative importance of the mechanisms

involved.

" The dispersion is strongly influenced by site-specific

factors, especially for negative buoyant clouds.

" The source conditions are not simple, either a very

intense flow at the spill or a complex volume source

of large size after the spill momentumbecomes small.

" Deterministic dispersion models are not far enough

advanced at the present time.

As an example of these observations, Burgess and Zabetakis (13)

estimated the flammable material involvement for the previously

mentioned pipeline rapture using a standard dispersion model. In

this case, a relatively low flow rate, continuous source spilled

liquid propane under known atmospheric conditions (a temperature

inversion was present). Their results indicate that the dispersion

model is capable of predicting the TNT equivalent yield to within

about half the value obtained from knowledge of the explosion

damage-distance data.

10
However, they assumed that the blast energy of the material

involved equals the detonation energy release. This is not the

case as will be shown later, and a better value is about 20% of

the materials's heat of combustion. Using the correct value of

blast energy, the dispersion model would predict blast effects

an order of magnitude less, i.e., at only about 10% of the TNT

equivalent yield established by the damage data.

Several common characteristics of vapor cloud explosions

must be remembered when applying notions of atmospheric dispersion.

The entire process from rupture to ignition is relatively fast,

on the order of minutes, for such large quantities of material.

Initial mixing by air entrainment and convection is capable of

producing only slightly rich mixtures under favorable circumstances.

The vapor cloud is heavier than air and, therefore,.has its own

flow properties.

Atmospheric diffusion mixing rates tend to decrease as the

concentration decreases. Dispersion of an already jet mixed

vapor is required over at least one order of magnitude of dilution before a large part of the cloud is below the lower flammable

limit. For a time then, atmospheric dispersion would tend to

favor the growth of a large material involvement.

Meteorological conditions tend to produce strong directional

effects resulting from the vapor cloud geometry which tends to

be elongated in the wind direction. This type of asymmetry is

peculiar to vapor cloud explosions and is of major importance

since it is a space effect. It should be noted that most large

accidental vapor cloud explosions are asymmetric.

A second type of asymmetry, common to all explosions, is

reflection of blast energy to the ground by atmospheric conditions,

most notably a temperature inversion. This effect produces localized caustics where the blast damage can be an order of magnitude

higher than the spatial propagation of energy would give.

11
1.3 Approach

The approach of the present study is to conduct a technical

review of the literature pertinent to vapor cloud explosions and

including accident reports, experimental data, and theoretical

models to establish criteria and a methodology for estimating TNT

equivalency.

TNT equivalency is widely used to related specific blast

effects of specific energy source types. For vapor cloud explosions, a generalized concept of TNT equivalency is implied since

specificity is lacking. Partly because of this and partly because

of a lack of information, considerable disagreement presently

exists in the application of TNT equivalency to the estimation of

potential blast damage resulting from accidental vapor cloud

explosions.

It has been suggested by the U.S. Nuclear Regulatory Commission

that a TNT mass equivalency of 10% be used to determine safe standoff distances from nuclear plants. The West German Reactor Safety

Commission guideline uses a 50% TNT mass equivalency for gases

liquified under pressure, 100% for hydrocarbons with carbon-tocarbon triple bonds or cumulated carbon-to-carbon double bonds

(e.g., acetylene), and 100% for nonliquified gases.

Estimates of TNT equivalency by various investigators in this

field vary even more widely. The Bureau of Mines (3) suggests the

energy release is 10% of the calorific energy content of the material released in 30 seconds. Bulkley and Jacobs (3) suggest an

equivalency for hydrogen of 10 pounds of TNT per pound of hydrogen

while Bradford (3) reports a deliberate hydrogen explosion of 0.3

pounds of TNT per pound of hydrogen. Strehlow (14) implies that

a 10% TNT energy equivalency is a more probable upper limit for

accidental explosions. Kletz (6) suggests a TNT energy equivalency

of 1% by arguing that a 10% energy yield of a 10% material involvement is a realistic scenario. Geiger (7) gives an equivalency

12
of 4 pounds of TNT per pound of hydrocarbons as the explosive

potential of hydrocarbon vapor clouds which is widely quoted in

the West German literature as by, for example, Jungclaus (15).

Lee (16) recently completed a study in which he computed the

blast energy necessary to produce the same airblast as observed

experimentally for hydrocarbon-air detonations. He found that the

blast energy is about 20% of the calorific energy which translates

directly into TNT energy equivalency. In general then, estimates

of TUT equivalency range from a fraction of a percent to the

theoretical energy content of the material.

The approach taken herein is to establish TNT equivalency at.

the 1 psi blast overpressure level for accidental vapor cloud

explosions, near nuclear plants. Geiger (7) presents results of

structural response calculations for the blast loading of a

specific wall of a reactor building, shown in Figure 3. At the

1 psi level, the structure is sensitive to diffraction loading

and insensitive to impulsive loading. Although no general conclusions can be drawn, this case is assumed here to be representative

of nuclear plants, and, therefore, the customary practice of calculating TNT equivalency with respect to overpressure will be

followed.

5-1

0.-I

0

4-I

1 psi

i I I I ! I I I

Reflected impulse

Figure 3 Loading response curves for a reactor building

wall element as a function of peak overpressure

and impulse (7)

13
2. CRITERIA AND METHODOLOGY OF TNT EQUIVALENCY

The generally accepted definition of TNT equivalency is that

an arbitrary energy release is equivalent to a TNT explosion if the

same specific blast effects are produced. This is not a universal

concept but one that provides a parametric study of explosive effects

in terms of known and well-understood, reproducible, and scalable

explosions.

The converse of this statement, that is, predicting specific

blast effects from knowledge of the TNT equivalency, depends upon

the reproducibility and scalability of the explosion. Vapor cloud

explosions are known to be among the least reproducible and scalable

in accident and even controlled conditions. Therefore, a systematic

exposition of the TNT equivalency of vapor cloud explosions must

underlie its use in a safety and regulatory context.

2.1 Definition and General Criteria

TNT equivalency may be defined on either an energy or mass

basis, 'the latter yielding an immediate and unambiguous physical

interpretation. Energy equivalency is more basic in terms of the

blast mechanisms involved thereby permitting a generalized formulation of the class of hydrocarbon-air vapor cloud explosions.

Accordingly,

eTNTWTNT (2.1)

e eHCWHC

where eTNT and eHC are the energies per unit mass of the explosives,

WTNT is the equivalent TNT weight, and WHC is the weight of the

actual or potential hydrocarbon material involvement. Mass equivalency is given by

WTN eri

a W TNT HC ae (2.2)

m W HG e ýTNT e

Equivalency is established by choosing the value of WTNT on

the basis of equal specific blast effects. In general, TNT equivalency can vary with distance, the type of blast effects used to

establish equivalency, and among vapor cloud explosions depending

on their reproducibility and scalability.

14
The interpretation of a e depends on the values assigned to

the specific energies. Thus, if eTNT is the blast energy of TNT

and eHC the calorific energy content of the hydrocarbon fuel, ae

is a measure of the vapor cloud blast effectiveness for specific

blast effects. If e C is defined as blast energy, then ae provides

a direct measure of the scalability of vapor cloud explosions.

It is reasonable to limit the type of blast effects to peak

overpressure in calculating WTNT, for the reason stated in Section

1.3, i.e., the loading response of typical targets at low overpressure. In addition, the uncertainty in using corresponding

TNT impulse and dynamic effects is probably no greater than the

uncertainty in calculating them for vapor cloud explosions. For

certain types of deflagrations and at the higher overpressures

such as the 3 psi level (used by the West Germans in determining

safe standoff distances of nuclear plants), it may be necessary

to include blast loading effects beyond the diffraction cutoff time.

In the present study, TNT blast effects are represented by

the averaged peak overpressure-scaled distance data of Kingery,

et al (17) for hemispherical surface bursts. These data are welldefined, extensive, and scale well with other results for condensed explosives such as the Keefer data presented in the Distant Plain

report (18). Kingery does not provide corresponding energy data for his TNT,

and, therefore, an exact physical interpretation of TNT equivalency

is limited regardless of the choice of eTNT.

Thus, the customary valuation of eTNT as 1800 Btu per pound

of TNT is adequate. Consistency is the only criterion which is

satisfied if energy scaling of TNT blast effects is made with

respect to this value. It should be noted that this value is the

approximate blast energy of TNT which for condensed explosives is

also nearly equal to the chemical energy release upon detonation

(about 28% of the calorific energy content).

For a particular hydrocarbon-air explosion consistency in

the choice of eHC is also the major criterion. Obvious advantages

in the estimation of TNT energy equivalencies result, however, if

15
hydrocarbon-air explosions can be treated as a class independent

of the particular fuel through a suitable choice of eHC for each

fuel. Among the choices are the fuel's calorific heat of combustion, the energy release upon combustion, and the hydrodynamic

energy of the explosion products.

Calculations of chemical energy releases and blast energies

are exceedingly complex for air explosions and depend upon the

fuel-air concentration. Combustion and subsequent products expansion occurs at temperatures, about 2500°F to 45000 F, to which

dissociation processes are extremely sensitive. Furthermore, at

these low energy densities, the coupling of the available hydrodynamic energy of the explosion products to the blast wave is

complex. In general, making distinctions among different fuels

on the basis of these calculations would be subject to error of

the same order as the actual differences between the various fuels.

It is reasonable then to distinguish fuels on the basis of

their calorific energy content alone. This implies calorific

scaling of the energy partitioning of a vapor cloud explosion

which can be expected to introduce insignificant error compared

to the general scalability of these explosions. It has become

customary practice to use the low or net value of the heat of

combustion for this purpose since water vapor cannot condense at

these temperatures; appropriate values are given in Table 1 for

various combustible gases that have been involved in vapor cloud

accidents.

2.2 Asymmetric Model

Spatially asymmetric blast effects are unique to and commonly

observed in accidental vapor cloud explosions. Thus, the effective

blast energy in one general direction from the explosion may be

much greater than that in the opposite direction. It is presumed

that this type of asymmetry is associated with the cloud geometry,

location of the ignition source, and the nature of the explosive

combustion.

16
TABLE 1. HEAT OF COMBUSTION OF COMBUSTIBLE GASES

INVOLVED IN VAPOR CLOUD ACCIDENTSt

Material Formula Low Heat Value(Btu/ib)tt eHC/eTNT

Paraffins

Methane

Ethane

Propane

n-Butane

Isobutane

Alkylbenzenes

(CnH2n+2)

CH4

C2H6

C3H8

C4HI0

C 4111

(18,857-21,502) (10.48-11.95)

21,502

20,416

19,929

19,665

19,614

11.95

11.34

11.07

10.93

10.90

(17,259-17,984) (9.59-9.99)

Benzene C6 H6 17,446 9.69

Alkylcyclohexanes

Cyclohexane

Mono olefins

(CnH2n)

C6H1 2

(CnH2n)

(18,642-18,846) (10.36-10.47)

18,846 10.47

(19,214-20,276) (10.67-11.26)

Ethylene

Propylene

Isobutylene

Miscellaneous

Hydrogen

Ammonia

Ethylene Oxide

Vinyl Chloride

Ethyl Chloride

Chlorobenzene

.Acrolein

Butadiene

HC Groups(est)

C2 H4

C3 H6

C4 H8

20.276

19,683

19,367

11.26

10.94

10.76

H2

NH 3

C2H4 0

C2 H3 CI

C2H5 C1

C6H5Cl

C3H4 0 C 4H6

51,571

8,001.

11,482

8 239

8 246

11,754

11,830

20,200

19,000

28.65

4.45

6.38

4.58

4.58

6.53

6.57

11.22

10.56

tStrehlow (2) and Davenport (1)

ttChemical Engineers Handbook, 3rd edition, 1950; also Davenport (1)

17
A typical vapor cloud spatial blast pattern is shown in

Figure 4 as an isodamage curve at the ground surface, represented

by the peak overpressure, APs. equal to a constant. It is assumed

that other isodamage curves would scale similarly. The equivalent

TNT energy is found from the APs vs energy scaled distance, Ae2

curve for TNT at the given AP . Therefore, in terms of

E TNT (1) =(R 1 /X 3 •e

(2.3)

5(2) (R2/ 3

TNT 2 e

where R1 and R2 are the minimum and maximum isoblast radii, respectively. Letting ý = R2/RI, the degree of asymmetry,

E(2)/-(1) = 83 (2.4)

TNT TNT

These TNT equivalent energies are considered ideally to relate to

separate hemispherical blasts. Assuming that the actual explosion

is the net effect of the two blasts occurring in their respective

half surface-spaces shown in Figure 5, then each contributes half

of their hemispherical energies, and

=ETE(T + E(2)

TNT TNT 2 TNT

Since a e = ETNT/EIHC for symmetric blast effects,

e= 1⁄2( (I) + a(2)) (2.6)

where the e 's are the TNT equivalencies for the respective equivalent symmetric blast.

The maximum and minimum asymmetric TNT equivalencies and

nominal symmetric TNT equivalency are related, in terms of the

degree of asymmetry, by

= 1⁄2m(+ )mn i 

(2.7) = 1⁄2 i+83) max

18
where a is either mass or energy TNT equivalency. Alternatively,

amax/ 'cmin =_63 (2.8)

Release point

/

I

/

2

E (2)

TNT

Figure 4 Asymmetric isodamage (APs=constant) curve

Asymmetric limit, 2 ETNT

Observed maximum, E(2)

TNT

Figure 5 Half surface-space blast asymmetry model

19
3. TNT EQUIVALENCY OF CONTROLLED VAPOR PHASE EXPLOSIONS

The blast effects of controlled vapor phase explosions depend

upon the total energy release, rate of release, and energy density.

From theoretical analyses of ideal blasts, e.g., point source, uniform pressure, self-similar detonation, and piston-type deflagration,

among others, the influence of varied energy source conditions on

the blast wave can be computed.

A limited data base exists for these explosions but can be

used to establish ideal TNT equivalencies of hydrocarbon-air mixtures. The experiments consist of centrally ignited balloons of

various geometries having diameters from 1.5 to 62.5 feet.

3.1 Detonation Experiments

Blast data are obtained for tangent sphere, elevated sphere,

and hemispherical source geometries. In order to ascertain the

TNT equivalencies of these explosions, it is necessary to properly

scale the data with respect to energy.

Kogarko, Adushkin, and Lyarmin (9) conducted tangent sphere experiments

and found that the overpressure-distance data of various stoichiometric mixtures

fall into a fuel-oxygen or fuel-air class of blast effects when scaled by the low

value of their heats of combustion. They empirically represent

this result by the following equations:

APs A/X + B/X2 + C/X3, X = R/EI/3 > Xh

AP (3.1) s = D/XI 1. ' X 0 Xo< )' '

where AP is in psi and X in ft/Btu/3; the constants are given

i

in the table below:

20
Constant Fuel-Air Fuel-Oxv•en

Cos at Fuel-Air Fuel-Ox Ren

A 1.7685 1.9748

B 0.8552 1.0384

C 0.3165 0.4431

D 2.5527 3.3381

Xo0 0.166 0.104

.h 62 0.62

Measurements made within five balloon radii were at elevated locations and thereby represent free air or spherical blast effects

with no surface reflections; at larger distances, surface measurements were made and therefore represent hemispherical effects.

Solving Equations 3.1 at APs=1.0 psi gives X(air)=2.21 ft/

1/3S Btu and X(oxygen)=2.46 ft/Btul/ 3 . Thus, fuel-air detonations

are represented as Z7.5% less efficient in generating low overpressure blast effects than fuel-oxygen detonations.

Balcerzak, Johnson, and Kurz (18) detonated 10 ft and 13.5

ft diameter tangent spheres and a 32 ft diameter sphere at a 25 ft

height-of-burst. The experimental and scaled results of these

blasts are summarized in Table 2. It should be noted that the

overpressures are calculated from time-of-arrival data and, therefore, subject to basic errors of this procedure.

A 125 ft diameter hemisphere containing a 3.5 to I oxygen to

propane mole ratio was detonated as part of Operation Distant Plain.

Reisler's (19) results for this event are summarized in Table 3.

Since the mole ratio was not stoichiometric, it is necessary to

determine the proper calorific energy scaling. If the chemical

reaction goes to completion, then the energy content is represented

by simple stoichiometry calculations. However, rich mixtures can

yield a larger chemical energy release than stoichiometric mixtures

as shown by hydrodynamic detonation calculations including the

effects of dissociation. Thus, the calorific energy as used here

is the value associated with the total fuel mass to compensate

for these effects (the same approach is used for the Balcerzak,

et al data). A more detailed analysis of the etfect of stoichiometry on energy scaling is provided in Section 3.3.

21
TABLE 2. SPHERICAL DETONATIONS OF METHANE-OXYGEN (18)

Gas mixtures: 1.5:1 and 2,0:1

Ambient pressure: 13.4 psi

Experimental configurations:

0 2 - CH 4 mole ratios

Mole Est. mass Sach's scale

Test Diam(ft) H.O.B.(ft) ratio of CH 4 (lb) factor(Btu- 1 / 3 )

A 10 tangent 1.5:1 8.0 1.746(10-2)

B 10 tangent 2.0:1 6.6 1.856(10-2)

C 13.5 tangent 1.5:1 19.6 1.293(10-2)

D 32 25 1.5:1 260.9 5.456(10-3)

A P (psi) R(ft) X AP (psi) R(ft) X As (pi ~ t e s ,e

A 76.1

57.1

35.9

23.5

12.2

7.2

B 62.3

34.0

22.0

12.2

8.6

9

12

16

20

28

36

12

16

20

23

36

0.157

0.210

0.279

0.349

0.489

0.629

0.223

0.297

0.371

0.520

0.668

C 86.9

55.4

37.6

20.0

12.5

D 59.0

48.9

40.0

34.0

29.3

21.4

11.4

3.4

12

16

20

28

36

40. 3

45.0

50.4

55.2

60.0

70.4

100.0

201.1

0.155

0.207

0.259

0.362

0.465

0.220

0.246

0.275

0.301

0.327

0.384

0.546

1.097

* Ae - (ft/BtuI/3)

22
TABLE 3. HEMISPHERICAL DETONATION OF PROPANE-OXYGEN (19)

Gas mixture: 3.5:1 02-C 3H8 mole ratio

Ambient pressure: 13.71 psi

Balloon: 125 ft diameter hemisphere

Est. mass of C3H8: 12,000 lb

Sach's scale factor: 1.56(10-3) Btu-i/ 3

AP (psi) R(ft) X (ft/Btu1 / 3 )

178

47

35

36

35

22

23.2

22.5

16.5

15.6

11.7

7.2

4.0

3.1

1.8

0.36

71

116

156

156.3

160.8

201

202.2

213.4

250

250

295

382

564

678

998

4190

(10)*

(30)

(22)

(52)

0.111

0.181

0.243

0.244

0.251

0.314

0.315

0.333'

0.390

0.390

0.460

0.596

0.880

1.058

1.557

6.536

* Instrument elevation (ft)

23
The data of Woolfolk and Ablow (20) for spherical detonations

of hydrogen-oxygen-nitrogen balloons is summarized in Table 4.

Two balloon diameters, 3.0 ft and 5.25 ft, were used for 0%, 10%

and 20% nitrogen dilutions; the effect of these dilution levels

on detonation overpressures is small.

Figure 6 is the overpressure-energy scaled distance plot of

this experimental data. Also shown is the energy scaled TNT data

of Kingery for eTNT=1800 Btu/pound ot TNT. Superimposed on the

fuel-oxygen data are the hemispherical and corresponding spherical

TNT curves translated to fit the Kogarko fuel-oxygen curve at the

lower overpressures. Two important results are immediately seen

from this figure. The first is that the only fuel-air data are

that of Kogarko, and the second being the excellent general agreement of the fuel-oxygen vapor phase data with the translated

TNT data.

With respect to the latter result, the following observations

are made: (1) at the lower overpressures, below aboul 10 psi, the

spherical and hemispherical vapor phase and condensed phase explosions produce the same shock decay consistent with the point made

by Brinkley (21) and others that the details of the source conditions become unimportant at large distances; (2) the tangent sphere

data lie between the two limiting cases at the higher overpressures

and approach the hemisphere case as distance increases (except for

the elevated sphere where the Mach stem region is seen); and (3)

close-in, the data do not follow the TNT decay shape; in this region

source conditions are important and scaling by total energy is not

valid except as a parametric reference of blast effects.

3.2 Empirical Calculation of TNT Equivalency

The TNT energy equivalency of vapor phase explosions can be

computed from the experimental data. Note that the only hydrocarbonair data are that of Kogarko, et al for small balloons. Although

ae is approximately constant with distance at the low overpressures,

24
TABLE 4. SPHERICAL DETONATIONS OF HYDROGEN-OXYGEN-NITROGEN (20)

Gas mixtures: stoichiometric H2-0 2 with 0%, 10%, 20% N2 dilutions

Ambient pressure: 14.37 psi

Experimental configurations:

Sach's scale

Shot Radius(ft) N2 (%) AHLC(Btu/lb mixture) factor(Btu-I/ 3 )

26 1.493 0 5775 0.0732

27 1.483 10 4568 0.0761

31 1.503 20 3659 0.0789

36 2.625 0 5781 0.0401

35 2.592 10 4593 0.0415

AP (psi) R(ft) X e AP (psi) R(ft) e

26

5.9

6.3

2.0

0.94

0.81

27 19.1

6.0

6.0

1.9

0.96

0.82

31 20.8

5.9

5.9 2.0

0.99

0.75

4.63

9.19

9.29

15.72

26.94

29.86

4.63

9.19

9.29

15.72

26.94

29.86

4.63

9.19

9.29

15.72

26.94

29.86

0.34

0.67

0.68

1.15

1.97

2.19

0.35

0.70

0.71

1.20

2.05

2.27

0.37

0.73

0.73

1.24

2.13

2.36

36 20.5

15.4

10.1

2.1

1.7

1.2

7.19

8.92

11.75

26.67

29.66

35.53

7.19

8.92

11.75

26.67

29.66

35.53

35 21.5

16.9

11.6

2.2

2.0

1.2

0.29

0.36

0.47

1.07

1.19

1.43

0.30

0.37

0.49

1. 11

1.23

1.47

* Xe - (ft/Btu 1/3)

25
100

TNT hemisphere

(translated)

50

TNT (Kingery)

TNT sphere

'- (translated)

U)

P4

p-4

0.

0)

'-4

Fuel-oxygen

(Kogarko)

10

5

Fuel-air

(Kogarko)

0

0

V

Fuel-oxygen data

125 ft hemisphere(3.50 2 :1C 3H8 )

10 ft sphere(l.502 :iCH4 )

10 ft sphere(2.002 :ICH4 )

131⁄2 ft sphere(l.502 :1CH4 )

32 ft sphere(l.502 :iCH4 )

3,51⁄4 ft spheres(1⁄202 :iR 2 -no N2 )

3,51⁄4 ft spheres(1⁄202 :iH 2 1.0 -10%,20% N2)

0.1 0.5 1.0 5.0

Scaled distance, X (ft/Btul/3) e

Peak overpressure-energy scaled distance

for vapor phase and TNT detonations

Figure 6

26
the computation will be made specifically at the 1 psi peak overpressure level. Thus, at APs =1.0 psi,

X e(fuel-oxygen) = 2.46 ft/BtuI/3 (Kogarko)

X efuel-air) = 2.21 ft/Btu1 /3 (Kogarko)

X e(TNT) = 3.74 ft/BtuI/3 (Kingery)

From Equation 2.1 and the definition of X,

ae = 0 HC/ATNT) 3 (3.2)

and, therefore,

"e (fuel-oxygen) = 28.5% (3.3)

" e (fuel-air) = 20.6%

These results are consistent with the previously defined criteria

of TNT equivalency and, in particular, the use of the low value

of the heat of combustion since Kogarko's data is based on this.

Applying this result to Equation 2.2 yields the TNT mass

equivalency for hydrocarbon-air vapor phase explosions,

am(fuel-air) = 0.206 erHC (3.4)

eTNT

and a value representative of methane and propane is

am = 2..4 (240%)

In general,

a m = i.144(10- 4 )AHLC (3.5)

where AHLc is the low calorific heat in Btu per pound of fuel from

Table 1. Some valuations of interest are given:

Material TNT mass equivalency (°)

Methane 246

Propane 228

Propylene 225

Isobutane 224

Ethylene 232

Butadiene 231

27
As an example, 1 pound of propane is equivalent to 2.28

pounds of TNT for the same low overpressure symmetric blast effects.

Using the 1972 East St. Louis, Illinois rail tank car accident as

an example of asymmetric effects, B = 2.25, and for a detonative

average equivalency of 228%, the maximum and minimum mass equivalencies would be

Smin = 0.37 lb TNT/lb C3 H8

Ctmax = 4.19 lb TNT/lb C3 H8

A degree of asymmetry of B = 1.5 would give

(min = 1.04 lb TNT/lb C3 H8

max = 3.52 lb TNT/lb C31H8

Thus, the maximum TNT equivalency is quite sensitive to asymmetric

detonations of vapor phase mixtures.

The general applicability of overpressure TNT equivalency to

waveform effects can be seen from the overpressure impulse data of

Kogarko and Kingery, shown in Figure 7. Taking X = 2.5 ft/BtuI/3

e

as typical of the 1 psi overpressure region, the corresponding

vapor phase impulses can be scaled to their TNT equivalents from

TNT e o 1/3I(3.6)

I TNT = l°1/3e

ee

where a e and V0 are 0.206 and 0.079 psi-msec/Btul/ for air and

0.285 and 0.079 psi-msec/BtuI/ 3 for oxygen. The resulting general

agreement is apparent from Figure 7.

3.3 General Considerations of Vapor Phase Detonations

Limited theoretical considerations of vapor phase detonations

are of interest to put the empirical information of the preceding

sections in a better perspective. In particular, the partitioning

of energy, the effect of mixture composition, and the very important effects of source energy density and deposition rate will

be discussed.

28
1.0

en

U

Q)

C')

41

En

0.5

0.1

0.05

0.5 1.0 5.0

Scaled distance, X (ft/BtulI/3) e

Figure 7 Energy scaled static impulse-distance

for Kogarko vapor phase and TNT detonations

29
The calorific energy content of a fuel is released only if

the reaction goes to completion, i.e., water vapor and carbon

dioxide as the final combustion products. At the reaction temperatures of detonation, the chemical kinetics of dissociation

must be included in the hydrodynamic theory. The actual energy

release will, therefore, be some fraction of the calorific value

depending principally on the carbon monoxide formed (the heat of

formation of CO is 28% of that for C02 ).

The available hydrodynamic energy per unit mass of mixture

can be computed as

EH = W+EKE-ED (3.7)

where fv

W Pdv = expansion energy Vcj

EE 1⁄2uj2 EKE c - kinetic energy (3.8)

ED =1⁄2(P cj+P )(Vo-Vc.) = detonation compression energy

and the subscript cj indicates the Chapman-Jouget detonation conditions. This formulation is useful because it does not depend

on empirical data such as final cloud size and can be readily

computed since the detonation state does not vary as it propagates.

Assuming perfect gas behavior of the explosion products and an

isentropic expansion,

P = Pcj (v cj/V)Y (3.9)

and, therefore,

W= P c [T (-) /7)P (3.10)

Using the theoretical results of Johnson (18) for the detonation of various mixtures of methane and oxygen and a value of Y=1.24,

the following results are obtained as a function of the oxygen to

methane concentration ratio, ý (all energies are written as Btu per

pound of gas mixtures):

30
EH

AHLC Released EH EH (.%

LC Energy

1.0 3593 2466 1497 41.7

1.2 3805 2848 1578 41.5

1.5 4043 2790 1500 37.1

2.0 4313 2556 1323 30.7

2.5 3594 2350 1189 33.1

3.0 3081 2180 1084 35.2

Figure 8 is a plot of these data. Computing Xe at APs=1.8 psi

for the Distant Plain results in Table 3 in terms of the calorific

energy yields a e = 41.8%. Interpreting the ratio EH1 /AHLC as the

effective blast energy, and similarly interpreting cef excellent

general agreement is obtained. (It should be remembered that a e

is for propane-oxygen.)

Thus, for stoichiometric fuel-oxygen vapor phase mixtures,

about 60% of the fuel's calorific energy content is released and

about 50% of that is available as blast energy. About half of

the released energy remains in the products as residual heat. From

the theoretical values of detonation pressure and propagation

velocity computed by Kogarko, et al, values of EH/AHLC equal to

28.6% for methane-oxygen and 29.3% for propane-oxygen are obtained.

Similar calculations for air mixtures of methane, propane,

and acetylene can be made from Kogarko's values at the C-J state.

The resulting values of EH/AHLC are about 50% for hydrocarbon-air

mixtures, considerably higher than for oxygen mixtures. This is

not surprising since more chemical energy will be released at the

lower detonation temperatures. Using

'nt 1 - P0 (-)y(3.11)

as an approximate measure of thermal efficiency, then

48.5% for CH4 -0 2

nth {42.2% for CH4-air

31
dl

0

4-4

C.)

5000

4000

3000

2000

1000

0

1.0

Heat of combustion (low value)

Available hydrodynamic energy

2.0 3.0

Figure 8

Gas mixture mole ratio, moles 02: moles CH4

Theoretical energy partitioning of fuel-oxygen

explosions (methane)

32
Thus, consistent with the second law of thermodynamics, fuelair detonations make available a smaller proportion of their total

energy release as hydrodynamic energy, about 13% less, than fueloxygen detonations. Evaluating EH from equations 3.7 to 3.10 and

using the values of fth given above, approximate values of the

chemical energy released upon detonation can be computed.

(energy released) = 633% for CH4-O2

87.4% for CH4 -air

Therefore, fuel-air detonations release about 38% more chemical

energy than fuel-oxygen detonations, consistent with the chemical

kinetics of detonation combustion.

What is surprising is that less than half of the theoretically

available hydrodynamic energy appears as energy driving the air

shock based on the empirical calculations of ae" Kogarko, et al

relate the blast inefficiency of fuel-air compared to fuel-oxygen

detonations to their three to four difference in energy density.

Since, however, the energy deposition rate does not scale directly

with energy, it is possible that cloud size may be a factor through

the detonation velocity or some other mechanism.

It should be mentioned that Lee (16) has computed the effecctive blast energy as about 20% for fuel-air and 25% for fuel-oxygen

detonations. But his approach was to simply fit the Kogarko data

to the airblast calculation theory of Brinkley (21) by varying the

initial condition on the blast energy. Thus, this agreement sheds

no additional light on the efficiency of fuel-air explosions.

As mentioned in Sections 2.1 and 3.1, it is difficult to

assign an explosion scaling quantity on an a priori basis, especially for estimating accident conditions. In principal, a measure

of blast energy relative to specific blast effects would seem to

be the more universal' concept of a scale factor.

This energy concept can be approximated by the available hydrodynamic energy for the purpose of computing relative effects of

known explosions. Thus, it is possible to directly compare the

hemispherical detonations of the propane-rich oxygen mixtures used

33
in Distant Plain with the stoichiometric TNT equivalency of

accidental explosions and, in particular, with the stoichiometric

data of Kogarko, et al.

Since the stoichiometries of the gas mixtures are known, and

theoretical Chapman-Jouget detonation states including dissociation

have been computed by Johnson (33), Equations 3.7 to 3.10 can be

evaluated for the actual gas mixture (A) and a stoichiometric gas

mixture at the same ambient conditions (B). Using the hemisphere

test data for Event 2a, a 125 ft diameter balloon, and Shots 2 and

6, 17 ft diameter balloons, for which C-J data are available, the

following results are obtained (for y-=1.24):

Diam. -Mole ] (A) E(B)

Shot (ft) Ratio Po E.H. E H

2a 125 3.5 40.0 1409 1202

2 17 3.24 40.9 1418 1183

6 17 3.12 41.3 1450 1199

EH(A) -Btu/lb of actual mixture

EH(B) - Btu/lb of blast equivalent stoichiometric mixture

where P cj/Po=34.5 for a stoichiometric mixture. Thus, in order for

a stoichiometric mixture to have the same blast effects as a test

mixture, a quantity equal to the ratio of E(B) to E(A) would have H H

to be detonated. These stoichiometric blast equivalencies are

summarized below:

Shot 2a 2 6

Pounds of stoichiometric mixture 1.172 1.2 1.21

to 1 pound of test mixture

Decrease in scale factor (%) 5.4 6.2 6.6

Table 5 contains the relevant experimental data of these shots

scaled to the theoretical blast equivalent stoichiometric mixtures.

The overpressure-equivalent scaled distance data are plotted in

Figure 9 from Table 5 and Equation 3.1 for the Kogarko data where

the constants have been adjusted to a mass basis through the cube

root of 2400 kcal/kg of mixture. Excellent agreement of the data

34
TABLE 5. HEMISPHERICAL DETONATIONS OF PROPANE-OXYGEN (19,33)

Hemisphere 3

Shot dian.(ft) P (psi) To (R) Po(ib/ft)

Event 2a 125 13.71 534 0.08310

2 17 11.8 495 0.07753

6 17 11.8 525 0.07327

Moles 02 to Est. total Sach's scale

Shot moles C3H8 mass(lb) factor(Ib-I/ 3 )

Event 2a

2

6

3.4

3.24

3.12

42,490.0

99.7

94.2

0.02656

0.18867

0.19166

APs (psi) R(ft) X m AP (psi) R(ft) Xm

2a 178

47

35

36

35

22

23.2

22.5

16.5

15.6

11.7

7.2

4.0

3.1

1.8

0.36

71

116

156

156.3

160.8

201

202.2

213.4

250

250

295

382

564

678

998

4190

1.9

3.1

4.14

4.15

4.3

5.34

5.4

5.7

6.64

6.64

7.8

10.15

15.0

18.0

26.5

111.3

2 157

88.5

5;5 236-.8

23.1

13.2

7.7

4.5

2.9

1.75

6 121.4

74.3

47.9

20.5

11.5

7.9

4.53

2.74

1.5

10

14

18

22

28

38

52

73

100

145

10

14

18

28

38

52

73

100

145

1.9

2.64

3.4

4.15

5.3

7.2

9.8

13.8

18.9

27.4

1.9

2.7

3.45

5.4

7.3

10.0

14.0

19.2

27.8

I~ - distance scaled .by mass of blast equivalent stoichiometric

*m -mixture, (ft/lbl/3)

35
20

10

04

P4

75

0)

Co

Kogarko fuel-oxygen

(as published)

0

5 10 50

Scaled distance, Xm (ft/(lb of stoichiometric

mixture) 1/3)

Figure 9 Overpressure-distance of fuel-oxygen hemisphere

detonations scaled by mass of blast equivalent

stoichiometric mixture

36
is obtained thereby substantiating the choice of the Kogarko curve

in Section 3.2 to establish the TNT equivalency of hemispherical

detonations.

3.4 Deflagration Explosions

As pointed out in the introduction, a vapor cloud explosion

resulting from sufficiently rapid deflagration is a likely accident

scenario. The TNT equivalency of a general vapor cloud explosion

would be expected to vary with the mode of energy release, distance,

and specific blast effects. Before considering actual accident data,

it is the purpose of this section to examine the more general applicability and order of magnitude of TNT equivalency just developed.

Experimental data of Kogarko, et al (9) and Woolfolk and Ablow

(20) exist, for combustion initiation of fuel-oxygen mixtures. These

data have been energy scaled and plotted in Figure 10-along with the

detonation curve of Kogarko. The Woolfolk data are for stoichiometric mixtures of hydrogen and oxygen with 0%, 10%, and 20% nitrogen

dilutions and two balloon sizes, 3.0 ft and 5.25 ft diameters.

Noting that the spatial flame speeds are observed to be proportional

to a power of time, the kinematics of the combustion can be computed

and are presented in Figure 11.

These figures clearly show.the pronounced effects of balloon

size, spatial flame speed, and nitrogen dilution on the deflagration

process. Taking volumetric expansion of the burning gases into

account, the relative burning velocities are of the order of the

critical turbulent flame speeds of Lee (10). In fact, the transition to detonation might have occurred for the large balloon of

pure hydrogen and oxygen, rather than a crossover of deflagrationdetonation blast strength as reported by the authors. With either

interpretation, it appears that the energy deposition rates control

the airblast which is very sensitive to the magnitude of the flame

speed.

The major result of interest is that as the nitrogen concentration approaches that of air, the blast effects will depend on

37
20.0

10.0

5.0

H2+1⁄20 2+no N2

H2 +1⁄20 2 +10% N 2

H12+1⁄202+20% N2

w

C24

(U

01

0)

1.0

Deflagration

C3 H8 -0 2

(Kogarko)

0.5

0.3 -

0.2 0.5 1.0 3.0

Scaled distance, Xe (ft/Btul/ 3 )

Figure 10 Spherical blast effects of deflagrations

in fuel-oxygen mixtures

38
R=Ctm

H2+1⁄202 m C

no N2 1.36 7.71

10% N2 1.43 5.62

20% N2 1.49 3.97

1600 (104)

e small balloon(rb=l.5ft) 3.0

* large balloon(rb=2.6ft)

UU

a"

aM 1200 "

4-4

41

2.0 o 44.

• 4 -•

Q) 800 a) >U

°

Cd

4-1 ~no N2 Ia

CO 10% N2 1.0 , S400 -20% N2 Cd

Cua

0.P.

- Approximate end of deflagration

0 I I 0

0 .01 .02 .03 .04

Time (sec)

Figure 11 Deflagration kinematics for Woolfolk

and Ablow combustion tests

39
the vapor cloud size provided acceleration mechanisms are present.

As pointed out by Lee, the corresponding critical flame speeds

willalso increase due to the decreasing energy density.

Numerous theoretical models of deflagration have been constructed with a major emphasis on the piston representation of the

flame. The significant results of this work show the strong

dependence of blast on deposition rate. Lee (.16) calculates that

a minimum spatial flame speed of about 400 fps must be attained

to produce a propagating shock front. A parametric study by

Williams and presented in the Lind report (23) has recently yielded the significant result that there exists "a limiting shock strength which depends on the

efficiency of the wave pattern in the noncombustible gas." For

hemispherical deflagrations of methane in air, he suggests an

upper limit of P /P 0< 3 for the shock intensity, i.e., maximum

overpressures of 30 psi.

Calculations were made by Munday and Cave (22) for air deflagrations using an accelerating piston model which attains a constant

speed of two-thirds the acoustic value, approximately the critical

turbulent flame speed of Lee. Although results are not shown for

the 1 psi o-erpressure level, about 16 cloud radii, computed overpressures at 2.25 'cloud radii are about 10 psi at the flame and

4.5 psi at the shock (see Figure 10). Since the flame extinguishes

at about the same time, it is not clear whether this represents

the maximum shock pressure attainable.

Thus, the assumption that a detonation represents an upper

limit to the general far field blast effects of a vapor cloud

explosion is not unreasonable based on the available information.

It should be noted that the actual material involvement will tend

to be larger in a deflagration explosion.

3.5 Summary of Controlled Experimental Results

The analysis of controlled vapor phase explosion data contributes to the evaluation and calibration of potential vapor cloud

blast effects. The principal results are:

40
1. Kogarko's published results (9) must be viewed as hemispherical in the far field, i.e., instrument-readings,

to be consistent with other hemispherical and spherical

balloon tests. We note that many publications, e.g.,

West German papers, base TNT equivalency on sphericity

of Kogarko's work and are, therefore, too high by a

factor of two.

2. It appears that fuel-air mixtures yield a higher net

fraction of available hydrodynamic energy than fueloxygen mixtures even though the corresponding airblast

is less according to presently available experimental data.

3. Blast effects of rapid deflagrations are extemely

sensitive to the spatial flame velocity; thus, cloud

size can be expected to be a critical parameter of

accidental vapor cloud explosions even if detonation

is not achieved.

4. The mixture's stoichiometry significantly influences

the production of hydrodynamic energy (for fuel-oxygen

mixtures) and, therefore, possibly affects the flame

acceleration mechanisms; it is also possible that, for

a time, this effect of rich mixtures offsets a portion

of the dispersed-material losses.

41
4. TNT EQUIVALENCY OF ACCIDENTAL VAPOR CLOUD EXPLOSIONS

The nature of an accident inherently precludes its use in

the development of a rigorous methodology of vapor cloud explosions.

The objective of this section is, therefore, to determine if the

criteria and methodology of TNT equivalency developed in this study

are reasonable with respect to an accident environment.

After general considerations of the transportation accident

history, a detailed analysis of five major vapor cloud explosions

will be presented. Three of these are rail tank car incidents,

and the other two, one industrial and one pipeline, are included

because of their importance and identifiability with potential

bulk transportation accidents.

4.1 History

Napadensky (24) lists a recent average of 8,234 train accidents

per year. From Pierson (25), data collected by the Office of

Hazardous Materials Operations, DOT indicate that about 4.5% of

these involve hazardous materials of all types. According to

Napadensky (26), over a period from 1964 to 1974 there were 117

train accidents involving fire and/or explosions, 43 having both,

65 fire only, and 9 explosions only.

During this same period there were 120 rail accidents involving

tank cars. From these data an accident will involve one, two, or

three tank cars 63% of the time with almost equal probability for

each, four through nine tank cars 33% of the time and again with

equal probability, and 10 or more cars less than 5% of the time.

There have been accidents with fire involvement and secondary explosions of more than one tank car as the data would suggest.

However, there is no known transportation accident in which

the contents of more than one storage tank contributed to the

material involvement of a vapor cloud explosion. The criteria of

applying TNT equivalency to potential accidents can, therefore,

include the mass limitation equal to the contents of the largest

storage vessel under most conditions.

42
Davenport (1) lists a total of seven railroad and three truck

transportation accidents involving vapor cloud explosions. In

view of this and the general accident data, the probability of such

an explosion near a specific site is obviously extremely small.

4.2 Flixborough, England Industrial Process Accident

In 1974, a pipe failed releasing about 60 tons of hot cyclohexane under 136 psi pressure; ignition occurred in less than a

minute. Although this is an industrial accident, the quantity of

material involved and high pressure release mechanism are representative of tank car accidents. A detailed survey of the extensive

blast damage was conducted by the Safety in Mines Research Establishment. Results presented by Munday and Cave (_22) are analyzed

here to yield the TNT equivalency and its sensitivity to damage data.

The overpressure-distance damage data are shown in Figures 12

and 13; the latter log-log plot clearly shows the sensitivity of

TNT equivalency to blast damage data. At each damage point,

O WTNT ETNT - 7.96(10- 7 )WTNT (4.1)

ce (WAHLc)CH TN

6 12

where the equivalent TNT weight is computed from

WTNT = (Rdata/XTNT) 3 (4.2)

the XTNT found corresponding to each overpressure.

The calculated values of ce for the 39 damage points range

from 0.4% to 73.2% having an average value of 11.4% and standard

deviation of 12.4%. Assuming a symmetric explosion and, therefore,

eliminating the four data points with a e > 20.6% as unreasonably

high (from Equation 3.3) yields

= 7.8% (5.7% standard deviation)

m = 81.7%

This estimate of TNT equivalency is about 56% higher than most

estimates in the literature and corresponds to a TNT equivalent

43
10

I-N

'1)

s-I

a)

8

6

4

2

7"

Munday and Cave curve

)(

01

0

I*_ I A2000 4000 6000 8000

Figure 12

10.0 .

1.0 Cn.

> P-4 --

0

0.1 ----.-

100

Distance (ft)

Flixborough damage data points (22)

(estimated graphical interpolation

error of 0.05 psi and 20 ft)

1000

Distance (ft)

10,000

Figure 13 Flixborough data points and range of TNT

energy equivalency on log-log plot

44
weight of 49 tons. It should be noted that the eliminated data

all have less than 1 psi overpressure.

At a e = 7.8%, half of the data points lie above and half

below the average curve both close-in and far-out; for AP 2: 5 psi,

four of the six points are above the curve. The average ae of

the 10 points with AP a 2 psi is only slightly higher than the

overall average. This is a significant result since there has

been wide acceptance of the point made by Brasie and Simpson (3)

that maximum damage effects generally result in minimum TNT equivalencies and vice-versa.

In their damage assessments, Brasie and Simpson used impulse

loading calculations for some of the damage data. Impulse values

are generally subject to wide variations and must be considered

unreliable at the present time. Eliminating that data move the

Brasie and Simpson results in closer agreement with the above

observation Qf Flixborough data. Thus, added confidence is given

to adequate damage data in the low overpressure region of damage

effects.

Strehlow (27) provides the following formula for the.TNT

equivalent weight at low overpressures:

radius of 50% glass) 3

WTNT ( 200

where the scaled distance of 200 represents about 0.15 psi overpressure. A 50% variation in AP from 0.15 psi results in a 100% variation

in WTNT from this formula and, therefore, ae"

A general examination of the sensitivity of TNT equivalency

is provided by the Flixborough data. Representing the peak

overpressure-distance decay as. linear in logarithmic coordinates

below about 10 psi gives the following sensitivity equation:

Aca 3 (AR 5 AP(-•- + -- •-)(4.3)

a R 7)

where P is the overpressure and the decay exponent is taken as 1.4

for the Kingery TNT data. -The AR error reflects ambiguities in

defining an origin of the vapor cloud explosion and is less important

45
at large distances; the AP error relates to the estimation of a

structure's response to blast loading.

Overpressure sensitivity can.be examined by assuming AR=0

which is probably not too severe for the Flixborough data. Thus,

AP = 7 a(I- ) (4.4)

P 1 -5a

at each data point. Performing the calculations yields

AP- = 28%

which yields the overall sensitivity of the TNT equivalency to

overpressure as

or 3.1% < at < 12.5% on the average. Only nine data points had e

values of AP/P > 50%, four of which were eliminated for reasons

stated earlier.

Using the experimental data of Wiehle (28) in which known

structures were subjected to known blast environments, the following

empirical table for AP/P was constructed (representing the uncertainty of overpressure to within one standard deviation of ,the

average under known conditions):

AP (fachwork AP masonry

P(psig) - walls I P(psig) P cavity walls1

3.00 23% 2.75 11%

5.85 16% 5.15 8%

For the six data points having P 2. 5 psig, AP = 22 and for the

four points having P = 2,3 psig, AP/P = 27%. Thus, the iFlixborough

data are in general qualitative agreement with the above table.

Another useful way to view the data is to assume its accuracy

but that it represents asymmetry in the blast pattern. Then using

ae = 7.8% as the average symmetric yield and a min = 2%, the degree

46
of asymmetry would have been $ = 1.89 and amax = 13.6%, consistent

with the nominal standard deviation of the data. The importance

of this viewpoint, as well as the statistical approach, is that

the TNT equivalency should be associated with a reasonable upper

limit of accident data and not an average for purposes of estimating

safe standoff distances.

One final computation yields a distance of 2100 ft at which 1

psi overpressure occurs for ce = 7.8%; at that distance, ae 2%

gives 0.6 psi overpressure, and a e = 13% gives 1.3 psi overpressure.

4.3 Franklin County, Missouri Pipeline Rupture

In December 1970 an underground pipeline ruptured releasing

about 31,750 gallons of pressurized liquid propane over a 24 minute

period until an ignition source was found some 1500 ft from the

rupture (11). As mentioned in Section 1.2.3, this accident shows

the significance of adverse topographical and meteorological

conditions. It represents a potential transportation accident of

a rail tank car having a relatively small puncture.

Applying the TNT equivalency methodology developed in this

study to the damage data of Burgess and Zabetakis (13) yields

e= 8.7%

am 96%

compared with their estimation of 7.5% equivalency. The atmospheric

dispersion calculations were eliminated here for reasons stated in

Section'l.2.3; also, the glass damage statistical estimate was

eliminated as unreliable and so was one structural damage data

point which clearly was too high for spatial blast effects. The

corresponding TNT equivalent weight computed is 62 tons.

4.4 East St. Louis, Illinois Rail Tank Car Accident

In January 1972 a tank car containing 28,289 gallons of propylene (94%) and propane (6%) was punctured (8). A vapor cloud formed

while the car was still moving. The subsequent explosion injured

230 people and caused extensive structural damage; from 870 to 1000

47
homes and buildings were estimated to have suffered damage. Nonrailroad damage was estimated at about $6.3 million. Figure 14

shows the damage occurring in the immediate vicinity of the explosion area.

The blast was highly asymmetric and caustics occurred as

shown by the damage map in Figure 15. Serious structural damage

occurred in areas 1 and 5 and broken glass in area 6. From the

loading conditions, about 122,7700 pounds of material were being

transported and taking 19,700 Btu per pound of fuel mixture as

the heat of combustion gives for the TNT energy equivalency

a = 7.4424(10-7) [Rdamage 3

e TNT j

and assuming an asymmetry of B = 2.25 gives

Smin = 0.1614a

Umax = 1. 8 386a

The damage data are interpreted in the direction of maximum blast

output, since this area is larger and includes more structures, and

is listed below:

Region Damage Description Rmax (ft).

1 heavy structural 1500

2 light structural-heavy cosmetic 2650

3. light cosmetic-glass 4200

4 light glass 5750

Since isolated damage points are not being used, values of

Umax will be selected and the resulting overpressures computed

from XTNT'

48
I., *-. -

.3

* 7,.

,~,-.

Al

~-77 ~

~

~7.

Figure 14 Explosion area at East St. Louis accident (29)

,77-7~7~
THOUSANDS OF FEET

< J.

1 3

1 4l

I I

1/2 1

MILES

CODE FOR ALTON & SOUTHERN R. R.

EXPLOSION DAMAGE AREA MAP

AREA I Heavy Structural

AREA 2 Light Structural &

Heavy Cosmetic

AREA 3 Light Cosmetic & Glass

AREA 4 Light Glass

AREA 5 Heavy Structural,

Large Buildings

AREA 6 Plate Glass

Figure 15 East St. Louis isodamage map (j14)

50
Overpressure(psi) Blast effects

Region •max = 10% 20% 30% range of APt

1 1.76 2.41 2.92 2-5

2 0.85 1.14 1.36 1-3

3 0.49 0.63 0.75 0.25-1.5

4 0.34 0.44 0.50 0.1-1.0

= 5.4% 10.99% 16.3%

t These values represent a best judgment using several

sources of blast effects data.

Inspection of the above table clearly indicates that max 10%

is unreasonably low while even 'max = 30% is not too high. The

corresponding values of a are given as the last line of this table.

Thus, interpreting the possible average TNT equivalency of

this accident as a 10% yield is certainly reasonable. This should

be compared with Strehlow's (29) estimate of from 0.1% to 0.3% on

an energy basis. The TNT equivalent weight for a e = 10% is 67 tons

for a mass equivalency of 109%. It should be noted that this particular asymmetry effectively doubles the average blast output in one

general direction.

4.5 Decatur, Illinois Rail Tank Car Accident

In July 1974 a jumbo tank car was punctured releasing about

31,366 gallons of isobutane (.30). A vapor cloud formed from an

estimated spill rate of 5000 gallons per minute. An unknown ignition source was found some 8 to 10 minutes later.

The damage pattern was highly asymmetric with the following

results: 7 killed-356 injured; 283 freight cars demolished-312

others damaged; 700 residences damaged-67 buildings uninhabitable

due to collapsed roofs and walls; structural damage to 1 milebroken glass to 3 miles. Commercial damage was estimated at $4.9

million and residential damage at $2.5 million. Figure 16 shows

the damage to a newly constructed school building.

51
Figure 16 NTSB Report NTSB-RAR-75-4 damage to Lake View

School, Decatur, Illinois (30)

Strehlow (14) computed a weighted average TNT energy equivalency of from 0.5% to 2% corresponding to 5 to 10 tons of TNT.

Using 152,375 pounds of isobutane as the material involvement, the

TNT equivalency can be grossly estimated using the methods of this

study. Davenport (private communication) gives the distance of

the pictured school building as 1100 ft and estimating the incident

diffraction loading as 2 to 3 psi yields

= 4.3% to 10.2%

= 47% to 111%

and corresponding TNT weights of 35 to 84 tons. This estimate is

also consistent with the statement of structural damage to 1 mile.

52
4.6 Houston, Texas Rail Tank Car Accident

In September 1974 a jumbo tank car was punctured releasing

33,864 gallons of butadiene which formed a vapor cloud in an 11 mph

wind, igniting 2 to 3 minutes later (31). Figure 17 is a picture

of the damage in the immediate area; 231 railroad cars were destroyed

and 282 others damaged. There was major structural damage in the

surrounding area with nonrailroad damage (including liability)

estimated at $5.5 million.

Damage data were not available for the present study, but

Davenport (1) cites 2 to 3 psi overpressure at 1000 ft from the

puncture. This corresponds to 53,000 to 127,000 pounds of TNTand implies an equivalency of

e = 3% to 7%.

m = 34% to 79%

4.7 Summary of Accident Analysis Results

The-analysis of accidental vapor cloud explosion information

was based on the methodology developed in this report. The principal, results are summarized below:

1. Accidental vapor cloud explosions have occurred for

massive releases of pressurized hydrocarbon combustibles.

The resulting damage-distance patterns are representative,

in general, of airblast-phenomena indicating either an

extremely fast deflagration or detonation.,

2. Accident data analysis has inherent weaknesses associated

with it such that even the most exhaustive damage study

can be expected to pin down the magnitude of the explosion

by only a factor of two relative to a specific blast loading. The available data do, however, indicate large explosive involvement and, therefore, a considerable explosion

hazard of vapor clouds of the type that can occur in transportation accidents.

3. The five major accidental vapor cloud explosions reported

herein had TNT energy equivalencies of about 13.6% (7.8%

average), 8.7%, possibly over 30% (10% average), up to

10.2%, and up to 7%, using the available data. These values

represent hazards significantly larger than generally

reported in the literature, as for example, Strehlow and

Baker (32).

53
Figure 17 Explosion area of Houston accident (31)

54
5. CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions

We conclude that the concept Of TNT equivalency applied to

accidental vapor cloud explosions is a useful technique in evaluating their potential blast damage at the lower overpressures. A

quantitative methodology has been formulated in this study for

estimating the TNT equivalency of detonating vapor clouds based

upon the existing experimental and accident data. In addition, a

study of the general physics of the vapor cloud phenomenon has

yielded valuable insight into the various mechanisms that influence

the explosion event.

Although the probability of occurrence of a vapor cloud explosion can be defined statistically, an expected value of the blast

effects cannot be because (1) they occur infrequently, (2) postaccident data are inherently inadequate, and (3) too many critical

parameters are involved. Therefore, we conclude that estimates of

potential blast damage should be based on the total range of values

that is established by the state of the physics at the appropriate

time.

An accidental vapor cloud TNT mass equivalency of 10% (energy

equivalency of 0.8%) has been suggested, .n the absence of test data

by the NRC staff in Working Paper B of Regulatory Guide 1.91 (Revision 1) and entitled "Evaluations of Explosions Postulated to Occur

on Transportation Routes Near Nuclear Plants". We conclude that

this a priori judgment is unrealistic when compared to the existing

body of knowledge and actual accidents.

Similarly, we conclude that the TNT equivalencies appearing

in the West German Safety Codes and Guides and presumably based on

a moderate deflagrative explosion in the immediate vicinity of a

nuclear plant are nonconservative. Specifically, a TNT mass equivalency of 100% (energy equivalency of 8.4%) for hydrocarbons with

carbon-to-carbon triple bonds or cumulated carbon-to-carbon double

bonds, 100% (8.4%) for nonliquified gases, 50% (4.2%) for gases

liquified under pressure are all judged by us to be nonconservative

when compared with the results of this study.

55
The TNT equivalencies of gases liquified at low temperature

(cryogenic) cannot be specifically estimated from this report.

It should be noted that the vapor evolution from cryogenics is

determined by external heat transfer mechanisms which are generally

much slower than those occurring during pressure expansion and air

entrainment. Therefore, beneficial effects of a longer time frame

are generally realized.

In general, we conclude that the probability of occurrence of

a vapor cloud explosion at a specific site is extremely low, but

the potential destructive magnitude of an actual event, should it

occur, must be recognized. Additional conclusions of the present

study are made as follows:

1. Energetic materials of interest can be represented with

few exceptions as a class of hydrocarbon-air explosions distinguished by their low value of heat of combustion.

Other differences such as transition to detonation amplification factors and flammability or detonability limits

should, at the present time, be incorporated into appropriate probability models. In general, a distinction

must be drawn between probability considerations and the

tractable physics of the phenomena.

2. The principal factors controlling the blast energy release

are material involvement, combustion process, and topographical and meteorological conditions. Present theoretical and empirical knowledge is too limited to quantitatively evaluate realistic accidental vapor cloud explosion

scenarios. However, each factor can contribute, at certain stages of the event, in the direction of producing maximum blast effects. In particular, point of ignition,

terrain, and atmospheric conditions can create highly

directional blast energy coupling to the surroundings resulting in asymmetric damage patterns. A priori limitations of these factors as made, for example, by Jungclaus

(15) are not considered realistic in this study.

3. Asymmetric spatial effects are unique to and commonly

observed in vapor cloud explosions. An important, product

of the current research is a model for treating these

effects on a TNT equivalency basis. As a result we conclude that asymmetry of the blast yield can increase the

effective TNT equivalency by up to a factor of two over

the symmetric estimate.

56
4. In terms of the presently available data, ,the maximum expected TNT

equivalencies of-symmetric vapor cloud explosions is about 20% on,

an energy basis and 240% on a mass basis; for an asymmetric allowance,

up to a maximum of twice these values should be definitely considered.

The value of, 20% energy equivalency is based upon the assumed validity

of Kogarko's experiments; it should be noted that the corresponding

theoretical value computed herein is about 37%, but this discrepancy

cannot be resolved within the scope of the present study.

5.2 Recommendations

At the present time we recommend that safety standards for

determining reasonable standoff distances of nuclear plants near

potentially hazardous transportation routes be based on TNT energy

equivalencies of from 20% to 40% for all pressurized hydrocarbon

combustibles. The appropriate standoff distance formula is

SeW AHL 1/3

R= XTNT eHC LC

5 TNTT

(5.1)

where R = standoff distance (ft)

X TT TNT scaled distance corresponding to design or other

•TNT incident overpressure level (ft/lb-TNT1 / 3 )

a e = TNT energy equivalence

WHC = weight of hydrocarbon in largest single pressurized storage tank being transported (lb)

AHLC.= low value of hydrocarbon's heat of combustion

(Btu/lb-HC)

eTNT = 1800 Btu/lb-TNT

At 1 psi incident overpressure, X TNT 45.5 ft/ib 1 /3 assuming

a typical value of AH to be 20,000 Btu/lb of fuel,

R s(1 psi) = 101.5 (e WHC )1/3 (5.2)

Referring to Figure'18, we therefore recommend selecting the standoff distance as a value between the a =20% (nominal a'=240%) and

e m

=e 40% (nominalcL =480%) curves at the appropriate material weight. e .m

A precise value within these limits must be guided by judgment at

the present time.

In view of, the significant hazards posed by accidental vapor

cloud explosions, we recommend that further investigations be pursued.

57
In particular, more results must be obtained regarding the hydrodynamic and blast aspects of violent fuel-air deflagrations, cloud

generation and mixing mechanisms associated with pressurized fluids,

and the asymmetric blast coupling of vapor cloud explosions.

5000

4j)

L4-

Lý~4

0

4.

01)

-4

in.

z4

4000

Ote=40%

3000 IOe=20%

2000 I1000 --

0 I I I i I | | | • |

0

Figure 18

50 100 150 200 250

Fuel weight (thousands of ib)

Estimated standoff distance of nuclear plant

as function of potential combustible material

involvement for 1 psi blast overpressure (heat

of combustion of 20,000 Btu/lb of fuel assumed)

58
CITED REFERENCES

1 Davenport, J. A.; A Study of Vapor Cloud Incidents,

Industrial Risk Insurers, Hartford, Connecticut, Presented

to 83rd National Meeting of American Institute of Chemical

Engineers, Houston, Texas, Paper 24a (to be published)

2 Strehlow, R. A.; Unconfined Vapor-Cloud Explosions - An

Overview, Department of Aeronautical and Astronautical

Engineering, University of Illinois, Urbana, Illinois, 14th

Symposium (International) on Combustion, The Combustion

Institute, 1189-1200, 1973

3 Brasie, W. C.; Simpson, D. W.; Guidelines for Estimating

Damage Explosion, Dow Chemical Co., Midland, Michigan,

Loss Prevention, Vol. 2, 91-102, February 1968

4 Hardee, H. C.; Lee, D. L.; Expansion of Clouds from

Pressurized Liquids, Criteria and Heat Transfer Division,

Sandia Laboratories, Albuquerque, New Mexico, SAND74-5210,

September 10, 1974

5 Brasie, W. C.; Guidelines for Estimating the Hazard

Potential of Chemicals, Dow Chemical Co., Midland, Michigan,

Presented to 81st National Loss Prevension Symposium, AIChE,

Kansas City, Missouri, April 1976

6 Kletz, T. A.; Unconfined Vapour Cloud Explosions - An

Attempt to Quantify Some of the Factors Involved, Presented

to 83rd National Meeting of American Institute of Chemical

Engineers, Houston, Texas, (to be published).

7 Geiger, W.; Generation and Propagation of Pressure Waves

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64