NUREG/CR-3330

SAND83-1178

R4, RP

Printed August 1983

Vulnerability of Nuclear Power

Plant Structures to Large

External Fires

David E. Bennett

Prepared by

Sandia National Laboratories

Albuquerque. New Mexico 87185 and Livermore, California 94550

for the United States Department of Energy

under Contract DE-AC04-76DP00789

Prepared for

SF 29•4o•6-5,. NUCLEAR REGULATORY COMMISSION
NOTICE

This report was prepared as an account of work sponsored by an

agency of the United States Government. Neither the United

States Government nor any agency thereof, or any of their employees, makes any warranty, expressed or implied, or assumes any

legal liability or responsibility for any third party's use, or the

results of such use, of any information, apparatus product or

process disclosed in this report, or represents that its use by such

third party would not infringe privately owned rights.

Available from

GPO Sales Program

Division of Technical Information and Document Control

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555

and

National Technical Information Service

Springfield, Virginia 22161
NUREG/CR-3330

SAND83-1178

R4, RP

VULNERABILITY OF NUCLEAR POWER PLAN'I

SIRUCTURES 1"0 LARGE EXTERNAL FIRES

David E. Bennett

Date Published: August 1983

Sandia National Laboratories

Albuquerque, New Mexico 87185

operated by

Sandia Corporation

for the

US Department of Energy

Prepared for

Division of Risk Analysis

Ottice ot Nuclear Regulatory Resoarch

US Nuclear Regulatory Commission

Washington, DC 20555

Under Memorandum of Understanding DOE 40-550-75

NRC FIN No. A1214

ABSTRACT

This report examines the inherent vulnerability of

nuclear power plant structures to the thermal environments

arising from large, external fires. The inherent

vulnerability is the capacity of the concrete safety-related

structures to absorb thermal loads without exceeding the

appropriate thermal and structural design criteria. The

potential sources of these thermal environments are large,

offsite fires arising from accidents involving the

transportation or storage of large quantities of flammable

gases or liquids.

A realistic thermal response analysis of a concrete

panel was performed using three limiting criteria:

temperature at the first rebar location, erosion and

ablation of the front (exterior) surface due to high heat

fluxes, and temperature at the back (interior) surface. The

results of this analysis yield a relationship between

incident heat flux and the maximum allowable exposure

duration.

A simple fire analysis method was developed to predict

the thermal flux incident upon a target as a function of

range. A key feature is the use of an experimentally

observed specific power emitted from the surface of large

fires.

Example calculations for the break of a 0.91 m (3')

diameter high-pressure natural gas pipeline and a 1 mZ

hole in a 2-1/2 million gallon gasoline tank show that the

resulting fires do not pose a significant hazard for ranges

of 500 m or greater.

iii

TABLE OF CONTENTS

Page

1.0 Introduction 1

1.1 Background 1

1.2 Analysis Methodology 2

1.3 Design Criteria for Concrete Structures 3

2.0 Thermal Response Analysis of a Concrete Wall 4

2.1 Wall Model 5

2.1.1 Concrete Thermal Properties 5

2.1.2 Surface Erosion Model 8

2.1.3 Boundary Conditions 8

2.2 Numerical Calculations 9

2.3 Wall Thermal Capacity 12

3.0 Fire Modeling 12

3.1 Radiant Energy 15

3.2 Flame Area 16

3.3 Flame Shape and View Factor 17

3.4 Incident Thermal Energy 20

3.5 Fuel Flow Rates 20

3.5.1 Flow From a Tank 22

3.5.2 Discharge From a High-Pressure

Pipeline 23

4.0 Example Calculations 24

4.1 High-Pressure Natural Gas Pipeline 24

4.2 Gasoline Storage Tank 26

4.3 NG Pipeline (1/2') and Comparison With Tests 28

5.0 Summary 28

References 30

6.0 APPENDIX--Discharge Fron a High-Pressure Natural

Gas Pipeline 32

References 35

V
LIST OF FIGURES

Page

2-1 Thermal Hazard Posed by a Large Fire in the

Vicinity of a Power Plant Structure 6

2-2 Thermal Properties for Concrete-Volumetric

Specific Heat. 7

2-3 Thermal Properties for Concrete-Thermal

Conductivity 7

2-4 Typical Time-Temperature Curve at the 0.15 m

Location 10

2-5 Position of Erosion Front as a Function of

Exposure Time 11

2-6 Incident Heat Flux Versus Maximum Allowable

Exposure Time 14

3-1 Flame-to-Target View Factors 19

3-2 Atmospheric Transmissivity as a Function of

Relative Humidity 21

vi
LIST OF TABLES

Page

2-1 Tabulated Results of Wall Response Analysis 13

3-1 Maximum Discharge Flow Rates for NG Transmission

Pipelines 23

A-1 Data for Large Pipeline Fires 36

vii
ACKNOWLEDGMENT

The author would like to thank Douglas Cline for

pertorming the CINDA calculations and for his many helpful

suggestions and discussions, Gilbert Weigand for his help on

the Appendix, and David Lee for reviewing this work.

viii
1.0 INTRODUCTION

This report examines the inherent vulnerability of

nuclear power plant structures to potential thermal environments arising from large, external fires. The inherent

vulnerability is the capacity of the concrete safety-related

structures to absorb thermal loads without exceeding the

appropriate thermal and structural design criteria. The

sources of these thermal environments are large, offsite

fires arising from accidents involving the transportation or

storage of large quantities of flammable gases or liquids.

1.1 Background

This, work is part of a program to evaluate the hazards

to nuclear power plants due to nearby, but offsite, accidents involving hazardous materials. Five generic hazardous

environment categories were identified in a preliminary

assessment: 1 toxic, anoxic, corrosive, overpressure, and

thermal. This report is a follow-on to the work described

in Reference 1.

In Reference 1, the hazards from thermal environments

due to fires involving truck or rail car quantities of flammable fluids burning at an accident site assumed 500 m from

the plant were determined to be negligible. Note that for

about 90 percent of the nuclear power plants in the US, the

distance from a safety-related structure to the exclusion

area boundary is greater than 500 m. Thus, road and rail

transport of flammable materials do not pose a thermal threat

to the plant if the fire occurs at the offsite accident

location.

There remained to be considered the cases of:

(1) delayed ignition of a vapor cloud, which could occur in

close proximity to plant structures, and (2) much larger

fires involving pipeline or storage facilities. In the

first case, the fire duration would be short, on the order

of 10 seconds. But the heat flux (units of kW/m 2 ) incident

upon a plant building could be essentially the same as that

emitted from the surface of the fireball, due to small standoff distances. In the second case, there would still be a

moderate standoff distance from the fire to the plant to

offer some protection, but the fire could be much larger

than for the rail car case and the fire duration could be on

the order of I to 10 hours or longer.

A wide variety of flammable fluids are found in commerce

in the United States. In terms of resultant fire characteristics, a few categories or types of fuels appear sufficient

for vulnerability modeling:

-1-
1. LNG -- liquified natural gas (cryogenic liquid,

ambient pressure)

2. NG -- natural gas (compressed gas, ambient temperature)

3. LPG -- liquified petroleum gas (liquid under pressure, ambient temperature)

4. Liquid Products -- gasoline, kerosene, etc. (volatile and semivolatile liquids,

ambient temperature, and pressure)

5. Crude-Oil -- less volatile than liquid products.

The storage conditions listed in parentheses are for

normal or nonaccident environments. This report will consider natural gas and liquid products as examples. Appropriate release and fire models are then used to estimate

fire size and thermal output for a reasonable range of

accident conditions.

1.2 Analysis Methodology

The evaluation of the hazard which large fires could

pose to nuclear power plants can be subdivided into two

relatively independent parts. The first is a thermal

response analysis of concrete panels, which defines the

capacity of concrete structures to absorb heat without

exceeding the thermal (and structural) design criteria. The

second part is an estimation of the thermal output of large

fires. Combining these results defines a relationship

between standoff distance and exposure time as a function of

various parameters describing the fire.

The thermal response analysis uses a realistic conduction

model for concrete wall panels typical of safety related

structures at nuclear power plants. A wall thickness of

0.61 m (2 feet) was assumed. The effects of reradiation from

the (hot) front surface, convective cooling of the back

surface, and ablation or decomposition of the front surface

due to high heat flux-high temperature reactions, are

included. Three criteria were used in estimating. the

resulting thermal capacity: a limit for erosion of the front

surface to one-half of the distance to the first rebar, a

maximum temperature at the first rebar location, and a

maximum temperature at the back (inside) surface of the

wall. The results of this analysis can be expressed as a

function of incident heat flux versus maximum allowable

exposure time.

The fire analysis uses relatively simple and realistic

(but still conservative) models for estimating the size of a

large fire and the radiative component of the thermal output.

The analysis considers the chemical and physical properties

of the flammable fluid, the fuel combustion rate, combustion

efficiency, air entrainment, shape factors, and standoff

-2-
distance. The objective of this analysis is to express the

thermal flux incident upon a target (eg, the plant) as a

function of range and as few other variables as is possible,

such that the results are realistic bounds for actual severe

thermal environments.

1.3 Design Criteria for Concrete Structures

The concrete structures at nuclear power plants are

currently designed to meet a variety of loads and environments. Reactor containment buildings are designed to withstand the elevated temperatures due to loss-of-coolant

accidents. This is accomplished by a combination of containment. cooling systems to ensure that the concrete structure itself remains within acceptable temperature limits.

The American Concrete Institute2 and the American Society

of Mechanical Engineers 3 have specified the following

maximum temperatures for concrete:

Maximum Allowable'Temperature

Bulk Local

Short Term (ie, following 177 0 C (350-F) 343 0 C (650-F)

accidents)

Long Term 66-C (150-F) 93 0 C (200 0 F)

Considering the large scale of potential fires, a considerable portion of a building could be exposed for several

hours. The outer surfaces of concrete wall panels will,

under high heat fluxes, be heated to much higher temperatures

than any of the above criteria would allow. The structurally

significant portion of the wall (the interior region containing the reinforcing steel) must be maintained within the

temperature limit. For this interior region, the extent of

the exposure would suggest the use of the bulk criterion in

the above table rather than the local one, while the relatively short exposure times expected would correspond to a

short-term condition, as compared to long term. For this

study, the short-term, bulk 'temperature criterion will be

used to define an acceptable temperature limit at the first

rebar location. This will ensure that the entire interior

region remains within the limit.

Additionally, for heat fluxes above 350 to 400 kW/m 2 ,

erosion or ablation can occur due to chemical decomposition

of the concrete surface. A criterion for how much of the

outer portion of the concrete wall can be sacrificed due to

-3-
high temperature, ablation, or erosion can be developed from

seismic response considerations.

The flexing of a reinforced concrete panel under seismic

loadings results in cracking of the outer layer of concrete

(between the surface and the first layer of reinforcing

steel). During each oscillation, the convex surface is in

tension, and hence fine cracking occurs. In a seismic safety

analysis, no credit for strength is given to this outer

layer. 1 7 For the thermal response analysis in this work,

a reasonable criterion would be to apply the short-term,

bulk temperature criterion at the first rebar location and

allow higher temperatures in the outer layer. For an

erosion-ablation criterion, loss of one-half of the outer

layer would not result in a reduction of seismic capacity

(other than the loss of mass).

The final criterion involves setting a maximum allowable

temperature for the inside of the concrete wall. Since this

would apply to the auxiliary and control buildings, safetyrelated equipment mounted on the inside surface should not

be compromised. A reasonable maximum allowable temperature

is 500C (120 0 F). As will be seen later, this criterion is

never exceeded; rather, the thermal capacity is controlled

by the allowable temperature rise at the first rebar location.

In summary, three thermal criteria are chosen to define

acceptable levels of exposure from large-scale fires:

Thermal Criteria Description

1 Temperature at the first rebar

location not to exceed 177 0 C

(350 0 F).

2 Thermal decomposition (erosion)

not to penetrate more than

one-half the distance to the

first rebar.

3 Temperature of the interior

surface not to exceed 500C

(120 0 F).

2.0 THERMAL RESPONSE ANALYSIS OF A CONCRETE WALL

The development of a rigorous, yet conservative hazards

analysis, based on the previously defined thermal criteria,

requires that the thermal response of the concrete wall be

characterized over a wide range of incident heat fluxes.

The arrangement of the fire and concrete wall to be analyzed

-4-
is illustrated in Figure 2-1. A large fire plume, at a

distance R, is assumed to emit thermal radiation uniformly

in all directions. Some of this radiation is incident on

the concrete surfaces of the power plant. Following the

method of Parker, 4 a steady-state approach is taken whereby

a target element of unit area dA is identified on the building surface. For a range of (constant) heat fluxes incident

on the target area, it is desired to find the exposure times

necessary to exceed the thermal criteria defined in Section

1.3. Since these criteria address both internal wall temperature rise, as well as surface erosion processes, a closed

form analytic solution is not possible and numerical solution

techniques must be used.

2.1 Wall Model

A planar, one-dimensional wall constructed of reinforced

concrete is considered. The target element is taken to be

1 m2 , with a wall thickness of 0.61 m (2 feet). This

corresponds to the wall thickness of a typical control building at a nuclear power plant, and is the thinnest of typical

reinforced concrete walls for seismic- and tornado-rated

structures. The internal structural rebars are neglected in

this thermal wall model, as they constitute only a few percent of the volume of the wall and they run transverse to

the direction of heat flow.

2.1.1 Concrete Thermal Properties

Cement-based materials undergo a series of decomposition

processes at high temperatures, 6 , 7 and the usual assumptions of constant thermal properties may lead to appreciable

errors in thermal diffusion calculations. To more accurately

model the thermal response of concrete, Harmathy 5 has

developed thermal property relationships for concrete materials which include the effects of latent heat absorption

(heat of decomposition). Basically this method requires

that the specific heat capacity of the concrete be expressed

in the following form:

Cp = Cpc + CpHD (2.1)

where Cp is the total heat capacity, Cpc is the caloric

heat capacity, and CpHD is the effective heat capacity due

to the absorption of latent heat (heat of decomposition).

The total volumetric heat capacity used in the present

analysis is shown in Figure 2-2 as reproduced from

Harmathy. The principal peaks of this curve are associated

with the decomposition process. The dashed line indicates

the approximate value for the volumetric heat capacity in

the absence of any decomposition processes. Note that the

-5-
f

"I

/

FIRE SIZE D

RANGE R F

TARGET

AREA (1 m2)

POWER

PLANT BUILDING

RADIATING

FIRE PLUME

Figure 2-1. Thermal Hazard Posed by a Large Fire in the Vicinity

of a Power Plant Structure
~0.61

C*)6

o0.4 -

0.2

CPC 0

u 0.0 I I I I I ! !

0 200 400 600 800 1000

TEMPERATURE, 0C

Figure 2-2. Thermal Properties for Concrete-Volumetric

Specific Heat

0.002

> 0.001

0

o 0.000

0 200 400 600 800 1000

TEMPERATURE, °C

wU

Figure 2-3. Thermal Properties for Concrete-Thermal

Conductivity

-7-
heat capacity due to latent heat effects is a significant

fraction of the total heat capacity, and thus cannot be

ignored.

For the thermal conductivity, Harmathy developed

governing relationships assuming the concrete to decompose

as a multiphase solid mixture. 5 In general, the thermal

conductivity of concrete is less affected by chemical

composition than the heat capacity, as shown in Figure 2-3.

Over a 1000 0C temperature range, the thermal conductivity

can be seen to change only moderately.

Neglecting thermal expansion effects, as well as changes

in internal porosity, the density of concrete may be taken

to be constant. The value for concrete density used in

the present wall model was 1.7 Mg/m 3 .

2.1.2 Surface Erosion Model

Since the thermal diffusiv ty for concrete is

comparatively low ( • 6.9 x 10- m /s or 0.25 m2 /hr),

the time scale governing heat conduction into the interior

of the wall is large. Consequently, the principal effect of

a large incident heat flux rate is to produce very large

temperature gradients near the exposed surface. Should the

wall temperature and the surface gradient become

sufficiently large, a steady erosion-ablation process is

established on the exterior surface. In the experiments

conducted by Muir, 6 surface erosion rates for ablating

concrete were measured for large values of radiant heat flux

(640 to 1180 kW/m 2 ). Later, Chu 7 demonstrated that the

surface erosion rate, 6 , could be correlated by the

one-dimensional ablation expression for concrete

t

f expq dt

0

6 =(2.2)

P[C p(Ta-T) + AH a]

where Ta and AHa are the effective ablation temperature

and the effective latent heat of ablation, respectively.

Correlation of Muir's concrete ablation data indicates that

Ta = 1350 0 C and AHa = 3.08 x 103 J/g give good predictions of surface erosion depths as a function of exposure

time.

2.1.3 Boundary Conditions

In the present wall model, the incident heat flux on the

exposed surface was assumed to be independent of time. A

surface absorptivity of 0.9 was assumed for the exterior

-8-
surface, with convective losses neglected. A natural convective coefficient of 5.7 W/m2 C was assumed to be present

on the interior surface; ie, at 0.61 m. The ambient temperature, as well as the initial temperature of the wall,

was assumed to be 32 0 C (90 0 F).

2.2 Numerical Calculations

With the previously described wall model, numerical

calculations were performed using the finite-difference heat

conduction code, CINDA-3G. 8 Subroutines available in the

code allowed the erosion-ablation process to be simulated in

accordance with Equation 2.2. Thermal solutions were generated for values of incident heat flux ranging from 15 to

1400 kW/m 2 .

In Figure 2-4, a typical time-temperature curve is shown

at an internal location in the wall for an incident heat

flux on the surface of 25 kW/m 2 . The x-position in the

wall is that pertaining to the first thermal criterion, the

first rebar location at 0.15 m (0.5 ft). Solutions for

three different values of exposure time are presented.

Notice that as expected, the temperature history of the wall

is identical for the three values of exposure time, up until

the termination of the exposure. Due to thermal conduction

in the wall, the maximum temperature at this location occurs

approximately four hours after the termination of the

exposure. For a given value of incident heat flux, the

exposure time may be varied to determine the minimum

exposure duration necessary to exceed any of the wall

thermal criteria. In Figure 2-4, this result is exemplified

by the solution for texp = 8 hours. For this particular

case, the maximum temperature just reaches the Tmax =

1770C criterion line. It may be concluded that for an

incident flux of 25 kW/m 2 , an exposure time of 8 hours is

necessary to exceed the first thermal criterion.

When the value of the incident heat flux is sufficiently

large, the temperature on the exterior surface of the wall

increases until the effective ablation temperature is

reached. An erosion front is established which propagates

into the wall as the exposure time is increased. The desired

solution is the time required to erode the first 0.076 m

(0.25 ft) of the exposed surface, as specified in the second

criterion. Results for this type of calculation are

exemplified by the CINDA solutions shown in Figure 2-5. The

temperature curves presented are those for an incident heat

flux of 600 kW/m 2 . The first curve, at texp = 0.033

hours denotes the temperature distribution in the wall at

the onset of erosion. Notice that the penetration of heat

into the wall is relatively low, on the order of 0.025 m.

Considering the low thermal diffusivity for concrete, this

low value of thermal penetration is to be expected. For

-9-
250

200

~150

100

0

0 2 4 6 8 10 12 14 16

TIME (hr)

Figure 2-4. Typical Time-Temperature Curve at the

0.15 m Location

-10-
1400

1200

1000

a

4

800

600

400

200

0

0 2 4 6 8 10 12

X-POSITION (cm)

Figure 2-5. Position of Erosion Front

of Exposure Time

as a Function

-11-
increasing exposure time, the erosion front propagates

through the wall with the incident thermal energy providing

a source for the latent heat of ablation. At an exposure

time of 0.75 hours, the erosion front reaches the 0.076-m

location. The residual thermal energy present in the wall

is insufficient to cause the temperature to reach 177 0 C at

the 0.15-m location (to exceed criterion 1) due to surface

cooling and the low thermal conductivity of concrete.

Therefore, for an incident heat flux of 600 kW/m 2 , an

exposure time of more than 0.75 hours is required to exceed

the erosion thermal criterion.

2.3 Wall Thermal Capacity

The calculations described above were repeated over a

range of incident heat fluxes (15 to 1400 kW/m 2 ). The

minimum exposure time necessary to exceed any one of the

three previously defined thermal criteria was determined.

Tabulated values for the incident heat flux and the required

exposure time are presented in Table 2-1. It is evident

from these values that the onset of erosion occurs at an

incident thermal flux of approximately 350 to 400 kW/m 2 .

Another important conclusion that may be drawn from these

results is that criterion 3 cannot be exceeded without first

exceeding criterion 1 (see Section 1.3). That is, by the

time the heat conducts to the interior surface of the wall

(at 0.61 m), the temperature at the first rebar will have

exceeded criterion 1 for all cases.

In Figure 2-6, the tabulated values appear in graphical

form.

Notice that for the low values of incident flux, criterion 1 was exceeded, while for high values of the incident

flux, criterion 2 was exceeded. Joining these two regimes

are solutions for which the conduction criterion was exceeded

with the onset of ablation occurring at the exposed surface.

The inflection in the curve is a result of the heat absorbed

in the erosion process. Thus, the results for an incident

flux of 350 kW/m 2 indicate a slightly longer exposure time

is necessary to exceed criterion 1 than for 300 kW/m 2 due

to the absorption of latent heat.

3.0 FIRE MODELING

For the purpose of estimating the vulnerability of

nuclear power plants to large external fires, a simple fire

model for estimating the radiative thermal output of the

fire is developed. The results are conservative so that the

vulnerability estimates are bounds. The simplicity of the

model arises from the use of macroscopically observable

quantities (eg, heat of combustion and surface heat flux).

-12-
1400

1200

1000

0

4

800

600

400

200

10

0 2 4 6 8

X-POSITION (cm)

Position of Erosion Front as a

of Exposure Time

10 12

Figure 2-5. Function

-11-
increasing exposure time, the erosion front propagates

through the wall with the incident thermal energy providing

a source for the latent heat of ablation. At an exposure

time of 0.75 hours, the erosion front reaches the 0.076-m

location. The residual thermal energy present in the wall

is insufficient to cause the temperature to reach 177 0 C at

the 0.15-m location (to exceed criterion 1) due to surface

cooling and the low thermal conductivity of concrete.

Therefore, for an incident heat flux of 600 kW/m 2 , an

exposure time of more than 0.75 hours is required to exceed

the erosion thermal criterion.

2.3 Wall Thermal Capacity

The calculations described above were repeated over a

range of incident heat fluxes (15 to 1400 kW/m 2 ). The

minimum exposure time necessary to exceed any one of the

three previously defined thermal criteria was determined.

Tabulated values for the incident heat flux and the required

exposure time are presented in Table 2-1. It is evident

from these values that the onset of erosion occurs at an

incident thermal flux of approximately 350 to 400 kW/m 2 .

Another important conclusion that may be drawn from these

results is that criterion 3 cannot be exceeded without first

exceeding criterion 1 (see Section 1.3). That is, by the

time the heat conducts to the interior surface of the wall

(at 0.61 m), the temperature at the first rebar will have

exceeded criterion 1 for all cases.

In Figure 2-6, the tabulated values appear in graphical

form.

Notice that for the low values of incident flux, criterion 1 was exceeded, while for high values of the incident

flux, criterion 2 was exceeded. Joining these two regimes

are solutions for which the conduction criterion was exceeded

with the onset of ablation occurring at the exposed surface.

The inflection in the curve is a result of the heat absorbed

in the erosion process. Thus, the results for an incident

flux of 350 kW/m 2 indicate a slightly longer exposure time

is necessary to exceed criterion 1 than for 300 kW/m 2 due

to the absorption of latent heat.

3.0 FIRE MODELING

For the purpose of- estimating the vulnerability of

nuclear power plants to large external fires, a simple fire

model for estimating the radiative thermal output of the

fire is developed. The results are conservative so that the

vulnerability estimates are bounds. The simplicity of the

model arises from the use of macroscopically observable

quantities (eg, heat of combustion and surface heat flux).

-12-
1400

1200

1000

zi C

800

600

400

200

0

0 2 4 6 8 10 12

X-POSITION (cm)

Figure 2-5. Position of Erosion Front

of Exposure Time

as a Function

-11-
increasing exposure time, the erosion front propagates

through the wall with the incident thermal energy providing

a source for the latent heat of ablation. At an exposure

time of 0.75 hours, the erosion front reaches the 0.076-m

location. The residual thermal energy present in the wall

is insufficient to cause the temperature to reach 177 0 C at

the 0.15-m location (to exceed criterion 1) due to surface

cooling and the low thermal conductivity of concrete.

Therefore, for an incident heat flux of 600 kW/m 2 , an

exposure time of more than 0.75 hours is required to exceed

the erosion thermal criterion.

2.3 Wall Thermal Capacity

The calculations described above were repeated over a

range of incident heat fluxes (15 to 1400 kW/m 2 ). The

minimum exposure time necessary to exceed any one of the

three previously defined thermal criteria was determined.

Tabulated values for the incident heat flux and the required

exposure time are presented in Table 2-1. It is evident

from these values that the onset of erosion occurs at an

incident thermal flux of approximately 350 to 400 kW/m 2 .

Another important conclusion that may be drawn from these

results is that criterion 3 cannot be exceeded without first

exceeding criterion 1 (see Section 1.3). That is, by the

time the heat conducts to the interior surface of the wall

(at 0.61 m), the temperature at the first rebar will have

exceeded criterion 1 for all cases.

In Figure 2-6, the tabulated values appear in graphical

form.

Notice that for the low values of incident flux, criterion 1 was exceeded, while for high values of the incident

flux, criterion 2 was exceeded. Joining these two regimes

are solutions for which the conduction criterion was exceeded

with the onset of ablation occurring at the exposed surface.

The inflection in the curve is a result of the heat absorbed

in the erosion process. Thus, the results for an incident

flux of 350 kW/m 2 indicate a slightly longer exposure time

is necessary to exceed criterion 1 than for 300 kW/m 2 due

to the absorption of latent heat.

3.0 FIRE MODELING

For the purpose of estimating the vulnerability of

nuclear power plants to large external fires, a simple fire

model for estimating the radiative thermal output of the

fire is developed. The results are conservative so that the

vulnerability estimates are bounds. The simplicity of the

model arises from the use of macroscopically observable

quantities (eg, heat of combustion and surface heat flux).

-12-
TABLE 2-1

Tabulated Results of Wall Response Analysis

Incident Heat Flux

(kW/m 2 )

15

25

50

100

200

300

350

400

450

500

600

700

800

900

1000

1200

1400

Exposure Time

(hours)

11.6

8.1

4.95

3.15

2.03

1.65

1.70

1.79

1.53

1.15

0.74

0.55

0.44

0.37

0.32

0.25

0.20

Criterion

Bound

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

-13-
N

of%

X

LL

wILI.

Iz,<

-w

I1500

1000

100

10 •

0.

- e WALL EROSION TO 0.076m (0.25 ft)

-AA LOCAL TEMPERATURE 1770C (3500 F) - AT 0.15m (0.5 ft)

OPEN SYMBOL DENOTES ONSET'

OF WALL EROSION AT - EXPOSED SURFACE I "1 I I I I I I !I I I I 1 I IlII 

I 1 12

MAXIMUM ALLOWABLE EXPOSURE TIME (HR)

Figure 2-6. Incident Heat Flux Versus Maximum Allowable

Exposure Time

-14-
Details of combustion processes and fire dynamics are

included to the extent that they affect the macroscopic

characteristics of the fire.

The model is described in three sections:

Radiant Energy

Flame Area

Flame Shape and View Factor.

In the first section, an estimate is made for the fraction

of the total available energy leaving the flamie by radiation. The second describes a method for estimating the size

of the flame, and hence the radiative area which would

irradiate the target. The last section uses shape factor

relationships to predict the thermal flux incident upon the

target area as a function of range.

3.1 Radiant Energy

The large fires under consideration burn as turbulent

diffusion flames. The fuel (as a vapor) enters the flame

zone and mixes with entrained air. Due to the turbulent and

nonuniform mixing, there is both incomplete combustion and

excess air entrained in the plume. The combustion products

(at their elevated temperatures) radiate thermal energy to

the surrounding environment. This results in an average

flame temperature which is lower than the adiabatic flame

temperature. The adiabatic flame temperature would be

observedý if the fuel vapor were premixed with the proper

amount of oxygen and burned stoichiometrically with no heat

loss to the surroundings. The difference between the adiabatic and the actual flame temperature (for the stoichiometric mixture) is then primarily a measure of the radiant

energy output of the flame. The remaining energy leaves the

flame zone as hot combustion products at the (actual) flame

temperature.

Assuming the combustion volume to have uniform characteristics, the rate at which energy is emitted as radiation

from the burning plume can be expressed as follows:

PR = MF [YAHC - (Tf - Ta)(flS(l + X)Cpa + Cpf)]/103 (3.1)

where

PR = total radiated power (kW)

MF = fuel flow rate or consumption rate (kg/s)

n = fraction of fuel burned (0 S n s 1)

AHC = heat of combustion of fuel (J/kg)

-15-
Tf = flame temperature of combustion products (K)

Ta = ambient air temperature (K)

x = fraction of excess air ( X = 0 for stoichiometric

combustion)

S = stoichiometric air/fuel ratio (kg-air/kg-fuel)

Cpa = mean heat capacity of air (J/kgK)

Cpf = mean heat capacity of fuel vapor (J/kgK)

Ignoring minor heat losses such as convection and molecular

dissociation, the radiated energy is simply the total energy

produced, less that needed to heat the entering fuel vapor

and air to the flame temperature. For this study, it will

be conservatively assumed that all of the fuel burns

(77 = 1). It is noted that if Tf equals the adiabatic

flame temperature, then PR is ideally zero.

The fraction of excess air, x , entrained in the burning

plume is relatively difficult to measure and has been correlated from experimental data only for small-scale fires.

Values reported in the literature range from 2 to as high as

10, for small turbulent fires on the order of a few meters

in height. 2 0 , 2 1 , 2 2 Data for large-scale fires (eg, hundreds of meters in height) is lacking. For this study, a

conservative value of 0.25 will be used.

3.2 Flame Area

An estimate of the surface area, and hence the size of

the burning plume, can be made from knowledge of the specific

emissive power (per unit area) at the flame surface. For

large pool type fires (eg, gasoline, liquid petroleum

products), measured values for the emission power range from

62 to 174 kW/m 2 . The range of heat fluxes from the surface

of large NG and LPG fireballs is 120 to 500 kW/m 2 . 1 9

Much of the difference in (per area) thermal output between

these two types of fires is due to variations in a number of

fire characteristics, including fuel type, mean flame temperature, and optical properties of the combustion products.

For the purposes of conservatively estimating flame surface

area, and hence the size of the fire plume, a value for the

specific emissive power should be selected that is from the

lower end of the range. This will then give a bounding

estimate for the flame surface area. For this study, a

specific emissive power PSL, of 75 kW/m 2 for pool fires

and 150 kW/m 2 for fireballs will be used for estimating

flame area.

There is very little experimental data on the plume size

for the very large fires for which the fuel burning rate is

-16-
well characterized. In Chapter 4 an example calculation for

a 6" NG pipeline provides a comparison with flame sizes

obtained during a series of fire extinguishing tests. Based

on this data, a more realistic estimate of the flame size

might be obtained by using a central estimate for the specific emitted power per unit area, rather than a lower bound

(conservative) estimate as described above. The difference

in specific powers for lower bound and central estimates is

about a factor of 2, while the difference in flame area

estimates in Section 4.3 for our method and Reference 16 is

about a factor of 4.

In summary, the effective emitting surface area AF of

the fire plume is:

AF = P R/PSL (3.2)

where PR is given by Equation 3.1. From this and an

assumed flame shape (sphere, upright circular cylinder,

etc), the size of the flame can then be estimated.

3.3 Flame Shape and View Factor

The previous sections considered the thermal output from

the flame and the resultant flame surface area. The thermal

energy incident upon a target area located at a range R from

the flame is determined by the radiative output of the fire

source and the view factor between the flame and target: 9

Qi = PSUTAFFF-T (3.3)

where

Qi = thermal power received by target (kW/m 2 ).

PSU = specific thermal power emitted from the surface

of the flame, upper bound estimate (kW/m 2 ).

T = transmissivity of the atmosphere.

AF = flame surface area (m2 ).

FFT = view factor -- flame to target.

The target is assumed to have unit area; eg, 1 m2 .

Since Qi should be a conservative estimate of the

radiative flux incident upon the target, the values for

PSU for pool fires and fireballs should be selected from

the upper end of the observed ranges. Using the ranges of

values cited in Section 3.2, and based on a review of the

specific experimental conditions cited in the literature,

-17-
specific emissive powers of 150 kW/m 2 for pool fires and

350 kW/m 2 for fireballs will be used for PSU.

The reciprocity relationship between the emitting (flame)

and receiving (target) areas can be expressed as:

AF F-T = ATFTP (3.4)

Since the target area is actually an unspecified unit area

on a building, these two expressions can be combined to give

the thermal energy received by the target per unit area

Qi(kW/m 2 ):

Qi = P suTFT-F (3.5)

Analytic expressions for the view factor FT-F have

been developed extensively in the literature. 9 One of the

simplest relationships describes the view factor between a

differential element and a sphere, with the element oriented

perpendicular to a radial line:

FT-F = D+ 2R (3.6)

where

D = diameter of sphere

R = range from the surface of the sphere to the target.

A spherical shape is probably most appropriate for a fireball.

For high pressure pipeline fires, the shape can be

approximated by a vertical circular cylinder. The analytic

expression for the view factor is very complex. 9 It is

instructive to compare the view factor for a sphere and

cylinder as a function of range. For this comparison, the

two objects have the same total surface area. A relatively

conservative aspect ratio (length/diameter) of 2 was chosen

for the cylinder. The target area is conservatively assumed

to be offset from the center of the cylinder and not from

one end. The view factors for two sphere sizes (200 m and

400 m diameters), and the corresponding equivalent cylinders,

are shown in Figure 3-1. Also shown are the view factors

for plane discs having the same diameter as the spheres.

While the view factor for a sphere would tend to underestimate that for a cylinder, the factor for a plane disc would

bound the values for both spheres and cylinders, without

being unduly conservative, especially for ranges above

1000 m. For this work, the view factor for a plane disc

will be used:

-18-
Figure 3-1. Flame-to-Target View Factors

-19-
FT-F = (D2 D+ 2 (3.7)

where D, the diameter of the disc, is the same as the diameter of the spherical flame:

AF = rD2 = PR/PSL (3.8)

Remember that PSL is a lower bound estimate of the thermal

power emitted from the surface of the flame.

The principal reduction of the thermal flux with distance

is the shape factor developed above. Having a lesser effect

is the reduction due to absorption in the intervening atmosphere, principally by water vapor. Normal levels of dust

do not significantly contribute to the attenuation as compared to water vapor. For LNG flames, the transmissivity T

of the atmosphere as a function of path length for several

relative humidities is shown in Figure 3-2.10,1 The use

in an analysis of the upper curve would almost always be

conservative, since the actual transmissivity would be less.

3.4 Incident Thermal Energy

Expressions have been developed in the previous sections

for estimating the radiative flux incident upon a target

area from large hydrocarbon fires. The thermal energy

incident upon the target is given by

Qi = P SUTD 2/(D2 + 4R 2 )" (3.9)

Since each step in the analysis is conservative, Qi is an

upper bound estimate for the radiative thermal flux incident

on a target.

3.5 Fuel Flow Rates

The application of the previously developed models for

estimating thermal output of typical large fires requires

knowledge of fuel characteristics and an estimate of the

fuel consumption rate. This latter estimate is dependent on

accident conditions; eg, fuel release rate, fuel consumption

rate, air entrainment rate, etc, which are very difficult to

quantify. In practice, the fuel discharge rate will

probably be different than the burning rate or consumption

rate by the fire, especially at the beginning and termination

of the fire. Under a steady-state approximation, the consumption or burning rate is the same as the discharge rate

from the tank or pipe. This steady-state discharge rate can

be estimated from conditions known prior to the accident

-20-
1.0 I.0 I I I 11151 I I I liii ............. I V I

0.8

z

I0.6

0.4

a S i as lii

IAmbient Temperature = 293 K

Source Blackbody = 1150 K

Temperature

I i i I Iill

I I I I I I I I I T 1 11I I i

Relative Humidity

I I I I " II

20%I Ia I

0.2

0.0 I I I I I I I I I I I I I I I J I . . . . . . .

I 10 100 1,000 10.000

PATH LENGTH THROUGH THE ATMOSPHERE (meters)

Figure 3-2. Atmospheric Transmissivity as a Function of Relative HumidityI 0 'II
(pressure, level in the tank, etc) and an assumed value for

discharge area. This obviates the need for detailed

information describing the fire dynamics of a particular

accident situation.

In the following two sections, methods for estimating

fuel flow rates from a liquid fuel tank and a high-pressure

pipeline are presented. The tank model is time-dependent,

while the pipeline analysis uses an approximate,

steady-state solution.

3.5.1 Flow From a Tank

Consider a tank discharging a liquid fuel through an

opening of area A. For simplicity, the tank is assumed to

have a constant cross-sectional area S as shown.

AREA S

h

DISCHARGE HOLE AREA A

The discharge mass flow rate MF is given by: 1 2

MF = PVA (3.10)

where p is the density of the fuel, and V is the discharge

velocity. Application of Bernoulli's principle gives

V = CT 2gh (3.11)

where C is the orifice flow coefficient (typical value

0.6). Developing a solution for h, the level of the fuel in

the tank, as a function of time and substituting gives a

linearly decreasing function for MF:

MF = PAC 2gh.- PgC A t (3.12)

where hi is the initial height of the fuel in the tank

relative to the discharge opening. Note that the initial

flow rate (t = o) is directly proportional to the discharge

area. The time required for the tank to drain is given by:

-22-
1.0

0.8

: 0.6

N)I 0z 0.4 .<

Ambient Temperature = 293 K

Source Blackbody = 1150 K

0.2 Temperature

1 10 T E.000 10P 10.000

PATH LENGTH THROUGH THE ATMOSPHERE (meters)

Figure 3-2. Atmospheric Transmissivity as a Function of Relative HumidityI 0 '

1 I
(pressure, level in the tank, etc) and an assumed value for

discharge area. This obviates the need for detailed

information describing the fire dynamics of a particular

accident situation.

In the following two sections, methods for estimating

fuel flow rates from a liquid fuel tank and a high-pressure

pipeline are presented. The tank model is time-dependent,

while the pipeline analysis uses an approximate,

steady-state solution.

3.5.1 Flow From a Tank

Consider a tank discharging a liquid fuel through an

opening of area A. For simplicity, the tank is assumed to

have a constant cross-sectional area S as shown.

AREA S

h

DISCHARGE HOLE AREA A

The discharge mass flow rate MF is given by: 1 2

MF = PVA (3.10)

where p is the density of the fuel, and V is the discharge

velocity. Application of Bernoulli's principle gives

V = C 2gh (3.11)

where C is the orifice flow coefficient (typical value

0.6). Developing a solution for h, the level of the fuel in

the tank, as a function of time and substituting gives a

linearly decreasing function for MF:

M = PAC 2gh. - PgC2 A t (3.12) MF =1A ~g S

where hi is the initial height of the fuel in the tank

relative to the discharge opening. Note that the initial

flow rate (t = o) is directly proportional to the discharge

area. The time required for the tank to drain is given by:

-22-
1.0 1.0. . . . ... . . . . . . . . l . . . . . ... . . . . .

0.8

w

;5

Ca

z

I.-

0.6

0.4

I I I II III~

I

I

Ambient Temperature = 293 K

Source Blackbody = 1150 K

Temperature

I I I I I I I Ii

I I I I I I iII I I I I I I I II I I I I I IuIdI

Relative Humidity

20%

60%

0.2

0.0 I I I I 1 11 I I I I I I I I

1 10 100 1.000 10.000

PATH LENGTH THROUGH THE ATMOSPHERE (meters)

Figure 3-2. Atmospheric Transmissivity as a Function of Relative HumidityI 0 'II
(pressure, level in the tank, etc) and an assumed value for

discharge area. This obviates the need for detailed

information describing the fire dynamics of a particular

accident situation.

In the following two sections, methods for estimating

fuel flow rates from a liquid fuel tank and a high-pressure

pipeline are presented. The tank model is time-dependent,

while the pipeline analysis uses an approximate,

steady-state solution.

3.5.1 Flow From a Tank

Consider a tank discharging a liquid fuel through an

opening of area A. For simplicity, the tank is assumed to

have a constant cross-sectional area S as shown.

43 

h

DISCHARGE HOLE AREA A

The discharge mass flow rate MF is given by: 1 2

MF = PVA (3.10)

where p is the density of the fuel, and V is the discharge

velocity. Application of Bernoulli's principle gives

V = C 2gh (3.11)

where C is the orifice flow coefficient (typical value

0.6). Developing a solution for h, the level of the fuel in

the tank, as a function of time and substituting gives a

linearly decreasing function for MF:

MF = PAC 2ghi -

- PgC2 A S 2t (3.12) ( . 2

where hi is the initial height of the fuel in the tank

relative to the discharge opening. Note that the initial

flow rate (t = o) is directly proportional to the discharge

area. The time required for the tank to drain is given by:

-22-
'2~1/2

t=S (2h) 12(3.13) tD CA'

3.5.2 Discharge From a High-Pressure Pipeline

High-pressure pipelines are used principally for the

transport of large quantities of methane (natural gas, NG),

and to a lesser extent, liquified petroleum gas (propanebutane). This study will consider only NG pipelines, whose

sizes range up to 1.1 m (3-1/2') diameter, with operating

pressures from 4.8 to 6.9 MPa (700 to 1000 psi) 1 8 and

normal flow velocities about 10 to 15 m/s (25 to 35 mph).

Breaks in such pipelines produce choked flow, in which

the discharge velocity is near sonic and the mass flow rate

is relatively independent of the downstream (atmospheric)

pressure. In Appendix A an approximate steady-state analysis is developed for the blowdown of a high-pressure,

natural gas pipeline, in which the long pipe acts as the

reservoir and as a flow restrictor (through friction).

Since such a complex model is relatively difficult to use,

the detailed calculations are presented in Appendix A and a

range of blowdown flow rates are summarized for various

pipeline diameters in Table 3-1. Also listed for each size

are the estimated flame heights, based on correlations from

Reference A3 for turbulent diffusion flames, and equivalent

spherical flame diameters, based on this work.

TABLE 3-1

Maximum Discharge Flow Rates for NG

Transmission Pipelines

Equivalent

Spherical

Pipeline Diameter Mass Flow Rate Flame Height Diameter

meters (feet) (kg/s) (m) (i)

.15 (0.5) 14-25 56-61 27-36

.30 (1.0) 80-140 110-140 65-84

.45 (1.5) 270-280 170-210 110-140

.61 (2.0) 520-810 240-290 160-200

.91 (3.0) 1400-2100 370-440 270-330

1.07 (3.5) 2000-3200 430-530 320-400

-23-
4.0 EXAMPLE CALCULATIONS

For illustrative purposes, three example fire accident

scenarios are analyzed for the purpose of predicting the

resultant heat flux as a function of range and maximum allowable exposure duration. The first is a 0.91 m (3') diameter

high-pressure, natural gas pipeline with an assumed hole

diameter equal to the pipeline size. The second is a large

gasoline storage tank with a 1 m2 diameter discharge hole

area. The third analysis considers a 0.15 m (1/2') diameter

high-pressure, NG pipeline and provides a flame size comparison with some experimental data.

4.1 High-Pressure Natural Gas Pipeline

Consider the discharge from a 0.91 m (3') diameter

natural gas transmission line exhausting through a 0.91 m

(3') circular hole. The standard operating pressure is

assumed to be 69 MPa (1000 psig). From Appendix A, the mass

flow rate ranges from 1400 to 2100 kg/s; an average value of

1700 kg/s will be used for MF. The radiated power PR

obtained assuming complete combustion is given by Equation 3.1:

= MF [7lLHC - (Tf - Ta)( S(l + X)Cpa + Cpf)]/103

where

n = fraction of fuel burned

AHC = heat of combustion of fuel

= 2.13 x 105 cal/mole 1 3

= 5.6 x 107 J/kg

Tf = flame temperature or temperatures of combustion

products

= 1500 K1 4

Ta = initial air temperature

= 300 K

X = fraction of excess air

= 0.25

S = stoichiometric air/fuel ratio

-24-
= 1713

Cpa = mean heat capacity of air

= 1150 J/kg K13

Cpf = mean heat capacity of fuel

= 2200 J/kg K1 3

Substituting, we have:

PR = (1700 kg/s)1(5. 6 % x 107) - 1500 - 300) x

[(17.2)(1 + 0.25)(1150 J/kg) + (2200 J/kg)]1/103 j

- (1700 kg/s) 1(5.6 x 107 J/kg) - (3.2 x 10 7 J/kg)l/103

= 4.1 x 10 7 kW

The intermediate line above shows that about 60 percent of

the theoretically available energy is used to heat up the

fuel and entrained air.

Using a surface emittance of 150 kW/m 2 from Section

3.2 gives a surface area of 2.7 x 105 m2 . For an assumed

spherical flame, the diameter is approximately 295 m. From

Section 3.3, the shape factor is

2952

F =TF - 2 2 (4.1)

295 + 4R

Some nuclear power plants have medium to large natural gas pipelines as close as 500 m from the nearest safety-related

structure. For the purposes of this example calculation,

standoff distances of 500, 1000, and 1500 m will be used.

The incident flux upon the target PT is given by:

Qi = P suTFT-F (4.2)

Using a value of 350 kW/m 2 for PSU from Section 3.3, the

values for Qi for the three ranges are:

Range FTF Qi

500 m .080 19.6 kW/m 2

1000 .021 4.6

1500 .010 2.0

-25-
Thus, at slightly under two fire diameters away (500 m), the

heat flux on the target is reduced from the specific emission

power by a factor of about 18.

The wall response model described in Chapter 2

(Table 2-1) indicates a maximum allowable exposure time of

about 9.5 hours for an incident heat flux rate of

20 kW/m 2 . This is greatly in excess of expected fire

durations, as transmissions pipelines have automatic

isolation values at regular intervals.

The combination of heat fluxes and exposure durations

estimated above are high compared to the heat required to

produce third-degree burns on exposed skin. Hardee and

Lee 1 5 give a condition for third-degree burns of 130 kJ/m2

for a 10 to 30 second exposure. This corresponds to heat

fluxes of 4 to 13 kW/m 2 . The short exposure times, as

compared to postulated fire durations, could severely

restrict personnel movement and emergency response near such

a fire.

4.2 Gasoline Storage Tank

A typically large storage tank for gasoline and other

liquid petrochemicals is on the order of 2-1/2 million

gallons (60,000 bbls or 9460 m3). Tank dimensions are

30 m diameter by 14 m high (100' x 40'). For a discharge

hole of 1 m2 area, the initial mass flow rate MF is:

MF = (800 kg/mi3)(l m2 (0.6)[((2) x (9.8 m/s 2)(14 m)]

= 7950 kg/s

The radiated power PR is

P = M F[)AH - (Tf - Ta)(llS(l + X )Cpa + Cpf)]/103 PRFC

where

n = fraction of fuel burned

AHC = heat of combustion of fuel

= 1.3 106 cal/mole 1 3

= 4.8 107 J/kg

Tf = flame temperature or temperature of combustion

products

= 1500 K

-26-
Ta = initial air temperature

= 300 K

X = fraction of excess air

= 0.25

S = stoichiometric air/fuel ratio

= 1513

Cpa = mean heat capacity of air

= 1150 J/kg K1 3

Cpf = mean heat capacity of fuel

= 1670 J/kg K1 3

Substituting, we have

PR (7950 kg/s)i(1)(4.8 x 107 J/kg) -

(1500 - 300)[(1)(15)(1.25)(1150 J/kg K) +

(1670 J/kg K)]II

(7950 kg/s 4.8 x 107 J/kg - 2.8 x 107 J/kg1/10

- 1.6 x 108 kW

Using a surface emittance of 75 kW/m 2 from Section 3.2,

the estimated flame surface area is 2.1 x 106 m2 . For

an assumed spherical flame shape, the diameter is approximately 820 m. From Section 3.3, the shape factor is

F = - 8202 T-F 8202 + 4R 2

For the three standoff distances used in the previous section, and using a specific emissive power of 150 kW/m 2

from Section 3.3, the shape factors, incident radiant energy,

and maximum exposure times are

Range FTF Qi tMAX

500 m 0.40 42 kW/m 2 ý 5.5

1000 0.14 14 -12

1500 0.07 6.3 -

-27-
Even at the shortest range, the maximum allowable exposure

time is about 5.5 hours. These maximum allowable exposure

times should be compared to total fuel consumption times of

less than 1 hour (9460 m3 x 800 kg/m 3 + 7950 kg/s).

4.3 NG Pipeline (1/2') and Comparison With Tests

As part of a series of tests involving extinguishment of

natural gas fires, measurements were made of the flame size

and fuel flow rate. 1 6 Their correlation for flame area

versus fuel flow rate V (in standard cubic feet per second)

is

A - 122 V2/ 3 (4.4)

Their largest fuel flow rate was approximately 2600 ft 3 /sec,

which gives a flame surface area of 23100 ft 2 (2150 m2 ).

Applying the methodology of this report, the fuel flow

rate is 52.6 kg/s and the radiated thermal power is

1.26 x 109 W. Using a value of 150 kW/m 2 for the

specific emissive power gives a flame surface area of

8400 m2 . This is a factor of 4 larger than the experimental data, suggesting that a more realistic or central

estimate for the surface emittance might be more appropriate

for calculating the flame surface area. Using 300 kW/m 2

gives an area of 4200 m2 . Other parameters which could

affect these estimates include combustion efficiency, fraction of excess entrained air, and flame temperature.

5.0 SUMMARY

The vulnerability of and hazards to nuclear power plant

structures arising from large, external fires is examined.

The inherent vulnerability of a plant is the capacity of the

concrete safety-related structures to absorb thermal loads

without exceeding the thermal and structural design criteria.

First, the passive capacity of reinforced concrete panels

to absorb high heat fluxes was determined. The range of

heat fluxes considered was 15 to 1400 kW/m 2 . The latter

corresponds to the emissive power of a gas volume radiating

as a black body at the adiabatic flame temperature. Two

phenomena were considered: heat conduction into the wall,

and, for heat fluxes above 350 kW/m 2 , ablation or erosion

of the front surface. Reradiation heat loss effects at the

exposed concrete surface are included. For each value of

the heat flux, three criteria were used to determine the

maximum allowable exposure time:

1. Maximum temperature at the first rebar location

of 177 0 C (350 0 F); short-term bulk ACI and ASME

criteria.

-28-
2. For high heat fluxes, erosion limited to 1/2

the distance to the first rebar.

3. Maximum temperature at the inside surface of

the wall of 50 0 C (120 0 F).

For heat fluxes above 500 kW/m 2 , the erosion criterion

applies. Below this flux, the first criterion defines the

acceptable exposure duration of the fire. For the range of

heat fluxes considered (15 to 1400 kW/m 2 ), the temperature

limit of the third criterion is never reached. Therefore,

it may be concluded that external fire events pose no direct

threat to safety-related equipment or systems located inside

concrete power plant structures.

Second, a relatively simple model for estimating the

thermal output of large fires was' developed. Based on the

estimated fuel flow rate and the total thermal energy produced, the experimentally observed specific power emitted

from the surface of large flames was used to estimate the

emitting area and the flame size. Using an assumed spherical

flame shape, the view factor and the heat flux incident upon

the target are developed as a function of range.

To help in accident evaluations, methods are presented

for estimating fuel flow rates for high-pressure natural gas

pipelines and large liquid petrochemical storage tanks.

Three example calculations are presented: rupture of a

0.91 m (3') NG pipeline, a 1 m2 hole in a 2.5 M gallon

gasoline tank, and rupture of a 0.15 m (1/2') NG pipeline

(including comparison with experimental data). For a fire

to plant range of only 500 m, none of these accidents would

pose a threat to the safety-related structures -of a nuclear

power plant based on the combinations of heat flux and

exposure duration given in Table 2-1 and Figure 2-6.

One of the original goals of this study was to develop

for general use an explicit (graphical) relationship between

the maximum allowable exposure time and the range, for

several selected values of the fuel flow rate. The results

of Chapters 3 and 4 show that only very large fires at close

ranges produce heat fluxes on the target above the lowest

value considered, 15 kW/m 2 , which corresponds to an exposure time of 12 hours. While the graphical relationship

could not be developed in a useful form for standoff distances of interest (-500 m); the analysis methods can still

be applied on a case-by-case basis.

-29-
REFERENCES

1. Bennett, D. E., and N. C. Finley, "Hazards to Nuclear

Power Plants From Nearby Accidents Involving Hazardous

Materials--A Preliminary Assessment," Sandia National

Laboratories, Albuquerque, New Mexico, SAND80-2334,

NUREG/CR-1748, April 1981.

2. American Concrete Institute, Sections SP-4, SP-55.

3. American Society of Mechanical Engineers, Code Section

III. 440.

4. Parker, R. 0., "Calculating Thermal Radiation Hazards

in Large Fires," Fire Technology, Vol. 10, May 1974,

pp. 147-152.

5. Harmathy, T. Z., and L. W. Allen, "Thermal Properties

of Selectea Masonry Unit Concrete," American Concrete

Institute Journal, February 1973, pp. 132-142.

6. Muir, J. F., "Response of Concrete Exposed to a High

Heat Flux on One Surface," November 1977, SAND77-1467,

Sandia National Laboratories, Albuquerque, New Mexico.

7. Chu, T. Y., "Radiant Heat Evaluation of Concrete--A

Study ot the Erosion of Concrete Due to Surface Heating," January 1978, SAND77-0922, Sandia Laboratories,

Albuquerque, New Mexico.

8. Lewis, D. R., J. D. Gaski, and L. R. Thompson, "CINDA3G-Chrysler Improved Numerical Differencing Analyzer

for Third Generation Computers," Report NASA-CR-99595,

National Aeronautics and Space Administration,

October 20, 1967.

9. Siegel, R., and J. R. Howell, Thermal Radiation Heat

Transfer, McGraw-Hill Book Co., New York, NY, Second

Edition, 1981.

10. Hottel, H. C., and A. F. Sarofim, Radiative Transfer,

McGraw-Hill Book Co., New York, NY, 1967.

11. Raj, P. K., "Atmospheric Attenuation of Thermal Radiation, Exhibit 1005, Rebuttal Testimony," Docket

CP-73-47, CP-73-132, et al, Hearings before FPC,

February 1976.

-30-
12. Cline, D. D., and L. N. Koenig, 'The Transient Growth

of an Unconfined Pool Fire,' Sandia National Laboratories, Albuquerque, New Mexico, SAND82-1512J, to

appear in Fire Technology, May 1983.

13. Bolz, R. E., and G. L. Tuve, Editors, Handbook of Tables

for Applied Engineering Science, Second Edition, The

Chemical Rubber Co., Cleveland, Ohio, 1976.

14. Raj, P. K., N. A. Moussa, K. Aravamudan, and C. D.

Lind, "LNG Spill Fire Tests on Water--An Overview of

the Results," Proceedings Transmission Conference,

American Gas Association, May 21-23, 1979, New Orleans,

Louisiana, #79-T-50.

15. Hardee, H. C., and D. 0. Lee, "A Simple Conduction

Model for Skin Burns Resulting From Exposure to Chemical

Fireballs,' Fire Research, 1, 199-205, (1977/78).

16. Guise, A. B., "Extinguishment of Natural Gas Pressure

Fires," Fire Technology, Vol. 3, pp. 175-193, 1967.

17. Structural Analysis and Design of Nuclear Plant Facilities, Committee on Nuclear Structures and Materials,

Structural Division, American Society of Civil

Engineers, New York, NY. Manuals and Reports on

Engineering Practice, No. 58, 1980.

18. Natural Gas Survey, Volume III, Transmission, Task

Force Reports, Federal Power Commission, Washington,

DC, 1973, p. 128.

19. Hardee, H. C., D. 0. Lee, and W. B. Benedick, "Thermal

Hazards From LNG Fireballs,' Combustion Science and

Technology, Vol. 17, pp. 189-197, 1978.

20. Steward, F. R., "Linear Flame Heights for Various

Fuels," Combustion and Flame, Vol. 18, pp. 171-178,

1964.

21. Steward, F. R., "Prediction of the Height of Turbulent

Diffusion Bouyant Flames,' Combustion Science and Technology, Vol. 2, pp. 203-212, 1970.

22. Zukoski, E. E., T. Kubota, and B. Cetegen, "Entrainment

in Fire Plumes," National Bureau of Standards,

Washington, DC, NBS-GCR-80-294, March 1981.

-31-
6.0 APPENDIX--DISCHARGE FROM A HIGH-PRESSURE NATURAL GAS

PIPELINE

The rupture and subsequent discharge of a high-pressure

natural gas pipeline is a time-dependent blowdown problem.

The exit mass flow rate is a complex decaying function of

time, in addition to being dependent on accident conditions

(eg, hole shape, roughness, orientation, etc). A simpler

approach is to evaluate steady-state flow rates which will

bound the problem. For the purposes of safety analyses,

such an approach is both sufficient and conservative.

Let us consider a pipeline of diameter D, cross-sectional

area A, initial pressure P, and initial temperature T filled

with natural gas. For typical US pipelines, the initial

conditions are:

T = 300 K

P = 6.9-106 Pa (1000 psi)

p = 44.4 kg/m

where P is the density. The normal transmission velocity of

10 to 15 m/s (25 to 35 mph) can be neglected in the blowdown

analysis. Sizes range up to 1.07 m (3-1/2') in diameter;

this analysis will consider 6 sizes from 0.15 m (1/2') to

1.07 m (3-1/2').

The discharge flow rate MF is given by:

MF = pAV = PAMC

where V is the discharge velocity, M is the Mach number, and

C is the sound speed. Immediately after rupture of the

pipeline, the flow velocity is near sonic (M • 1). For an

ideal gas, the sound speed is given by

C = (YRT) 1 /2

where R is the gas constant (518.2 J/kg K for methane), and

Y is the ratio of the specific heats. In Table A-l, this

maximum discharge flow rate is listed in the fifth column.

In the first four columns are the diameter, cross-sectional

area, volume of a 30 km length of pipeline and the total

mass contained in the 30 km length. The choice of 30 km is

based on a reasonable but still conservative estimate of the

distance between automatic block (or safety) valves in pipelines.

As the pipeline blows down, the flow can be characterized

as adiabatic (or isentropic) with friction between the gas

and the pipe wall. The high initial pressure means that the

flow is choked; that is, the flow conditions are not

-32-
influenced by conditions after the pipe exit (eg, backpressure or atmospheric pressure). Steady-state, adiabatic

flow with friction is described by the Fanno line equations,

which are given in several texts.AlA2

A steady state problem consisting of the discharge of a

semi-infinite reservoir through a length of pipe, L, is

readily solvable. The steady-state flow rates for several

pipe lengths should provide reasonable estimates for actual

blowdown flow rates. The reservoir is assumed to be at the

same temperature and pressure as in the pipeline prior to

the accident. For this analysis, two pipe lengths of 2 and

5 km were chosen. The friction factor was taken to be 0.003.

Tabulated values for the Fanno line equations can be

used to estimate the flow velocity at the entrance to the

length, given that the exit velocity is sonic (M = 1). In

Table A-i, column 6 lists the entrance Mach numbers for the

two pipe length, and column 7 lists the corresponding mass

flow rates.

A rough estimate of the blowdown time can be made using

a fraction of the mass flow rate for the 5 km pipe. For

this safety analysis, the fraction was taken to be onefourth. This, in a sense, represents an "average" flow rate

over the entire discharge time. Using the total mass in the

pipeline, estimates for the blowdown times are listed in

column 8, and they range from about 2 hours for small pipes

to less than 3/4 of an hour for large ones. As will be

seen, these times are relatively short compared to maximum

allowable concrete exposure times.

Estimates of the visible height of turbulent diffusion

flames can be made using the correlations developed by Becker

and Liang.A 3 Using their notation except for H for the

flame height and MF for the mass flow rate, the appropriate

correlation is:

= 0.18 + 0.022VH

where

(DsO ) 2/3

H =H 1

= e c4 MFUs d

Ds =effective source diameter

-33-
_ ( M 1/2

WI = (1 + air/fuel ratio)-I

= (I + 17)-i = 1/18 for methane

Us = effective gas velocity at source

= 450 m/s

g = graviational constant

= 9.8 m/s 2

Po = ambient air density

= 1.29 kg/m3

Ml = mean molecular weight of stoichiometric combustion

products at the adiabatic combustion temperature

= 26.7 kg/kg mole

M = mean molecular weight of air

= 28.8 kg/kg mole

T1 = adiabatic combustion of a stoichiometric air/fuel

mixture

= 2220 K

Tm = ambient temperature

= 300 K

Performing the substitutions, the equation for 0 reduces to:

1.78 MF H

H H2/3 2/3 _ = 0.18 + 0.00618 FH1

For each of the mass flow rates in Table A-i, this equaton

was solved numerically for the estimated flame height.

These values are listed in column 9.

-34-
Finally, the fire model developed in Sections 3.1 and

3.2 and illustrated in Section 4.1 can be used to estimate

the equivalent sphere diameter for fires with the mass flow

rates as listed in column 6. The total radiated power is

listed in column 10, the flame surface area in column 11 and

the equivalent sphere diameter in column 12. The flame

heights predicted by the correlations of Becker and Liang

range from about twice the sphere diameter for smaller pipelines to about 25 percent greater for large pipelines.

Since large flames would be expected to have heightto-diameter ratios in the range of 2 to 5, the use of the

equivalent sphere for estimating fire vulnerability is conservative. That is, the radiating area for an inverted cone

(using the height in column 9) would be less than the radiating area for a sphere (column 11).

REFERENCES

Al. Zucrow, J. J., and J. D. Hoffman, Gas Dynamics, John

Wiley and Sons, Inc., New York, 1976.

A2. John, J. E. A., Gas Dynamics, Allyn and Bacon, Boston,

1969.

A3. Becker, H. A., and D. Liang, "Visible Length of Vertical

Free Turbulent Diffusion Flames," Combustion and Flame,

Vol. 32, pp. 115-137, 1978.

-35-
TABLE A-1

Data for Large Pipeline Fires

Mass Flow Discharge

Cross Volume Total Maximum Mach Number Rates for Time Using Total Flame Equivalent

LI

Diameter

(m)

(.5.)

.30

(I'*

.45

(1.5')

.61

(21)

.91

(3')

1.07

(3..5' )

Section.al

Area

2

.01.

-071

of 30 km

Length

(m3)

5. 3E2

2.. 1E3

Mass

In 30 km

4(kg)

2.* 4E4

Flow

Rate

(kg3a)

3-5E2

.16 4.,E3

.29 8.893

9. 3E4 1.4E3

2.1E5 3.2E3

3.9E5 5.8E3

8.5E5 I1 3.34

1-2E6 1.BE4

for

5 km & 2 km

Pipes

.04

.07

.06

.10

.07

.12

.09

.14

.11

.16

.11

.18

5 km & 2 km

Pipes

(kg/s)

14

35

80

140

220

380

520

810

1400

2100

2000

3200

Rate Height

(hrs) (m)

1.9 51

66

1.3 110

140

1.1 170

210

.8 240

290

.7 370

440

.7 430

530

Power

(J)

3.4E8

6.0E8

I .9E9

3.4E9

5. 3E9

9.1E9

I .3EJ0

I 9E1 0

3.4E] 0

5 OEI 0

4.8E]0

7.7E] 0

1/4 of 5 km Flame Radiated Surface Sphere

Area

(m2)

2.2E3

4.0E3

1.3E4

2. 2E4

3.5E4

6.1E4

8.3E4

1.3E5

2.2E5

1.4E5

3.2E5

5.JE5

Diameter

(m)

27

36

64

84

110

140

160

200

270

330

320

400

.64 l.9E4

.90 2.7E4
Distribution

US NRC LIstribution Contractor (CDSI)

7300 Pearl Street

Bethesda, MD 20014

405 Copies for R4, RP

Kenneth G. Murphy (5)

Division of Risk Analysis

US Nuclear Regulatory Commission

Washington, DC 20555

1510 D. B. Hayes

1513 D. W. Larson

1513 D. D. Cline (5)

1520 i.. B. Lane

1824 J. N. Sueet

3141 L. J. Erickson (5)

3151 W. L. Garner

6255 D. 0. Lee

6400 A. W. Snyder

6410 D. J. McCloskey

6412 J. W. Hickman

Attn: G. J. Kolb

6414 D. M. Ericson, Jr.

6414 D. L. Berry

6415 D. C. Aldrich

6415 D. E. Bennett (20)

6422 D. A. Powers

6440 D. A. Dahlgren

6442 W. A. Von Riesemann

6443 D. D. Carlson

b446 B. E. Bader

6448 L. 0. Cropp

7530 W. E. Caldes

8214 M. A. Pound

-37-

I

NRC FORM 335 1. REPORT NUMEER (Assigned by DOC)

U.S. NUCLEAR REGULATORY COMMISSION NUREG/CR-3330

BIBLIOGRAPHIC DATA SHEET SAND83-1178

4. TITLE AND SUBTITLE (Add Volume No., if appropriate) 2. (Leave blank)

VULNERABILITY OF NUCLEAR POWER PLANT

STRUCTURES TO LARGE EXTERNAL FIRES 3. RECIPIENT'S ACCESSION NO.

7. AUTHOR(S) 5. DATE REPORT COMPLETED

David E. Bennett MONTH YEAR

August 1983

9. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS (Include Zip Code) DATE REPORT ISSUED

Sandia National Laboratories MONTH j YEAR

Albuquerque, NM 87185 September 1983

6. (Leave blank)

8. (Leave blank)

12. SPONSORING ORGANIZATION NAME AND MAILING ADDRESS (include Zip Code)

Division of Risk Analysis 10 PROJECT/TASK/WORK UNIT NO.

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555 A1214

13. TYPE OF REPORT PERIOD COVE RED (Inclusive dares)

Technical

15. SUPPLEMENTARY NOTES 14. lLeave Wlank)

16. ABSTRACT (200 words or less)

This report examines the inherent vulnerability of

nuclear power plant structures to the thermal environments

arising from large, external fires. The inherent

vulnerability is the capacity of the concrete safety-related structures to absorb thermal loads without exceeding the

appropriate thermal and structural design criteria. The

potential sources of these thermal environments are large,

offsite fires arising from accidents involving the

transportation or storage of large quantities of flammable

gases or liquids.

A realistic thermal response analysis of a concrete panel was performed using three limiting criteria:

temperature at the first rebar location, erosion and

ablation of the front (exterior) surface due to high heat

fluxes, and temperature at the back (interior) surface. The

results of this analysis yield a relationship between

incident heat flux and the maximum allowable exposure

duration.

A simple fire analysis method was developed to predict the thermal flux incident upon a target as a function of

range. A key feature is the use of an experimentally observed specific power emitted from the surface of large fires.

Example calculations for the break of a 0.91 m (3'

17. KEY WORDS AND DOCUMENT ANALYSIS diameter high-pressure natural gas pipeline and a 1 ml

hole in a 2-1/2 million gallon gasoline tank show that the

resulting fires do not pose a significant hazard for ranges

of 500 m or greater.

17b. IDENTIFIERS/OPEN-ENDED TERMS

18. AVAILABILITY STATEMENT 19. SECURITY CLASS (This report) 21. NO. OF PAGES Unl a ssi fi ed 3 7

Unlimited 20. SECURITY CLASS (This$page) 22 PRICE

NRC FORM 335 111.81)


0 rg. Bldg. Name Rec'd by jOrg. Bldg. Name Rec'd by'

Org. Bldg. Name Rec'd by fOrg. Bldg. Name Rec'd by

Sandia National Laboratories