A computer simulation of a derailment accident: Part I - model basis

Journal of Hazardous Materials, 25 (1990) 121-147 Elsevier Science Publishers B.V., Amsterdam

A COMPUTER

SIMULATION

121

OF A DERAILMENT

ACCIDENT:

Part I - Model Basis

A. M. Birk’ R. J. Anderson’ A. J. Coppens 1. 2.

Department of Mechanical Engineering Queen’s University, Kingston, Ontario, Canada W.R. Davis Engineering, Ottawa, Ontario, Canada

ABSTRACT A prototype

computer

program

some of the consequences from a number liquid spills, dangerous

of models

commodities,

explosion

and train consist post-processor present

technical

fire impingement

blast over-pressure

mechanics,

flammable

on tank cars carrying

and thermal

Most of these sub-models

is made up

radiation,

have previously

and been

and are available in the open literature.

The overall program

The

accident. The program

which account for train derailment

fire effects on remote targets,

heavy plume and puff dispersion. developed

has been developed which is capable of simulating

of a train derailment

consists

of a pre-processor

data, a simulation which presents

the results

paper briefly describes

basis of the simulation

for inputting

module containing

the surroundings

the various

of the simulation

models

data

and a

in graphical form.

the overall organization

of the program

and the

models.

INTRODUCTION In recent years there have been many studies consequences

of train derailment

are those that could potentially liquids

accidents.

of hazardous

resulted

in the development

of models

activities

The consequences

or vapours,

and some resulted

in computer

fires,

and explosions.

for predicting models.

remained

as stand alone tools and many require

estimated

from accident statistics

0 -

to estimate

Many of these

these

1990 Elsevier Science Publishers B.V.

studies

the effects of these models

detailed input which must

or just guessed.

interest

such as accidental

quantitatively

However,

the

of particular

cause harm to people or property

releases

0304-3894/90/$03.50

performed

usually be

have

The objective of the present for simulating simulate

study was to develop a prototype

the consequences

what happens

of train derailment

in a derailment

leaves the track to when the last tank car empties The program was to be based on current taking place in such an accident. demonstration The study

version

consequences integrated

of the most significant

into a single

The simulation

models

was to

its relief valve or explodes.

of modelling

the various

processes

of the program was to be a

program.

and techniques

accident related phenomena

of new models as required.

data input and results program

The first version

program

from the time when the first car

through

methods

The

program

and as such was to be limited in its capabilities.

involved a search for current

the development

accidents.

accident starting

computer

These

various

Pre-and post-processors

models

for estimating

the

and in some cases were then

were then developed for

presentation.

program

is presently

running

is called DERACS on an IBM/AT

order of one half hour, depending

for Derailment compatible

Accident

Simulation.

machine with run times

on the number of vehicles

The in the

and the consequences

involved. This

program

program

is the prototype

which is somewhat

limited in scope. At present

can handle up to forty cars in a train, and of these,

cars carrying

propane, chlorine

or hexane. These

they include a toxic gas, a flammable environment.

Future

versions

commodities

gas and a flammable

of DERACS

were chosen

1

Example

because

liquid when released

into the

will be expanded to include more cars and

additional commodities_

Figure

the

up to eight can be tank

of Map Generated using

DERACS

Pre-Processor

123

The intended team training techniques,

applications

of the program

and risk analysis. it is possible

Because

that the simulation

and used as one input for response possible

after considerable

PROGRAM

post-processor.

The

response

tool

and validation.

consists

of the pre-processor,

pre-processor

the simulation

software,

is used to create the surroundings

in which the

of the train at the time

will also allow the user to bypass

and input the locations

and the

of the derailed vehicles

the derailment along with

of punctures.

The pre-processor mouse

response analysis

latter application would only be

additional development

The pre-processor

simulation

descriptions

is a user friendly

to draw a map including

different

could be used as an on-site

tactics. This

is to take place and also reads in the initial conditions

of the derailment. mechanics

is based on current

ORGANIZATION

The overall program derailment

include accident reconstruction,

the simulation

sizes,

single

elevation contour

routine that allows the user with the aid of a

such things

as: rivers

or double railway tracks,

and lakes, forests,

buildings,

property

roads of

boundaries,

and

lines. The total map area is IOkm by 1Okm and the user can input

part or all of this area when creating the map. Figure created using the pre-processor

and Figure

1 presents

an example

2 is a key to the symbols

of a map

appearing

on the

map. In addition, the pre-processor information

Figure

2

for the simulation,

DERACS

has the function

including

of reading in all the other necessary

environmental

Key Page for Map Symbols

conditions,

such as wind speed

124 and direction,

ambient

temperature

such as car type, commodity, Depending derailment

on the options

and atmospheric

pressure,

initial_fill and temperature, selected,

point and the car number,

data

etc.

the pre-processor truck number

and train consist

will read in the location

and axle number

of the

of the car which

initiates the derailment. The train speed desired

and direction

is also read in during the pre-processor

the user has the option of overriding

portion of the overall simulation. placement

and orientation

what kind of ruptures

fashion.

it presents

of vehicles

and presents

of the simulation. simulation the accident

part of the DERACS

and

is one of the most important

to the user in a easily understandable

is used to read files that contain the results of the

this information

in graphical the

or text form to the user at the end

user can page through the

and look at various instants in time during the simulation

gives a plan view of the surroundings

after the derailment

to see how

spills, gaseous

releases,

fires, thermal

a typical image of an accident

Post-Processor

and shows placement

and the various events that are taking ruptures,

any instant in time and print out a snapshot

Figure 3

which cars are ruptured

progressed.

The post-processor the vehicles

software

By using the post-processor,

process

simulation

the user must specify the final

after the derailment,

the results of the simulation

The post-processor

sjmulation

mechanics

If

have occurred.

The post-processor because

the derailment

If this option is chosen,

session.

scene as shown

Image

explosions,

of the derailment

etc. The user can select scene.

Figure 3 presents

using the post-processor_

of Derailment

Scene

of

place such as

In this figure

at One Instant in Time

125 we have zoomed

in close to the accident location and we see the derailed cars, the

location of a spill and the beginnings The simulation consequences

starting

safely or BLEVE contains

of a heavy gas plume.

module of DERACS

carries

out the time integration

from the time of the derailment

(boiling liquid expanding

all the sub-models

to when the last car empties

vapour explosion).

that are used to simulate

of the accident

The simulation

the various

processes

module taking

place during the accident.

BASIC

ASSUMPTIONS

To carry out the simulation the consequence

resulting

propane is ruptured

a number

1) Catastrophic

Instantaneous persion

3)

Continuous

release

release

Other consequences rupture,

were necessary

For example,

and the size,

can happen, including: with resulting

explosive

of the propane gas with possible are possible.

The

it was necessary

However,

to assume

propane car case, it is assumed

and fire ball. In the event of a finite puncture results

significant The

assumptions

DERACS

therefore

version

relationships.

it is assumed

1 presents

For

would result

Eventual of DERACS

ignition more

of the most

of DERACS.

by the simulation

noted in Table

are limited to those

1,

noted.

BACKGROUND

used to simulate

the various

consider

module of DERACS

processes

the following

contains

i)

derailment

mechanics

ii)

derailment

impact induced rupture

iii)

liquid and vapour release

iv)

flammable

liquid spill growth

all the sub-models

taking place during the accident. The

processes: of tank cars

in

that a

a summary

was developed around assumptions shown

at the time of for the development

of containment

fn future versions

used in the present

As stated earlier the simulation sub-models

at present. Table

simulation

simple

of a cloud of propane.

will be considered.

the consequences

TECHNICAL

a total loss

in the dispersion

the propane cloud is not considered scenarios

dis-

that occur are a

the lading properties

an explosion

sophisticated

of the contents

ignition at some time.

exact consequences

including

shape and location of the rupture.

of DERACS,

release

release

in the form of a toxic heavy gas puff with subsequent

the ruptured continuous

with regard to

when a tank car carrying

ignition at some time.

of many variables

of this first version

of assumptions

ignition to form a fire ball.

and possible

complex function

of things

failure of the vessel

and subsequent 2)

a number

from some actions.

of

126 4

plume and puff dispersion of heavy gases

vi)

liquid pool fires and effects on surroundings

vii)

fire impingement on tanks and thermal ruptures

viii)

blast and thermal effects of explosions/BLEW3

Table 1 briefly describes the technical basis for the main sub-models.

More

complete technical descriptions can be found in Reference [l]. Action

Commodity

Consequence

DERACS Output

derailment

all

possible impact punctures of tank cars

punctured tanks identified

puncture/ rupture

chlorine

toxic release

plume extent

propane

toxic release

plume extent

hexane

flammable spill

spill diameter

chlorine

toxic release

puff eMent

propane

explosion/BLEVE

blast and thermal hazards

hexane

flammable spill

spill diameter

pool fire

thermal radiation dose and, fire impingement of tank cars within spill region

chlorine

toxic release

plume extent

propane

burning flare

flare size

hexane

burning flare

flare size

total loss containment

flammable spill

tank car relief valve action

fire impingement of tank cars within range of flare

burning flare

explosion/ BLEVE

explosion and fireball with blast overpressure and thermal radiation

blast and thermal hazard distances

tank fire impingement

possible thermal rupture (total loss of containment)

tank and lading properties at time of failure

Table 1

Assumed Cause and Effect Relationships for Tank Cars and Commodities Considered in DERACS

Derailment Mechanics The derailment mechanics sub-model involves the solution of the governing equations for rigid body motion of the vehicles allowing for four degrees of freedom ( x,

y, yaw, roll). These to the derailment

variables

are defined in Figure

point. This

sub-model

was developed specifically

unique in that it allows for vehicle uncoupling vehicle roll. The only previous uncoupling

for DERACS

in the event of coupler

model (by Yang and Manos

their relationship

breakage

and is and

[2]) could not allow vehicle

and vehicle roll.

The vehicles

are assumed

to consist

of a car body supported

having two wheel sets each. To limit the number been assumed sets

4 which also shows

that the truck frames

of resulting

on two trucks,

differential

each

equations,

it has

are fixed relative to the car body and the wheel

are fixed relative to the truck frames. The forces

couplers,

assumed

to act on the vehicles

and the wheel/rail

The couplers assumed

to release

2.3 million

or wheel/ground

are assumed

to be infinitely

when a threshold

strong

for compressive

are modelled

as a simple

loads but are

load is exceeded. The assumed stiffness

the cars are free to move apart. Because

applied by the

forces.

N which is the elastic limit for the coupler shanks

The couplers coupler

include the inter car forces

element.

of the assumed

threshold

as reported

load is

by Wallace

Once the couplers

release,

use of shelf couplers,

simple

refease due to relative verticai motion is not considered.

Ground forces being opposite friction forces

are assumed

to act as a Coulomb

type friction force, the direction

to the vehicle velocity vector at the point of contact with the ground. are assumed

vehicle linear and rotational truck centres

and these

to act at the two truck centres velocities

for an upright

car. The

are used to calculate the velocities

are used to determine

at the two

the friction force directions

and

I DERAILMENT

POINT

1 DX TANGENT

TO POINT 0

4 RADIAL LINE OUTWARD Y

Figure

[3].

4

Definition

of Degrees

of Freedom

of Car Relative to Derailment

Point

The

128

Figure

5 Free-Body

magnitudes

Diagram of a Car

assuming

each truck supports

half the car weight. Figure

5 shows

the free

body diagram for a car. The equations

of motion for the x, y and yaw degrees

of freedom

are as shown

below: longitudinal

force

balance:

.

(11

MCu-Vr 1 = FCLX-FLX-FTX-FCT

lateral

force

X

balance:

(2)

M( V+ur 1 = FCLy-FLY -FTy-FCT Y

yaw

moment balance:

(3)

II- = FCLY(a+l)-FLY(l)-FTY(l)-F~y(a+l)

The model only allows roll of uncoupled tank cars (ie. coupler forces to assist imminent

in maintaining

tanks

in an upright orientation).

Roll-over

when either of the wheel normal forces approaches

are assumed

is considered

zero. It is assumed

that

129

the car losses

its trucks

and the tank becomes

amount of roll is calculated energy considerations. the maximum

a rolling cylinder.

using the foliowing

Because

expression

of the presence

If roll-over

occurs

the

which was derived by using

of a dome on the top of the tank car,

roll angle is limited to 120 degrees.

0=s-

V2

-

R

(4)

WgR

where,

0

= roll

angle

S

= rolled

R

= tank radius

V

= velocity

distance

component

I-1 = friction

The initiation

coefficient

= gravitational

g

acceleration

of the derailment

derails.

The derailment

shown

in Figure

in y direction

is an input and specifies

point is the origin for all subsequent

4. It is assumed

that all cars passing

assumed

to be engaging second

differential

emergency

This

equations.

Cars that have passed

are manipulated

Figure

6 presents

into first order

Fehlberg

[4] technique

an example of a predicted

scene.

program

has not been validated as yet and therefore

purposes

Derailment

lmoact Induced Ruoture

sub-model

of Tank

simulation,

The impacts

on car shells.

results

are presented

for

only.

For the overall derailment induced ruptures. impacts

equations

A variable run time Runge-Kutta

discussion

simulation

forces.

braking.

order differential

was used to solve the equations. derailment

as previously

point ahead of the derailed car are guided by the rails. All cars are

The resulting ordinary

calculations

this point on the rail leave the rails

and are from then on only guided by the soil interaction the derailment

the car and the truck that

it is important

are occurring

The impacts described

Cars to be able to predict impact

during the derailment

between the cars is modelled

earlier.

due to coupler using the derailment

130 NO. OF CARS TOTAL NO. OF CARS

Figure

= 35

DERAILED

6

Typical

= 24

Result

of Derailment

INTIAL TRAIN SPEED

= 100 Km/hr

TRACK CURVATURE

= TANGENT

Mechanics

Simulation

1 The prediction

of impacts

and impact induced ruptures

the following

analysis

the program

would run in a reasonable

In the present comes

is a first attempt. Significant

model, it is assumed

is a very complex

simplifications

matter and

were necessary

so that

length of time on a micro computer. that puncture

will only occur when a free coupler

in contact with a tank shell and the relative velocity between the coupler and the

impacted tank is greater than 20 m/s. hole with a diameter

This

type of puncture

of 0.3m and is assumed

the tank. If the relative velocity

is assumed

to be located at 0.5m

above the bottom of

parallel to the tank axis is greater than 25 m/s, and the

relative axial velocity is much larger than the lateral, then it is assumed is a long tear resulting This ruptured.

simple

At present

the total loss

in a total loss

impact rupture

that the puncture

of containment.

model is used to identify tank cars that have been

only the two cases

of containment,

to be a round

above, namely the 0.3m

are possible.

Future

developments

diameter

puncture

of DERACS

and

will likely

incorporate a more complex impact rupture analysis with additional possible outcomes. Liquid and Vapour

Release

Liquid and vapour release tanks

carrying

dangerous

is of importance

goods.

in the event of accidental rupture

The rate of release

of

and the phase of the released

131 commodity disperse

determine

whether

a liquid pool will form or a toxic or flammable

into the atmosphere.

If a pool of flammable consequences

liquid forms

including

vapour is released, flammable

geometries. releases,

vapour explosion

and vapours

LEAKR

of different chemicals,

performs

is possible

commodity).

or two phase subsonic

program sizes

Redlich-Kwong

[5], gaseous

and sonic gaseous

of the release of material from a tank and gives a The calculation

properties releases,

accounts

properties

et al [7] and from Perry and Chilton

are calculated from Lyman et al [9] and Perry coefficient

assumed

to be 0.61.

CLORINE

DISCHARGE

NOMOGPAPH

7

Comparison

- HOLE

of LEAKR

RUPTURE

Results

flow with a where

and the flow rate is

IN BOTTOM

OF RAILWAY

TANK

Cm

10

1 FROM

[8]. For gaseous

For single phase liquid releases

0.1 TIME

are calculated

compressible

is not taking place, the flow is treated as incompressible

by

using the

[8]. The liquid state

and Chilton

for isentropic

for heat

As described

are calculated in the program

the flow rates are based on relations

discharge flashing

properties

[6] equation of state and thermodynamic

using the method of Balzhizer

can

and

releases.

effects between the tank lading and the ambient surroundings.

Belore and Buist

If a

(in the case of a

and puncture

rates can be predicted for both subsonic a time integration

radiation

in a later section.

[S]. The LEAKR

tank shapes,

prediction for the time required to empty the vessel. transfer

further

are calculated using a modified version

by Belore and Buist

single phase liquid releases

LEAKR

on local objects and thermal

effects will be discussed

of liquids

program

Release

with resulting

or a toxic plume (in the case of non-flammable

The rates of release handle a number

These

then an unconfined

commodity)

of the computer

then a pool fire is possible

fire impingement

loading of remote targets.

Figure

cloud will

(minutes)

with TIPS

---

TIPS

LEAK PATE

-

NEW

MODEL

Nomogram

NOMOGRAMS

RESULTS

(from Ref. (5))

132 calculated from Dodge et al [IO]. At very small pressure accounted for using the methods

presented

coefficients

for both single-phase

air ingestion

by Dodge et al [IO]. When flashing

the flow rates are calculated from Mayinger rates are calculated using the methods

differentials,

[11]. For choked two-phase

of Henry

[12] and Delhaye

liquid and two-phase

is occurs,

flows the flow

1131. The flow

flows were taken from Dodge et

al [lo]. Figure LEAKR

7 presents

and release

the Environment

a graph from Reference rate calculations

Canada TIPS

these calculations

documents

and the LEAKR

[5] which shows

based on nomographs (see Reference

program

a comparison

for chlorine

between

published

[14]). For further

in

details of

the reader is directed to Belore

and Buist

[51. For use in DERACS, only calculates puncture

the original

an instantaneous

LEAKR

release

type and location, and the commodity

DERACS,

only horizontal

punctures

are assumed

longer performs

insulated

function

time steps

during the accident simulation.

liquid spills

and structures.

radiation hazards

is performed

are important

models

over a series

of

because of the fire hazard to neighbouring

simulation

it was desired

fire induced ruptures

exist for predicting

based on the assumptions

to select a spill model

of tanks as well as the thermal

spill sizes

as a function

of time for any given

that the ground is flat, smooth

However

shallow

for large shallow

pools and therefore

spills.

His model is

and impermeable. is conservative

pools, the fire durations

This

will be short.

For the

it was desired to have pools that burn for significant

periods

(20 to 60 minutes)

because these are the fires that can lead to thermal

ruptures

later on in an accident. For example, full scale fire tests

cars carrying ruptured

propane have been conducted after 24 minutes

For time dependent spills pool growth. This

by Phillips

model

for estimating

purposes,

tanks

no

of the time to

to remote targets.

tends to give large diameter,

tanks

in and

by the DERACS

For example Raj [15] developed a model for instantaneous

pool sizes.

rate calculations are considered

obtained from the modified LEAKR

For the present

that could be used to simulate

present

tanks

the

Liquid Spill Growth

Flammable

Several

cylindrical

of the release with the prediction

module using the results

release.

properties,

to be round with random petals jagged in. The program

the time integration

simulation

Flammable

has been modified such that it

fill level. For release

or uninsulated,

empty for the tank. The time integration

tanks

program

rate given the commodity

of unprotected

of time of

rail tank

[16] and in these tests

the

of fire engulfment.

Cline and Koenig

[17] developed a model for transient

model is based on mass conservation

considerations

and can

133 account for ground requires

seepage

that a uniform

For the DERACS mass

conservation

However

effects.

a simple

pool model was developed

No account has been made for momentum

considerations

rates. The model is based on the assumption

the shape of the surface.

calculated as a function for mass

this model

based purely on

up a concave shape in the region of the spill. One radius

used to describe expression

actions.

pool depth be specified.

simulation

which affect pool spreading ground takes

and other fuel consuming

of the mass

conservation

that the

of curvature

is

In the model, the size of the spill is

of liquid currently

in the pool. The following

applies for the case of spilled

liquid: (51

M = Ms-Ma-Me where, M = mass

of

liquid

in the spill

MS = mass

of liquid

spilled

Ma = mass

of

liquid

absorbed

Me = mass

of

liquid

evaporated

The volume

of

liquid

in the spill

by the ground (and

burned)

is

V = M/p

(61

= n (Rh2-h3/3)

(7)

where, R = local

radius

h = pool depth

p = average For typical spills resulting

of curvature

of the ground

at the pool centre

liquid

density

h c R and therefore

pool depth and radius

the pool volume can be simplified

can be calculated directly,

as expressed

and

below:

h = d V/(nR)

(8)

r=.

(9)

L_l,-

where,

r = the liquid

The various

mass

Euler type integration

spill

terms

radius

in equation

scheme.

(5) are calculated separately

using

a simple

134

The spilled mass is based on the puncture release models described in the previous section. The mass flow rate of liquid calculated from these models

is assumed

constant

over a single time step and the resulting mass of spilled liquid is calculated as the

product of the release rate and the time interval. The mass of liquid absorbed by the ground must be specified by some method and in the present study this effect was neglected. The mass of liquid evaporated is based on a constant pool surface regression rate based on experimental results of Hottel [18] for large pool fires involving hydrocarbon fuels. A single constant surface regression rate of 0.000083 presently used in the model. The mass of liquid evaporated

m/s is

in one time step is then:

Me = pVsnr2At where, Vs

=

surface

At

=

time

regression

rate

(10)

step

At present a single constant ground curvature of 2000m has been selected. With this curvature a liquid spill of 50000kg of hexane will result in an initial pool diameter of 19.5m and the fire will burn for approximately 26 minutes. An unprotected tank car engulfed in such a fire is likely to suffer a thermal rupture.

CYLINDER

TO REPRESENT

POOL

FIRE

Y REMOTE

TARGET

SURFACE

t

POOL FIRE BASE

Figure 8

Model for Thermal Radiation from a Pool Fire to a Remote Target

135 Thermal

Effects

of Pool Fires

The thermal are impinged thermal

effects of pool fires are important

directly

radiation

by the fire, and also on remote targets

emanating

tank cars is presently section.

The

model

because of the effect on objects that

from the fire. In DERACS

that are loaded by the

only direct fire impingement

accounted for and this will be described here considers

described

thermal

of

in more detail in a later

radiation

loads on remote

targets. Cracker

and Napier [19] have shown

be modelled Figure

by assuming

that the thermal

radiation from pool fires can

the fire acts as a vertical right circular cylinder

as shown

in

8. The radiation from the pool fire to the target can be calculated from the

following

expression

intervening

for radiant exchange

between surfaces

separated

by an absorbing

gas.

Q=FrE (11)

where,

The

Q

=

heat

transferred

r

=

atmospheric

E

=

pool fire

F

=

surface

equation

(12).

This

radiation

transmissivity

emissive to surface

pool fire emissive

than 50m in diameter.

by thermal

power exchange

power is assumed

For smaller

factor

to be 250 kW/m2

pool fires the emissive

relation was based on data presented

for pool fires greater

power is calculated by in Reference

[20].

E = 250(1-e-‘2DP) (12)

where, Dp = pool fire

An approximate Reference T=e

diameter

expression

[21] and is shown

for the atmospheric

transmissivity

was taken from

below:

(-7X10-4L)

where, L = distance from the fire edge to the target (path length through air).

(13)

136

For this configuration for the present

the radiant exchange factor was compiled by Howell

case has been simplified (H2+S2+1

to the following

[22] and

expression:

1 (14)

Hd3+Hd2 I BZ+4H2

where. x = distance

from

the pool centre

R = pool fire

radius

L = pool fire

height

S = x/R H = L/R A = H2-Sz+l

.

B = H2+S2-1 dl = acos(A/B) d2 = acos(l/S) d3 = acos(A/SB)

With these expressions different distances these equations

it is possible

to estimate the heat flux from the pool fire at

from the fire centre. In the present

to estimate

distances

application it was desired

three levels of steady state fire damage reported in Reference present

model for describing

In the DERACS

simulation

pool fire thermal

concentric

in Table 2. These

hazards

are shown with three are displayed

rings centred at the pool fire centre.

HAZARD

I

Table 2

[I91 and used in the

radiation hazard levels.

graphical output, pool fire sites

levels of fire hazard as described

to use

to specified levels of danger. Table 2 presents

HAZARD DESCRIPTION

STEADY STATE HEAT FLUX

1

4.7 Kwtm*

Human Pain

2

12.6

Wood Building Ignition after some time

3

37.8

Damage to other vessels

Steady State Fire Damage Levels

Used

In DERACS

as

137

Plume and Puff Dispersion At present gases.

DERACS

of Heavy Gases

can consider

In the event of a puncture

show the extent of the dispersing containment dispersion The

gases

and propane and both of these

simulation

is a time integration

the release

sources

to use time dependent

to

In the event of a total loss

type release, through

are varying

models

are heavy

it is important

of

release will occur and a puff type

model is needed. For a continuous

present

of a derailment,

that are released.

of a tank car, an instantaneous

time integration, desired

chlorine

as a consequence

in strength

for tracking

a plume model is needed.

a derailment

event. During this

and therefore

it was

plume and puff type releases

of

heavy gases. Numerous models

dispersion

models

range in complexity

the solution dependent

from simple

of the 3-dimensional

the effects of turbulence.

are available in the open literature. Gausian

continuity,

For the present

purposes

type model that can run quickly

Box type model was selected,

type models

momentum

These

to those

and energy

it was desired

on a micro-computer.

various

which involve

equations

including

to have a time For this reason

which is accurate for the near field of a release

the

of heavy

gas. In a Box type model, the heavy gas cloud is modelled radius

R and height H as shown

in Figure

9. This

cylinder

is assumed

I 3

9

,,,

F ]H t

Sketch Showing box Model of Dispersing Properties of Actual Puff (from ref. [23]).

box of

to contain gas of

2

2

Figure

as a vertical cylindrical

3

Puff in Comparison

with

138 uniform

concentration.

entrainment,

As the box moves down wind, its dimensions

gas expansion

concentration

and gravitational

slumping.

As air is entrained,

in the box is reduced. Air is entrained through

box. The gas

is also assumed

cloud

change due to air

to have heat transfer

the gas

the top and sides

interaction

of the

with the ground

and the surroundings. At present

both plume and puff releases

Puff Model of Meroney Model is straight

forward.

Each puff represents seconds).

to over estimate However,

For a continuous

the rate of gas dispersion. that air is entrained

air entrainment

dispersion

of simple

in one simulation

Box Puff Models

through

for plumes

version

puffs are used.

time step (20

the sides

are developed

based on

and top of the cylindrical

box.

is effected by the reduced air/gas interface area.

of DERACS,

has been accepted. This

this inaccuracy

weakness

in the modelling

of plume

in the model will be corrected

in future

of DERACS.

In DERACS,

plumes

and puffs are displayed

size of the patch indicates some preselected immediately selected

as a coloured

patch on the map. The

the size of the area where the gas concentration

value. For chlorine

dangerous

this level is the 0.000075kg/m3

exceeds

which is

to life and health. For propane the concentration

was arbitrarily

to be 0.06 kg/m3.

Fire lmpinoement

on Tanks

Fire impingement TANKCAR

and Thermal

Ruptures

on tank cars is handled using the tank thermal

developed

cylindrical engulfing

a series

using the Box of the Box Puff

be noted that this type of approach is not very accurate and is likely

For the present versions

in DERACS

the application

release,

the quantity of gas released

It should

the assumption

are modelled

[23]. For a puff type release,

by Birk

[24]. The tank car thermal

computer

model can simulate

tank filled partially with liquid and partially with vapour exposed type fire, such as caused

model a long

to either an

by a burning

pool, or a torch type fire, such as that

caused by a relief valve flare from a neighbouring

tank. The model can account for the

effects of a number

of thermal

protection

thermal

insulation,

radiation shielding,

internal

protection

devices

including

devices such as pressure

temperature heat dissipating

sensing

relief valves,

retief valves,

matrices.

The

and novel

model can simulate

the effects of roll and pitch of the tank. The overall thermal various

processes

model is made up of a series

of sub-models

heat transfer

sub-models

can account for either an engulfing

fire or a two-dimensional

torch.

convection.

radiation is calculated as a function

position

the

taking place within the tank.

The flame-to-tank

The thermal

The pool fire model accounts

on the tank by accounting

absence of cross

which represent

for thermal

radiation

of the circumferential

for the typical shape of large pool fires in the

wind effects. The convection

calculations

are based on empirical

pool and

139

relations

for convection

based on empirical

to horizontal

relations

The temperature through

in a cross-flow.

for a jet impinging

distribution

The torch sub-model coverings

The finite difference solution

the tank wall and insulating

also accounts for the heat transfer

layers.

is calculated

accounts for pure

The finite difference

from the fire to the tank outer surface,

tank inner surface to the lading. The inner surface heat transfer convection

is

on a flat plate.

in the tank wall and associated

using finite difference techniques. conduction

cylinders

and radiation in the vapour space, and convection

solution

and from the

sub-models

account for

and boiling in the liquid

region. The thermodynamic

process

sub-model

the vapour space, the liquid boundary, vapour and liquid boundary equilibrium

and saturated.

treats the lading as three distinct

and the liquid core.

(near wall and free surface) The core is assumed

some period of venting it reaches equilibrium

It is assumed

regions:

that the

are in thermodynamic

to be sub-cooled

initially,

with the liquid boundary

but after

and vapour

space. The pressure

relief valve sub-model

relief valve and the fluid mechanics.

accounts

for both the mechanical

Valve cycling effects on flow rates are accounted

for by a steady state valve model which assumes representing

the valve to be partially open,

the reduced flow capacity during cycling. The valve flow sub-models

account for dry vapour flow and for frozen The wall stresses experiences stresses

action of a

are calculated at the point on the wall circumference

the highest

temperature,

due to radial temperature

is based on the maximum material strength

and includes

gradients

normal stress

with increases

can

liquid flow. pressure

which

induced (hoop) stress

and

in the tank wall. The tank failure analysis

theory of failure. Degradation

in temperature

is accounted for using

in the wall available data for

tank car steels. The computer

model is capable of predicting the tank internal pressure,

lading temperatures, tank wall stresses impingement. comparing fifth-scale

wall temperature

distribution,

relief valve flow rates, liquid level,

and tank failure, all as functions

The model has been extensively

its predictions

with the results

rail tank cars exposed

example of validation results actual test results

showing

validated (see Reference

fires.

comparison

for full scale fire tests.

of time from initiation of the fire

of numerous

to engulfing

mean

fire tests

Figures

[24]) by

involving full and

10 to 13 present

between TANKCAR

one

predictions

and

The Fire test data shown is from Reference

[161. Thermal

Effects

of Exolosions/BLEVES

In the event of a thermal propane, DERACS

assumes

rupture or total loss

of containment

a fire ball type explosion

will result.

of a tank containing In the DERACS

140

a -

5

0

10

5

_ TEST RESULTS -

15

SIMULATION

20

25

3”o

TIME FROM FLRE IGNITION (MIN.)

Figure 10

G g

Predicted & Meas. Tank Pressure vs Time for Full Scale Tank Car, Propane, Engulfing Fire

700,,

o

qoo

_

TESTRESULTS

TIME FROM FIRE IGNITION (MIN.)

Figure1 1

Predicted & Meas. Tank Wall Temp. vs Time for Full Scale Tank Car, Propane, Engulfing Fire

simulation the resulting fire ball will have both blast and thermal effects of the surroundings. This section describes the techniques used to estimate the thermal effects of the explosion. As discussed in Reference [25], the consequences of a total loss of containment of a pressurized flammable liquid depend on the conditions at release. The consequences range from a slow burn-off to a violent explosion and fire ball.

141

180, D _ TEST RESULTS --

SIMULATION

60 .

I 0

5

10

15

20

TIME FROM FIRE IGNITION

Figure

12

25

30

(MIN.)

Predicted & Meas. Liquid Level vs Time for Full Scale Tank Propane, Engulfing Fire

2

700

2 1

600 TENSILE

z. cn 500 % 2 400

Car,

STRENGTH

OF TC 128s STEEL INDICATED

E UJ 300 d 3 Y $

200 \ STRESS

100

IN OUTER FIBRES ACTUAL RUPTURE

0

5

10

15

20

TIME FROM FIRE IGNITION

Figure

13

Predicted Tank Wall Stresses Propane, Engulfing Fire

For the case of a car containing containment

will result

& Strength

a commodity

The resulting

in a large fire ball.

vs Time for Full Scale TankCar,

such as propane, a total loss

result

in significant

of

The rapid flashing

liquid droplet entrainment.

(boiting liquid expanding vapour explosion),

an explosion.

30

in a very rapid boil-off of part of the contents.

and the high exit velocities a BLEVE

25 (MIN.)

In the case of

the boil-off is so rapid it acts like

cloud of vapour and entrained liquid droplets

usually

result

142

As discussed in Reference [25], it is difficult to estimate the amount of remaining liquid after the boil-off period. Reference [25] states that, if more than 35% of the lading flashes, it is likely that all of the contents will be consumed

in a fire ball. If less than 35%

flashes then some liquid will remain and will burn-off slowly. In DERACS it is assumed that all of the liquid contents will be consumed

in the fire ball. The resulting fire ball

diameter is calculated from Reference [20] using the following expression: D

max

= 5.33m0’32’

(151

where, m = fuel D

max

mass

(kg)

= the maximum

fire

ball

diameter

This relation is based on experiments for fuel masses ranging from 3 - 31 kg but the validity has been verified for much larger masses [20]. The fire ball will have a growth stage and a shrink stage and these stages will take some finite time to develop. The fire ball’s effective duration as described in [20] can be estimated from the following expression: (161

ta = 0.9Z3m0~303

where, m = fuel %

= time

mass

(kg)

(set)

During the development

of the fire ball, the diameter grows and the fire bat1 rises

due to buoyancy. In the present situation it is desired to calculate a thermal radiation dose resulting from the fire ball. Therefore it has been assumed that the fire ball has a diameter Dmax and is located with its centre at ground level. The fire ball duration is assumed to be ta. The emissive power of the fire ball is calculated for Reference [20] using the following expression: -bD E = Emax(l-e

‘)

where, E

max

= 469 kW/m’

b = .18 m-l Ds = fire ball

diameter

(17)

143

The flux reaching a remote target can now be easily catculated from the following: Q=ErF

(IX)

where, r = atmospheric transrmssivity F = radiatit exchange view factor

As with the case of the pool fire radiation, the atmospheric calculated from Reference

[21] using the following

transmissivity

is

expression:

r = e(-7x10-4x)

(19)

where. x = distance

from

the fire

edge

The radiant exchange view factor was based on a sphere oriented towards expression

the fire ball at ground

is shown

level and as reported

radiating to an object in Reference

[21]. This

below:

( H/Ds+O

.5 )

(201

F= 4{(H/Ds+O. where,

5)2+WDs)2}3’2

R = radial distance of target point directly below fire H = height

of fire

ball

from ball

centre

The radiation dose is calculated from the simple

expression:

(21)

Dose = Qt,

As with pool fires, three hazard levels are calculated for thermal balls. Table 3 presents

the dose criteria used for the displayed

levels and their effects were taken from Reference

Blast

Effects

When outwards

radiation from fire

hazard levels.

Dose

[19].

of Explosions/BLEVES

an explosion

or BLEVE

occurs,

from the blast centre. This

a pressure

pressure

disturbance

disturbance

will propagate

or over-pressure

is followed

144 HAZARD

Table 3

LEVEL

DOS kJ/M”

DESCRIPTION

1

375

Third Degree Burns

2

250

Second Degree Burns

3

125

First Degree Burns

I

Thermal Hazard Levels for Fire Ball Thermal Radiation

by a rush of high velocity air. The combination of the over-pressure

and air can be very

destructive to property and life. In DERACS, if an explosion occurs the level of the blast hazard and the distance from the centre of the explosion are estimated. In the explosion calculation, the initial mass of the explosive is assumed to equal the total mass of lading in the tank. This mass is then converted to an equivalent mass of TNT using data from Reference [26]. Table 4 contains a partial listing from the above reference. The equivalent TNT mass is then reduced by multiplication of an explosion efficiency for unconfined vapour cloud explosions. As discussed in Reference [27], this explosion efficiency varies widely for unconfirmed vapour cloud explosions.

COMPOUND

Table 4

(1 kg)

EQUIVALENT

TNT MASS (kg)

methane

11.95

ethane

11.34

propane

11.07

butane

10.91

ethylene

11.26

Conversion

As shown in

Factors for TNT Equivalency {from Ref. [26])

Reference [27], the range of efficiencies is between 0.05 and 0.65. The efficiency of the blast is determined by the vapour cloud conditions at the time of ignition. In DERACS, it is assumed that, if a BLEVE occurs, the explosive efficiency will be high (ie. = 0.65) while if a BLEVE is unlikely, the efficiency will be low (ie. = 0.10). These explosion efficiencies are used to estimate explosion hazards. Based on the TNT equivalent mass and the explosive efficiency, it is possible to estimate the free field over-pressure

as a function of distance using the following

empirical relation from Reference [26]: For display of explosion hazards DERACS uses three preselected free-field over-pressures

to calculate hazard distances from the centre of explosion.

145

po

808

-=

Pa

where,

J-zzz7-

P 0

P

a

fire

field

=

ambient

2 = scaled

and,

w4.5)21 2

1+(2/.32)

=

= [

[1+

LL.3512

(22)

overpressure pressure

distance

qo.333 [ qo.333L+

d = actual W = TNT

distance equivalent

To and P

0

mass

= reference

atmospheric

temperature

and pressure

TYPE OF DAMAGE

OVER-PRESSURE

Windows shattered, plaster cracked; minor damage to some buildings Personnel

knocked

35-75

down

70-l 00

Failure of wooden or asbestos siding for conventional homes

75-l 50

Failure of walls constructed of concrete blocks or cinder blocks

125-200

Self-framing

paneled

Oil storage

buildings

collapse

200-300

tanks ruptured

200-300

Serious damage to buildings with structural steel framework Eardrum Reinforced

concrete Railroad

Probable

Table 5

350-l 000

severely

damaged

400-600 400-600

cars overturned

total destruction

Blast

300-500

rupture

structures

700-800

of most buildings

Lung damage

2000-5000

Lethality

7000-l 5000

Damage

--Side

(mbars)

on Over-Pressure

Correlation

(Large Explosion)

146

Over-pressure Reference

levels and their associated

damage estimates

[26]. A partial listing from Reference

Presently, Destruction explosion

in DERACS,

[26] is summarized

of Buildings

(700m bar), and Storage tank ruptured

based on the temperature

then determines

these are displayed

in Table 5.

(200m

of a tank containing

lading mass is converted into an equivalent TNT DERACS

in

the three levels of damage selected are: Lethal (7000m

is indicated (total loss of containment

determined

are presented

bar). When an

propane), the

mass and an explosion

efficiency is

of the lading at the time of containment

the three distances

bar),

loss.

to the above stated hazard levels and

using the post-processor.

CONCLUSIONS A prototype

computer

simulation

program

predicting some of the major consequences where dangerous

commodities

The present

version purposes.

reconstruction,

response

applications,

significant

Possible

sophisticated

approaches,

include risk studies,

accident

training and tactics development

and possibly

before the program can be used for any

development

is required.

will involve sub-model

on the targeted applications,

that are presently

are based on

is limited in scope and is intended for

However,

further

sub-models

accidents

in the open literature.

applications

personnel

The next phase of development Depending

published

of DERACS

on-site tactical assistance.

has been developed for with train derailment

are involved. The simulation

models that have been previously demonstration

(DERACS) associated

testing

some sub-models

and some new sub-models

and refinement.

will be replaced with more

will be added for consequences

not accounted for, such as tank rocketing.

REFERENCES 1.

Coppens, A.J., Wong, J.D.E., Birk, A.M., Anderson, R.J., Development of a Derailment Accident

2.

Yang, T.H. et al., A Study Continuation of Derailment Behaviour: Final Report, Pullman-Standard

Computer Simulation Model, Transport Canada Report TP 9254E, March 1988. Research Project No. 39-l 833, RPI-AAR Railroad Tank Car Safety Research and Test Project, Report RA-O8-I-12, 3.

February, 1972.

Wallace, W.D., Evaluation of Railway Draft Gears, ASME Paper Number 57-RR-8, Anthology of Rail Vehicle Dynamics, Vol. I, Freight Car Impact. pp.l-8.

4.

An Introduction to Numerical Computation,

1971.

S. Yakowitz. F. Szidarovszby,

Macmillan Publishing Co.

ISBN Q-02-430810-2. 5.

Before, R., Buist. I.. A Computer Model for Predicting Leak Rates of Chemicals from Damaged Storage and Transportation Tanks, Report EE-73, Environmental Emergencies Technology

Division,

Environment Canada. 6.

Redlich and Kwong, 1949. Chem. Rev. 44, 233 (in Perry and Chilton, 1973).

7.

Balzhizer, R.E., Samuels, M.R. and Eliassen, J.D. 1972. Chemical Engineering thermodynamics. Prentice-Hall,

Toronto.

147 8

Perry, R.H. and Chilton, C.H. (eds). 1973, Chemical Engineers’ Handbook, Lyman, W.J., Reehl, W.F. and Rosenblatt, D.H. 1982, Handbook Methods, McGraw-Hill,

IO.

of the 1980 National Conference

Mayinger, F., 1981, Scaling and Modelling Laws in Two-Phase Two-Phase

Toronto. 9.

Toronto.

Dodge, F.. Bowels, E. and White, R., 1980, Release Rates of Hazardous Cargo Vessels. Proceedings

11.

McGraw-Hill.

of Chemical Property Estimation Chemicals from Damaged

on Control of Hazardous

Material Spills.

Flow and Boiling Heat Transfer in

Flow and Heat Transfer in the Power and Process Industries, Hemisphere

Publishing,

Washington. 12.

Henry, R.E. 1981. Calculational (1979) on Two-Phase

13.

Delhaye, J.M. 1981. Instrumentation Industries, Hemisphere Environment Canada,

15.

Raj, P.P.K., Calculations Art, Transmission Railroad Tank-Car AAR-RPl,

I?.

- Critical Flow, Proceedings

in Two-Phase

of the Japan-U.S.

Seminar

Toronto. Flow and Heat Transfer in the Power and Process

Publishing, Washington.

14.

16.

Techniques

Flow Dynamics, McGraw-Hill,

1983, Technical Information for Problem Spills (TIPS) Series, Ottawa. of Thermal Radiation Hazards from LNG Fires -- A Review of the State of the

Conference,

American Gas Association, St. Louis, MO. 1977.

Safety Research and Test Project: Phase II Report on Full Scale Fire Tests,

RA-11-6-31,

AAR-R-201.

US6AFl

17-75 ENG (BK), 1973.

Cline, D.D., Koenig, L.N., The Transient Growth of an Unconfined Pool Fire, Fire Technology,

Vol. 19.

pp. 149, 1983.

18. Hottel, H.C., Fire Research Abstracts and Review, I, 41, 1959. 19.

Cracker, W.P., Napier, D.H., Quantification Proceedings

of Fire Hazards of Liquid Spills from Tank Trucks,

of the 4th Technical Seminar on Chemical Spills. 1987, Environment Canada,

EN

40-32711-1987.

20.

Moorehouse,

J., Pritchard, M.J., Thermal Radiation from Large Pool Fires and Fire balls: A Literature

Review, I Chem E., Symposium, 21.

Series No. 71, Pergamon

7. Pergamon

Series No.

Press, Oxford, 1982.

22.

Howell, J.R., A Catalog of Radiation Configuration

23.

Meroney,

Factors, McGraw Hill Book Company.

R.M., Lohmeyer, A.. Prediction of Propane Cloud Dispersion by Wind Tunnel Data

Calibrated Box Model, Journal of Hazardous 24.

Press, Oxford, 1982.

Litiou. D.A., Maund. J.K., Thermal Radiation Hazard from Fire balls, I Chem E. Symposium.

Birk, A.M., The Development

Materiais 8, 205-221,

and Validation of a Mathematical

1984.

Model of a Rail Tank Car Engulfed in

Fire, PhD Thesis, Queen’s University, Kingston, Ont., Canada, June 1983. 25.

Roberts, A.F., The Effect of Conditions Prior to Loss of Containment Symposium,

Series No. 71, Pergamon

on Fire ball Behaviour, I Chem E

Press, Oxford, 1982

26.

Kinney, G.F., Grapham,

27.

Gugan, K., Unconfined Vapour Cloud Explosions, The Institute of Chemical Engineers,

K.J., Explosive Shocks in Air, 2nd Ed. Springer-Verlag.

1985. 1979.