fred 5.1 technical guide

Shell Global Solutions

Shell Research Ltd. P.O. Box 1, Chester CH1 3SH, England, Tel: +44 (0) 151 373 5000

Registered in England No. 539964, Registered office: 3 Savoy Place London WC2R 0DX

Shell Global Solutions is a trading style used by a network of technology companies of the Royal Dutch/Shell Group

Shell FRED Fire, Release, Explosion, Dispersion

Hazard consequence modelling package

Technical Guide

Shell FRED Technical Guide

2 14 December 2007

Amendment History

Issue Date Author Description

1.0 July 2000 G.A.

Chamberlain

Initial version

2.0 November 2001 T.M. Cresswell Updated for Fred 3.2

3.0 April 2004 T.M. Cresswell

A. Crerand

Updated for FRED 4.0

4.0 March 2006 A.B.Hopwood

T.M. Cresswell

Updated for FRED 5.0

5.0 December 2007 L. Phillips Updated for FRED 5.1

This document is made available subject to the condition that the recipient will neither use nor disclose the contents except as agreed in writing with the copyright owner. Copyright is vested in Shell Global Solutions International B.V., The Hague.

© Shell Global Solutions International B.V., 2006. All rights reserved.

Neither the whole nor any part of this document may be reproduced or distributed in any form or by any means (electronic, mechanical, reprographic, recording or otherwise) without the prior written consent of the copyright owner.

Shell Global Solutions is a trading style used by a network of technology companies of the Shell Group.


14 December 2007 3

Table Of Contents

1. INTRODUCTION ...................................................................................................................................6

2. PRESSURISED RELEASES ..................................................................................................................8

2.1. THE NATURE OF RELEASES................................................................................................................8 2.2. HOLE SIZES........................................................................................................................................8 2.3. MODELS USED ...................................................................................................................................9 2.4. LIQUID RELEASES ..............................................................................................................................9

2.4.1. Liquid Pool Formation...........................................................................................................10 2.4.2. Droplet Atomisation, Rainout and Evaporation (DARE).......................................................11

2.5. GAS/VAPOUR RELEASES ..................................................................................................................16 2.5.1. Noise.......................................................................................................................................17

2.6. PRV RELEASE .................................................................................................................................21 2.7. TWO PHASE JET RELEASES ..............................................................................................................22

2.7.1. Pool Evaporation ...................................................................................................................23 2.7.2. Time Dependent Gas Releases from Pipelines.......................................................................24

2.8. TWO PHASE BLOWDOWN .................................................................................................................26 2.8.1. Introduction............................................................................................................................26 2.8.2. The Two Phase Blowdown Problem.......................................................................................26 2.8.3. Homogeneous Equilibrium Model .........................................................................................27 2.8.4. Experimental Releases ...........................................................................................................29

2.9. SUBSEA RELEASES...........................................................................................................................29 2.9.1. Bubble Plume .........................................................................................................................29

3. FIRE MODELLING..............................................................................................................................32

3.1. POOL FIRE........................................................................................................................................32 3.1.1. Size Of Liquid Pool ................................................................................................................32 3.1.2. Length Of The Flame .............................................................................................................33 3.1.3. Angle Of Flame Tilt................................................................................................................33

3.2. TRENCH FIRE MODEL ......................................................................................................................34 3.2.1. Basic Flame Geometry ...........................................................................................................34 3.2.2. Length Of The Flame .............................................................................................................35 3.2.3. Flame Drag and Tilt...............................................................................................................35 3.2.4. Height Of The Clear Flame....................................................................................................36 3.2.5. Surface Emissive Power .........................................................................................................36

3.3. GAS/VAPOUR JET FIRE .....................................................................................................................37 3.3.1. Flame Stability .......................................................................................................................42

3.4. GENERALISED JET FIRE....................................................................................................................46 3.4.1. Model Flame Shape................................................................................................................46

3.5. OTHER FIRE MODELLING PACKAGES ...............................................................................................47 3.5.1. CHIC - compartment fires......................................................................................................47 3.5.2. SEAFIRE - fires on the sea.....................................................................................................47 3.5.3. CLOUDF - cloud or flash fires ..............................................................................................48

4. RECEIVER OF THERMAL RADIATION ........................................................................................49

4.1. RECEIVER OF RADIATION .................................................................................................................49

4.1.1. Calculation of view factor, Φ ................................................................................................49

4.1.2. Atmospheric Transmissivity, τ, for Hydrocarbon Fires .........................................................50

4.1.3. Atmospheric Transmissivity, τ, for Hydrogen Flames ...........................................................51 4.1.4. Radiation Heat Flux from Pool Fires.....................................................................................52 4.1.5. Radiation Heat Flux from Jet Fires (Chamberlain Model)....................................................53 4.1.6. Thermal Radiation from Generalised Jet Fire Model ...........................................................56

4.2. THERMAL RADIATION HAZARD TO PEOPLE......................................................................................56 4.2.1. Design for Operation in Emergency Systems.........................................................................56 4.2.2. Probit Concept .......................................................................................................................58


4 14 December 2007

4.3. THERMAL RESPONSE OF STRUCTURES TO FIRE ................................................................................61 4.3.1. Equilibrium Surface Temperature..........................................................................................61 4.3.2. Temperature Rise with Time of Vessel/Pipe Wall Exposed to Fire ........................................62

4.4. RADIATION DOSE TO A RETREATING RECEIVER (ESCAPE) ...............................................................65

5. VESSEL MODELLING........................................................................................................................67

5.1. HEAT UP ..........................................................................................................................................67 5.1.1. Introduction............................................................................................................................67 5.1.2. Physical Processes .................................................................................................................67 5.1.3. HEATUP ................................................................................................................................68 5.1.4. Mass transfer out of the vessel ...............................................................................................73 5.1.5. Mass transfer through pressure relief valves .........................................................................74 5.1.6. Change in composition...........................................................................................................76 5.1.7. Mass and heat transfer within the vessel................................................................................76 5.1.8. Mass and heat transfer within the liquid phase......................................................................77 5.1.9. Total heat energy transfer ......................................................................................................77 5.1.10. Mass and heat transfer between the liquid and gas phases ...................................................77 5.1.11. Vessel failure ..........................................................................................................................78 5.1.12. Extra Considerations..............................................................................................................79

5.2. VESSEL BURST MODEL....................................................................................................................79 5.2.1. Energy of Vessel Burst ...........................................................................................................79 5.2.2. Vessel Burst Pressure.............................................................................................................80 5.2.3. Blast Wave..............................................................................................................................80 5.2.4. Scaled Distance......................................................................................................................81 5.2.5. Scaled Pressure at Vessel.......................................................................................................81 5.2.6. Pressure Decay ......................................................................................................................81 5.2.7. Impulse at Receptor................................................................................................................83 5.2.8. Vessel Type & Elevation.........................................................................................................83 5.2.9. Gas Dispersion With Fireball ................................................................................................84

5.3. BLEVE............................................................................................................................................85 5.3.1. TNO BLEVE...........................................................................................................................85 5.3.2. SHELL Research Ltd BLEVE Model......................................................................................85 5.3.3. Safety Distance (probit variable) ...........................................................................................94

6. DISPERSION MODELLING...............................................................................................................96

6.1. METEOROLOGY................................................................................................................................96 6.1.1. Stability Classes .....................................................................................................................96 6.1.2. The Lapse Rate.......................................................................................................................97 6.1.3. Surface Roughness .................................................................................................................98 6.1.4. Wind .......................................................................................................................................98 6.1.5. Sampling Times ....................................................................................................................100

6.2. TYPES OF DISPERSION....................................................................................................................100 6.3. DISPERSION MODELS .....................................................................................................................102

6.3.1. Gaussian Model ...................................................................................................................102 6.3.2. HEGADAS............................................................................................................................104 6.3.3. AEROPLUME ......................................................................................................................104

6.4. FLAMMABILITY ..............................................................................................................................105 6.5. TOXICITY .......................................................................................................................................106

6.5.1. Toxicity Data........................................................................................................................106 6.5.2. Protection by being In-House ..............................................................................................107

7. EXPLOSION MODELLING..............................................................................................................109

7.1. THE EXPLOSION PROCESS..............................................................................................................109 7.2. VAPOUR CLOUD EXPLOSION CHARACTERISTICS ............................................................................111 7.3. HAZARD ASSESSMENT OF EXPLOSIONS..........................................................................................112

7.3.1. Congestion Assessment Method (CAM) ...............................................................................113 7.3.2. SCOPE Model ......................................................................................................................126 7.3.3. TNT Model ...........................................................................................................................139 7.3.4. TNO Multi-Energy Method ..................................................................................................141

7.4. EXPLOSION DAMAGE EFFECTS.......................................................................................................142


14 December 2007 5

7.4.1. Overpressures at which Glass Windows Fail.......................................................................143 7.4.2. Damage to Buildings............................................................................................................144

7.5. OTHER VAPOUR CLOUD EXPLOSION PACKAGES ............................................................................145 7.5.1. VEXDAM - For Modelling Effects of Shielding ...................................................................145 7.5.2. EXSIM - CFD.......................................................................................................................145

8. ADDITIONAL REFERENCES..........................................................................................................146


6 14 December 2007

1. Introduction

Shell FRED (Fire, Release, Explosion, Dispersion) is a system which models the consequences of

a release of product, both accidental and intentional. Its aim is to assist designers to produce safe

and cost effective modifications to existing or new site layouts and design. Alternatively, it may

assist in the development of site operational procedures or provide a screening tool for “effect

calculations” in Quantitative Risk Assessment studies.

An accidental release of flammable hydrocarbon results in a variety of consequences, dependent

on the type and initial state of the hydrocarbon and whether or not ignition occurs. These

consequences are conveniently displayed by means of an event tree such as shown in Figure 1. By

means of gross simplification this tree covers ALL INITIAL outcomes - fire, explosion or safe

dispersion.

Release

More obstacles

Greater confinement

Flame acceleration

Ignites?

Jet fireInternal

explosionPool fire Cloud fire Fast flame

Safe

dispersion

Dispersing cloud

Ignites?

No

Yes No

Yes

Figure 1 Event tree showing all consequences of flammable release.

Further analysis reveals that just three event trees, determined simply by reference to the state of

the fluid before release, are required to cover all the different physical effects from the possible

range of fire types and explosion scenarios. The three fluid pre-release conditions determining the

"source term" for the event trees are:

1. Liquid at ambient pressure, e.g. diesel, gasoline or oil tank,

2. Liquid at pressure above ambient, e.g. separator contents, pumped crude oil,

3. Gas or vapour above ambient pressure, e.g. gas pipeline, vapour space in separator, gas blow-

out.

Complete definition of the source term then requires calculation of the outflow rate, and the

physical form and dimensions of the release.

For example, a flammable liquid release from an atmospheric storage tank will always result firstly

in the formation of a liquid pool, immediate ignition of which results in a transient fireball which

burns back to a spray jet fire and burning pool. If ignition is delayed, the pool first spreads and

partially evaporates. The vapour cloud disperses. If the surroundings are confined, such as for a

release inside a building or module, then a vented explosion could occur on ignition. A cloud

dispersing in the open produces a flash fire with no blast. An ignited release in a congested but

unconfined plant environment could lead to the generation of fast flames with associated blast. The

combination of confinement and congestion, such as in a typical offshore module, can lead to

significant blast.

A liquid release from pressurised storage initially leads to a spray jet. The spray would consist of

both vapour and liquid phases, in the form of droplets, if the liquid is volatile e.g. condensate, or


14 December 2007 7

simply droplets for non-volatile releases e.g. stabilised crude oil. Mechanical and thermodynamic

forces both play a role in causing the jet to break up in to droplets. Just 1 or 2 bar is required for

atomisation of the jet independent of any flashing processes that may be occurring. The effect this

has on subsequent dispersion, degree of liquid rain-out and fire behaviour is critical to an

assessment of the hazardous consequences, and hence the extent and type of protection system

required. Jet and pool fires can occur on immediate ignition after an initial transient fireball, but

liquid rain-out is unlikely if a released liquid, such as LPG, readily flashes to vapour in the

atmosphere. The fate of a cloud undergoing delayed ignition depends on the degree of confinement

and congestion in the surroundings, as before. Catastrophic loss of containment and ignition of

pressurised liquid stored above its atmospheric vapour pressure, such as LPG, results in a type of

fireball known as a BLEVE (boiling liquid expanding vapour explosion). The underlying physical

processes are now well enough understood for model formulation and prediction of the transient

fireball heat flux and explosion overpressure pulse.

A pressurised gas release normally results in a dispersing gas jet which may contain aerosols if the

gas cools sufficiently during release to allow condensation of some or all of the components.

Entrainment of air normally is sufficient to re-evaporate the aerosol droplets. Ignition creates the

classic jet fire, typified by refinery flares. In extraordinary cases the release of hot gas containing

heavy components could lead to condensation and agglomeration of droplets and a rain-out pool.

In all cases however, as before, delayed ignition results in either a cloud fire or explosion

dependent on the geometry and layout of the surroundings in which the release occurs.

Methodologies, models, rules and guidance now exist with varying degrees of sophistication to

allow engineers to quantify ALL of the above physical effects. In most cases the models, usually in

the form of computer tools, have been validated over large ranges of conditions. Shell FRED is one

such computer code.

Interaction with the Shell FRED program is via a site map, which may be a blank screen or an

imported site plan. Onto the map, the user positions objects such as a pressure relief valve leak and

receivers. Scenarios may be associated with multiple models which are automatically chained

together by the system, simplifying and speeding up the user interaction with the tool. Receivers

provide a means of measuring at points on the map, the thermal radiation heat flux and blast wave

response and its effect on process equipment and people. Multiple scenarios may be attached to a

plan, although the additive effects of their results are not considered.

Having positioned a scenario, the user must enter its properties. Having done this, a list of relevant

hazard consequence predictions is displayed. These are dependent on the scenario being run and its

attributes. On selecting a prediction, it is displayed in textual or graphical format. The graphs may

be charts or plots overlaid on the plan. To review the radiation and blast wave information,

receivers may be browsed. Copies of graphs may be imported into documents or printed.

Typical users of Shell FRED are technical staff in all disciplines who are likely to be involved in

plant design safety, accident investigation or safety case discussion and reporting. The Shell FRED

package is Windows based with a graphical user interface allowing results to be displayed on the

site map.

This guide describes the technical basis of the Shell FRED v5 package. Methods used in the

calculation of release scenarios are described in Section 2. Fire models and the effects of thermal

radiation on structures and people are given in Sections 3 and 4. Two BLEVE models are available

in Shell FRED; TNO model and the Shell model. A detailed description of these can be found in

Section 5. Atmospheric dispersion models are discussed in Section 6. For the analysis of explosion

scenarios three models are provided in the Shell FRED package. They are: TNT model, TNO

Multi-energy method and the Shell Global Solutions’ CAM (Congestion Assessment Method) and

SCOPE (Confined module) models. Detailed description of these methods is given in Section 7.

This section also includes a discussion of the explosion damage effects.


8 14 December 2007

2. Pressurised Releases

The General release model is the basis of the pressurised release scenario in Shell FRED. This has

been split into two scenarios; one based on a knowledge of the source pressure the other based on

a knowledge of the flow rate. The latter scenario may only be used for gaseous releases (e.g.

flares) and it has been extended to include all gaseous fluids in the Shell FRED data-base.

The pressurised release scenario provides a fully integrated link from the release model to the

Aeroplume jet dispersion model.

For liquid spills a simple pool model has been attached to the pressurised release model.

Evaporation from the pool may be directly fed into the Hegadas heavy gas dispersion model. A

droplet atomisation and rainout model has also been attached to the pressurised release model.

The pressurised release scenario provides the link from the release to the liquid/two-phase jet fire

model

2.1. The Nature of Releases

Both the physical state of the contained material and the characteristics of the particular failure

(pipe rupture, vessel rupture, pump seal failure, gasket blow-out, etc.) are important factors

affecting the release rate. A release may consist of liquid (boiling or non-boiling), vapour, or both

phases, and it may take place over land or water.

Moreover, a liquid spill may evaporate thus forming a source for dispersion of the material in the

environment. The calculation methods presented in the following sections comprise:

• liquids stored either at ambient temperatures or refrigerated vapours

• superheated liquids stored under elevated pressure or from lines carrying materials

• two-phase behaviour.

In practice neither the failure location nor the prevailing physical conditions are well defined, so

that the calculation of release rates cannot generally be carried out with great precision. Hence it is

acceptable that some simplifying assumptions are made which allow the necessary calculations to

be performed manually.

2.2. Hole Sizes

Leaks are much more common in pipework than in the walls of storage tanks. A hole in a pipe may

vary from a tiny pinhole to a full bore rupture. For other components, the following guidance for

hole size is based on the work of Cox et al1.

1A.W. Cox, F.P. Lees and M.L. Ang, Classification of Hazardous Locations., IChemE 1990, ISBN 0 85295 258 9


14 December 2007 9

Component Hole Area Details

FLANGE Hole area = gasket

thickness × arc length

between bolts.

Typical gasket thickness:

Compressed asbestos fibre 1.6mm

Spiral wound joint 0.05mm

Ring type joint 0.05mm

VALVES Typically:

0.25mm2 < hole area <

2.5mm2

0.25mm2: Normal Duty valves.

2.5mm2: Severe duty valves or line larger

than 150mm diameter.

DRAIN/

SAMPLE

POINT/

SIGHT

GLASS

Use actual hole size.

PUMP SEAL Hole area =πLD

where L=clearance,

D=shaft diameter

Reduce area by factor of 4 if throttle bush

present on mechanical pump seal.

2.3. Models Used

General model

Release

Poolliquid

gas/two-phase

Fire Dispersion

Pool

Jet dispersion

Heavy gas dispersion

Liquid/2-phasejet fire

Key

Fred Model

Fred Scenario

Vapour

Definedflow rate

Reservoirpressure

PIPA Model

HGsystem model

HGsysteminterface

Pressurised Release

Scenario

Droplet

atomisation &

rainout (DARE)

General model

Release

Poolliquid

gas/two-phase

Fire Dispersion

Pool

Jet dispersion

Heavy gas dispersion

Liquid/2-phasejet fire

Key

Fred Model

Fred Scenario

Vapour

Definedflow rate

Reservoirpressure

PIPA Model

HGsystem model

HGsysteminterface

Pressurised Release

Scenario

Droplet

atomisation &

rainout (DARE)

Figure 2-1 Flow Chart of Models within FRED

2.4. Liquid Releases

The mass flow rate from a hole in a vessel below the liquid level can be calculated using the

Bernoulli equation2.

2TNO Yellow Book : Methods for the calculation of the physical effects of the escape of dangerous material : liquids and gases. Second Edition (1988) Dutch Directorate of Labour, Ministry of Social Affairs.


10 14 December 2007

+ ∗∗∗∗ hg

PPAreaCm d

-2 = 1

ρρ&

Equation 2-1

Where,

&m = Mass discharged, kg/s

Cd = Discharge coefficient (0.60 recommended for liquids)

ρ = Density of the liquid, kg/m3

Area = Hole area in m2

Pl = Absolute pressure at which the liquid is stored, Pa

P = Ambient pressure, Pa

g = Acceleration due to gravity, 9.81 m/s2

h = Static head of liquid, m

2.4.1. Liquid Pool Formation

A liquid release will form a jet or pool depending on the fluid properties at the release conditions.

When FRED releases the fluid it performs a flash calculation to the ambient pressure, calculating

the vapour pressure, P the vapour fraction at ambient pressure and atmospheric pressure bubble

point temperature. A pool is judged to be formed if the following condition is met:

Superheat<10°C and P<0.99bara and vapour fraction <1.0

The superheat is defined as the process temperature minus the atmospheric pressure bubble point

temperature.

There are three different types of pools which can be formed a non-evaporating liquid pool, an

evaporating liquid pool and a boiling liquid pool, see Figure 2-2

Figure 2-2 Pool Formation

2.4.1.1. Non Evaporating Pool

A non evaporating pool is seen not to be a hazard within FRED, therefore there will be no

dispersion distances calculated.

T b.p. = Boiling Point of liquid at atmospheric pressure

T b.p +10°C

T b.p

Fluid temperature

Ground (Ambient) temperature

Boiling Pool

Evaporating Pool

No pool formation

Release goes into a dispersing cloud


14 December 2007 11

2.4.1.2. Evaporating Pool

The release calculation provides a mass release rate and a mass fraction of liquid, which is used

with the release density and mass evaporation rate to calculate the volume of liquid available for

the initial pool. The mass evaporation rate is calculated from a formula developed by Sutton3, see

section 2.7.1

2.4.1.3. Boiling Liquid Pool

If the atmospheric bubble point temperature < ambient temperature then a boiling liquid pool is

assumed to be formed. For modelling purposes this is assumed to be of 1m diameter and have an

evaporation rate equal to the input mass flow rate. An example of a boiling liquid pool would be a

LNG spill.

2.4.1.4. Liquid Pool Depth

The pool depth is calculated using the following rules set which is based on experience from

spillages of different refinery materials.

hmin = 0.02m for low viscosity products , mol wt 180 average or less

= 0.08m for high viscosity products, > mol wt 180 average,

2.4.2. Droplet Atomisation, Rainout and Evaporation (DARE)

The Droplet Atomisation Rainout and Evaporation model (DARE) estimates the fraction of the

accidental release of a liquid jet that rains out forming a liquid pool on the ground. It models both

the flashing, and non-flashing but evaporating droplet rainout. The atomisation of the liquid jet is

estimated by using the available empirical correlations for non flashing liquid jet sprays, and a

simple correlation estimates the reduction of the droplet diameters caused by external flashing at

moderate superheat levels. Given the estimated exit conditions the individual droplet trajectories

are calculated in a 3-D geometry with transient heat and mass transfer from the droplet surface

given the specified wind field. The assumption of a Rosin-Rammler type droplet size distribution is

used to integrate the droplet ensemble to calculate the overall droplet rainout fraction for a

particular release scenario together with the location of the pool formation in a 3-D geometry.

2.4.2.1. Non-flashing Liquid release

If there is no internal flashing before the exit nozzle then the mass release rate is defined using the

Bernoulli flow equation.

2.4.2.2. Two-Phase Release

For two-phase releases the values of the exit pressure ratio (a

e

P

P ) and the vapour fraction at the

exit nozzle ( FracX ) due to internal flashing are obtained from the FRED release calculations

Where Pe is the exit pressure and Pa is ambient pressure.

3O.G. Sutton, Micrometeorology, McGraw Hill, New York, 1953.


12 14 December 2007

2.4.2.3. Droplet break-up and atomisation for liquid release

The break-up of the liquid core into droplets, and further atomisation by the fluid flow is a

complex but well-studied subject with various regimes of droplet break-up observed 4. In this

model a simplified mechanical droplet break-up approach is used. For a non-flashing liquid jet,

where the liquid temperature is lower than the bubble point, the atomisation is characterised by the

liquid properties using an experimental correlation by Bowen and Maragkos5.

The liquid-properties-based numbers are:

σρ eeL

L

DUWe

2

= WeL = Weber number

L

eeLL

DU

µρ

=Re ReL = Reynolds number

σµ eLU

Ca = Ca = Capillary number

eL

L

DOh

σρ

µ= Oh = Ohnsorge number Equation 2-2

Where:

De is the nozzle diameter,

P0, is the liquid storage pressure,

Lρ is the liquid density defined at the bubble point temperature at the ambient pressure (Pa ).

Ue is the velocity of the jet at exit

The atomisation process is characterised by the Sauter Mean Diameter ( smdD ) which is well

defined if Bowen and Maragkos correlation is applicable. This is shown below as a logic diagram:

Figure 2-3 Logic Diagram used to determine effective Sauter Mean Diameter

Where:

maxD is the maximum stable droplet diameter based on a critical Weber number approach

Dsmd is the empirical sauter mean diameter

4 G. M. Faeth, L. P. hsiang and P. K. Wu. Structure and breakup properties of sprays. Int.J.Multiphase Flow 21, 99-127. 1995.

G. M. Schmehl and S. Wittig. CFD analysis of fuel atomisation, secondary droplet breakup and spray dispersion in the premix duct of a LPP combustor. 2000. Proceedings of Eight International Conference on Liquid atomisation and Spray Systems.

P. J. Bowen and L. C. Shirvill, Combustion hazards posed by the pressurised atomisation of high-flashpoint liquids. J Loss Prev Process Ind 7, 233-241 (1994).

5 P. J. Bowen and A. Maragkos. Flammability hazards posed by pressurised releases of high-flashpoint liquids. Mistex Final Report. 2000. Cardiff School of Engineering.


14 December 2007 13

When Dmax < Dsmd the spray is not fully atomised and the Sauter Mean Diameter is assumed to be

the same as Dmax .

If the atomisation process is outside the range of validity of the above empirical correlation then an

effective value for the Sauter Mean Diameter, ( )EffsmdD , is chosen as shown in the diagram

above. In Fred both the empirical SMD as calculated from the Bowen correlation and effective

SMD as used in the rainout calculations are displayed.

The application of this correlation to the two-phase release scenarios ( 0>FracX ) , and wider

range of the liquids requires caution and further validation.

The following sections describe the droplet atomisation process for a single component fluid.

Where multi component fluids are used, an additional equation for conservation of momentum is

included.

If the release conditions are such that instantaneous flashing of the liquid occurs ( 0>x ) at

ambient conditions then an additional thermodynamic break-up of the liquid jet produces smaller

droplets than predicted by the above formulae.

In the present model the effective jet velocity in the maximum stable droplet diameter correlation

is increased above the exit velocity as a function of the available expansion energy during the

external flashing. This approach is a simplistic approximation to a very complex phenomenon,

which is expected to model the effect of the external flashing for small superheat temperatures

)(*22

s

aLeeff

PHxKUU

ρ−∗∗+= Equation 2-3

where K is an empirical constant

ρs is the density of the vapour at the bubble point

x is the fraction of the liquid jet which flashes instantaneously as it emerges into the ambient

2.4.2.4. Calculation of droplet trajectories and the evaporation

The Lagrangian motion of the individual spray droplets is modelled together with the transient heat

and mass transfer from the droplet surface. The approach includes the transient evaporation from

the droplet surface, and cooling of the droplets. The single-component liquid droplet is assumed to

have uniform internal temperature, and be in thermodynamic equilibrium with the vapour phase at

the surface. The droplets are assumed to move into fresh ambient gas with a well-defined ambient

fuel mass fraction, i.e. they are independent from each other. The droplet size distribution used to

model the spray is:

−−=32.5

422.0exp1)(smdD

DDP

Equation 2-4

Where P(D) is the fraction of the total volume of the spray contained in droplets of sizes less than

D.


14 14 December 2007

A range of droplets between a minimum and maximum diameters, selected as certain multiples of

the smdD , are calculated to represent the whole spray. In general, a liquid droplet of diameter D,

which will be referred as fuel, is assumed to move with a velocity of U in an ambient gas flow of

temperature aT , and velocity V. For a vaporising droplet the fuel would leave the surface by

convection and diffusion. If the gas at the surface is assumed to be saturated with the vapour of the

liquid at the surface temperature the evaporation rate of the droplet may be expressed as:

−

−−=

s

ams

L

s

y

y

DD

dt

d

1

1ln

14 ϕα

ρρ

Equation 2-5

Where:

sα is the diffusivity of the fuel vapour at an effective temperature of (2

aseff

TTT

+= ),

sT is the surface temperature of the droplet.

For a Lewis number of unity it may be approximated as: pVs

ss

Cρλ

α = . Equation 2-6

where ss and ρλ are thermal conductivity and density of the vapour phase calculated at effT .

pVC is the specific heat of the fuel vapour,

ay , and sy are the fuel vapour mass fraction at ambient, and at droplet surface respectively.

For a dilute spray the ambient fuel vapour mass fraction may be set to zero.

mϕ is a multiplicative correction term for turbulent flow conditions recommended by Kuo[6]:

3

2

2

1

3

1

2

1

Re232.11

Re278.01

−−+

+=

Sc

Scmϕ Equation 2-7

Where

s

se

UVDR

µ

ρ −=

ss

sScαρ

µ=

The vapour phase viscosity sµ , and the specific heat pVC used in the definition of the Reynolds,

and Schmidt numbers are assumed to be constant and evaluated at the bubble point temperature

( bT ) at ambient pressure.

6 K. K. Kuo, Fuel droplet in a convective stream. In Principles of Combustion. p. 579, John Wiley & Sons, 1986


14 December 2007 15

The mass fraction of fuel vapour at the droplet surface is defined as:

)1(a

sair

a

sF

a

sF

s

P

PW

P

PW

P

PW

y

−+= Equation 2-8

Where WF and Wair are the molecular weight of the fuel, and ambient mixture respectively. sP is

the partial pressure of the vapour at the surface.

The fuel mole fraction at the droplet surface may be related to the surface temperature by making

use of the Clausius-Clapeyron equation:

−∆=

sbg

F

a

s

TTH

R

W

P

P 11exp Equation 2-9

Where gR is the universal gas constant, and H∆ is the latent heat of vaporisation.

If the radiation heat transfer is ignored, and the liquid droplet is assumed to have uniform

temperature, which is equal to the temperature at the surface, the energy balance for the droplet

evaporation may be written as:

( )dt

dD

DC

HTT

CD

Nu

dt

dT

pL

Lsa

pLL

ss 3122

+−=ρ

λ Equation 2-10

Where s

c DhNu

λ2= is the Nusselt number, Lρ is the liquid density, ch is a heat transfer coefficient.

The Nusselt number correlation recommended by Kuo[12] is used in the present model:

( )B

BNu

+

+

+=−−

1ln

PrRe232.11

PrRe278.01

3

2

2

1

3

1

2

1

Equation 2-11

Where s

spVC

λ

µ=Pr is the Prandtl number,

and s

as

y

yyB

−

−=

1 is the Spalding Transfer Number.


16 14 December 2007

θ

x (North)

y

z (Vertical)

x`

y`

z`

Coordinate system

φ

θ

x (North)

y

z (Vertical)

x`

y`

z`

Coordinate system

φ

2.4.2.5. Calculating Droplet Trajectories

Figure 2.4 shows the coordinate system adopted for

the model. Z-axis is vertical; X-axis is always north.

The spray jet is initially aligned with the North and

rotated an angle of φ clockwise from the north, and

an angle of θ counter clockwise from the XY plane.

The ground will be placed at a distance of L in the

negative Z direction. Although the actual model

formulation is for an angle φ measured counter

clockwise the input angle to the computer model is -

(φ) so that a clockwise definition is adapted here for

convenience.

Figure 2-4 DARE Co-ordinate system

The differential equations for the droplet motion in each coordinate axis may be given as:

( ) iiiwiiiwiD

li gUUVUUV

D

CU

dt

d−−+−+=

ρρ

4

3 Equation 2-12

Where g is the acceleration due to gravity, and CD is the drag coefficient for an evaporating

spherical droplet. i refers to the x, y, and z coordinates. The drag coefficient, modified for an

evaporating droplet may be expressed as

( )1000 Re

1000Re if

≥

++

=

<+

=

6

Re1

1Re

24

1

44.0

3

2

eD

eD

BC

BC

Equation 2-13

Where L

sapVe

H

TTCB

)( −=

2.5. Gas/Vapour Releases

Two cases are distinguished: one where the flow is sonic, the other where it is subsonic. The

critical pressure ratio, Pcrit, is calculated from :


14 December 2007 17

1

1

2 −

+=

γγ

γcritP Equation 2-14

Where γ = isentropic expansion factor (Cp/Cv)

If the pressure ratio P/Pg is below the critical pressure ratio the flow is sonic and the mass flow

rate through the hole can be calculated from:

1

1

1

2

8314 =

−

+

∗∗

∗

∗∗

+

γγ

γγ

g

g

d

TMw

PAreaCm&

Equation 2-15

Where,

&m = Mass flow rate, kg/s

Cd = Discharge coefficient (~0.8 for gases)

Area = Hole area in m2

Mw = Molecular weight in kg/kmol

Tg = Temperature of the vessel in K

Pg = Absolute pressure of the gas in Pa

P = Ambient pressure in Pa

If the flow is subsonic the mass flow rate can be calculated from:

1

1

01

2

8314 =

−

+

+∗∗

∗

∗∗∗γγ

γγψ

g

g

d

TMw

PAreaCm&

Equation 2-16

where

1

111

02

1+

1

2 1 =

−

+−

−∗

−∗

γγ

γγ

γ γγ

ψgg P

P

P

P

Equation 2-17

2.5.1. Noise

The noise hazard is only a problem in the event of release of high pressure jets. There are then

three possible sources of noise which contribute to the sound level. These are:

1. Jet noise, which is always present and which originates from turbulent mixing of the jet.

2. Shock noise, which is present when the jet is choked, and which is caused by expansion of

the jet.

3. Combustion noise, which is present when the jet is ignited and which is caused by

unsteady heat release.

The intensities of all three noise sources are combined and converted to a noise level in dBA for

comparison with prescribed probit limits.


18 14 December 2007

Some validation of the model has been carried out by comparing the predictions with measured

noise levels in dBA from experiments on high-speed flares.

2.5.1.1. Definitions

Some terms need to be defined and understood before proceeding with a description of the model.

It is customary to describe sound pressures and intensities through the use of logarithmic scales (to

base 10) known as sound levels. One reason for so doing is the wide range of sound pressures and

intensities encountered in the acoustic environment. Audible intensities range from approximately

10-12

to 10 W/m2. A second reason is that humans judge the relative loudness of two sounds by the

ratio of their intensities, a logarithmic behaviour.

The most generally used logarithmic scale for describing sound levels is the decibel scale. The

sound pressure level (SPL) is defined by,

SPL = 10 log (I / Iref ) , dB Equation 2-18

Where,

I = the sound intensity

Iref = is a reference intensity.

The reference standard for airborne sounds is 10-12 W/m2, which is approximately the intensity of

a 1000 Hz pure tone that is barely audible to a person with unimpaired hearing. The ear has a

frequency dependent sensitivity and a scale, called the A weighting, is used to convert dB to a

meaningful human response. The resulting sound levels are then expressed as dBA.

A point to remember is that it is correct to sum the intensities, and NOT the dB, when combining

several sound sources.

2.5.1.2. Noise Source Terms

Jet Mixing and Shock Noise

These noise sources are not isotropic and the noise heard at any point will therefore depend on the

orientation of the jet axis and the position of the receiver. The starting point, assuming that the jet

is cylindrically symmetrical about its axis, is to calculate the sound pressure level at a discrete

number of angles θ from the hole axis.

The calculation of the source sound pressure level due to jet mixing and shock noise is based on

the standard methods adopted by the aircraft industry [7]. The original formulations calculate the

sound pressure levels in 1/3 octave frequency bands, from 25 to 10160 Hz centre frequencies, at

10o intervals of angle θ from 10o to 170o inclusive, at a reference distance √(do2π/4) from the

source, where do is the hole diameter. These results require some manipulation to make them

suitable as input to the noise model used here, and to allow calculation of atmospheric

transmission effects.

7 Gas turbine jet exhaust noise prediction, ARP 876B, June 1978.


14 December 2007 19

The source of jet mixing is assumed to occur at 6 exit diameters downstream of the hole. The noise

model calculates the intensity at a reference distance of √(1/4π) over the surface of a sphere

centred at the source location. The intensity is dependent both on frequency and on the angle from

the jet axis. It is assumed that the range of angles over which the intensity must be averaged to

obtain the noise emitted towards a given receiver point is 20o above the line joining the source to

the receiver point. The SPL in the direction of the receiver is therefore given, for each octave band,

by

SPL (freq) = 10 log. Ij,av (freq)/ Iref Equation 2-19

Where,

Ij,av (freq) = the average sound intensity in the direction of the receiver.

Iref = a reference intensity.

In cases where the flow is choked the sound pressure level of the shock noise is included. Shock

noise is more strongly anisotropic and is treated in much the same way as is the jet mixing noise.

The source is again assumed to be located at a point 6 hole diameters downstream of the leak.

Combustion Noise

For combustion noise the source is assumed to be at the base of the flame. In the Thornton flame

model this is idealised as the point of intersection of the jet and frustum axes. The sound pressure

level of the combustion noise SPLc (freq) at the reference distance √(1/4π) is given by [4].

SPLc (freq) = 10 log (0.0011 m uj2/ Iref ) + 120 - a (freq) Equation 2-20

Where,

a (freq) = the "roll-off" of combustion noise as a function of frequency

m = the mass flow rate of leaking gas

uj = the expanded jet velocity.

Unlike jet and shock noise, combustion noise is isotropic so there is no directivity component of

the receiver to be considered.

Noise Propagation

The attenuation of the noise during its propagation from source to receiver is calculated next. The

sound pressure level from any source in each octave band at the receiver point is given by,

SPL (freq) (receiver) = SPL (freq) (source) - Dd - Da (freq) - Dw

(freq) - Dg Equation 2-21

Where,

D = the attenuations (in dB) due to various factors.

Dd = the attenuation in dB due to the change in distance from the reference distance to the

receiver distance r and is given by,


20 14 December 2007

Dd = 10 log [ r2 / (1/4π) ] = 20 log r +11.0 Equation 2-22

Where,

Da = the absorption by the air, which is frequency dependent and standard values are

used.

Dw = the attenuation caused by walls or buildings, calculated by assuming that sound is

not transmitted but may be refracted around the obstacle. This depends on the sound

frequency and the size of the obstacle. The maximum value allowed for Dw is 10

dB.

Dg = the term allowing for ground effects and may be positive or negative. The formulae

have already been adjusted for reflection by the ground around the source.

Final Summation

Having obtained the SPL at the receiver for each source, the intensities are obtained by inverting

the equation, summed, and the combined SPL obtained by again applying the relationship between

SPL and intensity.

Finally the frequency dependent sensitivity of the ear is allowed for by adjusting the SPL at each

frequency by the appropriate A weighting and then summing the A weighted intensities to obtain

the overall sound pressure level in dBA.

Contours are obtained over the plane of interest by calculating the dBA levels at a number of grid

points and interpolating linearly.

Validation

Predicted noise levels have been compared with measured values during tests on high velocity

flares of natural gas [2].

At low Mach numbers (<0.75) the noise model tends to underpredict noise levels by about 2 dBA

in the near field (20m) and by 5 dBA in the far field (60m). However, the noise levels are normally

well within prescribed safety limits. It is possible that the model could be improved in this flow

regime by adjusting the atmospheric absorption factors.

For Mach numbers in the range 0.7 to 1.1 the model tends to overpredict slightly, even if ground

reflection is discounted, but is sufficiently accurate for hazard assessments.

At high Mach numbers (>1.1) it is recommended that the noise levels are predicted without ground

reflection and that the result in dBA should be reduced by 5%. Improvements in the noise model

could be made by investigating the assumption that the noise received originates from the noise

emitted in the angular range 20o above the line joining source to receiver.


14 December 2007 21

2.6. PRV Release

Pressured Relief Valve (PRV) leaks are formulated only for flow of gas through the PRV.

Stack pipe

PRV

Vessel

Figure 2-5 Vessel PRV

The flow is modelled as a two stage process. The first through the PRV constriction, the second

through the stack pipe.

From the ideal gas law, the specific volume of gas (1/density) in the vessel is given by:

ν00

0

8314=

T

P Mw Equation 2-23

where T0 temperature of vessel (K)

P0 pressure of gas in vessel (Pa)

Mw molecular weight of gas (kg/kmol)

The flow through the constriction in the PRV is assumed to be sonic, whence the mass flow rate is

given by:

2

1

1

1

0

01

1

2

+=

−

+

γγ

γνγP

CAm d&

Equation 2-24

Where

&m = mass flow rate

A1 = area of PRV constriction

Cd = coefficient of discharge (taken to be 0.9 for PRV)

The gas velocity at the constriction in the PRV is given by:

um

C Ad

11

1

=&ν

Equation 2-25

First assume the stack pipe acts as a Laval nozzle assuming isentropic flow. The exit velocity, u2 ,

is calculated from the numerical solution of:

[ ]( )11

1

2211

2

12

12

22

1/

1νν

γγ γγ PmuAPuu −−

+= −& Equation 2-26


22 14 December 2007

and the exit pressure from:

( )γ

γνmAu

PP

&/22

112 = Equation 2-27

where

u2 Velocity at exit plane

P2 pressure at exit plane (back pressure in stack pipe)

A2 area of stack pipe

If P2 calculated from the above two equations gives a pressure which is less than atmospheric

pressure Patm, then the two equations above are invalid and the expansion in the stack pipe can not

be isentropic. In which case, the flow will be adiabatic but not reversible and so

P Patm2 =

2

1

11

2

122

2

2

2

2

2

222

1

2

)1(1

−−+

−+

−= ν

γγ

γγ

γγ

Pum

PA

m

PAu

&&

Equation 2-28

If P2>Patm, then the gas will expand further downstream of the orifice.

2.7. Two Phase Jet Releases

Two phase flow occurs when both a gas phase and liquid phase are present in the flow of fluid

through an orifice or pipe. Gases have a much lower density than liquids (apart from close to the

critical temperature). For this reason, the volume fraction of gas in a pipe or orifice will be much

larger than the mass fraction of gas. Thus, because the average density of a two-phase mixture is

lower than that of a liquid, the mass flow rate for a given pressure difference tends to be lower

than for all- liquid flow.

Two-phase flow occurs when

• The fluid at the inlet to the pipe/orifice is liquid but the liquid flashes whilst in the

pipe/orifice.

• The fluid at the inlet to the pipe/orifice is two-phase.

Two-phase discharges through pipes are accounted for by a homogeneous equilibrium model

(HEM), whereby the two-phase fluid is assumed to be homogeneous and at true thermodynamic

equilibrium at all positions in the pipe. Fauske8 and Leung9 used a simplified equation of state

which describes a flash (at a particular value of enthalpy) of a single component or multi-

component two-phase mixture.

8H.K. Fauske, Flashing flow or: Some practical guidelines for emergency releases. Plant Operation Progress, 4 (1985) 132-134.

9J.C. Leung, A generalised correlation for one-component homogeneous equilibrium flashing choked flow, AIChE J. 32 (1986) 1743-1746.


14 December 2007 23

s

sl

s

ssl

PP

PPP

P

> 1

11

=

≤+

−=

ρρ

ωρ

ρ

Equation 2-29

Where

ρ = density (kgm-3

).

ρsl = density of saturated liquid (kgm-3

).

P = pressure in Pa.

Ps = saturation (bubble point pressure) of liquid in Pa.

ω = Constant parameter. (parameter varies with enthalpy

but is constant for adiabatic flash).

Application of equations of continuity, momentum conservation, energy conservation and a critical

flow condition (if required), yield a closed set of equations for describing the two-phase flow.

The assumption of thermodynamic equilibrium may not be valid for orifices and short pipes. In

such circumstances the flow is considered to be that of a metastable liquid.

2.7.1. Pool Evaporation

Various pool evaporation mechanisms can occur depending on the liquid spilled and the substrate.

In hazard analysis the main considerations are non boiling liquids on land or water and boiling

liquids on land or water.

The evaporation of liquids from a pool with a vapour pressure below 0.4 bar, can be calculated

from a formula developed by Sutton10

∗

∗

∗∗∗

PTR

Mwrum

5-

5 11.0-78.0

10-1

1ln

10 002.0 = & Equation 2-30

Where,

&m = evaporation rate, kg/m2 s

u = wind speed at 10 metres height, m/s

Mw = molecular weight liquid, kg/kmol

R = gas constant, 8314 J/kmol K

T = liquid temperature, K

P = vapour pressure, Pa

r = radius of the pool, m

The method should not be used for liquids with a vapour pressure above 0.4 bar, boiling liquids or

multi-component mixtures where the composition and vapour pressure changes as a function of

time.

10O.G. Sutton, Micrometeorology, McGraw Hill, New York, 1953.


24 14 December 2007

2.7.2. Time Dependent Gas Releases from Pipelines

The release rates as calculated in this section are the release rates at a given pressure and

temperature. During the blowdown of a vessel line pressure and temperature will change and this

will affect the release rate. Very complicated models exist to model this, however their accuracy

and complexity of use is often not needed in consequence assessment. More simple and empirical

methods will be discussed. All models assume a pipeline which is blocked in between two valves.

2.7.2.1. Small holes

When the product of hole cross-sectional area and discharge coefficient is less than 3% of the line

cross-sectional area, it can be assumed that the release rate will be dominated by the resistance in

the hole and any frictional resistance down the pipeline can be ignored. The depressurisation is

assumed to be adiabatic and heat exchange with the environment is neglected.

The initial release rate ( &m o ) can be calculated from the equations in Section 2.5.

The reduced mass flow rate as a function of time can be calculated by multiplying the gaseous

mass flow rate as calculated in Section 2.5 by the following dimensionless factor:

[ ]

−+

−∗−+= 1

1

)1(5.01 γγ

γ rr tm& Equation 2-31

Where the dimensionless reduced time tr is given by:

t C Areat

mPr d

o

g o =

∗∗

∗β

ρ Equation 2-32

Where t = time in seconds , mo the initial releasable mass, and

1-

1+

1+

2 = γ

γ

γγβ

Equation 2-33

Using these equations the release rate can be evaluated as a function of time. The time the outflow

switches from critical to sub-critical flow can be calculated from :

( )

−1

2 -

)1- ( 5.0 + 1 = γγ

γ rosubc tPP Equation 2-34

The complete methodology is also described in the TNO "Yellow Book" section 2 on releases.

2.7.2.2. Medium sized holes

When the hole area times the discharge coefficient is greater than 3% and less than 30% of the line

area, the resistance over the pipe starts playing a significant role and influences the release rate as

a function of time.

Weiss et al.11, have developed a method to calculate the blowdown time of gas pipelines. Although

the method has been developed to calculate the total blowdown time of a gas pipeline, also release

rates as a function of time can be calculated when rearranging the equations.

11M.H. Weiss, K.K. Botros and W.M. Jungowski, Simple method predicts gas-line blowdown times, Oil and Gas Journal, Dec 12, 1988, pp 55-58 and Oil and Gas Journal, July 10, 1989, pp101.


14 December 2007 25

2.7.2.3. Full bore releases

When the hole area times the discharge coefficient is greater than 30% of the line area the program

assumes that it is a full bore rupture and an empirical "double exponential" model as developed by

Bell12 is used. The following formulas are used to calculate release rates as a function of time

∗∗

∗∗

∗

∗

−

+

−

+= B

t

eBm

MM

mBt

e

Bm

M

mm

2

2

1 0

00

0

0

0

0

&

&

&

&&

Equation 2-35

Where B is a time constant given by:

67.0 = p

p

s

p

d

Lf

u

LB

∗∗γ

Equation 2-36

Where &m o = initial release rate calculated to include the effect of the decompression wave

travelling back down the pipe (TNO Yellow Book, p13 section 3.1.2) ;

[ ]

−+

+=

1

1

5.0

00101

2 γγ

γρ gPAm&

Equation 2-37

Mo = initial total releasable mass of gas in the pipeline in kg

= Total mass in pipe ∗ 0

0

P

PP a−

P0 = Initial pressure in pipe, Pa

Pa = Atmospheric pressure, Pa

ρ0 = initial density of gas in pipeline, kg/m3

t = time, s

γ = gas specific heat ratio (Cp/Cv)

f = pipe friction factor

Lp = pipe length, m

dp = pipe diameter, m

us

= speed of sound in the gas, m/s

12R.P. Bell, Isopleth calculations for ruptures in sour gas pipelines, Energy Processing/Canada, (1978), pp 36-39.


26 14 December 2007

2.8. Two Phase Blowdown

2.8.1. Introduction

This multi-component two phase blowdown model has been developed by Shell using known time

dependent, one dimensional equations of mass, momentum and energy. The model is based on the

Homogeneous Equilibrium Model and assumes that there is homogeneous (no-slip) thermal

equilibrium flow through a horizontal pipe. Once a numerical solution had been developed it was

validated against experimental release from 2” and 6” pipelines filled with LPG.

2.8.2. The Two Phase Blowdown Problem

Two phase flow occurs when any liquid stored at a temperature above its atmospheric boiling

point is released to a lower pressure, resulting in flashing of the liquid. As a liquid in a pipe flows

to the lower pressure the pressure in the pipe decreases due to frictional effects of the pipe creating

a liquid and vapour flow within the pipe, two phase flow. A critical measure of the extent of two

phase flow is the mass vapour fraction (volumetric void fraction of vapour).

The problem of two phase blowdown is illustrated in Figure1 Which show the various physical

phenomena that need to be modelled.

Figure 2-6 Pipeline Blowdown/Depressurisation Problem Overview

Assuming initially, the fluid in the pipe is in the single phase liquid or dense phase mode, after

(partial) opening of the pipe and exposure to a much lower (often atmospheric) pressure

conditions, the fluid at the opening enters the two phase regime and a two phase front will

propagate into the pipe. Since the sound speed for a two phase mixture is lower than that of either

of the two phase, critical flow conditions will easily develop therefore choking at the pipe outlet

has been addressed within the model. Also in deriving the numerical formula for the model, two

phase wall friction, liquid hold up, flow patterns and the delay of the thermodynamic state to reach

equilibrium conditions need to be addressed. Lastly the thermodynamic/flash calculations will be

required for the multi component fluids to calculate the physical properties.

Pre

ssure

Temperature

Single Phase

Tw o Phases

Two Phase Envelope

Two Phase Front

Choked Flow

W (kg/s)

Problems to be treated:

• Chocked outlet flow

• Two phase flow (flow pattern, liquid hold up, friction)

• Propagation of two phase front

• Thermal non equilibrium

Pre

ssure

Temperature

Single Phase

Tw o Phases

Two Phase Envelope

Two Phase Front

Choked Flow

W (kg/s)






Pre

ssure

Temperature

Single Phase

Tw o Phases

Two Phase Envelope

Two Phase Front

Choked Flow

Two Phase Front

Choked Flow

W (kg/s)







14 December 2007 27

2.8.3. Homogeneous Equilibrium Model

As a starting point for this model a previous model based on homogeneous and thermal

equilibrium flow, called HEM (Homogeneous Equilibrium Model) was used. According the

“Yellow Book” 13 HEM is the generally accepted and widely used giving reasonable predictions

when the mass fraction of vapour is greater than 1%. Also it has been seen that the thermodynamic

equilibrium between the vapour and liquid phases exists after 100mm of pipe work therefore HEM

applied to pipes longer than 100mm.

2.8.3.1. HEM Model

The HEM model is one dimensional with the variables referring to the cross sectional averages and

only varying along the length direction of the pipe. Two phase flow is described assuming there is

no slip between the phases. The two phases are combined to one phase with average mixture

properties to simplify the calculations. Also by assuming that the phases are in thermal equilibrium

the thermodynamic state of the fluid will follow without delay the temperature and pressure and

both phases will have the same temperature.

The pipe is assumed to be horizontal and that there is no heat transfer to or from the pipe wall.

The conservative equations for mass, momentum and energy for the HEM model are:

)()(

usx

uF

t

u=

∂∂

+∂∂

Equation 2-38

where

),,( evu ρρ= = vector of conserved variables

),,(2

vHpvvF ρρρ += = flux vector where 2

2vhH +=

)0,/2,0( Dvvfs ρ−= = source vector

with

t = time (s)

x = distance (m)

ρ = mixture density (kg/m3)

v = mixture velocity (m/s)

e = (total) energy per volume (J/m3)

p = pressure (N/m2)

h = specific enthalpy (=enthalpy per mass) (J/kg)

13 Methods for calculation of physical effects Part 1 CPR14E


28 14 December 2007

f = Fanning friction factor

D = pipe diameter

The source terms contains the effect of pipe wall friction. The following thermodynamic relations

hold

+=2

2ve ερ Equation 2-39

ρε ph += Equation 2-40

with ε = specific internal energy

the system of equations is completed with a thermodynamic equation of state

),( hpρρ = Equation 2-41

For example, for an ideal gas

RT

pM

h

p=

−=

1ττ

ρ Equation 2-42

with

=τ ratio of specific heats

M = molecular weight

R = gas constant

T = absolute temperature

Similar equations of state are used for single component and multi-component gas/liquid two

phase systems.

2.8.3.2. Mixture Density

The mixture density is calculated either from a model for single component fluid or from the

thermodynamics/flash calculations for each of the components within a mixture. The model uses

the SMIRK equations of state to carryout the thermodynamic/flash calculations.

For the single component fluid the mixture density is calculate after firstly calculating the mass

fraction of gas, secondly calculating the density of each of the gas and liquid phases and lastly by

combing the density of each of the phases.

Using the SMIRK equations of state the following data is calculated and stored for a grid of

pressure enthalpy values to be used in the HEM calculations. Data stored are quality (mass fraction

of gas), temperature, liquid density, gas density, liquid viscosity, gas viscosity and derivations of

density with respect to pressure and enthalpy.

The model has it’s own specific database of thermodynamic properties which are based on the

Shell thermodynamic properties database.


14 December 2007 29

2.8.3.3. Full Bore & Partial Releases

The exit velocity and mass flow rate are calculated using the calculated mixture density and user

specified orifice size. For a partial release the coefficient of discharge is taken as 0.8 and for a full

bore release as 1.

2.8.3.4. Numerical Solution

Along the length of the pipeline there can be regions with sharp transitions such as between single

phase and two phase which can appear quickly during a pipeline release. For this reason an explicit

method was chosen to solve the HEM equations. The differential equations are solved using a

matrix method, which has been chosen to limit the numerical loss errors during the calculations.

2.8.4. Experimental Releases

To validate the derived HEM code a number of experiments were carried out using LPG.

2.8.4.1. Details of experiments

Experiments were carried out for steady state and transient propane releases from 2” and 6”

horizontal pipes with a length of 100m. In the transient tests a pipe was filled with liquefied

propane and closed, then suddenly exposed to the atmosphere at one end to release the propane.

Various release pressures were used between slightly above saturated vapour pressure to 20 bar.

Various pipe aperture sizes and shapes were used for about 100 release tests in total of which 34

were transient.

2.8.4.2. Comparison with HEM Model

HEM calculations of the discharge flow rate for the full bore releases are in good agreement with

the test results although for the partial opening the HEM model under predicts. In comparison with

the Bernoulli equation, which would give the maximum discharge rate, assuming all the fluid was

an incompressible liquid over predicts the discharge rate.

2.9. Subsea Releases

2.9.1. Bubble Plume

The bubble plume scenario has been developed by Shell Global Solutions based on experimental

data and a study of historical empirical equations. This work developed a series of equations,

which follow the development of the bubble at depth, it’s progress to the surface including the

effects of turbulence and increase in velocity until bubbles are formed on the surface. Once the

bubble reaches the surface further work was carried out to develop an empirical equation, which

models the dispersion on the sea and a resulting fire if there is an ignition source.

The model is only valid once a plume has been established. The time to establish a plume for a full

bore pipeline rupture, can be taken as the rise time based on the initial velocity.

The bubble plume scenario has been independently validated against experimental results for small

scale releases with a close similarity and is believed to be applicable for larger release due to the

understanding of the underlying turbulent characteristics controlling the plume development.


30 14 December 2007

2.9.1.1. Bubble Radius

The bubble radius is the mean radius of the bubble plume due to the size of the gas release.

Work by Milgram14 has shown that a Gaussian velocity profile can be assumed to calculate the

mean centre-line velocity, U0 (m/s) and mean bubble radius (in the absence of surface effects), b0

(m):

41

41

00 /4 dVU &= Equation 2-43

43

41

00 6.0 dVb &= Equation 2-44

where 0V& is the volumetric gas flow rate at ambient conditions, and d the release depth. To take

account of the bubbles reaching an asymptotic state when the release depth exceeds 42m, d is

automatically changed to 42m within the model.

2.9.1.2. Plume Radius

The plume radius takes account of the action of the bubble plume which does not always appear on

the surface in the same place but “wanders”. It has been found that this wandering is limited to the

plume radius which was calculated by Fannelop and Sjoen15 using an equivalent top-hat profile.

Plume Radius = 02b Equation 2-45

2.9.1.3. Surface Velocity

The surface velocity has been approximated using a knowledge of the mean near surface centre

line velocity, U0 and the depth of the receptor, dr. To avoid the effects of the surface a modified

mean near surface centre line velocity U1 has been used.

32

01 )/(1.1 rsurf dbUV = Equation 2-46

2.9.1.4. Loss of Buoyancy

This is an approximate calculation of loss of buoyancy at the surface based on the release depth,

rdepth mean surface centre line velocity, U0 and volumetric flow rate, Q0. Since the surface

interactions are to be avoided within this calculation a conservatively modified mean near surface

centre velocity U1 has been used.

14 Milgram J.H. and J.J. Burgess(1984) Measurements of Surface Flow above Round Bubble Plumes. Applied Ocean Research, Vol6 No1.

15 Fannelop T.K. and K. Sjoen (1980). Hydrodynamics of Underwater blowouts. AIAA-80-0219, Aeronautic ad Astronautics, 1290 Avenue of Americas, New York


14 December 2007 31

Loss of Buoyancy = 1

04

1

0 **2.0

U

UQ Equation 2-47

The model returns a value of percentage loss of buoyancy due to the gas entrainment.

2.9.1.5. Velocity at Depth

This is the radial velocity of the water at the receptor depth due to the movement of the gas

bubbles within the established plume through the water. This has been estimated based on the

surface velocity at the receptor distance, depth of receptor and water depth.

Velocity at receptor depth = )/2(1(* wrsurf ddV − Equation 2-48

Where dw is the water depth.

2.9.1.6. LFL Distance

The distance to LFL and half LFL are calculated using equations derived from the results of

Phoenix CFD runs using methane as the dispersing gas over the sea. The equations within this

model use the mass flow rate of gas, gas density, LFL, wind speed, and plume radius to calculate

the distance to LFL and half LFL. The derived equations from the experimental CFD runs gave

good agreement with the CFD calculated distance although these equations have not been verified

against any other gases other than methane.

2.9.1.7. Fire Modelling

From experiments it has been found that most of the fires expected on the sea surface from an

underwater gas release can be approximated to a pool fire.

Therefore the fire on the sea calculations are carried out as if it were a pool fire with a diameter

equal to the bubble diameter.

Pool Fire Regime 32

/ FdL pα Equation 2-49

where L is the flame length

dp is the pool diameter or equivalent diameter for jet flames

F is the Froude Number, which is fuel specific, and is set to methane within the

model.

The above equation is valid except when the release causes a low momentum jet.

Low Momentum Jet Fire Regime 52

/ FdL pα Equation 2-50

These equations are a simplification of the equations used within the FRED pool fire model.


32 14 December 2007

3. Fire Modelling

3.1. Pool Fire

3.1.1. Size Of Liquid Pool

If not bunded or contained in e.g. a tank, liquid pool size will be a function of leak/spill rate and

duration, and burning rate. Pool size is particularly important as all correlation's quoted include

pool diameter (D) as a parameter, and are based on circular pool fires. For non circular pools an

equivalent pool diameter can be calculated by :

= DArea

PP4 Equation 3-1

Where,

Area = surface area of the pool (m2)

PP = perimeter of the pool (m)

This equation is not applicable to trench fires, or for pool fires with an aspect ratio greater than

about 2:1.

3.1.1.1. Liquid Burning Rate

In general the burning rate (linear regression rate of liquid surface) increases with pool diameter as

the surface to volume ratio of the flame decreases and more heat is available to evaporate liquid

from the surface of the pool. The following correlation is recommended by Babrauskas16 1983):

( )DKeMM

∗∗ -

0 -1 = && Equation 3-2

Where,

&M = mass burning rate (kg/m2s)

&M o = maximum burning rate (kg/m2s)

K = burning rate size coefficient (1/m)

D = pool diameter (m)

Typical values for M& o and K are given in Table 3-1

&M o , kg/m2s K , m

-1

LNG 0.141 0.136

LPG 0.13 0.271

Butane 0.078 0.5 m

Gasoline 0.055 2.0 m

Kerosine 0.06

2.6 m

Table 3-1 Burning Rate for Materials

16 V. Babrauskas, Fire Technology 19 (1983) 251-56.


14 December 2007 33

3.1.2. Length Of The Flame

The flame length from a pool fire is related to the burning rate, pool size and ambient air density.

These factors have been correlated by Thomas17 in the equation:

61.0

42

=

gD

M

D

L

aρ

&

Equation 3-3

Where,

L = flame length (m)

ρa = air density (average 1.23 kg/m3)

g = acceleration due to gravity (9.81 m/s2)

This correlation was derived from observations on the burning of wood piled in rectangular cribs,

but its applicability has been confirmed for other types of fire and is generally accepted as being

universally applicable.

3.1.3. Angle Of Flame Tilt

A general correlation of wind tilting of the flame has been developed by Welker and Sliepcevich18

in the equation:

6.0-7.02

07.0

2.3 =

)(cos

)(tan

a

fa

a

a

Dg

uDu

ρ

ρ

νθθ

Equation 3-4

Where,

θ = flame angle from the vertical (degr.)

ua

= wind velocity (m/s)

νa

= air dynamic viscosity (averaged 2*10

-5 m

2/s)

ρf = vapour density of burning fuel (kg/m

3)

For the specific case of LNG the following correlation is used:

428.02

09.10

2.3 =

)(cos

)(tan

Dg

uDu a

a

a

νθθ

for ua > 0.4 m/s

= 0 for ua ≤≤≤≤ 0.4 m/s

For LNG, Shell FRED also contains a correlation for the flame being dragged downwind of the

downwind pool edge.

Vapour fuel densities at their normal boiling points for specific fuels are given in Table 3-2.

17P.H. Thomas, Ninth Symposium on Combustion Science, Academic press, New York, 1963, 844-859.

18J.R. Welker and C.M. Sliepcevich, Fire Technology 2 (1966) 127


34 14 December 2007

Fuel vapour density kg/m3

LNG 1.758

LPG 2.341

Butane 2.589

Gasoline 2.9

Kerosene 3.7

Table 3-2Fuel vapour density

It is difficult to take account of the effect of the presence of structures on flame size and the fire

characteristics in the case of a strong wind (over 15 m/s). The wake flow behind tanks and the

wind flow over dike walls may influence the burning significantly.

3.2. Trench Fire Model

3.2.1. Basic Flame Geometry

Figure 3-3 Trench fire model geometry - cross-section perpendicular to long axis of trench.

The flame is modeled as a tilted solid rectangular parallelepiped.

A useful correlating parameter for the fire geometry is the Froude number, rF ′′

( )ψψ cossin2/ LWgurF +=′′ Equation 3-5

where

u is the wind speed, m/s

W is the trench width, m

L is the trench length, m

W

W’

H

Lcθ

W

W’

H

Lcθ


14 December 2007 35

g is acceleration due to gravity, m/s2,

ψ is the angle between the long axis of the trench and the wind direction.

3.2.2. Length Of The Flame

The flame length, H , is based on the correlation by Croce et al 19, with a modification to take into

account the variation in burning rate between LNG pool fires and other fuels.

61.0

2.2/

=

LNGm

mWH

&

&

for rF ′′ > 0.25

( ) 65.0

61.0

88.0/−′′

= rF

m

mWH

LNG&

&

for 0.1 ≤≤≤≤ rF ′′ ≤≤≤≤ 0.25

61.0

0.4/

=

LNGm

mWH

&

&

for rF ′′ < 0.1

Equation 3-6

where m& and &mLNG are the mass burning rates for the fuel in the trench and LNG fire respectively

, in kg/m2/s.The mass burning rates are given by the correlation

& & ( )m m ekD= −∞

−1 Equation 3-7

Most of the data for the &m∞ and k values is taken from a publication by Rew et al20. D is the

hydraulic diameter, in m, given by

LW

WL

Perimeter

AreaSurfacePoolD

+==

2)(4 Equation 3-8

where L is the length of the trench.

The coefficient of 0.61 is taken from the Thomas correlation for flame length21.

3.2.3. Flame Drag and Tilt

To determine the flame drag and tilt another Froude number is define Fr ′

19 Croce, P.A., Mudan, K.S., Wiersma, S.J., “Thermal radiation from LNG trench fires”, Gastech 85, 11th

Int. LNG;LPG Conf & Exhibition, 12-15/11/85, Nice France, Vol 42 N 11, 1986.

20 Rew, P.J., Hulbert, W.G., and Deaves, D.M., “Modelling of thermal radiation from external hydrocarbon pool fires”, Trans IChemE, Vol 75, Part B, pp 82-89, May 1997.

21 Thomas, P.H. “The size of flames from natural fires”, 9th Int. Combustion Symp., pp 844-859, (Combustion

Institute, Pittsburgh. Pa. USA), 1963.


36 14 December 2007

Fr u gWw′ = / 2 Equation 3-9

where

uw is the wind speed, m/s in the direction perpendicular to the long axis of the trench

The flame drag ′W is given by

( )′ = ′W W Fr/ ..

23 31 37

for 0.1 ≤ Fr ′ ≤ 0.25 Equation 3-10

The flame tilt θ is given by

( )cos( ) ..θ = ′ −

0 360 32

Fr for 0.042 ≤ Fr ′ ≤ 0.25 Equation 3-11

3.2.4. Height Of The Clear Flame

The height of the highly emissive clear flame Lc , taken from Rew et al, is given by

))cos(,)()(404.11min(

49.2

179.0*13.1* θHH

CumDLc

−

= & Equation 3-12

where

&*m is a dimensionless mass burning rate & & /*

m m gDair= ρ ,

u* is a dimensionless wind speed

3/1* )//( airDmguu ρ&= and

C H/ is the carbon to hydrogen atomic ratio in the fuel.

3.2.5. Surface Emissive Power

The SEP of the lower clear flame, EL , in kW/m2, is given by

E E eL

k Dm= −∞−( )1 Equation 3-13

The SEP of the upper, smoke obscured, layer, EU , in kW/m2, is given by

E U E U EU R L R S= + −( )1 Equation 3-14

where U R is the unobscured ratio, and ES is the surface emissive power of smoke (approximately

20 kW/m2). The U R value is read from a data base of values that depend on fuel type and pool

diameter.

The flame geometry (length, drag and tilt) is independent of the ambient conditions for Froude

numbers greater than about 0.25. For a 1m width trench, the critical wind speed is about 1.6 m/s.

For wind speeds greater than this, the flame geometry does not change.


14 December 2007 37

The SEP of the top of the flame ET is either EU or EL , depending on whether the clear flame

height is less than the model flame height.

The maximum radiative heat flux q , in kW/m2, to a surface outside the fire plume is calculated

from

TTTEUEUSUSUUELELSLSLL VFmxEVFmxVFmxEVFmxVFmxEq τττττ ++++= )()( Equation 3-15

where τ is the atmospheric transmissivity, VFmx is the maximum view factor and the subscripts

S and E refer respectively to the upwind/downwind or end surfaces of the flame .

3.3. Gas/vapour Jet Fire

The term "jet" or "torch" fire is used to describe the flame produced from an ignited, pressurised

release through a hole, e.g.

• a flare

• ignited vapour or vapour/liquid released from a relief valve

• ignited leakage's from high pressure pipe work- either gas, liquid or two-phase.

The difference from pool fires is that the flame shape is influenced by the initial momentum and/or

orientation of the release and width of the source. The most widely used method for this type of

calculation has been that recommended in API RP521. This uses a point source and has proven to

be moderately satisfactory for its main application in sizing and locating elevated flare stacks. This

type of calculation generally involves gas exit velocities in the range 0.2 to 0.5 Mach and "targets"

of interest relatively distant from the "point source" of heat.

A gas or vapour jet fire is a turbulent diffusion flame resulting from the release of gas or vapour

with a considerable momentum. Fuels stored under pressure could result in a jet fire when released

to the atmosphere. Two phase releases of hydrocarbons can also result in jet fires if the gas/liquid

volume ratio (under ambient conditions) exceeds 6000.

For hazard calculations, the following characteristics are of importance:

• mass flowrate,

• extent of flame spread,

• flame size and shape, and fire duration

• thermal radiation emitted by the flame surface,

• composition of products of combustion (e.g. smoke)


38 14 December 2007

Figure 3-4 Idealised Jet Fire Model

For a release in still air at an angle θ to the vertical, the position of the end of the flame relative to

the (X’, Y’) axes is given by:

θξξ

θξ

sin)('

45.055.0'

0

)sin)((

0

hL

Y

eL

X

B

f

B

=

+= −

Equation 3-16

where, the Richardson number, ξ, based on the visible flame length for vertical releases in still air

LB0 is given by:

3/13

04

)(

=

G

LgL

air

B

ρπξ

Equation 3-17

and the functions f and h are given by:

78.8

2

11)(

11.5)11.5(3.0168.0)(

11.5168.0)(

−

+=

>−+=

≤=

ξξ

ξξξξ

ξξξ

h

forf

forf

These relations model the following processes:

1. Flames from jets released in still air at an angle to the vertical are buoyant and therefore the end

of the flame lies above the release axis,

2. The flames from high momentum jets are less buoyant than from low momentum jets,


14 December 2007 39

3. In still air, the maximum distance from the release point to the end of the flame occurs for

vertical releases,

4. As the angle of the release increases away from vertical, buoyancy has an increasing effect

reducing the X’ distance and increasing the Y’ distance.

The (X, Y, Z) position of the end of the still-air flame is given by:

0

sin'cos'

cos'sin'

0

0

0

=

+=

−=

Z

YXY

YXX

θθ

θθ

Equation 3-18

The model for the effect of wind on the jet flame length includes the following physical behaviour.

1. For vertical releases, the flame is always foreshortened because the wind blowing across the

jet increases air entrainment and because the flame is bent over in a curved trajectory.

2. For releases that are not vertical and the wind is blowing away from the release point, the

wind will tend to elongate the flame and make the flame lay flat.

3. For releases that are not vertical and the wind is blowing towards the release point, the wind

will tend to foreshorten the flame and make the flame rise up.

For vertical releases, Chamberlain[4] derived the following simple relationship to describe the

wind-shortening of the flame length:

)49.051.0( 4.0 += − v

Bo eLL Equation 3-19

where v is the wind speed in m/s.

The angle that the flame tilts away from vertical depends on the ratio of the wind speed to the jet

velocity R and also on the ratio of the buoyancy force to the jet momentum, characterised by the

still-air Richardson number )( BoLξ . For a given Richardson number, the flame tilts more for

higher values of R . Thus slow, lazy flames are more easily wind-blown. For a given value of R ,

increasing the Richardson number (e.g. by increasing the hole diameter) decreases the flame tilt.

Thus big flames are less easily wind-blown than small flames.

For horizontal releases, two parameters are used to characterise the effect of the wind on the

flame length:

jvBoair

XG

vgLθ

πρ

cos/4

2/122

=Ω

Equation 3-20

is a measure of the ratio of the wind force in the jet release direction versus the jet momentum

flux;

jvBoair

ZG

vgLθ

πρ

sin/4

2/122

=Ω

Equation 3-21


40 14 December 2007

is a measure of the ratio of the wind force perpendicular to the release direction versus the jet

momentum flux. XΩ indicates the extent to which the wind is blowing along or against the release

direction and is used respectively to elongate and flatten the flame or to shorten and raise-up the

flame. ZΩ indicates the extent to which the flame is blown to either side of the release direction.

The ),,( ZYX position of the end of the flame is given by:

Zaa

Xoa

Xoa

bXZ

YY

jXX

Ω−=

Ω−=

Ω+=

|sin|178.0

)02.01(

))(1(

θ

ξ

ξ

Equation 3-22

where b is the flame lift-off distance and

( ) ( )( )

>−

≤= −− 3.31082.0

3.303.35.0 ξ

ξξ ξe

j Equation 3-23

This relationship shows that the wind-effect on the flame ),( YX position is modified by the

balance between the buoyancy force and jet momentum fluxes, characterised by the Richardson

number. If the jet momentum is relatively high ( 3.3≤ξ ), the wind has no effect on the X position

of the flame end but it changes the flame elevation above horizontal. If the jet momentum is lower

( 3.3>ξ ), the wind extends the flame if it is blowing from behind the release point.

This model for flame deflection by a wind has only been validated for | |ΩX < 7 and | |ΩZ < 3. The

correlations may well be inaccurate if the wind speed is high enough for ΩX and ΩZ to be outside

this range. If flames are to be calculated in very high cross-winds then Software Support should be

consulted.

For releases that are inclined at angles less than 45o from vertical and for wind speeds greater than

2 m/s, the flame length is modified according to the relationship derived by Chamberlain[4]:

L L eBov

jv= + − × −− −( . . )[ . ( )].0 51 0 49 1 6 07 10 900 4 3 θ Equation 3-24

This equation shows that the flame length in a co-flowing wind can be longer than the still air

flame length. The greatest extension in flame length for releases inclined at up to 45o from vertical

is obtained for a wind speed of 2 m/s, blowing in the same direction as the release, when the

release is 45o from vertical. The flame length is then 20% longer than the still air flame length.

The position of the end of the flame for general release conditions is obtained by a linear

interpolation of Equation 3-18, Equation 3-22 and Equation 3-24 and the correlations derived by

Chamberlain for the angle of flame tilt away from the release axis.

The flame lift-off distance, bshown in Figure 3-4, serves two purposes.

1. It defines the point along the flame trajectory at which the first yellow flame appears and

hence the start of the emission of significant amounts of thermal radiation.

2. It defines the point at which the model flame axis tilts away from the release axis.

The maximum width of the frustum modelling the flame, W2 shown in Figure 3-4, is used for two

purposes.


14 December 2007 41

1. Together with the minimum width, W1, and frustum length RL , it defines the surface from

which thermal radiation is emitted to external objects.

2. It is used together with the flame length in the determination of the probability that the flame

will impinge on nearby objects.

The still air maximum flame width, W2o is given by :

≤

>+−=

63.21.0

63.20396.0004.02 ξ

ξξBoo LW Equation 3-25

Thus the ratio of the maximum flame width to the flame length increases for slow lazy flames.

The influence of wind on the maximum flame width is different depending on whether the release

is vertical or inclined away from vertical.

For vertical releases, the wind always blows across the release. As the wind flows around the sides

of the flame it drags flame gases downwind, causing the flame to become wider. Eventually,

however, as the wind speed increases further, the flame is bent over towards the horizontal. The

wind is then blowing more along the flame axis, which tends to stretch the flame and make it

thinner. The ratio W2 /LB thus increases to a maximum of 0.45 when the ratio of wind speed to jet

velocity, R = 0 15. , and thereafter decreases to level off at 0.31 for R > 2 8. .

For horizontal releases, the flame is blown flatter and thinner if the wind is in the release direction

and conversely the flame rises up and is made fatter if the wind blows against the release. This

behaviour is characterised by the formula:

W X Y Wa a o X22 2 1 2

27 50 0094 9 5 10/ ( ) ( . . )/+ = − + × −Ω ξ

Equation 3-26

where Xa and Ya are given by Equation 3-22 and ΩX is given by Equation 3-20. This formula

shows that the width to length ratio W22/122 )/( aa YX + decreases linearly with increasing wind

speed. There is also a strong influence of the Richardson ratio ξ which shows that slow, lazy

flames are much more easily wind-affected than fast high-momentum flames. A linear

interpolation is made between the maximum width for the vertical flame and the maximum width

given by Equation 3-26 as the release angle varies from vertical to horizontal.

Finally, the minimum width in still air is given by

W1o0 ξ081.018.0/ +−=b Equation 3-27

with a minimum limit imposed for W1o of either 0 12. b or the expanded jet diameter.

For vertical releases in a cross-wind, the minimum width varies with the ratio of the wind speed to

exit velocity, R , in a similar manner to the maximum width. It increases to a maximum and then

decreases as R increases.

Whilst the above model is capable of handling LPG mixtures, Shell FRED also contains a special

surface emitter model for LPG flames. This has been formulated using constants for industrial

LPG and should preferably be used for the calculation of horizontally released LPG flames.


42 14 December 2007

3.3.1. Flame Stability

3.3.1.1. Introduction and overview

Flame stability, in the context of accidental releases, is concerned with the question "under what

conditions will flames go out?" Some flames lift off from the release point and self extinguish. In

windy conditions, some flames stabilise in the wake of the burner, other flames are lifted and

tilted. Spray flames can extinguish if the feedback of heat is insufficient to vaporise incoming fuel

droplets. Other flames stabilise in the wake of engulfed objects (bluff body stabilisation).

Thus there is a whole range of phenomena concerned with flame stability. The first studies were

pioneered by Thornton in the early eighties on lifted flames, and later extended to wake burning

flames. Many of the results have been subsequently confirmed by other workers, but fundamental

understanding is only just emerging, and regimes of flame stability are currently best expressed as

empirical correlations using appropriate non-dimensional groups.

A knowledge of flame stabilisation in hazard analysis and flaring has, perhaps surprisingly, a

number of important applications. In QRA studies, leaks of natural gas from small holes will not

support flames over a large range of pressures and this could influence the frequency weighting

given to such events. These types of leaks may also lead to build-up of flammable gases in poorly

ventilated or confined areas. In accident analysis, an appreciation of this same phenomenon could

help to clarify a proposed sequence of events. In flaring, flame stabilisation in the wake of the flare

tip leads to corrosion and heat stress. Optimisation of flare design could be achieved by judicious

combination of tip diameter and stack height. In venting studies, the minimum purge rate required

to maintain a flame at the tip can be evaluated. Addition of inerts to the fuel stream or to the

surrounding air promote flame extinction with implications, for example, for the design of water

based fire protection systems.

Since gas jet diffusion flames are most prone to flame extinction all the main studies refer to these

flames. An experimental campaign was carried out by Thornton to reduce some of the

uncertainties in the wake stability regime. The final outcome in terms of a new universal stability

diagram is reported here.

3.3.1.2. Flame stability in still air conditions

Imagine you are burning natural gas on a Bunsen burner with the air hole closed in the laboratory.

Now increase the flow rate of fuel. There comes a point when the flame lifts off from the burner

rim. The flame continues to burn albeit in a turbulent manner. Now increase the flow rate even

further. The flame continues to lift off and eventually lifts off altogether. In effect you have

measured the flame extinction (blow-out) limit for this burner/fuel arrangement. Different fuels

have their own blow-out limits. Natural gas is one of the less reactive fuels and so blows out at

lower flow rates than the more reactive fuels, such as propane or ethylene.

Now replace the burner tube with a smaller diameter tube. The flame blows out at lower flow rate.

Thus the flame blow-out limit depends on burner diameter and fuel composition.

These are essentially the experiments that Kalghatgi [22] carried out. He correlated his results for

the blow-out velocity ujb in terms of a Reynolds number RH characterised by the laminar burning

velocity of the fuel Su, the distance along the jet axis where the concentration falls to the

stoichiometric limit H, and the fuel kinematic viscosity νexit. The parameter H was taken from an

empirical correlation [23] with the burner diameter d. Kalghatgi found that if d was replaced by the

expanded jet diameter dj for under expanded jets in his correlation, then there would be a critical

22 G.T.Kalghatgi, "Blow-out stability of gaseous jet diffusion flames. Part 1: Still air", Comb. Sci. and Tech., 26, 233-239 (1981).

23 A.D.Birch, D.R.Brown, M.G.Dodson, and J.R.Thomas, "The turbulent concentration field of a methane jet", J.Fluid Mech, 88, 431-449 (1978).


14 December 2007 43

diameter beyond which the flame would NEVER blow out in still air conditions and would always

burn as a stable but lifted flame. Furthermore, for diameters less than the critical diameter there

exist TWO blow-out limits. A flame is able to re-stabilise if the flow rate is greater than the upper

blow-out limit.

He was not able to test these predictions since the size of the release would have far exceeded the

safe working limits of the test rig. However, since then several other combustion research groups

(see for example [24] and [25]) have repeated and extended this work and confirmed the existence

of the critical diameter and upper stability limit, see the figure below. We have found [26] that all

the results for natural gas can be described by the relationship (also shown below in the stability

plot),

ujb/Su = 0.0028 RH1.1 ( ρj/ρair )

-1.5 Equation 3-28

Where.

ρ = is the fluid density

j and "air" = the expanded jet and to ambient conditions respectively.

H = distance to the stoichiometric concentration in the Reynolds number, (Equation 3-29)

Where,

H = [ (4 θ / W') ( ρj/ρair )0.5 + 5.8]. d Equation 3-29

Where,

θ = the fuel mass fraction at the hole (equal to unity for pure fuels),

W' = the fuel mass fraction in a stoichiometric fuel/air mixture.

The hole diameter must be replaced by the expanded jet diameter for choked releases, as discussed

above.

24 A.D.Birch, D.R.Brown, D.K.Cook, and G.K.Hargrave, "Flame stability in under expanded natural gas jets", Comb. Sci. and Tech., 58, 267-280 (1988).

25 B.J.McCaffrey and D.D.Evans, "Very large methane jet diffusion flames", 21st Symposium (International) on Combustion, The Combustion Institute, 25-31 (1986).

26 G.A.Chamberlain, "An experimental study of water deluge on compartment fires", International Conference and Workshop on Modelling and Mitigating the Consequences of Accidental Release of Hazardous Materials, Sept. 26-29, pp. 763-776 (1995).


44 14 December 2007

Flame Stability Correlation and British Gas blow-out data

Hole diameter, m

Sta

gn

ati

on

pre

ss

ure

, b

ara

0

10

20

30

40

50

60

70

80

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

British Gas b low-out d a ta

Fla me stab ility c orrela tion for

na tura l gas

Figure 3-5 Flame stability correlation

Some values recommended for use in the above stability criterion are:

Fuel Mol.

weight,

kg/kmole

Laminar

burning

velocity,

m/s

Density

at

10oC,

kg/m3

Kinematic

viscosity

10oC,

m2/s x105

Stoich.

fuel/air

mass

fraction

Ratio of

specific

heats γ

methane 16 0.39 0.68 1.56 0.055 1.31

propane 44 0.43 1.91 0.42 0.06 1.13

butagas 54 0.44 2.40 0.30 0.06 1.11

ethylene 28 0.75 1.20 0.81 0.063 1.25

acetylene 26 1.63 1.11 0.88 0.07 1.25

hydrogen 2 3.06 0.086 9.88 0.028 1.41

The constants in the stability correlation have been matched to natural gas jets. The critical

diameter is then about 30mm. Interestingly the critical diameter for propane is predicted to be

around 12mm, a value that remains to be tested but which seems reasonable from experience. Note

that the blow-out velocity is correlated with the square of the laminar burning velocity and helps to

explain the grossly more stable behaviour of the more reactive fuels, particularly hydrogen,

acetylene and the olefins.

3.3.1.3. Flame stability in steady winds

Let's return to our Bunsen burner. Starting with a lifted flame, increase the cross wind steadily

from zero. Surprisingly the lift-off distance initially decreases! The flame becomes more stable.

Increasing the wind speed further, however, eventually blows off the flame. Tilting the burner into

the wind makes the flame more stable, tilting away less stable.


14 December 2007 45

Kalghatgi [27,28] studied these extinction limits also. He plotted the results in the ujb/W, v/W

plane to obtain a universal flame stability diagram for lifted flames. Here v is the wind speed and

W is a dimensional (m/s) grouping containing all the proposed important parameters, i.e.

W = Su ( RH ) ( ρair/ρj )1.5 Equation 3-30

Kalghatgi noted that at low flow rates the flame was bent over and stabilised in the wake of the

burner tube. This additional stability region was studied recently by Chamberlain and Chart [29]

and confirmed by Huang and Chang [30], and a number of new stability regimes were identified.

1. At very low flow rates the flame is able to stabilise inside the burner tube in the wake of the

leading edge.

2. At increased flow rates the flame stabilises in the boundary layer created by the top of the

burner. This effect is more pronounced if the top of the burner has a well defined rim, i.e. the hole

diameter d is less than the outer burner tube diameter D.

3. At higher flow rates still, the fuel stream becomes drawn into the burner wake and the flame has

the appearance of a two-dimensional vortex. Plant engineers often refer to this condition as flame

lick, as it is commonly seen at the top of flare stacks. The top edge of the flame becomes detached

from this vortex at higher flow rates and is swept downstream by the wind. In a separate study we

found that the flame vortex is further stabilised by tilting the burner away from the wind, in

marked contrast to the behaviour of lifted flames.

4. At even higher flow rates the detached part of the burning fuel flow dominates the appearance

and the vortex disappears. We called this "boundary layer stability".

5. Eventually at higher flow rates the boundary layer flame detaches itself from the burner, lifts

away and is extinguished. Note however that with reactive fuels, such as ethylene, the flame can

make a direct transition to a lifted flame of the type studied by Kalghatgi.

In the absence of a fundamental theory to explain this complexity, we decided to non-

dimensionalise all the results using groupings similar to those derived by Kalghatgi. In this way a

complete stability map can be generated, and the result is shown in Figure 3-6 Flame stability

graph. The axes have been scaled by dividing the velocities by:

( Su/W' ) ( d Su /νexit ) ( ρair/ρj ) Q Equation 3-31

Where,

Q = D/d (set to unity for lifted flames), and d must be replaced by dj for choked flow.

Future research will be needed to unravel the true nature of flame stability including behaviour in

unsteady winds and fuel flows.

27 6. G.T.Kalghatgi, "Blow-out stability of gaseous jet diffusion flames. Part II: Effect of cross wind", Comb. Sci. and Tech., 26, 241-244 (1981).

28 G.T.Kalghatgi, "Blow-out stability of gaseous jet diffusion flames. Part III: Effect of burner orientation to wind direction", Comb. Sci. and Tech., 28, 241-245 (1982).

29 G.A.Chamberlain and D.Chart, "Wake stabilised flames", unpublished work.

30 R.F.Huang and J.M.Chang, "The stability and visualised flame and flow structures of a combusting jet in cross flow", Comb. and Flame, 98, 267-278 (1994).


46 14 December 2007

-1

-2

-3

-4

-5

-6

0.0 0.002 0.004 0.006

Lifted Flames

Vortex Stablised

Bound

ary

Laye

r

Stabi

lised

Rim

Stabi

lised Unstable Flames

Unstable Flames

10

10

10

10

10

10

Scale

d g

as v

elo

city

Scaled wind speed

Universal flame stability map

Uncertain boundary

Data boundary

Q =

1onl

y if

Q >

1

Figure 3-6 Flame stability graph

3.4. Generalised Jet Fire

The model described in this section applies to volatile liquids and to mixtures of gases and liquids.

If the pipe /orifice through which the material is escaping is of sufficient length to reach

thermodynamic equilibrium, then the liquid will flash whilst in the pipe orifice. If it is not of

sufficient length, then the fluid will remain a liquid and flash downstream of the orifice.

3.4.1. Model Flame Shape

The flame is modelled as a conical frustum(Figure 3-7) This is of length RL, minimum width (at

the end nearest the release) w1 and maximum width (at the end furthest from the release) w2. The

centre of the base of the frustum is located on the release axis at distance b from the release point.

The centre of the far end of the conical frustum is located at the end of the 50% flame (i.e. the

region where the flame exists at least half the time); it is not necessarily on the release axis

because of the effects of wind and buoyancy on the flame. The distance from this point to the

release point is denoted Lb.

The axis system used in this report is also shown in the figure. The unit vectors i, j and k are in the

x, y and z co-ordinate directions respectively


14 December 2007 47

W2

RL

b

W1

X (EAST)

Y ( NORTH)

Z(UP)

Lb

RELEASE POINT

Figure 3-7 The cone frustum model and axis system used.

Jet flames are by their nature turbulent and the flame may only be present at certain points in space

on an intermittent basis. For a vertical jet the wind is assumed not to alter the flame length. For a

non-vertical release, the wind will modify the length of the jet flame.

3.5. Other Fire Modelling Packages

Several specialist fire packages (not included in Shell FRED) have been recently developed at

Shell Global Solutions.

3.5.1. CHIC - compartment fires

CHIC∗ (Combustion Hazards In Compartments31) is a time dependent model which predicts the

physical effects arising from the confinement of a jet or pool fire in a compartment, e.g. an

offshore module. Internal heat fluxes, smoke layer thickness and temperature, CO and soot

concentration and the extent, if any, of external flaming are predicted. The model has been

validated by experimental work using propane, diesel and gas condensate as fuel.

3.5.2. SEAFIRE - fires on the sea

SEAFIRE* predicts the behaviour of a subsea release of product at sea, from e.g. a broken pipeline.

The release may occur above/on or below the sea surface and for the latter a new model predicts

the behaviour of the rising bubble plume and subsequent surface spreading due to wind, waves and

gravitational effects. Release products may be mixtures of gas and oil. The fire characteristics of

the burning pool are based on experiment. Run time graphics show the development of fire with

time.

∗ Contact Software Support for information. (See Section “Technical And Administrative Help”)

31 M.A Persaud, G.A Chamberlain, C Cuinier, “A model for predicting hazards from large scale compartment jet fires” in Proceedings of Hazards XIII Process Safety - the future, IChemE Symp Series 141, p163-174, (1997)


48 14 December 2007

3.5.3. CLOUDF - cloud or flash fires

Cloud or flash fires are transient in nature and are the product of the delayed ignition of a

dispersing cloud in an unconfined environment. Two types of cloud fire are modelled32 with

radiation dose predictions being supplied at user specified locations.

The first is the delayed ignition of the cloud formed from a vertical release. This results in a

fireball dying back to a steady state jet flame from the source.

The second is the delayed ignition of the cloud formed from a horizontal negatively-buoyant

release. Such a flame, when not accelerated by obstacles, will travel horizontally through the cloud

at relatively low speeds (less than 20 m/s). Because of the short duration of the fire, radiation

effects are generally not significant outside the burning cloud.

32 R.F. Cracknell and A.J. Carsley “Cloud fires: A methodology for hazard consequence modelling:, in Hazards XIII: Process safety - the future, IChemE Symp. Ser 141 (1997) 139.


14 December 2007 49

4. Receiver of Thermal Radiation

Receiver of radiation object in the Shell FRED package is a general receiver of either radiation or

blast. Thermal radiation at a point can be quickly calculated by specifying the location of a

receiver in the form of downwind and crosswind distances from the release point and height above

ground.

4.1. Receiver of Radiation

If a flame is represented by an idealised geometrical shape that emits uniformly from its surface

with emissive power SEP (kW/m2), i.e. a surface emitter model, the flux at some point outside the

flame is given by:

q = τ ∗Φ ∗ SEP Equation 4-1

where,

q = radiation received, kW/m2

τ = atmospheric transmissivity

Φ = view factor

The view factor is defined as the fraction of the field of view at the receiving surface that is filled

by the flame. It is important to recognize that the instantaneous shape of the flame, even on a large

pool, does not, in general, resemble that of any idealised geometrical shape. However a tilted

cylinder is a fairly good representation of the time averaged shape of a wind tilted pool fire.

The maximum amount of radiation will be received by a surface, the normal of which points

approximately at the geometric centre of the flame.

4.1.1. Calculation of view factor, ΦΦΦΦ

The view factor quantifies the geometric relationship between the emitting and receiving surfaces;

it describes how much of the field of view of the receiving surface is filled by the flame. The view

factor is 1 if the flame completely fills the field of view of the receiving surface, otherwise it is a

fraction of 1. It is dependent of the orientation of the receiving surface and for a small oriented

surface it is given by:

∫∫=ΦR

dAr

12

21coscos

πθθ

Equation 4-2

where,

R part of the model flame surface (A1) that is visible from the small oriented receiving

surface dA2 (that part of the receiving surface for which both cos θ1 and cos θ2 are

greater than zero,

r is the distance along a line from the receiving surface dA2 and a differential area

element dA1 of the flame,

θ1 is the angle between the local normal to the surface at dA1and that line,

θ2 is the angle between the normal to dA2 and that line

A typical flame-receiving surface configuration is shown in Figure 4-1. The location of the

receiving surface is defined by the (X,Y,Z) co-ordinate system, where the positive X-axis points

North and the positive Y-axis points West. View factors are calculated for a horizontal receiving

surface and a vertical receiving surface facing the centre of the flame.


50 14 December 2007

The view factor is calculated by converting the integral over the visible flame surface to a contour

integral around the boundary of the visible flame surface. In the case of pool fires, it is calculated

for ground-based pool fires with smoky plumes above the top of the flame zone. Therefore, no

contribution is made for radiative heat transfer from the bottom or top of the model flame.

θ1 θ

2

r

dA1

dA2

Figure 4-1Typical configuration of a pool fire flame and receiving surface

The maximum view factor maxV , for a receiving surface oriented so as to receive the maximum

radiative heat flux, can also be calculated using this contour integration technique.

2/1222

max )( zyx VVVV ++= Equation 4-3

where each of the variables xV , yV , and zV , is given by a surface integral similar to Equation 4-2.

xV , yV , or zV 1

max

2

21 coscosdA

rR

∫∫=π

θθ Equation 4-4

where for xV , yV , and zV , the small receiving element dA2 is located at the receiving point with

its normal pointing in the X, Y, and Z direction respectively and R max is the maximum model

flame surface visible from the receiving point, i.e. that part of the model flame surface for which

cosθ1 is greater than zero.

4.1.2. Atmospheric Transmissivity, ττττ, for Hydrocarbon Fires

Hydrocarbon fires emit radiation in the infra-red (IR) part of the electromagnetic spectrum (wave

length range 0.5 to 15 microns). If the flame burns very cleanly and contains very little luminous

yellow incandescent soot, most of the radiation emitted will be in particular bands of the IR

spectrum associated with emission from hot combustion gases such as water vapour and carbon

dioxide. In contrast, luminous flame emits radiation over the whole IR spectrum from the

incandescent soot.


14 December 2007 51

Absorption and scattering by water vapour, water droplets, carbon dioxide, dust and smoke in the

atmosphere can have a significant effect on levels of radiation reaching targets some distance from

the flame. The attenuation over a specified path, due to the presence of water vapour and carbon

dioxide, can be calculated from the temperature and relative humidity of the atmosphere provided

the emission spectrum is known. The calculation can be performed in a straightforward and

economical manner if the fire can be assumed to emit continuum radiation (i.e. there is emission at

every wavelength) in the range considered. In the Shell fire models within the Shell FRED

program, the atmospheric transmissivity is given by the formula:

2

210210

2

210210

))((log001164.0)(log03188.0

))((log02368.0)(log01171.0006.1

COXCOX

OHXOHX

+−

−−=τ

Equation 4-5

In this equation )/65.288()( 2 ammLH TSPROHX =

where,

HR is the relative humidity expressed as a fraction,

LP is the path length through the atmosphere in m,

mmS is the saturated water vapour pressure in mm Hg at the ambient temperature, Ta K,

aL TPCOX /273*)( 2 = .

This formula was derived from transmissivity data sets derived for a black body source at 1500 K

and atmospheres at 297 K with different relative humidities and path lengths. The source

temperature is important because black bodies at different temperatures have different percentages

of their emitted energy lying in the atmospheric absorption bands.

The path length used in the Shell FRED model is the distance from the receiving point to the

model flame surface, along a line from the receiving surface to the geometric centre of the model

flame. This transmissivity algorithm is used for path lengths between 10 and 1000 m and for

atmospheric temperatures between 253 K and 313 K. If the relative humidity is zero, )( 2OHX is

set to 1.0. If the path length is less than 10m, the transmissivity is set to 1.0. If the path length is

greater than 1000m, the value of the transmissivity for a path length of 1000m is used instead.

If water droplets or sprays, dust or smoke are in the atmosphere, this formula can significantly

underpredict the attenuation of radiation. The formula will also underpredict the attenuation if the

flame burns very cleanly without any soot because the hot water vapour and carbon dioxide flame

emission bands will match-up with the water vapour and carbon dioxide absorption bands in the

atmosphere, thus attenuating a larger percentage of the emitted energy than if the emission was

over the whole IR spectrum.

4.1.3. Atmospheric Transmissivity, ττττ, for Hydrogen Flames

For hydrogen flames the radiation emitting species are predominantly water vapour and carbon

dioxide and no soot. A path length of 8m is assumed to be at 2200K and a path length of 1m at

600K. An average atmospheric transmittance can be described by:

∫

∫∞

∞

=

0

0

)(

)()(

λλ

λλτλτ

dI

dI

av

Equation 4-6


52 14 December 2007

where,

I is the Intensity of radiation

λ is the wavelength of radiation

The values of τav are calculated numerically for a range of path lengths and partial pressures of

water. The following correlation is then developed to describe the atmospheric transmissivity of a

hydrogen flame:

22 002215894.00005241033.0030740.0015196.0984891.02 RRRRH ββαατ −+−+= Equation 4-7

where,

αR = log10 (PH2O L/T)

βR = log10 (273.0 L/T)

PH2O is the partial pressure of water along atmospheric path (Pa)

T Temperature (K)

L Path length (m)

The partial pressure of water along the path will be given by the product of the saturated vapour

pressure of water at temperature T, and the fractional relative humidity of the atmosphere (range

0.1 to 1.0). The correlation is applicable for PH2O L > 100 Pa m.

4.1.4. Radiation Heat Flux from Pool Fires

The radiation from the hot gases and incandescent soot deep within the flame passes through the

visible "surface" to external objects. The amount of heat emitted varies with the distance over

which emission occurs and the concentration and type of emitting species within that path. As the

thermal radiation passes through the atmosphere outside the flame it is attenuated by absorption of

energy in the infrared wavelengths corresponding to the absorption bands of the atmospheric gases

(principally carbon dioxide and water vapour). The attenuating effect on radiation is significant

even over path lengths of a few tens of metres. Water sprays, mists and smoke can also strongly

attenuate radiation.

The radiative heat emission process is modelled by assuming that the radiation comes from the

visible surface. The surface emissive power, SEP, of a flame is the heat radiated outwards per unit

surface area of the flame. Thus the use of SEPs is a two-dimensional simplification of a very

complex three-dimensional heat radiation problem. These models can be used for reliable

prediction of external radiative heat fluxes to within about a flame length of the fire. They cannot

be used for near impingement conditions however.

The model average SEP depends on the fuel type and on the pool diameter. A uniform SEP is used

over the whole of the sides of the model flame shape. This results in underprediction of the

radiative heat flux near the base of large pool fires because the model fails to take account of the

small bright, highly emissive region at the base of the flame.

The following formulae are used in Shell FRED. For land-based LNG pool fires

bottom and topincluding area, flame Total

area Pool*)1(*2260153.0 D

eSEP

−−=

D < 11m

Equation 4-8


14 December 2007 53

bottom and topincluding area, flame Total

area Pool*)(e*) e -(1*2260 11)--0.012(D -0.153D

=SEP

D > 11m

The physical effects modelled by this equation are the increase in SEP with increasing emitting

path length, given by the first exponential term )1( 153.0 De−− and the appearance and increase in

the amount of dark obscuring smoke on the outside of the flame, given by the second exponential

term )11(012.0 −− D

e .

For LPG and propane the SEP is given by:

)1(*50**50 )18(09495.015.0 −−− −+= DD eeDSEP , kW/m2, Equation 4-9

The second term is only included if the pool diameter exceeds 18m.

For butane, gasoline and kerosene, the SEP is given by:

)1(*20*140 1.01.0 DD eeSEP −− −+= , kW/m2, Equation 4-10

Figure 3-4 shows the variation of SEP with pool diameter. There is a peak SEP for all three classes

of fuels, representing a fire when the emission from bright areas of flame is at a maximum, but

before significant amounts of smoke have appeared outside the flame. The peak occurs earlier for

heavier hydrocarbons because the flames contain higher soot concentrations.

Pool Fire model average SEP

0

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100

Pool diameter, m

LNG

LPG, propane

Butane, gasoline, kerosene

Figure 4-2 Variation of model average SEP with pool diameter for different fuels

4.1.5. Radiation Heat Flux from Jet Fires (Chamberlain Model)

The term "jet" or "torch" fire is used to describe the flame produced from an ignited, pressurised

release through a hole, e.g.

• a flare

• ignited vapour or vapour/liquid released from a relief valve

• ignited leakage's from high pressure pipe work- either gas, liquid or two-phase.


54 14 December 2007

The difference from pool fires is that the flame shape is influenced by the initial momentum and/or

orientation of the release and width of the source. Gaseous jet flame shapes vary so much that it is

very difficult to correlate the SEP directly with jet release conditions. Instead, the SEP is

determined from the fraction of combustion heat energy that is emitted from the flame as thermal

radiation, the "F factor" Fs. In the current version of the Shell Research jet fire model in the Shell

FRED program Fs for saturated hydrocarbon fuels is determined by the a correlation of the

following form:

γβα +−=∞ )exp( js uF Equation 4-11

This is the F factor for a large flame where the radiating paths through the flame are long enough

for the emission to have reached a maximum. This equation shows that the F factor decreases as

the jet velocity increases, indicating that the flame burns more cleanly, producing less

incandescent soot when the jet velocity is higher.

The constants, α, β and γ and, have been derived from natural gas and propane flame experiments.

For a general saturated hydrocarbon fuel:

)1(13142.017179.0

)1(00415.001113.0

)1(21755.051933.0

gvgv

gvgv

gvgv

YqYq

YqYq

YqYq

−+=

−+=

−+=

γ

β

α

Equation 4-12

where Yqgv is a linear interpolation parameter for variation of fuel type, given by:

( )

≥

<<−

≤

=3

3

3

901

90484248

480

mMJq

mMJqq

mMJq

Yq

gv

gvgv

gv

gv

Equation 4-13

and gvq is the neat calorific value of the fuel in MJ/m3.

It can be seen that the F factor for propane is higher than that for methane but reduces more rapidly

with increasing jet velocity. This reflects the fact that propane produces more soot when it burns

than methane.

The radiative emission through the model flame surface is given by:

A

QeFS

kL

s )1( −∞ −

= Equation 4-14

where,

Q is the energy that is released by stoichiometric combustion of the fuel, kW,

A is the total surface area of the frustum modelling the flame, m2, and

the emissivity term ( )1− −e kL describes how far the emission along a radiating path is away

from its maximum.

The grey gas absorption coefficient k is given by:

k Yq Yqgv gv= + −0 94782 0 78977 1. . ( ) Equation 4-15

The absorption coefficient increases as the net calorific value increases, reflecting the fact that

heavier hydrocarbon fuels produce higher concentrations of incandescent soot. The average path


14 December 2007 55

length for emission through the sides of the frustum modelling the flame is taken as the average

flame width L W W= +( ) /1 2 2 m. The average path length for emission through the ends of the

frustum is the frustum length L RL= .

The model average SEP reported by the Shell FRED program is given by:

S S Area S Area Aavg side side end ends= +( ) / Equation 4-16

and the average F factor reported by the Shell FRED program is given by:

F S Area S Area Qsavg side side end ends= +( ) / Equation 4-17

At present there are no correlations within the Shell FRED program for calculating the F factors

and SEPs for jet fires fuelled by unsaturated hydrocarbons such as acetylene, ethylene, propylene

etc., which produce much more soot per kg than saturated hydrocarbons such as ethane, propane

etc., when burnt in a jet flame, and hence higher external radiative heat fluxes. Fuels with

significant amounts of unsaturated hydrocarbons (e.g. propylene) can produce up to about twice as

much thermal radiation heat flux at a point outside the flame, in comparison with the heat flux for

the saturated version of the hydrocarbons (e.g. propane). Experiments using unsaturated

hydrocarbons have been carried out and Software Support should be contacted for further

information.

The radiation flux &q received by an object outside the flame is calculated using the formula:

)( endendsideside SVSVq +=τ& Equation 4-18

where τ is the atmospheric transmissivity, the fraction of emitted energy not absorbed or scattered

by the atmosphere and, sideV and endV are the view factors for the sides and ends of the flame.

The view factor Φ quantifies the geometric relationship between the emitting and receiving

surfaces; it describes how much of the field of view of the receiving surface is filled by the flame.

The view factor is 1 if the flame completely fills the field of view of the receiving surface,

otherwise it is a fraction of 1. The view factor varies with the orientation of the receiving surface

with respect to the flame. The jet fire model in the Shell FRED program assumes that the model

flame shape is a grey diffuse Lambertian radiator. The method of calculating the view factor is the

same as described above, except that the jet flame view factor is included for the ends of the model

flame.

The atmospheric transmissivity is calculated as described above, with the path length taken as the

distance from the receiving surface to the centre of the model flame. The atmospheric

transmissivity for a given path through the atmosphere is taken to depend on the concentrations of

water vapour and carbon dioxide in that path. These concentrations can be calculated from the air

temperature and relative humidity.

Whilst the above model is capable of handling LPG mixtures, Shell FRED also contains a special

surface emitter model for LPG flames. This has been formulated using constants for industrial

LPG and should preferably be used for the calculation of horizontally released LPG flames.

The plot below (Figure 4-3) shows the approximate variation of fraction of heat released as

radiation for the gas jet fire model.


56 14 December 2007

Fraction of heat released as radiation for

gas jet fire model

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250

exit velocity (m/s)

Fra

cti

on

rad

iate

d (

-)

C1

C2

C3

Figure 4-3 Fraction of heat released as radiation fpr gas jet fire model

4.1.6. Thermal Radiation from Generalised Jet Fire Model

The radiation from the flame is interpreted in terms of the fraction of the combustion energy of the

flame released as radiation, the F factor. This is related to the expanded jet parameters. Further

information is available from Software Support.

4.2. Thermal Radiation Hazard to People

The assessment of the hazards of a major fire event, requires a relationship between the thermal

load (a function of the radiation intensity and exposure time) and the effects on people.

The issue can be addressed from two perspectives.

• How long can a worker continue to operate in an emergency situation whilst exposed to a

given level of radiation?

• What fraction of the population will die or sustain serious injury given exposure to a certain

dose of radiation.

4.2.1. Design for Operation in Emergency Systems

Values for time to pain for exposed bare skin are tabulated in Table 4-1 [API-52133.]

33American Petroleum Institute, Guide for pressure relief and depressuring systems, API RP521, 3rd edition, November 1990.


14 December 2007 57

kW/m2 Time to pain

(seconds)

1.74 60

2.33 40

2.9 30

4.73 16

6.94 9

9.46 6

11.67 4

19.87 2

Table 4-1 Time to pain for exposed bare skin

In reality, a worker will be appropriately clothed in order to carry out a given task in an emergency

situation. The worker will be moving around and so bare skin will not be continuously exposed.

This results in design maximum radiation levels (Table 4-2) recommended in API -521.

kW/m2 Conditions*

15.77 Heat intensity on structures and in areas where

operators are likely to be performing duties and where

shelter from radiant heat is available (for example,

behind equipment)

9.46 Design flare heat release at any location to which

people have access (e.g., at grade below the flare or a

service platform of a nearby tower), exposure should

be limited to a few seconds, sufficient for escape only.

6.31 Heat intensity in areas where emergency actions

lasting up to 1 minute may be required by personnel

without shielding but with appropriate clothing

4.73 Heat intensity in areas where emergency actions

lasting several minutes may be required by personnel

without shielding but with appropriate clothing

1.58 Design flare heat release at any location where

personnel are continuously exposed

Table 4-2 Design maximum radiation levels (API-521)

When applying the API-521 recommended levels, note that:

a. the accuracy of prediction of the Shell FRED thermal radiation models are in the

region of 20%

b. it is generally recommended that solar radiation should not be included 34,35

c. for equipment, pre-heating by the sun could have a small effect on failure time in the

event of a impinging fire.

34Tsao and Perry, 1979, "Modifications to the Vulnerability Model: A simulation system for assessing damage resulting from marine spills (VM4),ADA 075 231, US Coast Guard NTIS report no. CG-D-3879”

35 P.J.Rew, “LD50 equivalent for the effect of thermal radiation on humans”, prepared by WS Atkins for the HSE, HSE books RSU3520/R72.027, Contract research report 129/1997.


58 14 December 2007

The API 521 design guidelines given above have been converted in to a number of formats that are

more readily accessible to design engineers. Essentially the data-points in the API-521 guidelines

have been interpolated so that a maximum exposure time may be calculated for a given level of

radiation. This method36,37 is used in the Shell FRED program. These guidelines assume that a

worker is appropriately clothed and will not remain static during a task.

Radiation level, q kW/m2 Exposure time limit, seconds

q > 9.5 less than 5 s

9.5 > q > 4.6 10(11.3-q)/2.81

4.6 > q > 1.89 10(7.57-q)/1.2

1.89 > q infinite

Table 4-3 Shell FRED maximum design thermal radiation levels

If the radiation level is varying with time, it may be more appropriate to use methods discussed in

the following section.

4.2.2. Probit Concept

The thermal load parameter, V (also known as the Eisenberg Probit Variable) is given by,

V = I4/3 t Equation 4-19

or, for non steady intensities

∫ dtI3/4

s(kW/m2)4/3 Equation 4-20

where,

t = exposure time in seconds

I = Intensity of radiation kW/m2

There have been several studies to investigate the effect of different thermal loads on pig or rat

skin and the results can be summarised as follows (Table 4-4) as a guideline for humans. The data

is for bare static skin.

V (kW/m2)

4/3

s

Effect on Static Skin

114 Unbearable pain on static skin

210-700 Limit of first degree burns

1030 Threshold second degree burns

1200 Average second degree burns

2600-3200 Average third degree burns

Table 4-4 Effects of thermal radiation on human skin

First Degree Burns: e.g. mild sunburn. Persistent redness of the skin. No scar formation.

36 G.A. Chamberlain, “Development in design methods for predicting thermal radiation from flares”, Chem.Eng.Res.Dev. 65, July 1987,299-309

37 A.D Johnson, H.M Brightwell, and A.J Carsley, "A model for predicting the thermal radiation hazard from large scale horizontally released natural gas jet fires", Trans. IChemE., Vol. 72, Part B (1994).


14 December 2007 59

Second Degree Burns: Persistent pain is accompanied by blistering, redness, swelling and loss of

elasticity. Wound will heal in 1-2 weeks if infection absent. Usually no scars.

Third Degree Burns: Skin destroyed to at least 2mm depth Several weeks required for healing.

Scars will form. Skin grafts may be necessary.

Death from burns usually results from the onset of Toxic Shock. Whether a given level of burns

leads to death depends amongst other things on the fraction of skin burnt and on the age of the

victim. The probability of death can be computed from Probit relations.

In general the probit function has the form

Y = k1 + k2 ln(L) Equation 4-21

where,

Y = probit, a measure of the percentage of the vulnerable resource which

might sustain damage.

k1,k2 = constants

L = thermal load s(kW/m2)

4/3

Probits and expected percentage of an event happening, e.g. a fatality, are linked by the error

function. The probit values can be converted into % fatalities using Table 4-5. (Numbers in bold

give % fatality, numbers in table give probit value, e.g. probit of 4.61 gives 35% fatality, probit of

7.58 gives 99.5% fatality). Probit methods can be equally well applied to the dose of toxic gases as

to thermal radiation.

% 0 1 2 3 4 5 6 7 8 9

0 - 2.67 2.95 3.12 3.25 3.36 3.45 3.52 3.59 3.66

10 3.72 3.77 3.82 3.87 3.92 3.96 4.01 4.05 4.08 4.12

20 4.16 4.19 4.23 4.26 4.29 4.33 4.36 4.39 4.42 4.45

30 4.48 4.50 4.53 4.56 4.59 4.61 4.64 4.67 4.69 4.72

40 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4.92 4.95 4.97

50 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.23

60 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.50

70 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.81

80 5.84 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.23

90 6.28 6.34 6.41 6.48 6.55 6.64 6.75 6.88 7.05 7.33

- 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

99 7.33 7.37 7.41 7.46 7.51 7.58 7.65 7.75 7.88 8.09

Transformation of probit to percentage (Finney, 1971, Cambridge University Press),

also Hazard Assessment, Lees 9/73

Table 4-5 Transformation of Probits to percentage fatality

The two commonly used Probit relations for fatality from radiation are summarised as follows,

Eisenberg38 :

Y = -14.9 +2.56* ln(V) Equation 4-22

Lees39 :

Y = -10.7 +1.99 ln (L'), [Valid up to 70% mortality] Equation 4-23

38Eisenberg N.A., Lynch, C.J. and Breeding, J.R., 1975. Vulnerability model: A Simulation System for assessing Damage from Marine Spills, Rep CG-D-136-75 (Enviro Control, Rockville, M.D. USA)

39F.P. Lees, The Assessment of Major Hazards: A Model for Fatal Injury from Burns., Trans I Chem E, Vol 72, Part B August 1994, pp127-134.


60 14 December 2007

where L' is a function of V depending on whether clothing ignites.

The Lees probit equation is valid up to a mortality of 70% and the following relations for

mortality, Pm are used thereafter:

Pm = 0.70 + 0.0003(L'-3500) L' < 4500 Equation 4-24

Pm = 1.0 L' ≥ 4500 Equation 4-25

The overall calculation of mortality in the Lees method can be approximated to:

Pm= 0.0279(L'-920) Equation 4-26

The Eisenberg model is derived from nuclear weapons fatalities in Japan. The origin of the Lees

method is more transparent than that of Eisenberg. It is for normally dressed people and is based

on 20% exposed skin area, modern medical treatment of burn injuries and an average burn depth of

0.25mm. Introduction of a factor φ allows for the fact that a person would be able to take evasive

action such that only half the bare skin would be exposed to the radiation at a given time. If

clothing ignites for an incident load, Vc , a larger area of skin will be burned.

In the original Lees formulation, the effective thermal load is related to the incident thermal load

according to:

L'= φV V<Vc

L'=(V-Vc)+φVc V≥Vc

Equation 4-27

where,

thermal load at which clothing ignites Vc≈3600 s (kW/m2)4/3 (somewhat conservative)

fraction of bare skin exposed to radiation before clothing ignites φ=0.5

The Thornton BLEVE model (Section 5.3.2) uses a slightly modified form of Lees method which

is more conservative than Lees' original formulation, once clothing has ignited:

L'= φV Equation 4-28

where φ=1 if clothing ignites at any point during the radiation pulse and

φ=0.5 if it does not ignite.

Clothing is assumed to ignite, if the integral over the heat flux transient satisfies the following

inequality.

∫ ≥ s)(kW 35000 22dtI Equation 4-29

This is the mid-range value of the equation given by Lees and the TNO green book40 Note that the

actual value of V at which clothing is assumed to ignite will now depend on the intensity of the

radiation. The modified Lees method is generally considered to be the most appropriate

methodology for the calculation of death from radiation. A graphical comparison of the Eisenberg

method and the Lees methods is given below (Figure 4-4).

40Committee for the Prevention of Disasters, 1992, "Methods for the Determination of Possible Damage to People and Objects Resulting from Releases of Hazardous materials", Rep CPR 16 E [Voorburg, Netherlands]


14 December 2007 61

Thermal Load, (kW/m^2)^4/3 s

Mo

rta

lity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1000 2000 3000 4000 5000 6000 7000

Eisenberg

Lees

Lees (mod)

Figure 4-4 Comparison of Eisenberg and Lees method

The following graph (Figure 4-5) provides an indication of expected effect on humans upon

exposure for a given time to a set level of thermal radiation, this has been generated according to

the method of Lees.

Time seconds

Rad

iati

on

kW

/m2

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35 40 45 50 55 60

no effect

1st degree burnsHeavy sunburn

2nd degree burns

Fatalities

Pain

Figure 4-5 Effect on humans of exposure to thermal radiation

4.3. Thermal Response of Structures to Fire

4.3.1. Equilibrium Surface Temperature

When a surface of a structure is exposed to radiation it will rise in temperature and reach a steady

state temperature after a long exposure time. However the actual temperature reached is very

dependent on specific circumstances. Predictions should be regarded as an indication whether or

not more detailed calculations would be worthwhile.

A heat balance equation (McMurray)41 that is typical of enclosed partially-reflective structures

such as tanks and pipes is presented. The equation accounts for heat losses by radiation and

41R. McMurray, Flare radiation estimated, Hydrocarbon Processing, 175-181, November 1982


62 14 December 2007

convection, including wind cooling, from the receiving surface. The non-receiving back surface is

assumed to be perfectly insulated. A surface emissivity of 0.9 is assumed and conduction to a

cooler part is ignored. In general the result will be conservative. The surface temperature T is

solved iteratively from the heat balance expression :

( ) )- ( + - = 44

aa TTh

TTqε

σ Equation 4-30

where q = radiation incident on the surface kW/m2

h = convective heat transfer coefficient

= 0.007377 + 0.0113 ∗ u 0.45 in kW/m2/K

u = wind speed in m/s

σ = Stefan-Boltzman constant 5.67∗10-11 kW/m2/K

4

ε = surface emissivity 0.9

Ta = Ambient temperature K

4.3.2. Temperature Rise with Time of Vessel/Pipe Wall Exposed to Fire

When an object such as a structural member, pressure vessel or pipeline is exposed to fire attack

the subsequent rate of temperature rise determines the time to failure. In those scenarios where

failure can be associated with a critical temperature, for example when the hoop stress generated

by fluid pressure inside a pipeline or vessel exceeds the yield stress of the steel at a given

temperature42, then the problem reduces to one of predicting the temperature rise of the object with

time. At the heart of the problem is the heat transfer between the fire and the object, which is by

radiation for a non-impinging fire and by both radiation and convection for an impinging or

engulfing fire. Heat is lost from the outside surface by radiation during an impinging fire, and by

both radiation and forced convection (wind) for a non-impinging fire. In the presence of wind,

natural convective heat loss from the outer wall surface is small and can usually be neglected.

For conservative predictions of the temperature rise of the wall, it can be assumed that the inner

wall surface is perfectly insulated so that all the heat absorbed from the fire goes into heating up

the wall itself, with a resulting loss of strength. This assumption is appropriate for bare structures

and the region of a vessel or pipework containing gas/vapour. However, the assumption is

definitely not appropriate for vessel walls in contact with liquid inventory. A further conservative

approximation which greatly simplifies the calculation is to assume one dimensional heat

conduction within the wall. The temperature response of the pipe/vessel is then given by solution

of the 1D transient heat conduction equation:

[ ] [ ]

= Tx

kx

Tt

c∂∂

∂∂

∂∂

ρ Equation 4-31

where ρ is the wall density (kg m-3

), c is the specific heat capacity (Jkg-1

K-1

), k is the thermal

conductivity (Wm-1

K-1

) and T is the local wall temperature (K). The temperature dependence of ρ,

c, and k is important for steel and many other materials (such as passive fire protection, PFP).

The boundary conditions relevant to a target engulfed in flame are:

Outside (fire-side) surface

q kdT

dxq T T h T T Tabs o

o

o rad o amb o m fire o= − = + − + −0 4 4ε ε σ( ) ( )( ) Equation 4-32

42"Experimental Data Relating to the Performance of Steel Components at Elevated Temperatures", Health and Safety Executive, Report OTI 92 604, (1992).


14 December 2007 63

qabs is the net thermal flux absorbed by the target surface.

The first term on the right hand side of the equation defines the fraction of incident radiation

absorbed by the surface. qrad is the incident fire radiation flux (kW m-2

). Note that only ε0qrad is

absorbed by the surface (the rest of the incident radiative flux, 1 - ε0qrad , is reflected).The second

term on the right hand side of the equation is radiative heat flux exchange between the object, with

surface temperature, To, and its surroundings, at ambient temperature, Tamb. σ is the Stefan-

Boltzmann constant (5.67 x 10-11

kW m-2

K-4

).

The third term on the right hand side of the equation is convective heat transfer from the

surrounding gas to the target surface. h(Tm) is the surface averaged convective heat transfer

coefficient which is generally a function of the mean film temperature (and is therefore variable)

and is also a function of the gas (flame) velocity. T T Tm fire= +( ) /0 2 is the mean film temperature

(K), T0 and Tfire are the object (vessel wall) surface temperature (K) and surrounding bulk fluid

temperature (K) respectively. Note that Tfire has a value equal to the ambient surrounding air

temperature for non-impinging fires (i.e. Tfire = Tamb) or is the kinetic fire temperature for

impinging fires (typically around 1200 °C).

There are a number of restrictions pertaining to situations where the hemispherical total

absorptivity and emissivity can be assumed equivalent, a full discussion can be found in

reference43. In this analysis the thermal absorptivity of the outside surface is assumed equal to the

emissivity, ε0 , this grey body approximation is reasonable in our case. The surfaces of many

materials, including steel and most passive fire protective materials, approximate to diffuse grey

surfaces. A diffuse grey surface is one which absorbs a fixed fraction of incident radiation from

any direction and at any wavelength. It also emits radiation that is a fraction of blackbody radiation

in all directions and over all wavelengths. Hence, for thermal response purposes, the hemispherical

total absorptivity/emissivity of the target material is assumed to be independent of the nature of

incident radiation and the spectral properties of the fire. For guidance a table of total emissivities is

given below (Table 4-6). The carbon steel values have been taken from work carried out by

Persaud et al.44. Other values are taken from literature45.

43 R. Siegel, J.R. Howell, "Thermal Radiation Heat Transfer", Chapter 3, McGraw-Hill, (1992).

44M.A. Persaud, L.C. Shirvill, A. Gosse, J.A. Evans, "Emissivity Measurements of Steel Exposed to a Jet Fire" in Proceedings of Eurotherm Seminar No. 37 - Heat Transfer in Radiating and Combusting Systems 2, p221-228, EUROTHERM, (1994).

45F.P.Incropera, D.P.DeWitt, "Fundamentals of Heat Transfer", John Wiley, 1981


64 14 December 2007

Material Emissivity

Carbon steel, not impinged by fire 0.8 - 0.9

Carbon steel, inside fire impingement zone 0.65

Carbon steel, sooty edge of fire

impingement zone

0.95

Paint, black 0.98

Paint, white acrylic 0.9

Paint, white zinc oxide 0.92

Concrete 0.88 - 0.93

Aluminium oxide at 900, 1300, 1800 °C 0.69, 0.55, 0.41

Red brick 0.93 - 0.96

Wood 0.82 - 0.92

Sand 0.9

Soil 0.93 - 0.96

Rocks 0.88 - 0.95

Water 0.96

Table 4-6 Emissivity of Materials

At the inside surface two possible boundary conditions are modelled,

Either, a perfectly insulated interior surface of the exposed wall, where the boundary condition is:

q kdT

dxin = − = 0 Equation 4-33

Or, free convection in air ;

)()( 44

iambmiambiin TTThTTdx

dTkq −+−=−= σε Equation 4-34

where subscript i denotes the inside boundary.

Critical Parameters

In most thermal response scenarios, the most critical parameters are:

• qrad, the incident radiative heat flux from the fire. This value is scenario dependent, and can be

obtained from running the fire models within Shell FRED (non-impinging fires) or from

guidance notes in the user guide section of this manual and literature46 (impinging fires).

Typical values range between a few kW m-2 for distant fires to a few hundred kW m

-2 for

impinging jet fires.

• mTh , the convective heat transfer coefficient. For impinging fires this is not an input

parameter in the computer models, but is calculated from the fire properties, such as fire

temperature, flame velocity and turbulent intensity. Typical values for jet fires are in the order

80 W m-2

K-1

. Generally, the value of h diminishes as the object heats up.

46"Interim Guidance Notes for the Design and Protection of Topside Structures against Explosion and Fire, The Steel Construction Institute, SCI-P-112/011, (1992).


14 December 2007 65

The PCRIG model47,48 used in Shell FRED can cater for up to five different material layers. Each

layer is sub-divided into many (program default 50) smaller layers. The program employs a

differential equation solver, which automatically steps along in discrete time steps solving the heat

conduction equation, subject to the user defined boundary conditions. Material properties are

automatically evaluated for each of these layers at each time step used by the program. These

material properties are obtained from a data-base which is in-built into the program and may not be

modified by the user. A simultaneous set of differential equations linking each layer is solved at

each time step to provide layer temperatures, heat fluxes etc.. The accuracy of the solution

obtained depends on the number of layers used - the default of 50 for each material is normally a

sufficient number of layers. The number of layers may of course be increased for a check on

accuracy (max 250 total number of layers). Note that computation time may be up to several

minutes if a large number of layers are used to provide a solution at a long time.

Effect of Geometry

To a first approximation, it may be assumed that geometry has negligible effect on the value of qrad

during impingement by jet fires and pool fires. For non-impinging fires, Shell FRED can be used

to estimate a value for qrad. However, geometry can have a significant effect on boundary layer

flow and therefore affects the value of h.

To a first approximation, PCRIG can be applied to cylindrical geometries of any diameter,

although the models are not recommended for use with instrument pipework with a diameter less

then 10 mm. In these models the temperature dependent thermophysical material property data are

pre-programmed into the software, and therefore are not accessible to the user.

For spherical surfaces such as storage spheres, the forced convection boundary layer effects are

similar to those found for cross-flow over cylindrical surfaces. Given the uncertainties associated

with the fire scenario, it is reasonable to apply PCRIG to spherical as well as cylindrical

geometries, providing the sphere diameter is greater than 500 mm.

N.B. The thermal response prediction is based on surface averaged values for forced convective

heat transfer in large engulfing fires. This method is not applicable to those scenarios where

localised jet fire impingement on large surfaces may result in 'hot-spots'.

The model is not valid for complex geometries but, with care, may be used to find approximate

solutions for structures such as fire protected I-beams. For accurate solutions of such scenarios

alternative calculation methods using commercial finite element software will be more appropriate.

4.4. Radiation Dose to a Retreating Receiver (Escape)

In this analysis the receiver is assumed to be able to run away from a flame at constant speed.

Initially there is a 3.5 second reaction time before the receiver decides to run. For the escape from

horizontal flames where the escapee moves directly away from the flame centre, the equation for

the probit variable can be written as:

∫

+=

safet

dtstr

rIV

0

3/4

2

1

2

11

)(

Equation 4-35

where,

s escape velocity (m/s)

47 Persaud MA, Shirvill LC, Gosse A, Evans JA, "Emissivity Measurements of Steel Exposed to a Jet Fire" in Proceedings of Eurotherm Seminar No. 37 - Heat Transfer in Radiating and Combusting Systems 2, p221-228, EUROTHERM (1994).

48 Cracknell, RF, Davenport, N, and Carsley, AJ "A model for heat flux on a cylindrical target due to the impingement of a large-scale natural gas flame", 2nd European Conf. on Major Hazards Onshore and Offshore, IChemE. Symp. Series 139, Oct. (1995)


66 14 December 2007

I1 is the initial steady flux at r1

rt is the distance of the receiver from the flame centre at time t

and the escape time becomes,

−

= 1

2/12

111r

I

rI

st

safe

safe Equation 4-36

The integration can be performed analytically and the result is,

( )

−=

−

−

6/52

113/5

1

3/42

115

3

safeI

rIrrI

sV

Equation 4-37

It has been argued that receivers (personnel) suddenly exposed to unsafe conditions take a finite

time to react to the situation before escape. Letting tr be the reaction time (assumed to be 3.5

seconds), and introducing the Lees’ orientation factor φ, the modified probit variable V’ becomes:

VItV r 2

3/4

11' φφ += ( tsafe > tr ) Equation 4-38

where, φ1 is not necessarily equal to φ2.

Generally, φ1 = 1.0 and φ2 = 0.5 (personnel occasionally looking back at the flame).

By assuming these values, V’ can be calculated and the extent of human injury can be estimated

according to the values given in Table 4-4.


14 December 2007 67

5. Vessel Modelling

5.1. Heat Up

5.1.1. Introduction

Gases are commonly stored in large pressurised vessels as liquefied gasses. If these vessels are

subjected to engulfing pool or impinging jet fires significant amounts of heat may be transferred to

the vessel. If the fire exposure lasts for sufficient time, the vessel may fail catastrophically,

resulting in a Boiling Liquid Expanding Vapour Explosion (BLEVE). In these events, it is the

temperature rise and subsequent loss of strength of the steel wall which determine the time to

failure. Although vessels are usually protected with pressure relief valves, failure can occur in just

a few minutes.

The use of water deluge systems or passive fire protection (PFP) materials decrease heat flow to

the vessel contents and can reduce or eliminate the risk of a BLEVE occurring49. In order to be

able to assess this behaviour and the hazards posed from fire-engulfment of liquefied gas storage

vessels it is important to understand the mechanism of failure and to be able to predict the response

of vessels under such conditions.

The HEATUP scenario within FRED, has been developed in order to model the behaviour of

vessels containing liquefied gases exposed to fire and produce suitable data as input for hazard

consequence analysis tools.

HEATUP quantifies the thermodynamic properties in the vapour and liquid phase of the contents

of vessels exposed to a range of fire scenarios. The code allows for fluid loss though a PRV

whenever the set pressure of the valve is exceeded and it can also be set up to model vessels with

PFP coatings. By calculating the thermodynamic properties of the fluid remaining inside the tank,

at the point of catastrophic tank failure, HEATUP effectively determines the source terms essential

to evaluating the hazards associated with the resulting BLEVE. The tank pressure, liquid fill level,

fluid and wall temperatures and fluid enthalpy in the liquid and vapour zones are all predicted up

to the point of vessel failure.

5.1.2. Physical Processes

There are many different physical processes occurring when a flame interacts with a vessel

containing liquefied gases due to the complex behaviour of the flame, the vessel and the vessel

contents. The important processes occurring during jet-fire impingement on vessels containing

liquefied gas include:

• Heat transfer between the fire and outer surface of the vessel, in the vapour and liquid

'zones', by radiation and convection.

• Heat transfer through the vessel walls by conduction. The wall may comprise of an outer

passive fire protection (PFP) coating plus the underlying steel wall.

• Heat transfer into the vessel fluids by predominantly radiation in the vapour space, and by

natural convection or nucleate boiling in the liquid phase.

49 T.A. Roberts, S Medonos and L.C. Shirvill, HSE Offshore Safety Report, OTO 2000 051 (2000).


68 14 December 2007

• Mass transfer from the bulk liquid or vapour to the outside environment through any holes in

the vessel.

• Mass transfer out of the vessel through any open or partially open pressure relief valves

(PRVs).

• Mass transfer within the liquid phase by flow of heated fluid into a stratified 'hot' layer lying

above the bulk liquid. The hot layer may or may not be stable.

• Mass transfer between the liquid and vapour phases by evaporation.

• Pressure, enthalpy and liquefied gas composition changes in the fluid during each of the

above processes.

• Catastrophic vessel failure resulting in a possible BLEVE.

The heat transfer processes described above are shown schematically in Figure 5-1.

Figure 5-1 Heat transfer processes involving the fire and the vessel

5.1.3. HEATUP

The methodology utilised to calculate the thermal response of vessels is outlined below. The

methods of heat transfer to and within the vessel are considered.

5.1.3.1. Heat transfer through the vessel wall

Heat transfer from the fire into the vessel is considered as follows:


14 December 2007 69

5.1.3.2. External boundary condition

Figure 5-2 shows the external boundary conditions connecting heat transfer between the fire and

the outer wall of the vessel or coating. The equations describing the heat flow are given below.

The net absorbed heat flux by the outer wall in the liquid zone, qabs_liq, (W m-2

) is given by:

( ) ( )liqfireFCliqatmradliqabs TThTTqq 0

4

0

4

00_ −+−+= σεε Equation 5-1

where ε is emissivity, σ is the Stefan-Boltzmann constant, radq is the Heat Flux due to thermal

radiation and the net absorbed heat flux by the outer wall in the vapour zone, qabs_vap (W m-2

) is

given by:

( ) ( )vapfireFCvapatmradvapabs TThTTqq 0

4

0

4

00_ −+−+= σεε Equation 5-2

where the forced convection heat transfer coefficient, hFC (W m-2 K-1), is given in terms of an

average Nusselt number according to:

FC

m

FC NuD

Tkh = Equation 5-3


70 14 December 2007

∆xa

T0vap

T1vap

T2vap

Qabs_vapQrad +QFC

FIRE

(Qref +Qemit)vap

∆xa

T0liq

T1liq

T2liq

Qabs_liqQrad +QFC

FIRE

(Qref +Qemit )liq

LIQUID

VAPOUR

Qin_liq = QNC or Qboil

Qin_vap = Qrad

(distributed between vapour and liquid)

a b

PFP steel

Tatm

Tatm

Tfire

Tfire

OUTSIDE 2 LAYER VESSEL WALL INSIDE

Tavap Tbvap

TbliqTaliq Tlpg

Tvap

0 1 2

Figure 5-2 Schematic diagram showing the heat transfer through the wall. T represents a

local temperature and Q represents total heat flow.

In equation 5-3, < > denotes spatial averaging over the surface of the impinged target and the

thermal conductivity of the 'fire' is taken as that of air at the mean film temperature, mT , given by:

+=

2

fireo

m

TTT

Equation 5-4

for impinging fires.

5.1.3.3. Internal boundary condition for the vessel wall in contact with the vapour space

The internal boundary condition for the wall in contact with the vapour space is of the general

form:


14 December 2007 71

( ) ( )vapvapNCvapvapvapin TThTTq −+−= 2

44

22_ σε Equation 5-5

The natural convection term is omitted within the program on the assumption that its contribution

to the total heat transfer is small compared with the radiative term throughout most of the heating

process.

5.1.3.4. Internal boundary condition for the vessel wall in contact with the liquid space

The variation in heat flux transferred to the liquid is described by a general 'boiling curve'. The

dominant mode of heat transfer into the liquid space is initially by natural convection when there is

a small temperature difference between the inner wall and bulk liquid. The heat transfer between

the wall and liquid is however enhanced slightly through the turbulent effects of 'bubble stirring'50.

As the difference in temperature between the wall and liquid increases, the liquid enters the

nucleate boiling regime and, in theory, the heat transfer increases up to a local maximum at the so-

called 'critical boiling' point. Beyond the critical boiling point, the net heat transfer to the liquid

reduces again (transitional boiling) due to the insulating effects of the formation of a thin vapour

film when the bubbles at the wall surface start to coagulate. As the temperature difference

increases further still, the net heat flux transfer increases again due to the increasing dominance of

radiative heat transfer across the vapour film gap. In practice, for a fire-engulfed LPG storage

vessel it is unlikely that the critical boiling and film boiling regimes will ever be attained. If critical

or film boiling regions are entered the program stops calculations.

A comparison of natural and radiative heat fluxes between carbon steel and propane vapour

T2vap - Tvap Natural Convection

Heat Flux

Radiative Heat Flux

(assuming 8.0=ε )

50 °C 0.2 kW m-2

1.0 kW m-2

100 °C 0.5 kW m-2

1.6 kW m-2

500 °C 4.5 kW m-2

21.9 kW m-2

Table 5-1 Natural and Radiative Heat Fluxes

5.1.3.5. Natural convection in the liquid

In the natural convection regime the internal boundary condition for the wall in contact with the

liquid space is given by:

( )liqliqNCliqin TThq −= 2_ Equation 5-6

where:

NC

liq

NC NuL

Tkh =

Equation 5-7

50 M. Jakob, Heat Transfer, Vol. 1, Wiley, (1967).


72 14 December 2007

and the Nusselt number is chosen to be that relevant to horizontal surfaces, as recommended by

Jakob:

( ) 31Pr16.0 GrNuNC = Equation 5-8

Equation 5-8 includes the effects of bubble stirring, in the coefficients, 0.16 which is higher than

that recommended for natural convection in vapours (0.13)2. Treating the wall as a horizontal

surface has the additional advantage that the length scale, L, in Equation ?-7 cancels and only the

thermophysical properties of the wall and liquid are required.

5.1.3.6. Nucleate boiling

There are numerous empirical correlations in the literature describing the heat transfer in the

nucleate boiling regime for single component liquids51525354. These correlations vary considerably

in predictions of heat flux values for a given temperature difference. Some of the differences can

be attributed to surface roughness effects, because many of the experiments were undertaken under

ideal laboratory conditions using apparatus designed with smooth surfaces. Also some correlations

do not include the effects of pressure. One popular correlation38

has the disadvantage that the final

result is extremely sensitive to a generally unknown parameter whose value depends on the

'surface-liquid combination'. However, one correlation presented in reference41

has the following

advantages:

• There are no unknown parameters that have to be either pre-guessed or pre-calibrated.

• The functional form of the correlation is similar in construction to those widely accepted for

natural convection and forced convection heat transfer. i.e. it has a Pr (Prandtl Number) and

an effective Re (Reynolds Number) group.

• Pressure forces are included and treated in a physically realistic way.

• All parameters involved are readily calculated using the available thermodynamic computer

packages and databases.

In the nucleate boiling regime the internal boundary condition for the wall in contact with the

liquid space, according to McNelly41 is given by:

( )liqliqboilliqin TThq −= 2_ Equation 5-9

where the heat transfer coefficient is related to the Nusselt number according to:

33.031.069.0

_

69.0

_1225.0

−

=≡ •

v

l

fg

liqin

pboil

boilnucleate

Pd

h

dq

k

c

k

dhNu

ρρ

σµ

µ

Equation 5-10

51 W.M. Rohsenow, Trans. ASME, 74 (1952) 969

52 C.T. Sciance, C.P. Clover, C.M. Sliepcevich, Fundamental Research on Heat and Mass Transfer, Chemical Engineering Progress Symposium Series, p 109-114

53 R.H. Perry, D.W. Green, Perry's Chemical Engineers' Handbook, McGraw-Hill, 6th Ed., (1984).

54. M.J. McNelly, Journal - Imperial College Chemical Engineering Society, 7 (1953) 18.


14 December 2007 73

The first term in brackets on the right hand side of Equation 5-10 is simply the Prandtl number, the

second term represents an equivalent 'Boiling Reynolds Number', the third term relates bubble to

pressure forces, and the final term accounts for the change in volume. Equation 5-11 has been

simplified into an equivalent heat transfer coefficient and a temperature difference according to:

226.2

06.123.2

3 11013.8 TPk

h

ch

v

l

fg

boil ∆

−

×= −

ρρ

σ

Equation 5-11

5.1.3.7. Heat conduction through wall

The mathematical formulation describing heat transfer through the vessel wall in the single layer

(bare steel) case is simply:

inabsw

www qqt

Txc −=

∆∆

∆ρ Equation 5-12

For the double layer wall (Figure 5-2) the heat conduction is obtained by discretising the transient

heat conduction equation as follows:

At boundary 0:

( )100

2TT

x

kq

t

Txc

a

aabs

aaa −

∆−=

∆∆∆

ρ Equation 5-13

At boundary 1:

( ) ( ) ( )21101 22

TTx

kTT

x

k

t

Txcxc

b

b

a

abbbaaa −

∆−−

∆=

∆∆

∆+∆ ρρ Equation 5-14

At boundary 2:

( ) in

b

bbbb qTT

x

k

t

Txc −−

∆=

∆∆∆

212

2ρ

Equation 5-15

Solving Equations 5-13-15 for both the vapour and liquid wall zones gives the temperature

distribution within the wall layers at each interface.

5.1.4. Mass transfer out of the vessel

5.1.4.1. Pipes

Mass transfer of either vapour or liquid through pipes in the vessel wall are treated in the same

way as in other parts of FRED. A mass transfer equation is employed to calculate the vapour mass

release rates assuming the flow is sonic. For liquid releases the Bernoulli equation is used. The

pipe is assumed to discharge to atmospheric pressure


74 14 December 2007

5.1.5. Mass transfer through pressure relief valves

PRVs fitted to liquefied gas spheres or cylinders have distinctive opening and closing

characteristics as a function of vessel pressure. There are three PRV characteristics available

corresponding to a 'square' , a 'triangular', and a 'trapezium' response. Figures 5-3-5 below

represents the characteristics of these three valves.

P (bara)

% Open

100

0 P reseat P set

Square Characteristic

Figure 5-3 PRV with a square characteristic


14 December 2007 75

P (bara)

% Open

100

0Preseat Pset

Triangular Characteristic

Figure 5-4 PRV with a triangular characteristic

P (bara)

% Open

100

0Preseat Pset

Trapezium Characteristic

Pfull

Figure 5-5 PRV with a trapezium characteristic


76 14 December 2007

5.1.6. Change in composition

Mass transfer through PRVs on the vessel wall alters the composition of the remaining fluid. The

changes in the composition of the contents of the tank and the associated changes in enthalpy as

the different components are differentially vented are calculated within the program.

5.1.7. Mass and heat transfer within the vessel

Mass transfer in the liquefied gas tank occurs within the liquid phase by virtue of mass flow of

heated liquefied gas liquid into a stratified hot layer, as depicted in Figure 5-6. If the stratified hot

layer is stable, then the liquid phase within the vessel splits into two zones. One zone, known as

the 'hot liquid layer' lies on top of the other zone, known as the 'bulk liquid layer' as illustrated in

Figure 5-6. If the stratified layer is not stable due to the movement of hot fluid being too fast, then

the program reverts back to there being only a single liquid zone. Heat transfer from the walls to

the liquid, as described in previous sections, remains unaffected by the presence or not of a hot

liquid layer, because the differences in the temperature gradient across the steel for the two layers

is negligible.

Figure 5-6 Schematic of a liquefied gas vessel showing the mass flow of liquid into the hot

layer.


14 December 2007 77

5.1.8. Mass and heat transfer within the liquid phase

Calculation of the mass flow rate of heated liquid into a stable stratified hot layer follows the

analysis of Yu et al.55. The program builds on the analysis and assumes that the mass flow rate per

unit length scale, mhot, is always turbulent in nature

5.1.9. Total heat energy transfer

The total heat energy transfer (in J) into the vessel from the fire in a time step, t∆ , is given as:

( )[ ] tFFAqFAqQ gasfireggingashotfirehotinliqinhot ∆−+= −− 1 Equation 5-16

[ ] tFAqQ bulkfirebinliqinbulk ∆= − Equation 5-17

[ ] tFFAqQ gasfireggingasingas ∆= − Equation 5-18

for the hot liquid layer, bulk liquid layer and vapour layer, respectively. Here, q represents the heat

flux (in W m-2) into the various fluid zones and A is the surface area of the vessel in contact with

these fluid zones. The subscripts b, g and hot refer to the bulk liquid, the gas and the hot layer,

respectively. The gasfirebulkfirehotfire FFF −−− and , , are variables to represent the fraction of surface

area affected by the incident heat flux from the fire, in each of the zones (hot liquid zone, bulk

liquid zone and gas/vapour zone, respectively). The use of gF represents a method of allowing the

radiative energy emitted from the inner vessel wall to be re-distributed between the gas/vapour

zone and the hot liquid zone according to the fraction of vessel surface area in contact with the

gas/vapour. Thus )1( and gg FF − are analogous to radiation 'view factors' but are much more

simple to evaluate.

5.1.10.Mass and heat transfer between the liquid and gas phases

Mass transfer between the liquid and gas phases takes place through evaporation or flashing of the

liquid during heating. These processes are performed in a number of stages within the program.

The objective is to evaluate the thermophysical properties of the liquid and vapour phases and to

find the new vessel pressure. There are two cases of interest, one case is when there is no hot layer

in the liquid (single liquid layer) and the other is when there is a hot liquid layer above the bulk

liquid layer (double liquid layer). In both cases the underlying equation of state to be satisfied in

all fluid phases is:

PVUH += Equation 5-19

where changes in each time step obey:

PVVPUH ∆+∆+∆=∆ Equation 5-20

Here H is enthalpy, U is internal energy, P is pressure and V is volume. For the whole system,

there is no volume change. Also, for the gas and liquid phases considered separately, the expansion

work done through evaporation is negligible. Typically:

55 C.M. Yu, N.U. Aydemir, J.E.S. Venart, J. Therm. Sci., 1 (1992) 114


78 14 December 2007

06.0≈∆∆

PV

VP

Equation 5-21

Thus:

PVQH insys ∆+=∆ Equation 5-22

applies and forms the basis of all thermodynamic calculations. It is also assumed that negligible

work is done by the system during operation of the PRV.

5.1.11.Vessel failure

For design purposes, the yield stress point (which can often be approximated as the elastic limit

point or the proportionality limit point, because these all lie in close proximity on the stress-strain

diagram for low carbon steels) of the steel vessel wall represents the limit of steel strength in most

applications. However, the vessel does not actually fail through rupture until the fracture stress or

ultimate tensile strength (UTS) of the steel is reached56. Within the input information to the

program it is possible to specify a UTS multiplier (safety factor) which is used to set the failure

point of the vessel based on a fraction of the UTS value. If set to 0.5 the vessel will fail at 50% of

the UTS value.

In the program, vessel failure for both a cylindrical vessel and a spherical vessel is treated simply

by comparing the internal circumferential or 'hoop' stress (assumed to be most appropriate for a

thin walled vessel) at each time step with the UTS of the steel. For a cylindrical vessel, the hoop

stress, σ'h, is calculated using:

x

rPcylinderh ∆

=)('σ Equation 5-23

and for a spherical vessel:

2

)(

2)('

cylinder

x

rPsphere h

h

σσ =

∆=

Equation 5-24

where r is the vessel radius, P is the pressure and ∆x is the thickness of wall. The longitudinal

stress, xrPlong ∆= 2'σ for both the cylinder and sphere, cannot exceed the hoop stress and

therefore is not considered.

In general the UTS can be derived from the known mechanical properties of the steel as a function

of temperature. In the program, the variation of UTS with temperature was derived by considering

steel data curves found in Lees11. The derived form is:

560)(' =MPaUTSσ for CTwall °≤ 400 Equation 5-25

4737.121.1164)(' wallUTS TMPa −=σ for CTwall °> 400 Equation 5-26

56 F.P. Lees, Loss Prevention in the Process Industries, Vol 1., 2nd Edition, Chapter 12, Butterworth-Heinemann, (1996).


14 December 2007 79

It should be noted here that there is no such thing as 'generic' steel data and that, in reality, the

strength of the steel and other properties are highly dependent on the steel composition in addition

to the temperature. Measurements carried out on the remains of an LPG tank used in a HSE jet-fire

impingement test show that values used within the program are in reasonable agreement with the

measured ones.

5.1.12.Extra Considerations

5.1.12.1.Vessel coatings

HEATUP can handle two types of material layers in the vessel wall, namely an optional outer

material of Passive Fire Protection (PFP) layer and an inner wall of low carbon steel.

5.1.12.2.Ramped fires

To accommodate fires which do not reach their maximum heat fluxes immediately (e.g. pool fires

in which the fire takes time to spread and get established) there is an option to apply a time ramp to

the fire radiation and kinetic fire temperature.

5.1.12.3.BLEVE

The BLEVE event itself is not modelled within HEATUP, but the fluid conditions at the point of

vessel failure are available to provide input into a suitable BLEVE model.

5.2. Vessel Burst Model

There are two distinct modelling regimes for this type of phenomenon, bursting vessels containing

compressed gas or vapour, and BLEVE of flashing liquid. The description here is for calculating

the blast from bursting vessels containing compressed gas or vapour. The Shell BLEVE model

should be used where a significant fraction of the liquid under pressure will flash on release.

The method is a derivation of classical work originated by Baker et. al57 , and summarised and

extended in Lees58 who refers to the Yellow Book.59.

5.2.1. Energy of Vessel Burst

The energy associated with the explosion in a vessel burst has been calculated assuming that the

fluid under pressure will behave as an ideal gas. This assumption is conservative and if available

energy equations for non ideal gases are used similar answers are obtained.

There have been a number of studies carried out to calculate the energy of the explosion with this

model following the work of Brode. Brode assumed that the explosion energy is that associated

with raising the pressure of the gas from atmospheric pressure to the bursting pressure at a

constant volume.

57 Baker et. Al (1983) Explosion Hazards and Evaluation, Elsevier

58 Lees (1996) Loss Prevention in the Process Industries Volume 2 Butterworth Heinmann

59 Method of Calculating Physical Effects, CPR 14E Part 2, 3rd

edition 1997. TNO “Yellow Book” IASBN 90 12 08497 0


80 14 December 2007

( )11

1

−−

=γ

VPPE

a

Ex Equation 5-27

Where EEx is the Brode energy of explosion, P1 is the burst absolute pressure, Pa is the atmospheric

pressure, V is the volume of the vessel, and 1γ is the ratio of the specific heats.

5.2.2. Vessel Burst Pressure

A vessel can fail due to over pressure or over temperature which will influence the burst pressure.

As a guide there are four possible failure scenarios, overpressure, mechanical failure, fire

engulfment and runaway reaction.

5.2.2.1. Vessel Failure due to Overpressure

If the vessel is exposed to an operational overpressure and the relief valves fails then the burst

pressure for a mild steel vessel can be taken typically as 4 times the design pressure, reference

Lees45

.

5.2.2.2. Vessel Failure due to Mechanical Failure

If the vessel fails due to corrosion or impact the burst pressure can be taken as the operating

pressure, reference Lees45

.

5.2.2.3. Vessel Failure due to Fire Engulfment

If the vessel is exposed to an engulfing fire and the relief valves works then the burst pressure can

be taken as the accumulation pressure, reference Lees45

. The accumulation pressure can be

calculated using the FRED Heat Up scenario.

5.2.2.4. Vessel Failure due to Runaway Reaction

If runaway reaction occurs in the vessel resulting in an increase in temperature the burst pressure

can be taken operating pressure, reference Lees45

.

5.2.3. Blast Wave

The vessel wall is assumed to disappear instantaneously on failure, and a one-dimensional set of

conditions is applied at the wall, so that the internal pressure before failure is the sum of the

outward-moving blast-wave, and the inward moving rarefaction pulse (shock-tube theory). A

scaled distance and scaled pressure are calculated based on the explosion energy, which will be

used to calculate the overpressure and impulse at the receptor.

The explosion energy as well as generating the blast wave can be used to generate missiles and

heat radiation. Inline with the Shell BLEVE model the default setting is to assume 60% of the

explosion energy is used for the blast wave. The remaining 40% goes into the fragments and

missiles.

To allow for the reflected blast wave, which could be caused due to the ground the available

energy, needs to be modified. The user needs to specify if the vessel is at ground level or high

level. For vessels at ground level the calculated energy will be multiplied by 2. A vessel at ground

level is less than 15° above the horizontal as seen from the receptor as defined in the TNO “Yellow

Book”. Vessels higher than this require no modifications to the available energy.


14 December 2007 81

5.2.4. Scaled Distance

A scaled distance is calculated using the proportion of explosion energy assigned to produce a

blast wave. The scaled distance is required for the vessel and the receptor to calculate the

corresponding scaled over pressure values. The scaled distance is a dimensionless number.

3

1

=Ex

a

E

prR oo

Equation 5-28

3

1

=Ex

a

E

prR

Equation 5-29

Where ExE is the explosion energy, pa is the absolute pressure of the ambient air, ro is the vessel

radius, r is the distance to the receptor, oR is starting distance and R is the scaled distance to the

receptor.

5.2.5. Scaled Pressure at Vessel

The initial scaled pressure soP for the blast wave at the vessel is solved by iteration of the shock-

tube equation.

( ) ( )( )

( ) [ ]

( )12

2

1

111

1

1

122

/111

−−

++

−−+=

γγ

γγγ

γ

soaaa

soaso

aP

PaaP

p

p

Equation 5-30

1−

=

a

soso

pp

P Equation 5-31

where

p1 = initial absolute pressure of compressed gas

pa = ambient temperature

soP = non-dimensional scaled peak overpressure after the burst which corresponds

to oR .

pso = peak shock pressure directly after burst

aγ = ratio of specific heats of ambient air

1γ = ratio of specific heats of compressed gas

aa = speed of sound in ambient air

a1 = speed of sound in compressed gas

5.2.6. Pressure Decay


82 14 December 2007

The scaled pressure soP and radius oR (the initial conditions) are used to enter a set of decay

curves which were originally derived by Baker et. al, by numerical modelling of the near-field

decay of the high-pressure spherical waves, and validated them against data from bursting glass

spheres. These decay curves have been collapsed to a series of equations, which are solved to

return the scaled overpressure at the receptor. The series of equations generate decay curves,

Figure 5-7 which are a close fit to those derived by Baker et al. When the initial values of soP &

oR are in the lower left hand quadrant of the Baker curve the pressure decay from this point using

Bakers methodology is considered to be inappropriate. Consequently the predictions using the

Baker curves and the derived curves will generate different answers in this region. It is believed

that the derived equations are a better estimation of the values in this area of the decay curves

which are shown in Figure 5-8.

Figure 5-7 – Comparison of FRED decay formulation against data points from Baker et al

Decay Curves


14 December 2007 83

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E-02 1.E-01 1.E+00 1.E+01

Ps

R

Figure 5-8 –FRED interpretation of Baker et al decay curves

5.2.7. Impulse at Receptor

Baker et. al. also gives a scaled decay chart for impulse, generated from data gathered from

exploding Pentolite spheres. The fit of his numerical model to this line was poor and the scaled

decay chart is a conservative top-estimate known as a “limit curve”, the same curve being used

whatever the source pressure. At large R all the curves are within 25% of this line, and below it.

The non-dimensional impulse I is read off the scaled decay chart of I versus R which were

derived by Baker et. al.

5.2.8. Vessel Type & Elevation

The method describe so far is for a symmetrical blast wave, due to a spherical vessel burst in free

air or a burst on the ground with hemispherical symmetry. In reality vessels are either spherical or

cylindrical and will be at a ground level or a height above ground. To take into account these

differences sP and I must be adjusted by the multipliers listed in Tables 5-2 & 3.

R sP I

3.0< 4 2

1.6R0.3 ≤< 1.6 1.1

3.5R1.6 ≤< 1.6 1

5.3> 1.4 1

Table 5-2 Adjustment factors for cylindrical vessels


84 14 December 2007

R sP I

1< 2 1.6

1> 1.1 1.0

Table 5-3 Adjustment factors for vessels slightly elevated above ground

5.2.9. Gas Dispersion With Fireball

It is straightforward to calculate the volume of the vapour cloud once it has mixed down to the

Lower Flammable Limit (LFL). It is incorrect to use the concentrated volume, since air will mix

into the cloud as it expands, similar to the effects noted in the development of a BLEVE. A fireball

size can be estimated by burning this volume, so that typically the volume increases by a factor of

8.

For a typical depressurised vapour, which is denser than air (1.4 – 1.7 kg/m3) and flammable limit

4 – 5 %, then

3/19.2 MR f = Equation 5-32

Which, is also a good fit for BLEVE fireballs, indicating that the entrainment on expansion

follows the same mechanism in each process. Within the model this has been fixed therefore it is

not calculated for any specific chosen fluid.

There is no data available for the Surface Emissive Powers (SEP) of such fireballs. However, once

again the BLEVE model can be used, since the SEP is calculated from a heat balance using the

expanded vapour only. Since the fireballs are the same size, then the best that can be done at the

moment is to use the hot BLEVE data, modified to remove the droplets, as follows:

The turbulent burning velocity in the BLEVE experiments is roughly a constant value of 26 m/s, so

that the fireball will expand in time

3/1

exp 11.026

MR

tf ==

Equation 5-33

seconds, and then go out (this is very much shorter time than for BLEVEs where there is

significant liquid to burn in droplet form). If the SEP is conservatively estimated to be constant at

peak value (typically 240kW/m2 for a sphere), then, assuming the sphere grows as for a BLEVE, it

is easy to calculate the impact in thermal dose units, V

∫= dtIV3/4

Equation 5-34

where I is the instantaneous flux, and to show that, up to and around 50 tonnes of vapour, then no

fatalities occur from radiation outside the fireball radius, so that the use of a normal BLEVE model

is conservative.


14 December 2007 85

5.3. BLEVE

A Boiling Liquid Expanding vapour Explosion (BLEVE) is caused by the catastrophic failure of a

pressure vessel containing a liquid which is well above its boiling point at atmospheric pressure.

Although rare events, the consequences of a BLEVE can be catastrophic, leading to the prominent

position of the phenomenon in the safety analysis of LPG transport and storage.

Many correlation's for the fireball dimensions and duration have been proposed in literature. These

correlation's for both hydrocarbons and rocket fuels have been reviewed by Lihou60 and TNO61.

The models available in the Shell FRED package are those developed by TNO and Shell Research

Ltd.

5.3.1. TNO BLEVE

The model proposed by TNO was subsequently checked by Pietersen62 (1985) against the data

from the Mexico City incident and good agreement with the observations was obtained.

The diameter, D of a BLEVE can be calculated from the amount of flammable material in the

fireball in kg (W) using :

D = 6.48 ∗ W0.325

Equation 5-35

The duration of the fireball in seconds (t) can be calculated from:

t = 0.852 ∗ W 0.26

Equation 5-36

The view factor Φmax of a ball at a receiver distance x from the centre of the fireball in metres can

be calculated from:

∗

2

2

max 25.0 = x

DVF

Equation 5-37

The estimated Surface Emissive Power, SEP, of a fireball is assumed to be 184 kW/m2. The

radiation, I, in kW/m2 at a distance x can now be calculated from :

I = Φmax ∗ τ ∗ SEP Equation 5-38

5.3.2. SHELL Research Ltd BLEVE Model

This model63,64 is used to calculate the radiation and over-pressure from BLEVE's (Boiling Liquid

Expanding Vapour Explosions). The model differs from the TNO model in its ability to model the

BLEVE process. In the TNO model the heat wave is, very crudely, released as a square wave

pulse. In the Shell Research Ltd model fireball growth, rise and variation of radiation as a function

60D.A. Lihou and J.K. Maund, Thermal radiation hazards from fireballs. Symposium on the assessment of major hazards, Manchester, p397-428 in I.Chem.E.Symp.Ser. No71.

61TNO, LPG a study. Dutch Ministry of Housing, Physical planning and the environment. 1983.

62C.M. Pietersen and S. Cendejas Huerta, Analysis of the LPG incident in San Juan Ixhuatepec, Mexico City, 19 Nov 1984. TNO report 85-0222, The Hague

63 S.R. Shield, AIChE/ASME National Transfer Conference, Atlanta, Georgia, 8-11 August 1993

64 S.R. Shield, IChemE Conference, Major Hazards Onshore and Offshore II, October 1995


86 14 December 2007

of time has been modelled. Currently only three pressurised liquids are included viz. propane,

butane and propylene.

5.3.2.1. Fireball Development

Experimental observations show five distinct stages in the development of fireballs.

Stage 1: The vessel fails, missiles are generated and ejected and an initial overpressure wave, Ps1,

is produced by the expanding vapour phase. The overpressure pulse is followed by a rarefaction.

Stage 2: The bursting vessel ejects a cloud of liquid droplets which flash adiabatically as the

pressure in the cloud drops. The mass, and therefore ultimately volume, of vapour flashed from the

liquid droplets vastly exceeds that of the vapour initially released in Stage 1. There is little mixing

with the surrounding air. The cloud pressure, eventually drops to the surrounding atmosphere and

the volume of the cloud then becomes equal to the volume of flashed vapour at saturation

temperature and pressure.

If the outward radial velocity of the cloud exceeds the local speed of sound in the rarefaction

following Ps1, then a blast wave can form as a result of the vapour expansion from the flashing

liquid. As it separates from the outer cloud boundary, this blast wave, Ps2, leaves the cloud in a

highly turbulent state at ambient pressure. It has been observed from experiments that the blast

wave is only associated with the initial high fill ratio. At lower levels of fill the blast wave is

unlikely to occur.

Stage 3: At this stage the overpressure peaks Ps1 and Ps2 leave the cloud. The cloud continues to

expand due to outward radial momentum but the radial expansion velocity slows as the turbulent

mixing entrains more and more air. Rapid expansion continues until the random velocities in the

turbulent eddies overwhelm the radial expansion velocity, further expansion being due to the

turbulence alone.

Stage 4: Ignition occurs near the centre of the cloud and an hemispherical fireball develops. The

expansion is suddenly arrested as the last visible part of the vapour cloud is consumed by flame. At

this point the fireball is at its brightest. Since the cloud contains air, it is assumed that during this

stage the flashed vapour is consumed, there being insufficient time for radiation to substantially

heat and flash the cold liquid droplets. The expansion causes an overpressure pulse in the

surrounding atmosphere which travels outwards from the cloud. The pulse is followed by a

rarefaction caused by the sudden arrest in cloud expansion. The expansion velocity of the fireball

is equal to the flame propagation velocity through the turbulent vapour cloud. The heat radiation

pulse from the fireball peaks at the end of this stage.

Stage 5: The hemispherical fireball rises to become a sphere sitting on the ground. Combustion

continues but the fireball does not expand, indicating that the air required for combustion is

already pre-mixed into the cloud. The fuel for combustion is supplied by the liquid droplets. The

fireball then rises at approximately constant velocity and volume, and assumes a typical mushroom

shape. The visible flame area decreases as the fireball becomes patched with sooty combustion

products. Once combustion is substantially complete, the smoky torrid of hot combustion products

rises, expands and dissipates with a flow pattern similar to a thermal. The heat radiation pulse

decreases systematically to zero during this phase.

5.3.2.2. The Cloud Size

During Stages 1 and 2, and for the initial part of Stage 3, the development of the major dimensions

of the asymmetrical vapour cloud can be described by:

( ))/(

0 1 ptt

p etUR−−= Equation 5-39

where,

R is the characteristic length (m),


14 December 2007 87

U0 is a characteristic initial velocity (m/s),

tp is a time scale (s),

t is the elapsed time.

At later times during Stage 3 the cloud growth, as in turbulent dispersion, is of the form:

2/1.tconstR = Equation 5-40

The length scale of the turbulent eddies (or puffs) within the cloud is approximately equal to the

radius of the cloud at the end of Stage 2. The length scale L is given by:

0

3

v

ML

ρβα

= Equation 5-41

where,

M the fluid mass,

α the initial liquid mass fraction (before vessel rupture),

β the mass fraction of vapour flashed from the liquid when the pressure drops to

ambient,

ρv0 is the saturated vapour density at atmospheric pressure, P0

The turbulent eddies comprising the cloud expand with the cloud. Given there are N number of

eddies within the length scale L in the expanded cloud, and provided N remains constant, then the

length scale of each eddy is simply given by L/N when the blast wave Ps2 is formed. By assuming

that the eddy viscosity of the eddies remains unchanged as they grow from L/N to L, it can be

shown that:

NLtU p =0 Equation 5-42

LuNU2

0= Equation 5-43

where uL is a characteristic turbulent velocity of an eddy size L.

By equating the energy available from the flashing liquid to do work against the atmosphere with

the turbulent kinetic energy of the vapour cloud, and by assuming that dissipation is negligible in

the turbulent eddy production process, a value of N could be found by:

3/1

101

0

11

2

1

0 )1(1

−++−=

ρβρβ

ρβαρ

ρ GGGuG

PN v

a

vo

La

Equation 5-44

so that all the unknowns are now defined in terms of uL; G1 being a factor equal to 4π/3. Empirical

correlation for uL is given by:

µσ

αβ 9/1)(47.0=Lu Equation 5-45

This correlation for Lu has been derived from work carried out to calculate the size of the largest

droplet formed with in the cloud. Where σ is the surface tension and µ is the viscosity.

5.3.2.3. Fireball Diameter

The volumetric expansion of the initially unburnt vapour is the product of two factors. The first is

due to the volumetric change which occurs in combustion due to the increased volume of the


88 14 December 2007

combustion products at constant temperature. For a pure stoichiometric butane/air mixture this

factor, f1, is 1.148, and for a similar propane mixture, 1.125. The major factor, f2, is due to the

temperature change of the combustion products and unburnt air. This is calculated by taking all the

components of the mixture as real gases, so that , Vf (m3), the fireball volume after expansion is

given by:

==

0

121T

TfVffVV c

ccf Equation 5-46

The fireball diameter being:

3/127/5)( MD f αβ∝ Equation 5-47

so that the diameter of the expanded fireball is independent of the value of uL. Increasing uL

decreases the diameter of the vapour cloud, but this decrease is compensated by the increase in Tc.

The turbulence model is therefore only necessary for the prediction of growth and lifetime

timescales.

5.3.2.4. Fireball Surface Emissive Power (SEP)

By ignoring the heat loss by radiation, and by assuming that only the flashed vapour fraction is

consumed as the fireball expands, a heat balance for fireball temperature is derived:

))(( TTcMcMhM cpaapvc −+= βαβα Equation 5-48

where hc is the gross calorific value of the fuel vapour, and Tc the average temperature of the

fireball at maximum size The SEP is found by assuming that the fireball is a perfect black body:

4

cTSEP σ= Equation 5-49

where σ is the Stefan-Boltzmann constant.

5.3.2.5. Fireball Lifetime

The duration of the expansion phase, texp (s) is given by:

u

Rt

f

′≈exp

Equation 5-50

where Rf is the fireball radius, and u’ the isotropic root mean square (r.m.s) turbulent velocity,

taken as :

Luu 3/2=′ Equation 5-51

Following the expansion the fireball is assumed to maintain an approximately constant volume

throughout the remainder of its lifetime. Calling this period ts, the total duration of the fireball is

given by:

td = texp + ts Equation 5-52

then ts is found from another heat balance. The heat produced by the combustion of the liquid

droplets is assumed to be equal to the sum of the heat radiated and retained in the combustion

products as the fireball remained at constant temperature, Tc. Thus:

))(()1( 0

42TTchMtTD cplcscf −−−−= λβασπ Equation 5-53


14 December 2007 89

5.3.2.6. Initial Blast Overpressure (Vessel Rupture)

If a volume V contains a perfect gas at absolute pressure, P0, and absolute temperature, T0 then by

definition:

00 nRTVP = Equation 5-54

where n is the number of moles of gas and R the gas constant. If a quantity of Q is added to this

volume so that the pressure rises to P1 and the temperature to T1 then:

)1(

)()( 01

01 −−

=−=γ

VPPTTcnQ V

Equation 5-55

where cV is the specific heat at constant volume and γ the specific heat ratio for the gas. The initial

overpressure wave is modelled as a sinusoidal distribution of pressure (or density) in space, giving:

)(

)(

)1(

)()1(6.0

0

22

max

1

01

a

txpPPM

a

p

VV ρ

π

ργα ∆

=−

−−

Equation 5-56

and the peak overpressure, ∆pmax, is found to obey Hopkinson’s blast scaling law. The impulse, I+,

of the half-sinusoidal overpressure pulse is found from:

πptp

Imax∆

=+

Equation 5-57

5.3.2.7. Blast Wave from the Flashing Liquid

By matching the Rankine Hugoniot equations for a blast wave to the cloud expansion velocity at

radius L, the magnitude of the flashing liquid overpressure, Ps2, is found from:

)())/1(1(

)( 1

2

002 LPN

NULP sVs −

−=ρ

Equation 5-58

where the final term models the fact that the flashing blast wave forms on the rarefaction following

Ps1. The impulse at L is found from:

N

tLPLI

ps

2

)()(

2=+

Equation 5-59

by assuming that the blast was an ideal triangular wave. Values at distances, x, greater than L, are

found by multiplying Ps2(L) and I+(L) by the factor L/x.

5.3.2.8. Combustion Overpressure

The peak overpressure at radius Rf is given by:

aLf uRp ρ2

max )3/4(2)( =∆ Equation 5-60

At x > Rf


90 14 December 2007

x

RRpxp

ff )()(

max

max

∆=∆

Equation 5-61

5.3.2.9. Thermal Radiation Hazard

The received dose at a point is given by:

peakpeak tIDose 2= Equation 5-62

where the peak incident radiation, Ipeak (KW/m2) at time, tpeak is given by:

))/(1(

242

2

ppeakpeak ttt

t

I

I

+=

Equation 5-63

with I being the incident flux at time t.

Using the shape factor for a hemisphere, and ignoring atmospheric transmissivity:

2

2

2x

SEPRI

f

peak

×=

Equation 5-64

where Rf is radius of the fireball and x the distance from fireball centre to the observer. Similarly:

2

3

'xu

SEPRDose

f ×=

Equation 5-65

and if a safety distance is defined by a critical dose, Dosecrit, then:

2/13

'

×=

crit

f

critDoseu

SEPRx

Equation 5-66

The thermal dose for auto-ignition of clothing is given as 350KJ/m2 which is also, conservatively

assumed to be the fatality limit.

5.3.2.10.Modelling BLEVE Fireball Transients

It is necessary to model the transient as accurately as possible since a safety distance based on

Eisenberg's probit variable, V, defined by:

∫= dtIV3/4

Equation 5-67

where I is the incident heat flux at the receiver, and V is the integral over time, varies dramatically

depending on the shape of the transient. This transient varies with the initial conditions in the

vessel before rupture, so the liquid temperature and vessel fill are inputs to the model.

When the level of pre-heat is low, the liquid droplets within the fireball can be large enough to rain

out to the ground, forming a pool fire. In some conditions, there is insufficient air within the

fireball to burn all the droplets, but they evaporate before they reach the ground. All these effects

are modelled, conservative estimates being given where there is no experimental data.


14 December 2007 91

This description of the BLEVE transient model is based on the paper by Shield65. The model is

built upon a turbulence model which makes an equivalence between the developing turbulence to

that found near the source of a steady state jet, i.e. in the region where the eddies are forming,

rather than in the later self-similar regime, and the necessary turbulent length scales and velocities

are already generated within the code.

The droplets formed in Stage 2 (see Section 5.3.2.1 ), and their combustion dictates the lifetime of

the burning cloud. Once formed, and if the fireball ignites, the droplets evaporate in the fireball,

fuelling its existence during Stage 5. If the temperature in the fireball were constant, then the drop

lifetime would be given by:

( )5.0

2

Re22.01)(

1ln8 D

bfpg

gp L

TTc

c

k

Dt

+

−+

=

ρ

Equation 5-68

where,

ρ is the density of the gaseous phase (or fuel vapour at atmospheric pressure),

ud is the turbulent velocity of an eddy size D.

ε is the energy dissipation rate per unit mass, (m2/s3),

cp specific heat of gas at constant pressure

Tf is the fireball temperature,

ReD is the flow Reynold’s number based on D

L is the length scale such that L3 is the total volume of flashed vapour on depressurisation

In practice, the variation of Tf with time as the fireball burns is not predictable, since the main

process of combustion is by pyrolysis, and the heat released at any stage before combustion has

proceeded to completion cannot be predicted. Therefore a semi-empirical approach is taken to

predict the remainder of the transient. This approach consist of:

a) From ignition to peak diameter, the fireball parameters are taken from the existing model, the

radius and surface emissive power increasing linearly with time.

b) The average temperature of the fireball at break-up, Tend, is found by an energy balance

which assumes complete combustion of as much fuel as can be burned by the air contained

within the fireball. This is satisfactory for "hot" BLEVEs, but, where this calculated

temperature is less than 0.88 of the peak, it is found by inspection of the data in the

experimental BLEVEs studied that the temperature never fell below this value, so that Tend

is set with 0.88Tpeak as the minimum value.

c) The time to fireball break-up is calculated from the drop lifetime, using Equation 5-68 for

drop lifetime, and Tend both for Tf (the effective fireball temperature), and for calculating

the reference temperature (which is used to find the fluid properties such as k and Re). The

agreement between observed and predicted time from ignition to break-up is good (Figure 5-

9) .

d) The fireball temperature (from which the surface emissive power is calculated) is modelled

as decreasing linearly with time from Tpeak to Tend when break-up commences, and

thereafter is fixed at Tend. (Figure 5-10)

65S. R. Shield: The Modelling of BLEVE Fireball Transients, TNGR.95.071.


92 14 December 2007

e) It is assumed that, since drops which ignite immediately burn out as the fireball begins

breaking up, then break-up would be complete (and the fireball cease being an effective

emitter) once drops which are not ignited until the fireball had peaked at the end of Stage 4

had themselves burnt out. During this break-up phase, the radius of the fireball decreases

linearly with time (taking the broken fireball as an equivalent sphere).

f) As the development of the fireball with time is calculated, the height of a single drop is

tracked (Figure 5-11). The drop is assumed to start at the top of the (spherical) expanded

fireball, with a rise velocity equal to one half the fireball expansion velocity (by symmetry).

The rising fireball is tracked, and the parameters controlling the vertical motion of the drop

(including its diameter) calculated from Tf if the drop is in the fireball, and ambient

temperature if outside, at each time step. The fireball is, in fact, a rising vortex, but is

represented as a rising column of air moving at fireball rise velocity (this is a conservative

modelling method, since drops will be thrown outwards and downwards by the vortical

motions in the fireball). For all the experimental BLEVEs, the drops tracked to within a few

meters of the fireball centre at extinction (again taking the broken fireball as an equivalent

sphere).

g) Tracking the evaporating drop, the mass of fuel in the fireball is calculated at each time step,

assuming that all the fuel is contained in drops of this size. If the fireball runs out of fuel,

then it extinguishes after the break-up period. However, if the drops hit the ground, then the

mass of fuel is assumed to form a pool extending over the maximum (spherical) fireball

diameter. In-house LPG pool fire correlations are used to predict the flux from the resulting

pool fire, and its burning time (which is normally short). Since the fireball collapses back

into a pool fire, and in the absence of data, the following conservative method is employed to

generate the flux transient. As the fireball develops, the height of its centre is set as equal to

the height of the tracked drop, unless this becomes less than the height at the end of Stage 4,

when the fireball is assumed to remain sitting on the ground at constant radius. The fireball

flux transient is cut-off when all the air initially mixed into the fireball has been consumed,

and the flux connected linearly to that emanating from the pool fire formed after the drops

have hit the ground.

h) In the case where, after expansion, the fireball contains insufficient air for the drops to burn

completely, but the drops evaporate prior to hitting the ground and forming a pool, then the

fireball break-up model is used to generate the flux transient until drop evaporation is

complete.

i) Having generated the flux transient to the receiver using appropriate view factors, markers

such as dose, mean flux, or Eisenberg's Probit Variable V (Equation 5-67) can be found by

numerical integration.


14 December 2007 93

Predicted time to break-up

Observed time to break-up

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5 6

butane

propane

end-cap

vertical releases

Figure 5-9.Predicted and Observed time to fireball break-up (seconds) for Hasegawa and

Sato (HS) and Moorhouse and Pritchard (Spadeadam experiments) data. The points marked

"vertical releases" are HS small scale experiments. The point marked "end cap" rocketed

some fuel away from the fireball.

Incident Radiation Flux (kW/m2)

Time (s)

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8

Figure 5-10. Typical representation of measured data. Incident heat flux at 175m west of a 2

tonne butane BLEVE from an initial pressure of 7.7 bar gauge (fast response radiometer).


94 14 December 2007

DROPLETS TRACKFIREBALL RISE

DROPLETS BURN OUT TO PREDICT BREAK-UP ANDLIFETIME

TYPICAL HEAT FLUX TRANSIENT

FLUX

TIME

Figure 5-11. Illustration of transient and droplet modelling

5.3.3. Safety Distance (probit variable)

Times to pain, clothing ignition, and mild second degree burns are predicted by calculating V

(ignoring any contribution from the pool fire). Percentage Fatality from Eisenberg's probit method

gives an estimate that does not allow for human reaction - i.e. on feeling pain no avoiding action

(turning around, taking cover, running away) is allowed for. Percentage fatality by Lees is more

realistic, accounting to some extent for turning around, and for the protective effect of clothing.

The calculation of probability of fatality by Eisenberg and Lees differs in the Shell BLEVE model

from the method given in Section 4.2.2.

It is well known that the probit method of Eisenberg is flawed. Also, the convolution of the

variable V (kW4/3

s) into a probit variable Y, which has then to be re-convoluted into a probability

of fatality P, results in a straight line relationship between P and lnV. This relationship is also a

good fit to the original data. Because of this fit to the original data and because the linear

relationship is that implemented by the UK HSE in e.g. RISKAT, a linear fit is used in Shell

FRED:

Death by Eisenberg (%) 95.6)ln(291.63 −= VP Equation 5-69

This gives threshold at V= 1043, 1% at V=1059, 50% at V= 2298, 90% at V=4324

The method of Lees is better but still not right. We follow Lees’ paper, section "Model for fatal

burn injury" (right hand column above Table 6). With his assumptions about population, age, etc.:

Using V: the thermal load at which the death and mortality are zero is V=920

Pm=1 at V=4500

Thus Pm=0.000279(V-920) or, in percentage:


14 December 2007 95

Death by Lees (%) )920(0279.0 −= VP Equation 5-70

Lees correction factor, ϕ, is 0.5 unless clothing ignites, when it is unity. Thus the BLEVE code

has:

Death by Lees (%) )920(0279.0 −= VP ϕ Equation 5-71

where the clothing ignition correlation is also implemented to step change ϕ.

It will be seen from above that the formulations are indeed not much different, the values of V for

threshold and near unity being similar. In our experience of the BLEVE model, the difference is

normally due to choice of the correction factor ϕ.


96 14 December 2007

6. Dispersion Modelling

It is important to be able to predict the distance taken for a vapour cloud to disperse and to dilute

to specific concentration levels in order to quantify the hazard arising from the release of a toxic or

a flammable material. This section describes the tools available within Shell FRED for analysing

problems involving the dispersion of either gases or aerosol mixtures and provides an overview of

the different input parameters needed to use the models.

6.1. Meteorology

Dispersion is the dilution of the vapour cloud by mixing with air. Some of this mixing is associated

with the fluid dynamics of the release itself, the rest is dictated by the properties of the

atmosphere. The role played by atmospheric turbulence is more important for dilution to (non)

toxic concentrations than to (non) flammable concentrations but generally accounts for more than

half of the mixing to a dilution of a few percent of pure gas. Because of the importance of

atmospheric turbulence on dispersion, most models include a parameterisation of the atmospheric

wind. A general knowledge of why various parameters are needed, and what their significance is,

is therefore important because they can have a profound effect on the results obtained.

6.1.1. Stability Classes

Atmospheric turbulence in the lowest part of the atmosphere is predominantly generated by drag at

the earth’s surface. The surface drag is dependent on terrain and for practical purposes is

accounted for using a surface roughness coefficient (q.v.).

Atmospheric turbulence is strongly modified by the thermal structure of the boundary layer

because density differences in a gravitational field give rise to buoyancy forces and because air

density is a function of temperature. These buoyancy forces may enhance turbulence or destroy it.

The general term given to this phenomenon is atmospheric stability. Unstable, or convective

conditions, enhance turbulence and stable conditions destroy turbulence. Neutral stability occurs

when there is no net effect. The thermal structure of the boundary layer is characterised by the

lapse rate (q.v.) which is related to the change in temperature with height. A particular temperature

profile arises because heat is transferred between the earth’s surface and the overlying air.

Fundamental measures of atmospheric stability relate transport properties, responsible for mixing,

to this heat transfer rate however, a majority of models in use today utilise a simple classification

of atmospheric stability.

There are several typing schemes in use but the most widely used is the Pasquill stability

classification. This divides the possible combinations of atmospheric conditions into six classes*

coded: A, B, C, D, E and F. Class A is the most unstable and is associated with low wind speeds

and strong sunlight heating a land surface. Class F is the most stable and is associated with low

wind speeds, night time, and a cold surface caused by radiative cooling to a clear sky. Neutral

conditions are associated with higher wind speeds and the restricted influence of heat transfer

resulting from an overcast sky.

The following table (Table 6-1) contains the criteria for the Pasquill stability classes and taking

time of day, wind speed and cloud cover influences into account.

* Some authorities use an extra class G for ultra-stable conditions


14 December 2007 97

Wind m/s Day time insolation Night time

Strong Moderate Slight >4/8 low

clouds

<3/8

cloudiness

<2 A A-B B - -

2-3 A-B B C E F

3-5 B B-C C D E

5-6 C C-D D D D

>6 C D D D D

Table 6-1 Pasquill Stability Classes

There are other ways of characterising stability, for example, the following table gives typical

lapse rate values. Lapse rate (Table 6-2) is routinely recorded by weather stations using balloon

ascents. It is one input to commercially available meteorological data, which are routinely

packaged into Pasquill Chart form for use with commercial dispersion models. Other methods of

characterising stability will not be described here but include the variability of the wind direction,

and the relative rate of vertical transport of heat and momentum.

Lapse rate °C/100 m

A Very unstable <-1.9

B Unstable -1.9/-1.7

C Slightly unstable -1.7/-1.5

D Neutral -1.5/-0.5

E Stable -0.5/1.5

F Very stable >1.5

Table 6-2 Lapse Rate

The effect of stability class on dispersion is two fold. In unstable conditions gas clouds dilute

quickly, however, because convective motions are large in scale the concentration at any

downwind position can be quite variable in time and while concentrations are low when averaged

high values can occur intermittently. Conversely, under stable conditions, concentrations remain

higher but clouds have a better defined trajectory and dimension.

6.1.2. The Lapse Rate

The lapse rate is a measure of the vertical temperature profile and, as such, is an indicator of the

change in air density with height. This has important implications for atmospheric stability (q.v.).

However, atmospheric pressure also decreases with increasing altitude and the effect of this

pressure change on density must also be taken into account. Assuming that atmospheric pressure is

hydrostatic we can estimate that a rising parcel of air will expand and cool by about -1°C/100 m.

This is called the "dry adiabatic lapse rate". If the rising air contains moisture in the form of water

vapour, then the moisture will eventually condense, releasing heat energy equal to the latent heat

of condensation. Hence, the adiabatic lapse rate for moist air is less than for dry air (-0.6°C/100

m).

The adiabatic lapse rate for air in motion is different from the actual ambient temperature gradient

that exists at a given time at a given location. This is a function of the time of day, season of the

year, solar radiation, wind velocity, heat transfer from the ground and many other factors. It is the

difference between the measured temperature gradient and the adiabatic lapse rate, and the

concomitant effect on density, that has a pronounced effect on the turbulence or stability. The

difference between the actual temperature at height and that following the adiabatic lapse rate

profile is called the potential temperature.


98 14 December 2007

If the lapse rate is smaller than -1°C/100m, a parcel of air which is moved upwards, will by

expansion cool with 1°C/100 m, this means that at a certain altitude the parcel will be colder and

have a greater density compared with the surroundings and so experience a force downwards. This

damps the turbulence in the air. If the lapse rate is greater than adiabatic a parcel of air displaced

upwards will again cool off with 1°C/100m, but will remain warmer and less dense than the

surrounding air. It will therefore experience an upwards directed force. This enhances turbulence.

6.1.3. Surface Roughness

Except under conditions of very light winds and strong insolation, atmospheric turbulence is

produced by drag at the earth’s surface. This drag has a straightforward frictional component but

also an aerodynamic component caused by the complex flow around trees, buildings, etc. The

overall effect is hard to predict but, by analogy with the laboratory flow over a rough plate, is for

practical purposes characterised by a surface roughness coefficient. This coefficient is not

generally predictable - it needs to be derived from measurements but there are guide values for

different terrain. Typical roughness lengths, as used in many models, are given in the following

table. The roughness values are NOT the actual size of the obstacles on the ground. There is no

hard and fast relationship but generally the surface roughness length is approximately 10 - 30 times

smaller than the physical obstruction size.

Roughness,m Description Comments

0.0001 Quiet sea, sand Used for transport on water

0.001 Short grass Used for transport on land

0.03 Fairly level grass plains

Used for transport on land

0.10 Farmland, isolated trees, houses

Also process sites

0.30 Many trees, hedges few buildings

Also process sites

1.0 Industrial area, village Care needed to account for topography for near ground releases

3.0 Centre of cities Don't use for dense gas dispersion

Table 6-3 Roughness lengths

Roughness length values need to be used with care as model predictions can be very sensitive to

the value input. Roughness length properly describes flow at a height of at least twice the size of

the physical elements i.e., at about 60 times its own value. Clearly, for roughness lengths greater

than a few mm the parameterisation becomes problematic for ground based plumes and for dense

gas clouds in particular. However, experiments show that roughness lengths of up to about 0.5 m

can be used for ground based plumes where the layout of the roughness elements promotes mixing.

Such large values are inappropriate for configurations that restrict mixing, for example where flow

is channelled along streets. Here a value representative of the intervening surface would be more

appropriate.

6.1.4. Wind

Because of drag at the ground wind-speed increases with height. Fluid dynamic theory shows that

this variation is logarithmic close to the ground and is increasingly modified by the effect of

atmospheric stability (q.v.) as height increases. At the top of the boundary layer the wind speed

matches the gradient wind which is determined by a balance between the horizontal pressure

gradient and the Coriolis force that arises from the Earth’s rotation.


14 December 2007 99

Because wind speed increases with height it is usually specified by a value at a fixed height

together with a form for the vertical profile. The reference height should always be stated but a

height of 10 m is usually taken as a meteorological standard. The wind profile function can be

explicitly written as a function of the surface roughness, wind speed and surface heat flux. It may

alternatively be approximated by a power law function of the form:

p

ref

refz

zuu

=

Equation 6-1

where:

u = wind velocity at height z

uref = wind velocity at ground station height zref

zref = reference height at which wind speed is measured

(usually 10 metres)

p = exponent dependent on stability class

This equation is very commonly used in wind engineering applications. In neutral stability the

power law index has an approximate value of 1/7 for rural terrain. The dense gas model

HEGADAS uses a power law function of this form as an approximation to the logarithmic law but

alters the power index to account for changing roughness length and stability class.

Wind direction also changes with height as a result of the Earth’s rotation. This change is usually

neglected in performing what-if dispersion calculations but becomes more important when

dispersion is integrated into medium scale (30-300 km) meteorological models.

The dispersion models in Shell FRED accept wind speeds measured in m/s. Wind force data at sea

may be recorded in unit of knots, m/s or miles/hour or by the Beaufort Force number. The Beaufort

scale is the most commonly used for visual estimates of wind speed since it defines the wind force

by its effect on the sea surface. The following table (Table 6-4) presents mean wind speeds in

various units and the descriptions and wave heights that define the Beaufort scale.

Beaufort

number

knots mph m/s description Probable height of waves

in feet

0 < 1 < 1 0.0-0.2 Calm Average Maximum

1 1-3 1-3 0.3-1.5 Light air 0.25 0.25

2 4-6 4-7 1.6-3.3 Light breeze 0.5 1

3 7-10 8-12 3.4-5.4 Gentle breeze 2 3

4 11-16 13-18 5.5-7.9 Moderate breeze 3.5 5

5 17-21 19-24 8.0-10.7 Fresh breeze 6 8.5

6 22-27 25-31 10.8-13.8 Strong breeze 9.5 13

7 28-33 32-38 13.9-17.1 Near gale 13.5 19

8 34-40 39-46 17.2-20.7 Gale 18 25

9 41-47 47-54 20.8-24.4 Strong gale 23 32

10 48-55 55-63 24.5-28.4 Storm 29 41

11 56-63 64-72 28.5-32.6 Violent storm 37 52 12 >64 >73 >32.7 Hurricane 45 -

Table 6-4 The Beaufort Scale


100 14 December 2007

6.1.5. Sampling Times

When looking at the plume emitting from e.g. a stack, one sees an irregular meandering band. If

one were to take a photograph with a shutter speed of 10 minutes, then most of the meandering

effect will be dampened and one would see a broader and more regular plume. Dispersion models

aim to give a prediction of concentration within such a plume at a certain distance from the source.

As described, in practice the concentration is time varying and exhibits significant variation.

Modern instruments are able to resolve this variation and some advanced dispersion models

attempt to predict the statistical distribution of concentrations. Older instruments, such as bag

samplers, measured a fixed volume of air drawn over a given sampling time and so measured an

average concentration for the sample. Most dispersion models in use today aim to predict averaged

concentrations of this type.

Unfortunately, because atmospheric turbulence has a wide length of scales, the averaged

concentration obtained at a point does not have a unique value but is a decreasing function of time.

This is quite unlike averaging of a signal to remove noise where, averaging over any time longer

than the duration of the lowest frequency component, gives one unambiguous residual value.

Concentration averages must therefore be referenced to the sampling time used. Typical values

that may be encountered are 3, 10 and 60 minutes. These are practically useful for evaluating

hazards and, because of the distribution of length scales involved in atmospheric turbulence (the

turbulence spectrum) they represent averaging times over which measurements are, to a degree,

repeatable.

A practical, and empirical correction factor for converting concentrations from one averaging time

to another is:

2.0

600

t 600 =

C

C

t

Equation 6-2

Where t = time in seconds.

The reference time of 600 s is a pragmatic choice. Many field experiments have provided

consistent data for this ten minute data and these experiments have given rise to accepted,

empirical, formulae for plume dimensions that are used in the simplest models. Field experiments

show that peak concentrations in a plume are roughly twice that of the ten minute average.

Substituting this factor 2 into the above equation gives a notional effective “instantaneous”

averaging time of 18.75 s. This is used as input to dispersion models when performing worse case

predictions, e.g. in assessing flammable or toxic hazard.

Shell FRED restricts the values of averaging times that can be used to either the instantaneous or

the 10 minute values. This is sufficient for screening purposes and for comparison with

measurements. Some types of environmental impact calculation require 60 minute averages. Shell

FRED is generally unsuitable for this type of calculation because some necessary modelling

assumptions needed for ambient impact assessments over large distances or for emissions from tall

stacks, are not included in the Shell FRED models.

6.2. Types of Dispersion

There are several parameters which influence the dispersion behaviour of gas in air, and they have

an effect on the choice of dispersion model used in calculating dispersion distances. For practical

purposes releases are divided into two categories: releases result in a jet (high momentum releases)

and discharges at ambient pressure (low momentum releases). These two cases are then further

subdivided according to whether the released material is denser than air or not.


14 December 2007 101

High momentum releases are always associated with events involving breakdown of a high

pressure system with material ejected through a hole. Many materials of practical interest stored

under pressure are inherently denser than air at atmospheric pressure (e.g. Propane). However,

many chemical process conditions are such that a mixture of vapour and liquid is formed at the

discharge point. The liquid burden need only be small to make the jet significantly dense.

Low momentum releases fall into two main categories: discharges from stacks or vents and

evaporation from liquid pools. Stack discharges are almost always buoyant to ensure that ground

level concentrations are minimised. Buoyancy is assured by maintaining the discharge at a

relatively high temperature. For combustion products this serves also to minimise corrosion

problems. For an ideal gas the density can be calculated from :

ρgRT

= M

1000

P

Equation 6-3

where,

ρg = density in kg/m3

P = pressure in Pa

T = temperature in K

M = molecular weight in g/mol

R = the gas constant 8.314 J/(mol K)

Evaporation from liquid pools usually produces vapour that is denser than air. Either because the

material has a high molecular weight or because it is stored as a cryogenic liquid. LNG is an

important example of the latter.

Generally speaking, if the density of the released material is less than that of air (1.23 kg/m3 at 15°

C ) the plume will rise by an amount determined by the initial density difference and the density

stratification in the atmosphere. If the material is denser than air then the plume will fall, and if in

contact with the ground, will spread. Dense plumes that are spreading on the ground mix more

slowly with air than neutrally buoyant clouds released at ground level for the same atmospheric

turbulence. This inhibition of mixing by a positive density difference needs to be accounted for in

the modelling. The fate of buoyant clouds released near to the ground is not precisely known. They

may rise, as if from a ground based stack but they may also break up into local convective cells

and this can enhance the local rate of mixing and quite quickly and reduce density differences to

small values.

High momentum releases themselves generate turbulence and this will usually enhance the mixing

rate. They also have a trajectory that is determined first by the release momentum and which only

later adjusts to follow the wind direction as more and more air is entrained. Differences in jet

trajectory and wind direction can enhance mixing.

As a general rule jet releases of a given mass-flow rate will tend to have a shorter dispersion

distance than the same mass release from a low momentum source where the dispersion distance is

appropriate to a fairly high concentration. This is true for steady state releases, i.e. where the

release rate does not diminish in time. All accidental releases are, of course, transient because

there is always a finite amount of material to spill, however, the steady state assumption is a good

approximation many problems. A general guide is whether the distance, or strictly the time taken

for the cloud to travel the distance to a given concentration, calculated using the steady assumption

is small compared with the time taken for the inventory to discharge.

Jet releases may give a greater dispersion distance for problems where the release duration is very

short. Shell FRED does not directly provide a means of assessing time varying releases so we will

not discuss this further. This capability is provided by the HGSYSTEM package.



6.3. Dispersion Models

Shell FRED provides several models which can be used to assess a wide range of dispersion

hazards. There are some cases that can not be adequately modelled. These include time varying

release rates and buoyant releases from tall stacks.

6.3.1. Gaussian Model

A standard dispersion model, which forms the basis for many commercial models when paired

with sub-models for buoyant plume rise and for building wake influences on dispersion, is the

Gaussian plume model. This model is applicable to releases that are similar in density to air and

which are low momentum sources. The model encoded in Shell FRED is for point releases but the

Gaussian plume model can also be found generalised to describe area, volume and line sources.

The model is called the Gaussian Plume model because it assumes (on the basis of empirical data)

that a Gaussian distribution can adequately describe the concentration profiles in both horizontal

and vertical directions. The Gaussian distribution can also be derived as a solution to the equations

describing the diffusion of a tracer under some (restricted) conditions.

There are a number of limitations for use of the model.

- It is only applicable for open and flat terrain.

- It does not take into account the influence of obstacles.

- It assumes uniform meteorological and terrain conditions over the distance it is applied.

- It should only be used for gases having a density of the same order as that of air (see below).

- It should only to be used with wind speeds greater than 1 m/s

- Predictions near to the source may be inaccurate.

The Gaussian plume model defines the concentration at a point (x, y, z) downwind of a source at

(0,0,h) to be66,67:

2

2

2

2

2

2

2

)+(-

2

)-(-

2

-

+ 2

= ),,( zzy

hzhzy

zy

eeeu

mzyxC

σσσ

σσπ

Equation 6-4

where,

m = source strength, kg/s

u = wind velocity, m/s

h = release height, m. = plume centre line

z = height above ground, m

y = lateral displacement from plume centreline, m.

66TNO Yellow Book: methods for the calculation of the physical effects of the escape of dangerous material: liquids and gases. 2 Vols. Dutch Directorate of Labour, Ministry of Social Affairs.

67 Atmospheric Dispersion, European Process Safety Centre, Institute of Chemical Engineers, 1999, ISBN 0 85295 404 2.



Note that there is no buoyancy in the model. In practice initial mixing with the atmosphere is rapid

and the released gas then gets transported with the atmosphere, its associated turbulent behaviour

dominating the dispersion. This is known as passive dispersion and is a common phenomena.

Molecular diffusion, which might tend to separate the lighter gases from the heavier gases, is

happening on a much lower level and its contribution is insignificant. It is acceptable to model

releases at near atmospheric temperature containing pollutants which have molecular weight of the

same order as the atmosphere (e.g. methane with a molecular weight half that of oxygen is

acceptable).

The above equation contains a ground reflection term (the second exponential in the brackets). The

effect of the ground reflection is only seen in plumes released near ground level. The effect is such

that the maximum plume concentration at a distance downwind, depending on the contour value

being looked at, may well be at a lower height than the release height e.g. at ground level.

Reflection by the ground means that negative values of z, which are below ground level, are not

allowed.

The lateral and horizontal dispersion parameters σy and σz are functions of distance, of stability

class and roughness length, and of averaging time. They are empirical parameters derived from

results of field trials in which controlled amounts of tracer are released and downwind

concentrations measured. Such experiments are necessarily incomplete given the practical

difficulties in obtaining data for a full range of meteorological conditions - even for a single site -

and of measuring the vertical concentration in particular. Consequently there are many different

correlations for the dispersion parameters. Some models also take advantage of theoretical results

to shape the correlations but, overall, results using different formulae tend to give very similar

results.

The Gaussian Plume model in Shell FRED uses simple power law approximations for these

functions. These are accurate for distances up to 1000 m from the source. Concentrations may be

underestimated at larger distances.

σy = Ct * a * xb σz = Cz * c * x

d Equation 6-5

Shell FRED also applies a correction for averaging time which multiplies the lateral dispersion

parameter and a roughness correction that multiplies the vertical dispersion parameter. These

factors are applied in this way because the large scale turbulence responsible for the averaging

time dependence of concentration arises from horizontal motions whereas the turbulence

responsible for vertical mixing arises mostly from friction at the ground surface and these two

effects are largely independent of each other.

2.0

600

t 600 =

C

C

t * 10 = 22.0-53.0

0 xzCz Equation 6-6

Where,

t = time in seconds

x = downwind distance in metres

z0 = roughness in metres

The indices in the power law, factors a, b ,c and d are given in the following table:



a b c d

Very unstable A 0.527 0.865 0.28 0.90

Unstable B 0.371 0.866 0.23 0.85

Lightly unstable C 0.209 0.897 0.22 0.80

Neutral D 0.128 0.905 0.20 0.76

Stable E 0.098 0.902 0.15 0.73

Very stable F 0.065 0.902 0.12 0.67

Table 6-5 Power law factors

6.3.2. HEGADAS

HEGADAS is a dense gas model specifically developed to account for the restricted mixing of

dense gas clouds. We recall that most liquid releases will form pools which evaporate to form

dense gas clouds because the material has a higher molecular weight than air or because the

material is so cold that it is denser than the surrounding atmosphere. Releases with a liquid

fraction that is suspended as an aerosol also behave as dense gas clouds.

Dense gas clouds tend to have a broad, flat shape. The cloud spreads sideways due to gravitational

effects and this growth is generally larger than that due to turbulent mixing. Gravitational effects

also inhibit vertical mixing so that vertical growth is less than for the corresponding neutrally

buoyant cloud. HEGADAS takes account of heat and water vapour transfer from the substrate to

the cloud. These are important for cryogen dispersion where heat transfer, either directly or as

sensible heat, can make a big difference to dispersion.

HEGADAS is part of the HGSYSTEM suite of programs. A detailed description of the model and

its wider capabilities are given by Post68,69 .

6.3.3. AEROPLUME

AEROPLUME is a jet dispersion model that can describe either gaseous jets or two phase releases.

The model can describe releases for a range of different release directions and can predict jets that

contact the ground. This latter capability is primarily for dense jets that are initially horizontal or

even upwards directed and then sink to the ground. Jets that are aimed at the ground at short range

may give rise to some numerical difficulties. AEROPLUME can predict the dispersion of buoyant

as well as dense gases.

AEROPLUME itself describes the jet as having a single averaged concentration across the jet

cross-section which changes shape according to whether the jet is airborne or touching the ground.

For use in Shell FRED a Gaussian profile is superposed upon the AEROPLUME calculation and

this is used to draw concentration contours on the screen. The contouring program assumes that the

peak concentration in the Gaussian profile is higher than the averaged concentration output by

AEROPLUME. Thus there is generally a small difference between the distance to a contour

concentration drawn on the screen and the tabulated AEROPLUME results saved in the Shell

FRED work directory.

AEROPLUME is intended to predict the near source behaviour. Far from the source the dispersion

is better modelled by a far-field model. AEROPLUME therefore invokes either HEGADAS or

another model PGPLUME to finish its calculations. PGPLUME is a standard Gaussian dispersion

model as described above but using correlations for the dispersion parameters more suited to

longer distances (the name is derived from the Pasquill-Gifford gas dispersion model). It can only

be run automatically by Shell FRED to complete a dispersion calculation and in general the user

will not be aware that it has run. If HEGADAS is run because the plume is dense and on the

68 L. Post, HGSYSTEM 3.0 User's Manual, www.hgsystem.com

69 L. Post, HGSYSTEM 3.0 Technical Reference Manual, www.hgsystem.com



ground then, because the two model assumptions are very different, it is not possible to combine

the HEGADAS and AEROPLUME contours in a meaningful way. Therefore, in this case, only the

HEGADAS contours are drawn.

AEROPLUME is one of the HGSYSTEM models and a full description is given by Post37,38

.

6.4. Flammability

Flammable limits (LFL and UFL, also sometimes called Explosive limits, LEL, UEL), flash points

and auto-ignition temperatures are given in Table 6-6 for a selection of common flammable

compounds.

LFL

% vol.

UFL

% vol.

Heat of

Comb kJ/kg

Flash

point °C

Auto ignition

temp °C

Hydrogen 4.1 74 119882 572

Methane 5 15 49971 537

Ethylene 2.8 34 47130 450

Ethane 3.2 12.5 47447 472

Acetylene 1.5 82 47869 304

Propylene 2 11.7 45725 443

Propane 2.1 9.5 46314 415

Isobutane 1.9 8.5 45583 507

n-Butane 1.6 8.5 45670 -60 282

Isopentane 1.4 7.8 45231 420

n-Pentane 1.3 7.6 45324 -40 287

n-Hexane 1.2 6.9 45140 -26 234

Benzene 1.2 8 40592 -11.1 538

Cyclohexane 1.3 8.3 * -17 260

n-Heptane 1 6.7 * -4 223

Methylcyclohexane 1.2 * -4 285

Toluene 1.3 7 40914 4.4 536

n-Octane 0.8 6.5 * 13 220

Ethylbenzene * 15 432

para-Xylene 1.1 7 41244 529

meta-Xylene 1 7 * 18.8 528

ortho-Xylene 1 7.6 * 17 463

n-Nonane 0.8 5.6 * 31 206

n-Decane 0.7 5.4 * 46 208

Motor gasoline 1.4 7.6 * -46 280

Aviation gasoline 1.1 7.2 * -34 454

Kerosine 0.7 6 * 49 229

JP-1 0.7 6 * 43 228

JP-4 1 7 * <-18 242

JP-5 0.7 6 * 43

Crude oil 1 6 * <-18 230-250

CO 12.5 74 10095 610

H2S 4.3 46 15198 260

NH3 15.5 27 18580 656

• Estimated between 40000 and 45000 kJ/kg.

Table 6-6 Flammability limits



Note that auto-ignition temperatures can be much higher (and occasionally lower) in practical

situations. They are also geometry and scale dependent. They are a function of contact time with

the hot surface, this is determined by the geometry and scale of the equipment and the resulting gas

convection through the equipment.

6.5. Toxicity

As in the case of fire radiation, the probit concept is now generally used for estimating the

expected percentage of a population killed by toxic poisoning when exposed to a toxic gas cloud.

The probit function for exposure to toxic gases is of the form:

)ln(Pr tCba n+= Equation 6-7

where k1, k2, n are constants and C is the concentration in mg/m3.

Probit values can be converted to % fatalities as follows:

1. Find the probit constants k1, k2, n from Table 6-7,

2. Calculate the probit, )ln(Pr tCba n+= , where C is the gas, concentration in mg/m3 and

t the exposure time in minutes.

3. Use Table 4-5 to determine the % fatality.

Note that the units of concentration in the above Table 6-7 is mg/m3, and a unit conversion is

required for use in conjunction with the dispersion programs which report gas concentrations in

ppm.

At STP : 1 mg/m3 is equivalent to 22.4/Mol.Wt. ppm

6.5.1. Toxicity Data

Probit constants for humans calculated on basis of extrapolated 30 min. LC50-values70 are

summarised in Table 6-7.

70Committee for the Prevention of Disasters, Methods for the Determination of Possible Damage to People and Objects Resulting from Releases of Hazardous Materials, Rep CPR 16 E (The Green Book), Voorburg, The Netherlands, 1992



Substance 30 min.

LC50

mg/m3

n k2 k1

Acroleine 304 1.0 1 -4.1

Acrylnitril 2533 1.3 1 -8.6

Allylalcohol 779 1.0 (1) 1 -5.1

2.0 (2) 1 -11.7

Ammonia 6164 2.0 1 -15.8

Bromine 1075 2.0 1 -12.4

Chlorine 1017 2.3 1 -14.3

Ethylene oxide 4443 1.0 1 -6.8

Phosphamidon 568 0.7 1 -2.8

Phosphine 67 1.0 (1) 1 -2.6

2.0 (2) 1 -6.8

Phosgene 14 0.9 1 -0.8

Carbon monoxide 7949 l.0 1 -7.4

Methylbromide 3135 1.1 1 -7.3

Methylisocyanate 57 0.7 1 -1.2

Nitrogen dioxide 235 3.7 1 -18.6

Tetra-ethyl lead 300 1.0 (1) 1 -4.1

2.0 (2) 1 -9.8

Hydrogen

chloride

3940 l.0 1 -6.7

Hydrogen cyanide 114 2.4 1 -9.8

Hydrogen fluoride 802 1.5 1 -8.4

Hydrogen

sulphide

987 1.9 1 -11.5

Sulphur dioxide 5784 2.4 1 -19.2

(1) No "n" values available, calculated on basis of n = 1

(2) No "n" values available, calculated on basis of n = 2

Table 6-7 Probit constants for toxicity analysis

6.5.2. Protection by being In-House

In general being indoors is quite an effective way to mitigate the effects of a toxic release. As the

toxic cloud passes, the concentration indoors will only slowly rise, caused by the air changes in the

house. A typical frequency for such an air change might lie between 1 and 3 times per hour.



A simple method to assess the effect of being indoors is described by Davies71. Assuming a top hat

concentration distribution of the toxic cloud passing the house, the concentration indoors as a

function of time can be calculated from:

Ci(t)= Co ∗ [1 -exp (-λ∗ t)] Equation 6-8

Where,

Ci(t) = Concentration indoors at time t

Co = Concentration outdoors

λ = number of air changes per hour

t = time in hours since the toxics reached the building

71P.C. Davies and G. Purdy, Toxic risk assessment, the effect of being indoors. IChE North Western Branch Papers 1986, 1, 1.1



7. Explosion Modelling

Advances in understanding and assessment of explosion hazards has been rapid in recent years.

Where previously explosions were regarded as an inevitable consequence of ignition of a cloud of

flammable material, which sometimes did and other times did not occur, we now have much

clearer insights into what factors contribute to the explosive behaviour that may accompany the

combustion of a vapour cloud.

Of course, the ignition of a cloud of flammable material in which the concentration of the material

lies between certain limits is still a primary condition for the occurrence of an explosion. But it is

now realised that to get an explosion more conditions must be fulfilled particularly for

hydrocarbons that make up most of the inventory of petrochemical installations. Of great

importance are the geometrical features of the environment in which the cloud is located. The

degree of confinement or the presence of obstacles through which the flame must pass have been

found to be necessary conditions for an explosion.

An example of the outdated concept is the lingering use of the terms "Lower Explosive Limit"

(LEL) and "Upper Explosive Limit" (UEL) for concentrations of a particular fuel within which an

explosion would be possible. The terminology of "Flammable Limits", expressed as LFL and UFL,

is more appropriate since these are indeed properties of material and denote the limits of

concentration within which a fuel-air mixture is flammable. We recommend the use of

flammability terminology since it leaves room for the distinction between combustion and

explosion, the latter not being just a property of material but also a characteristic of the

environment.

The current insights into explosions are derived from a series small and large-scale (field) tests,

carried out by various laboratories, and work is still continuing.

7.1. The Explosion Process

When a cloud of flammables in the open, e.g. a meadow or the beach, is ignited by a spark or an

open flame, a reaction front starts travelling through the cloud. The reaction products will be

heated up by the combustion process. For a stoichiometric, flammable/air mixture the volume

increase for most hydrocarbons is about a factor 8. This build up of pressure will equalise with its

surroundings pushing out gas in all directions. This pressure wave will make the slow moving

flame front unstable and the front will distort and thereby enlarge its surface. This will result in a

acceleration of the flame. For the open spaces mentioned above flame speeds will stabilise at

around 10-15 m/s.

The relation between flame speed and pressure (Figure 7-1) indicates that ignition of clouds of

flammables in open spaces which will result in low flame speeds will also result in low

overpressures, this has been demonstrated in numerous experiments.



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200 250

Flame speed m/s

Over

pressure

bar

Figure 7-1 Variation of overpressure with flame speed

Effects of congestion

However, when the flammable cloud is not in the open, but in a congested region, the expansion of

the reaction products will create turbulence. The turbulence is created principally in the wake of

obstructions. This can lead to continued flame acceleration and, as a consequence, higher

overpressures. Generally, the laminar burning velocity of a hydrocarbon flame is of the order of

0.5m/s. However, the flame speed in a turbulent flow is much greater than the laminar flame speed

principally because turbulent mixing caused by, for examples obstacles, further enhances

combustion by entraining surrounding air thereby creating a much greater area for reaction. This

increased rate of burning in turn generates high level of turbulence which is enhanced further by

the next group of obstacles. The more intense turbulence results in even faster burning, and so on.

This process is known as the Schelkin mechanism as illustrated in Figure 7-2.

Flame

Flow

Volume Prediction Turbulence

Blast

Figure 7-2 The Schelkin Mechanism

Understanding of the mechanism described above allows us to characterise the types of congested

but unconfined plant likely to cause high overpressures even without confinement.. These are

typically chemical or refinery plant with large amounts of pipework or other obstructions.

Locations where obstacles block more than 40% of the path a flame may have to travel through, or

where there are closely repeated rows of obstacles, are particularly bad. On the other hand, lightly

congested plant no longer needs to be treated as if were as hazardous as the most congested

regions. Furthermore, since the explosion is generated only by the congested region, the volume of

the explosion source is related not to the whole flammable cloud, but only to the volume of the

congested region. This means that the overpressures experienced at a distance are lower than they

would be if derived from a larger dispersing cloud.



Effects of confinement

If the flammable cloud is in a confined region, for example in a building, the volume produced by

the combustion cannot flow away from the flame and so a high pressure is generated. Such burning

in a completely enclosed volume will produce an overpressure of about 8 bars because of this

volume generation. Even if there are vents in the walls (partial confinement), high pressures may

still be generated because the gas cannot flow fast enough through the vents to relieve the pressure.

Explosions in areas which are more than 60% enclosed by a combination of walls or other

obstructions may be treated as confined, vented explosions.

With such partial confinement, the potential explosion overpressure is increased if the area

available for venting is small, if the obstructions to the flow provide large blockage, or if the path

from a possible ignition location to the main venting involves passing many obstacles.

Another feature of such incidents is the "external explosion" Harrison and Eyre72. As the flame

burns through a vented enclosure, most of the gas is pushed out of the vent ahead of the flame.

This is a consequence of the 8:1 volume expansion. Outside of the vent it forms a mushroom-

shaped, highly turbulent "starting jet". When the flame emerges through the vent, it burns rapidly

through this gas, creating an external explosion. The external explosion may cause damage at some

distance from its source. The external explosion also has influence on the pressure inside the

enclosure, so that the maximum internal pressure is usually reached after the external explosion.

Detonation

It should be noted that the flames discussed above consist of the normal type of burning known as

a deflagration. Almost all gas cloud explosions are deflagrations. In a deflagration, the burning

velocity is limited by the diffusion of heat and species through the flame front. In a detonation, by

contrast, the gas mixture ahead of the flame is heated by a shock wave coupled to the flame. A

detonation is supersonic and self-sustaining, and, once initiated, will continue to propagate at the

same speed even through an unconfined, uncongested cloud. A deflagration flame slows down

soon after leaving a congested region, as the turbulence decays. The pressure generated by

detonation in a hydrocarbon/air mixture is about 18 bar, with velocity around 2000 m/s.

In less severe cases, there may still be explosion effects which go beyond deflagration. The strong

flow ahead of the flame in a severe explosion may be sufficient to trigger auto-ignition near

obstacles ahead of the flame. This results in pressure spikes which may be two to three times

stronger than the main deflagration pressure peak; however, the spikes are usually of very short

duration and limited source size, and therefore may not have much effect at a distance.

Gases vary in their susceptibility to detonation; for methane, in virtually all practical situations,

detonation would not occur. Propane can generate the auto-ignition spikes in the presence of

severe congestion. For ethene, detonation may be a possibility, but this would only occur in a very

highly congested region.

7.2. Vapour Cloud Explosion Characteristics

A number of parameters influence the outcome of an vapour cloud explosion:

Cloud volume

Cloud shape

Reactivity of the gas

Degree of congestion

and it is of interest to model/predict the following;

72 A. J. Harrison and J. A. Eyre (1987) External explosions as a result of explosion venting. Comb.Sci.Tech.52,92-106.



Blast wave behaviour

Peak overpressure

Damage effects

Cloud Volume

The flammable cloud volume is defined as the volume of the cloud between the upper and lower

flammable limit. It can be calculated using an appropriate dispersion model from the mass or mass

per unit time released and the ambient conditions. Often simple estimates based on the mass

released and fraction flashed (including aerosol formation) are used because available dispersion

models cannot predict the dispersion in and near structures like, e.g., process plants.

Cloud shape

Dense gas unconfined vapour clouds are often pancake shaped, with an aspect ratio of about 5. All

of the simple models discussed in this paper (TNT, TNO and Congestion Assessment Method)

assume a hemispherical stoichiometric cloud with ignition occurring at the centre.

Reactivity of the gas

Gases like hydrogen, acetylene are more reactive than ethylene, or propylene, which are more

reactive than propane or methane. This difference in reactivity manifests itself in e.g. the flame

speeds for the gases in unconfined, uncongested environments. Furthermore the more reactive

gases tend to produce higher overpressures when ignited in a congested structure compared to the

gases with lower reactivities.

Degree of congestion

If the cloud forms amongst obstacles such as structures and equipment, flame acceleration will

occur leading to an increase in overpressure. A measure of the degree of congestion is used in the

various models as a parameter to predict the overpressure on targets outside the cloud.

Blast wave behaviour and peak overpressure

The potential energy produced by the explosion is redistributed in a blast wave, the profile of

which changes with time. On a pressure/time scale the wave consists of a positive pressure pulse

followed by a negative pressure pulse. Close to the explosion source the pulse has a smooth rise

and fall. Further away from the explosion the pulse becomes sharp fronted, the peak overpressure

will be less but the duration does not change much. When a blast wave strikes an object, some

reflection from the face of the object will occur. The rest of the wave will diffract around the

object. Rarefaction waves will cross the front face, applying a suction which may cause as much

damage as the initial positive overpressure. While the peak positive overpressure alone is

frequently used in making simple damage predictions it is the impulse of the blast wave as defined

by the overall shape in the pressure/time domain which is important, i.e. the peak overpressure,

rise time and duration of both the positive and negative pulses and this should ideally be used in

time- dependent modelling of the response of a structure. The complexity of such response

modelling may vary from simple spring/dashpot systems representing the overall behaviour of a

structure to full time-dependent elasto-plastic finite element calculations.

7.3. Hazard Assessment of Explosions

Shell FRED has the capability for predicting overpressures from congested vapour cloud

explosions for both unconfined and confined cases. Of these models, the Congestion Assessment

Method (CAM) is recommended for unconfined situations, and the Shell Code for Overpressure

Prediction in Gas Explosions (SCOPE) is recommended for confined situations. However

calculations using the TNT and TNO models are discussed below as they may still be required by

regulatory authorities. Other models have been developed by Shell Global Solutions, but are not

available in FRED: these are also discussed here in order of increasing complexity.



7.3.1. Congestion Assessment Method (CAM)

The TNO multi-energy method, although sound in its approach in taking into account the factors

influencing the resulting overpressure from an explosion, has some drawbacks in the ambiguity of

making a choice of the curve and efficiency to apply. Building on research and previous models a

method has been devised73,74 which removes a large amount of user guesswork and is an

improvement on previous methods for predicting overpressures from congested vapour cloud

explosions.

The following sections describe the CAM method in details as implemented in Shell FRED.

7.3.1.1. Unconfined Explosions (Regular and Symmetrical Congestion)

The correlation for the peak overpressure generated in a symmetrical unconfined congested region is

given by:

( )( ) ( ) 31

2

55.071.2

00 exp1a

d

apbandEUaP −= Equation 7-1

where,

a0, a1, a2, a3 are constants (determined from experimental measurements)

U0 is the laminar burning velocity,

E is the expansion ratio (ρu / ρb) ,

ρu is unburned gas density,

ρb burned gas density,

n is the number of rows of obstacles in each direction, counting from the centre,

rpd pitch to diameter ratio

= (distance between the rows of obstacles/obstacle diameter)

b is the blockage of rows of obstacles

The above correlation is derived from a series of experimental tests in a gas-filled region of

congestion comprising regular rows of cylinders with central ignition source. The region is of length

and width of 2L, and height L. Since the ground can be regarded as a reflective surface, this is

equivalent to central ignition in a cubical region (side 2L) in free space. To reach the open space the

flame passes a number of similar grids in each direction. From the correlation it is clear that the

overpressure is dependent of the following parameters:

a) the fuel. Much higher overpressures are produced by a reactive fuel such as ethene

(ethylene) than by methane, for example.

b) the number of rows of obstacles in each direction, n (counting from the centre).

c) the blockage of the rows of obstacles, as an area blockage ratio b.

d) the obstacle diameter d. Since the remaining parameters are expressed as ratios, this

determines the effect of overall scale on the overpressure, which is known to be

important.

e) the spacing between the rows of obstacles, expressed as a pitch-to-diameter ratio rpd.

73A.T. Cates, A non-specialist guide to semi-confined vapour cloud explosions, Int.Conf. Fire and Explosion hazards: Energy Utilisation, Gloucestershire, 1 May 1991.

74J.S. Puttock, Fuel Gas Explosion Guidelines - The Congestion Assessment Method, Major Hazards Onshore and Offshore II, IChEME Symposium series 139, 267-275



7.3.1.1.1.Severity Index

Comparisons with experimental data show that at high overpressures Equation 7-1 generates

unrealistic predictions. With congestion much more severe than that in the experiments, for example

higher blockage, more rows and larger scale, the expression might predict an overpressure of many

bars. This is usually not realistic if we are trying to predict the typical pressure in the congested

region.

As an example, suppose that we change from one hydrocarbon fuel to another, which is more

reactive, and that the second fuel generally gives overpressures double those obtained with the

first. Then for an overpressure of 40 mbar with the first fuel, it would be correct to allow that the

overpressure would be 80 mbar with the second. But if the overpressure with the first were 4 bar,

the change to the second fuel could not produce a (mean) overpressure of 8 bar. A hydrocarbon

fuel reaches an overpressure of about 8 bar when burned at constant volume, i.e. with no flow at

all. Thus, in an explosion, if the gas were being compressed to nearly 8 bar as it burned, there

would be no flow, and therefore no turbulence to create the high overpressure! In this range there

is a negative feedback effect, which reduces the flow and limits the increase of pressure. 4 bar

would probably be increased to between 5 and 6 bar by a change which would double the result at

low pressures.

The converse of this is that (proportionate) reductions in overpressure are also smaller in the high-

pressure range. Examples are the effects of change in stoichiometry or ignition location.

In order to allow easy application of correction factors or error bounds to explosion model

predictions for vented explosions, a "severity index", S is often used. S is directly related to the

overpressure P. It is defined to be equal to overpressure, in bars, at low overpressure, but to

increase by the same ratio for a similar perturbation (say, a change of fuel), whether at low or high

overpressure. Consequently S eventually increases very much faster than P (Figure 7-3). Such an

approach, with a suitable expression for S, can be used here for explosions in open, congested areas.

Figure 7-3 The severity index is equal to the pressure in bars at low overpressure, but

increases rapidly as an overpressure of just over 8 bars is approached.

For ease of use, an analytical expression has also been fitted to the empirical curve of Figure 7-3.

This is:



−−=

PE

PPS

14.0exp

08.1 Equation 7-2

where P is the overpressure in bars, and E is the expansion ratio at atmospheric pressure.* It is not

possible to invert this equation analytically, but the inversion can easily be done, for example, by a

lookup process.

The significance of the severity index in the current context is that, if the expression in Equation 7-1

is indeed a useful approximation for P at fairly low overpressures, then it would equally be a good

expression for S; this is true because S is equal to P at low overpressure. As pressure increases, the

correlation takes no account of the negative feed-back discussed above, but if the correlation is used

for S, then the median overpressure P is automatically limited in a realistic way.

From the experimental measurements the value of a3 was estimated to be 0.55. The experimental fit

for S was derived to be:

( )( ) ( )banlEUaSa

2

55.071.2

00 exp1 1′−= Equation 7-3

where 55.011 −=′ aa , and dnrl pd≡ is the length of the congested region through which the

flame has to pass. This change provides the considerable benefit that it is no longer necessary to

specify the diameter of obstacles. Although defining a typical obstacle diameter can be easy in

idealised experiments, it is often difficult in real plant.

By fitting the results of Equation 7-3 to experimental data the values of various constants are found

to be:

5

0 109.3 −×=a , 99.11 =′a , 44.62 =a .

The value of the dimensional constant a0 is based on burning velocity in m/s, length in metres and

pressure in bars.

7.3.1.2. Plant with a Roof

The correlation for S derived from data from experiments with rows of cylinders and a roof is as

follows:

( )( ) ( )bnlEUS 24.7exp1108.4 21.255.071.2

0

5 −×= − Equation 7-4

It should be noted that this correlation would only be expected to apply when the flame travel is

essentially in two dimensions, normally horizontal. Thus if the height is greater than half of either

of the other dimensions, there would be significant vertical flame travel for ignition on the ground

at the centre, and so the correlation from the previous section should be used if it gives a higher

pressure.

* For hydrocarbons, E1.08

is a good approximation to the absolute pressure resulting from combustion at fixed

volume; it is not equal to Eγ, as might be expected, because the expansion ratio decreases as the pressure increases.



7.3.1.3. Obstacle Complexity Factor for Real Plants

The obstacles in a real plant environment are typically much more complex than the simple arrays

of cylinders used in most idealised experiments. In particular, there is a great range of length

scales present. The effect of this is to increase the "macroscopic" flame area generation above that

pertaining to rows of uniform cylinders. Based on the detailed analysis of experimental data four

“complexity levels” are defined in semi-quantitative terms as follows:

Level 1 Idealised arrangements of obstacles of the same diameter, or very few obstacles

of significantly different dimension than the dominate obstacle diameter. (Note

that, e.g., interconnecting pipes, and fittings on vessels may all count as

obstacles).

Level 2 Rather more complex than level 1, for example with two obstacle sizes an order

of magnitude apart.

Level 3 Much more like real plant but with much of the detail missing.

Level 4 The full complexity of typical congested refinery or offshore plant.

For each complexity level, the results are modified by multiplying the S values by a factor taken

from Table 7-1.

Complexity Level Complexity Factor

1 1.0

2 1.7

3 2.8

4 4.0

Table 7-1 Values of the factor for obstacle complexity

7.3.1.3.1.Sharp-edged Obstacles

All the experiments used in developing the correlations involved cylindrical obstacles. The drag

of obstacles which are sharp edged, for example of square cross-section, is higher; the drag

coefficient is typically 2.0, compared with 1.2 for cylinders. The importance of the area blockage

of obstacle grids is in its influence on the drag; therefore allowance must be made for the greater

effect of sharp obstacles. This can be done approximately with an increase in the blockage

ascribed to the sharp obstacles, by dividing by 0.6.

7.3.1.4. Non-symmetrical Congestion (Central Ignition Source)

Real plants are not symmetrical. Therefore a way is needed for estimating the overpressures when

the congestion is different in the different direction.

Suppose, counting from the centre the nominal blockage ratio in the three directions (length, width

and height) are bx%, by% and bz% respectively. S values can then be calculated with the same

blockage ratio in each direction as shown in Table 7-2.

% blockage S value

x-direction y-direction z-direction

bx bx bx Sx

by by by Sy

bz bz bz Sz

Table 7-2 S values for symmetrical blockages



Then the average S value for blockage bx%, by%, bz% is given by:

3

)(%),%%,(

zyx

zyx

SSSbbbS

++=

Equation 7-5

In the case of plant with a roof, there would be two values to average, as upward flow would not

normally be considered.

7.3.1.5. Plant with One wall

If there is a wall along one side of the plant, an assessment can still be performed, as the wall can be

considered as a reflecting surface. Thus source calculations can be performed for a plant twice the

size of the actual plant, taking a reflection in the wall. Near-field pressure decay would also need to

use the doubled plant volume. For distances much greater than the dimensions of the wall, the

actual plant volume could be used.

7.3.1.6. Long, Narrow Areas of Plant

If a plant is very long, but small in the other two dimensions, it is possible that the lateral venting

of combustion products will be sufficient to limit the acceleration of the flame along the length of

the plant. Then a steady flame speed may be reached, with the volume production due to

combustion balanced by lateral venting, or at least the acceleration along the length will be

reduced. In the case of a steady flame speed, beyond a certain length, adding more length does not

increase the overpressure further. The “certain length” will be dependent on the other two

dimensions, and the relative blockage in the various directions.

Along the length L of the plant there are nL rows of obstacles, of typical area blockage bL , along

the width W, nW rows of area blockage bW. The height of the congested region is H. If there is no

“roof” on the plant, we also count nH horizontal grids of area blockage bH. Also if H is greater

than L/2 or W/2, ignore any roof and calculate nH and bH. Calculations of area blockage are based

on rounded obstacles, and should include an enhancement for sharp-edged obstacles, as discussed

above.

Calculations are carried out in two stages: calculation of source pressure and the pressure at a

distance.

7.3.1.6.1.Calculation of Source Overpressure

For the open geometry:

Set l1, l2 and l3 to be the largest, middle and smallest of L/2, W/2 and H.

Set n1, n2 and n3 to be nL/2, nW/2 and nH reordered in the same way.

Set b1, b2 and b3 to be bL, bW and bH reordered in the same way.

With a roof:

Set l1 and l2 to be the largest and smallest of L/2 and W/2. Set l3 = H.

Set n1and n2 to be nL/2 and nW/2 reordered in the same way.

Set b1 and b2 to be bL and bW reordered in the same way.

If the region is partially filled, set the expanded (quarter) gas volume to be:

γ)1(

)4/(

P

EVV

g

e +

×= 2.1=γ

Equation 7-6

Note that the overpressure P is not known at this stage, so set it equal to 0 initially; it can

eventually be determined by iteration.



Set ii ll =′ , ( 3,2,1=i ) if no partial fill or 321 lllVe ≥ otherwise determine 321 ,, lll ′′′ , such that

ii ll ≤′ and eVlll =′′′321 .

Long, narrow correction:

Define

=

11

331

11

22120 2,2,2max

bn

bnl

bn

bnlll

( )

33

22

1011 ,min

ll

ll

llll

′=′′

′=′′

′′=′′

Adjust the number of grids for the change in effective dimensions:

i

i

ii n

l

ln

′′=′′ , 2,1=i (and 3 if open)

Note that, in general, in ′′ will not be an integer.

)44.6exp(1089.0 54.255.03

iiii bnlcFS ×′′×′′××××= −, ( 3,2,1=i ) Equation 7-7

3/)( 321 SSSS ++= Equation 7-8

With a roof:

)24.7exp(1010.1 21.255.03

iiii bnlcFS ×′′×′′××××= −, ( 2,1=i ) Equation 7-9

2/)( 21 SSS += Equation 7-10

where the distances are expressed in metres.

S is related to P (in bars) via the relation:

−−=

PE

PPS

14.0exp

08.1

Equation 7-11

which can be solved iteratively for P. Alternatively, it is conservative to take the pressure to be

equal to S.

For a partial fill Equation 7-6 is solved iteratively.

The resulting pressure is the source overpressure P0 which can be used to calculate the pressure at

some distance from the source (see later).

The source volume is given by:

( )eVHWLV 4),2)(4)(4(min0 +++= Equation 7-12

Some Practical Considerations



The distance l was defined as the number of grids times the grid spacing, i.e. the length of

congestion through which the flame has to pass from central ignition to open space. In some plant

there is an extensive open area in the centre ( e.g. sufficient space to drive vehicles through); in

such cases it is legitimate to take, for example, l2 to be less than W/2.

For the correlation of experiments where the obstacles started a few diameters from the ignition,

the value of n was reduced. We do not recommend trying to reproduce this in practical application

of the method for two reasons; a) it is difficult to know exactly where the ignition might take

place; b) the obstacles are generally not entirely large smooth cylinders - the diameter of the

smaller obstacles is relevant since these can distort the flame much sooner.

7.3.1.7. "Bang-box" ignition

The pressure estimates derived here would not apply in the case of high-energy ignition, which

could increase the overpressure considerably. One such source of high-energy ignition which could

be easily overlooked is a "bang-box". We use this term to refer to the ignition of gas inside a small,

nearly-enclosed area. If such a nearly-enclosed volume vents into or near a congested region, the

overpressures resulting could be very high, and detonation cannot be ruled out.

Fuel Fuel factor

F

Expansion ratio

E

Methane 0.6 7.8

Toluene 0.7 8.4

Pentane 1.0 8.4

Cyclohexane 1.0 8.4

Butane 1.0 8.3

Propane 1.0 8.2

Methanol 1.0 8.2

Acetone 1.0 8.8

Benzene 1.0 8.3

Ethanol 1.5 8.3

Propylene (Propene) 2 8.4

Butadiene 2 8.5

Ethylene (Ethene) 3 8.3

Table 7-3 Fuel properties. The expansion ratio is dependent on initial temperature; these

values have been calculated for 288K.



7.3.1.7.1.Calculation of Pressure at a Distance (Receptor)

Let the source pressure be P0 bar (Equation 7-11), and the effective source volume V0 (Equation

7-12). Consider a receptor at a distance r′ from the edge of the congested region. Then define:

3 00

2

3

πV

R = Equation 7-13

rRr ′+= 0 Equation 7-14

39.128.363.1592.008.0log234

1 +−+−= rrrr llllP Equation 7-15

where 0

0

02.02.0log PR

rlr −+= (N.B. logarithms to base 10)



Then the pressure in bars at the receptor is:

= 100 ,min PP

r

RP

Equation 7-16

The curves are plotted for a number of source pressures in Figure 7-4. They are similar in shape to

the TNO multi-energy curves, but the point at which the faster decay commences is different, and

the curves do not all coincide after transition This is a result of the more realistic behaviour of the

"spherical piston" representing the source, which we have now been able to base on the

experimental data. It can be seen in Figure 7-4 that at 1 bar source pressure the pressure decay

extends to about nine times the source radius. For lower source pressures, this extends much

further. Thus, for pressures up to 1 bar, the simple assumption of pressure decay inversely

proportional to distance is reasonable, although in the far field the pressures calculated now would

be lower.

Figure 7-4 The pressure decay curves given by Equation 7-16 for source overpressure of 0.2,

0.5, 1, 2, 4 and 8 bar

Note that the peak pressure of the front face of a building may be doubled (or much more for large

P) by pressure wave reflection. For 0Rr <′ , the dynamic pressure may also be significant, and

"edge of the hazard area" should be carefully defined to allow for the expansion of the explosion

source beyond the congested region. The calculations also take no account of the effect of

atmospheric inversion, which typically occurs at night, particularly after a sunny day or with low

wind speeds. An inversion will tend to act as a reflector, resulting in a much slower pressure

decay with distance; lensing effects can also be produced, with locally higher overpressures.



Pulse duration and shape

If estimated pressures are to be used with structural response calculations, then information is

needed on the duration of the pressure pulse and its rise time. Defining the times t1, t2 and t3, as

shown in Figure 7-5, the pulse is defined by the peak pressure, already determined above, and a

duration and "shape factor". (t3 - t1) is the duration and (t2 - t1) /(t3- t1) is denoted the shape factor,

which is the ratio of the rise time to the duration; this becomes zero as the front of the wave

becomes fully shocked.

Figure 7-5 An example of a triangle fitted to the positive part of a pressure pulse, showing

the definition of t1, t2 and t3.

The rate of change of the pressure wave shape is much greater for higher pressures. This leads to

the use of a distance parameter:

2

0

0

′=

a

fP

P

R

rd

Equation 7-17

where Pa is atmospheric pressure.

Then

aP

RCtt

ρ0

013 ′

=− Equation 7-18

where ,



f

f

f

f

d

d

d

dC

<

<>

<

+=

20

205

5

3.1

15

1065.0

65.0

Equation 7-19

Note that the maximum pressure has been denoted 0P′ here to emphasise the fact that consistent

units must be used, e.g. when using SI units 0P′ must be in Pascals, i.e. bars multiplied by 105.

Equation 7-18 is not valid inside the explosion source.

The shape factor is well represented by taking a linear decay with distance:

( )( )0,25.1165.0max13

12fd

tt

tt−=

−−

Equation 7-20

From the simple expressions in Equation 7-18 and Equation 7-20, a good, if slightly idealised,

representation of the positive pressure pulse can be obtained.

It should be noted that the positive overpressure pulse is followed by a negative pulse (rarefaction)

typically of lower amplitude and longer duration. This may in some circumstances be as damaging

as the positive pulse.

7.3.1.8. Detonation

The flames discussed above consist of the normal type of burning known as a deflagration. Almost

all gas cloud explosions are deflagrations. In a deflagration, the burning velocity is limited by the

diffusion of heat and species through the flame front. In a detonation, by contrast, the gas mixture

ahead of the flame is heated by a shock wave coupled to the flame. A detonation is supersonic and

self-sustaining, and, once initiated, will continue to propagate at the same speed even through an

unconfined, uncongested cloud. A deflagration flame slows down soon after leaving a congested

region, as the turbulence decays. The pressure generated by detonation in a hydrocarbon/air

mixture is about 18 bar, with velocity around 1800 m/s.

A detonation is likely to have a devastating effect on the plant directly involved in the explosion,

but so would a deflagration producing three or four bars overpressure. At a distance from the

explosion also, there is not a great difference between the effects in these two cases, because the

shape of the pressure decay curves is such that the overpressure ratio at a distance is much less

than that at the source. Thus the principal increase in hazard due to a detonation is that the

explosion source may not be confined to the congested region; if the gas cloud is larger than the

congested region, it could all be involved in the explosion, although with no expansion.

Gases vary considerably in their susceptibility to detonation. For methane, virtually in all practical

situations, detonation would not occur. Propane can generate auto-ignition spikes in the presence

of severe congestion. For ethene, detonation may be a possibility, but this would only occur in a

very highly congested region.

The overpressure which would be expected from a deflagration, given by the correlations already

presented, may be a guide as to when a detonation is a possibility. In an environment without

confinement, the overpressure is related to flame speed, and a minimum flame speed is needed for

transition to detonation to occur. A little empirical guidance can be obtained from some of the

experimental series. Overpressure exceeding 18 bar, and so possible detonation, was obtained from

experiments using ethylene where the deflagration overpressure would have been expected to be

about 3 to 3.5 bar. From experimental measurements it can be estimated that the overpressure just

before transition to detonation in propane is about 5 bar.



It should be noted that the detonability of gases decreases as the concentration moves away from

stoichiometric. Thus, compared with the ideal uniform stoichiometric experiments, detonation

may be significantly less likely to occur in real dispersing gas clouds; if initiated, detonation may

subsequently fail when gas of a different concentration is encountered. There have been no

incidents involving gas cloud explosions in congested, unconfined plant which have clearly

involved detonation.

In less severe cases, there may still be explosion effects which go beyond deflagration. The strong

flow ahead of the flame in a severe explosion may be sufficient to trigger auto-ignition near

obstacles ahead of the flame. This results in pressure spikes which may be two to three times

stronger than the main deflagration pressure peak; however, the spikes are usually of very short

duration and limited source size, and therefore may not have much effect at a distance.

7.3.1.9. Partial Fill

It is possible to estimate the effect of only having a small volume of gas-air mixture available to

take part in an explosion. The volume which is relevant for pressure generation is the volume after

combustion. A first estimate of this is to take the flammable volume and multiply by the

expansion ratio E (ρu/ρb) for the gas in question, which is about eight for most hydrocarbons.

However, if an appreciable overpressure is developed the final volume will be less (by a factor of γ/1−P , assuming ideal gas) owing to the compression. γ is the ratio of specific heats for the

combustion products, usually about 1.2. In general, not only is the volume dependent on the

pressure, but the pressure will depend on the volume, as discussed below. However, a result can

easily be obtained by iteration. If a first calculation is made using the full expanded volume, then

an overpressure can be calculated; the volume can then be corrected for this overpressure and a

new pressure calculation done. We have found that the calculation converges after a few

iterations.

In order to use the source volume, it must be related to a length (l), width (w) and height (h) of a

gas cloud. For a small volume, we assume that the cloud is a half-cube, i.e. equal height (h), half-

width (w/2) and half-length (l/2), at the centre of the congestion. If the volume is large enough for

this to extend beyond the congested region, then one or two dimensions are reduced, and others

increased, in order to keep the cloud within the congested region. In reality, of course, the

expanded cloud may well extend outside the congested region in one or two directions, even if its

volume is less. The approach is intended to be conservative, and it can be simply applied.

The calculation gives a half-length, half-width and height hwl ′′′ ,, of the burnt-gas region to

compare with equivalent dimensions of the congested region l, w, h.

If l′ < l, then the effective number of grids along the length is given by:

ll nl

ln

′=′

Equation 7-21

This value can then be used in Equation 7-3 to calculate the overpressure. In real plant, obstacles

are not usually present as planar grids, so taking the flame to be influenced by part of a grid is not

an inconsistent assumption.



7.3.1.10.Non-central Ignition

The above correlations have been developed on the basis of experiments with ignition at the centre

of the congested region. This is based on the assumption that central ignition represents a worst

case for the quantity we are trying to predict, which is the typical, or median, overpressure

generated over the congested region. However, a series of experiments was also conducted by

Shell to test this hypothesis. Several of the “unconfined” congested experiments were repeated

with the ignition point moved from the centre to the centre of one edge, and to a corner of the rig.

It was found that the ratio of maximum overpressure generated with edge ignition to that from the

central ignition varied from 0.32 to 0.67. With corner ignition, this ratio was between 0.33 and

0.44. Additional larger scale experiments with more complex layouts appear to confirm this

conclusion. However, localised peak overpressures may be greater for the cases when the flame

travel distance is longer.

7.3.1.11.Localised Peak Overpressures

There can be limited regions with significantly higher overpressure than the general overpressure

generated in a congested region. In experiments which produce low overpressures, up to a few

hundred millibars, measurement usually show little variation of pressure with location. But, as the

overpressure increases, the peak-to-mean ratio increases also. The “hotspots” can be caused by:

a) waves from pressure generated at two different locations happening to meet and

constructively interfere at some location;

b) pressure wave reflection if there are surfaces of significant area in the congested

region;

c) localised auto-ignition.

Each of these mechanisms produces high overpressures which are quite localised, i.e. giving a

small source radius at that pressure. Pressure spikes due to (c) are generally very short. Because

the effects at a distance are strongly dependent on source radius, away from the explosion the

influence of such "hotspots" is usually masked by the pressure generated by the overall explosion.

Very short duration pulses are also of less significance in their effect on structures.

7.3.1.12.Source Volume

The overpressure at a distance from the explosion is strongly influenced by the size of the

explosion source. It is thus important to estimate the source volume. What matters is the spatial

extent of the region over which the peak overpressure is generated. In the ideal case when this is a

sphere (or a hemisphere on a ground plane), the pressure initially decays inversely with distance

from this level, and the distance scaling is determined by the radius of the sphere.

A number of methods (for example the TNT equivalence approach) have based the source volume

(and hence the radius) on the combustion energy of the fuel, or better of the fuel burning in the

congested region. Since the energy content of most stoichiometric hydrocarbon-air mixtures is

very similar, this is just a convoluted way of deriving a number proportional to the volume of the

congested region. But for high pressures or for a material with a different energy density, the

approach is likely to be misleading, as well as unnecessarily complex.

The source volume recommended for use in CAM is therefore (L+4)(W+4)(H+2) (dimensions in

metres), or the expanded partial-fill volume discussed above, if that is smaller. The 2 metres can

be modified if the size of obstacles is untypical, for example when analysing small-scale

experiments.

7.3.1.13.Uncertainty and Assumptions

The accuracy of predictions from the simple correlations used in the CAM method, is, of course,

limited. Comparisons with experimental measurements show that most predictions are within a

factor of two. However, it should be noted that these results are from idealised experiments. Any

real plant does not have well-defined rows of obstacles of equal blockage, and so there is

additional uncertainty arising from the need to idealise the real layout into equivalent regular rows.



It is helpful that the nature of the pressure decay curves often leads to a much smaller

(proportional) uncertainty in the pressure at a distant receptor than the uncertainty at the source.

Even with limited accuracy, the method does provide a useful screening tool. On many occasions, it

can be used to show that the likely overpressure at a structure is well within the capacity of the

structure to withstand the blast. There will be occasions when the results do not provide enough

confidence, and more sophisticated methods may be needed for the analysis Then it may be

necessary to use a phenomenological model such as SCOPE, or full computational fluid dynamics,

for example EXSIM.

7.3.2. SCOPE Model

SCOPE is a "phenomenological" model for predicting confined, vented explosions, developed and

maintained by Shell Global Solutions. In order to estimate the overpressure which could be

generated by an explosion in a vented enclosure such as a control room or offshore module,

SCOPE calculates the progress of a flame as it develops from ignition and accelerates past

obstacles. This modelling is based on experiment. The volume is assumed to be rectangular with a

main vent in one face, but possibly with further vents in other walls. The worst case ignition point

is assumed typically to be in the centre of the wall opposite the main vent. Obstacles, if present,

are idealised as a number of rows placed across the box between the ignition point and the main

vent. The peak internal overpressure is calculated, together with the "external explosion"75, which

can be a significant cause of damage away from the enclosure.

SCOPE has been extensively validated using experimental data, about sixty DnV 35m3

experiments76, the Shell Research Ltd. SOLVEX box experiments77,78 and about 150 smaller scale

confined explosion experiments.

7.3.2.1. Phenomenological Approach

There is a hierarchy of predictive tools used to assess explosion hazards. The simplest level are

models based on correlations of small-scale data. At the other extreme of complexity are the

Computational Fluid Dynamics (CFD) models.

In the middle ground are phenomenological models such as SCOPE.

The formulation of SCOPE, although simplified, is based on an understanding of the physical

processes involved in the development of the explosion. The robustness of such an approach

derives from the fact that, wherever possible, the parameters used are derived from specific

experiments to study the individual physical processes, rather than "calibrated" by adjusting the

model predictions to fit explosion data.

75Harrison A.J. and Eyre J.A., Vapour cloud explosions - the effect of obstacles and jet ignition on the combustion of gas clouds, Proc. 5th Int. Symp. on Loss Prevention and Safety Promotion in the Process Industries, Vol. I, p.38-1 (1986).

76Det Norske veritas (1982-3) Internal reports on "Gas explosion research programme", unpublished

77Bimson et al, An experimental study of the physics of gaseous deflagration in a very large vented enclosure. 14th Int. Coll. on the dynamics of explosions and reactive systems, Coimbra, Portugal, 1995

78 Puttock, J.S., Yardley, M.R., and Cresswell, T.M., “Prediction of vapour cloud explosions using the SCOPE model”, International Symposium on Hazards, Prevention and Mitigation of Industrial Explosions, Schaumburg, Illinois, Sept.1998



7.3.2.2. Model Geometry

The environment to be modelled is idealised as a vented enclosure that is assumed to be

filled with a homogeneous gas air mixture, as shown in the Figure below. At one end of this box is

a vent (the "main" vent) of area Av Ignition is assumed, on a worst-case basis, to take place in the

centre of the opposite face. The length of the box, along the direction from main vent to opposite

wall, is L, and the cross-sectional area is A. Obstacles, such as vessels or pipework, within the box

are represented as a series of grids positioned normal to the main flow direction from the ignition

point to the main vent. Additional venting can be added as either side vents of total area As or a

rear vent of area Ar.

Figure 7-6 SCOPE Basic Geometry

Immediately following ignition at the back wall, the shape of the flame is an expanding

hemisphere. However, once the flame reaches the sides of the box, it stops increasing in size, but

retains its roughly hemispherical shape as it advances down the box. The distance of leading edge

of the flame from the back of the box is denoted by X.

The basic principles of the model are unchanged from the Cates and Samuels approach: a

one-dimensional model based on a series of obstacle grids, with the flow through each grid used to

determine turbulence and hence turbulent combustion downstream of the grid. Figure 7-7

summarises the overall structure of the model.



Figure 7-7 An Overview of the SCOPE Model

7.3.2.3. Basic Differential Formulation

As the gas air mixture within the geometry under investigation is burnt, additional volume

is generated by the expansion of the gas. Of this “extra volume”, some flows out of the vents, and

the remainder contributes to increasing the pressure. To take the balance between vent flow and

pressure generation properly into account, SCOPE keeps track of the development of two variables

as a function of time; these variables represent the amounts of unburned and burned gas in the box.

Consider the stage where the flame has already reached the sides of the box, and assume

that there are no side vents. The mass of unburned gas in the box, Mu, is decreasing as some is

consumed by the flame and some is pushed out of the vent. If the flame area is sA, the turbulent

burning velocity Ut, and the unburned gas density ρu, then the rate of consumption by the flame is

sAUtρu. The mass flow through the main vent is UvcDAvρu, where cD is the discharge coefficient

and Uv depends only on the pressure P. Thus

Equation 7-22

where T is time. (Some of the burnt and unburned gas may be expelled through side vents;

this aspect is covered later.) For the burned gas, it is not sufficient to keep track of the mass, since

this does not provide information on the thermodynamic state of the gas. It turns out that it is

convenient to use the quantity B= P1/γ

Vb, where γ is the ratio of specific heats. Then the equation

for the rate of increase of burned gas is

Equation 7-23



where E is the expansion ratio.

The expressions used to calculate Ut, Uv and s are discussed below.

It is also useful to keep track of the mass of gas emitted from the main vent, for use in the

external explosion calculations:

Equation 7-24

7.3.2.4. Early Flame Development

In the early stage after ignition, until the flame reaches the sides of the box, the equations

are different, since the flame is expanding as a hemisphere, rather than travelling longitudinally

down the box. At this stage, the flame surface area is 2πX2 , and the rate of consumption of

unburned gas 2πX2Ut ; so the differential equations become

Equation 7-25

Equation 7-26

7.3.2.5. Laminar Burning Velocity and Expansion Ratio

The laminar burning velocity has two important roles in explosion modelling. Firstly, it

describes the behaviour of the flame just after ignition, before it encounters any obstacles. Here,

the flame is moving slowly and hence this period is relatively long when compared with the

duration of the main pressure pulse. Secondly, the laminar burning velocity is used in the

determination of the turbulent burning velocity, as discussed later.

The values for U0 in stoichiometric mixtures at normal pressure are derived from [79]. The

form of the variation of laminar burning velocity with stoichiometry is derived from the data of

Taylor [80], as reported by Tseng et al.[81]. Since the values at stoichiometric are not entirely

consistent with other data, we have scaled Taylor's curves to meet the desired stoichiometric

values. Two polynomials were fitted for each gas in order to obtain a best fit.

Both the laminar burning velocity and the expansion ratio change as the pressure is

increased (adiabatically). P.H. Taylor (private communication) used the SANDIA computational

model [82] which incorporates full chemistry and transport, to investigate the properties of laminar

flames under adiabatic compression. Power laws were fitted to the results and are used in the

model.

7.3.2.6. Self-acceleration of the flame (quasi-laminar burning)

Even in the absence of turbulence, the expanding laminar flame develops instabilities that

cause some wrinkling of the flame front and an acceleration of the flame. Reliable experimental

measurements of this process are sparse, but the available data can be fitted by taking the burning

velocity to increase linearly with distance:

79 J. Warnatz. (1981) The structure of laminar alkane, alkene and acetylene flames. 18th Intl.Comb.Symp., 369.

80 S.C. Taylor. (1991) Ph.D. Thesis, University of Leeds

81 L.-K. Tseng, M.A. Ismail, and G.M. Faeth. (1993) Laminar burning velocities and Markstein numbers of hydrocarbon/air flames. Comb.Flame 95, 410.

82 R.J. Kee, J.F. Grcar, M.D. Smooke, and J.A. Miller. (1985) A Fortran program for modeling steady laminar one-dimensional premixed flames. Sandia report SAND85-8240 (December 1985).



Equation 7-27

where R is the radius of the flame. (Cates and Samuels introduced a delay distance, after

which the acceleration starts, but this does not appear to be necessary.)

The data of Lind and Strehlow [83] give a value of 0.25 s-1 for k in the case of propane (at

stoichiometry λ =1.25) and 0.16 s-1 for methane (λ = 1.05). The experiments of Brossard et al. [84]

show self-acceleration in ethene, and the plots from one test allow a rough estimate to be made for

k as 0.64 s-1. Degener and Forster's [85] turbulent burning velocity experiments also include some

measurements without turbulence. Resulting values of k are reasonably consistent with the above.

These values are used in the model.

The limit of self-acceleration

The process of self-acceleration is unlikely to continue indefinitely, since the extent to which

surface instabilities can increase the flame area is limited. The above data give no clear indication

of where this limit occurs. The SOLVEX experiments [86], involved explosions in a 550 m3 vented

box; the first two experiments, without obstacle grids, provided useful data.

SCOPE predictions of flame travel have been compared with SOLVEX measurements. For

methane, without a limit to self-acceleration, the model overpredicts the flame speed in the later

stages, but if the self-acceleration is stopped when the flame radius reaches 3m, a good fit is found.

A similar result is found for propane if the self-acceleration is stopped after 2m. For both these

gases, these limits correspond to a cessation in the acceleration when the burning velocity reaches

two and a half times the laminar burning velocity U0 ; this limit is used in the SCOPE model.

A similar limit, 3 U0 , was independently derived by Hjertager (private communication) for use in

the EXSIM model.

7.3.2.7. Turbulent burning velocity

A suitably accurate and fully theoretical expression for turbulent burning is not available.

Experiments to measure turbulent burning velocity are also difficult, mainly due to the problems of

creating a large volume containing homogeneous turbulence and allowing a flame to propagate

without boundary effects. Experiments at the largest values of Reynolds number likely to be

encountered in full-scale gas explosions have not been performed.

Thus, in SCOPE, a semi-empirical approach has been taken. The aim in choosing a turbulent

burning relation has been to derive an expression that is believed to have roughly the right

functional form, but with constants that allow the expression to be fitted to experimental data. The

choice of functional form is important, for example, to achieve a correct dependence of the

burning rate on turbulent length scale.

The turbulent burning velocity is given by a smoothed function between two turbulent burning

velocity relations, one that describes the behaviour at low turbulence intensity, Ut | L , and the other

at high turbulence intensity, Ut | H .

83 C.D. Lind and R.A. Strehlow. (1975) Unconfined vapor cloud explosion study. Loss Symposium, Florida.

84 J. Brossard, D. Desbordes, J.C. Leyer, J.P. Saint-Cloud, N. Di Fabio, J.L. Garnier, A. Lannoy, and J. Perrot. (1985) Truly unconfined deflagrations of ethylene-air mixtures. 10th International Colloquium on the Dynamics of Explosions and Reactive Systems.

85 M. Degener and H. Forster. (1990) Investigation of flame propagation: influence of turbulence on flame propagation. EC Resaerch Area: Major Technological Hazards Project no. EV4T0011-D(B), final report, December 1990

86 S.J. Bimson, D.C. Bull, T.M. Cresswell, P.R. Marks, A.P. Masters, A. Prothero, J.S. Puttock, and B. Samuels. (1993) An experimental study of the physics of gaseous deflagration in a very large vented enclosure. 14th International Colloquium on the Dynamics of Explosions and Reactive Systems. Coimbra, Portugal.



Several relations are available in the literature. We have performed a new fit for two reasons.

Firstly, we wished to extend to higher Reynolds numbers than can be obtained in the laboratory by

using the computations of Bradley et al. [87]; very large length scales and thus Reynolds numbers

can apply in real industrial explosions. The second factor was that we were adjusting the ut / ul H

formulation so that the combined expression [88] fitted the data best. Thus the fit for ut / ul H

should be biased more to the higher turbulence data.

The fitted expression was of the form

Where K is the Karlowitz number [89]

The best fit was obtained with c1 = 1.00, and c2 = 0.33.

Following this, two changes were made to reach the final expression: 0.33 was changed to the

simple 1/3. Secondly, it is believed that the effect of turbulent stretch on burning velocity is

represented by a (stretch) Markstein number Ma, and so it is preferable to have the expression

dependent on K Ma, rather than K Le. To make this change K Le was replaced by K Ma/4.1. This

simplistic substitution was based initially on equation 5 of [90], taking the reduced activation

energy β to be 10; however, data on Markstein numbers confirm that this is a reasonable

approximation for stoichiometric and lean methane and propane, which covers much of the data

included in the Bradley, Lau and Lawes compilation.

Thus the turbulent burning velocity used in SCOPE is given by the previous equations and

the following expression:

Equation 7-28

There are no suitable direct experimental determinations of the effect of length scale on

turbulent burning velocity; this aspect is important since the response of the model to changes of

scale is largely determined by the form of the turbulent burning velocity expression. Comparisons

of SCOPE predictions with data from the SOLVEX large-scale explosion experiments and the

corresponding small-box experiments are therefore very encouraging; these show that the change

of explosion pressure with scale (for a factor of 220 increase in volume) is reproduced very well

by the model.

7.3.2.8. Flame shape

After the end of the hemispherical expansion, i.e. when the flame reaches the walls of the box, a

value must be chosen for s, the ratio of the flame surface area to the box cross-sectional area.. This

is taken to be the same as the surface area/base area ratio for a hemisphere, i.e. 2. However, for

87 D. Bradley, P.H. Gaskell, and X.J. Gu. (1994) Application of a Reynolds stress, stretched flamelet, mathematical model to computations of turbulent burning velocities and comparison with experiment. Comb.Flame 96, 221.

88 R.G. Abdel-Gayed, K.J. Al-Khishali, and D. Bradley. (1984) Turbulent burning velocity and flame straining in explosions. Proc.R.Soc.London A391, 393.

89 R.G. Abdel-Gayed, K.J. Al-Khishali, and D. Bradley. (1984) Turbulent burning velocity and flame straining in

explosions. Proc.R.Soc.London A391, 393

90 G. Searby and J. Quinard. (1990) Direct and indirect measurements of Markstein numbers of premixed flames. Comb.Flame 82, 298.



sufficiently long aspect ratios, it might be expected that this should be increased, since a flame

tends to elongate as it travels down a long tube. On the other hand, only the front part of the flame

will have passed through the latest grid, and so will be contributing at the fastest burning rate.

Based on data from the small-box experiments, the value of s is increased linearly with distance if

the aspect ratio exceeds 1.3:

Equation 7-29

where

This was originally fitted using experiments with aspect ratio up to 2; it was later

found to provide good results for further experiments with aspect ratio up to 4.9.

If the main vent is significantly smaller than the cross-section of the module, then the flow

converges as it approaches the vent. The flame similarly narrows as it follows the flow. A grid near

a small vent thus has a smaller effect than would otherwise be expected, since the part of the flame

front which reaches the turbulent region downstream of the grid has a smaller area. This effect is

now taken into account in the model.

7.3.2.9. Grid effects

The drag coefficient cs of a cylinder is dependent on flow velocity, decreasing from 1 at low

Reynolds number to about 0.4 at a Reynolds number of 5x105, and thereafter increasing to 0.7 [91].

The existence of the minimum is a problem for application in the model. Although the formal

model assumption is a flow uniform across a grid, the reality is that there would be a variation of

velocity across the width of the box; in the vicinity of a minimum in cs, the average drag would be

higher than given by the drag relevant to the average flow velocity. To avoid underprediction in

such cases, therefore, the dip to 0.4 is "bridged" in the formula used in SCOPE

Equation 7-30

where , U is flow velocity, D is cylinder diameter and v is gas viscosity, with cs

decreasing from 1 to 0.7 linearly in log10(Re) from 5.3 to 5.5.

The drag of a grid of such obstacles as a function of the blockage ratio σ is derived from

Roach [92]

Equation 7-31

Similarly, the drag of individual sharp-edged obstacles, e.g. square bars, is dependent on incident

turbulence intensity. The dependence is based on data from Graf and Mansour [93]:

91 K.C.S. Kwok. (1986) Turbulence effect on flow around circular cylinder. J.Eng.Mech. 112, 1181.

92 P.E. Roach. (1987) The generation of nearly isotropic turbulence by means of grids. Heat and Fluid Flow 8, 82.

93 W.H. Graf and F.F. Mansour. (1975) Turbulent drag coefficients of sharp-edged obstacles. Journal of Hydraulic Research 13, 127.



Equation 7-32

For grids of sharp-edged obstacles, the dependence on the blockage s is given by Hoerner [94]:

Equation 7-33

Naudascher & Farell[95] have tabulated experimental data on grid drag coefficients from ten

different sources, involving single-plane and biplanar grids of circular rods and sharp-edged bars.

The values are plotted in the Figure below together with curves from the formulae of Roach and

Hoerner. The results are in good agreement with the formulae.

cg is used in determining the turbulence generated by a grid, which is taken to be proportional to

, where U is the flow velocity through the grid as the flame reaches it.

Figure 7-8 The Drag of Round Pipe Grids

94 S.F. Hoerner. (1950) Fluid Dynamic Drag. Midland Park, NJ, published by the author.

95 E. Naudascher and C. Farell. (1970) Unified analysis of grid turbulence. J.Eng.Mech.Div.ASCE 96, 121.



Figure 7-9 The Drag of Square Pipe Grids

7.3.2.10.Flame area downstream of a grid

As a flame passes through a row of obstacles the time-averaged, large-scale flame surface

area increases as a result of the flame 'fingering'. This mechanism is different from the stochastic,

small-scale increase in flame area due to wrinkling, which is taken into account in the turbulent

burning velocity. Because of the lack of detailed experimental data in this area, computational

fluid dynamics (CFD) was used to give some indication of the behaviour of an initially planar

flame as it passes through a regular grid and a simple model was derived from the computational

data. It was found that the flame area showed a near-linear increase with flame position (measured

from the obstacle) in a region close to the obstacle; the gradient was roughly proportional to the

square root of the blockage ratio σ.

Equation 7-34

Further downstream of the obstacle, the flame must 'relax' and will tend towards a planar

flame front if there are no more obstacles in its path, owing to the flame's burning across the

wakes.

Thus the model includes a flame area enhancement factor, which increases rapidly

downstream of a grid (at a rate proportional to ), and then decays slowly.

7.3.2.11.Obstacle complexity

The obstacles, e.g. vessels and piping, in a real plant environment are typically much more

complex than the simple arrays of cylinders used in most idealised experiments. In particular, there

is a great range of length scales present. The effect of this is to increase the ”macroscopic" flame

area generation above that pertaining to rows of uniform cylinders.

We have performed experiments to demonstrate these effects, using idealised obstacles but

with a range of obstacle sizes. Using the results of these experiments and others, we account for

these effects by increasing the macroscopic flame area generation in the model for the higher

levels of obstacle complexity.



7.3.2.12.Vents

Standard relations for compressible vent flow are used in the model, allowing correct

calculation of the dependence of vent flow on pressure up to and including choked flow. A "vent

flow velocity" Uv is defined as the mass flow through the vent divided by the vent area, the

discharge coefficient and the gas density; dividing by the speed of sound gives the dimensionless

"vent flow velocity"

Equation 7-35

uv thus defined is the same for all vents where unburned gas is being vented, being a function only

of the pressure ratio p. If p is less than the critical pressure ratio

Equation 7-36

then venting is subsonic, otherwise sonic flow occurs in the vent.

The expressions for uv are:

Equation 7-37

The discharge coefficient for an orifice is dependent on the pressure ratio, increasing from 0.6 for

1/p=1 to 0.9 for 1/p=0.

A further beneficial consequence of taking the differential equation approach described above is

that side vents can be taken into account. It is straightforward to include the loss of burned and

unburned gas through the side vents. For example, if the area of side vents ahead of the flame is

Asa, then an additional term -cDuv(asa/a) is added. The side vent areas ahead of and behind the

flame are determined by taking the boundary to be where the edge of the hemispherical flame

touches the side of the box.

The simple form of the side vent flux given above is correct for the venting of unburned gas, which

has density ρu at pressure P0. If the gas density is lower, the mass flow through the vent decreases

in proportion to√ρ, but the volume flux increases in proportion to √ρ. Thus for burned gas the

dimensionless "vent flow velocity" is √E uv, where uv is defined in Equation (7.35), since E= ρ u/ ρ

b (This is only strictly correct if E is constant, but it is taken to be a reasonable approximation as E

varies with pressure.)

This formulation was introduced into the model and was found to give good predictions of the

effects of various side vents without any adjustment.

A rear vent, i.e. a vent in the ignition wall, is simply handled in the same way as a side vent

in that burnt and unburned gas is expelled through the vent. However, the calculation of the

relative sizes of the venting area ahead and behind the flame front depends upon whether the flame

front is still expanding over the surface of the rear wall rather than travelling down the length of

the box. A pessimistic approach is taken in that the vent area is assumed to be positioned away

from the ignition location; so no rear venting takes place until the flame ball has grown to a size

where the base area of the hemisphere is larger than the cross sectional area of the module minus

the rear vent area.

Vent opening

The effect of vent covers (on side, main or rear vents) can be simulated using SCOPE. For

each vent, the user must specify an opening pressure and time delay. The vent area is taken to be



zero until the internal pressure in the box first reaches the opening pressure. The vent area then

increases linearly with time so that the vent is fully open after a further time equal to the time

delay.

Quite complex behaviour can be simulated. For example, if there are two vents with

similar properties, the user is advised not to enter identical opening pressures since there will in

practice be some differences between the vents. In such cases, the predicted result is often that the

pressure rises rapidly at first and opens one vent; as a consequence, the pressure falls again and

does not rise high enough to open the other vent until late in the explosion. At that stage the

second vent may not have much effect. We have observed such behaviour in experiments with vent

covers.

7.3.2.13. External explosion

The dynamics of the turbulence and flame travel in the external explosion, and its

interaction with the internal pressure, are complex and not well understood.

External Explosion Geometry

An idealised shape is assumed for the external explosion, as shown in the Figure below.

The mushroom of unburned gas, at the time of flame emergence, is modelled as a hemisphere

surmounting a cylinder. The cross-sectional area of the cylinder is taken to be the area of the vena

contracta outside the vent, i.e. cDAv . There are two parameters to determine: the radius of the

hemisphere, Rh, and the length of the cylinder. The amount of gas expelled through the main vent

up to this time, Me, is calculated using Equation 7.24. A correlation between jet tip position and

head diameter was derived from an experiment in the Buxton 2.5m3 box ; this completes a set of

equations that can be solved for length of the cylinder and the radius of the hemisphere.

Figure 7-10 The Idealised External Explosion

The pressure in the external explosion, Pext, is taken to be proportional to the pressure

reached in the enclosure when the flame emerges from the main vent, Pemerg. The correlation used

has Pext / Pemerg dependent on the ratio of vent area to box cross-sectional area, the aspect ratio of

the box, and Me. It is also found experimentally that the external explosion pressure is lower for a

single main vent than when there are several openings in that wall; in the latter case, the vent

blockage is similar to an extra obstacle grid. This is also taken into account in the correlation.

The correlation does not allow for the compression of the gas in the external explosion

when the pressure is high. At high pressures the expansion ratio from the ambient initial condition

is low, so the ratio of flame speed to turbulent burning velocity is lower, and the overpressure

depends on the flame speed. Assume that the overpressure is

p - 1 = α U 2

f Equation 7-38

with



U f = U t ( E – 1 )

where α is a constant, Uf and Ut are flame speed and turbulent burning velocity, and E is

the expansion ratio. An iterative calculation in the model effectively replaces the above with

U f = U t ( E p1/γ

– 1 ) Equation 7-39

where γ is the ratio of specific heats.

Since geometries without any obstacles do not easily fit the same trends as cases with

obstacles, they are treated as a special case, although empty boxes are not often encountered in

real-life geometries.

Maximum Internal Pressure

The interaction between the external explosion and the further development of the internal

pressure is complex and not well understood. In the majority of experiments in our rectangular

boxes, the external explosion has the effect of increasing the internal pressure further. It is not

clear whether this is best viewed as the effect of a pressure wave travelling into the box, or as the

result of the external pressure restricting the vent flow while burning still continues into the

corners of the box. For this reason the treatment of this phenomenon in SCOPE is empirical. The

experiments also show that the effect of the external explosion on the internal pressure is larger

where no grids are present in the module, consequently this is modelled differently.

The effect of the external explosion on the internal pressure is modelled by adding a

proportion of the external pressure Pext to Pemerg to obtain Pmax. Surprisingly, this very simple

approach works well for many cases. The main exception is that in some explosions, the internal

pressure has decayed markedly before the influence of the external explosion is felt; then the

external explosion produces a peak that is not as high as the "emerging" peak, i.e., the maximum

pressure is Pemerg. We do not know enough to predict when this will occur, but the assumption that

the external explosion always adds to the internal pressure is conservative.

7.3.2.14. Stoichiometry changes

SCOPE handles stoichiometry variations by altering the laminar burning velocity of the

fuel, and the Markstein number, using multiple polynomials. For propane, the Markstein number

decreases for an increase in stoichiometry, which, for a constant laminar burning rate would lead

to an increase in the overpressure. Combined with the decrease in laminar burning velocity

between stoichiometry of 1.1 and 1.3, this results in the overpressure remaining roughly constant

over this range. By contrast, for methane, the Markstein number increases with increasing

stoichiometry, hence the overpressure decreases rapidly with increasing stoichiometry on the rich

side.

7.3.2.15.Gas Mixtures

All properties for a given fuel are specified in a “gas file”. A linked model “gasmix” can

be used to generate a new gas file based upon a mixture of pure fuels, or a single fuel at given

ambient conditions. This gas file can then be used by SCOPE in a similar way to the pure fuels

supplied with the program. The laminar burning velocity of the mixture is estimated by performing

a full calculation of the flame temperature; then the adiabatic flame temperature is used in

conjunction with a series of parameters for each pure fuel, which are derived from the SANDIA

flame code, or other data, to determine the laminar burning rate of the mixture. Some other

parameters required by the SCOPE model, e.g. self-acceleration rates etc. are calculated by

interpolation between the values used for the pure fuels.

7.3.2.16.Accuracy of Predictions

It is important to keep in mind the accuracy of the predictions made by any mathematical model,

which by definition is a simulation of reality. The engineer should endeavour to consider all

aspects of the case to ensure that the prediction is as accurate as reasonably practicable.



SCOPE has been validated against experiments involving explosions in rectangular boxes with

regular grids at scales of 2.5 m3 , 8.5 m

3 and 35 m

3 ; some of these experiments were also used for

guidance in the development of the model. Further confidence, in particular regarding the

correctness of the scaling, has been provided by validation against data from the SOLVEX large-

scale experiments at 550 m3 . Data at larger scale were provided by a Joint Industry Project which

involved explosion tests in a large-scale rig (28m x 8m x 8m) typifying the layout, confinement

and congestion found in offshore process modules.

For all scenarios where the overpressures are in the realistic range of over 500 mbar, SCOPE

generally predicts these idealised experiments within a factor of 2 as shown in the plot below.

There is a clear reduction in the scatter on the predictions towards the higher more realistic

overpressures. For overpressures below 500 mbar there is slightly more scatter on the predictions.

Figure 7-11 Validation: Peak Internal Overpressure

The validation of the model against the Joint Industry Project deluge experiments is also shown in

the plot above; it shows that in all cases the predictions were well within a factor of 2.

On average there is some tendency to overpredict the experimental data set; this is shown in the

histogram of the observed to predicted overpressure ratio below.



0

5

10

15

20

25

<0

.31

0.3

5

0.4

0.4

5

0.5

0.5

6

0.6

3

0.7

1

0.7

9

0.8

9 1

1.1

2

1.2

6

1.4

1

1.5

9

1.7

8 2

2.2

4

2.5

2

2.8

3

>3

.17

Range of observed / predicted overpressure

Fre

qu

en

cy

Figure 7-12 Validation for Experiments over 100mbar

Additional allowance must be made for the uncertainty in translating the real geometry to the

idealised representation used in SCOPE. The best approach to assessing the uncertainty resulting

from the idealisation of the geometry is to perform repeat runs of the model whenever several grid

layouts can be found which appear to be equally valid representations of the true geometry. The

variations in the predicted overpressure will give an indication of the accuracy of the average

overpressure prediction due to this aspect of the modelling.

It is for the user to decide whether, in the particular circumstances, the resulting overall accuracy of

the prediction of average overpressure is sufficiently conservative. It is up to the user to decide on

any safety margins to be used, or a probabilistic approach (for example, in quantitative risk

analysis), along with consideration of other factors such as the likelihood of the module being filled

with an ideal near-stoichiometric gas mixture, and of the ignition being at the worst location.

It must be remembered that SCOPE predicts the average internal pressure inside the module for the

idealised geometry, and makes the assumption that the pressure is uniform at all internal locations.

In reality localised higher pressure peaks may be observed, but these will generally be of short

duration. For example in the recent Joint Industry Project (JIP) experiments at Spadeadam test case

4 (test 7), the average internal overpressure was typically 2 bar, but with very localised pressure

peaks of short duration which were in excess of 4.4 bar. In this case SCOPE would be attempting to

predict the 2 bar typical internal pressure.

7.3.3. TNT Model

The TNT model used to be widely used for a quick estimate of the effects of a vapour cloud

explosion by equivalencing the explosive mass in a vapour cloud to a point source TNT

detonation. Better methods are now available and the model is only included in Shell FRED so that

users can carry out calculations which may be required by regulatory authorities.



mTNT = µ ∗ Hc ∗ mHC / HcTNT Equation 7-40

Where,

mTNT

= equivalent mass of TNT (tonne)

µ = explosion yield (-)

Hc = lower heat of combustion of the hydrocarbon (MJ/kg)

mHC = mass of hydrocarbon in the flammable range (tonne)

HcTNT = energy content of TNT (4.52 MJ/kg)

Gugan96 has plotted the yield against combustible mass for 22 unconfined vapour cloud

explosions. This shows no correlation, but it shows that a yield of 0.1 is seldom exceeded. Brasie

and Simpson97 suggest that a lower values of yield, 0.03, should be used to estimate potential

damage. More recently the ACMH98 advised a yield of 0.042.

The lower heat of combustion can be found in many handbooks, a typical value for n-hydrocarbons

is 46 MJ/kg.

A scaled distance G, is determined using :

333.0

=

TNTm

rG

Where r = distance from the explosion centre to the target(m)

The scaled distance G is related to the peak overpressure P, this curve may be approximated by the

equation :

log10 (G) = 0.082 ∗ log10 (P)2 -0.529 * log10 (P) + 1.526 Equation 7-41

P is the overpressure, 0.01 < P < 1.0 bar.

It should be noted that this curve has a practical upper limit of 1 bar. See section 4.6 for estimating

damage effects. There are some important features of a VCE which differ from a TNT explosion.

• Volume of the cloud is far larger

• The pressure at the centre is lower

• The pressure wave decays approximately with 1/r for a VCE not 1/r2 as for TNT.

• Blast wave duration is longer

• VCE's are deflagrations, TNT yields a detonation and gives a different shape of the blast wave

Such differences mean that the TNT model is wholly unsuitable, and SHOULD NOT BE USED

for estimating the blast effects of a vapour cloud explosion.

96Gugan K., Unconfined vapour cloud explosions, I. Chem. Eng. 1979.

97Brasie W.C. and Simpson D.W., Guidelines for estimating damage explosion, Loss Prevention, Vol 2, AIChE, pp 91-102, (1968).

98Advisory committee on Major hazards, Second report (Chapter 5), HMSO 0 11 883299 9, London (1979).



7.3.4. TNO Multi-Energy Method

The TNO multi-energy method99 (van den Berg, 1985) recognises that strong blast is only

generated in places characterised by a considerable degree of congestion, while other parts of the

cloud just burn out without any significant contribution. It has the possibility to calculate static and

dynamic overpressure and the phase duration of several consecutive explosions in congested

regions separated by unobstructed volumes. For the simplicity we will restrict ourselves to the

single explosion and only the static overpressure. A stoichiometric hydrocarbon-air mixture

contains approximately 0.1 kg/m3 hydrocarbon and has a heat of combustion of approx. 3.5 MJ/m

3.

When the mass of hydrocarbons in the confined region is known, the energy released can be

calculated from:

= E mass Heff

concc∗ ∗ Equation 7-42

Where,

E = energy released (MJ)

mass = mass of hydrocarbons in the confinement (kg)

Hc = Heat of combustion (3.5 MJ/m3)

conc = concentration of hydrocarbons in air (0.1 kg/m3)

eff = efficiency of the explosion (0.15 - 0.4)

The combustion energy scaled distance R can now be calculated from:

3

1

6

0

10 =

∗∗

E

PxR

Equation 7-43

Where,

R = energy scaled distance

x = distance at which overpressure calculation is required.

P0 = ambient pressure in Pa

Using the data provided by TNO, which is reproduced in the figure below, a static overpressure can

be read as a function of scaled distance, R. Two problems remain; (i) which curve to use (1-10) and

(ii) what efficiency is appropriate. The curve to use is dependent on the degree of congestion in the

structure and the reactivity of the gas, and could range in process equipment from 4 to 7. The

efficiency from experiments ranges from 0.15 to 0.4, depending on the resulting flame speed. In

general one should use the higher efficiencies for the curves with the higher numbers. To give an

indication of the volume occupied by a flammable cloud, (stoichiometric content is about 0.1 kg of

hydrocarbons per m3), a 1 ton release gives a cloud with a radius of 17 metres, and a 10 ton release a

radius of 36 metres.

99Berg A.C. van den, The Multi-Energy method - a framework for vapour cloud explosion blast prediction, J. Haz. Mat., Vol. 12,(1985)1-10.



Figure 7-13 Variation of pressure with the scaled distance R (TNO curve)

7.4. Explosion Damage Effects

It is clear that the damaged caused by the explosion is a function of the overpressure, the form of

the blast wave and the equalisation of pressure inside e.g. a building. To indicate what the damage

of an explosion could be, Mercx100 tabulated the damage effects as a function of peak overpressure

based on data from experimental and accidental explosion. It should be noted that the use of peak

overpressure as a damage indicator is only very approximate. It is the time/pressure profile, i.e.

impulse, of the blast wave combined with the structural response to that loading which determines

the amount of damage.

100Mercx W.P.M.,De uitwerking van explosie-effekten op constructies, PML 1988-C-74, Juni 1988.



Failure Overpressure

bar

No structural damage 0.002

Loud noise similar to sonic boom, occasional glass breakage

0.003

5% Window shattering 0.005

50% Window shattering 0.02

Most windows shattered, occasional damage to frames 0.035

Collapse of roof of a tank 0.07

Connection failure of corrugated panelling 0.07-0.14

Slight distortion of steel framework of clad building 0.08-0.1

Wall of concrete blocks shattered 0.15-0.2

Collapse of steel framework 0.2

Collapse of self-framing steel panel building 0.2-0.3

Ripping of empty oil tanks 0.2-0.3

Small deformations on pipe bridge 0.2-0.3

Big trees topple over 0.2-0.4

Panelling torn-off 0.3

Displacement of pipe bridge, failure of piping 0.35-0.4

Damage to distillation columns 0.35-0.8

Collapse of pipe bridge 0.4-0.55

Loaded train wagons overturned 0.5

Brick wall (0.2-0.3 m thick) shattered 0.5

Movement of round tank, failure of connecting piping 0.5-1.0

7.4.1. Overpressures at which Glass Windows Fail

Glass is a material which is often used in constructions. Pieces of glass from an explosion are

known to injure people. A method has been developed by TNO101, to calculate at which

overpressure a glass window of a certain length, width and thickness will fail.

The following relation has been found for the mean breaking strength of ordinary glass under

shock wave load

= . .

fA d

t

20000000 18 0 7

∗

Equation 7-44

Where A = area of the glass in m2

d = thickness of the glass in m

The relation between external static load and tension is strongly governed by membrane effects. If

the bending is sufficiently great, the tension in the corners becomes determining.

= . f

P a

dt

st0 225 2

2

∗ ∗

Equation 7-45

Where a = smallest dimension in m

Pst = yielding load in Pa

This formula can only be used if the bending, B, with respect to the thickness d has a certain

critical value. This value is depended on the length/width ratio b/a (b>a).

101Mercx W.P.M.,De uitwerking van explosie-effekten op constructies, PML 1988-C-74, Juni 1988.



5.1

6 =

∗

a

b

d

B

crit

Equation 7-46

The value for B / d follows from

= -B

dP a

b

dst706 10 15 3

4∗ ∗ ∗ ∗

Equation 7-47

If condition is not met a correction factor, n, has to be used

∗

d

B

d

Bn

crit

- 9

1 + 1 =

Equation 7-48

The expression for the tension then becomes

= . f

n P a

dt

st∗ ∗ ∗0 225 2

2

Equation 7-49

Using these formulas the yielding load can be determined for normal glass.

A more generalised probit function (see section 2.3.4) for window breakage is

Pr = -11.97 + 2.12 ln Ps For older buildings

Pr = -16.58 + 2.53 ln Ps For newer buildings

where Pr is the probit value and Ps the overpressure in Pa. (not the reflected overpressure Prefl which is for a vertical plane in the pressure wave 2 ∗ Ps).

7.4.2. Damage to Buildings

The TNO green book gives a correlation for the overpressure and the damage to brick buildings

like houses based on the work by Jarret102. The results are presented as a number of Probit

functions for various levels of damage

Light damage, defined as windows broken, displaced doors, damage to the roof

Pr = 5 - 0.26 ln V

0.59.3

1104600

+

=

ss IPV

Equation 7-50

where Pr is the probit value and Ps the overpressure in Pascal. (not the reflected overpressure Prefl which is for a vertical plane in the pressure wave 2 ∗ Ps). Is is the impulse in Pa s

Structural damage, defined as the above plus cracks in the walls and some walls collapsed

Pr = 5 - 0.26 ln V

3.94.8

29017500

+

=

ss IPV

Equation 7-51

Collapse, the damage is the extensive that the building has collapsed

Pr = 5 - 0.22 ln V

3.114.7

46040000

+

=

ss IPV

Equation 7-52

102 D.E. Jarret, Derivation of the British explosives safety distances. Annuals of the New York Academy of Sciences, vol . 152 (1968).



7.5. Other Vapour Cloud Explosion Packages

7.5.1. VEXDAM - For Modelling Effects of Shielding

Calculations to obtain accurate predictions of blast loading in a situation where structures are

shielded are quite complex. A moderately simple code exists which treats the problem as one of

several sources and sinks in potential flow theory. The code is called VEXDAM and has been

found to be quite acceptable as an aid to engineering concept design. Further details are available

through Software Support.

7.5.2. EXSIM - CFD

Computational fluid dynamics (CFD) can be used for explosion overpressure prediction. Such

packages aim to model the explosion process through the numerical solution of the equations for

the turbulent flow and combustion on a three-dimensional grid. Such a code is the EXSIM CFD

code. EXSIM is the ideal tool for critical assessments which require detailed explosion hazard

modelling using the latest combustion science, and further details are available through Software

Support.



8. Additional References

Acton, MR, and Evans, JA (1997) “Horizontal jet fires of oil and gas”, report to the Blast and Fire

Engineering Project for Topside Structures Phase II, Steel Construction Institute.

Baughn, JW, and Shimizu, S, (1989), “Heat transfer measurements from surface with uniform heat

flux and impinging jet”, Int. J. Heat and Mass Transfer, Vol. 111, pp 1096-1098.

Birch, AD, Brown, DR, Cook, DK, and Hargrave, GK (1988). "Flame stability in under expanded

natural gas jets", Comb. Sci. and Tech., Vol. 58.

Bowen, PJ, and Shirvill, LC (1994). "Combustion hazards posed by the pressurised atomisation of

high-flashpoint liquids", J.Loss Prev. Process Ind., Vol. 7, No. 3.

Bray, KNC. (1990) Studies of the turbulent burning velocity. Proc.R.Soc.London A431, 315

Catlin, CA (1991). "Scale effects on the external combustion of offshore modules caused by

venting of a confined explosion", Comb. Flame, Vol. 83.

Chamberlain, GA (1987). "Developments in design methods for predicting thermal radiation from

flares", Chem.Eng.Res.Des. Vol. 65.

Chamberlain, GA (1994). "An Experimental study of large scale compartment fires", Trans.

IChemE, Vol. 72, Part B.

Chamberlain, GA (1995). "An Experimental study of water deluge on compartment fires",

International Conference on Modelling and Mitigating the Consequences of Accidental Releases

of Hazardous Materials, AIChE, New Orleans.

Chamberlain, GA (1996). "The hazards posed by pool fires in offshore platforms", Trans.

IChemE., Vol. 74, Part B.

Chamberlain, GA, Persaud, MA, Wighus, R, and Drangsholt, G, (1997), “Blast and Fire

Engineering for Topside Structures. Test Programme F3, confined jet and pool fires. Final

Report”, Steel Construction Institute.

Cates, AT (1991). "Fuel gas explosion guidelines", Intl. Conf. on Fire and Explosion Hazards,

Moreton-in-the-Marsh, Inst. Energy.

Caulfield, M, Cook, DK, Docherty, P, and Fairweather, M (1993). "An integral model of turbulent

jets in a cross flow. Part 2 - fires", Trans. IChemE, Vol. 71.

Cotgreave, T (1993), “Long-term durability studies at Shell’s Holyhead maritime test site”, NACE

Technical Seminar, Aberdeen, 23-29 Oct.

Cracknell, RF, and Chamberlain, GA (1997) “Interpretation of experimental data for unconfined

crude oil jet fires”, report to the Blast and Fire Engineering Project for Topside Structures Phase II,

Steel Construction Institute.

Cracknell, RF, Davenport, N, and Carsley, AJ (1995). "A model for heat flux on a cylindrical

target due to the impingement of a large-scale natural gas flame", 2nd European Conf. on Major

Hazards Onshore and Offshore, IChemE, Oct.

Considine, M (1984). "Thermal radiation hazard ranges from large hydrocarbon pool fires", Safety

and Reliability Directorate Report SRD R297, UKAEA.

Coulson, JM, Richardson, JF, Backhurst, JR, and Harker, JH (1990). "Chemical Engineering, Vol.

1 Fluid Flow, Heat Transfer and Mass Transfer", 4th edition, Pergamon, Oxford.

Cowley, LT, and Pritchard, MJ (1990). "Large scale natural gas and LPG jet fires and thermal

impact on structures", Gastech 90, 14th International LNG/LPG Conference, Amsterdam.

Davenport, N (1994a). "Large scale natural gas/butane mixed fuel jet fires. Final report to the

European Commission", Shell Research report no. TNER.94.030.



Davenport, N (1994b). " "Large scale natural gas/kerosene mixed fuel jet fires. Final report to the

American Petroleum Inst.", Shell Research report no. TNER.94.061.

Gouldin, PC (1987). "An application of fractals to modelling premixed turbulent flames", Comb.

and Flame, Vol. 68.

Harrison, AJ, and Eyre, JA (1987). "External explosions as a result of explosion venting", Comb.

Sci. and Tech., Vol. 52.

Haque, MA, Richardson, SM, and Saville, G (1992). "Blowdown of pressure vessels - 1. Computer

Model", Trans. IChemE, part B, Proc. Safety Environ. Protection, Vol. 70.

Hirst, WJS (1986). "Combustion of large scale jet releases of pressurised liquid propane",

Proceedings 3rd Symposium on Heavy Gas Risk Assessment III, D.Reidel Publishing Co.,

Netherlands.

Hunt, RJ, Shirvill, LC, and Earles, GA (1997) "Design and application of passive fire protection

for the deck of the Mars tension leg platform", Offshore Technology Conference, Houston.

Imrie, BW (1973). "Compressible Fluid Flow", Butterworths, London.

Interim Jet Fire Test for Determining the Effectiveness of Passive Fire Protection Materials,

(1993), Offshore Technology Report OTO 93-028, UK HSE.

Johnson, AD, Brightwell, HM, and Carsley, AJ (1994), "A model for predicting the thermal

radiation hazard from large scale horizontally released natural gas jet fires", Trans. IChemE., Vol.

72, Part B.

Johnson, AD, Ebbinghaus, A, Imanari, T, Lennon, SP, and Marie, N (1997). "Large-scale free and

impinging turbulent jet flames - numerical modelling and experiments", IChemE Symp. Series

141, Hazards XIII, UMIST, Manchester.

Johnson, A.S, (1992), “A Model for predicting thermal radiation hazards from large-scale LNG

pool fires” presented at (a) I.Chem.E. symposium Major Hazards - Onshore and Offshore, UMIST,

Manchester 20-21 October 1992; (b) Inst. Chem Eng. Symp.Ser., 1992, v13, p507-57

Johnson, DM, and Shale, GA (1995). "Research on the mitigation of explosions on offshore oil

and gas Platforms", International Conference on Modelling and Mitigating the Consequences of

Accidental Releases of Hazardous Materials, AIChE, New Orleans.

Johnson, DM, Shale, GA, Lowesmith, BJ, and Campbell, D (1997), “Blast and Fire Engineering

for Topside Structures, Phase 2: Final Report on the explosion test programme”, Steel

Construction Institute.

Johnson, DW, and Woodward,JL, (1999) In RELEASE A model with data to predict aerosol

rainout in accidental releases. Center for Chemical Process Safety of the AICHE.

Kalghatgi, GT (1981). "Blow-out stability of gaseous jet diffusion flames. Part 1: Still air", Comb.

Sci. and Tech., Vol. 26.

Leung, JC (1990). "Two-phase flow discharge in nozzles and pipes - a unified approach", J. Loss

Prev. Proc. Ind., Vol. 3, 27.

Lord Cullen (1990), “The Public Inquiry into the Piper Alpha Disaster”, Den (HMSO), Nov.

McCaffrey, BJ, and Evans, DD (1986). "Very large methane jet diffusion flames", 21st

Symposium (International) on Combustion, The Combustion Institute.

Persaud, MA, Chamberlain, GA, and Cuinier, C (1997). "A model for predicting the hazards from

large scale compartment jet fires", IChemE Symp. Series 141, Hazards XIII, UMIST, Manchester.

Persaud, MA, Wighus, R, and Chamberlain, GA (1997), “Blast and Fire Engineering for Topside

Structures. Test Programme F3, confined jet and pool fires. Interpretation Report”, Steel

Construction Institute.



Puttock, JS, Cresswell, TM, Marks, PR, Samuels, B, and Prothero, A (1995). "Explosion

assessment in confined vented geometries. SOLVEX large-scale explosion tests and SCOPE model

development", Shell Research report to UKHSE, OTO 96 004.

Puttock, JS (1995). "Fuel gas explosion guidelines - The Congestion Assessment Method", 2nd

European Conf. on Major Hazards Onshore and Offshore, IChemE, Manchester.

Pritchard, MJ, and Binding, TM (1992). "FIRE2: A new approach for predicting thermal radiation

levels from hydrocarbon pool fires", IChemE Symposium Series No. 130.

Samuels, B (1993). "Explosion hazard assessment of offshore modules using 1/12 scale models",

Trans. IChemE, Vol. 71, Part B.

Sekulin, AJ, and Acton, MR (1995). "Large scale experiments to study horizontal jet fires of

mixtures of natural gas and butane", British Gas report to CEC, GRC R0367.

Shield, SR (1993). "A model to predict the radiant heat transfer and blast hazards from LPG

BLEVEs", AIChE Symp. Series, Vol. 89.

Shirvill, LC (1992), “Performance of passive fire protection in jet fires”, Major Hazards Onshore

and Offshore, I.Chem.E Series No. 130, Manchester.

Shirvill, LC (1993), “Using composite materials to protect vulnerable equipment against jet fires”,

First International Workshop on Composite Materials for Offshore Operations, Houston, 26-28

Oct.

Shirvill, LC, and White, GC (1994). "Effectiveness of deluge systems in protecting plant and

equipment impacted by high velocity natural gas jet fires", International Symposium on Heat and

Mass Transfer in Chemical Process Industry Accidents, Rome.

Shirvill, LC, and White, GC (1995). “Fire testing - A review of past, current and future methods”,

OMAE Conference, Copenhagen.

Schneider, ME, and Kent, LA (1989). "Measurements of gas velocities and temperatures in a large

open pool fire", Fire Technology, Feb.

Taylor, PH, and Hirst, WJS (1988). "The scaling of vapour cloud explosions: a fractal model for

size and fuel type", 22nd Intl. Symp. on Combustion, Poster paper.

TNO (1992). "TNO Yellow Book", 2nd edition, Chapter 2.

Welker. J.R., 1997, “Radient Heating from LNG fires”, AGA report IS-3-1, Section F.

Wighus, R, Meland, O, and Vembe, B (1991). "Smoke hazard in offshore platform fires", SINTEF

Report STF25 A91007.

Wighus, R (1991). "Active fire protection: extinction of enclosed gas fires with water sprays",

SINTEF Report STF25 A91028.

Wighus, R, and Shirvill, LC (1992), “A test method for jet fire exposure”, 7th International

Symposium on Loss Prevention and Safety Promotion in the Process Industries, Taormina.

Witlox, W. M. H. and Bowen, P. J. (2002), “Flashing liquid jets and two-phase dispersion”. In

Contract Research Report 403/2002. U. K. Health and Safety Executive.

fred 5.1 technical guide

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