discovery.ucl.ac.uk · abstract this thesis presents the development of a number of mathematical...

Modelling the Transient Thermal Response of

Pressurised Vessels during Blowdown under Fire

Attack

A thesis submitted to the University of London for the degree of

Doctor of Philosophy

By

GBOYEGA BISHOP O YEW ALE FALOPE

Department of Chemical Engineering

University College London

Torrington Place London WCIE 7JE

November 2002

ProQuest Number: U642716

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ABSTRACT

This thesis presents the development o f a number of mathematical models for

simulating the transient response of pressurised vessels containing condensable

hydrocarbon mixtures during vapour space blowdown under fire attack. This is

followed by the quantitative evaluation o f the consequent failure risks associated with

such operations.

Accounting for non-equilibrium effects between the constituent fluid phases, the

models simulate the multi-dimensional transient thermal and pressure stress profiles

generated in both the wetted and unwetted wall sections o f different geometry vessels.

A comparison o f this information with the vessel material o f construction yield and

ultimate tensile stress data at the prevailing conditions, allows an evaluation o f the

risk of failure and, if applicable, the rupture mode during depressurisation.

The study considers cylindrical as well as spherical vessels, as their different spatial

3-D structures result in different stress containment capabilities. Two types of fire

scenarios involving total engulfinent by a pool fire as well as high heat intensity

localised jet fire attack are modelled.

A major part o f the study involves the application o f the above models to hypothetical

failure scenarios involving blowdown of condensable multi-component hydrocarbon

mixtures. For example the blowdown under fire attack o f a cylindrical and a spherical

vessel with the same volume, initial pressure and equivalent orifice diameter of 3.02

m^, 116 bara and 10mm reveals that in both cases failure (plastic deformation) occurs

at approximately the same time. In each case failure occurs in the vapour space due to

the mechanical weakening of the vessel wall combined with the total thermal and

pressure stresses. This is in contrast to the blowdown of the same vessels under

ambient conditions where rupture due to low temperature induced ductile/brittle

transition may occur in the wetted wall section.

In the case of localised jet fire attack on the other hand the effect o f the jet flux heating

is to expose the vessel to severe thermal stresses, which far exceed the accompanying

pressure stresses. Failure in this case is signified by the total stresses being in excess of

the ultimate tensile strength o f the vessel wall material.

Finally, the importance o f accounting for real fluid behaviour at the discharge orifice

when modelling the characteristic dimensions and heat intensity of jet fires are

highlighted. This is considered to be important since the most likely fate o f the

released inventory during blowdown is its instantaneous ignition thereby resulting in a

jet fire. Application o f a real fluid model based on homogenous equilibrium flow to

the Chamberlain's [1987] empirical je t fire correlations produces good agreement with

the published field data. The salient manifestations o f real fluid behaviour such as

two-phase flow on jet fire characteristics on the other hand are demonstrated by

simulating a hypothetical jet fire formed during the blowdown o f the 116 bara

spherical vessel under fire attack.

DEDICATION

... to my very dear parents.

For everything...

ACKNOWLEDGEMENTS

I would like to express my profound gratitude to the following people and

organisations.

For the financial support received for this work: My parents, UCL fiiends scholarship

programme, UCL old students’ scholarship award, Dr Haroun Mahgerefteh, and the

Department of Chemical Engineering, UCL.

My supervisor Dr Haroun Mahgerefteh: for his endless support and guidance

throughout the duration o f this work. A PhD is indeed “a different kettle o f fish”!

My colleagues with whom I shared the same office - Ade, Sayeh and Dr Gerazounis,

for making everyday a little more pleasant and being true friends.

Members o f the office and technical staff of the department o f Chemical Engineering,

UCL especially Pat Markey, Anna Harrington, Martin Vale and Mark Spurgeon.

All members of staff, Arcadia University, centre for study abroad, most especially

Sharon Harvey: for giving me the opportunity to serve as the warden in Thoresby

house and for the free accommodation that came with it.

Olumide Elesin: for the 9 months you gave me your studio flat to live in. Thank you.

Wanyeki Maihiafii: for your profound words, listening ear and prayers. Thank you.

Ed S hep ley - glad to squeeze you in! Thanks for all you’ve done and are yet to do!

Finally to the most important person in my life, my dearest Titilope - my best friend

and now also my wife; for everything, for everyday, for every dream we share. Now

you have my undivided attention, both now and always.

Most importantly, to God the Almighty creator and my inspiration. You are a good

God and I am eternally grateful for everything.

LIST OF CONTENTS

ABSTRACT........................................................................................................................1

DEDICATION.................................................................................................... 3

ACKNOWLEDGEMENTS.............................................................................................4

CHAPTER 1

INTRODUCTION.............................................................................................................9

CHAPTER 2

THE BLOWDOWN UNDER FIRE PHENOMENON.............................................15

2.1 INTRODUCTION.................................................................................................. 15

2.2 DEPRESSURISATION M O D E.......................................................................... 16

2.3 FIRE SCENARIOS................................................................................................16

2.4 HEAT CONDUCTION ACROSS VESSEL W ALL........................................20

2.5 WALL RESIDENT STRESSES..........................................................................20

2.6 EFFECT OF THERMAL IMPACT - FAILURE MECHANISMS AND

THEIR CONSEQUENCES................................................................................... 22

2.7 HEAT TRANSFER BETWEEN VESSEL WALL AND VAPOUR SPACE 24

2.8 HEAT TRANSFER BETWEEN VESSEL WALL AND LIQUID SPACE .. 30

2.9 HEAT AND MASS TRANSFER BETWEEN VAPOUR AND LIQUID

PHASES.................................................................................................................... 36

2.10 FLOW THROUGH THE RELIEF VALVE................... 37

CHAPTER 3

LITERATURE REVIEW.............................................................................................. 39

3.1 INTRODUCTION................................................ 39

3.2 API RECOMMENDED PRACTICE [API RP 520, 1990].. :.......................... 41

3.3 SPLIT FLUID MODEL [OVERA ET AL., 1994]............................................ 44

3.4 HEATUP [B e y n o n e t a l ., 1988]......................................................................... 53

3.4.1 Basis for HEATUP Mathematical M odel................................................... 53

3.5 THE ‘ENGULF’ COMPUTER PROGRAM - ENGULF I

[Hunt AND Ramskill, 1985] & ENGULF II [Ramskill, 1988].....................62

3.5.1 Engulf I [Hunt and Ramskill, 1985]........................................................... 62

3.5.2 Engulf II [Ramskill, 1988].......................................................................... 70

3.6 THE TCTCM MODEL [BiRK, 1988].................................................................. 75

3.7 PLGS-1 AND PLGS-2D M o d e l s [A y d e m ir et a l ., 1988 a n d

H a d j is o p h o c l e o u s , 1989].................................................................................... 81

3.7.1 PLGS-1 Model [Aydemir et al., 1988]....................................................... 81

3.7.2 PLGS-2D Model [Hadjisophocleous, 1989]............................................. 89

3.8 CONCLUSION....................................................................................................... 89

CH A PTER 4

M ODELLING THE TRANSIENT RESPONSE OF PRESSURISED

CYLINDRICAL VESSELS DURING BLOW DOW N UNDER ENGULFING FIRE

A TTA CK ............................................................................................................................... 92

4.1 INTRODUCTION...................................................................................................92

4.2 MODEL DEVELOPMENT.................................................................................. 93

4.2.1 Energy Conservation Equation...................................................................94

4.2.2 Material Conservation Equation.................................................................99

4.2.3 Solution procedure - Application o f Finite Difference M ethod 102

4.3 THERMODYNAMIC TRAJECTORIES FOR FLUID PHASES.................102

4.3.1 Vapour Phase Thermodynamic Trajectory..............................................103

4.3.2 Liquid Phase Thermodynamic Trajectory................................................ 105

4.4 VESSEL WALL ANALYSIS.............................................................................. 106

4.4.1 Heat Conduction Across Vessel W all.......................................................106

4.4.2 Calculation of Pressure and Thennal Stresses ...i............... ................... 112

4.4.3 Heat Transfer Between Vessel Wall and Vapour Phase...................... 114

4.4.4 Heat Transfer between Vessel Wall and Liquid Phase............................121

4.5 DISCHARGE CALCULATION.........................................................................128

4.5.1 Ideal Gas M ethod..........................................................................................131

4.5.2 Real Fluid Method........................................................................................ 133

4.6 MATHEMATICAL ALGORITHMS.................................................................136

4.6.1 Mathematical Algorithm for Discharge Calculation................................136

4.6.2 Mathematical Algorithm for Blowdown Calculation..............................139

4.6.3 Single Phase Discharge Algorithm; Figure 4.5b...................................... 142

4.6.4 Two-Phase Algorithm; Figure 4.5c............................................................145

4.7 RESULTS AND DISCUSSION.........................................................................150

4.8 CONCLUSION.....................................................................................................166

CH A PTER 5

M ODELLING TH E TRANSIENT RESPONSE OF SPHERICAL VESSELS

DURING BLOW DOW N UNDER ENGULFING FIRE A TTA CK ..................... 168

5.1 INTRODUCTION.................................................................................................168

5.2 MODEL DEVELOPMENT - WALL ANALYSIS.........................................169

5.2.1 Heat Conduction Across a Spherical Vessel Exposed to External

Heat F lux........................................................................................................ 169

5.2.2 Thermal and Pressure Stresses Across Vessel W all................................172

5.2.3 Heat Transfer, Thermodynamics and Fluid F low ....................................173

5.3 RESULTS AND DISCUSSION........................................................................ 174

5.4 CONCLUSION.............................................. 187

CH A PTER 6

M ODELLING DUCTILE FAILURE PROPAGATION DURING BLOW DOW N

UNDER LOCALISED JE T FIRE A TTA CK .............................................................189

6.1 INTRODUCTION................................... 189

6.2 MODEL DEVELOPMENT................................................................................ 190

6.2.1 Vessel Wall Analysis...................................................................................190

6.3 RESULTS AND DISCUSSION......................................................................... 194

6.3.1 Effect o f Material of Construction.............................................................198

6.4 CONCLUSION..................................................................................................... 209

CHAPTER 7

TWO PHASE RELEASE JET-FIRE MODEL DEVELOPMENT.................... 211

7.1 INTRODUCTION................................................................................................. 211

7.2 REVIEW OF EXISTING CORRELATIONS FOR PREDICTING

JET FIRE SIZE AND CHARACTERISTICS.................................................. 212

7.2.1 Simple Jet Fire Models................................................................................212

7.2.2 More Rigorous M odels...............................................................................218

7.3 TWO PHASE JET FIRE MODEL DEVELOPMENT................................... 227

7.4 MODEL RESULTS AND VALIDATION.......................................................229

7.5 CONCLUSION.....................................................................................................242

CHAPTER 8

CONCLUSIONS AND RECOMMENDATION FOR FUTURE WORK 244

8.1 CONCLUSIONS................................................................................................... 244

8.2 RECOMMENDATION FOR FUTURE WORK.............................................. 250

8.2.1 Failure at the wall vapour-liquid interface................................................250

8.2.2 Temperature Stratification..........................................................................250

8.2.3 Two or three dimensional temperature profile during local

impingement.................................................................................................. 251

8.2.4 Accounting for vessel wall heat loss at elevated temperatures due to

back-radiation................................................................................................ 251

8.2.5 More detailed analysis o f failure criteria and its consequences.............251

8.2.6 Effect o f Vessel Wall Thickness................................................................ 252

R EFER EN C ES.................................................................................................................. 253

Chapter 1 Introduction

CHAPTER 1

INTRODUCTION

The considerable increase in the use o f pressure-liquefied fuels in the oil and gas

industries over the past two decades has resulted in the commensurate rise in the

quantities o f such materials being stored or transported. The above pose the combined

risks associated with high pressures as well as storage or handling o f large quantities

o f flammable inventory. Indeed, a relatively large number o f accidents involving

storage tanks and transport containers have been reported in the recent years with

some having resulted in many fatalities and extensive damage to the environment. The

San Juan incident in 1984 is probably the most severe example o f a fire involving

liquefied petroleum gas [Pietersen, 1988]. In that accident, over 500 deaths and 7,000

serious injuries occurred with the facility being almost totally destroyed.

Blowdown, or the rapid depressurisation o f vessels, is often a common way of

reducing the consequences associated with the above risks in an emergency situation.

Blowdown under non-fire conditions posses the threat o f vessel failure arising from

the dramatic temperature drops resulting from the relatively rapid quasi-adiabatic

expansion process [Haque et al. 1992a; Mahgerefteh and Wong, 1999] o f the

pressurised inventory. Should the wall temperature fall below the ductile-brittle

transition temperature o f the vessel wall material, rupture is likely to occur. This poses

an important question as to what the optimum depressurisation rate should be in order

to allow the fastest possible evacuation rate without running the risk o f vessel rupture.

The modelling of blowdown is especially complex, requiring detailed consideration of

several competing and often interacting heat transfer, mass transfer and

thermodynamic processes. In recent years, several models simulating the

depressurisation process have been proposed. By far the most comprehensive

blowdown model to date accounting for most of the important processes taking place

during blowdown was reported by Haque et al., [1992a], However, though extensively

validated against experimental data, the simulation mainly deals with blowdown


under ambient surroundings. The fact that the most common hazard in the oil and gas

industries is a fire [Lees, 1990], a highly plausible and indeed, most catastrophic

blowdown scenario should involve depressurisation under fire attack. The

combination of the external impinging heat load and the resulting fluid expansion

induced internal temperature drop introduces severe temperature stress gradients

across the vessel wall. Apart from the above, any such modelling must also take

account o f the accompanying multi-dimensional pressure stresses due to the

pressurised inventory as well as the thermal weakening o f the vessel wall.

The capability to quantitatively model the risks associated with blowdown under fire

attack as opposed to conducting expensive experimental procedures clearly represents

significant cost savings. Furthermore, such modelling is particularly timely

considering the fact that environmental groups in the US are currently pressing for

legislation to allow citizens to file lawsuits against high-pressure pipelines that pose

‘imminent and substantial endangerment to health or the environment’ [Barlas, 1999].

In the event o f its success, it is only a matter of time before the same legislation is

extended to hydrocarbon storage vessels particularly since these are frequently used

for storage o f domestic fuel gases in populated areas.

Although extensive experimental studies have been carried out to investigate the

effect o f fire impingement on vessels fitted with oscillating pressure relief valves

(PRV), unfortunately no data during blowdown o f such vessels exists. PRV’s operate

in a cyclical manner via pressure relief each occasion the safe working pressure is

exceeded. In contrast, blowdown is intended to ensure depressurisation to ambient

conditions as any further pressure rise during the prevailing hazardous conditions is

undesirable.

The vessel response for both oscillating PRVs and blowdown valves is very similar,

the main difference being the oscillating internal pressure for the former, as opposed

to the latter where pressure oscillations are rare. Also, for oscillating PRV, while the

boiling liquid and hence the vapour pressure controls the PRV action, for blowdown,

the valve opening at the high pressure is what induces the boiling in the first place.

The heat from the impinging fire further supports this pressure-induced boiling. As a

0


result more rigorous boiling will be expected during blowdown and hence intense

bulk liquid mixing would be achieved more rapidly. Though this differing behaviour

may have a considerable effect on rupture times, similar vessel-fluid interaction is

expected. Hence, in this work, the results of experiments with PRV operated venting

are used as a basis for which the modelling of blowdown is developed.

A number o f models for determining the response o f pressure vessels to impinging

fires have been reported with varying degrees o f sophistication. Apart from the

general empirically based guidelines provided by American Petroleum Institute [API

521, 1990], more vigorous modelling relating to the simulation o f pressure relief

valve depressurisation under some fire scenarios has also been reported (see for

example, Hunt and Ramskill, [1985], Ramskill, [1988], Birk [1988], Beynon et al.,

[1988], Aydemir et al., 1988], Sumathipala et al., [1992], Overa et al., [1994], and

Kielec and Birk [1997]).

While some models do not consider wall temperature gradients [Split Fluid blowdown

model - Overa et al., 1994], others fail to account for the rupture inducing thermal

and pressure stress gradients [see for example ENGULF I - Hunt and Ramskill, 1985;

ENGULF II - Ramskill, 1988; HEATUP model - Beynon et al., 1988].

The TCTCM computer model [Birk, 1988] successfully predicts the tank internal

pressure, the mean fluid temperatures and wall temperature distribution of a long

cylindrical tank exposed to an engulfing and torch type fires. Little detail on the

formulation o f the wall triaxial pressure and thermal stresses is however given, and

hence the co-ordinate stress component responsible for rupture is unknown.

Other reported models are PLGS-1 and PLGS-2D [Sumathipala et al., 1992] which

were validated by results obtained from small-scale experiments by Venart et al.

[1988] and Sumathipala et al. [1988] as well as data obtained by the UK Health and

Safety Executive [Moodie et al., 1988]. Both models predict lading mass, vessel

internal pressure as well as fluid and vessel wall temperature variations with time.

Kielec and Birk [1997] propose a correlation to simulate the relationship between

failure severity and the tank condition at failure. The model is however limited in its

11


scope as it ignores the contributing effect o f thermal stresses and attributes the

parameters effecting rupture to the extent o f deformation prior to failure and the

transient pressure history.

With the failure mechanism ultimately leading to failure usually being a creep or

ductile-failure process [Venart 2000], a more thorough analysis would be to consider

the stress distribution within the vessel wall in order to predict the time, mode and

hence the consequence o f vessel rupture.

The aim o f the present study is to develop a mathematical model to simulate the

blowdown o f pressurised vessels containing a two-phase hydrocarbon under fire

attack and to evaluate the consequent risks associated with such an operation. The PR

[Peng & Robinson, 1976] equation of state is used for thermodynamic property

predictions o f the expanding inventory. Total engulfing pool fire as well as partial jet

fire impingement are to be simulated. A constant external heat flux is however

assumed to impinge on the vessel in both cases, however.

Two types o f failures are identified. These include plastic deformation and rupture.

The former refers to failure resulting when the total stresses exceed the yield stress of

the vessel material resulting in inelastic or permanent material deformation. Rupture

on the other hand refers to failure resulting from total stresses in excess o f the vessel

material’s ultimate tensile strength resulting in material ‘tearing’. As the response of

the vessel wall to the combined thermal and pressure environment is critical in

determining the possible failure characteristics, a rigorous analytical method of

solution is used to obtain the wall temperature profiles from which the resulting

thermal stresses are determined. The pressure profile along the vessel wall is also

obtained in the radial, tangential and longitudinal directions.

The important parameters accounted for in the model include:

• Non-equilibrium effects between the liquid and vapour phase

• Orifice two-phase discharge

• Fluid non-ideality

12


• Heat transfer between vessel wall and fluid

• Total and partial fire engulfinent

• Vessel geometry; cylindrical and spherical vessel

• The wall temperature gradient

• Transient pressure and thermal stresses

Typical results o f the simulation include

• Variation o f the fluid (vapour and liquid) and wall (wetted and dry)

temperatures with time

• Pressure and inventory variations with time

• Tri-axial pressure and thermal stress variation with time

• Time and mode o f vessel failure

• Ductile-brittle propagation rate

• Dominant stresses (pressure or thermal) responsible for vessel failure

• Resulting jet fire characteristics following the ignition o f the pressurised

inventory at the release orifice

• Flare size and heat radiation intensity following the ignition of the released

inventory

The thesis is divided into eight chapters.

In chapter 2, a description of the main processes involved during blowdown under fire

is explained based on published experimental observations.

Chapter 3 presents a comprehensive review of published models in the open literature

for pressure relief venting and blowdown under fire impingement.

Chapter 4 and 5 respectively describe the development o f a mathematical model for

simulating vapour space blowdown of cylindrical and spherical vessels under

engulfing fire attack.

13


Chapter 6 extends the modelling work in Chapter 4 to account for localised high

intensity jet fire torching.

Chapter 7 presents the development of a fire model simulating the release and

instantaneous ignition o f pressurised hydrocarbon inventory. A brief literature survey

o f the pertinent empirical fire models is first presented. The results from these form

the basis for the development o f a jet fire model applicable to single or two-phase

releases, which is validated by comparison with available field data.

Chapter 8 is a general conclusion o f this study as well as recommendations for future

work.

14

Chapter 2 The blowdown under fire phenomenon

CHAPTER 2

THE BLOWDOWN UNDER FIRE PHENOMENON

2.1 INTRODUCTION

This chapter represents a review o f some o f the pertinent experimental studies

conducted in the past three decades, which elucidate the important processes taking

place during the blowdown o f hydrocarbon containing vessels under fire attack. These

findings form the basis of the modelling work presented in chapter 4.

In 1985, The Health and Safety Executive in association with British Gas and Shell

Research conducted trials to experimentally assess the fire engulfinent behaviour of a

5 tonne LPG vessel [Moodie et al., 1988]. Five tests were conducted using an

extensively instrumented vessel filled with commercial propane in the range 22-72%

volume fill capacity. Data were collected at a frequency of 1 Hz from 128 analogue

instrumentation channels. Measurements included lading, wall and fire temperatures,

liquid and vapour pressure, wind speed and direction, heat intensity and tank mass.

Prior to this however, a series o f fire engulfinent tests had been carried out on

uninsulated 1/4 and 1 tonne LPG tanks [Moodie et al., 1985]. These vessels were also

instrumented with thermocouples both internally and externally, pressure transducers

and in some cases were supported on load cells. Data was obtained on heat transfer

rates to the total system and tank contents, the boiling regime, average wall

temperature, PRV discharge rates and tank failures.

In addition, the Fire Science Centre of the University o f New Brunswick, Canada

provides detailed experimental observations on a small-scale (40 litre) tank [Venart et

al., 1988]. Radiant electric heaters strapped around the test cylinder, by which the

intensity and distribution could be varied, simulate external accidental fire exposure.

Visual observation was made possible by fitting the vessel wall with 25-mm-thick

sheet acrylic windows. Automatically recorded measurements include, vessel wall

15


temperature, tank mass, thrust exerted by mass exiting through the PRV and fluid

temperatures.

The following is a study of blowdown under fire attack phenomenon as elucidated by

the above important experiments as well as those that followed in the subsequent

years by other workers.

2.2 DEPRESSURISATION MODE

Pressurised vessels containing hydrocarbon mixtures may be depressurised by placing

a relief valve either at the top (vapour space) or bottom (liquid space). The deciding

mode o f pressure relief and inventory evacuation is dependent on the magnitude o f the

pressure and also ease o f disposal or storage o f the evacuated mixture. Vapour space

depressurisation is considered in this work, as it is the most common in practice due to

the possibility o f the immediate flaring of the vented inventory as opposed to liquid

space blowdown where this mode of disposal represents considerable practical

difficulties. Depressurisation and heat transfer to the relatively volatile hydrocarbon

liquid causes it to boil, while transfer of heat to the gas phase results in superheated

vapour. The blowdown valve, modelled as an orifice, prevents possible pressure rise.

Single or two-phase fluid can be discharged depending on the fluid state upstream of

the orifice.

2.3 FIRE SCENARIOS

A potential hazard in Liquefied Petroleum Gas (LPG) storage and transportation is the

impingement o f vessels, pipework and supporting structure by a pool or jet fire. As

pointed out by Birk [1995], fire heat transfer to a tank is very case-specific. Also as

stated by Overa et al. [1994], “there is no standard fire”. The specification of a single

heat flux depending on the fuel and type of fire has therefore been resorted to by a

number o f authors.

The heat flux from a fire depends on many variables such as fuel type, wind

16


conditions, the size o f the fire and the degree o f enclosure. Heat is transferred to the

vessel wall by thermal radiation and convection, the balance between the two

depending on the scale o f the fire, the fiiel type and whether the fire impinges the

vessel as a pool or high momentum jet. A jet fire source may be a gaseous discharge

jfrom a relief valve, or a pressurised liquid or flashing two-phase discharge from the

leakage or rupture o f a liquid line. A pool fire source on the other hand can be from an

ignited spillage o f flammable liquids.

Typical heat transfer rates to cool surfaces from pool fires vary widely from fuel to

fuel [Moorehouse and Pritchard, 1982]. LNG pool fires have higher heat fluxes than

aviation fuels such as JP4 when burning in large pools. For pools larger than 1 m in

diameter, JP-type fuels generally give heat fluxes o f 70-100 kW/m^ [Moorehouse and

Pritchard, 1982] and based on the work by Keltner et al. [1990] these heat fluxes may

be expected to reach effective flame temperatures of between 700 - 800 °C. Heat

fluxes to engulfed targets may also vary significantly depending on the size and

thermal properties o f the target [Keltner et al. 1990]. When JP fuels are involved, the

maximum wall temperature on a tank engulfed by fire is expected to be just about 700

°C. If the fire is only partially engulfing, less heat will be added to the contents of the

tank, but locally the heating of the tank wall could be the same as if the tank were

completely engulfed. If the fire is due to a local jet fire torching, the heat flux is higher

than a pool fire, leading to even higher wall temperatures and hence shorter time

scales are involved in this type o f scenario. The US department o f transport conducted

severe torch tests from propane jet fires (the analysis was carried out by Birk [1989])

with effective heat transfer coefficients of approximately 180 Wm'^K ' being reported.

With fire temperatures o f 1400 K, heat fluxes o f 230 kWm'^ were possible.

Based on experiments with LNG pool fires, Mizner and Eyre [1982], obtained an

average surface emissive power (SEP) of 153 kW /m l For LPG and kerosene pool

fires, the SEPs obtained were 48 kW/m" and 35 kW/m^ respectively.

Cowley [1989] carried out a series of full-scale experiments on LPG (propane) jet

fires in which the external flame radiation field was determined using radiometer

17


arrays and the SEP o f the nominal flame surface measured along the length of each

flame. Instrumented targets were placed inside some flames to measure directly the

incident total heat flux densities to engulfed objects. The internal heat transfer

measurements revealed an incident heat flux density distribution that varies both

transversely across and with distance along the flame. The complex heat flux density

distribution precluded the use o f a single ‘typical’ heat flux density value for flame

impingement. The value for the maximum incident heat flux density from jet fires,

deduced from a combination o f the direct flux density measurements, flame

temperatures, surface emmissivity and consideration of the internal radiative path

length was taken as 250 kW /m\ This predominated from soot radiation with a minor

convective component.

Moodie et al. [1988] carried out extensive experiments on the behaviour o f a 5 tonne

horizontal cylindrical LPG tank engulfed by kerosene pool fires. Figure 2.1 shows the

fire fluxes measured by immersed calorimeter loops for three of their tests. From the

figure it can be seen that the fire flux histories are remarkably similar with fluxes

peaking at about 85 kW/m^ in spite o f the variability o f the fires and wind conditions

between tests. The flux densities presented here are not corrected for the absorptivity

of the calorimeter loop surfaces. If this is assumed to be 0.8, then the maximum

average flux densities were 105 kW/m^, fully consistent with other measurements

made by the authors. The heat flux range based on experimental data by Overa et al.

[1994] was in the range 90 - 160 kW/m^ for the pool fires considered. This heat flux

was strongly dependent on the selected pool fire flame and ambient air temperature.

Based on reported large-scale fire exposure tests, the authors selected a default flame

temperature o f 1075°C. This gives an initial flux o f 130 kW/m^ when the vessel is in

the temperature range 0 - 50°C.

18

Chapter 2 The blowdown under f ir e phenomenon

0 0 -1

72%esH3

22%

To0)a:

7 0 -38%

60300 600 900

Time, s1200 1500 1600

Figure 2.1 Calorimeter heat fluxes for three fill levels (Moodie et al., 1988]

19


The fire impingement results in the heating of the tank wall and its contents. The latter

results in energy storage in the tank and consequently a pressure rise. The heating of

the tank wall is a major determining factor for tank failure. However, a tank may fail

even if the bulk o f the contents have not been heated, provided the tank wall has been

weakened sufficiently due to intense local fire impingement. Birk and Cunningham

[1994a] demonstrated this case with tests on 400 L tanks (0.6m diameter, 3 or 6 mm

wall thickness) where a torch fire was applied at the tank top. In some cases, the tanks

failed catastrophically resulting in BLEVEs even though the average liquid

temperature did not rise above the ambient temperature o f 20°C. In a situation where

the fire impingement is on the liquid side o f the vessel, the high heat transfer

coefficient between the heated wall and the liquid is usually capable o f maintaining

the wall temperature at 'safe levels'. Under conditions o f film boiling (i.e. when the

liquid in contact with the wall vaporises forming a thin vapour film), the vessel wall

experiences a ‘dry walT interface and failure can occur.

2.4 HEAT CONDUCTION ACROSS VESSEL WALL

Heat from a fire is conducted through the vessel wall at a rate dependent on the vessel

material’s thermal diffusivity; the ratio of thermal conductivity to the product of

density and specific heat capacity. The heat input from the fire, in conjunction with

the heat removal from the vessel inside results in a temnerature gradient across the

vessel wall The tests reported by Moodie et al., [1985, 1988] presented the inner and

outer wall temperatures, from which the temperature gradient can be inferred.

2.5 WALL RESIDENT STRESSES

Due to the wall temperature gradients and internal vessel pressure, thermal and

pressure stresses co-exist during blowdown under fire attack. Thermal stresses result

from non-uniform heating of a material. A metal expands on the application of heat

and contracts upon its extraction. For example, during blowdown under fire, the

heating on the outside of the wall by the fire causes the outer wall metal to expand.

This coupled with the cooling on the inside wall results in a bending moment referred

20


to as thermal stresses [Popov, 1999]. These may either be compressive (negative

stress value) or tensile (positive stress value) in action and are transient during

blowdown under fire attack. If the heated outside wall o f the cylinder is prevented

from expanding by restraining ends, compressive stresses are induced. Conversely, if

the inside wall is prevented from contracting, tensile stresses are induced. A pipe

heated on the inside and cooled on the outside will result in the reverse.

Pressure stresses exist as a result o f the force exerted by the contained pressure on the

vessel wall. These are the most commonly considered cause for vessel failure under

fire attack and therefore often used for design specification. The tangential stress

(often referred to as the hoop or circumferential stress) is used to determine the safe

vessel wall thickness of pressure vessels. On fire impingement, the pressure stresses

are dictated by the pressure history within the vessel and are accounted for in most of

the models existing in the literature.

In comparison with pressure stresses, thermal stresses are more complex to model. A

detailed analytical solution for the transient thermal stresses in cylindrical and

spherical vessels under various homogeneous boundary conditions was presented by

Russo et al. [1995]. The analytical method of separation of variables was employed,

and using the appropriate equations for stress in hollow cylinders presented by

Timoshenko and Goodier [1987], the triaxial transient thermal stresses were obtained

for nine different boundary conditions.

Taler [1997] also presented a technique for determining the transient temperature

distribution, from which the thermal stresses were obtained, based on recorded

thermocouple temperature responses at several interior locations within a spherical or

cylindrical vessel wall. An analytical solution o f the inverse heat conduction problem

was presented and comparison was made with numerical examples and with

measurements. Good agreement was observed.

An addition of triaxial thermal and pressure stresses give the total resident stresses

within the vessel wall at any point in time during blowdown under fire attack. A

21


comparison between the total stress and the yield and ultimate tensile strength of the

vessel wall material at the prevailing temperature enable an estimation o f the ductile-

failure process. This knowledge further enables a determination o f the direction of

failure within the 3D structure.

Most models in the literature ignore the thermal stress contribution to vessel failure.

For example, in considering the failure hazard associated with blowdown by stress

effects, Overa et al. [1994] used a hoop stress model for predicting the vessel burst

pressure. The same hoop stress model was adopted in the ENGULF models. The

HEATUP [Beynon et al., 1988] and PLGS-1 models [Aydemir et al., 1988] do not

simulate the stress distribution within the vessel wall and hence do not allow the

evaluation o f the risk and mode of failure. The TCTCM computer model [Birk, 1988]

considers the wall temperature distribution, however little detail on the formulation of

the wall triaxial pressure and thermal stresses is given and hence the co-ordinate stress

component responsible for rupture is unknown.

2.6 EFFECT OF THERMAL IMPACT - FAILURE MECHANISMS AND

THEIR CONSEQUENCES

In the experiments by Moodie et al. [1985], the test with the 40% fill provided the

opportunity to study the consequence o f the failure o f the PRV to open subsequently

after its first opening. Hence the vessel pressure and vapour wall temperature rose to

35 bar and 600°C respectively, at which point failure occurred resulting in a fireball

with an estimated diameter o f 21 m and lasting 1-2 seconds. On metallurgical

examination o f the vessel remains, the membrane wall was observed to have deformed

and ruptured along the top (vapour space) of the vessel, presumably where the wall

temperature was highest. By using a thick walled cylindrical theory, which accounts

for rupture due to pressure and material property at elevated temperatures [Nicols,

1971], the burst pressure was determined within an accuracy o f 8% for the 40% fill

and 18% for the other tests.

Based on the tests by Birk and Cunningham [1994a] on a 400 litre propane tank,

22


Kielec and Birk [1997] presented an in-depth analysis o f BLEVE and non-BLEVE

ruptures with the aim of understanding the variation in tank deformation that were

observed. In the analysis, the main parameters effecting thermal rupture were

attributed to the extent of deformation prior to failure and the transient pressure

history during vessel blowdown. According to the author, at elevated temperatures the

wall loses strength, and the pressure would do work on the wall causing it to

plastically deform. The size o f this plastically deformed zone will depend on the hoop

stress, the top wall temperature distribution and the fire exposure duration. If the

plastic work done on the tank wall is not sufficient, and the PRV operates properly,

then the vessel will vent its contents through the PRV and avoid failure. But if the

plastic work done on the tank wall is high enough, a tear will form which could

propagate rapidly along the tank and lead to a very rapid total loss o f containment and

BLEVE (boiling liquid expanding vapour explosion).

Furthermore, during blowdown in an engulfing fire scenario, a result o f the thermal

weakening leading to metal degradation in the dry wall coupled with combined

pressure and thermal stresses has been shown to cause failure [Birk, 1989]. The

thermal weakening originates from the high temperatures in the dry wall due to the

relatively low heat transfer coefficient.

The failure consequence has been shown to depend on the energy stored within the

liquid in the tank [Birk, 1995]. If the tank fails, the vapour is released and the pressure

drops in the vessel causing the liquid to flash. The rapid liquid flashing and the liquid

superheat caused by the pressure drop upon initial failure, could lead to internal vessel

overpressures and BLEVEs. Specifically, higher liquid energies mean a higher chance

o f a BLEVE occurring if the tank fails [Birk and Cunningham, 1994b]. Furthermore,

liquid fill levels have been shown to affect the level o f liquid superheat and failure

consequence [Venart, 2000].

A recent study has shed new light into the mechanism and causes of BLEVEs [Venart,

2000]. The above work highlighted a more specific relationship between the liquid

superheat and the failure mode. The extent of catastrophe was also observed to be

23


related to the difference between the speed of sound in the discharging fluid (liquid,

vapour or two-phase) compared to the speed of crack propagation. In subcooled LPG,

the speed of sound is about 650m/s and that o f the vapour approximately 200m/s.

Furthermore for homogeneous two-phase, the speed o f sound is even less than that of

the vapour. The speed o f sound determines the rate o f pressure discharge (pressure

unloading), and hence implies that for a liquid, the pressure unloads the most rapidly

o f the three. On the other hand, the speed of the ductile crack propagation is o f the

same order as the velocity with which the pressure wave travels in the vapour. Hence

for a two-phase release, the pressure cannot ‘unload’ rapidly at all and any cracks will

propagate to a much greater extent leading to a BLEVE. This complex interplay

between the speed of sound/phase discharge, the ductile-failure propagation rate and

the resulting consequence is primary in determining failure mode and consequence.

The precise relationship requires a more detailed study and is outside the scope o f this

thesis. The contribution o f the liquid superheat is as follows. The liquid swelling

generates two-phase choking at the fissure and discharge valve. This results in a

‘choked unloading’ o f the pressure due to the low speed o f sound within the two-

phase fluid in comparison to the often rapid crack propagation at the rupture point. In

such a situation, a BLEVE will be inevitable. However for a subcooled liquid, vapour

only is discharged as the possible generation o f two-phase flow at the orifice is

eliminated. With pure vapour discharge, the pressure-unloading rate is o f the same

order as the ductile-fracture propagation rate; hence a ‘secondary’ discharge source is

introduced resulting in a less 'risky'jet release.

In this thesis, a mathematical prediction of the stress propagation with time is

presented, from which the failure time can be estimated.

2.7 HEAT TRANSFER BETW EEN VESSEL W ALL AND VAPOUR

SPACE

Heat transfer between the wall and vapour may either be by natural or forced

convection or a combination of both for blowdown under ambient or fire attack.

Reynolds and Kays [1958] experimentally analysed the discharge of a small air tank

24


for a short time (ca. 20s) by measuring the bulk gas temperatures. The authors

developed a method for predicting gas temperatures by assuming that only natural

convection took place in the vessel. The calculated gas temperatures agreed with

measured values.

Byrnes et al., [1964], in their experiments using small hydrogen tanks, also observed

the dominance o f natural convection over forced convection as the main mode o f heat

transfer in the vapour phase. The forced convection results from vapour expansion

within vessel due following valve opening.

Experiments by Haque et al. [1992b] during the blowdown o f nitrogen further indicate

that natural convection induced by temperature gradients was dominant for wall-

vapour heat transfer. Figure 2.2 shows the isotherms and flow pattern obtained by

these authors. Similar observations were also made by Overa et al. [1994] who

measured gas temperatures during blowdown at different elevations along the vessel

and filmed the outside o f the vessel with a heat sensitive film. The authors were able

to map the fluid flow pattern for the vapour space during blowdown. Figure 2.3

illustrates the general pattern and gives very similar results to those o f by Haque et al.

[1992b]; Figure 2.2.

Apart from demonstrating the dominant heat transfer mode in the vapour space, these

figures also highlight the temperature stratifications within the vapour. Overa et al.

[1992] also made the same observation.

25


2 2 0 K !

ID

^ 2 0 0 K ’

195 k)

_ , y

Figure 2.2 Isotherms (left-hand side) and flow pattern (right-hand side)

during blowdown of nitrogen [Haque et al., 1992b].

26


Figure 2.3 Flow pattern of the gas phase in a vertical vessel during blowdown

[Overa et al., 1992]

27


The presence of temperature gradients and the observed isotherms for blowdown

under non-fire conditions are similar to those under fire attack. For example, Venart et

al. [1988] and Sumathipala et al. [1988] observed that from initiation o f uniform

heating, heat transfer to the vapour was initially by free convection leading to

significant temperature gradients due to low fluid motion. Moodie et al. [1988] noted

substantial vertical temperature stratification both before and during the Pressure

Relief Valve (PRY) operation. This is illustrated in figure 2.4 for the 22 % fill test

(22% o f vessel volume filled with liquid). The vapour temperature fell on PRY

opening, but the stratification was maintained. The authors attributed this to poor

vapour space mixing (as also noticed by the same authors during blowdown under

non-fire), and the absence of any significant flashing or frothing o f the tank on a 5

tonne scale. The same observation was made in smaller scale tests [Moodie et al.,

1985]. The temperatures shown in Figure 2.4 increased again after PRY closure, and

indeed after the pool fire was put out. This was because the tank walls remained hot

and continued to transmit heat to the vapour space. The vapour was superheated,

making vapour condensation impossible.

Under fire attack, high vapour wall temperatures imply the existence o f heat transfer

by radiation alongside convective between wall and vapour [Moodie et al., 1988]. The

peak dry wall temperatures as a function o f time for different % fill tests shown in

Figure 2.5 demonstrate this. Overa et al. [1994] attributed transfer to and from the

vapour within the tank to radiation and convection, however the radiation term was

neglected, being the lesser.

28

C hapter 2 The blowdown under f ir e phenomenon

400-1

3 0 0 -

OFRY opens / 43

- 59


2.8 HEAT TRANSFER BETWEEN VESSEL WALL AND LIQUID SPACE

In the experiments by Eggers and Green [1990] for the depressurisation under ambient

conditions o f a small vessel containing 86 vol. % of liquid carbon dioxide, the

recorded temperature/time profiles at different positions along the tank reveal the

wall-liquid heat transfer interaction. These are shown in Figure 2.6 and 2.7. Figure 2.7

indicates that before formation of dry ice (where the pressure remains constant, i.e. at

time « 180) the liquid temperature (curve T6) is very similar to the temperature o f the

inner wall by the liquid (curve T i l ) at the bottom of the tank. The similarity of liquid

and inner wall temperatures indicates good heat transfer between the liquid and vessel

wall. Haque et al. [1992a] attributed this to nucleate, transition and film boiling o f the

liquid phase, yielding high heat transfer coefficients when compared to natural

convection in the gas phase [Welty et al., 1984]. Detailed experiments even under fire

conditions and for PRY venting however refute the existence o f boiling beyond the

nucleate regime [Moodie et al., 1985].

Under fire conditions, the liquid within the tank will typically be at its boiling point

with, at least, nucleate boiling heat transfer expected, yielding high heat transfer

coefficients. Moodie et al. [1985], in their experimental tests on the 1/4 and 1 tonne

tanks determined the average rates o f heat transfer into the propane and tank wetted

wall from the bulk temperature and pressure data. Changes in specific heat and

thermal expansion were taken into account. Assuming all the heat to be transferred to

the liquid propane via the liquid surface, the average rate o f heat input into the

propane was 73 kW/m^. The average heat flux into the system during boil-off was also

calculated fi’om the mass discharge rates and found to be 80 kW/m^. These

calculations show that the critical heat flux [Butterworth and Hewitt, 1977] necessary

to take the boiling mode into film boiling is not reached, providing a further indication

o f the dominance of nucleate boiling.

30

C hapter 2The blowdown under f i r e phenomenon

A u v h s m o

X

X

X

XXX

V=501X XT6 T16

i X

Figure 2.6 Position of thermoelements within tank containing carbon dioxide

[Eggers and Green, 1990].

31

C hapter 2 The blowdown under f ir e phenomenon

120

*20 100

T15T13

J7

-20 -

— \ T6 \

CL

-80840720240 360120 I 460

Time / s60(

Figure 2.7 Time profiles of Pressure, Fluid and wall temperatures of a COj

containing tank (Eggers and Green, 1990].

32


Moodie et al. [1988], in their experiments on the 5 tonne tank, observed the existence

o f spatial variations in the measured temperatures in the liquid space. These variations

were attributed to a number o f factors, such as, the extent o f liquid mixing and/or bulk

circulation, boundary layers, the presence of hot vapour bubbles (in only one of the

tests), and the possibility o f liquid slopping and splashing, so that some

thermocouples alternatively see liquid and hot vapour. The range o f temperatures

recorded is illustrated by the measurements made during the 72% fill test shown in

Figures 2.8 and 2.9 (bulk liquid) and figure 2.10 (close to wall). During blowdown

(PRV operation), parts o f the tank show little vertical temperature stratification and

liquid thermocouples (45, 46, and 47 in Figure 2.8) all read about 40°C before

becoming uncovered.

Based on the results o f experiments mentioned above, Beynon et al. [1988] concluded

that the liquid could therefore be considered isothermal and well mixed. In another

test in the same series o f experiments by Moodie et al. [1988], for the 36% fill test, the

bulk liquid was essentially found to remain uniformly at the saturation temperature

and therefore another confirmation of good liquid mixing. The authors noticed no

evidence o f a hot thick boundary layer in the liquid. Also, in agreement with

experimental observations by Eggers and Green [1990], the temperatures near the tank

sides (Figure 2.10) were not significantly greater than those in the bulk liquid.

Temperature measurements just above the initial liquid level (e.g. 44 in Figure 2.8)

indicate some up welling o f the liquid once the fire was established.

33


300-1

45

^ 2 0 0 -

u3£aa

1 0 0 -

SECTJON 8-8 «1000

600 1200 18000 2400 3000Time, s

Figure 2.8 Liquid tem peratures for the 72% fill test [Moodie et al., 1988]

3 0 0 -1

,TZXIU

U 2 0 0 -

SECTICX 0-0 • 3170Q.

u 1 0 0 -

23

25

2400 300018001200600Time, s

Figure 2.9 Liquid tem perature for the 72% fill test [Moodie et a!., 1988]

34


80-1

6 0 -

O0)u

BSECTION C-C • 1 7 7 0

56

2 0 -

3600300024001 000 T in ie. s

600 1200

Figure 2.10 Boundary layer temperatures for the 72% fill test [Moodie et al.

19881

liquidCurve B

vap ou r

Curve A-30-50

0

Figure 2.11 Variation of pressure with time (curve A) and fluid tem perature

with pressure (curve B) for depressurisation of saturated liquid refridgerant R12

[Mayinger, 1982|

35


2.9 HEAT AND MASS TRANSFER BETW EEN VAPOUR AND LIQUID

PHASES

During blowdown of condensable gases or two-phase mixtures, heat and mass transfer

take place by condensation and evaporation due to temperature and pressure drops.

Additionally the process of phase separation o f evaporated liquid and condensed

vapour from corresponding phases can however be relatively slow when compared

with high rates o f depressurisation [Mayinger, [1982]. The author demonstrated the

effects o f delay and phase separation in boiling liquid by depressurising a vessel 2/3

filled with saturated liquid refrigerant R12 from 7.4 atm and 30 °C to ambient pressure

within 15 s. The variations o f pressure with time and fluid temperatures are shown in

Figure 2.11.

Referring to curve A, depressurisation starts at point B. During the very steep pressure

gradient between points B and C, the measured liquid temperatures markedly exceeds

the saturation temperature (see curve B), which indicates considerable liquid

superheat. At point C, bubble formation starts in the liquid. Due to the relatively slow

process o f phase separation, the dispersion level moves upwards during the period C-

D and reaches the release valve. The vapour flow at release valve containing only

traces o f liquid droplets is superseded with a two-phase discharge containing large

amounts o f liquid. As the maximum velocity o f two-phase mixture is much lower than

the sonic velocity o f the vapour, vapour formation in the vessel exceeds the

volumetric discharge rate between time D and F. As a result, pressure starts to build

up within the vessel until point F where the rate o f flashing starts to fall and the

pressure decreases steadily to point H.

Under fire attack, the vapour-liquid interface mass transfer is governed by liquid

boiling as experiments [Moodie et al., 1988] show the vapour to be superheated.

36


2.10 FLOW THROUGH THE RELIEF VALVE

When the valve is open during pressure relief or blow^down, material is discharged

and both heat transfer and material ejection influence the pressure in the vessel.

Depending on the level o f the liquid/vapour interface, valve discharge could be either

single-phase vapour or two-phase mixture. Large fills and large valve sizes cause

significant swelling o f the liquid by void formation due to internal flashing, resulting

in liquid entrainment. This was also demonstrated by some o f the data fi"om the HSE

and University o f New Brunswick tests. Furthermore, this phenomenon exerts a

considerable influence on the thermofluid behaviour o f the contents and its pressure

relief [Sumathipala et al., 1990; Sumathipala et al., 1988].

As material continues to exit, the two-phase level decreases until single-phase vapour

flow results. Haque et al., [1990] indicated that for blowdown under ambient

conditions, the fluid in the relief valve could either be in the metastable state or in

thermodynamic and phase equilibrium. The authors compared predictions based on

the above assumptions with experimental measurements and concluded that the latter

assumption gave better results.

The experimental observation by Venart et al., [1988] shed the best insight on the

PRV behaviour during blowdown. According to the authors, the ability o f a pressure

relief or blowdown valve to maintain a safe pressure in the vessel is influenced by its

size and the possibility o f liquid entrainment and vapour pull through [Sumathipala et

al., 1992]. In the case o f liquid entrainment, liquid is picked up off the liquid or two-

phase surface in the proximity o f the valve. In vapour pull through, a vapour exit

stream is pulled into the valve through the liquid by a vortex formed upon discharge.

In both cases (as mentioned in the analysis by Sumathipala et al., [1992]), the pressure

relieving capacity of the valve changes and the ability of the contents to absorb energy

is altered.

For oscillating pressure relief venting, the interactive transient thermodynamic and

fluid dynamic processes occurring between the fire, tank contents, and the relief valve

37


can result in pressure increase followed by pressure stabilisation and decrease (see for

example Sumathipala et al. [1992]). In addition, the fluid within the orifice can either

be choked or unchoked depending on the upstream and downstream pressure

difference.

38

Chapter 3 Literature Review

CHAPTERS

LITERATURE REVIEW

3.1 INTRODUCTION

This chapter presents a review o f the mathematical models reported in the open

literature over the last three decades for depressurisation o f vessels under fire attack.

Most o f the models reviewed are for depressurisation by use o f oscillating pressure

relief valves. The review starts with an overview of the early work followed by a

more detailed examination o f the more rigorous models.

In the past three decades, a considerable amount of work has been undertaken in the

UK and North America to understand the nature of the processes involved when a

vessel is exposed to external fire impingement. The main incentive for these types o f

study arise from the safety issues associated with the storage and transport o f highly

flammable, pressurised inventory, brought about by the considerable increase in the

use o f pressure-liquefied fuels (e.g. butane and propane).

In the early 1970’s the US Federal Railroad Administration/Department o f Transport

(FRA/DOT), the Railway progress Institute and the American Association o f

Railroads (AAR), in cooperation with major railroads, tank builders and operators

carried out an extensive rail tank-car safety program. This was called the Railroad

Tank car Safety Research and Test Project (TCSRTF) [Birk, 1988] and the project

looked at all aspects o f tank-car safety including thermal and mechanical aspects. The

TCSRTF included significant experimental and analytical studies and resulted in

technological improvements in tank-car design. The project further resulted in the

development o f a computer program that simulated the effect o f fire impingement on

a rail tank-car [Graves, 1973].

Also, in the late 1970’s, the Transportation Development Centre o f Transport Canada

carried out an independent tank-car safety project focusing primarily on the thermal

aspects o f tank-car design and involved the evaluation of novel concepts in thermal

protection [Appleyard, 1980]. This work further resulted in the development o f the

39


Tank-Car Thermal Computer Model (TCTCM) - a computer model for prediction o f

the effect o f fire impingement on tankers [Birk, 1985].

The Safety and Reliability directorate [Hunt and Ramskill, 1985] developed the

ENGULF computer code for the Health and Safety Executive, UK, to assess the

safety o f liquid filled tanks when engulfed by fire. The way in which the temperature

o f the tank, its contents, and pressure vary with time was theoretically determined. A

modification o f the ENGULF code led to the development o f ENGULF II [Ramskill.

1988] which, amongst other things, accounts for partial engulfinent and more

importantly vessel failure prediction.

The Fire Science Centre o f the University o f New Brunswick, Canada has been using

data obtained from moderate [Droste and Schoen, 1988; Moodie et al., 1988] and

small-scale [Venart et al., 1988] experiments to elucidate the complex

thermodynamics o f pressure liquefied gas tanks exposed to accidental fire engulfitnent.

Based on the fluid thermo-hydraulic behaviour observed in the small-scale

experiments [Venart et al., 1988], the PLGS-1 model [Aydemir et al., 1988] was

developed and soon followed by the PLGS-2 model [see Sumathipala et al. 1992].

Also from the above experimental studies, and in view of mitigating the possible risks

associated with fire impingement on pressure vessels, Sumathipala et al. [Sumathipala

et al., 1992] undertook a study to determine how best to prevent boiling liquid

expanding vapour explosions (BLEVE). The work resulted in an extensive validation

o f both the PLGS-1 [Aydemir et al., 1988] and PLGS 2 models [Hadjisophocleous,

1989] from which good agreement with experiment was observed.

In 1991, the Health and Safety Executive UK (HSE), with the participation o f the

offshore industry, completed Phase 1 of a Joint Industry Project on Blast and Fire

Engineering for Topside Structures. This comprehensive project included the thermal

response of vessels and pipework exposed to fire and other closely related topics. The

study resulted in the ‘Interim Guidance Notes for the Design and Protection of

Topside Structures Against Explosion and Fire’. Following this, an HSE review was

carried out (see HSE Report 051, 2000). Its aims were to

address the response of pressurised process vessels and equipment to fire attack,

40


review the current knowledge and available analysis techniques relating to this, and

identify any gaps in knowledge that may need to be filled before new and

comprehensive guidance can be given. The document, though not leading to the

development o f a mathematical model, highlighted the need for sound modelling

procedures.

Several standards and recommendations exist for estimation o f temperature and

release rates during pressure release under fire conditions [see for example

API RP 520, 1990; Farr and Jawad 1998]. The most common method employed for

depressurisation under fire is the API RP 520 [1990]. This will be examined later

alongside the more rigorous models. The rigorous models to be presented in more

detail include the following: the ENGULF and ENGULF 11 models [Hunt and

Ramskill, 1985, Ramskill, 1988], the HEATUP model [Beynon et al, 1988], the Tank-

car Thermal Computer Model (TCTCM) [Birk, 1988], the SPLIT FLUID MODEL

[Overa et al, 1994] and finally the PLGS-1 and PLGS-2D models [Sumathipala et al.,

1992].

3.2 API RECOMMENDED PRACTICE [API RP 520,1990]

There are several methods available for calculation o f fire relief rates and sizing of

pressure relief safety valves in the case of fire. According to Overa et al. 1994, these

methods typically fall into two categories:

• Models that attempt to calculate the vessel and fluid response to a fire

• Sizing equations for use in determining the required relief (orifice) area

The most commonly used method for sizing relief devices for fire is the recommended

practice published by the American Petroleum Institute [API, RP 520, 1990]. Some

parts o f this practice are open for interpretation by the user, and it is not uncommon

for different companies to apply criteria differently [Overa et al., 1994].

Heat input to f luid

The API 520 equation for fire heat flux, which is commonly used for calculations of

fire engulfment o f hydrocarbon vessel, is given as

41


= 21()0(W?/,o«: 2 I

where Q^pj = Heat flux to fluid in Btu/hr

A = wetted area in

F = insulation factor, (zero for insulated and 1.0 for

non-insulated vessels)

According to the recommendation, wetted area more than 25ft (7.62m) above the

source o f flame should be excluded from the area used in the equation. The constant

21000 is used when there is good drainage from the vessel and prompt fire fighting

efforts are expected. Otherwise, a factor of 34,500 should be used. Qapi is to be taken

as the heat input into the liquid inventory only, but is commonly applied to the entire

fluid within the vessel [Blackburn, 1992]. Another misinterpretation by the users of

the API 520 recommendation is to apply the heat flux to the vessel rather than the

fluid. Though the above equation (Bqn 3.1) has been developed for use in refineries it

is however normally used for all calculations o f fire engulfrnent o f hydrocarbon

vessels. It is based on the energy input from Eqn 3.1 that fluid temperatures and

pressures are calculated. An orifice diameter that allows the pressure to be maintained

below 110% o f the relief set pressure is considered acceptable.

D is c h a r g e c a lc u la t io n s

In the application o f the API recommended practice, the vapour to be released is

assumed to be the liquid vaporized due to the heat input from the fire only. The

corresponding mass flow rate is therefore calculated simply by dividing the fire heat

flux input (Q api), by the latent heat of vaporization of the liquid. The presence o f pre

existing vapour and the vaporization resulting from the pressure decrease are ignored.

The latent heat may be found from charts or monographs as suggested in API RP 521

[1990]. Other sources have suggested that the latent heat o f vaporization be

determined from composition [Coker, 1992]. The relief rate, W , is therefore found

by:

W = 3.2A,

where À is the latent heat of vaporization

42


The orifice area may then be found from normal orifice area sizing procedures.

For vapour filled vessels, the required discharge area may be calculated directly from

the vessel area exposed to fire and vessel pressure. This is given by

where = required discharge area

F ' = API factor (range 0.01-0.045) determined from vessel

and fluid temperatures

= Surface area exposed to fire

P, = Upstream relieving pressure

F lu id th e r m o d y n a m ic p a th s

In the implementation o f the API RP 520 [1990], the thermodynamic path selected for

the fluid is either a fully isenthalpic or 50% 'expansion efficiency'. Heat transfer is

considered by assuming constant heat transfer coefficients.

S tr e s s c o n s id e r a tio n s

The API guidelines for depressurisation state that pressure should be reduced

sufficiently so that stress rupture is not o f immediate concern. For sizing criteria, API

recommends reducing the equipment pressure from initial conditions to 50% of the

vessel design pressure within 15 minutes. This criterion is said to apply to vessels

with wall thickness of 25 mm or more, while thinner walled vessels will require more

rapid depressurisation. In practice however, the most usually applied criterion is the

reduction o f pressure to 50% of design pressure, or seven bara, whichever is lower.

43

Chapter 3 L itera tu re Review

3.3 SPLIT FLUID MODEL [OVERA ET AL., 1994]

Work by Overa et al. [1994], led to the development of the SPLIT FLUID MODEL.

Figure 3.1 gives an overview of the depressurisation model and the terms included in

their calculations.

vw

LW

Keys :

Mle Mass o f evaporated liquid

Myc Mass o f condensed vapour

Mvd Total mass o f discharged vapour

P Vessel pressure

Heat input (or loss) to ambient

Ql Heat flow between vessel and liquid

Heat flow between vapour and liquid

Heat flow between vessel and vapour

Liquid phase temperature

Wetted wall temperature

ambtctit

Q lv

Qv

T

Toutskfc Temperature at the surface of the vessel

Ty Vapour phase temperature

Tyu Discharge gas temperature

Tyw Unwetted wall temperature

( ) Vapour phase

Liquid phase

^ 0 Metal wall layer

^ 0 Insulation wall layerLW

Figure 3.1 Depressurisation model for the Split Fluid Model [Overa et a!.,

1992]

44


With this model, bulk temperatures o f vapour and liquid phases, as well as the dry and

wetted walls are calculated. Temperature stratification is ignored. Heat and mass

transfer are also considered between the phases through vapour condensation and

liquid vaporization. The composition in the vapour phase is calculated from the mass

flux leaving by discharge condensation ( M y ^ ) and evaporation from

the liquid. The liquid composition is found from evaporation and condensation of the

vapour. It is assumed that no pressure gradients exist within the vessel, and that

single-phase discharge takes place from the vapour filled part o f the vessel. An in-

house simulation was used for equilibrium and thermodynamic property predictions.

The heat transfer terms included in the model are:

• Energy flow due to mass flux between vapour and liquid

• Energy leaving through mass flux out o f the tank

• Convective heat transfer to liquid from vessel wall

• Natural and forced convection between vessel and vapour

• Natural and forced convection between vapour and liquid

• Heat flux to vessel from surroundings or from an external heat flux. For each

iteration step, the corresponding heat flux is calculated from fluid composition,

fluid properties, and heat transfer correlations selected from temperature, flow

conditions and the geometry o f the vessel.

The model calculates the following

• Vapour and liquid temperatures

• Vessel wall temperatures in vapour and liquid filled parts o f the vessel

• Pressure within the vessel

• Burst pressure o f the vessel at vessel temperature

• Vapour temperature downstream of the relief valve

• Heat flux to the tank due to fire (radiative and convective fluxes)

• Mass flux o f discharged vapour

• Composition o f vapour relieved

45


S o lu tio n P r o c e d u r e

Variable time steps were used in the implementation o f the solution procedure.

Simply reducing the duration o f each time step reduced the errors introduced by using

finite time intervals. On implementation, the procedure involves the determination of

all required parameters and calculating the temperatures and pressures repeatedly,

keeping track o f the elapsed time.

C a lc u la tio n o f L iq u id a n d V a p o u r T e m p e ra tu re s

The liquid temperature, 7 ̂ is determined from a Pressure-Enthalpy (PH) flash

performed at vessel pressure, P. The enthalpy used is the specific enthalpy o f the

liquid and is determined by:

' i Q L - Q L v ) à t ' ^H l -

N l

where H f = specific enthalpy o f liquid at previous stage

= specific enthalpy o f condensed liquid

^ number of moles o f condensed vapour and evaporated

liquid respectively

= heat transfer rate between vessel and liquid

= heat transfer rate between liquid and vapour

A t = finite time interval

The flash calculation will give the equilibrium amount o f vapour and liquid at the

calculated temperature. The amount of vapour generated is added to the vapour

already present within the vessel. The liquid properties are determined at the

temperature found in the P/H flash. The liquid level is then updated to reflect changes

due to corresponding changes in equilibrium and specific volume. The updated

vapour composition is then used for the calculation o f the amount o f vapour leaving

the vessel.

The entropy change of the vapour phase is determined utilising the second law of

thermodynamics in the following form

46


a t T3.5

number o f moles o f evaporated liquid, vapour

vented and condensed vapour

specific entropies o f evaporated liquid, vapour

vented and condensed vapour

vessel temperature

A volume-entropy (V/S) flash at the vapour volume was performed with the entropy

determined from:

r* /+1=

/r ( 2 v + e i v ) i

\

T .A t

I \ >

+N

3.6

where S ^ ‘ = specific entropy at previous stage

= number o f moles of vapour

Ty = vapour temperature

The condensed liquid from this equilibrium calculation is then added to the liquid

within the vessel.

D is c h a r g e c a lc u la tio n th ro u g h r e l i e f v a lv e

The calculation procedure for fluid discharge employed in the SPLIT FLUID

MODEL is applicable for both sonic and sub-sonic releases, with the equations

determining the actual flow rate through the relief device (valve or orifice). The valve

may be specified either as a blowdown valve that stays open until a specified pressure

is reached, or as a safety pressure relief valve (PRV) that opens and closes at

predefined pressures. Temperatures in the downstream piping was calculated by

performing an isenthalpic flash to the flare system back pressure, while temperatures

downstream of the valve were calculated as a function of upstream conditions.

47


C a lc u la tio n o f v e s s e l w a l l te m p e ra tu re s

For the vessel wall temperatures, energy balances are performed between the fluid and

surroundings. The wall metal specific heat capacity as a function of temperature is

used in the calculations.

The wetted (r^^) and unwetted wall temperatures ( 7 ^ ) are calculated respectively by:

rr /+i _ T’ / . f e i + Qo 1 T^Lw ~ ^ L w + /

T '+1 _ T ' ■ ̂ op

where = previous liquid and vapour wall temperatures

respectively

^ L w » weight of wetted and unwetted sections o f vessel

C p = specific heat capacity o f vessel wall

is set equal to if the vessel is exposed to fire, while Qa„i,ient will be used for

atmospheric exposure. Aximuthal heat transfer was ignored as the cross-sectional area

available for this is much less when compared to the surface area available for heat

transfer between wall, fluid and the surrounding environment. Heat variation across

the radial vessel wall was also ignored and a constant, radial wall temperature profile

was assumed even under fire conditions.

H e a t t r a n s fe r f r o m v e s s e l to v a p o u r a n d l iq u id p h a s e s

Heat transfer between vessel and vapour was considered to be by convection and

radiation though the radiation term was neglected, being the minor o f the two. The

convective term included the effect of natural convection - due to temperature

differences between vessel wall and vapour, and forced convection - due to vapour

flowing out o f the vessel. The total energy transfer per unit time was found from

Q v = V ^ va p o u r ^ .9

where ( 7 = overall wall-to-vapour heat transfer coefficient

r,, = vapour temperature

48


was obtained from Nusselt number correlations calculated for forced and natural

convection based on correlations by Kreith and Black [1985] and Incropera and

DeWitt, [1985] respectively [fnempera-an&Be^^%tr^-9^. Thus

N u = [N u g ^ + N u i f ^ y ' 3.10

The natural convection Nusselt number, N uq , was given as

N u a = b { G r P r y 3,11

and N uj^ given as

2N u n — 0.Q296 R e — P r ^ 3,12

where G r, P r and R e are Grashof, Prandtl and Reynolds numbers respectively. The

constants, a and b depend on Grashof and Prandtl numbers for turbulent or laminar

flow.

Some form of nucleate boiling was suggested to be the dominant heat transfer mode

between vessel wall and liquid in contact with it. Based on a series o f experiments, the

authors found reasonable agreement with data simply by introducing a linear increase

in heat transfer coefficient as a function of net heat flux to the liquid. This gives a

total heat transfer coefficient expressed as

3.13

where = net heat input to liquid from vessel and is the heat transfer

coefficient under zero external heat flux, set within the range 1000 - 3000 W/m^K.

The total energy transfer per unit time was then obtained from:

Q l - ^ L w L ̂ liquid 3.14

H e a t tr a n s fe r f r o m l iq u id to v a p o u r

Heat transferred from the liquid surface to the gas phase was accounted for by treating

the liquid surface as a radiating surface and adopting a similar equation as used for the

wall-to-fluid transfer. The heat transfer coefficient was obtained as used for vapour

phase heat transfer (Eqn 3.11), where the constants, a and b depend on Grashof and

Prandtl numbers, and also the temperatures [McCabe and Smith, 1976].

49


H e a t f l u x to v e s s e l f r o m s u r r o u n d in g f i r e

For depressurisation under fire conditions, the authors assumed engulfing pool fire

with constant flame temperature for the specified fire duration. The heat flux was

uniformly applied to all sides o f the vessel (view factor equals unity). Changes in

emissivity due to soot or other phenomena were ignored.

The total energy input from the fire was given as:

Qfire ~ ^fiame^vessel^B flame ~ '^vessel )" ̂^pool flame ~ '^vessel ) 3.15

The flame temperature depending on various factors such as fuel type and wind

conditions was selected based on reported large-scale fire exposure tests as 1075°C.

This gives an initial flux o f 130 kW/m^.

The following values were used for the various parameters in Equation 3.15.

Aflame ^ 0.85 flame emissivity o f hydrocarbon flame

'vessel 0.70 vessel emissivity

Og = 5.67xlO‘̂ W/m^k'^ Stefan Boltzman’s constant

^pooi ~ 20 W/m^k convective heat transfer coefficient

between vessel and surrounding air

= 800°C temperature o f surrounding air

'Aflame ^ 1075°C flame temperature

S tr e s s c o n s id e r a tio n s

A hoop stress model at each time step predicted the vessel burst pressure, /J ,. It was

assumed that the vessel failed in the longitudinal tensile mode. To incorporate the

stress due to the fire, a curve fit o f the yield stress as a frmction o f temperature for a

typical vessel material was used. The burst pressure, /J, was given as:

2 r + tPfj — j— Gcc In — 3.16

V3 r

Where

a = 2 - ^ 3.17a

50

Chapter 3 Literature R eview

□ □ EXPV^xx o o EXPUqud WpxCakwbW ----- UyâfrWcuWmd ------- 50%Bki#ncy

I10 H

Figure 3.2 V ariation of bulk gas and bulk liquid tem peratures with time for

depressurisation of a hydrocarbon two-phase mixture [Overa et

al., 1994].

52


3.4 HEATUP [Beynon et al., 1988]

Beynon et al. [1988] developed a predictive model, HEATUP, for the depressurisation

o f horizontal LPG vessels engulfed by fire. Complete fire engulfinent was treated with

a vertically varying, time dependent heat flux. The model incorporated conductive

heat transfer through vessel walls, convective and radiative transfer from vessel to

fluids and also heat and mass transfer between liquid and vapour phases. HEATUP

was developed in conjunction with, and validated against measurements on the

behaviour o f 0.25, 1 and 5 tonne LPG tanks filled to a range o f levels and engulfed in

kerosene pool fires [Moodie et al., 1987, Moodie et al., 1985].

3.4.1 Basis for HEATUP Mathem

discovery.ucl.ac.uk · abstract this thesis presents the development of a number of mathematical...

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