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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
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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
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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.
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DEDICATION
... to my very dear parents.
For everything...
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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.
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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
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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
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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
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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
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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
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Chapter 1 Introduction
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
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Chapter 1 Introduction
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
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Chapter 1 Introduction
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
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Chapter 1 Introduction
• 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.
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Chapter 1 Introduction
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.
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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
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Chapter 2 The blowdown under fire phenomenon
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
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Chapter 2 The blowdown under fire phenomenon
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
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Chapter 2 The blowdown under fire phenomenon
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.
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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]
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Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under f ir e phenomenon
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
-
Chapter 2 The blowdown under f ir e phenomenon
Figure 2.3 Flow pattern of the gas phase in a vertical vessel during blowdown
[Overa et al., 1992]
27
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under f ir e phenomenon
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
-
Chapter 2 The blowdown under f ir e phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
-
Chapter 2 The blowdown under fire phenomenon
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
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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
-
Chapter 3 Literature Review
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
-
Chapter 3 Literature Review
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
-
Chapter 3 Literature Review
= 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
-
Chapter 3 Literature Review
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.
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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]
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Chapter 3 Literature Review
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
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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
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Chapter 3 Literature Review
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.
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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
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Chapter 3 Literature Review
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].
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Chapter 3 Literature Review
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
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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].
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Chapter 3 Literature Review
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