2008 norman

KATHOLIEKE UNIVERSITEIT LEUVENFACULTEIT INGENIEURSWETENSCHAPPENDEPARTEMENT WERKTUIGKUNDEAFDELING TOEGEPASTE MECHANICAEN ENERGIECONVERSIECelestijnenlaan 300A, B-3001 Heverlee (Leuven), België

INFLUENCE OF PROCESS CONDITIONS ON

THE AUTO-IGNITION TEMPERATURE OF

GAS MIXTURES

Promotor:Em. prof. dr. ir. J. BerghmansCopromotor:Prof. dr. ir. F. Verplaetsen

Proefschrift voorgedragen tot hetbehalen van het doctoraat in deingenieurswetenschappen

door

Frederik NORMAN

Juni 2008

KATHOLIEKE UNIVERSITEIT LEUVENFACULTEIT INGENIEURSWETENSCHAPPENDEPARTEMENT WERKTUIGKUNDEAFDELING TOEGEPASTE MECHANICAEN ENERGIECONVERSIECelestijnenlaan 300A, B-3001 Leuven, België

INFLUENCE OF PROCESS CONDITIONS ON

THE AUTO-IGNITION TEMPERATURE OF

GAS MIXTURES

Jury:Prof. dr. ir. E. Aernoudt, voorzitterEm. prof. dr. ir. J. Berghmans, promotorProf. dr. ir. F. Verplaetsen, copromotorProf. dr. ir. E. Van den BulckProf. ir. J. PeetersProf. dr. ir. J. DegrèveProf. dr. ir. B. Merci (Universiteit Gent)

Proefschrift voorgedragen tot hetbehalen van het doctoraat in deIngenieurswetenschappen

door

Frederik NORMAN

UDC 614.8 Juni 2008

© Katholieke Universiteit Leuven - Faculteit IngenieurswetenschappenArenbergkasteel, B-3001 Leuven, België

Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd en/of openbaargemaakt worden door middel van druk, fotokopie, microfilm, elektronische of op welke anderewijze ook zonder voorafgaandelijke schriftelijke toestemming van de uitgever.

All rights reserved. No part of this publication may be reproduced in any form by print,photoprint, microfilm, or any other means without written permission from the publisher.

Wettelijk Depot: D/2008/7515/69ISBN 978-90-5682-960-5

To Ilse and Janne

Voorwoord v

VoorwoordEen zelfontsteking wordt bepaald door het evenwicht tussen de warmteproduc-tie ten gevolge van de chemische reacties en het warmteverlies naar de omge-ving. Daardoor kan een zelfontsteking heel traag op gang komen en pas nalange tijd tot ontsteking komen. Dankzij de hulp van vele personen kende mijndoctoraat geen dergelijk verloop. Aan het einde van mijn doctoraatsonderzoekwil ik daarom nog eens iedereen bedanken die in kleine of in grote mate heeftbijgedragen tot de realisatie van deze doctoraatsthesis.

In de eerste plaats wil ik mijn promotor, prof. Jan Berghmans, en mijncopromotor, prof. Filip Verplaetsen, bedanken voor de kansen, het vertrouwenen de vrijheid die ze mij gegeven hebben om dit explosieonderzoek uit te voeren.Zonder jullie jarenlange inzet voor het explosieonderzoek was het niet mogelijkgeweest dergelijke hoogstaande experimenten uit te voeren. Jullie hebben mijbinnengeloodst in de boeiende wereld van de explosieveiligheid.

Ook de andere leden van de examencommissie, prof. Erik Van den Bulck,prof. Jozef Peeters, prof. Jan Degrève en prof. Bart Merci wil ik bedanken voorde interesse en het kritisch nalezen van mijn doctoraatstekst. Prof. EtienneAernoudt bedank ik voor het opnemen van de taak van voorzitter.

Ik dank het Instituut voor de Aanmoediging van Innovatie door Weten-schap en Technologie in Vlaanderen (IWT-Vlaanderen) dat door middel vaneen specialisatiebeurs mij de afgelopen 4 jaar financieel gesteund heeft.

Uiteraard was mijn doctoraatsonderzoek niet hetzelfde geweest zonder deaanwezigheid van mijn collega’s. In de eerste plaats wil ik Luc en Filip van deexplosiegroep bedanken. Luc, samen met jou heb ik mijn eerste explosieproevenin de bunkers uitgevoerd en meteen werd duidelijk welk gevaar dergelijke proe-ven inhouden. Jouw werk rond zelfontsteking was voor mij van onschatbarewaarde en vormde de basis van mijn doctoraat. Filip, bij jou kon ik steedsterecht met mijn explosievragen. Eveneens bedank ik je voor het toffe gezelschaptijdens de talrijke conferenties. Voor mijn experimentele opstelling kon ik steedsberoep doen op de kennis en ervaring van de techniekers. Hans, Ivo en Jos,merci voor jullie hulp en de vele babbels. Verder wil ik ook mijn bureaugenoten(Wim, Frederik en Frederic) bedanken om mijn bureautijd een pak aangenamerte maken. Tenslotte wil ik alle andere (ex-)collega’s bedanken, van wie ik denamen niet zal opnoemen opdat ik niemand zou vergeten, voor de babbels, deTME-weekends, de koffiepauzes, ... Dankjewel.

Omdat het werk niet het enige is wat belangrijk is, wil ik eveneens mijnfamilie en vrienden bedanken. Een groot woord van dank gaat naar mijnouders die me altijd hebben gesteund en bij wie ik steeds terecht kon. Mercimoeke en papa.

Als laatste, maar zeker niet minst belangrijk, wil ik mijn twee vrouwenbedanken. Ilse, jij staat steeds aan mijn zijde. Tegen jou kan ik alles kwijt. Jijbent mijn luisterend oor, je bent mijn ruggensteun, kortom je bent mijn groteliefde. Twee en een half jaar geleden zijn we in het huwelijksbootje gestapt.Dit leek een grote stap, maar deze dag verdwijnt in het niets in vergelijkingmet de geboorte van onze dochter, Janne. Janne, je bent nu nog heel klein,

vi

maar toch reeds een groot wonder. Janne, jij geeft zin aan ons leven. Je vultons leven met vele verrassingen. Ilse en Janne, aan jullie draag ik dit werk op.

Heverlee Frederik Normanjuni 2008

Voorwoord vii

AbstractMany chemical processes use combustible gases and vapours at elevated pres-sures and high temperatures. In order to evaluate the auto-ignition hazardinvolved and to ensure the safe and optimal operation of these processes, it isimportant to know the lowest possible temperature at which spontaneous ig-nition of these gases and vapours takes place. The auto-ignition temperatures(AIT’s) found in literature usually are determined by applying standardisedtest methods in small vessels and at atmospheric pressure. However, since theAIT is not constant but decreases with increasing pressures and increasing vol-umes, these AIT values are often not applicable in industrial environments.The lack of auto-ignition data at elevated pressures and the lack of compre-hensive auto-ignition models are the motivations for this study. Therefore thepresent study consists of an experimental and a theoretical simulation part.

The experimental study consists of the determination of the auto-ignitionlimits of methane, propane and butane mixtures at elevated pressures up to3 MPa for a wide range of concentrations. It is shown that the auto-ignitionlimits decrease significantly with increasing pressure. The concentrations thatare most sensitive to auto-ignition are high concentrations and depend on theinitial pressure. The auto-ignition limits of the propane/butane mixtures cor-respond well with the auto-ignition limits of the component with the lowestauto-ignition temperature, which is n-butane. The location of the auto-ignitionareas could explain the observations of the upper flammability limits at elevatedtemperatures and pressures of propane and n-butane mixtures.

The numerical study focuses on the modelling of the auto-ignition process ofmethane/air mixtures at elevated pressures. First a zero-dimensional approachis adopted, based upon the model of Semenov. The chemistry is modelled bymeans of a detailed reaction mechanism. A methane reaction mechanism ofthe British Gas Corporation shows the best agreement with the experimentalresults. To take thermal and mass diffusion and the natural convection insidethe vessel into account, a two-dimensional model is built including the kineticmechanism. A CFD-model is used to compute the heat transfer and the buoy-ant flows inside the vessel. The coupling of the reaction mechanism to thismodel results in an accurate prediction of the auto-ignition conditions at ele-vated pressures. This model is also used to investigate the volume dependencyof the auto-ignition temperature for both spherical and cylindrical vessels.

viii Abstract

Korte samenvattingVele chemische processen maken gebruik van brandbare gassen en dampen bijverhoogde drukken en temperaturen. Om het zelfontstekingsrisico te kunneninschatten en om de veilige en optimale werking van deze processen te verze-keren, is het belangrijk om de laagst mogelijke temperatuur te kennen waarbijspontane ontsteking kan optreden. De zelfontstekingstemperaturen (AIT’s) diein de literatuur beschikbaar zijn, zijn meestal bepaald volgens gestandaardi-seerde methodes in kleine volumes en bij atmosferische druk. Aangezien dezelfontstekingstemperatuur niet constant is maar daalt bij toenemende drukkenen toenemende volumes zijn deze AIT’s niet rechtstreeks toepasbaar voor in-dustriële condities. Het gebrek aan zelfontstekingsdata bij verhoogde drukkenen grote volumes en het gebrek aan uitgebreide modellen van de zelfontste-king waren de drijfveren van deze studie. Daarom bestaat deze studie uit eenexperimenteel en een numeriek gedeelte.

De experimentele studie bestaat uit de bepaling van de zelfontstekingsgren-zen van methaan, propaan en butaan mengsels bij verhoogde drukken tot 30 baren voor verschillende concentraties. Het is aangetoond dat de zelfontstekings-temperaturen significant dalen bij verhoogde drukken. De alkaanmengsels dieaanleiding geven tot de laagste zelfontstekingstemperaturen hebben een rijkebrandstof/lucht verhouding, die eveneens afhangt van de initiele druk. De zelf-ontstekingsgrenzen van propaan/butaan mengsels komen goed overeen met dezelfontstekingsgrenzen van de component met de laagste zelfontstekingstem-peratuur, namelijk n-butaan. De ligging van de zelfontstekingsgebieden koneveneens het verloop van de bovenste explosiegrenzen bij verhoogde drukkenen temperaturen van propaan en n-butaan mengsels verklaren.

De numerieke studie concentreert zich op de modellering van de zelfontste-king van methaan/lucht mengsels bij verhoogde drukken. Eerst werd een nul-dimensionale aanpak toegepast, die gebaseerd is op het model van Semenov.De chemie van de ontsteking is gemodelleerd door middel van gedetailleerdereactiemechanismen. Een methaan reactiemechanisme van de British Gas Cor-poration toonde de beste overeenkomst met de experimentele data. Om dethermische en massa diffusie en de natuurlijke convectie in rekening te bren-gen, werd een tweedimensionaal model opgebouwd met inbegrip van het reac-tiemechanisme. De warmteoverdracht en de natuurlijke convectie binnenin hetgesloten volume worden gemodelleerd door middel van het CFD programma.De koppeling van de reactiekinetica met de stromingsmodellering resulteert ineen nauwkeurige voorspelling van de zelfontstekingsgrenzen van methaan/luchtmengsels bij verhoogde drukken. Dit model is eveneens aangewend om de vo-lumeafhankelijkheid van de zelfontstekingstemperatuur voor sferische en cilin-drische vaten te onderzoeken.

List of symbols

Latin Symbols

A pre-exponential factorcp heat capacity at constant pressure J kg−1 K−1

cv heat capacity at constant volume J kg−1 K−1

c concentration kg m−3

B,C constantsD diameter mEA activation energy J mol−1

EC conduction error KER radiation error KF view factor –g gravitational acceleration m s−2

h heat transfer coefficient W m−2 K−1

hi specific enthalpy of species i J kg−1

H enthalpy JL length mm mass kgM molar mass kg mol−1

n (overall) reaction order –n(t) number of chain carriers –P pressure kg m−1 s−2

qc convective heat flux J s−1

qd conduction heat flux J s−1

qr radiant heat flux J s−1

Q heat release Jr radius mR universal gas constant J mol−1K−1

RR reaction rate kg m−3 s−1

S surface area m2

SC convective heat transfer area m2

SR radiation heat transfer area m2

t time sT temperature KT0 initial temperature K

ix

x List of symbols

Tc critical temperature KTG temperature of the gas KTJ temperature of the probe junction KTM temperature of the probe stem KTw temperature at the wall of the vessel Ku internal energy per unit mass J kg−1

v velocity m s−1

V volume m3

W molar mass kg mol−1

x spatial coordinate mX molar fraction –Y mass fraction –

Greek symbols

α absorbance –αth thermal diffusivity m2 s−1

β coefficient of thermal expansion T−1

βi temperature exponent –δ Frank-Kamenetskii parameter –ε mass fraction kg kg−1

εJ emissivity of the junction probe –κ ratio of specific heats –κM Planck mean absorption coefficient –λ thermal conductivity J s−1 m−1 K−1

λair excess air factor –µ dynamic viscosity kg m−1 s−1

µb bulk viscosity kg m−1 s−1

ν kinematic viscosity m2 s−1

ρ density kg m−3

σ Stefan-Boltzmann constant J s−1 m−2 K−4

φ equivalence ratio –Ψ Semenov parameter –τ time constant sτ ′ transmittance –ω reaction or production rate kg m−3 s−1

Dimensionless numbers

Bi Biot number hL/λ

Nu Nusselt number hD/k

Pr Prandtl number ν/αth

Ra Rayleigh number βgL3(Tcentre − Tw)/αthνRe Reynolds number vD/ν

Contents

Voorwoord v

Abstract vii

Korte samenvatting viii

List of symbols ix

1 Introduction 11.1 The auto-ignition process . . . . . . . . . . . . . . . . . . . . . 11.2 Gas explosions in industry . . . . . . . . . . . . . . . . . . . . . 31.3 Aim and scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Background on auto-ignition 92.1 Factors influencing the auto-ignition temperature . . . . . . . . 9

2.1.1 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.2 Fuel type . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.3 Fuel concentration . . . . . . . . . . . . . . . . . . . . . 112.1.4 Volume of the test vessel . . . . . . . . . . . . . . . . . . 122.1.5 Material effect . . . . . . . . . . . . . . . . . . . . . . . 132.1.6 Auto-ignition criterion . . . . . . . . . . . . . . . . . . . 14

2.2 Experimental determination of the AIT . . . . . . . . . . . . . 142.2.1 Standardised test methods . . . . . . . . . . . . . . . . . 152.2.2 Experimental methods . . . . . . . . . . . . . . . . . . . 19

2.3 Auto-ignition theories . . . . . . . . . . . . . . . . . . . . . . . 202.3.1 Chain spontaneous ignition . . . . . . . . . . . . . . . . 212.3.2 Semenov theory of thermal ignition . . . . . . . . . . . . 232.3.3 Frank-Kamenetskii theory . . . . . . . . . . . . . . . . . 27

3 Experimental set-up and procedures 313.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1.1 Mixture preparation equipment . . . . . . . . . . . . . . 313.1.2 Buffer vessel . . . . . . . . . . . . . . . . . . . . . . . . 363.1.3 Explosion vessel . . . . . . . . . . . . . . . . . . . . . . 36

xi

xii Contents

3.1.4 Data acquisition . . . . . . . . . . . . . . . . . . . . . . 373.2 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . 383.3 Analysis of the temperature measurement error . . . . . . . . . 413.4 Fuel Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Experimental results: 494.1 Auto-ignition limits at atmospheric pressure . . . . . . . . . . . 504.2 Auto-ignition limits of propane/air mixtures . . . . . . . . . . . 514.3 Auto-ignition limits of butane/air mixtures . . . . . . . . . . . 55

4.3.1 Auto-ignition limits of n-butane/air mixtures . . . . . . 554.3.2 Auto-ignition limits of i-butane/air mixtures . . . . . . 584.3.3 Auto-ignition limits of LPG/air mixtures . . . . . . . . 58

4.4 Comparison between the AIT and the UFL . . . . . . . . . . . 624.5 Auto-ignition limits of methane/air mixtures . . . . . . . . . . 64

5 Numerical study of the auto-ignition 715.1 Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.1.1 Background on auto-ignition modelling . . . . . . . . . 715.1.2 Mathematical model . . . . . . . . . . . . . . . . . . . . 725.1.3 Reaction mechanisms . . . . . . . . . . . . . . . . . . . 745.1.4 0-D model . . . . . . . . . . . . . . . . . . . . . . . . . . 745.1.5 1-D and 2-D CFD-Kinetics model . . . . . . . . . . . . 775.1.6 Auto-ignition criterion . . . . . . . . . . . . . . . . . . . 78

5.2 Numerical results of methane/air mixtures . . . . . . . . . . . . 805.2.1 0-D model . . . . . . . . . . . . . . . . . . . . . . . . . . 805.2.2 1-D model . . . . . . . . . . . . . . . . . . . . . . . . . . 845.2.3 2-D model . . . . . . . . . . . . . . . . . . . . . . . . . . 855.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3 Numerical results of propane/air mixtures . . . . . . . . . . . . 93

6 Influence of the vessel size on the AIT 956.1 Models for the volume dependency of the auto-ignition temper-

ature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.2 Model evaluations for spherical vessels . . . . . . . . . . . . . . 976.3 Model evaluations for vertical cylindrical vessels . . . . . . . . . 1016.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7 Conclusions and recommendations 1057.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.2 Recommendations for further research . . . . . . . . . . . . . . 107

A Test results 113

B Chemical kinetics mechanism 127

Nederlandse samenvatting 131

Contents xiii

Bibliography 139

Curriculum vitae 147

List of publications 147

xiv Contents

Chapter 1

Introduction

Life is a flame that is always burning itself out, but it catches fireagain every time a child is born.

George Bernard Shaw, Irish literary Critic, Playwright and Essayist(1856 – 1950)

Since ancient times, people consider a flickering flame a charming mystery.Fire is one of the basic elements of the world. For thousands of years people havemade use of it. It has been the object of curiosity and scientific investigation.Fire or combustion can be of great benefit, but it can also cause severe damageif it occurs uncontrolled. Many chemical processes use combustible gases andvapours at elevated pressures and high temperatures. In order to evaluate theauto-ignition hazard and to ensure the safe and economic operation of theseprocesses, it is important to obtain knowledge about the influence of the processconditions on the lowest possible temperature at which spontaneous ignitiontakes place.

1.1 The auto-ignition processFire or combustion is a chemical reaction in which a fuel reacts with oxygenand heat is released. The well-known fire triangle (Figure 1.1) represents thethree prerequisites that are needed for a fire: the fuel (1), the oxidiser (2) andheat (3). If one of these conditions is missing, fire does not occur or a fire canbe extinguished if one condition is removed. The fuels that are used in thisstudy are the low alkanes, such as methane, propane and butane. The oxidiserused in this study is air but can also be pure oxygen, chlorine (gas), bromine(liquid) or sodium bromate (solid). The lower and the upper concentrationvalues of a combustible gas within which a flame is able to propagate are calledthe flammability limits. Outside these limits the gas mixture is non-flammable.It should be taken into account that these flammability limits are depending on

1

2 Chapter 1 Introduction

Oxi

dise

r

Fuel

Energy

FIRE

Ignition Source

Spontaneously, without Ignition Source

Figure 1.1: The fire triangle.

temperature and pressure and that these limits do not apply for auto-ignitionreactions. The third condition of the fire triangle is a source of heat. Usuallythis is an ignition source, such as a spark or a flame. A second way to ignitea gas mixture is to heat it up until it ignites spontaneously. This process iscalled a spontaneous ignition or an auto-ignition.

The auto-ignition temperature (AIT) of a gas mixture is the minimum tem-perature at which a mixture of a fuel and an oxidiser ignites spontaneouslywithout ignition source. The AIT values of hydrocarbon-air-mixtures found inliterature are usually determined according to standard test methods in smallvessels and at atmospheric pressure (e.g. EN 14522, DIN 51 794, ASTM E659–78 and BS 4056–66). The auto-ignition temperature is, however, not con-stant but dependent on, for example, the following factors: pressure, volumeof the vessel and flow conditions. In industry, gas mixtures are present at highpressures and large volumes. Consequently, the standardised AIT values areoften not directly applicable to industrial conditions.

Although the auto-ignition process is very complex, some trends caused bychanges in process conditions can be predicted using a simple representationof the auto-ignition process. The auto-ignition is a balance between the heatproduction and the heat loss. If the rate of heat production is higher thanthe rate of heat loss, the temperature of the gas mixture will increase and anauto-ignition is likely to occur. An increase of pressure increases the rate ofheat production more than the rate of heat loss, which causes the ignition tem-perature to decrease. Increasing the flow and the turbulence will increase theheat loss, which make the auto-ignition more difficult to occur. Consequentlythe auto-ignition temperature will increase with increasing flow and turbulence.These influences will be described into more detail in section 2.1. The followingparagraphs will describe two other auto-ignition processes that can occur.

Auto-oxidation or self heating is a slow oxidation process that can resultinto an ignition if the heat cannot be dissipated adequately. The process ofself-heating is similar to the auto-ignition process. It is a balance between the

1.2 Gas explosions in industry 3

0 50 100 150 200 250 300 350

Refinery plants

Petrochemical plants

Gas processingplants

Number of accidents

1987-19911992-19961997-2001

Figure 1.2: Evolution of large accidents outside the USA (Marsh, 2003).

heat production due to the chemical reactions and the heat loss. Self-heatingcan occur if materials are handled in driers or with materials stored in piles. Awell known example is the spontaneous combustion of coal piles stored on theground.

Investigating the auto-ignition process is not only of interest for the identifi-cation of hazards, it can also be of benefit in combustion systems, such as dieselengines. This ignition is called a compression ignition. Adiabatic compressionresults in high temperatures according the following equation:

T2

T1= (

P2

P1)

(κ−1)κ (1.1)

where subscripts 1 and 2 refer to the initial and final state, T is the absolutetemperature and P is the absolute pressure and κ is the ratio of the specificheats. Consequently by means of compression the temperature can be increasedabove the auto-ignition temperature to cause an auto-ignition.

1.2 Gas explosions in industryOver the last 20 years there has been an increased emphasis on gas explosionsafety because of a number of serious accidents. In spite of the improvement ofthe safety management and technological development a lot of accidents stilloccur and take away human lives or cause huge financial losses. As can be seenfrom figure 1.2 the number of large accidents outside the United States remainshigh. The number of incidents in refinery plants and gas processing plants haseven increased in the period from 1997 to 2001 compared to the previous years.


Table 1.1 shows the property damage losses and casualties for some of themajor accidents in the (petro)chemical industry over the past 40 years. Thelosses are the direct damage losses and do not include additionally productionloss, down time, employee injuries and fatalities, and legal or environmentalpenalties. The ratio of the total cost of the accident to the direct propertydamage costs can be a factor of 2 to 5 according to Pekalski (2004). Theseincidents demonstrate the horrific consequences of explosions with methane,propane or butane and of explosions caused by auto-ignitions. These accidentscaused many deaths and huge financial losses. It is vital that process safetyhas a high priority in the design and operation of chemical plants. Engineersmust be able to identify and estimate the explosion hazard in order to takepreventive and protective measures. Many explosion data, such as explosionlimits, minimum ignition energies and auto-ignition temperatures can be foundin standard texts or databases. In spite of this large amount of data, un-wanted explosions still occur. One of the reasons is that most of these dataare determined at atmospheric pressure and ambient conditions, while mostindustrial processes operate under different conditions. These changes in pro-cess conditions strongly affect the values of the explosion data. For example,the auto-ignition temperature is significantly influenced by changes in processconditions, such as increased pressure, increased volume and flow conditions.Therefore large safety margins are needed in order to apply the standardisedauto-ignition temperatures to industrial processes. A poor knowledge of theinfluence of the different process conditions can lead to unsafe situations aswell as to non-economic situations. A profound study of the phenomena thatlead to auto-ignition is indispensable for a safer and more economical design ofprocess installations.

1.3 Aim and scopeIn literature a large amount of auto-ignition data is available on gas mixturesat atmospheric pressure. Auto-ignition experiments at elevated pressures are,however, scarce and the volumes in which the auto-ignition temperatures aredetermined are small (0.5 up to 1 litre). Little information is available on theauto-ignition temperature of mixtures of different fuels. It can be concludedthat the available auto-ignition data concerning the composition of the gasmixtures, the pressure and the volumes of the test vessels are limited.

Concerning the numerical simulation of the auto-ignition process there isstill a lot of work to perform. There only exist a few models (Semenov (1935),Frank-Kamenetskii (1955) and Shell Global Solutions (2001)) for the deter-mination of the auto-ignition temperature. These models contain simplifiedassumptions for the heat production inside the gas mixture and for the heatloss to the surroundings. This implies that the applicability of these models isvery limited. Besides this shortcoming these models are only validated by ex-periments at atmospheric pressure and in small volumes. The question shouldbe put whether these models are able to predict the auto-ignition temperature

1.3 Aim and scope 5

year

location

plan

ttype

substance

eventtype

aprop

erty

casualties

damageloss

b(deaths/injuries)

1966

Feyzin,F

rance

storage

prop

ane

BLE

VE

$85,000,000

18/81

1977

Umm

Said,Q

atar

gasplan

tLP

Gfire

$172,000,000

7/13+

1978

Texas

City,

USA

storage

LPG

BLE

VE

$115,000,000

7/10

1979

Goo

dHop

e,LA

,USA

tank

barge

butane

fireba

ll$20,000,000

12/25

1984

MexicoCity,

Mexico

storage

LPG

BLE

VE

$29,000,000

650/6400

1984

Ft.

McM

urray,

Can

ada

refin

ery

light

gasoil

auto-ig

nition

$109,000,000

0/0

1987

Antwerp,

Belgium

petrochemical

ethy

lene

oxide

explosion

Unk

nown

0/14

1989

Antwerp,

Belgium

petrochemical

ethy

lene

oxide

explosion

$99,000,000

32/11

1989

Pasad

ena,

TX,U

SApe

trochemical

isob

utan

eVCE

$869,000,000

23/314

1990

Warren,

PA,U

SApe

trochemical

LPG

explosion,

fire

$32,000,000

Unk

nown

1996

Yok

kaichi,J

apan

refin

ery

fuel

oil

auto-ig

nition

$750,000

0/0

1997

Martinez,

Califo

rnia,U

SArefin

ery

light

gasoil

auto-ig

nition

$22,000,000

0/0

1997

Yok

kaichi,J

apan

refin

ery

fuel

oil

auto-ig

nition

$900,000

0/4

1999

Thessalon

iki,Greece

refin

ery

light

gasoil

auto-ig

nition

$43,000,000

0/0

2001

Aruba

refin

ery

oil

auto-ig

nition

$134,000,000

0/0

2003

Geleen,

Nethe

rlan

dschem

ical

naturalg

asau

to-ig

nition

Unk

nown

3/2

Tab

le1.

1:Exa

mples

ofsomemajor

disasterswithmetha

ne,prop

aneor

butane

anddisasterswhich

arecaused

byan

auto-ig

nition

obtained

from

Lees

(1996),Marsh

(2003),theMARSda

taba

sean

dtheJS

Tfailu

rekn

owledg

eda

taba

se./aBLEVE

stan

dsforbo

iling

liquidexpa

ndingvapo

urexplosionan

dVCE

stan

dsforvapo

urclou

dexplosion,

bThe

losses

arestated

inJa

nuary2002

USdo

llars.


at elevated pressures and other process conditions with sufficient accuracy.It can be concluded that both on a theoretical and an experimental level

further research is necessary in order to determine the influence of the differentprocess conditions on the auto-ignition temperature of different gas mixtures.Therefore this study aims to accomplish the following objectives:

• Firstly, the pressure and concentration dependence of the auto-ignitiontemperature will be determined experimentally for different gas mixtures.These experiments are conducted inside an 8 litre explosion vessel atpressures up to 3 MPa and temperatures up to 720 K. The combustiblegases that will be studied are methane (CH4), propane (C3H8), n-butane(C4H10) and i-butane (C4H10). First the auto-ignition limits are de-termined for the separate components. Thereafter two LPG (LiquefiedPetroleum Gas) mixtures will be tested to investigate the influence of thedifferent components on the auto-ignition limits of the mixture.

• Secondly, a numerical model will be developed in order to describe thethermo-chemical process of the auto-ignition and to calculate auto-ignitiontemperatures at real process conditions. The auto-ignition model will fo-cus on the heat production by the comparison of different reaction mech-anisms that describe the chemical kinetics. A second focus will be onthe heat loss. Firstly the heat loss will be modelled by a zero- or one-dimensional model. Thereafter the heat loss will be modelled more ac-curately by means of computational fluid dynamics. This technique alsoallows to model the auto-ignition process under real process conditions.

1.4 OutlineIn Chapter 2 a theoretical background is given. First an overview of processconditions that affect the auto-ignition temperature is given. Secondly, a largenumber of existing standards for the determination of the auto-ignition temper-ature are compared in order to find their shortcomings and to draw lessons forthe new operating standard of this study. Finally, three auto-ignition theorieswill be described in detail. These theories will be used in the numerical modelof this study (Chapter 5).

Chapter 3 describes the experimental set-up and procedures that are usedin this study to determine the auto-ignition temperature. An analysis of thetemperature measurement error is given at the end of this chapter.

Chapter 4 presents the experimental results of the auto-ignition limits at at-mospheric and at elevated pressures. At first the results are given for propane/air,n-butane/air and i-butane/air mixtures. Thereafter the auto-ignition limits oftwo LPG (Liquefied Petroleum Gas) mixtures are compared with the auto-ignition limits of the separate fuels. The last part of the experimental studyfocuses on the auto-ignition limits of methane/air mixture. The concentrationand pressure dependence and the reproducibility of the determination of theauto-ignition limit is investigated extensively.

1.4 Outline 7

Chapter 5 describes first the numerical methods that are used in this studyto determine the auto-ignition temperature. Thereafter in section 5.2 the nu-merical results of the auto-ignition limits for methane/air mixtures are pre-sented and compared with the experimental results.

In Chapter 6 the influence of the volume on the auto-ignition temperaturewill be investigated numerically by the application of the numerical modeldeveloped in this study. Finally, the auto-ignition temperatures in sphericalvolumes are compared with the AIT in cylindrical volumes.

Chapter 2

Background on auto-ignition

Murphy’s Law about Thermodynamics: Things get worse underpressure!

anonymous

First an overview is given of the factors that influence the auto-ignitiontemperature, such as pressure, fuel type, fuel concentration, volume and auto-ignition criterion. Before describing the experimental apparatus and procedureapplied in this work, it is important to review the different methods available forthe determination of the auto-ignition temperature. Therefore the standardisedmethods are presented and compared. Subsequently, the principal experimentalmethods, which have been used to investigate auto-ignition, will be described.Finally, three ignition theories of chain and thermal ignition on which thenumerical model of this study is built, are described.

2.1 Factors influencing the auto-ignition temper-ature

The auto-ignition of a gas mixture is a complex phenomenon influenced bymany factors. The parameters which play an important role can be subdi-vided into three categories: the mixture parameters, secondly the parameterswhich are dependent on the test apparatus and finally the parameters whichare dependent on the test method:

• The mixture parameters: pressure, fuel type, fuel concentration, influenceof additives and oxidiser.

• Test apparatus parameters: volume of the test vessel, material effect ofthe test vessel and flow.

• Test method parameters: auto-ignition criterion.

9

10 Chapter 2 Background on auto-ignition

This section will only treat the factors which are investigated for this thesis.These are the pressure, fuel type, the fuel concentration, the volume of the testvessel, the material effect and the auto-ignition criterion.

2.1.1 PressureAn increase in pressure generally decreases the auto-ignition temperature of agas mixture. Since many processes in the chemical industry are conducted atelevated pressure, it is important to have knowledge of the pressure dependenceof the auto-ignition temperature. Several hydrocarbon fuels obey Semenov’sequation (see also Section 2.3.2) over a limited pressure range (Zabetakis et al.,1965):

ln(PcT0

) =EA

2RT0+ C (2.1)

where Pc and T0 are the initial pressure and temperature at the critical con-dition, EA is the activation energy of the applied Arrhenius reaction, R is theuniversal gas constant and C is a constant depending on different factors in-cluding the surface/volume ratio of the vessel and the heat transfer coefficient.A main difficulty to obtain the pressure dependency of the auto-ignition tem-perature is the determination of the activation energy. This activation energyis not only dependent on the fuel mixture, but also on the pressure and thetemperature at which the reactions occur. This activation energy can be de-termined experimentally by means of measurements of the ignition delay timeor the rate of temperature rise. These measurements are time-consuming andit is difficult to represent the industrial conditions, such as volume and pres-sure by means of an experimental set-up. Since the auto-ignition temperaturedecreases with increasing pressure, the auto-ignition temperatures determinedby the standardised methods, which are generally determined at atmosphericpressure, should not be used to assess the auto-ignition risk at elevated pres-sure. Accordingly, further research and the experimental determination of auto-ignition temperatures at elevated pressure is necessary if the auto-ignition riskof industrial processes at elevated pressure needs to be assessed.

2.1.2 Fuel typeThe auto-ignition temperature is strongly dependent on the fuel type. As canbe seen from table 2.1 the auto-ignition temperature for hydrocarbon/air mix-tures decreases with increasing molecular weight and increasing chain length.The auto-ignition temperature is also higher for branched chain hydrocarbonsthan for straight chain hydrocarbons. The auto-ignition temperature of i–butane is almost 100K higher than the auto-ignition temperature of n–butane,as can be seen from table 2.1. This behaviour can be explained qualitativelybecause for the branched i–butane a higher activation energy is needed to dis-tract a CH3-radical than for the straight n–butane. Zabetakis et al. (1965)discovered that the auto-ignition temperature of pure components obtained ina 200 ml Erlenmeyer flask according to the ASTM standard can be correlated

2.1 Factors influencing the auto-ignition temperature 11

AIT [K] Fuel868 methane788 ethane743 propane733 i–butane638 n–butane533 pentane503 hexane

Table 2.1: Summary of the auto-ignition temperatures (AIT) of alkane/air mixturesaccording to the Chemsafe (2006) database.

to the average carbon chain length Lave, defined as:

Lave =2∑giNi

M(M − 1)(2.2)

where gi is the number of possible chains, which contain Ni carbon atoms andM is the number of methyl groups. The auto-ignition temperatures of 20 hy-drocarbons are plotted as a function of the average carbon chain length onfigure 2.1. The gases that are used in this thesis are low hydrocarbons, such asmethane, propane, n–butane and i–butane. The addition of components with alower auto-ignition temperature to a mixture decreases the auto-ignition tem-perature of the mixture. An inaccurate prediction of the auto-ignition temper-ature for a fuel mixture is the auto-ignition temperature of the component withthe lowest AIT. A more precise prediction for the auto-ignition temperature ofalkane/air mixtures is a linear empirical correlation given by Ryng (1985):

AITmix =∑

XiAITi (2.3)

where Xi is the molar fraction of component i and AITi is the auto-ignitiontemperature of component i.

Some additives can also promote the auto-ignition behaviour of an alkane/airmixture although they themselves might have a higher auto-ignition temper-ature. For example, the addition of small amounts of ammonia lowers theauto-ignition temperature of a methane/air mixture (Caron et al., 1999). Thispromotion effect of ammonia has been researched numerically by the author ofthis thesis but will not be treated in this text. Further information about thisstudy can be found in (Norman et al., 2007) and (Van den Schoor et al., 2008).

2.1.3 Fuel concentrationThe concentration most sensitive to auto-ignition is generally not the stoi-chiometric concentration. The lowest auto-ignition temperature occurs at aricher concentration between the stoichiometric concentration and the upperflammability limit (Bartknecht, 1993). This is schematically shown in figure


Figure 2.1: The auto-ignition temperatures of hydrocarbon/air mixtures as a func-tion of the average carbon chain length (Zabetakis et al., 1965).

2.2. Methane/air mixtures constitute an exception to this rule according tomeasurements of Kong et al. (1995). The lowest auto-ignition temperature formethane/air mixtures occurred in the lean range of 3.0–8.0 mol% CH4, whilethe stoichiometric concentration is 9.5 mol% CH4.

In this thesis the dependence of the fuel concentration on the auto-ignitionwill be researched for the low alkane/air mixtures. Therefore different concen-trations varying from lean to rich mixtures will be tested in order to find theconcentration with the lowest auto-ignition temperature.

2.1.4 Volume of the test vesselThe auto-ignition temperature decreases with increasing vessel size. This vol-ume dependency can be determined by the Semenov model, see Section 2.3.2.For spherical vessels this model results in the following relationship betweenthe pressure and the gas temperature at auto-ignition (see equation 2.41):

ln(PcT0

) =EA

2RT0+ ln(

C√D

) (2.4)

The experimental determination of the auto-ignition temperature is charac-terised by the small volume of the test vessel (Section 2.2.1). On the otherhand, most of the industrial processes involve large vessel volumes. There-fore knowledge of the volume dependency of the auto-ignition temperature is

2.1 Factors influencing the auto-ignition temperature 13

Fuelconcentr

ation

Temperature

Mists

Saturated vapour/airmixtures

Flammable mixtures

Upper flammability limit

Lower flammability limit

AIT

Auto-ignitionzone

Figure 2.2: A typical flammability diagram

indispensable for the industrial safety. In Chapter 6 this dependency will beresearched numerically in detail.

2.1.5 Material effectBesides the volume of the test vessel, there is an influence of the material ofthe test vessel on the auto-ignition temperature. The material surfaces canpromote as well as inhibit the ignition because they can:

• create or destruct active radicals

• act as a heat source or heat sink

• modify the mass transport

• adsorb intermediary products

The material effect is more distinct for the auto-ignition at hot surfaces andfor gases with high auto-ignition temperatures. Frank and Blackham (1952)reported that a change in the metal surface had no consequence when the auto-ignition temperatures was below 290 ◦C. Coward and Guest (1927) investigatedthe ignition over heated metal strips of natural gas. Catalytic surface such asplatinum had the highest hot surface ignition temperatures (1150 ◦C up to


1400 ◦C) and the ignition temperature lowered by 100-150 ◦C if a stainlesssteel surface was applied. Smyth and Bryner (1997) also observed differencesbetween the ignition temperatures of alkanes at nickel, steel and titanium sur-faces. The highest temperatures were observed for the nickel surface, while thelowest were for the stainless steel surface and the values for titanium surfacewere intermediate.

Hilado and Clark (1972) investigated the effect of ferric oxide powder on theauto-ignition temperature of organic compounds. They found that the auto-ignition temperatures decreased if the organic compounds were in contact withrusty iron or steel. This effect was only observed for the organic compoundswith an auto-ignition temperature above 290 ◦C.

The material effect is important for chemical industries because differentmaterials can be present in the process installations. It is also possible thatcatalytic material may spread unknowingly throughout the process equipment.It is concluded that the auto-ignition temperature of organic compounds can besignificantly affected by the different materials if the auto-ignition temperatureis above 290 ◦C.

2.1.6 Auto-ignition criterionThe most commonly used auto-ignition criterion is the visual observation of aflame (see section 2.2.1). Other methods are temperature or pressure measure-ments and the analysis of the reaction products. A first disadvantage of thevisual observation is that it can not be used for the detection of invisible flamesof e.g. hydrogen. A second disadvantage is that this method is only applicableif the test set-up has visual access and no soot formation occurs. At elevatedpressure it is more difficult to obtain visual access. Therefore temperature andpressure measurements can replace the visual criterion. It is important to havean adequate criterion of the temperature and pressure rise. A change of thetemperature rise criterion from 50 K to 200 K can have a major influence onthe auto-ignition limit. The analysis of the reaction products is often timeconsuming and expensive. It is also difficult to determine by means of reactionproducts analysis if auto-ignition has occurred. This thesis focuses on findingan appropriate auto-ignition criterion for the experiments conducted at highpressure.

2.2 Experimental determination of the AITThe auto-ignition temperature of a gas mixture is influenced by many factors.Therefore it is difficult to standardise a determination method. A large numberof standards exist, which will be discussed in the following paragraph. Further-more many researchers use an experimental set-up which is adapted to theirspecific situation.

The differences in the auto-ignition temperature of methane determined bydifferent test methods are presented in table 2.2. As can be seen from this table,the auto-ignition temperature of methane is not a constant value, but depends

2.2 Experimental determination of the AIT 15

AIT [K] Test method Reference793 standard DIN 14011 Freytag (1965)810 NFPA (1951) Zabetakis et al. (1954)813 standard ASTM D-2155 Coffee (1980)813 NFPA-325M Affens and Sheinson (1980)868 standard DIN 51794 Chemsafe (2006)890 0.8/1 dm3 closed cylindrical vessel Reid et al. (1984)893 standard EN 14522 This study (Section 4.1)913 1 dm3 closed cylindrical vessel Kong et al. (1995)923 DIN 14011 Affens and Sheinson (1980)

Table 2.2: Comparison of the auto-ignition temperature (AIT) of methane/air mix-tures determined by different test methods at atmospheric pressure.

on the test method. The following paragraph will discuss and compare thedifferent standardised test methods. Paragraph 2.2.2 will describe the principalexperimental methods which have been used to investigate auto-ignition.

2.2.1 Standardised test methodsThere exists a large number of standards for the determination of the auto-ignition temperature at atmospheric pressure, e.g. EN 14522, DIN 51 794, IEC60079–4, ASTM D2155–66, ASTM E 659–78 and BS 4056–66. Each of thesestandards makes use of a similar set-up. Therefore only the European StandardEN 14522 will be described in detail. Afterwards the differences between thestandards will be described. ASTMD2883–95 is the only standard which can beused for the determination of the auto-ignition temperature at high pressurefor liquids and solids. Unfortunately no standardised method exists for theauto-ignition temperature at high pressure of gases. Therefore a new operatingprocedure will be developed in this thesis.

The European Standard EN 14522, approved on 1 August 2005, is intendedfor the determination of the auto ignition temperature of gases and vapours atambient pressure up to temperatures of 923 K. The standard test apparatusconsist of a 200 ml Erlenmeyer flask of borosilicate glass positioned in an elec-trically heated hot-air oven (Figure 2.3). Two thermocouples T1 and T2 areused to measure and to control the temperature of the flask. The fuel gasesare introduced by means of a removable filling tube and the flow rate shouldbe 25 ± 5 ml/s. In case of liquid fuels, the liquid is supplied by a syringe,which can produce droplets having a volume of 25 ± 10 µl. The test shall beclassified as an ignition if any visible flame is observed via the mirror within 5minutes after introducing the substance. Because of the visible ignition crite-rion the apparatus shall be positioned in a darkened room. The auto-ignitiontemperature is the lowest temperature at which an ignition of a flammable gasor flammable vapour in mixtures with air or air/inert gas occurs. This limitis determined by varying the temperature of the test vessel and the amount of


Mirror

Test vessel

T1

T2

Hot-air oven

Figure 2.3: Test apparatus for the determination of the auto ignition temperatureaccording to the EN 14522.

flammable substance.The other standards for the determination of the auto-ignition temperature

at atmospheric pressure are based upon on the same principle of injecting aliquid or a gas in a hot open reservoir. A summary of the existing standards isgiven in table 2.3. The majority of the standards makes use of a 200 ml erlen-meyer made of borosilicate glass. Only in the IEC 60079–4 and the BS 4056–66standard it is described that other materials like quartz or metal can be usedfor special conditions. The ASTM E 659–78 (1989) standard prescribes the useof a round bottomed vessel of 500 ml instead of a 200 ml erlenmeyer. Becausea larger volume lowers the auto-ignition temperature (see section 2.1.4), it isexpected that ASTM E 659–78 (1989) results in lower auto-ignition tempera-tures. Every standard at atmospheric pressure prescribes a visual criterion forthe detection of an auto-ignition. Only the ASTM E 659–78 (1989) and the EN14522 (2005) standards draw a distinction between a cool flame temperatureand a hot flame temperature. The maximum induction period at which theflask is observed until ignition occurs, differs from 5 for most standards to 10minutes for the ASTM E 659–78 (1989) and ASTM D 2883–95 (1995) standard.These standards also include the observation of cool flame phenomena.

There exists only one standard for the determination of auto-ignition tem-peratures of liquids and solids at pressures above 1 atm, namely ASTM D2883–95 (1995), which can be used for pressures from low vacuum up to 0.8MPa. This standard prescribes the use of a closed steel spherical vessel with


a volume of 1 dm3. A standard ampoule with 0.2 ml of the testing sample isinserted in the closed vessel. The ampoule is opened through the activationof an electromagnet, which releases the sample. There is no visual criterionsince the closed vessel has no optical access. The temperature and pressure arerecorded for a minimum of 10 minutes. The cool flame and hot flame reactionsare detected by the evolution of heat that raises the temperature and the pres-sure. There are no quantitative criteria based on a temperature or a pressurerise for the cool flame and hot flame temperature. The standard describes thedifferent types of reactions by means of illustrations of the temperature pro-files. Pre-flame reactions can last hundreds of seconds and have a temperatureincrease of about 10 K. Cool flame reactions have a duration of the order ofhundred seconds and a maximum temperature increase of 50 K, while hot flamereactions are rapid reactions with a typical duration of less than 25 seconds anda temperature rise from 80 K to 200 K.

To summarize, many standards thus exist for the determination of the auto-ignition temperature. They have several similar limitations:

• The auto-ignition temperatures of gases can only be determined at atmo-spheric pressure. There exists only one standard for the determination ofliquids and solid at a pressure up to 0.8 MPa.

• The concentrations cannot be verified and the mixing with air is nothomogeneous.

• Most of the standards use a borosilicate erlenmeyer and the influence ofother materials on the auto-ignition temperature is not examined.

• No procedure exists for oxygen enriched or oxygen depleted mixtures.

• There is no preheating of the fuel.

• Most standards only have a visual criterion without temperature mea-surements.

• Almost all set-ups are open cup systems in which volatile componentscan easily evaporate and disappear from the system.

• The test vessels are small compared to industrial installations and sincethe auto-ignition temperature decreases with increasing volume, it is im-portant to have knowledge about the volume dependency.

The new operating procedure for the experiments of this thesis will answersome of the previous shortcomings:

• The auto-ignition temperatures of gases will be determined at elevatedpressure.

• The fuel concentrations will be verified and the mixing with air will behomogeneous.


EN

DIN

IEC

BS

AST

MAST

MAST

Mmetho

d14522

51794

60079–4

4056–66

D2155–66

E659–78

D2883–9

5

p=

1atm

p=

1atm

p=

1atm

p=

1atm

p=

1atm

p=

1atm

p≤

0.8MPa

scop

eT≤

923K

T≤

923K

T≤

923K

T≤

923K

gases/vapo

urs

gases/vapo

urs

gases/vapo

urs

gases/vapo

urs

liquids

liquids

liquids/solids

borosilicate

borosilicate

borosilic

ate/qu

artz/

borosilic

ate/qu

artz/

borosilic

ate

borosilic

ate

steel

erlenm

eyer

erlenm

eyer

metal

erlenm

eyer

metal

erlenm

eyer

erlenm

eyer

roun

dbo

ttom

edexplosionvessel

test

V=

200ml

V=

200ml

V=

200ml

V=

200ml

V=

200ml

V=

500ml

V=

1l

vessel

open

open

open

open

open

open

closed

auto-ign

ition

visual

visual

visual

visual

visual

visual

temp./p

ress.

criterion

flame

flame

flame

flame

flame

flame

recordings

timecriterion

t≤

5min

t≤

5min

t≤

5min

t≤

5min

t≤

5min

t≤

10min

t≤

10min

Tab

le2.

3:Com

parisonbe

tweenstan

dardised

metho

dsforthede

term

inationof

theau

to-ig

nition

tempe

rature.


• The auto-ignition criterion will be based on temperature and pressuremeasurements.

• The vessel used in this study, as can be seen in section 3.1, has a volumeof 8 litres which is large in comparison with the volumes applied in thestandardised methods.

2.2.2 Experimental methodsNext to the standardised set-ups, a number of experimental methods existwhich have been used to investigate auto-ignition. These experimental methodscan be subdivided into four categories:

• Unstirred and stirred closed vessels

The unstirred set-up resembles the standardised methods. The majordifference is that the vessel is not open, but closed. An advantage ofthis method is that auto-ignition experiments can be conducted at ele-vated pressures. This method has been used widely by researchers, suchas Melvin (1966), Reid et al. (1984), Kong et al. (1995), Chandraratna(1999) and Pekalski et al. (2005). A disadvantage of the closed static ves-sel is the asymmetric gradient in temperature that arises from the naturalconvection because of the self-heating of the gas. Only at extremely lowgas densities or in micro-gravity environment (Foster and Pearlman, 2006)the effect of the buoyancy is small and can be neglected. An alternativeway to reduce the effect of buoyancy, developed by Griffiths et al. (1974)and Reid et al. (1984), is to incorporate a mechanical stirrer in the closedvessel. The temperature distribution will be more homogeneous becauseof the higher convection. Since the stirring improves the heat transfer atthe wall, it is expected that the auto-ignition temperature will increase.The disadvantages of these systems are the long injection time, heatingtime and stagnation time of the mixture. These disadvantages make thistechnique not suitable for experiments with a small ignition delay time,which is the time lag between the injection of the test mixture and themoment of auto-ignition. The long injection and the long heating timecause a significant uncertainty about the ignition delay time.

• Rapid compression machines

Auto-ignition may also be brought about by adiabatic compression in aRapid Compression Machine (RCM). The rapid heating of the gas mix-ture is caused by the mechanical compression ahead of a piston. Thistechnique was applied by Griffiths et al. (1994), Minetti et al. (1995),Westbrook et al. (1998) and Tanaka (2003). Contrary to the closed ves-sel set-up, the temperature of the cylinder wall of the combustion cham-ber is far from the auto-ignition temperature. In order to minimise theheat loss, the compression must be conducted very rapidly. Therefore theRCM is well suited to investigated auto-ignitions at high pressures withvery small timescales. However, this process is not fully adiabatic because


of the high pressures, high temperature gradients and considerable fluidmotions (Griffiths and Hasko, 1984). This system is commonly adoptedfor the determination of the auto-ignition behaviour of engine fuels.

• Shock Tubes

A third method to ignite a fuel mixture is by a shock wave. In a shocktube arrangement a diaphragm initially separates a high and a low pres-sure chamber. By the instantaneous bursting of the diaphragm a shockwave is generated which propagates through the low pressure chamber. Ifthe chamber is filled with the fuel mixture, the reactants are heated andcompressed instantly. This method is applied by Burcat et al. (1971),Brown and Thomas (1999) and Petersen et al. (1999). The advantage ofthis technique is the short heating time to reach temperatures up to 5000K. Therefore this technique is mainly applied for auto-ignition tests withvery low induction times.

• Continuous flow apparatus

The last type of experimental apparatus consists of the continuous flowdevices, such as the well-stirred flow reactor and the flow tubes. The well-stirred flow reactor was developed first by Longwell and Weiss (1955). Inthe Longwell jet-stirred reactor the reactants are centrally injected intoa spherical chamber through a perforated tube. These reactants igniteat some distance from the injection point, depending on the temperatureand the flow conditions. The products exit through outlets at the spherewall. The occurrence of auto-ignition is determined by the observationof a flame or a rapid increase of the temperature at the flame front. Thekinetics of the oxidation can be followed by means of gas chromatographyanalysis. This type of jet-stirred reactors was also applied at elevatedpressures by Lignola et al. (1989) and Dagaut et al. (1991).

An alternative way to ignite a reactant mixture is in a heated tube underlaminar flow conditions (Griffiths and Scott, 1987). In this set-up theignition occurs not in time but in space. For example, a two stage ignitionis observed as a spatial separation of a cool flame followed downstreamby a hot flame area. The kinetics of the oxidation can be measured byprobe sampling and gas chromatography analysis or by the spectroscopyof the chemiluminescent emissions.

2.3 Auto-ignition theoriesThe auto-ignition process can be considered as a thermal explosion or as achemical/chain explosion. For the thermal explosion theories, the auto-ignitionis considered a consequence of the imbalance between the heat production be-cause of the chemical reactions in the gas mixture and the heat loss to thesurroundings. If the heat production is greater than the heat loss, the temper-ature of the gas mixture will increase and an explosive condition arises. In the

2.3 Auto-ignition theories 21

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

�

��

��

��

�

��

��

Figure 2.4: Reaction path.

opposite case, as long as the heat loss can keep pace with the heat productionthermal explosion is impossible. The critical condition is achieved when theheat release equals the heat loss.

The chemical or chain auto-ignition theory investigates the auto-ignitionstarting from the chemical reactions and in particular the chain reactions thattake place during the auto-ignition. Although chemical auto-ignition cannot beseparated from thermal auto-ignition, because both processes take place simul-taneously, first the chemical or chain spontaneous ignition will be describedand thereafter the thermal ignition theories of Semenov (1935) and Frank-Kamenetskii (1955) will be described. Semenov (1935) was the first to describethe theory of thermal ignition in an analytical form. Later Frank-Kamenetskii(1955) extended the model to a one-dimensional one.

2.3.1 Chain spontaneous ignitionChemical reactions occur when molecules of one species collide with othermolecules. As a consequence one or more new molecules are formed. Detailedchemical kinetics are frequently used to describe the transformation at molec-ular level of reactants into products. For example, the oxidation of methanecan be described by the global reaction:

CH4 + 2O2 A CO2 + 2H2O

This reaction however does not happen like this at the molecular level. Theoxidation of methane actually consists of hundreds of elementary chain reac-tions with tens of species. An example of a reduced mechanism for the lowtemperature oxidation of methane of Reid et al. (1984) is shown in figure 2.4.Chain branching occurs when created radicals in their turn react with other


species to form more radicals. These radicals are called the chain carriers. Theamount of chain carriers n(t) generally changes as follows:

dn(t)dt

= k · n(t) + I (2.5)

The solution of this equation is:

n(t) = (n(t0) +I

k)ekt − I

k(2.6)

or for n(t0) = 0:

n(t) = (I

k)(ekt − 1) (2.7)

where t is the time and t0 is the initial time and I is the rate constant ofthe chain initiating reactions. If k > 0 the number of carriers will increaseexponentially and radical chain explosion occurs. If k < 0 which means thatthe rate constant for the chain termination is higher than that for the chaincarrier branching, the solution of equation 2.5 is, denoting that j ≡ −k:

n(t) = (I

j)(1− e−jt) (2.8)

The number of carriers will asymptotically approach I/j at steady state. Thisis a slow oxidation process. The critical point is consequently when k ∼= 0.For a system with hundreds of reactions, k is an average over all reactions tak-ing place. It is also referred to as the net branching factor φ. The group ofelementary reactions can be subdivided into four categories: chain initiating,propagating, branching or terminating reactions depending on their contribu-tion to the net branching factor. The different types of reactions can be ex-plained easily by a simple scheme that describes the low temperature oxidationof methane:

Chain initiating:

CH4 +O2 A CH3 +HO2 (2.9)

Chain propagating:

CH3 +O2 A CH3O2 (2.10)CH3O2 A CH2O + OH (2.11)

CH3O2 + CH4 A CH3OOH + CH3 (2.12)OH + CH4 A H2O + CH3 (2.13)

OH + CH2O A H2O +HCO (2.14)HCO +O2 A CO +HO2 (2.15)HO2 + CH4 A H2O2 + CH3 (2.16)

HO2 + CH2O A H2O2 +HCO (2.17)


Chain branching:

CH3OOH A CH3O + OH (2.18)CH2O +O2 A HO2 +HCO (2.19)

Chain terminating:

OH A wall (2.20)HO2 A wall (2.21)

CH3 + CH3 A C2H6 (2.22)

Reaction 2.9 is the initiation reaction in which the first radicals are formed.This reaction is slow because of the high bond energy of the first C-H bond ofCH4 which is 440 kJ/mol (McMillan and Golden, 1982). Reactions 2.10 to 2.17are propagating reactions, because as many radicals are formed as consumed.Reactions 2.10, 2.12, 2.13, 2.14, 2.15 and 2.16 are fast because they involve aradical and one of the initial reactants. The most important reactions are thebranching steps, reaction 2.18 and 2.19, in which two radicals are generatedand no radicals are consumed. These steps are necessary in order to obtain apositive net branching factor. The last class of reactions are the terminationreactions, in which more radicals are consumed than generated (reaction 2.20 toreaction 2.22). This reaction mechanism is useful for qualitative explanationsof the auto-ignition behaviour but cannot predict the auto-ignition limits quan-titatively. Therefore more extensive reaction mechanisms are needed which arevalidated with experimental studies.

2.3.2 Semenov theory of thermal ignitionThe Semenov theory of thermal ignition (Semenov, 1935) considers a zero-dimensional model of a closed vessel. The temperature of the gas mixture isassumed to be uniform across the whole volume of the system. The wall ofthe vessel is at a constant temperature and is equal to the initial temperatureof the gas mixture. The vessel has a volume V and an inside surface S. Theamount of heat release because of the chemical reaction per unit time, qr, isgiven by: by Arrhenius as:

qr = V QcnA exp(−EA/RT ) = V QρnεnA exp(−EA/RT ) (2.23)

in which Q is the heat of reaction, c is the overall concentration, n is the overallreaction order, A is the Arrhenius pre-exponential factor, EA is the activationenergy, R is the molar gas constant, T is the temperature. The concentrationc is written as the product of the density ρ and the mass fraction ε of thereacting species. The heat loss to the vessel wall is assumed to be convective,i.e. proportional to the gas-wall temperature difference:

qloss = h · S · (T − Tw) (2.24)


qr

qloss

C B A

Tstable

Tcrit ical

Tignit ion

He

at F

lux

TemperatureT0

Figure 2.5: The thermal fluxes against temperature according to the Semenovmodel.

with h the convective heat transfer coefficient, S the internal surface area, andT and Tw the temperature of the gas and of the wall, respectively.

The heat production and the heat loss are graphically represented in figure2.5. Three cases can be distinguished. The heat production can be less thanthe heat loss, or it can be the same as the heat loss or the heat productionis greater than the heat loss. Since the heat production is dependent on thepressure through the density term, three different curves A, B and C are shownin figure 2.5 which represent the heat production curves for increasing initialpressure. The straight line on figure 2.5 is the heat loss qloss. In case theheat production is represented by curve A and if the temperature of the gasmixture is below the temperature Tstable, the temperature will increase tillthe temperature Tstable is reached. If the temperature is somewhat higherthan Tstable the temperature will decrease and will remain constant aroundthe stable temperature. In case the heat production is represented by curveC, the heat production is always higher than the heat loss. The system willself-heat to explosion. The critical condition for auto-ignition exists when theheat production is represented by curve B of figure 2.5. The heat loss curveis tangential to the heat production curve at the critical temperature Tcritical.When the gas mixture is initially at a temperature T0, the temperature willslowly increase up to the unstable critical temperature. A small perturbationof the temperature will lead to the auto-ignition of the gas mixture. In orderto determine the auto-ignition temperature T0 two conditions must be fulfilled


at point Tcritical or Tc:qr = qloss (2.25)dqrdT

=dqlossdT

(2.26)

orV QρnεnA exp(−EA/RTc) = h · S · (Tc − T0) (2.27)

(EA/RT 2c )V QρnεnA exp(−EA/RTc) = h · S (2.28)

At the critical temperature it can be deduced from equations 2.27 and 2.28that:

(Tc − T0) =RT 2

c

EA(2.29)

This equation can be arranged into a quadratic form:

T 2c −

EATcR

+EAT0

R= 0 (2.30)

the solutions of which are:

Tc =12

(EAR±√E2A

R2− 4

EAT0

R) (2.31)

or

Tc =EA2R± EA

2R

√1− 4

RT0

EA(2.32)

The solution with the positive sign is not likely to occur because it results ina very high critical temperature, which is not physically possible. The secondroot with the negative sign does provide a solution for the critical temperature.This solution can be rewritten as:

Tc =EA2R− EA

2R[1− (2

RT0

EA)− 2(

RT0

EA)2 − ...] (2.33)

In general (RT0/EA) is a small number. The high order terms can thus beneglected to give the approximate equation for Tc:

Tc ≈ T0 +RT 2

0

EA(2.34)

The reaction rate ω at temperature Tc can be rewritten:

ω(Tc) = ρnεnA exp(−EA/RTc)

≈ ρnεnA exp(−EA

R[T0 + (RT 20 /EA)]

)

= ρnεnA exp(−EA

RT0[1 + (RT0/EA)])

≈ ρnεnA exp(−EART0

[1−RT0/EA)])

= ρnεnA exp[(−EA/RT0) + 1]= ρnεnA[exp(−EA/RT0]e= [ω(T0)]e (2.35)


Consequently, the reaction rate at the critical temperature is equal to the re-action rate at the initial temperature times e. The Semenov parameter Ψrepresents the ratio between the heat production potential of the reaction andthe heat loss potential through cooling:

Ψ ≡ V QρnεnA

hS ·RT 20

· exp(−EA/RT0) (2.36)

After combining equation 2.28 and equation 2.35 with previous equation, it canbe shown that at criticality the Semenov parameter Ψ = 1/e = 0.368.

In order to find the pressure dependency of the auto-ignition temperatureaccording to the Semenov model, equation 2.35 and equation 2.29 can be sub-stituted into equation 2.27. This results in:

eV QρnεnA exp(−EA/RT0) = hSRT 20 /EA (2.37)

The pressure at the critical temperature is given by the ideal gas law:

Pc =ρRTcM

(2.38)

where Pc is the total pressure at the critical point and M is the molar weight.Combining equation 2.37 and equation 2.38 results in:

(PncTn+2

0

) =hSRn+1

V QAεnMnEAe× exp( EA

RT0) (2.39)

or

ln(PncTn+2

0

) =EART0

+ ln(hSRn+1

V QAεnMnEAe) (2.40)

The order of most hydrocarbon reactions can be estimated to be 2 (Glassman,1996). Therefore equation 2.40 reduces to the following form:

ln(PcT 2

0

) =EA

2RT0+ ln(

√hSRn+1

V QAεnMnEAe) (2.41)

orln(

PcT 2

0

) =EA

2RT0+ C (2.42)

Equation 2.42 describes the pressure and temperature conditions for thermalauto-ignition. The auto-ignition limit can be represented as a straight line ona logarithmic plot as can be seen in figure 2.6. For a limited temperature rangethis equation is often reduced to:

ln(PcT0

) =EA

2RT0+ C ′ (2.43)


1/T0

auto-ignition area

no auto-ignitionln(P

/T

)c

0

2 slope = E /2RA

Pre

ssu

re

Temperature

auto-ignition area

no auto-ignition

)eEMVQA/hSRln( A223

�

Figure 2.6: The critical pressure of the vessel versus the temperature of the wallaccording to the Semenov model.

2.3.3 Frank-Kamenetskii theoryThe thermal ignition theory of Semenov is based on a zero-dimensional modeland does not allow for any temperature gradients inside the reacting system.This theory is useable as long as the temperature gradients inside the vessel aresmall in comparison with the gradient at the wall. Frank-Kamenetskii (1955)was the first to take a thermal gradient in space into account. This is importantfor reacting mixtures with a low thermal conductivity in parallel with a highheat transfer at the wall. The heat conduction equation for the vessel statesthat the increase or decrease in temperature is because of the thermal diffusionon the one hand and the heat generation by chemical reactions on the otherhand:

cvρdT

dt= ∇(λ∇T ) + q′ (2.44)

where cv is the specific heat at constant volume, λ is the thermal conductivityand q′ is the volumetric heat release rate. q′ can be expressed as:

q′ = Q ·RR = QZe−E/RT (2.45)

where Q is the volumetric heat of reaction from the mixture, RR is the reactionrate and Z is a constant containing the normal Arrhenius pre-exponential factorand a concentration term. The boundary condition at the wall of the vessel is:

− λdTdx x=L

= h · (TL − Tw) (2.46)

were TL is the temperature of the gas mixture at the wall of the system andthe other values have the same meaning as in equation 2.27 of the Semenovtheory. The Biot number Bi is a dimensionless number which relates the heattransfer resistance inside a body with that at the surface of the body and is


defined as:Bi ≡

hL

λ(2.47)

The Biot number is a measure for the temperature gradient at the wall of thevessel. A high Biot number results in a temperature TL that is approximatelythe same as the wall temperature, while a low Biot number results in a TL thatis not close to the wall temperature. For a typical reference case used in thiswork, i.e. a gas mixture of 60 mol% methane in air at a pressure of 5 bar and atemperature of 673 K, the Biot number equals about 10. This means that thetemperature gradient in the mixture is higher than the temperature gradient atthe wall. This also implies that a zero-dimensional model will result in a poordescription of the real situation, since this model does not allow gradients insidethe mixture. A one or two-dimensional model will result in a more accuratedescription of the auto-ignition process of gas mixtures. As a consequence ofthe high Biot number, the temperature boundary condition can be reduced to:

Tx=L = Tw (2.48)

A second boundary condition states that there is no temperature gradient atthe centre of the vessel:

dT

dx x=0= 0 (2.49)

The temperature of the gas mixture is initially equal to the surrounding walltemperature Tw:

T (x) = Tw at t = 0 and 0 ≤ x ≤ L (2.50)

The solution of equations 2.45 to 2.50 results in a radial temperature distribu-tion as a function of time. The mathematical solution of these equations willnot be repeated here, but can be found in Glassman (1996). In this work, seesection 5.1, computational methods will be used for solving these equations.However it is interesting to consider the solutions of the Frank-Kamenetskiimodel to gain insight into the combustion process. These two solution meth-ods are known as the stationary and the non-stationary method. At ignitionthere is a large temperature gradient. The initially small temperature rise sud-denly changes into a steep temperature rise. Therefore no stationary solutionof the energy equation exists. As a consequence the critical condition for auto-ignition is when the energy equation 2.44 has a stationary solution. By furtherderivations (Glassman, 1996) this condition can be described in terms of thedimensionless Frank-Kamenetskii parameter δ:

δ =Q

λ

EART 2

w

L2Ze−EARTw ≤ δcrit (2.51)

The Frank-Kamenetskii parameter δ is directly proportional to the reactivityand the pressure by means of Z, the dimensions of the system by L2 and alsoincludes the effect of the ambient temperature through Tw. For a spherical


vessel δcrit = 3.32, for an infinite cylindrical vessel δcrit = 2.00 and for infiniteparallel plates δcrit = 0.88.

The second approximation of the Frank-Kamenetskii theory for thermalignition is the non-stationary solution. This approximation is the same as thatposed by Semenov (1935) since no spatial variation is taken into account. Thismethod can be applied if the major temperature gradient is localised at thewall. However, the Biot numbers for the studied gas mixtures are high and theradial temperature gradient is important. Consequently, this non-stationarysolution method has less relevance for this study and will not be treated here,but can be found in Glassman (1996).

Chapter 3

Experimental set-up andprocedures

A theory is something nobody believes, except the person who madeit. An experiment is something everybody believes, except the per-son who made it.

Albert Einstein, German born American Physicist (1879 – 1955)

3.1 Experimental set-up

The auto-ignition experiments were conducted in the Laboratory for Indus-trial Safety. The laboratory contains four explosion bunkers in which it ispossible to perform safely experiments at high pressures and temperatures.This paragraph will describe the experimental set-up in more detail.

The experimental set-up, illustrated by figure 3.1, consists of four majorparts: the mixture preparation equipment, the buffer vessel, the explosionvessel and the data acquisition system.

3.1.1 Mixture preparation equipmentThe mixture preparation equipment consists of three mass flow controllers(MFC’s), a liquid pump, a mixing vessel and an evaporator. The differentcomponents of the gas mixture (e.g. air, methane, propane and butane) aresupplied in high pressure cylinders. The air and methane cylinders have a fillingpressure of 200 bar and therefore, they can be expanded directly throughout themixture preparation equipment to perform experiments with an initial pressureup to 100 bar. For the condensed fuels the pressure inside the cylinder is equalto their saturation pressure. At room temperature this pressure is equal to 7.3bar and 1.8 bar for propane and n-butane respectively. Because of this low sat-

31

32 Chapter 3 Experimental set-up and procedures

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ure

3.1:

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erim

entals

et-up.

3.1 Experimental set-up 33

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Figure 3.2: Calibration curve of Mass Flow Controller (MFC A) for methane.

uration pressure the pressure of the fuel needs to be raised by means of a liquidpump. To produce homogeneous mixtures of a desired composition, the fueland the air are supplied to the buffer vessel using the constant flow method,i.e. the different components of the mixture flow simultaneously through themixing vessel to the buffer vessel. The composition is determined based uponthe mass flow rates of the different components. Gas chromatography was usedat regular intervals to verify the mixture composition and the accuracy is foundto be 0.5 mol%.

MFC’s The three mass flow controllers A, B and C (Bronkhorst Hi-Tec) havedifferent nominal flow rates, namely 50, 20, and 4 Nl/min 1 for air. In caseother gases than air are used, conversion factors supplied by Bronkhorst canbe used to estimate the nominal flow rate. In order to increase the accuracy ofthe mixing method the MFC’s were calibrated by means of a volumetric drum-type gas meter (Ritter). The calibration curve with the standard deviations ofMFC A for methane is shown in figure 3.2. A five point calibration has beenperformed. The calibration of the mass flow controller shows excellent linearityover the total setting range. The nominal flow rate for methane is 38.2 Nl/mininstead of 50 Nl/min for air. The mass flow control panel is shown in figure 3.3.The pressure of each mass flow controller is adjusted by means of a pressurereducer before the MFC and a back pressure regulator after each MFC.

Liquid pump A volumetric metering pump was used to supply the liquidfuels. The pump is a combination of a Gilson HPLC driving unit and an Orlita

11 Nl = 1 l at 1 atm and 0 ℃.


MF65 membrane pumping head. A picture of the pump installation is shownin figure 3.4. The fuel cylinder is provided with a dip tube. The fuel is heldat a pressure of 12 bar under a nitrogen blanket. A water cooling device coolsthe fuel through a heat exchanger and maintains the pump head at a constanttemperature of 10 ◦C in order to prevent the evaporation of the fuel and toguarantee a constant mass flow. A back pressure regulator situated after thepump ensures that the outlet pressure remains constant at 50 bar. The liquidpump was calibrated with the liquid fuel and equal temperature and pressuresettings. The volume rate was measured by means of a pipette. The calibrationcurve of the pump for propane is shown in figure 3.5. The nominal flow of theliquid pump for water is 10 ml/min. In case liquid propane is used the nominalflow amounts to 7.15 ml/min only. The calibration curve shows an excellentlinear correlation.

Mixing vessel The gases, e.g. methane and air, coming from the mass flowcontrollers are mixed homogeneously inside the mixing vessel.

Evaporator The evaporator ensures evaporation of the liquid fuel. The liq-uid fuel drips into the gas flow and is subsequently heated. The evaporatorconsists of a 3 m copper tube embedded in an electrically heated concretemass. The evaporator has a design pressure of 300 bar at a maximum temper-ature of 300 ◦C. For all experiments with liquid fuels the temperature was setto 120 ◦C and the pressure was set to at least 10 bar by means of the backpressure regulator that is positioned after the evaporator. It is important thatthe pressure of the gas mixture is sufficiently below its vapour pressure in or-der to avoid condensation of the fuel. The vapour pressure is correlated withtemperature by numerous methods. The classic simple equation for correlationof low to moderate pressures is the Antoine equation:

lnP sat = A+B

T + C(3.1)

A, B and C are regression constants. At high pressure the Antoine equationdoes not fit the vapour pressure accurately (Perry and Green, 1999). Therefore,a regression with the modified Riedel equation (Equation 3.2) is used in thiswork to calculate the vapour pressure of the liquid fuel.

lnP sat = A+B

T+ C lnT +DTE (3.2)

A, B, C and D are regression constants and E is an exponent equal to 1 or 2depending on which regression gives the most accurate fit. These coefficientsare summarised in table 3.1 for the liquid fuels applied in this work. The tem-perature and concentration dependency of the vapour pressure for n-butane/airmixtures is shown in figure 3.6. From this figure, it can be deduced that fora temperature of 120 ◦C and a pressure of 55 bar the butane concentration ismaximum 40 mol% in order to avoid condensation.


Figure 3.3: Gas mixing installation.

Cooling

Pump

Back pressure

Figure 3.4: Liquid pump installation.

fuel A B C D Epropane 59.08 -3492.60 -6.07 1.09e-05 2n-butane 66.34 -4363.20 -7.05 9.45e-06 2i-butane 100.18 -4841.90 -13.54 2.01e-02 1

Table 3.1: Regression coefficients of the modified Riedel equation for propane, n-butane and i-butane.


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Figure 3.5: Calibration curve of liquid pump.

3.1.2 Buffer vesselThe homogeneous gas mixture flows from the evaporator into the buffer vessel.This spherical vessel has a volume of 8 dm3 (internal diameter of 248 mm) andis made of 26 Ni Cr Mo V 14 6 steel. It is designed to withstand explosionpressures up to 3500 bar at a wall temperature of 350 ◦C. The vessel can beused to determine flammability limits when an ignition source is introducedas is described in more detail by Van den Schoor (2007). In this study thebuffer vessel is used to maintain the premixed reactants at high pressure (upto 50 bar) and at a temperature of 120 ◦C in order to accelerate the fillingof the explosion vessel. On the one hand the temperature must be sufficientlyhigh to avoid condensation of the fuel and also pre-oxidation of the gas-mixturemust be avoided. Since the temperature of 120 ◦C is some 200 ◦C below theauto-ignition temperatures of the different fuels, pre-oxidation does not occur.The vessel is equipped with three electrical heating units to obtain uniformtemperature. The piping between the evaporator, the buffer vessel and theexplosion vessel is also heated to a temperature of 120 ◦C by means of electricalrope heaters to avoid condensation of the fuel.

3.1.3 Explosion vesselThe second vessel is the explosion vessel. It has a spherical volume of 8 dm3

and is made of X 2 Cr Ni Mo 18 10 steel. The vessel is equipped with threeelectrical heating units to obtain a uniform temperature. It is designed towithstand pressures up to 250 bar at temperatures up to 550 ◦C. The vessel


0

50

100

150

200

0 20 40 60 80 100 120 140 160 180 200Temperature [°C]

Satu

ratio

n pr

essu

re [b

ar]

20 mol%40 mol%60 mol%80 mol%100 mol%

Figure 3.6: Vapour pressure curve of n-butane/air mixtures as a function of then-butane concentration.

has one large opening at the top through which it is possible to clean the vessel.It also has several small gaps for the temperature and pressure measurementsand if necessary for an ignition source. A picture of the buffer vessel and of theexplosion vessel inside the explosion bunker is presented in figure 3.7.

3.1.4 Data acquisitionThe data acquisition system consists of a pressure and temperature measuringsystem. The data are collected by a data scanner (Labview 6.1 of NationalInstruments). The scan frequency is 1000 Hz, which is sufficient to followthe pressure and temperature rises during the auto-ignition. The followingparagraphs will discuss in detail the different measuring systems.

Pressure measuring system The pressures in both vessels are measuredwith Baldwin 5000 psi strain gauges. These static pressure transducers arebased on the piezo-resistive effect, in which the resistance of the transducerchanges depending on the applied force. To avoid temperature influence onthe pressure transducer a connecting pipe, cooled by a water bath at 10 ◦C, isplaced between the explosion vessel and the transducer. The pressure trans-ducers are connected to an amplifier, which transforms the pressure signal to a0-5 V signal. The maximum pressure of the pressure transducer is 5000 psi or350 bar. The amplification factor is adjusted that the measured pressure rangecorresponds to the 0-5 V range. The voltage signal is subsequently read in bythe computer by means of a 16 bits PCI-6032E data acquisition card produced


Buffer vessel Explosion vessel

Figure 3.7: Picture of the buffer and the explosion vessel.

by National Instruments. The pressure transducers were calibrated by meansof a static pressure system (Scantura B20: multifunction calibrator) and theirerror is below 1%.

Temperature measuring system The thermocouples used in this studyare Chromel-Alumel type K thermocouples. Thermocouples differ also in typeof construction, as can be seen in figure 3.8. With the ungrounded thermo-couple there is no direct contact between the junction and the covering. Asa consequence the thermocouple is highly wear-resistant and is also resistantto interference noise. A second type is the grounded thermocouple, in whichthere is direct contact between the junction and the shield. The third type isthe exposed thermocouple. The thermocouple junction here is exposed to thesurroundings and is not protected from wear. The advantage of this type ofthermocouple is its short response time. The number and type of thermocou-ples has changed several times during this study. At first the temperature wasmeasured with one ungrounded thermocouple (with an external diameter of 1mm) at the centre of the vessel. Since the temperature increase is most signif-icant at the top of the vessel because of the buoyancy, a second ungrounded 1mm thermocouple was added at the top of the vessel. In order to study thebuoyancy in detail a set-up was used with three exposed thermocouples with anexternal diameter of the junction of 500 µm. The thermocouples were locatedat the centre, 6 cm above the centre and at the top of the vessel. The error onthe temperature measurement is described in section 3.3.

3.2 Experimental procedureThe following procedure is applied to determine the auto-ignition limits and theignition delay times. First the evaporator, the buffer vessel and the explosionvessel are heated to the required temperature and kept at this temperature.Subsequently, the buffer vessel is brought to vacuum pressure and purged with

3.2 Experimental procedure 39

Ungrounded Grounded Exposed

Figure 3.8: Different types of thermocouple

300

400

500

600

700

800

900

1000

1100

0 10 20 30 40 50 60 70 80 90 100

Time [s]

Tem

pera

ture

[K]

0

0.5

1

1.5

2

2.5

3

Pressure [MPa]

Top Temp

Elevated Temp

Central Temp

PressureIgnition Delay Time

Maximum Ignition Delay Time

Figure 3.9: Recorded pressure and temperature histories in the explosion vessel("Top Temp" represents the temperature at the top of the vessel while "ElevatedTemp" and "Central Temp" respectively represents the temperature 6 cm above andat the centre of the vessel).

a mixture volume of at least ten times the volume of the buffer vessel. Next,the buffer vessel is filled to a pressure of 2 to 5 MPa depending on the initialpressure of the test. The evacuation and the subsequent flushing ensure anaccurate and homogeneous fuel mixture in the buffer vessel. Thereafter theexplosion vessel is evacuated to a pressure below 1000 Pa. Finally, the explo-sion vessel is filled to the desired pressure with the premixed gas mixture byopening the pneumatic valves between the buffer and the explosion vessel. Thisfilling procedure guarantees a constant filling time for a specific pressure of thebuffer vessel because of the choked gas flow in the connecting tubing. Aftereach experiment the explosion vessel is emptied and flushed with air during 2minutes to ensure that the amount of residual gases is negligible. Thereafterthe buffer vessel is refilled to its initial pressure and a new experiment can beperformed. Figure 3.9 shows a typical time history of pressure and temperatureinside the explosion vessel during an experiment. The filling time varied from


Type of reaction Temp.a and Rel. press. rise Ignition delay timeNo reaction < 50 K and < 10% > 15 minAuto-ignition > 50 K or > 10% < 15 min

Table 3.2: Classification criteria for propane and butane. /a The temperature riseis measured with two ungrounded thermocouples with a diameter of 1 mm.

Type of reaction Temperature rise b Ignition delay timeNo reaction < 50 K > 10 min

Slow Combustion > 50 K and < 200 K < 10 minAuto-ignition > 200 K < 10 min

Table 3.3: Classification criteria for methane. /b The temperature rise is measuredwith exposed thermocouples with a diameter of 0.5 mm.

5 to 30 seconds, depending on the pressures of the buffer and explosion vessel.This filling time causes an uncertainty in the ignition delay time (IDT), whichis the time lag between the completed injection of the test mixture and anyexothermic phenomenon (see figure 3.9). The IDT’s presented in this work donot include the filling time.

The occurrence of an auto-ignition is judged from the pressure and temper-ature histories. The classification criteria are slightly different from propaneand butane compared to methane as can be seen in tables 3.2 and 3.3. Forpropane and butane a combined temperature and pressure criterion is applied.When the temperature rise is smaller than 50 K within 15 minutes after fillingthe vessel and the pressure increase is smaller than 10%, it is concluded thatauto-ignition did not take place. A temperature rise of more than 50 K or apressure rise of more than 10% within a time period of 15 min is classified asan auto-ignition. The maximum ignition delay time is chosen to be 15 min-utes which is of the same order of magnitude as those used in other studies orstandards (Safekinex (2005), Kong et al. (1995), EN 14522 (2005)).

In order to compare the auto-ignition limits of the methane/air mixtures tothose obtained by Caron et al. (1999), their ignition criterion is adopted. Thiscriterion is a single temperature rise criterion. When the temperature rise issmaller than 50 K within 10 minutes it is concluded that auto-ignition did nottake place. A maximum temperature rise above 200 K is classified by theseauthors as an auto-ignition, while a temperature rise between 50 K and 200 Kis classified as a slow combustion.

Because of the thermal inertia of the explosion vessel, it is not feasible tochange the explosion vessel temperature between two experiments in order tofind the auto-ignition temperature. Instead of varying the temperature, theinitial pressure was varied at a constant vessel temperature. An example ofthe auto-ignition data of a 50 mol% n-butane/air mixture is presented in figure3.10.

3.3 Analysis of the temperature measurement error 41

0

0.5

1

1.5

2

2.5

490 500 510 520 530 540 550

Initial temperature [K]

Initi

al p

ress

ure

[MPa

]

Auto-ignitionNo reactionAIT limit

Figure 3.10: Determination of the auto-ignition limit of a 50 mol% n-butane/airmixture.

3.3 Analysis of the temperature measurementerror

In order to measure the gas temperature inside the explosion vessel, one ormore type K thermocouples are inserted inside the explosion vessel. The typeK thermocouple is commonly used and consists of a positive Ni-Cr wire incombination with a negative Ni-Al wire and has a temperature range from -270◦C up to 1372 ◦C. The sensitivity of this thermocouple amounts to 40 µV/◦C.The measurement errors have to be analysed. The error on gas temperaturemeasurement can be subdivided into three categories:

• First there is the error on the probe temperature measurement. The read-ing of the data acquisition system is not the actual probe temperature.The manufacturer of the thermocouples, OMEGA, prescribes a relativeerror of 0.5% for the type K thermocouples.

• The next group of errors originates from the temperature difference be-tween the gas temperature and the probe junction temperature. Theseerrors can be explained by the steady state energy equation:

qc + qr + qd = 0 (3.3)

where qc represents the convective heat flux from the boundary layer tothe probe junction, qr represents the heat transfer from the probe by radi-ation and qd the heat transfer by conduction. For type K thermocouplesthe catalytic reactions between the metals and the surrounding gases aregenerally negligible. Consequently there is no heat source term resultingfrom catalytic reactions in the energy equation. The respective errors are


the conduction error EC and the radiation error ER. The conductionerror is described by Arts et al. (2001):

EC = TG − TJ =TG − TM

cosh(L( 4hDλ )1/2)

(3.4)

where TG is the gas temperature, TJ is the junction temperature, TMis the temperature of the probe stem, L is the length for conduction, his the convective heat transfer coefficient, D is the diameter of the wirecomprising the thermocouple and λ is the thermal conductivity of thethermocouple material. The radiation error ER is calculated by consid-ering the energy equation and neglecting the heat transfer by conduction.The heat transfer by radiation has two parts. Firstly there is the thermalradiation from the probe to the cold wall of the vessel and secondly thereis the thermal radiation from the hot burning gas to the probe:

FJ→W τ′σSRεJ(T 4

J −T 4w)−FJ→GσSRεJ(T 4

G−T 4J ) = hSc(TG−TJ) (3.5)

where F is the view factor, τ ′ is the transmittance through the gas mix-ture, σ is the Stefan Boltzmann constant (5.67 10−8W/m2K4), SR is theradiation heat transfer area, εJ is the emissivity of the probe, TW is thetemperature of the surrounding walls and Sc is the area for heat transferby convection. The radiation error can be obtained from equation 3.5 byomitting the surface areas and the view factors:

ER = TG − TJ =τ ′σεJ(T 4

J − T 4w)− σεJ(T 4

G − T 4w)

h(3.6)

This equation has to be solved iteratively since the temperature of the gasis on both sides of the equality sign. Notice that this result is independentof the emissivity of the surrounding wall. After analysing the above equa-tions it becomes clear that the heat transfer coefficient is to be maximisedin order to reduce the conduction and radiation error. It is difficult todetermine the heat transfer coefficient when an auto-ignition occurs in-side a closed vessel. The heat transfer coefficient during the auto-ignitioncan be calculated for a forced convective flow along the thermocouple.The natural convective flow is in fact a forced flow from the point of viewof the thermocouple. The heat transfer coefficient is determined using acorrelation for the Nusselt number valid for forced convective flow alongcylinders which are normal to the flow direction:

Nu = (0.44± 0.06)(Re)0.50 (3.7)

With Nu = hcDλ and Re = v·D

ν , where λ is the thermal conductivity ofthe gas, D is the junction diameter, v is the flow velocity and ν is thekinematic viscosity of the gas.

• Finally the temperature of the junction is not immediately equal to thegas temperature. The response of a thermocouple may be modelled as a


first order system. When a thermocouple is subjected to a rapid temper-ature increase, it will take some time to respond depending on the timeconstant of the thermocouple. The transient error is given by:

ET = TG − TJ = τdTJdt

(3.8)

withτ =

mCphSc

=ρCpD

6h(3.9)

where τ is the thermocouple time constant, m is the mass of the ther-mocouple junction, Cp is the specific heat of the thermocouple material,Sc is the area for heat transfer by convection and ρ is the density of thethermocouple material. Figure 3.11 shows the responses of three thermo-couples with different time constants to a sudden temperature increase of200 K with a duration of 3 seconds. It can be seen from figure 3.11 thatonly the thermocouple with a time constant of 0.5 s is able to measure thesteep temperature increase. The exposed thermocouple used in this studywith a junction diameter of 500 µm has a time constant of 1.3 s, whilethe ungrounded 1mm thermocouple has a time constant of 4s accordingto Omega, the manufacturer of the thermocouples. This means that theexposed thermocouple responds 3 times faster than the ungrounded 1mmthermocouple. This ratio is also retrieved from the theoretical analysis.The exposed thermocouple with a time constant of 1.3 s has a maximumtemperature increase of 180 K, while the ungrounded thermocouple onlyshows a temperature increase of 100 K in comparison with the appliedtemperature increase of 200 K.

As an example, these errors on the temperature measurement are calculated foran auto-ignition experiment with a 60 mol% methane/air mixture at an initialtemperature of 683 K and an initial pressure of 1.7 MPa when a temperatureincrease of 200 K is measured with an exposed thermocouple with a diameterof 0.5 mm. The buoyancy driven flows have a velocity magnitude of 2 ± 1cm/s along the vertical axis of the sphere. This is retrieved from the CFDcalculations of this study, see section 5.2. For the calculation of the radiationerror, the transmittance τ ′ through the gas mixture has to be calculated. Thetransmittance is the fraction of the incident energy that passes through the gasvolume. This is equal to the incident energy minus the energy absorbed by thegas when the reflection or the scattering is neglected. Kirchhoff’s law statesthat the absorbance α is equal to the emittance ε:

τ ′ = 1− α = 1− ε (3.10)

According to Hubbard and Tien (1978) the emittance can be described infunction of the Planck mean absorption coefficient κM and the path length L,which is equal to the radius R of the vessel:

ε = 1− e(−κML) (3.11)


0

50

100

150

200

250

0 1 2 3 4 5 6 7 8 9 10 11

Time [s]

Tem

pera

ture

incr

ease

[K]

time constant = 0.5stime constant = 1.3stime constant = 4s

Figure 3.11: Response of a thermocouple to a temperature increase step of200K.

The Planck mean absorption coefficient κM is calculated from the Planck meanabsorption coefficients κp,i of the different radiating species, such as CH4, CO2,CO and H2O, via:

κM =∑i

piκp,i(T ) (3.12)

with pi the partial pressure of the radiating species and κp,i(T ) are obtainedfrom Hubbard and Tien (1978). The Planck mean absorption coefficient isdirectly proportional to the absolute pressure of the gas mixture. Consequently,the radiation error is depending on the pressure of the gas mixture. Since thepath length influences the absorption of the gas layer, the radiation error will bedifferent for the three thermocouples, positioned at the centre, 6 cm above thecentre and at 1 cm from the top of the vessel. For the thermocouple positionedat the top of the vessel the path length to the top side of the vessel is muchsmaller than for the elevated temperature and for the central thermocouple.Table 3.4 gives an overview of the error on the probe temperature and theerrors by conduction and radiation for a temperature increase of 200 K. It canbe seen that the radiation losses in particular for the thermocouple positionedat the top of the vessel give rise to a significant error on the temperaturemeasurement. Table 3.5 presents the influence of the pressure on the radiationerror. At a pressure of 1 bar or 0.1 MPa the radiation error is larger than ata pressure of 1.7 MPa due to the lower absorption capacity of the gas mixtureand consequently the higher radiation heat loss from the probe junction to the


Error type Valueprobe temperature error 3 K

conduction error 1 Kradiation error (top therm.) 17 K

radiation error (elevated therm.) 2 Kradiation error (central therm.) 0.06 K

Table 3.4: The absolute errors on the temperature measurement evaluated for atemperature increase of 200 K measured with exposed 0.5 mm thermocouples.

Error type Value for 0.1 MPa Value for 1.7 MParadiation error (top therm.) 45 K 17 K

radiation error (elevated therm.) 41 K 2 Kradiation error (central therm.) 40 K 0.06 K

Table 3.5: The influence of pressure on the radiation error evaluated for a temper-ature increase of 200 K measured with exposed 0.5 mm thermocouples.

wall. The effect of the position of the thermocouple increases with increasingpressure. At a pressure of 0.1 MPa the radiation error has only a temperaturedifference of 5 K for the different thermocouples, while at a pressure of 1.7MPa the radiation error differs 17 K between the central thermocouple and thethermocouple at the top of the vessel.

The last type of error is the transient error. Figure 3.12 presents the tem-perature history of an auto-ignition with a 60 mol% methane/air mixture at atemperature of 683 K and a pressure of 1.7 MPa measured with three exposedthermocouples. Figure 3.13 represents the temperature history if the thermo-couples would have a time constant of 4s instead of 1.3 s. After comparisonof both figures, it can be seen that the ungrounded thermocouples would notbe able to follow the steep temperature increase and the central thermocouplewould only measure a temperature increase of 122 K instead of a temperatureincrease of 202 K. Figure 3.14 presents the calculated temperature historiesin case three fast thermocouples with a time constant of 0.5 s would havebeen used. It can be seen that the maximum temperature would slightly in-crease (20 K) for the thermocouple at the top of the vessel while the maximumtemperature of the central thermocouple would measure the same maximumtemperature as the other thermocouples.

It can be concluded that the transient error and the radiation error giverise to the largest errors on the temperature measurement. Therefore attentionmust be paid if the auto-ignition criterion is based on a temperature measure-ment. As can be seen from this analysis, one ungrounded central thermocouplewith a large time constant is incapable of capturing the maximum temperaturerise. A combined temperature and pressure criterion is advised in order toassess the auto-ignition.


400

450

500

550

600

650

700

300 310 320 330 340 350 360 370 380 390 400

Time [s]

Tem

pera

ture

[°C

]

Top TempElevated TempCentral Temp

Original temperature historyTime constant = 1.3 s

Figure 3.12: Temperature history of an auto-ignition measured with three exposedthermocouples with a time constant of 1.3 s.

400

450

500

550

600

650

700

300 310 320 330 340 350 360 370 380 390 400

Time [s]

Tem

pera

ture

[°C

]

Top TempElevated TempCentral Temp

Time Constant = 4 s

Figure 3.13: Calculated temperature history of an auto-ignition measured withthree exposed thermocouples with a time constant of 4 s.

3.4 Fuel Type 47

400

450

500

550

600

650

700

300 310 320 330 340 350 360 370 380 390 400

Time [s]

Tem

pera

ture

[°C

]Top TempElevated TempCentral Temp

Time Constant = 0.5 s

Figure 3.14: Calculated temperature history of an auto-ignition measured withthree exposed thermocouples with a time constant of 0.5 s.

3.4 Fuel TypeThe combustible gases that will be studied are methane (CH4), propane (C3H8),n-butane (C4H10) and i-butane (C4H10). Methane is the simplest alkane. Itis the principal component of natural gas. It is commonly used as a fuel inthermal power stations or in households because it has a clean burning processwith low CO2 emissions compared to higher alkanes and coal. Methane is alsocommonly used in the chemical industry as a feedstock for the production of forexample, hydrogen, methanol, acetic acid and acetic anhydride. In this thesisthe experiments are performed with pure methane and not with natural gas inorder to avoid the influence of other unknown components on the auto-ignitionlimits. The methane gases are supplied in high pressure cylinders (200 bar)with a purity of 99.95%.

The other fuels studied in this thesis are the higher alkanes with three orfour carbon atoms. These can be classified under the name LPG (LiquefiedPetroleum Gas) which is commonly used for a mixture of propane, i-butaneand n-butane. LPG has many applications. For example, it can be a basematerial for many chemical processes, it is a well-known motor fuel. Propane isused as propellant in aerosols in substitution for the noxious chlorofluorocarbongases and propane can also serve as a cooling agent in refrigerating machines.Just as any other gas it consists of small traces of other fuel products. Themaximum quantity of these impurities is determined by the standard NBNT 52-706 (2000). The composition of LPG is not fixed, but depends on thecountry and may also change with the season. This variation in composition


Component Boiling temperature [◦C] Vapour pressure at 21◦C [MPa]propane -42.1 0.86i–butane -11.7 0.31n–butane -0.5 0.21

Table 3.6: The boiling temperature and the vapour pressure of the components ofLPG.

is due to the different boiling-points of the different components. Table 3.6presents the respective boiling temperatures at atmospheric pressure and thevapour pressures at a temperature of 21◦C.

Propane is the most volatile component of LPG. Increasing the concentra-tion of propane in the LPG mixture will lower the boiling temperature of theLPG mixture. A high volatility is necessary when the outside temperature islow. On the other hand in warm regions a high concentration of butane is ad-vised. In Belgium during winter the propane/butane ratio is 70/30, while dur-ing summer the propane/butane ratio is 60/40. In France the propane/butaneratio is about 35/65, while in Spain the LPG mixture consists mostly of bu-tanes. In this study at first the pure components of LPG were tested. Thesefuels were supplied in pressure cylinders with a purity of 99.9%. Instead of us-ing commercial LPG mixtures with traces of impurities to determine the auto-ignition behaviour, it is chosen to work with two pure mixtures of propane,i-butane and n-butane. The first LPG mixture studied has a composition of 50mol% propane and 50 mol% n-butane. The second mixture has the followingcomposition: 40 mol% propane, 30 mol% iso-butane and 30 mol% n–butane.The maximum error on the concentrations of the different components is 1.5mol%.

Chapter 4

Experimental results:

The men of experiment are like the ant; they only collect and use.But the bee . . . gathers its materials from the flowers of the gardenand of the field, but transforms and digests it by a power of its own.

Leonardo Da Vinci, Italian draftsman (1452 – 1519)

The main objective of the experimental part of this study is to obtain alarge set of auto-ignition temperatures at elevated pressures for different gasmixtures. On the one hand these data can be used directly to assess the auto-ignition risk of industrial installations and on the other hand these data willbe used for the validation of the simulation models. The experimental partof this study consists of the determination of the auto-ignition temperaturesof the lower alkane/air mixtures, in particular methane, propane, n-butaneand i-butane in air at pressures up to 3 MPa. This part consists first of ex-periments with propane/air and butane/air mixtures (Section 4.2 and Section4.3). These are the main components of liquified petroleum gas (LPG). Atfirst the auto-ignition limits are determined for each individual fuel componentin air. Thereafter two different LPG mixtures are tested in order to comparethe influence of the different components on the auto-ignition temperature ofa mixture.

The experiments with methane/air mixtures (Section 4.5) are an additionon the data obtained by Caron et al. (1999). Since the numerical study mainlyfocuses on the auto-ignition limits of methane/air mixtures, it was necessaryto gain more insight into the experimental phenomena in order to compare thenumerical results with the experimental data of methane/air mixtures.

Knowledge of the auto-ignition domain is also relevant for the determinationof flammability limits at elevated pressure and temperature. In section 4.4 theexperimental upper flammability limits of propane and n-butane are comparedwith their respective auto-ignition areas in order to clarify some observations.In section 4.1 the auto-ignition limits at atmospheric pressure of the differentfuels used in this study are presented.

49

50 Chapter 4 Experimental results:

Temperature [K] Quantity Flammable (+/-)733 60 ml +713 40 ml +703 20 ml +693 40 ml +693 20 ml +688 20 ml -688 60 ml +683 60 ml +678 60 ml -678 40 ml -678 20 ml -678 80 ml -673 60 ml -673 30 ml -668 60 ml -

Table 4.1: Determination of the auto-ignition temperature of n-butane according tothe European standard EN 14522 (2005).

An overview of the experimental data can be found in Appendix A. Partof the experimental results of propane/air mixtures have been published in aninternational journal with review (Norman et al., 2006).

4.1 Auto-ignition limits at atmospheric pressureFirst the auto-ignition temperatures are determined at atmospheric pressureaccording to the EN 14522 (2005). The standard is described in section 2.2.1.Table 4.1 presents the test series for the determination of the auto-ignitiontemperature of n-butane. From table 4.1 it can be deduced that the auto-ignition temperature of n-butane according the EN 14522 is 683 K or 410 ◦C± 5 K.

Table 4.2 gives a comparison of the auto-ignition temperatures obtainedin this study according to the EN 14522 with the auto-ignition data recom-mended by the Chemsafe (2006) database. It can be seen that the measuredauto-ignition temperatures are generally 20K higher than the respective tem-peratures from the Chemsafe database. This difference corresponds to the av-erage deviation in experimentally determined AIT-values in literature, whichis about 30K (Tetteh, J. et al., 1996). The auto-ignition temperature decreasessignificantly with increasing chain length and the branched i–butane has ahigher auto-ignition temperature in comparison with n–butane. The auto-ignition temperatures of the propane/butane mixtures is situated somewherebetween the auto-ignition temperatures of their respective components. Theauto-ignition temperature of different alkane/air mixtures can be predicted bythe rule of thumb of Ryng (1985), which is described in section 2.1.2. Table 4.3

4.2 Auto-ignition limits of propane/air mixtures 51

Fuel measured AIT AIT[EN 14522 (2005)] [Chemsafe (2006)]

[DIN 51794 (1969)]methane 893 K 868 Kpropane 763 K 743 Ki–butane 753 K 733 Kn–butane 683 K 638 K

50/50 n-butane/propane 743 K –40/30/30 propane/i–/n–butane 733 K –

Table 4.2: Comparison of the measured auto-ignition temperatures (AIT) deter-mined in this study with the AIT from the Chemsafe (2006).

Fuel measured AIT AIT [Ryng]50/50 n-butane/propane 743 K 723 K

40/30/30 propane/iso- and n-butane 733 K 736 K

Table 4.3: Comparison of the measured auto-ignition temperatures (AIT) ofpropane/butane mixtures with the predicted auto-ignition temperatures determinedby a correlation of Ryng (1985).

compares the measured data with the predicted ones. The predicted and themeasured auto-ignition temperature of the 50/50 mol% n-butane/propane mix-ture differ by 20 K, while for the 40/30/30 mol% propane/i–butane/n–butanemixture the measured AIT corresponds very well with the predicted value.

4.2 Auto-ignition limits of propane/air mixturesThis section and the following sections (Section 4.3 and 4.5) present the ex-perimental auto-ignition limits at elevated pressures determined according thenew standard operating procedure, which is developed in this study (see Sec-tion 3.2). This section present the results of the propane/air mixtures. Firstthe auto-ignition limit is determined for a mixture with a concentration of 40mol% propane in air. The propane concentration in air can also be expressedin terms of the excess air factor λair or the equivalence ratio φ:

λair =1φ

=[Xair/Xfuel]mixture

[Xair/Xfuel]stoichiometric(4.1)

where X stands for the molar fraction. Since the stoichiometric concentrationof propane in air is equal to 4.03 mol%, a 40 mol% propane/air mixture corre-sponds with an equivalence ratio φ of 16 or an excess air factor λ of 0.063. Themixtures that are tested in this study vary from rich to highly rich mixtures,because these mixtures have the lowest auto-ignition temperatures at elevatedpressures. This is also observed by Kong et al. (1995) for propane/air mixtures.


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

520 530 540 550 560 570 580

Temperature [K]

Initi

al P

ress

ure

[MPa

]AutoignitionNo reaction

ignition

no ignition

Figure 4.1: The auto-ignition limit of propane-air mixtures as a function of theinitial temperature, determined for 40 mol% propane in air.

A few tests with lower concentrations are performed with the different mixturesto confirm the increase of the auto-ignition limit at low concentrations.

Because of the thermal inertia of the explosion vessel, the auto-ignition limitis determined at a constant vessel temperature and a varying pressure. Theauto-ignition limit is determined with a step-size of maximum 0.05 MPa. Theauto-ignition criterion is a combined temperature and pressure rise criterion.When a temperature rise of minimum 50 K or a pressure rise of more than10 percent of the initial pressure is measured within a time span of fifteenminutes, it is concluded that auto-ignition occurred. In the first two series oneungrounded 1 mm thermocouple is positioned at mid-height near the wall of thevessel. In the third series of experiments two ungrounded 1 mm thermocouplesare used. One is positioned at mid-height near the wall and the other at thetop of the vessel. As can be seen from the error analysis of the temperaturemeasurement in section 3.3, these thermocouples have a large time constantand cause significant transient errors. Therefore attention must be paid whena temperature criterion is applied. From the experiments it is observed that themaximum ignition delay time of fifteen minutes is the determining criterion atlow concentrations and at low temperatures. For increasing initial temperaturesand concentrations the criterion that determines the auto-ignition shifts to thepressure rise criterion. The temperature rise is never the determining criterionbut can be used in order to assess the auto-ignition or to compare with thenumerical simulations made of this study.

The result of one test series with a 40 mol% propane/air mixture is sum-marised in figure 4.1. The pressure limit for auto-ignition increases with de-creasing initial temperatures. At atmospheric pressure the auto-ignition tem-perature is equal to 573 K, while at an initial pressure of 1.45 MPa the auto-ignition temperature decreases to 523 K. An exponential correlation can be

4.2 Auto-ignition limits of propane/air mixtures 53

4

5

6

7

8

9

1.70 1.75 1.80 1.85 1.90 1.95

1/T0 [1e-3/K]

ln(p

/T0)

Figure 4.2: Pressure dependency of the AIT for 40 mol% propane in air mixturecorrelated by a Semenov correlation.

deduced for the temperature influence of the auto-ignition limit. In figure 4.2the pressure dependency of the auto-ignition temperature is correlated by theSemenov correlation (Section 2.3.2):

ln(PcT0

) =B

T0+ C (4.2)

where Pc is the lowest pressure at which an auto-ignition occurs [Pa], T0 isthe auto-ignition temperature [K] and B and C are two fitting constants. Thisapproximation is acceptable for a limited temperature range as can be seen onfigure 4.2. Figure 4.3 shows the pressure dependence of the ignition delaytimes for three different ambient temperatures with a 40 mol% propane in airmixture. An increase of the temperature or the initial pressure causes a decreaseof the ignition delay time. The ignition delay time is inversely proportional tothe initial pressure. This correlation is also derived by the Frank–Kamenetskiitheory (Glassman, 1996).

The error margins are not shown on figure 4.1, but can be estimated tobe 0.05 MPa for the auto-ignition pressures, since the step-size introduces thelargest error in comparison with the temperature and pressure measurementerrors. The error on the pressure measurement is estimated to be below 1%,which corresponds to 0.02 MPa for a pressure of 2 MPa, and the error on thetemperature measurement is maximum 2 K.

A main difficulty in the determination of the auto-ignition limit is the re-producibility of the tests if they are performed at different times. Thereforethree series of tests spaced over one year were performed to investigate thereproducibility of the auto-ignition limit. Figure 4.4 presents the auto-ignition


0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Initial Pressure [MPa]

Igni

tion

dela

y tim

e [s

]

523 K536 K548 K

Figure 4.3: Ignition delay times as function of the initial pressure determined for40 mol% propane in air.

limits of the three different test series of a 40 mol% propane/air mixture. It canbe seen that for high temperatures the reproducibility is quite good while ata temperature of 523 K the reproducibility is poor. Because the auto-ignitionpressure increases exponentially at lower temperatures, a significant variationon the auto-ignition pressure reduces to an acceptable variation on the auto-ignition temperature.

Because the propane concentration which is most sensitive to auto-ignitioncan be dependent on the initial pressure, different concentrations from 10 mol%up to 70 mol% are tested at different auto-ignition pressures. The results aresummarised in figure 4.5. The concentration most sensitive to auto-ignition,which is 30 mol% to 40 mol% propane in air at a temperature of 573 K, increasesfor increasing pressure and decreasing temperature. At a temperature of 523 Kthe minimum auto-ignition limit lies at a concentration higher than 70 mol%propane. Because of the saturation pressure of propane it is impossible toperform tests at a temperature of 523 K with higher concentrations. The secondseries only consists of experiments with 40 mol% propane and is thereforenot shown on figure 4.5. The third series consists of experiments with 30 to60 mol% propane-air mixtures at a temperature of 523 K and 548 K. At atemperature of 548 K the reproducibility is reasonable, while at a temperatureof 523 K the reproducibility is rather poor. This poor reproducibility can beexplained by the remaining soot and other reaction products that stay behindfrom previous experiments in spite of the abundant purging with compressedair. These reaction products decrease the ignition delay times and consequentlyfacilitate auto-ignition. This influence is more significant at low temperaturesand elevated pressures. A second explanation for the poor reproducibility isthe material effect (see Section 2.1.5). A rust layer was formed at the insides

4.3 Auto-ignition limits of butane/air mixtures 55

0

0.5

1

1.5

2

2.5

520 530 540 550 560 570 580


Initi

al p

ress

ure

[MPa

]

First series

Second series

Third series

Figure 4.4: The reproducibility of the determination of the auto-ignition limit fora 40 mol% propane in air mixture.

of the buffer vessel and the explosion vessel. This could explain the long termshifting of the auto-ignition limit.

4.3 Auto-ignition limits of butane/air mixturesThe second fuel for which the auto-ignition limits are determined is butane.Since butane has a longer chain length than propane, the auto-ignition tem-perature is expected to decrease. First the auto-ignition limit is determined forn-butane/air and i-butane/air mixtures separately in order to assess the influ-ence of branching. Secondly two LPG mixtures are tested. By comparing theauto-ignition limits of the LPG-mixtures with the auto-ignition limits of thepure components, the influence of the different components to the auto-ignitionbehaviour can be estimated.

4.3.1 Auto-ignition limits of n-butane/air mixturesFigure 4.6 presents the auto-ignition limits of n-butane/air mixtures for con-centrations from 10 mol% up to 70 mol% n-butane and for temperatures from503 K to 548 K (230 ◦C to 275 ◦C). The auto-ignition limits are determinedwith constant vessel temperature and varying pressure with a maximum pres-sure step-size of 0.05 MPa. The auto-ignition criterion is again a combinedtemperature ( > 50 K) and relative pressure rise ( > 10%) criterion within a


0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80

Molar fraction propane [mol%]

Initi

al P

ress

ure

[MPa

]

523 K first series523 K third series548 K first series548 K third series573 K first series

Equivalence ratio [-] 0 5 10 20 40

Figure 4.5: Influence of fuel concentration on the auto-ignition limit of propane-air mixtures with equivalence ratio equal to the actual fuel/air ratio divided by thestoichiometric fuel/air ratio.

time span of fifteen minutes. It can be seen that the auto-ignition temperaturesare lower in comparison with the auto-ignition limits of propane of figure 4.5.As can be seen in figure 4.6, the auto-ignition limits decrease significantly withincreasing concentration in the low concentration region. The concentrationmost sensitive to auto-ignition increases from 30 mol% at a temperature of548 K to 60 mol% at a temperature of 511 K. At a temperature of 503 K theconcentration most sensitive to auto-ignition could not be determined becauseof the saturation pressure of n-butane.

The influence of pressure and temperature on the ignition delay times fora 50 mol% n-butane/air mixture is shown in figure 4.7. At a temperature of548 K the ignition delay times are smaller than 200 seconds. Consequentlythe auto-ignition criterion at this temperature is the temperature or pressurerise. The ignition delay times increase with decreasing temperature. At atemperature of 523 K and 511 K the ignition delay time shows a steep decreasewith increasing initial pressure. At a temperature of 511 K and 503 K themaximum ignition delay time of fifteen minutes is the determining criterion. Ata temperature of 503 K the ignition delay time decreases less with increasingpressure. Consequently the auto-ignition limit at elevated pressure and lowtemperature is not well defined, because a shift of the ignition delay timescause a large shift of the auto-ignition limit.


0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80

Molar fraction n-butane [mol%]

Initi

al p

ress

ure

[MPa

]

503 K

511 K

523 K

548 K

Figure 4.6: Influence of fuel concentration on the auto-ignition limit of n-butane/airmixtures.

0

200

400

600

800

1000

1200

0 0.5 1 1.5 2 2.5

Initial pressure [MPa]

Igni

tion

dela

y tim

e [s

]

503 K

511 K

523 K

548 K

Figure 4.7: Ignition delay times as function of the initial pressure determined for50 mol% n-butane in air mixture.


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 10 20 30 40 50 60 70

Molar fraction iso-butane [mol%]

Initi

al P

ress

ure

[MPa

]523 K

536 K

548 K

573 K

Figure 4.8: Influence of fuel concentration on the auto-ignition limit of iso-butane-air mixtures.

4.3.2 Auto-ignition limits of i-butane/air mixturesFigure 4.8 presents the auto-ignition limits of i-butane/air mixtures for con-centrations from 4 mol% up to 70 mol% iso-butane and for temperatures from523 K to 573 K (250 ◦C to 300 ◦C). The concentration most sensitive toauto-ignition is not dependent on temperature and is equal to 50 mol%. Theauto-ignition limits of iso-butane are comparable with the auto-ignition limitsof propane, while the auto-ignition limits of n-butane are significantly lower.This can be explained by the chemical structure of the different alkanes. It re-quires more energy to break a CH3 radical from a branched alkane than froma straight alkane (see Section 2.1.2).

4.3.3 Auto-ignition limits of LPG/air mixturesThe first LPG-mixture investigated is a mixture of 2 components of which theauto-ignition limits differ the most, namely 50 mol% propane and 50 mol%n-butane. The auto-ignition limits are determined for a fuel concentrationfrom 30 mol% to 70 mol% and for temperatures from 511 K to 536 K (238◦C to 263 ◦C) as can be seen in figure 4.9. The concentration most sensitiveto auto-ignition increases with decreasing temperature. This is similar to theobservations about propane and n-butane mixtures. The auto-ignition limitsof the LPG mixture at a temperature of 523 K are compared with the auto-ignition limits of the individual components in figure 4.10. It is seen that theauto-ignition limits of the LPG mixture resemble best to the n-butane AITlimits. It can be concluded that the auto-ignition limits of the LPG mixture


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

20 30 40 50 60 70 80

Molar fraction LPG (50/50) [mol%]

Initi

al p

ress

ure

[MPa

]511 K

517 K

523 K

536 K

Figure 4.9: Influence of fuel concentration on the auto-ignition limit of a LPG/airmixture containing 50 mol% propane and 50 mol% n-butane.

are in good agreement with the auto-ignition limits of the component with thelowest auto-ignition temperature.

The second LPG mixture consists of three components: 40 mol% propane,30 mol% n-butane and 30 mol% iso-butane. The auto-ignition pressures at atemperature of 523 K of two test series are presented in figure 4.11. Both seriesshow a significant decrease of the auto-ignition pressure at a concentrationof 60 mol%. The difference in the determination method between both testseries is that for the first series the auto-ignition pressure is determined withdecreasing pressure in contrast with the second test series where the auto-ignition limit is determined with increasing pressure. For the determinationwith decreasing pressure the auto-ignition limit is determined starting with anexperiment at a high pressure at which auto-ignition occurs. In the followingexperiments the initial pressure is decreased step by step until an experiment isperformed where no auto-ignition occurs. For the determination with increasingpressure the initial pressure of each successive experiment is increased untilan experiment with an auto-ignition is observed. It is concluded that thecombustion products of previous reactions could facilitate the auto-ignition ina following experiment. This effect was also observed with the propane/airmixtures (Section 4.2). In section 4.5 this influence will be researched in-depthfor the methane/air mixtures.

It can be concluded that two different auto-ignition limits are distinguished.The lowest limit determined with decreasing pressure is the safest auto-ignitionlimit for industrial purposes, while the highest limit determined with increasingpressure is of use for the auto-ignition modelling since the influence of soot is


0

0.5

1

1.5

2

2.5

10 20 30 40 50 60 70 80

Molar fraction fuel [mol%]

Initi

al p

ress

ure

[MPa

]AIT propane first seriesAIT propane third seriesAIT LPG (50/50)AIT n-butane

Figure 4.10: Comparison of the auto-ignition limits at a temperature of 523 Kof LPG/air mixtures (LPG = 50 mol% propane and 50 mol% n-butane) with theauto-ignition limits of the pure components.

not yet included in the chemical kinetics modelling.Figure 4.12 gives a comparison between the auto-ignition limits of both

LPG/air mixtures and n-butane/air mixtures at a temperature of 523 K. Itis concluded that the minimum auto-ignition pressure does not differ signifi-cantly for the three mixtures. The concentrations that are most sensitive toauto-ignition seem to differ for the three mixtures. However it should be notedthat the concentrations are presented as the total fuel concentrations and not asa function of the most sensitive component which is n-butane. A fuel concentra-tion of 60 mol% LPG (50/50 propane/n-butane) corresponds with a n-butaneconcentration of 30 mol% and a fuel concentration of 60 mol% of the secondLPG (40/30/30) mixture corresponds with 18 mol% n-butane. This explainswhy the auto-ignition limit of the second LPG mixture shows a sharp decreaseat a fuel concentration of 60 mol% while the decrease for n-butane starts below20 mol%. The auto-ignition limits increase for both LPG mixtures from a fuelconcentration of 70 mol% because of the oxygen deficiency.


0.2

0.4

0.6

0.8

1

1.2

20 30 40 50 60 70 80

Molar fraction LPG (40/30/30) [mol%]

Initi

al p

ress

ure

[MPa

]

First series: decreasing pressure

Second series: increasing pressure

Figure 4.11: Influence of fuel concentration on the auto-ignition limit of a LPGmixture containing 40 mol% propane, 30 mol% n-butane and 30 mol% iso-butane.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 20 30 40 50 60 70 80

Molar fraction fuel [mol%]

Initi

al p

ress

ure

[MPa

]

AIT LPG (40/30/30)

AIT LPG (50/50)

AIT n-butane

Figure 4.12: Comparison of the auto-ignition limits of two LPG/air mixtures withthe auto-ignition limits of n-butane/air mixtures at a temperature of 523 K.


0

10

20

30

40

50

60

70

280 330 380 430 480 530 580 630

Temperature [K]

Mol

ar fr

actio

n C

3H8 [

mol

%]

UFL 3.0 MPa

UFL 2.0 MPa

UFL 1.5 MPa

UFL 1.0 MPa

UFL 0.5 MPa

UFL 0.2 MPa

UFL 0.1 MPa

AIT 1.0 MPa

AIT 1.5 MPa

Figure 4.13: Comparison between the upper flammability limits and the auto-ignition limits of propane/air mixtures.

4.4 Comparison between the auto-ignition limitsand the upper flammability limits of propaneand n-butane in air mixtures

The upper flammability limit (UFL) is the upper concentration limit of a mix-ture of a combustible gas and an oxidiser below which a flame is able to prop-agate independently (See also Figure 2.2 in Section 2.1.3). This section willdescribe the transition area from the upper flammability limit to the auto-ignition area for propane/air and n-butane/air mixtures. Figure 4.13 showsthe temperature and pressure dependence of the upper flammability limit ofpropane/air mixtures determined in the 8 l buffer vessel. The auto-ignitionlimits for a pressure of 1.0 and 1.5 MPa are also shown on figure 4.13. Thesecurves are interpolated from the auto-ignition data described in the previoussection. The error bars indicate the scattering of the auto-ignition limit of thedifferent test series. Although a large variation on the auto-ignition pressurefor the different test series was measured (Figure 4.5), the error on the auto-ignition temperature is restricted to maximum 9 K. The upper flammabilitylimits are determined according to the European standard EN 1839 (2003) witha 5% pressure rise as flammability criterion. In general the upper flammabil-ity limit shows a linear increase with increasing temperature as was suggestedby Zabetakis et al. (1965). At a temperature of 523 K and at pressures from0.5 MPa to 1.5 MPa a more than linear increase is observed with increasingtemperature (see figure 4.13). This was also observed in a previous study byVan den Schoor and Verplaetsen (2006), who attributed this deviation to theproximity of the auto-ignition area. The upper flammability limit at a tem-

4.4 Comparison between the AIT and the UFL 63

0

10

20

30

40

50

60

70

280 330 380 430 480 530 580 630

Temperature [K]

Mol

ar fr

actio

n n-

buta

ne [m

ol%

]UFL 2.0 MPa

UFL 1.5 MPa

UFL 1.0 MPa

UFL 0.6 MPa

UFL 0.3 MPa

UFL 0.1 MPa

AIT 0.6 MPa

Figure 4.14: Comparison between the upper flammability limits (UFL) and theauto-ignition limits (AIT) of n-butane/air mixtures.

perature of 523 K and a pressure of 1.0 MPa lies just outside the auto-ignitionrange of 1.0 MPa, while the upper flammability limit at 523 K and 1.5 MPais located inside the auto-ignition range of 1.5 MPa. Consequently at 1.5 MPaa mixture with a concentration beyond the upper explosion limit can reactspontaneously. Thus, this mixture does not support flame propagation afterignition, but auto-ignites after a time period of more than 2 minutes, whichis the typical duration of a test for the determination of flammability limits.This might seem contradictive, but can be explained by the underlying phe-nomena. Propagation of a flame requires not only a fast chemical conversion,but also a high heat and mass transfer rate, whereas auto-ignition is initiallyprimarily governed by chemistry and a slow heat transfer rate. Therefore, it ispossible for a mixture which is too rich to sustain flame propagation, to haveauto-ignition.

Figure 4.14 presents the upper flammability limits of n-butane obtained byVan den Schoor and Verplaetsen (2006). These flammability limits are mea-sured in a 4.2 l vessel with a flammability criterion of 1% relative pressure rise.Van den Schoor (2007) has shown that the flammability limits obtained withthese conditions are in good agreement with the flammability limits accordingto the EN 1839 (2003). The upper flammability limit shows a linear increasewith increasing temperature. The slope of the curves increases with increas-ing pressure. At a pressure of 0.6 MPa a deviation from the linear increaseis observed at a temperature of 473 K. At a temperature of 523 K the upperflammability limit was not determined, but it was found that the mixture witha concentration of 66 mol% n-butane at 523 K and 0.6 MPa was still flammable.When the flammability limits are compared with the auto-ignition range, seefigure 4.14, it can be seen that this last condition lies beyond the auto-ignition


temperature of n-butane at a pressure of 0.6 MPa. This explains why the upperflammability limit shows a significant increase at a temperature of 523 K anda pressure of 0.6 MPa.

Two conclusions can be drawn from these comparisons. A first conclu-sion is that a mixture which is too rich to sustain flame propagation, still canauto-ignite. A second conclusion from these experiments is that the linear tem-perature dependence of the upper flammability limit as suggested by Zabetakiset al. (1965) is not valid for temperatures close to the auto-ignition area of thegas mixture.

4.5 Auto-ignition limits of methane/air mixturesCaron et al. (1999) determined the auto-ignition limits of methane/air mix-tures at elevated pressures and for methane concentrations from 30 to 80mol%.These experiments were performed in the same experimental set-up as used forthis study, which is the closed vessel of 8 litres. The top part of figure 4.15shows the three regimes that were identified by Caron et al. (1999). Whenno pressure or temperature increase was observed within 10 min, the attemptwas considered unsuccessful and the test is considered not to give rise to anexplosion. When both a pressure rise and a temperature rise larger than 200K are recorded, auto-ignition has taken place. A temperature rise between50 K and 200 K with a maximum pressure ratio of two or less was classifiedas a slow combustion. In contrast with Caron et al. (1999) who called thisphenomenon a cool flame, it is preferred to identify it as a slow combustion,since no visual proof of the presence of cool flames was given. For this study, itis important to have insight into the thermodynamic phenomena that are re-sponsible for the auto-ignition or that occur during the auto-ignition. Thereforenew experimental data are needed. In order to measure the thermal gradientsinside the explosion vessel three exposed thermocouples were used instead ofone ungrounded thermocouple as used by Caron et al. (1999). The thermo-couples were located at the centre, 6 cm above the centre and at the top ofthe vessel. First a new series of experiments was performed with a methaneconcentration of 60 mol% or an equivalence ratio of 14.3 and at a tempera-tures from 653 K to 713 K. In the bottom part of figure 4.15 these experimentsare compared with previous experiments from Caron et al. (1999) . The sameignition criteria are used for the new experimental data. It can be seen thatthe results of this study are in good agreement with the auto-ignition limitsof Caron et al. (1999). However no slow combustion area was observed in thisstudy. This difference can be explained by the type of thermocouples that wereused in both experimental set-ups. Caron et al. (1999) used one ungroundedthermocouple, which means that the thermocouple junction is detached fromthe probe wall, in the centre of the vessel with a diameter of 1 mm, while inthis study three exposed thermocouples with a diameter of 0.5 mm are used.These thermocouples are capable of following steep temperature rises and canmeasure consequently higher temperatures than the 1 mm thermocouple (see

4.5 Auto-ignition limits of methane/air mixtures 65

Section 3.3). A disadvantage of the exposed thermocouples is that they arefragile and that they can be destroyed by a severe explosion.

Figure 4.16 shows that the sequence of testing can have a major influenceon the value of the auto-ignition limit. The first two experiments with an initialpressure of 0.4 and 0.94 MPa do not lead to an auto-ignition. At a pressureof 1.22 MPa auto-ignition occurs. The following experiments with decreasinginitial pressure also ignite spontaneously. Only at an initial pressure of 0.43MPa no reaction occurs. Two auto-ignition limits can be distinguished fromfigure 4.16. The auto-ignition pressure determined at 713 K and increasingpressure is 0.94 MPa whereas for decreasing pressure the auto-ignition pressureis only 0.43 MPa. This last pressure is also in good agreement with the slowcombustion limit of Caron et al. (1999). Repeated testing could lower theauto-ignition limit determined with decreasing pressure. Because of the poorreproducibility and the differences on the auto-ignition limit a new testingprocedure is developed, which is discussed next.

The standard testing procedure between two successive experiments consistsof three steps. Firstly, the explosion vessel is emptied. Secondly the explosionvessel is flushed with compressed air for 2 minutes and then put under vacuum.Thirdly, the buffer vessel is filled to its initial pressure. During an auto-ignitionreaction products and soot are formed. If these products are not completelyremoved from the explosion vessel, they can facilitate the auto-ignition in fol-lowing experiments. A first modification to the testing procedure is that afterthe evacuation of the reaction products and the flushing with air, the vessel isbrought to vacuum and filled with pure oxygen to an absolute pressure of 0.2MPa. The pure oxygen accelerates the oxidation of any remaining products.After this the vessel is emptied and flushed with compressed air. After thismodification, there was still some interference between successive experiments.This was because of the residence time of the gas mixture in the buffer vessel.Because the buffer vessel was not emptied between two successive experimentsa part of the gas mixture stayed for longer time in the buffer vessel. This mightlead to pre-oxidation reactions. To avoid these reactions, the temperature ofthe buffer vessel was lowered to room temperature instead of 373 K. This modi-fication did not lead to the desired outcome. When the buffer and the explosionvessel were opened, a layer of rust was detected in the buffer vessel and a layerof soot and rust was detected in the explosion vessel. The vessels were cleanedby sandblasting the inner surfaces of the vessels. In the last test series thebuffer vessel was also emptied and refilled between two successive experimentsresulting in a significant improvement of the repeatability. At a temperature of683 K the auto-ignition pressure of a 60 mol% methane in air mixture has beendetermined four times with increasing and decreasing pressure by following thenew testing procedure and resulted in an average auto-ignition pressure of 1.55MPa with a standard deviation of 0.05 MPa. It can be concluded that the newtesting procedure improves the repeatability significantly.

Figure 4.17 makes the comparison between the data of Caron et al. (1999)and the data obtained by this study for different methane concentrations andat a temperature of 683 K. Three observations can be made:


0

1

2

3

4

5

6

600 620 640 660 680 700 720


Initi

al p

ress

ure

[MPa

]

Auto-ignitionSlow combustionNo reactionAuto-ignition limitSlow combustion limit

A

B

0

1

2

3

4

5

600 620 640 660 680 700 720


Initi

al p

ress

ure

[MPa

]

Auto-ignition (this study)

No reaction (this study)

AIT limit (this study)

AIT Caron et al. (1999)

Slow Combustion Caron et al. (1999)

Figure 4.15: Initial temperature-initial pressure diagrams for the slow combustionand the auto-ignition region, determined at 60 mol% methane in air: (A) data fromCaron et al. (1999), (B) data obtained in this study.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1 2 3 4 5 6 7 8 9

Number of experiment

Initi

al P

ress

ure

[MPa

] no reactionauto-ignition

Figure 4.16: Sequence of auto-ignition experiments with a 60 mol% methane/airmixture and a vessel temperature of 713 K.

• The slow combustion range is smaller for the new data. As can be seen onfigure 4.17, in the data from Caron et al. (1999) the slow combustion re-gion starts from a concentration of 50 mol%, while for the new data onlyslow combustions are observed from a concentration of 70 mol%. This canbe explained by the differences in thermocouples that are used in both ex-perimental set-ups. In the new experiments three exposed thermocouplesare used instead of one ungrounded thermocouple. These exposed ther-mocouples have a smaller time constant and are able to measure highertemperatures, see section 3.3. It is also observed that the slow combus-tions of this study had a maximum temperature rise of more than 100 Kand a relative pressure rise of more than 10%. Consequently these slowcombustions would be classified as auto-ignitions following the ignitioncriterion for propane and butane mixtures (see Section 3.2).

• The auto-ignition limits of this study are in general higher than the limitsobtained by Caron et al. (1999). These large differences in auto-ignitionlimits can be explained by the differences in the experimental procedure.The new data are obtained following the improved testing procedure,which shows no influence if the determination is performed with increas-ing or decreasing pressure. The experiments of Caron et al. (1999) areobtained with decreasing pressure and it is seen in figure 4.16 that this de-termination method could significantly lower the auto-ignition pressure.

• Despite the differences in experimental method it can be expected thatthe concentration most sensitive to auto-ignition (70 mol%) remains thesame, which is confirmed by the results.

Up to now only the auto-ignition limits of the methane/air experiments arepresented. Supplementary information can be obtained from the temperaturemeasurements by the three exposed thermocouples that are used for the ex-periments with methane/air mixtures. Figure 4.18 presents the temperature


A

0.0

0.5

1.0

1.5

2.0

2.5

3.0

20 30 40 50 60 70 80 90 100

Methane molar fraction [mol%]

Initi

al p

ress

ure

[MPa

]

Auto-ignitionSlow combustionNo reactionAIT limitSC limit

B

0.0

0.5

1.0

1.5

2.0

2.5

3.0

20 30 40 50 60 70 80 90 100


Initi

al p

ress

ure

[MPa

]

Auto-ignitionSlow CombustionNo reaction

Figure 4.17: Concentration-initial pressure diagrams for the slow combustion andthe auto-ignition region, determined at a temperature of 683 K: (A) data from Caronet al. (1999), (B) data obtained in this study.


600

650

700

750

800

850

900

950

1000

1050

1100

0 10 20 30 40 50 60 70

Time [s]

Tem

pera

ture

[K]

0

0.5

1

1.5

2Pressure [M

Pa]Top TempElevated TempCentral TempPressure

Figure 4.18: Recorded pressure and temperature histories of a test at 713 K and1.2 MPa of a 60 mol% methane/air mixture ("Top Temp" represents the temperatureat the top of the vessel while "Elevated Temp" and "Central Temp" respectivelyrepresents the temperature 6 cm above and at the centre of the vessel).

and pressure histories of an experiment at a wall temperature of 713 K andan initial pressure of 1.2 MPa. It can be seen that during the inflow of thegas mixture the temperature inside the explosion vessel decreases with 30 K.After closing the inlet the temperature of the gas starts to increase. After 20seconds the temperature has reached the temperature of the wall. This periodof time is relatively small in comparison with the total time of 10 to 15 minutesin which explosions are observed. In this experiment the explosion starts at59 s, which is 46 s after the closing of the vessel. Before the beginning of theexplosion, the temperature of the gas mixture slightly increases and from 45 sonwards the temperature at the top and the temperature at 6 cm above thecentre increase more than the temperature at the centre of the vessel. From59 s onwards the temperature at the top of the vessel increases exponentiallyand thereafter with an interval of about 1 second also the temperature at 6 cmabove the centre and at the centre starts to increase. From this measurementit can be concluded that because of the natural convection the auto-ignitionstarts at the top of the vessel and propagates downwards through the rest ofthe volume. This observation will also be confirmed by the simulation resultswhich will be presented in the following chapter.

Chapter 5

Numerical study of theauto-ignition of alkane/airmixtures

When I have an idea, I turn down the flame, as if it were a littlealcohol stove, as low as it will go. Then it explodes, and that is myidea.

Ernest Hemingway, American novelist (1899 – 1961)

This section describes the modelling of the auto-ignition of the alkane/air-mixtures that were investigated in the experimental part of this study. Themodelling is based upon detailed chemical kinetics and different heat transfermodels. This chapter starts with a short overview of the auto-ignition mod-elling available in literature (Section 5.1.1). In addition the numerical methodsare described. First a zero-dimensional approach is adopted based upon themodel of Semenov. The chemistry is based upon a detailed reaction mecha-nism. In order to model the heat transfer and convective flows more accuratelya 1-D and 2-D model are developed. In section 5.2 the numerical results for themethane/air mixtures will be presented and compared with the experimentaldata. Finally, in section 5.3 the numerical results for propane/air mixtures cal-culated with the 0-D model are presented and compared with the experimentaldata.

5.1 Numerical method

5.1.1 Background on auto-ignition modellingIn section 2.3 the theoretical auto-ignition models of Semenov and Frank-Kamenetskii were described. Over the last decades, because of the increased

71

72 Chapter 5 Numerical study of the auto-ignition

computer performance, numerical modelling has gained in importance as a newapproach to study the auto-ignition behaviour of gas mixtures (Gkagkas andLindstedt (2007), Minetti et al. (1995), Stauch and Maas (2007)). Neverthe-less, it is not yet feasible to include a detailed chemical kinetics mechanismwith hundreds of reactions and tens of species in a transient three-dimensional(3-D) computational fluid dynamics (CFD) simulation, as would be requiredto determine the auto-ignition temperature in complex geometries. There are,however, several simplifications possible to model the auto-ignition process.Firstly, the detailed chemical kinetics can be solved in a zero-dimensional (0-D) or in a one-dimensional (1-D) model (Buda et al., 2006). These modelsare based upon the work of Semenov (1935) and Frank-Kamenetskii (1955).This approach leads to a strong reduction of the calculation time. However,this is only suited for the modelling of auto-ignition phenomena with negligi-ble spatial gradients — for example, in well stirred reactors (Hughes, 2006).Secondly, the detailed chemical kinetics can be reduced and solved in a CFDcode (Campbell et al., 2007; Foster and Pearlman, 2006; Griffiths, 1995). Thismethod requires a strong reduction of the reaction mechanisms to keep thecalculation time within acceptable limits. Thirdly, the chemical kinetics andthe flow simulation can be treated separately. For example, in the Shell auto-ignition model (Shell Global Solutions, 2001) the temperature profile along astreamline is first calculated for a non-reactive flow by means of a CFD codeand it is subsequently used when solving the detailed chemical kinetics in azero-dimensional model. The main drawback of this last approach is that thereis no direct interaction between the chemical kinetics and the flow simulation.

5.1.2 Mathematical modelA complete model of the auto-ignition process has to include fluid dynam-ics and transport phenomena together with detailed chemical kinetics. Themathematical model consists of four governing equations: mass, momentum,energy and species conservation. A derivation of these equations can be foundin (Williams, 1985).

• Mass conservation:∂ρ

∂t+∇ · (ρ−→v ) = 0 (5.1)

with ρ the mass density, t time and −→v the mixture velocity.

• Energy conservation:

ρ∂u

∂t+ ρ−→v · ∇u = −∇ · −→q −

←→P : (∇−→v ) + ρ

N∑i=1

Yi−→gi ·−→Vi (5.2)

with u the internal energy per unit mass, −→q the heat flux vector,←→P the

stress tensor, Yi the mass fraction of species i, −→gi the gravitational forceper unit mass on species i and

−→Vi the diffusion velocity of species i.

5.1 Numerical method 73

The heat flux vector −→q is given by:

−→q = −λ∇T + ρ

N∑i=1

hiYi−→Vi +RT

N∑i=1

N∑j=1

(XjDT,i

WiDij

)(−→Vi −

−→Vj

)(5.3)

with λ the thermal conductivity, hi the specific enthalpy of species i, R theuniversal gas constant, DT,i the thermal diffusion coefficient of species iandWi the molar mass of species i. This equation states that the heat fluxis the result of thermal conduction, species diffusion and concentrationgradients (the Dufour effect). The radiant heat flux is neglected in thecalculations.

The stress tensor is given by:

←→P =

[p+

(23µ− µb

)∇ · −→v

]←→U − µ

[∇−→v + (∇−→v )T

](5.4)

with p the hydrostatic pressure, µ the dynamic viscosity and µb the bulkviscosity.

The diffusion velocities can be calculated from:

∇Xi =N∑j=1

(XiXj

Dij

)(−→V j −

−→V i

)+ (Yi −Xi)

(∇pρ

)

+ρ

p

N∑j=1

YiYj

(−→f i −

−→f j

)

+N∑j=1

[(XiXj

ρDij

)(DT,j

Yj− DT,i

Yi

)]∇TT

i = 1, ..., N (5.5)

with Xi the molar fraction of species i, Dij the binary diffusion coefficientof species i and j, DT,i the thermal diffusion coefficient of species i and Tthe absolute temperature. This equation states that concentration gradi-ents are supported by diffusion velocities, pressure gradients, differencesin the external forces on different species and temperature gradients (theSoret effect). The numerical simulations of this study have shown that ne-glecting the Soret effect (thermal diffusion) did not alter the auto-ignitionlimits of the methane/air mixtures.

• Momentum conservation:

∂−→v∂t

+−→v · ∇−→v = −∇ ·←→P /ρ+

N∑i=1

Yi−→gi (5.6)

• Species conservation:

ρ∂Yi∂t

= −ρ−→v · ∇Yi + ωi −∇ ·(ρYi−→Vi

)i = 1, ..., N. (5.7)


The chemical kinetics enter these equations via the species rate of pro-duction ωi. Since the chemical kinetics play an important role in theauto-ignition process, different reaction mechanisms will be used in thecalculations, as described in the next section.

5.1.3 Reaction mechanismsHydrocarbons are a family of compounds for which a number of detailed re-action mechanisms exist (Simmie, 2003). However, most of these mechanismsare only valid for high temperature combustion (> 1000 K). Kinetic data andmechanisms for the low temperature region are scarce (Pilling, 1997). The mainproblem is the lack of quantitative experimental data for the rate constants ofelementary reactions in the low temperature region.

For the numerical study of methane, the results of four different reac-tion mechanisms are compared with the experimental auto-ignition data ofmethane-air mixtures. These mechanisms are the GRI 3.0 (Gas Research In-stitute) mechanism (Frenklach et al., 1994), the C1–C2 reaction database ofthe L’Ecole Nationale Supérieure des Industries Chimiques (ENSIC) (Barbé etal., 1995), the hydrocarbon mechanism of the National Institute of Standardsand Technology (NIST) (Babushok et al., 1995) and a mechanism for methaneoxidation of the British Gas Corporation (BGC) proposed by Reid et al. (1984).These reaction mechanisms are summarised in table 5.1. The GRI 3.0 mecha-nism is optimised for methane and natural gas oxidation for temperatures byfitting the reaction rate parameters to a variety of experimental data. TheC1–C2 reaction database of the ENSIC has been developed through automaticgeneration and it is validated with methane and ethane oxidation experimentsin a jet-stirred reactor. The hydrocarbon mechanism of the NIST includes 240reactions and 34 species for the oxidation of methane and ethane for tempera-tures in the range 900–2000 K and pressures in the range 0.05–0.15 MPa. Themechanism of the BGC has been developed to model the spontaneous ignitionof methane by a hot surface in stirred and unstirred vessels. A detailed descrip-tion of these reaction mechanisms can be found in their respective references.

For the numerical study of propane, six kinetic reaction mechanisms arecompared. Table 5.2 summarises these mechanisms. The first five have beenpublished (San Diego Mechanism (2003), Westbrook (1984), Sung et al. (1998),Qin et al. (2000), Koert et al. (1996)), while the last one is part of the softwarepackage Exgas-Alkanes of Battin-Leclerc (2004).

5.1.4 0-D modelAs a first approach, in order to choose the most appropriate reaction mech-anism, we focus on the chemistry of the auto-ignition process by applying aphysical model that includes a detailed reaction mechanism but neglects dif-fusion and convection. For this zero-dimensional model, the equations 5.1–5.7


Reaction

Num

ber

Num

ber

Tem

perature

Pressure

mecha

nism

ofspecies

ofreaction

srang

eof

rang

eGRI3.0(Frenk

lach

etal.,1994)

53325

1000–2500K

0.001–1MPa

ENSIC

(Barbé

etal.,1995)

63439

773–1573

K0.1MPa

NIST

(Bab

usho

ket

al.,1995)

34240

900–2000

K0.05–0.15MPa

BGC

(Reidet

al.,1984)

2155

900K

0.1MPa

Tab

le5.

1:Su

mmaryof

thereaction

mecha

nism

sformetha

neoxidation.


Reaction

Num

ber

Num

ber

Based

onexpe

rimental

Con

centration

mecha

nism

ofspecies

ofreaction

sda

taof

rang

eSa

nDiego

39173

Rap

idCom

pression

2.05-7.73mol%

SanDiego

Mecha

nism

(2003)

shocktube

(0.1-3

MPa)

(φ=

0.5-2)

Westbrook

36168

Propa

nean

dprop

ene

Unk

nown

Westbrook

(1984)

oxidationan

dpy

rolysis

Princeton

92621

Cou

nterflo

wdiffu

sion

Richmixtures

Sung

etal.(1998)

flames

(0.1-1.5

MPa)

till16

mol%

Delaw

are

70463

Rap

idcompression

2.05-7.73mol%

Qin

etal.(2000)

flames

(0.1-1.5

MPa)

(φ=

0.5-2)

Koert

andPitz

155

689

Highpressure

flow

reactor

1.65

mol%

(φ=0.4)

Koert

etal.(1996)

(650-800

K,0

.1-1.5

MPa)

till16

mol%

EXGAS-Alkan

es118

713

Low

tempe

rature

oxidation

Unk

nown

Battin-Le

clerc(2004)

Tab

le5.

2:Su

mmaryof

thereaction

mecha

nism

sforprop

aneoxidation.


reduce to

ρcv∂T

∂t=qlossV−

N∑i=1

hiωi (5.8)

ρ∂Yi∂t

= ωi i = 1, ..., N. (5.9)

with cv the specific heat capacity at constant volume and V the internal volume.The heat loss to the wall of the vessel qloss is assumed to be convective, i.e.proportional to the gas-wall temperature difference:

qloss = h · S · (T − Tw) (5.10)

with h the convective heat transfer coefficient, S the internal surface area, andT and Tw the temperature of the gas and of the wall, respectively. Here, his taken to be 5 W/m2K. The choice of this value will be clarified in Section5.2.1. The internal surface area S is 1932 cm2, which corresponds to the surfaceof a sphere with an internal volume V of 8 dm3.

This model is implemented in Chemkin 4.0.2 (Kee et al., 2005) as a ho-mogeneous batch reactor. In order to obtain the evolution of the temperatureand of the species concentrations in time, the system of partial differentialequations must be solved by numerical integration methods. This system isgenerally stiff because of the chemical kinetics and it is most efficiently solvedby implicit techniques for time integration. For this purpose, Chemkin usesthe software package DASPK (Li and Petzold, 2000).

5.1.5 1-D and 2-D CFD-Kinetics modelIn order to simulate the diffusive and convective heat transfer more accurately,a one-dimensional and a two-dimensional model are implemented. The 1-Dmodel is able to describe the auto-ignition process in a spherical explosionvessel while neglecting the effect of buoyancy, whereas the 2-D model is ableto take buoyancy into account in an axisymmetric explosion vessel. In order tomodel the spherical auto-ignition vessel, an axisymmetric spherical geometrywith symmetry around the vertical axis is used in the calculations. The 1-Dmodel is derived from the 2-D model by eliminating the gravity forces. Thisresults in a spherically symmetric or 1-D simulation.

The model is solved as a transient problem using the Fluent code (Release6.3.26 2006). In Fluent the control volume method — sometimes referred to asthe finite volume method — is used to discretise the transport equations. Thetotal number of grid cells is 1400 and 5400 for the 1-D and the 2-D model, re-spectively. The composition of the 2-D grid is presented in figure 5.1. Only halfof a circle is modelled. The x-axis is the symmetry axis and the gravity forcelies according to the opposite direction of the x-axis. The grid independencewas checked by performing simulations with the number of grid cells doubled.The fluid is treated as fully compressible because the temperature and pressurerise can be considerable during auto-ignition. The density is calculated by the


X

Y g

Figure 5.1: Numerical grid for the 2-D spherical simulations.

ideal gas law. The pressure is handled as a floating operating pressure to ac-count for the slow changing of the pressure without using acoustic waves. Theflow is assumed to be laminar because the buoyancy driven velocities are small(∼ 10 cm/s) and the Rayleigh number (see equation 5.13 on page 88) doesnot exceed 108 (Bejan, 2004). The fluid temperature at the wall is requiredto be equal to the wall temperature. This temperature is also the initial tem-perature of the gas mixture. The chemistry is calculated and coupled to theflow calculations by means of a KINetics plug-in from Reaction Design. Thistechnology couples Reaction Design’s KINetics chemistry-solver module (Keeet al., 2005) to the flow simulation of Fluent. For transient analyses, the solversare coupled using an operator-splitting method. With this method, the speciesand energy conservation calculations are performed in two half time steps foreach time step, where the KINetics solver determines the change in time dueto the chemistry and Fluent determines the change in time due to fluid andheat transport. The time-step size was varied in the range 0.01–1 s to achieveresults that are independent of the time step size.

5.1.6 Auto-ignition criterionIn order to determine the auto-ignition limits of a mixture, the calculatedtemperature-time profiles are interpreted in the same way as the experimental


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Figure 5.2: Temperature histories for a 60 mol% methane-air mixture at an initialtemperature of 623 K and varying initial pressure from 2 MPa to 1.4 MPa using the1-D model with the BGC-mechanism.

profiles of this study. For the methane/air mixtures if the (maximum) tempera-ture rises at least 200 K within a period of 10 minutes, an auto-ignition is saidto have occurred. This corresponds exactly with the experimental criterion.For the propane and n-butane simulations the auto-ignition criterion is a max-imum temperature rise of 50 K within a duration of fifteen minutes as in theexperiments. The auto-ignition pressures, presented in section 5.2, are deter-mined with an accuracy of 0.01 MPa for the zero-dimensional model, while forthe 1-D and 2-D CFD model calculations, which are far more time-consuming,an accuracy of 0.1 MPa is obtained for the high pressures and 0.05 MPa for thelow pressures. As an example, figure 5.2 shows the temperature-time profiles ofdifferent 1-D simulations at different initial pressures at an initial temperatureof 623 K of a methane/air mixture. The induction time, i.e. the time beforean auto-ignition appears, decreases with increasing pressure. The calculationsat initial pressures of 2.0, 1.8 and 1.6 MPa resulted in induction times of 370 s,470 s and 640 s, respectively. At an initial pressure of 1.4 MPa the maximumtemperature rise was only 43K after 900 s. According to the above mentionedauto-ignition criterion, the simulations with an initial pressure of 1.4 and 1.6MPa are classified as no ignitions. Consequently, the auto-ignition limit at 623K is 1.6 MPa.


0

1

2

3

4

5

580 600 620 640 660 680 700 720 740

Temperature [K]

Pres

sure

[MPa

]NIST 0-D modelGRI 3.0 0-D modelBGC 0-D modelENSIC 0-D modelAIT of this studyAIT Caron et al. (1999)SC Caron et al. (1999)

Figure 5.3: Comparison between experimentally and numerically determined auto-ignition limits (0-D) of methane-air mixtures: pressure dependence of the auto-ignition limit determined at 60 mol% methane in air.

5.2 Numerical results of methane/air mixturesThis paragraph contains the comparison between the experimental auto-ignitiondata for methane/air mixtures and the computed data. First the results of thezero-dimensional model are considered. This model assumes a homogeneouscomposition and a uniform temperature over the entire volume. Afterwardsthe results of the one-dimensional and two-dimensional simulations are pre-sented and discussed.

5.2.1 0-D modelThe output of a zero-dimensional model typically consists of the time evolutionof the pressure, the temperature and the species molar fractions. In figure 5.3they are compared with data for a methane concentration of 60 mol% at ini-tial temperatures of 623–713 K, while in figure 5.4 the calculated auto-ignitionlimits are compared with experimental data at an initial temperature of 683K for methane concentrations of 30–80 mol%. As can be seen, there are largedifferences between the results of the different reaction mechanisms. More-over, the agreement between the numerical results and the experimental datais rather poor. As expected the NIST mechanism which is mainly valid at hightemperatures, gives values for the auto-ignition limit that are too high. TheGRI mechanism gives a good prediction of the auto-ignition limit of this studyat low pressures but has too steep an increase of the auto-ignition pressureat lower temperatures. For the GRI mechanism the concentration most sensi-tive to auto-ignition lies below 30 mol%, while the experimental data have a

5.2 Numerical results of methane/air mixtures 81

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90


Pres

sure

[MPa

]

NIST 0-D modelGRI 3.0 0-D modelBGC 0-D modelENSIC 0-D modelAIT of this studyAIT Caron (1999)SC Caron (1999)

Figure 5.4: Comparison between experimentally and numerically determined auto-ignition limits of methane-air mixtures: concentration dependence of the auto-ignitionlimit at 683 K.

0

1

2

3

4

5

6

600 620 640 660 680 700 720

Temperature [K]

Pres

sure

[M

Pa]

h=50 W/m²Kh=20 W/m²Kh=10 W/m²Kh=5 W/m²Kh=2 W/m²KAIT of this studyAIT Caron et al. (1999)SC Caron et al. (1999)

Figure 5.5: Influence of the heat transfer coefficient on the numerically determinedauto-ignition limits using the zero-dimensional model and the BGC reaction mecha-nism.


0

1

2

3

4

600 620 640 660 680 700 720

Temperature [K]

Pres

sure

[M

Pa]

timecrit = 300s

timecrit = 600s

timecrit = 900s

Figure 5.6: Influence of the time criterion on the numerically determined auto-ignition limits using the zero-dimensional model and the BGC reaction mechanism.

minimum auto-ignition pressure at a concentration of 70 mol%. The ENSICmechanism, mainly valid for the low temperature oxidation kinetics give valuesfor the auto-ignition limit that are too low. Overall, the best agreement isfound for the BGC mechanism, especially when the temperature dependenceof the auto-ignition pressure is observed. Consequently, this mechanism will beused in the 1-D and 2-D calculations.

The value of the heat transfer coefficient h was calculated from a correlationfor natural convective flow round spherical volumes (Bejan, 2004).

h =Nu · λD

with Nu = 2 +0.589Ra1/4

[1 + (0.469/Pr)9/16]4/9(5.11)

withNu the Nusselt number, Ra the Rayleigh number, Pr the Prandtl number,λ the thermal conductivity and D the diameter of the vessel. For a 60 mol%methane in air mixture with a temperature difference of 1 to 200 K betweenthe gas and the wall the heat transfer coefficient has a value between 2 and8 W/m2K. h is taken equal to 5 W/m2K for the calculations of figures 5.3–5.4. Since this coefficient has to be estimated, the influence of its value on thecalculated auto-ignition limits is investigated, the results of which are shown infigure 5.5. As expected, an increasing value of the heat transfer coefficientresults in a shift of the auto-ignition limit to higher temperatures. Whenfocusing on the experimentally determined auto-ignition limits it can be seenthat they are roughly located in the range h = 5 - 50 W/m2K. The auto-ignition limit obtained in this study has an excellent agreement with numericaldata obtained with a heat transfer coefficient of 50 W/m2K. This value isunrealistically high for natural convection flows inside a closed vessel (Bejan,2004). Therefore the heat transfer coefficient is chosen to be constant and


CH4

CH3

CH3O

CH2O

HCO

CO

C2H6

C2H5

C2H4

CH3O2

CH3O2H

+ HO2 / OH / H / O

+ O2

+ HO2 / OH

+ O2+ M

+ O2+ HO2 / CH3 / OH / H / O

+ O2+ M

CO2

+ HO2 / OH

CH4

CH3

CH3O

CH2O

HCO

CO

C2H6

C2H5

C2H4

+ HO2 / OH

+ HO2

+ O2

+ HO2 / CH3

+ O2

+ OH / CH3

+ O2

+ CH3

REDUCED BGC MECHANISMHIGH TEMP / LOW PRESSURE

(15 species, 17 reactions)

BGC MECHANISM(21 species, 55 reactions)

Figure 5.7: Reaction path diagrams of the full and reduced mechanism of BGC.

equal to 5 W/m2K for the numerical calculations of the 0-D model in orderto compare objectively the different reaction mechanisms. Another parameterthat has an influence on the auto-ignition limit is the ignition time criterion,as can be seen in figure 5.6. A decreasing time criterion increases the auto-ignition limit, but the influence is only noticeable at high pressures and lowtemperatures.

Reduction of kinetic mechanism

The BGC mechanism consisting of 55 reactions and 21 species was reduced by aformer colleague, ir. L. Vandebroek, to a mechanism consisting of 17 reactionsand 15 species by means of a rate of production analysis in order to reduce thecalculation time for the 2-D model. The mechanism is reduced for the hightemperature and low pressure region and is presented schematically in figure5.7. As can be seen from the figure the reaction path along the peroxides,which is important for the high pressure region (Westbrook, 2000), is removedin the reduced mechanism. Figure 5.8 compares the auto-ignition limits cal-culated with the full and the reduced mechanism at 60 mol% methane in air.The auto-ignition limit obtained with the reduced mechanism deviates only athigh pressure and low temperature from the limit obtained with the full mecha-nism. The reduced mechanism has a good agreement with the slow combustionlimit of Caron et al. (1999) over the entire pressure range. However there isstill a large difference with the experimental auto-ignition limits obtained in


0

1

2

3

4

5

620 630 640 650 660 670 680 690 700 710 720

Temperature [K]

Pres

sure

[MPa

]Full BGC-mechanismReduced BGC-mechanismAIT of this studyAIT Caron et al. (1999)SC Caron et al. (1999)

Figure 5.8: Comparison of the numerically determined auto-ignition limits usingthe zero-dimensional model with the full and the reduced mechanism of the BGC.

this study. It can be concluded that it is possible to fit the zero-dimensionalmodel to the experimental results by adapting the heat transfer coefficient or byadapting the reaction mechanism. The question should be put if the 0-D modelwill still be valid if other process conditions, such as the volume and the flowconditions, are changed. The main drawback of the zero-dimensional model isthe simplicity of the heat transfer model due to the time-independency of theheat transfer coefficient and the necessity of experimental data to determine itsvalue. The 1-D and 2-D models discussed next will simulate the heat transferin more detail.

5.2.2 1-D modelThe full mechanism of the British Gas Corporation (Reid et al., 1984) wasincorporated in a one-dimensional (without the effect of buoyancy) computa-tional fluid dynamics model. Contrary to the zero-dimensional model, there isno need to specify the value of the heat transfer coefficient h. The output ofthe calculations consists of the time evolution of the temperature, the pressureand the species molar fractions together with the spatial distribution of thetemperature and the species molar fractions. An example of the temperatureoutput is shown in figure 5.11 for a 60 mol% methane/air mixture at an initialtemperature of 713 K and an initial pressure of 0.4 MPa. The temperature in-creases exponentially which leads to the auto-ignition of the gas-mixture after80 s. Figure 5.9 shows the results of different simulations varying the initialpressure in order to find the auto-ignition limit at a certain temperature. Theinduction time, i.e. the time before auto-ignition appears, decreases with in-creasing pressure. Initial pressures of 0.6 to 0.3 MPa resulted in induction


Figure 5.9: Temperature histories for a 60 mol% methane/air mixture at an initialtemperature of 713 K and varying initial pressure from 0.6 MPa to 0.15 MPa usingthe 1-D model.

times lower than 130 s. The induction time increases significantly to 300 s foran initial pressure of 0.2 MPa. At an initial pressure of 0.15 MPa the maximumtemperature rise is only 13 K after 285 s. This run is classified as no ignitionbecause the temperature rise is below 50 K. The auto-ignition limit at 713 Kis consequently 0.15 MPa. Equivalent simulations were performed at tempera-tures of 673 K and 623 K and resulted in a respective auto-ignition limit of 0.4and 1.6 MPa.

Figure 5.10 compares the auto-ignition limit of the one-dimensional modelwith the zero-dimensional model. Strikingly, the results of the 1-D calculationsdeviate more from the experimental data than those of the 0-D calculations.However, it must be borne in mind that in order to perform the 0-D calculationsa heat transfer coefficient h has to be specified a priori. As already shown infigure 5.5, the choice of this parameter largely influences the outcome of thecalculation.

5.2.3 2-D modelA disadvantage of the zero- and the one-dimensional models is the absence ofnatural convection. The buoyant flow that arises after the birth of a hot kernelwill increase the heat loss and consequently will increase the auto-ignition tem-perature. A two-dimensional model was developed to model the flow and the


0

1

2

3

4

5

620 630 640 650 660 670 680 690 700 710 720

Temperature [K]

Pres

sure

[MPa

]0-D model1-D modelAIT of this studyAIT Caron et al. (1999)SC Caron et al. (1999)

Figure 5.10: Comparison of the numerically determined auto-ignition limits usingthe BGC mechanism in the 0-D and the 1-D with the experimental data at 60 mol%methane in air.

reactions in a closed vessel. The same reaction mechanism (BGC) is used as inthe one-dimensional model. Figure 5.12 shows an example of the spatial tem-perature field obtained with the 2-D model for a 60 mol% methane-air mixtureat an initial temperature of 713 K and an initial pressure of 0.6 MPa. To obtaina better insight into the initial temperature increase, two different temperaturescales have been used. Initially the temperature rise is homogeneous. After20 seconds the location of the maximum temperature moves to the top of thevessel. After 50 seconds the auto-ignition starts at the top of the vessel andexpands downwards to the entire volume of the vessel.

The results of the 2-D calculations for the full and reduced BGC mechanism(see Section 5.2.1) are shown in figure 5.13. It can be seen that reduced mech-anism overestimates the auto-ignition pressure at lower temperatures. Theoverall slope of the reduced mechanism is too steep in comparison with theexperimental data. Consequently, although the time savings, the reduction ofthe reaction mechanism leads to a worse prediction of the auto-ignition limitwith the 2-D model. In figure 5.14 the results of the 2-D calculations togetherwith those of the 0-D and 1-D calculations for the full BGC mechanism arecompared with the experimental data of this study. It can be concluded thatthe convective heat transfer — which is absent in the 1-D model — is impor-tant in the auto-ignition process and that, consequently, the constant value ofh = 5 W/m2K, which is used in the 0-D model, is a better estimate of the heattransfer coefficient than the one calculated when using the purely diffusive 1-Dmodel.

In order to compare the heat transfer in the 1-D and 2-D model with theheat transfer in the 0-D model an equivalent 0-D heat transfer coefficient is


760K

710K10 s 20 s 30 s 40 s 50 s 60 s 70 s 80 s

Figure 5.11: Temperature history of a 60 mol% methane-air mixture at an initialtemperature of 713 K and an initial pressure of 0.4 MPa using the one-dimensionalmodel with the full BGC mechanism.

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Figure 5.12: Temperature history of a 60 mol% methane-air mixture at an initialtemperature of 713 K and an initial pressure of 0.6 MPa using the two-dimensionalmodel with the full BGC mechanism.

0

1

2

3

4

5

620 630 640 650 660 670 680 690 700 710 720

Temperature [K]

Pres

sure

[MPa

]

0-D model full BGC0-D model reduced BGC2-D model full BGC2-D model reduced BGCAIT of this studyAIT Caron et al. (1999)SC Caron et al. (1999)

Figure 5.13: Comparison between the full BGC mechanism and the reduced BGCmechanism in the 0-D and 2-D model.


0

1

2

3

4

5

620 630 640 650 660 670 680 690 700 710 720

Temperature [K]

Pres

sure

[MPa

]

0-D model1-D model2-D modelAIT of this study

Figure 5.14: Comparison of the numerically determined auto-ignition limits usingthe full BGC mechanism in the 0-D, 1-D and 2-D model with the experimental dataof this study at 60 mol% methane in air.

defined as:h =

qlossS · (Taverage − Tw)

(5.12)

The heat loss qloss is calculated by the CFD model as the total heat fluxto the vessel wall. Figure 5.15 presents the evolution of the equivalent 0-D heat transfer coefficient (equation 5.12) and the evolution of the averagetemperature of the 1-D and 2-D simulation. The heat transfer coefficient hdecreases identically for both simulations during the first 20 seconds. From20 seconds onwards, however, the two profiles diverge. The 1-D simulation,which does not include natural convection, shows a decreasing heat transfercoefficient. The 2-D simulation, on the contrary, shows an increasing coefficientbecause of the increasing natural convection caused by the temperature rise.This explains why the auto-ignition limit determined with the 1-D model islower than that determined with the 2-D model.

Another means of comparing the 1-D and the 2-D simulation is by compar-ing the temperature profiles (Figure 5.16). Initially, the temperature evolutionis identical. After 30 seconds the maximum temperature in the 2-D simulationmoves upwards. This results in a lower volume averaged temperature in the 2-Dsimulation than in the 1-D simulation. Consequently, the 1-D simulation leadsto an auto-ignition, whereas the 2-D simulation has a maximum temperaturerise of only 59 K.

The induced convective flow is determined by the Rayleigh number:

Ra =(β · g · L3 · (Tcentre − Tw))

(αth · ν)(5.13)


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Figure 5.15: Evolution of the heat transfer coefficient and the average tempera-ture in the 1-D and 2-D simulation for a 60 mol% methane-air mixture at an initialtemperature of 713 K and an initial pressure of 0.5 MPa.

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Figure 5.16: Comparison of the temperature history of the 1-D simulation (a) andthe 2-D simulation (b) for a 60 mol% methane-air mixture at an initial temperatureof 713 K and an initial pressure of 0.5 MPa.


Time [s] Tcentre - Twall [K] Rayleigh Number [-]5 3.5 10−3 2.3 102

10 5.1 10−2 3.3 103

15 3.8 10−1 2.5 104

20 1.5 9.4 104

30 5.3 3.4 105

Table 5.3: Evolution of the Rayleigh number of the 2-D simulation for a 60 mol%methane/air mixture at an initial temperature of 713 K and an initial pressure of 0.4MPa.

where β is the coefficient of thermal expansion, L is the characteristic length(radius) of the vessel, αth is the thermal diffusivity and ν is the kinematicviscosity. The natural convection becomes important when the Rayleigh num-ber rises above 500 or 1.7 103 as stated by Campbell et al. (2007) and Bejan(2004), respectively. It can be seen from Table 5.3 that the Rayleigh numberrises above 103 at 10 seconds. At 20 seconds the temperature rise is 1.5 K andthe Rayleigh number is 105. This means that natural convection is important.

Figure 5.17 shows the temperature evolution along the vertical axis for a2-D simulation with an initial pressure of 0.6 MPa and an initial temperatureof 713 K. The temperature profiles are scaled to their respective maximumtemperatures, which can be seen on top of the separate figures of figure 5.17.At 10 seconds the temperature profile is symmetrical. From 20 seconds on-wards the maximum temperature shifts to the top of the vessel due to naturalconvection. The increase of the maximum temperature is accompanied by adecrease of the area of the hot zone. At 60 seconds the maximum temperatureis 200 K higher than the initial temperature and the simulation is classified asan auto-ignition. Because the maximum temperature is only present at a smallarea at the top of the vessel, it is important for the experimental determinationof the auto-ignition limit to measure the temperature at the top of the vessel.

Figure 5.18 presents the velocity profiles corresponding to the 2-D simula-tion of figure 5.17. It can be seen that the maximum velocity increases withtime. Initially the velocities caused by the buoyant flow are very small becausethe temperature rise is very small. From 20 seconds onwards the velocitiesbecome significantly larger and rise to values of almost 10 cm/s. Furthermore,a recirculation zone arises and shifts to the bottom of the vessel. During theauto-ignition the maximum velocities occur mainly at the wall of the vessel.

Although the two-dimensional auto-ignition limit shows an excellent agree-ment with the experimental data, it is also important to compare the tem-perature and pressure histories of the simulations with the experimental mea-surements in order to evaluate the validity of the two-dimensional model. Thetemperature and pressure histories of an experiment and a simulation with aninitial temperature of 683 K and an initial pressure of 1.4 MPa are presentedin figure 5.19. At first sight the simulation shows many similarities with theexperimental data. Initially the temperature and pressure rise are small. After


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Figure 5.17: History of the temperature profile along the vertical axis of a 2-Dsimulation of a 60 mol% methane-air mixture at an initial temperature of 713 K andan initial pressure of 0.6 MPa.

10 s 20 s 30 s 40 s 50 s

0.1 cm/s 3.5 cm/s 6.9 cm/s 7.9 cm/s 9.0 cm/s

Ver

tical

axi

s

Figure 5.18: Velocity profiles of a 2-D simulation of a 60 mol% methane-air mixtureat an initial temperature of 713 K and an initial pressure of 0.6 MPa.

some time, the temperature at the top of the vessel increases sharply. Thistime is called the auto-ignition delay time. Subsequently, the elevated temper-ature, i.e. the temperature 6 cm above the centre, and the central temperatureincreases. The temperature rises are accompanied by a pressure rise. Themaximum temperature of the measurements is similar to the maximum tem-perature of the simulation. There are nevertheless some differences betweenthe simulation and the experimental measurements. The ignition delay timeof the experiment is 110 s, while in the simulation the delay time is only 50 s.The measured temperature at the top of the vessel has a very sharp increaseafter 110 s, whereas the temperature rise of the simulation is smoother. Forthe experiment the elevated thermocouple has a sharp temperature increase 1second after the temperature increase at the top of the vessel. In the simu-lation this delay time is about 5 seconds. Consequently, the gas mixture cancool down more rapidly and the central temperature only increases to 910 K.As a result, the pressure rise of the simulation is smaller than the measuredpressure rise. Despite similarities between the simulation and the experiment,there is still need to refine the reaction mechanism by adding more reactionsteps or including wall interactions in order to simulate more accurately theauto-ignition process.


Simulation at 683 K and 1.4 MPa (60 mol% methane in air)

600

800

1000

1200

0 10 20 30 40 50 60 70 80

Time [s]

Tem

pera

ture

[K]

0.0

0.5

1.0

1.5

2.0Top TempElevated TempCentral TempPressure

Experiment at 683 K and 1.4 MPa (60 mol% methane in air)

600

800

1000

1200

100 105 110 115 120

Time [s]

Tem

pera

ture

[K]

0

0.5

1

1.5

2

2.5Top TempElevated TempCentral TempPressure

Pressure [MPa]

Pressure [MPa]

Figure 5.19: Comparison of the pressure and the temperature histories of an exper-iment and a simulation with an initial pressure of 1.4 MPa and an initial temperatureof 683 K.

5.3 Numerical results of propane/air mixtures 93

Model Reaction Mechanism Simulation time Calculation time0-D full BGC 600 s < 1 min1-D full BGC 100 s 2 h2-D full BGC 100 s 10 h2-D reduced BGC 100 s 2.5 h

Table 5.4: Calculation times of simulations.

5.2.4 DiscussionThe results of this study have shown that the coupling of computational fluiddynamics with detailed chemical kinetics is very promising for the modelling ofthe auto-ignition limits of gas mixtures. The accurate calculation of the auto-ignition limits of gas mixtures occurring in industrial installations at elevatedpressures and temperatures is, however, impeded by a number of factors. Firstthere is a need for reaction mechanisms that are capable to accurately describethe oxidation kinetics in the low temperature region, in which the auto-ignitionprocess occurs. Second, there is a need for accurate and detailed experimentaldata, preferably obtained in a spherical or an upright cylindrical test vesselsince this enables the use of a 2-D model. Third, the calculation time increasessignificantly with the dimension of the model as can be seen in Table 5.4, whichrepresents the calculation times on an Intel Core 2CPU 2.66 GHz system with 4GB of memory. The present computational capabilities restrict the calculationsto relatively simple reaction mechanisms in combination with a 2-D model.

5.3 Numerical results of propane/air mixturesThe numerical study of the auto-ignition of propane/air mixtures was limitedto a comparison of the auto-ignition limits calculated with the 0-D model. Ascan be seen from table 5.2 in section 5.1.3 the simplest chemical reaction scheme(Westbrook, 1984) consists of 36 species and 168 reactions. These mechanismswould require very long calculation times if they are included into a 1-D or2-D model. Figure 5.20 presents the 0-D auto-ignition limits predicted by thedifferent reaction schemes. The reaction mechanisms can be divided into twogroups. The first five overestimate the auto-ignition temperature. For thesereaction mechanisms the explosion criterion applied was a temperature rise of50 K. At the auto-ignition temperature of 572 K their respective ignition delaytimes were 18000 s, 10000 s, 5000 s, 13500 s and 23000 s. The explosion criterionwith the experiments was a combined temperature rise (> 50 K) and ignitiondelay time criterion (< 900 s). The model with the Exgas-alkanes kinetics alsouses this criterion. Nevertheless this mechanism overrates the auto-ignitionrisk compared with the experimental data. It can be concluded that there isstill a need for reaction mechanisms that are capable to describe accurately theoxidation kinetics in the low temperature region before the reaction mechanismscan be applied in more comprehensive heat transfer models.


0

0.5

1

1.5

2

2.5

3

3.5

450 500 550 600 650 700Temperature [K]

Initi

al P

ress

ure

[MPa

]

Exgas-AlkanesExperimentsKoert&PitzDelawarePrincetonWestbrookSanDiego

Figure 5.20: Numerical modelling of auto-ignition limit of a 40 mol% propane-airmixture, compared with the experimental data using the 0-D model.

Chapter 6

Influence of the vessel size onthe auto-ignition temperatureof combustible gas-airmixtures

Young love is a flame; very pretty, often very hot and fierce, butstill only light and flickering. The love of the older and disciplinedheart is as coals, deep burning, unquenchable.

Henry Ward Beecher, American clergyman and author (1813 –1887)

The experimental determination of the AIT is characterised by the smallvolume of the test vessel. It is typical to use test vessels with a volume lessthan 1 litre (see Section 2.2). Auto ignition is a thermo-chemical process inwhich heat is generated by the combustion reaction. The heat is absorbedby the gas and also transferred to the vessel walls. It is obvious from thisthat the size and shape of the test vessel must have an impact on the onset ofignition. The question should be put therefore whether these data are relevantfor large vessel volumes as is often the case under process conditions. Thischapter describes the modelling of the effect of vessel size on the auto ignitiontemperature (AIT). This is an application of the two dimensional model whichis described extensively in the previous chapter. This model takes the naturalconvection inside the vessel into account and is used to determine the AIT forspherical vessels from 10−3 to 1 m3. First an overview is given of the modelsfor the volume dependency of the auto-ignition temperature. Thereafter theresults obtained with these models in spherical vessels are presented. Finallythe auto-ignition temperatures in cylindrical vessels are compared to those in

95

96 Chapter 6 Influence of the vessel size on the AIT

spherical ones.

6.1 Models for the volume dependency of theauto-ignition temperature

In principle recourse can be taken to two theoretical models that describe thephenomena occurring during auto-ignition. The first model is the one developedby Semenov, see section 2.3.2. It considers the gas mixture to behave as a pointheat source. The heat is transferred to the vessel walls by means of convection.The combustion reaction is assumed to be a first order step reaction. Forspherical vessels this model results in the following relationship between thecritical pressure Pc and the gas temperature T at auto-ignition (see equation2.41):

ln(PcT0

) =EA

2RT0+ ln(

C√D

) (6.1)

with EA the activation energy, R the universal gas constant, D the diameter ofthe vessel and C a constant which is independent of the volume but dependson the convective heat transfer coefficient between the vessel wall and the gasmixture.

The second model comes from Frank-Kamenetskii (see Section 2.3.3), whostudied the heat transfer in the gas mixture considering heat conduction throughthe mixture to the (spherical) vessel wall assuming rotational symmetry andagain simple Arrhenius type reaction kinetics. He found that at auto ignitionconditions the Frank-Kamenetskii parameter is equal to:

δ =Q

λ

EART 2

w

r2Ze−EARTw ≤ δcrit = 3.32 (6.2)

in which r is the radius of the vessel, Q is the volumetric heat of reaction, λis thermal conductivity and δcrit is the critical parameter which depends ongeometry and is equal to 3.32 for spherical vessels. By comparison of equation6.1 and 6.2, it can be seen that the two theoretical models have a differentvolume dependency of the auto-ignition temperature.

Beerbower (Coffee, 1980) developed the following empirical correlation forthe AIT T2 at volume V2 as a function of the AIT T1 at V1:

T2 =T1 − 75

log(V1)− 12· log(V2) + [75− T1 − 75

log(V1)− 12] (6.3)

where the temperatures are expressed in degrees Celsius and the volumes indm3. This correlation was obtained by the analysis of the experimentally de-termined auto-ignition temperatures in different volumes for benzene, acetone,methanol, pentane, etc. It was observed that the auto-ignition temperaturedecreases linearly with the logarithm of the volume. Equation 6.3 expressesthat the auto-ignition temperatures for the different mixtures coincide at avolume of 1012 dm3 at a value of 75 ◦C. The Beerbower correlation can only

6.2 Model evaluations for spherical vessels 97

be applied to obtain an auto-ignition temperature of a gas mixture at a certainvolume if the auto-ignition temperature of that mixture is known at anothervolume. Furthermore the Beerbower correlation is not validated for the volumedependency of the auto-ignition temperature at elevated pressures.

The Semenov model requires the activation energy to be known. An alter-native method consists of analysing the detailed combustion reaction kinetics,to determine the rate equations for all of the radicals formed during the reac-tion and to combine the radical reactions into reaction paths. The 0-D model,which is extensively described in section 5.1 of the previous chapter, is differentfrom the Semenov model because this model uses a full kinetic mechanism in-stead of one simple Arrhenius reaction. The reaction mechanism is a methaneoxidation of the British Gas Corporation (Reid et al., 1984), which resulted inaccurate predictions of the auto-ignition limits in closed spherical vessels, ascan be seen in chapter 5.

It is clear that because of the combustion reaction and the heat transferwith the vessel wall temperature differences will occur giving rise to buoyancydriven flows of the mixture. Such flows will have an impact upon the heattransfer with the vessel walls (convective effect) and thus on the heat transfercoefficient occurring in the Semenov model. A two-dimensional CFD flow modelis applied in order to take this phenomenon into account. This model, calledthe 2-D model, also incorporates the detailed chemical kinetics of the 0-D modeland is described in more detail in section 5.1.

6.2 Model evaluations for spherical vesselsThe different models are evaluated for a 60 mol% methane in air mixture. Thetheoretical models, such as the Semenov and the Frank-Kamenetskii model,require the overall activation energy of the combustion reaction. At first theresults of the zero-dimensional model will be presented, which will be usedto determine the value of the overall activation energy. Up to now the auto-ignition limits were calculated in a closed vessel with a volume of 8 litres. Inorder to retrieve the volume dependency of the auto-ignition temperature fivedifferent volumes are considered. These spherical vessels have a volume of 1,8, 64, 512 and 4096 litres.

The auto-ignition temperatures of a 60 mol% methane/air mixture anddifferent volumes calculated with the zero-dimensional model are presentedin figure 6.1. It can be seen that for a pressure of 0.1 MPa and a volumebelow 10 litres, there is a sharp increase of the auto-ignition temperature.For higher pressures the decrease of the auto-ignition temperature is linearas a function of the volume. The slope of the curves slightly decreases forincreasing pressure. The results of the 0-D model and the experimental auto-ignition limits obtained in this study are presented in a Semenov plot in figure6.2. The overall activation energy can be retrieved from the slope of curves, seeequation 6.1. It can be seen that the slope of the experimental data is in goodagreement with the slope of limits obtained with the zero-dimensional model.


500

600

700

800

900

1000

1100

1 10 100 1000 10000Volume [dm³]

Aut

o-ig

nitio

n Te

mpe

ratu

re [K

]Limit @ 0.1 MPaLimit @ 0.3 MPaLimit @ 0.5 MPaLimit @ 1 MPaLimit @ 2 MPaLimit @ 5 MPaLimit @ 10 MPa

Figure 6.1: The volume dependency of the auto-ignition temperature calculatedwith the zero-dimensional model.

The average activation energy of the experiments and of the zero-dimensionalcalculations for a volume of 8 litres is found to be 160 kJ/mol. The activationenergy of rich methane/air mixtures was also measured by Melvin (1966), whofound an activation energy for a 60 mol% methane/air mixture of respectively170 KJ/mol and 183 kJ/mol depending if the activation energy was calculatedfrom measurements of the rate of temperature rise or measurements of theignition delay. These activation energies are in good agreement with the valueof 160 kJ/mol of this study, in particular if they are compared with the value of339 kJ/mol for the activation energy in the low pressure explosions of methaneand oxygen (Melvin, 1966). Consequently the value of 160 kJ/mol is used inthe Semenov model.

Figure 6.3 compares the results of the zero-dimensional model with the auto-ignition temperatures obtained with the Semenov correlation. At a pressureof 0.5 MPa, the limit obtained with the zero-dimensional model is similar tothe auto-ignition limit according to the Semenov theory. At 0.1 MPa thereis a significant difference between both limits for the small volumes. At highvolumes both limits have a similar volume dependency. For high pressures thelimits obtained with the Semenov correlation show a larger volume dependencythan the limit obtained with the 0-D model. The differences between bothlimits can be explained through the fact that the Semenov theory only includesone reaction with one activation energy. In the 0-D model a full chemicalkinetics mechanism is applied. The average global activation energy clearlydepends on the mixture pressure. From figure 6.2 it can be seen that the slopeof the auto-ignition limit significantly changes for the small volumes and hightemperatures. This explains the large differences at a pressure of 0.1 MPa.

Figure 6.4 presents the different auto-ignition limits obtained with the

6.2 Model evaluations for spherical vessels 99

4

5

6

7

8

9

10

0.001 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0019 0.002

1/T [1/K]

ln (p

/T)

1 litre 200K

8 litre 200K

64 litre 200K

512 litre 200K

4096 litre 200K

Experimental data

Figure 6.2: Semenov plot of the experimental AIT and the AIT calculated with thezero-dimensional model.

500

600

700

800

900

1000

1100

1 10 100 1000 10000Volume [dm³]

Aut

o-ig

nitio

n Te

mpe

ratu

re [K

]

0-D limit @ 0.1 MPaSemenov limit @ 0.1 MPa0-D limit @ 0.5 MPaSemenov limit @ 0.5 MPa0-D limit @ 1 MPaSemenov limit @ 1 MPa0-D limit @ 5 MPaSemenov limit @ 5 MPa

Figure 6.3: Comparison of the calculated auto-ignition temperatures of the zero-dimensional model with the results of the Semenov model.


500

600

700

800

900

1 10 100 1000 10000

Volume [dm³]

Aut

o-ig

nitio

n Te

mpe

ratu

re [K

]Semenov @ 0.1 MPa Semenov @ 1 MPa Semenov @ 5 MPaFrank-Kam. @ 0.1 MPa Frank-Kam. @ 1 MPa Frank-Kam. @ 5 MPaBeerbower @ 0.1 MPa Beerbower @ 1 MPa Beerbower @ 5 MPa

Figure 6.4: Comparison of the calculated auto-ignition temperatures using the Se-menov and the Frank-Kamenetskii model and the Beerbower correlation.

Frank-Kamenetskii and the Beerbower correlation for different pressures. Theauto-ignition limits of the Semenov model for a volume of 8 litres were usedfor the application of the Frank-Kamenetskii theory and the Beerbower corre-lation. Therefore the Semenov limits coincides with the limits at a volume of8 litres for both these models. The limit according to the Frank-Kamenetskiitheory decreases significantly more than the Semenov limit when the vessel vol-ume is increased. From equations 6.1 and 6.2 it follows that the Semenov AITat a volume of 512 litres is similar to the Frank-Kamenetskii AIT at a volumeof 64 litres. The auto-ignition limits according to the Beerbower correlation,which has no theoretical underpinning, lies between the limits determined withthe Semenov and Frank-Kamenetskii theory.

The previous models require the knowledge of the activation energy, theheat transfer coefficient or experimentally determined auto-ignition limits. Analternative approach is the 2-D CFD model which includes the full kineticsmechanism and incorporates natural convection. It is expected that the naturalconvection will play an important role in the determination of the auto-ignitiontemperature for large volumes. In figure 6.5 the 2-D model results are showntogether with the results of the Semenov models for an initial pressure of 0.5MPa, 1 MPa and 5 MPa. It can be seen that the auto-ignition limits of the2-D models lie higher in comparison with the Semenov limits. This can beexplained by the increasing heat loss due to the natural convection that istaken into account in the 2-D model which hampers the auto-ignition. Ata pressure of 0.5 MPa it can be seen that the limit obtained with the 2-Dmodel has a slightly higher decrease with increasing volume in comparisonwith the Semenov model. This effect disappears at a pressure of 5 MPa atwhich the Semenov limit and the 2-D model shows an identical decrease. By

6.3 Model evaluations for vertical cylindrical vessels 101

500

600

700

800

1 10 100 1000 10000

Volume [dm³]

Aut

o-ig

nitio

n Te

mpe

ratu

re [K

]Semenov @ 0.5 MPa Semenov @ 1 MPa Semenov @ 5 MPa

2-D model @ 0.5 MPa 2-D model @ 1 MPa 2-D model @ 5 MPa

Figure 6.5: Comparison of the calculated auto-ignition temperatures using the Se-menov and the 2-D model.

comparison of figures 6.4 and 6.5 it can be concluded that the 2-D model showsthe auto-ignition temperature to decrease less rapidly with increasing volumein comparison with the Frank-Kamenetskii and the Beerbower model.

6.3 Model evaluations for vertical cylindrical ves-sels

In process installations the reactors are mostly cylindrical vessels instead ofspheres because of their cheapness. Therefore it is important to know how theauto-ignition temperature behaves in cylindrical vessels with increasing volume.The question should be put how accurate are the auto-ignition temperaturesobtained with the Semenov model and the Beerbower correlation for changingcylindrical volumes because these models are not valid for cylindrical geome-tries. The Frank-Kamenetskii model was also derived for cylindrical geometries.The critical Frank-Kamenetskii parameter changes to 2.00 for infinite cylindersinstead of 3.32 for spheres and the length used in the parameter formula isequal to the radius of the cylinder, as can be seen in section 2.3.3. It followsfrom the Frank-Kamenetskii theory that the auto-ignition temperature insideinfinite cylinders depends solely on the radius of the cylinder. It is not pos-sible to include the effect of finite cylinders on the auto-ignition temperatureaccording to the Frank-Kamenetskii model.

Since the existing theoretical models cannot supply a satisfactory answer tothe question of the volume dependency of the AIT in cylindrical geometries, theauto-ignition temperatures are calculated by means of the 2-D CFD-kineticsmodel. At first a cylinder with a volume of 8 litres and a diameter/height ratio


500

600

700

800

900

1 10 100 1000Volume [dm³]

Aut

o-ig

nitio

n Te

mpe

ratu

re [K

] Sphere @ 0.5 MPa Cylinder @ 0.5 MPa

Sphere @ 1 MPa Cylinder @ 1 MPa

Sphere @ 5 MPa Cylinder @ 5 MPa

Figure 6.6: Comparison of the 2-D auto-ignition temperatures for spheres and ver-tical cylinders.

equal to 1 was modelled. A cylinder has similar to a sphere an axisymmetryaxis according to direction of the gravity force. Consequently the grid consistsof a 2-D rectangle. The grid size and the time step independence are checked byvarying their values until no influence on the result was observed. Next to the 8litres vessel similar calculations are performed with increasing cylinder volume.The surface area of the bottom and the top of the cylinder is not altered;the volume of the cylinder therefore is directly proportional to the height ofthe cylinder. The results are shown in figure 6.6. The auto-ignition limits ata volume of 8 litres are in excellent agreement with the ones obtained for thespherical vessel. At a pressure of 0.5 MPa the auto-ignition limit of the cylinderis in good agreement with the limit obtained for the sphere. At higher pressuresthe auto-ignition temperature for cylindrical vessels decreases less for increasingvolume than the limit for spherical vessels. At high pressures and at largevolumes, the auto-ignition temperature shows almost no volume dependency.This is because of the higher buoyancy creating a high temperature zone at thetop of the cylinder, see figure 6.7. Ignition is governed by the heat productionand heat loss at the top of the cylinder. Because the size of the top surface ofthe cylinder was not changed for increasing cylinder volume, the auto-ignitiontemperature does not change. At elevated pressures and for a height/diameterratio of more than eight the AIT is only dependent on the radius of the vessel,as was predicted by the Frank-Kamenetskii model for infinite cylinders.

6.4 ConclusionsIt is found that the existing models to predict the volume dependence of theauto ignition temperature of gas mixtures require the knowledge of param-eters such as activations energies, heat transfer coefficients (Semenov, Frank-

6.4 Conclusions 103

20s 40s 60s 70s 80s 90s 100s

680 K

780 K

730 K

Figure 6.7: Temperature evolution of a 2-D simulation of a 60 mol% methane/airmixture at 680 K and 1.0 MPa in a vertical cylinder with a volume of 64 litres.

Kamenetskii) or experimentally determined auto-ignition conditions (Beerbower).An alternative approach not needing these a priori data is possible but requiresdetailed chemical kinetics to describe the combustion reactions and the fluidflow. Such a method has been developed for methane-air mixtures and can beapplied to spherical as well as cylindrical vessels.

Chapter 7

Conclusions andrecommendations

7.1 Conclusions

The aim of this study is to investigate experimentally and numerically theinfluence of process conditions on the auto-ignition temperature (AIT) of differ-ent alkane mixtures. Although many AIT values of hydrocarbon-air mixturescan be found in literature, these values are generally determined accordingto the standard test methods in small vessels and at atmospheric pressures.Experimental auto-ignition data of hydrocarbon-air mixtures at elevated pres-sures are scarce. Since many industrial processes operate at high pressures andhigh temperatures, detailed knowledge about the auto-ignition temperatures atthese conditions is essential for the safe and economic operation of those pro-cesses. The aim of this study is to help fill this hiatus. This thesis encompassesfirst a theoretical part, in which an overview of parameters and factors thatinfluence the auto-ignition temperature and different auto-ignition theories arepresented. In the experimental part a large set of consistent auto-ignition datais generated for methane, propane and butane mixtures which can be of di-rect use for industrial applications or which can be used for the validation ofthe numerical models. The last part of this thesis consists of the numericalsimulation of the auto-ignition process.

Theoretical and literature studiesAlthough an auto-ignition process can be represented simply as a balance be-tween the heat production from the chemical reactions and the heat loss tothe surrounding walls, the literature study revealed the complexity of the auto-ignition phenomenon. The auto-ignition temperature is not constant for acertain combustible gas mixture, but is influenced by many factors and param-eters. In chapter 2 a broad overview of these influences are presented. Because

105

106 Chapter 7 Conclusions and recommendations

no standard method exists for the determination of the auto-ignition temper-ature at elevated pressures a new standard procedure was developed in thisthesis. Therefore the existing standards for the determination of the AIT arecompared and their shortcomings were revealed. The last section of chapter2 describes three auto-ignition theories, which will be applied in the differentparts of this study.

Experimental studyThe experimental study consists of the determination of the auto-ignition limitsof propane and butane mixtures at elevated pressures up to 3 MPa for a widerange of concentrations inside a closed vessel of 8 l (Chapter 4). A standard op-erating procedure is developed. It is shown that the auto-ignition temperaturesdecrease significantly with increasing pressure. The auto-ignition temperatureof a 40 mol% propane/air mixture is 573 K at atmospheric pressure and de-creases to 523 K at a pressure of 1.5 MPa. The AIT’s of n-butane/air mixturesare lower compared to the AIT’s of propane. For example, the AIT of a 50mol% n-butane/air mixture is 548 K at atmospheric pressure and decreases to503 K at a pressure of 1.7 MPa. The AIT’s of i-butane are comparable to theAIT’s of propane. The AIT of a 50 mol% i-butane/air mixture is 573 K atatmospheric pressure and decreases to 523 K at a pressure of 1.3 MPa. TheseAIT’s are significantly lower than the AIT’s determined by the standard meth-ods which are 743 K, 733 K and 638 K for propane, i-butane and n-butanerespectively. It is also found that the combustible concentration most sensitiveto auto-ignition depends on the initial pressure. The auto-ignition pressures(AIP) of two propane/butane (LPG) mixtures are determined and comparedto the auto-ignition limits of their respective components. The minimum AIPat 523 K are 0.39 MPa and 0.32 MPa for the 50/50 propane/n-butane mix-ture and the 40/30/30 propane/n-butane/i-butane mixture respectively. TheseAIP’s are in good agreement with the minimum AIP (0.30 MPa) of n-butaneat 523 K, which is the component with the lowest AIP.

The upper flammability limits (UFL) of propane and butane mixtures showa linear increase with increasing initial temperatures. At high temperature adeviation from the linear dependence of the UFL’s was found by Van den Schoor(2007). By comparison of the auto-ignition limits with the upper flammabilitylimits of propane and n-butane at elevated pressures it is concluded that thedeviating UFL’s lie inside or very close to the auto-ignition range (Section 4.4).

The last part of the experimental study consisted of the determination ofthe auto-ignition limits of methane/air mixtures at elevated pressures and fordifferent concentrations. Methane is the smallest alkane and has the highestauto-ignition temperature of the alkanes. The AIT of a 60 mol% methane inair mixture is 713 K at a pressure of 0.9 MPa and decreases to 653 K at apressure of 2.9 MPa. The experimental results were initially strongly affectedby the remaining reaction products and the rust formation inside the explosionvessel. Therefore the standard operating has been adapted and this resultedin a significantly improvement of the repeatability of the auto-ignition data.

7.2 Recommendations for further research 107

The temperature measurements at different locations inside the explosion vesselmake it possible to describe qualitatively the auto-ignition process at elevatedpressures.

Numerical studyAt the beginning of this research it was a major challenge to make a coupling ofthe detailed chemistry with computational fluid dynamics in order to simulatethe auto-ignition process. It soon became clear that the coupling of detailedchemical kinetics with hundreds of reactions and a two or three dimensionalfluid calculation is not feasible. Therefore certain simplifications are needed.The numerical study mainly focuses on the modelling of the auto-ignition ofmethane/air mixtures. Since methane is the smallest hydrocarbon, the exist-ing reaction mechanisms of methane are smaller compared to the mechanismsof higher alkanes. First a zero-dimensional approach is adopted in order tocompare the different reaction mechanisms. A methane reaction mechanismof the British Gas Corporation shows the best agreement with the experimen-tal results. Subsequently, to take thermal and mass diffusion and the naturalconvection inside the vessel into account a two-dimensional model is built in-cluding the kinetic mechanism. A CFD-model is used to compute the heattransfer and the buoyant flows inside the vessel. The coupling of the reactionmechanism to this model results in an accurate prediction of the auto-ignitionconditions of methane/air mixtures at elevated pressures inside a closed vessel.This model is also used to investigate the volume dependency of the auto-ignition temperature for both spherical and cylindrical vessels. The results arein good agreement with empirical and theoretical correlations. This 2-D modelcan also be applied for the auto-ignition modelling at real process conditions.These are, for example, the ignition at hot surfaces, the auto-ignition in specificvolumes and the auto-ignition in forced flows.

The 0-D auto-ignition modelling of propane/air mixtures reveals that thereis still need for accurate reaction mechanisms validated for the auto-ignition inthe low temperature region before the reaction mechanisms can be applied inmore comprehensive heat transfer models.

7.2 Recommendations for further researchThis study has hopefully contributed to a safer and more economic operationof industrial processes. The experimental part consists of a substantial enlarge-ment of the available auto-ignition data of low alkane/air mixtures at elevatedpressures. Additionally, the numerical study pioneers the coupling of detailedchemical kinetics with CFD calculations in order to model the auto-ignitioninside closed vessels. Although this study has taken next steps both on ex-perimental and numerical level, further research is necessary. In the followingparagraphs some recommendations for further research on both experimentaland numerical level are presented.


Experimental work• The experimental part of this study consisted of experiments with me-

thane, propane and butane mixtures. To complete the homologous se-ries of the lower alkanes, auto-ignition experiments with ethane mixturesshould be performed. Experimental auto-ignition data of higher alka-nes or alkenes at elevated pressures is essential for the validation of thechemical kinetics mechanisms.

• The oxidant used in this work was compressed dry air. Since manychemical processes are operating in oxygen rich or oxygen poor envi-ronments, the influence of the oxidiser should be investigated. Thereforeauto-ignition experiments with oxygen-enriched and oxygen-poor air orwith other oxidiser such as nitrous oxide should be performed. Thesedata could improve the applicability of the kinetic mechanisms.

• Many other influences on the auto-ignition temperature at elevated pres-sures still can be investigated experimentally. These are, for example, thevolume dependency, the material effect and the influence of turbulence.

• The experiments of this study were conducted in a homogenously heatedexplosion vessel. In many industrial situations the heat source that causesauto-ignition is not homogenous, but is a local hot spot. This can be ahot tube or a hot burner stone. Therefore the influence of the hot surfacearea on the ignition temperature should be investigated experimentally.

Numerical simulation• The numerical simulations of this study have revealed some shortcom-

ings of the chemical kinetics modelling at elevated pressures. First fewreaction mechanisms are validated for elevated pressures. Only a fewhydrocarbon reaction mechanisms exist for high pressures, but these aremainly validated by means of shock tube experiments with very short in-duction times. Therefore these reaction mechanisms are not appropriatefor the modelling of auto-ignition with long inductions times. Furtherresearch is necessary to improve these reaction mechanisms for the ex-perimental conditions. The experimental data of this thesis could servefor the validation of these reaction mechanisms.

• This study developed a CFD-kinetics model for the auto-ignition of me-thane inside closed vessels at elevated pressures. This model could havemany applications such as the auto-ignition modelling in different vol-umes and with changing flow conditions or the modelling of hot surfaceignitions.

• The numerical model described the gaseous reactions that take placeduring the auto-ignition. It was seen in section 2.1 that the materialhas an influence on the auto-ignition temperatures. Therefore, surface

7.2 Recommendations for further research 109

reactions should be included in order to predict the material effect on theauto-ignition temperature.

Appendices

111

Appendix A

Test results

During this study a large number of experiments were performed in the8 l spherical test vessel. In this appendix the auto-ignition experiments aresummarised.

Propane: First series

fuel T0 Tmax ∆T P0 Pmax Press. IDT Explo?[mol%] [K] [K] [K] [MPa] [MPa] ratio[-] [s]

10 573 577 4 0.775 0.775 1.00 x no10 573 577 4 0.810 0.810 1.00 x no10 573 578 5 1.010 1.010 1.00 x no10 573 577 4 0.850 0.850 1.00 x no10 573 1195 622 1.440 5.080 3.53 570 yes10 573 1156 583 1.250 5.080 4.06 400 yes10 573 1110 537 1.120 4.830 4.31 372 yes10 573 1111 538 1.060 4.550 4.29 425 yes10 573 1095 522 1.020 4.340 4.25 790 yes10 573 1111 538 1.030 4.480 4.35 575 yes10 573 1113 540 1.000 4.190 4.19 880 yes10 573 1107 534 0.970 4.080 4.21 700 yes10 573 1123 550 0.950 3.990 4.20 757 yes10 573 1075 502 0.920 3.850 4.18 755 yes10 573 1063 490 0.850 3.480 4.09 770 yes10 573 1110 537 0.850 3.510 4.13 863 yes10 573 573 0 0.820 0.820 1.00 x no10 573 573 0 0.820 0.820 1.00 x no60 573 703 130 0.825 1.240 1.50 45 yes60 573 683 110 0.580 0.840 1.45 60 yes60 573 627 54 0.320 0.393 1.23 138 yes

113

114 Appendix A Test results

60 573 628 55 0.280 0.386 1.38 172 yes60 573 629 56 0.250 0.308 1.23 204 yes60 573 621 48 0.205 0.246 1.20 210 yes50 573 653 80 0.280 0.390 1.39 85 yes50 573 640 67 0.200 0.280 1.40 150 yes50 573 573 0 0.110 0.110 1.00 x no50 573 620 47 0.156 0.190 1.22 570 yes60 548 648 100 0.580 0.740 1.28 220 yes60 548 608 60 0.380 0.445 1.17 480 yes60 548 599 51 0.345 0.394 1.14 580 yes60 548 576 28 0.290 0.310 1.07 850 no50 548 603 55 0.300 0.348 1.16 750 yes50 548 548 0 0.253 0.253 1.00 x no40 548 548 0 0.290 0.290 1.00 x no40 548 683 135 0.452 0.708 1.57 750 yes40 548 548 0 0.402 0.407 1.01 x no30 548 548 0 0.497 0.497 1.00 x no30 548 761 213 0.690 1.522 2.21 720 yes30 548 751 203 0.640 1.803 2.82 750 yes30 548 745 197 0.608 1.287 2.12 750 yes30 548 731 183 0.530 1.062 2.00 890 yes30 573 673 100 0.203 0.385 1.90 240 yes30 573 573 0 0.106 0.106 1.00 x no30 573 663 90 0.152 0.247 1.63 140 yes40 573 641 68 0.154 0.215 1.40 138 yes40 573 600 27 0.103 0.115 1.12 220 yes40 523 523 0 0.998 0.998 1.00 x no40 523 523 0 1.520 1.520 1.00 x no40 523 523 0 1.980 1.980 1.00 732 no40 523 768 245 2.210 4.160 1.88 900 yes40 523 768 245 2.145 3.960 1.85 940 yes50 523 769 246 2.157 3.345 1.55 390 yes50 523 743 220 1.850 2.741 1.48 570 yes50 523 523 0 1.590 1.590 1.00 630 no50 523 723 200 1.635 2.346 1.43 740 yes60 523 695 172 2.135 3.060 1.43 910 yes60 523 702 179 2.105 2.798 1.33 880 yes60 523 671 148 1.750 2.250 1.29 535 yes60 523 658 135 1.542 1.932 1.25 620 yes60 523 633 110 1.330 1.572 1.18 808 yes60 523 621 98 1.210 1.380 1.14 1005 yes60 523 626 103 1.277 1.493 1.17 870 yes60 523 523 0 1.235 1.235 1.00 980 no70 523 603 80 1.442 1.615 1.12 522 yes70 523 587 64 1.305 1.440 1.10 580 yes70 523 581 58 1.190 1.285 1.08 655 no

A.0 115

70 523 569 46 1.120 1.175 1.05 815 no70 523 571 48 1.150 1.218 1.06 753 no30 523 523 0 2.495 2.495 1.00 x no30 536 915 379 1.105 2.986 2.70 360 yes30 536 775 239 0.698 1.692 2.42 515 yes30 536 790 254 0.710 1.717 2.42 496 yes30 536 711 175 0.405 0.884 2.18 720 yes30 536 536 0 0.200 0.200 1.00 x no30 536 536 0 0.295 0.295 1.00 1010 no30 536 536 0 0.336 0.336 1.00 1030 no30 536 715 179 0.405 0.840 2.07 940 no30 536 719 183 0.455 0.908 2.00 820 yes40 536 685 149 0.445 0.733 1.65 640 yes40 536 536 0 0.245 0.245 1.00 x no40 536 536 0 0.342 0.342 1.00 x no40 536 690 154 0.453 0.742 1.64 898 yes40 536 536 0 0.400 0.400 1.00 x no50 536 652 116 0.453 0.624 1.38 540 yes50 536 536 0 0.255 0.255 1.00 x no50 536 536 0 0.342 0.342 1.00 x no50 536 536 0 0.400 0.400 1.00 1010 no50 536 625 89 0.455 0.560 1.23 707 yes60 536 536 0 0.395 0.395 1.00 x no60 536 636 100 0.537 0.666 1.24 476 yes60 536 603 67 0.410 0.472 1.15 896 yes60 536 536 0 0.352 0.352 1.00 x no

Propane: Second series

fuel T0 Tmax ∆T P0 Pmax Press. IDT Expl?[mol%] [K] [K] [K] [MPa] [MPa] ratio[-] [s]

40 536 799 263 0.91 1.648 1.81 460 yes40 536 805 269 0.78 1.37 1.76 589 yes40 536 785 249 0.71 1.215 1.71 720 yes40 536 779 243 0.59 1.004 1.70 908 yes40 536 856 320 1.44 2.805 1.95 294 yes40 536 833 297 1.17 2.185 1.87 408 yes40 536 790 254 0.722 1.234 1.71 810 yes40 536 765 229 0.57 0.89 1.56 1380 no40 536 865 329 1.52 2.95 1.94 267 yes40 536 776 240 0.61 0.985 1.61 873 yes40 536 786 250 0.588 0.953 1.62 706 yes40 523 523 0 1.2 1.2 1.00 x no40 523 533 10 1.45 1.46 1.01 980 no40 523 856 333 1.6 2.87 1.79 797 yes40 523 833 310 1.5 2.69 1.79 827 yes


40 523 829 306 1.46 2.596 1.78 853 yes40 573 703 130 0.192 0.33 1.72 50 yes40 573 573 0 0.1 0.1 1.00 x no40 573 728 155 0.15 0.24 1.60 93 yes40 573 687 114 0.13 0.16 1.23 92 yes40 548 756 756 0.51 0.903 1.77 303 yes40 548 747 747 0.415 0.72 1.73 430 yes40 548 738 738 0.36 0.58 1.61 564 yes40 548 723 723 0.3 0.46 1.53 765 yes40 548 548 548 0.26 0.26 1.00 x no40 548 773 773 0.595 1.094 1.84 206 yes

Propane: Third series


60 548 689 141 0.430 0.574 1.33 60 yes60 548 688 140 0.370 0.470 1.27 246 yes60 548 689 141 0.330 0.413 1.25 283 yes60 548 673 125 0.280 0.329 1.18 384 yes60 548 653 105 0.230 0.258 1.12 298 yes60 548 548 0 0.165 0.165 1.00 - no60 548 548 0 0.200 0.200 1.00 - no40 548 775 227 0.505 0.871 1.72 408 yes40 548 548 0 0.390 0.390 1.00 - no40 548 748 200 0.430 0.686 1.60 1000 no40 548 788 240 0.610 1.077 1.77 352 yes40 536 800 264 0.875 1.643 1.88 409 yes40 536 765 229 0.700 1.240 1.77 555 yes40 536 770 234 0.664 1.152 1.73 633 yes40 536 758 222 0.600 1.012 1.69 783 yes40 536 753 217 0.560 0.907 1.62 898 yes40 536 746 210 0.510 0.778 1.53 1160 no60 523 673 150 1.010 1.233 1.22 762 yes60 523 695 172 1.210 1.528 1.26 559 yes60 523 662 139 0.960 1.146 1.19 677 yes60 523 649 126 0.900 1.055 1.17 801 yes60 523 633 110 0.790 0.888 1.12 1006 no30 523 523 0 1.030 1.030 1.00 - no30 523 523 0 1.489 1.489 1.00 - no30 523 523 0 1.635 1.635 1.00 - no30 523 902 379 1.770 3.851 2.18 1200 yes30 523 909 386 1.830 3.966 2.17 1043 yes30 523 1005 482 1.950 4.615 2.37 1147 yes30 523 1157 634 2.120 5.000 2.36 522 yes30 523 1085 562 2.030 5.000 2.46 554 yes

A.0 117

30 523 909 386 1.780 4.334 2.43 583 yes30 523 918 395 1.585 3.745 2.36 636 yes30 523 851 328 1.290 2.916 2.26 712 yes30 523 817 294 1.030 2.258 2.19 916 no30 523 812 289 0.945 2.028 2.15 1034 no40 523 806 283 1.230 2.420 1.97 650 yes40 523 797 274 1.140 2.178 1.91 705 yes40 523 783 260 1.070 1.986 1.86 761 yes40 523 770 247 0.940 1.670 1.78 876 yes40 523 754 231 0.855 0.870 1.02 970 no

n-Butane


50 548 657 109 0.310 0.475 1.53 38 yes50 548 628 80 0.200 0.279 1.40 58 yes50 548 608 60 0.160 0.209 1.31 66 yes50 548 558 10 0.102 0.110 1.08 150 no50 523 523 0 0.300 0.300 1.00 x no50 523 663 140 0.800 1.130 1.41 228 yes50 523 637 114 0.605 0.800 1.32 260 yes50 523 609 86 0.500 0.622 1.24 365 yes50 523 581 58 0.420 0.480 1.14 554 yes50 523 559 36 0.375 0.414 1.10 700 yes50 523 551 28 0.355 0.391 1.10 752 yes60 523 583 60 0.485 0.552 1.14 420 yes60 523 571 48 0.440 0.500 1.14 450 yes60 523 548 25 0.352 0.380 1.08 690 no60 523 563 40 0.405 0.447 1.10 530 yes60 523 633 110 0.794 1.034 1.30 210 yes60 548 646 98 0.408 0.565 1.38 50 yes60 548 548 0 0.112 0.118 1.05 x no60 548 603 55 0.207 0.255 1.23 90 yes60 548 579 31 0.166 0.185 1.11 90 yes60 548 553 5 0.110 0.112 1.02 x no40 523 593 70 0.410 0.485 1.18 878 yes40 523 635 112 0.500 0.672 1.34 510 yes40 523 523 0 0.360 0.360 1.00 x no40 523 615 92 0.440 0.555 1.26 690 yes40 548 638 90 0.160 0.255 1.59 60 yes40 548 560 12 0.095 0.102 1.07 x no30 548 660 112 0.165 0.322 1.95 50 yes30 548 633 85 0.138 0.232 1.68 65 yes30 548 607 59 0.100 0.430 4.30 90 yes


30 523 648 125 0.400 0.567 1.42 720 yes30 523 528 5 0.365 0.365 1.00 1260 no20 523 733 210 0.485 1.186 2.45 720 yes20 523 728 205 0.475 1.160 2.44 740 yes20 523 523 0 0.385 0.385 1.00 x no20 523 523 0 0.443 0.443 1.00 1130 no20 548 705 157 0.195 0.580 2.97 52 yes20 548 638 90 0.115 0.300 2.61 64 yes20 511 511 0 1.490 1.490 1.00 x no20 511 1053 542 1.445 2.000 1.38 840 yes20 511 1113 602 1.395 4.850 3.48 160 yes20 511 511 0 1.400 1.400 1.00 x no30 511 765 254 1.385 3.010 2.17 756 yes30 511 511 0 1.320 1.320 1.00 1200 no30 511 768 257 1.350 2.880 2.13 847 yes40 511 721 210 1.335 2.280 1.71 620 yes40 511 723 212 1.280 2.186 1.71 600 yes40 511 715 204 1.205 2.024 1.68 665 yes40 511 707 196 1.140 1.892 1.66 725 yes40 511 687 176 1.005 1.570 1.56 851 yes40 511 678 167 0.950 1.445 1.52 910 no50 511 649 138 1.115 1.520 1.36 655 yes50 511 641 130 1.003 1.340 1.34 690 yes50 511 633 122 0.925 1.230 1.33 788 yes50 511 623 112 0.875 1.105 1.26 835 yes50 511 609 98 0.801 0.995 1.24 900 yes50 511 511 0 0.765 0.765 1.00 990 no60 511 608 97 1.025 1.235 1.20 570 yes60 511 583 72 0.810 0.980 1.21 750 yes60 511 555 44 0.710 0.770 1.08 890 no60 511 568 57 0.760 0.838 1.10 810 yes70 511 550 39 0.805 0.865 1.07 610 no70 511 558 47 0.870 0.955 1.10 540 no70 511 563 52 0.935 1.035 1.11 500 yes10 523 523 0 0.375 0.375 1.00 x no10 523 523 0 0.555 0.555 1.00 x no10 523 523 0 0.640 0.640 1.00 x no10 523 523 0 0.750 0.750 1.00 x no10 523 523 0 0.875 0.875 1.00 x no10 523 523 0 1.000 1.000 1.00 x no10 523 523 0 1.090 1.090 1.00 x no10 523 523 0 1.200 1.200 1.00 x no10 523 523 0 1.500 1.500 1.00 1080 no50 503 708 205 2.290 3.488 1.52 720 yes50 503 698 195 2.002 2.938 1.47 810 yes

A.0 119

50 503 675 172 1.700 2.360 1.39 920 no50 503 677 174 1.730 2.415 1.40 913 no50 503 669 166 1.795 2.515 1.40 891 yes40 503 503 0 2.005 2.005 1.00 1165 no40 503 503 0 2.488 2.488 1.00 960 no40 503 768 265 2.755 4.970 1.80 880 yes40 503 768 265 2.475 4.416 1.78 870 yes40 503 503 0 2.445 2.445 1.00 935 no40 503 503 0 2.465 2.465 1.00 970 no40 503 503 0 2.640 2.640 1.00 955 no40 503 503 0 2.750 2.750 1.00 x no40 503 768 265 2.460 4.420 1.80 850 yes40 503 503 0 2.390 2.390 1.00 918 no60 503 641 138 2.240 2.912 1.30 598 yes60 503 623 120 1.785 2.200 1.23 708 yes60 503 611 108 1.605 1.926 1.20 803 yes60 503 503 0 1.405 1.405 1.00 960 no60 503 611 108 1.505 1.778 1.18 861 yes60 503 605 102 1.449 1.725 1.19 862 yes

i-Butane


60 573 583 10 0.100 0.107 1.070 120 no60 573 633 60 0.205 0.256 1.249 60 yes60 573 618 45 0.165 0.190 2.364 60 yes60 548 573 25 0.300 0.320 1.067 330 no60 548 603 55 0.395 0.445 1.127 195 yes60 548 593 45 0.350 0.390 1.114 235 yes60 523 526 3 0.490 0.490 1.000 x no60 523 558 35 1.380 1.450 1.051 840 no60 523 578 55 1.510 1.640 1.086 660 no50 573 638 65 0.200 0.260 1.300 80 yes50 573 608 35 0.110 0.120 1.091 125 no50 573 633 60 0.165 0.190 1.152 60 yes50 548 548 0 0.215 0.215 1.000 x no50 548 583 35 0.305 0.340 1.115 440 yes50 548 613 65 0.355 0.410 1.155 315 yes50 523 593 70 1.355 1.500 1.107 890 yes50 523 523 0 1.300 1.300 1.000 1200 no40 523 523 0 1.250 1.250 1.000 x no40 523 523 0 1.350 1.350 1.000 x no40 523 768 245 2.000 3.318 1.659 530 yes40 523 768 245 1.810 2.816 1.556 640 yes


40 523 729 206 1.642 2.458 1.497 815 yes40 523 713 190 1.545 2.286 1.480 885 yes40 523 711 188 1.525 2.213 1.451 936 no40 548 548 0 0.365 0.365 1.000 x no40 548 548 0 0.496 0.496 1.000 x no40 548 753 205 0.830 1.320 1.590 240 yes40 548 703 155 0.605 0.855 1.413 830 yes40 548 548 0 0.550 0.550 1.000 1125 no40 573 658 85 0.210 0.310 1.476 120 yes40 573 573 0 0.170 0.170 1.000 x no30 573 573 0 0.190 0.190 1.000 x no30 573 703 130 0.285 0.555 1.947 84 yes30 573 698 125 0.238 0.458 1.924 60 yes30 573 703 130 0.240 0.458 1.908 50 yes30 523 523 0 1.660 1.660 1.000 x no30 523 523 0 1.810 1.810 1.000 1160 no30 523 768 245 2.215 4.915 2.219 550 yes30 523 768 245 2.010 4.170 2.075 680 yes30 523 768 245 1.855 3.582 1.931 890 yes30 548 548 0 0.332 0.332 1.000 x no30 548 769 221 0.654 1.290 1.972 282 yes30 548 757 209 0.605 1.205 1.992 590 yes30 548 741 193 0.546 0.970 1.777 557 yes30 548 729 181 0.504 0.893 1.772 450 yes30 548 684 136 0.412 0.620 1.505 870 yes30 548 548 0 0.357 0.357 1.000 x no4 548 553 5 0.220 0.220 1.000 x no4 548 548 0 0.293 0.293 1.000 x no4 548 548 0 0.700 0.700 1.000 x no4 548 548 0 1.200 1.200 1.000 x no4 548 1263 715 1.360 2.000 1.471 960 no4 548 1273 725 1.410 7.200 5.106 667 yes

20 548 548 0 0.525 0.525 1.000 x no20 548 851 303 0.630 1.808 2.870 299 yes20 548 843 295 0.555 1.700 3.063 174 yes60 536 620 84 0.798 0.948 1.188 390 yes60 536 569 33 0.590 0.645 1.093 660 no60 536 601 65 0.700 0.802 1.146 490 yes60 536 587 51 0.656 0.735 1.120 523 yes30 536 768 232 0.998 1.840 1.844 710 yes30 536 536 0 0.812 0.812 1.000 1105 no30 536 768 232 0.906 1.602 1.768 870 yes30 536 756 220 0.848 1.450 1.710 870 yes50 536 575 39 0.552 0.605 1.096 890 no50 536 596 60 0.602 0.688 1.143 860 yes40 536 536 0 0.651 0.651 1.000 x no

A.0 121

40 536 536 0 0.710 0.710 1.000 x no40 536 536 0 0.760 0.760 1.000 x no40 536 703 167 0.910 1.327 1.458 730 yes40 536 673 137 0.795 1.296 1.630 820 yes20 536 536 0 0.985 0.985 1.000 x no20 536 768 232 1.204 3.568 2.963 850 yes20 536 768 232 1.136 3.692 3.250 425 yes

LPG mixture 1: 50 mol% propane and 50 mol% n-butane


40 523 523 0 0.495 0.495 1.00 x no40 523 791 268 1.205 2.212 1.84 362 yes40 523 741 218 0.815 1.400 1.72 470 yes40 523 687 164 0.580 0.870 1.50 793 yes40 523 523 0 0.440 0.440 1.00 x no40 523 668 145 0.535 0.765 1.43 890 yes40 523 651 128 0.508 0.697 1.37 917 yes50 523 635 112 0.545 0.688 1.26 560 yes50 523 523 0 0.415 0.415 1.00 922 no50 523 613 90 0.485 0.593 1.22 730 yes50 523 604 81 0.455 0.534 1.17 809 yes60 523 583 60 0.450 0.498 1.11 624 yes60 523 558 35 0.396 0.432 1.09 791 no70 523 557 34 0.452 0.480 1.06 522 no70 523 574 51 0.548 0.605 1.10 403 yes70 523 567 44 0.503 0.551 1.10 457 no30 523 523 0 0.515 0.515 1.00 x no30 523 770 247 0.707 1.342 1.90 888 yes30 523 523 0 0.655 0.655 1.00 1050 no30 536 678 142 0.303 0.494 1.63 596 yes30 536 536 0 0.148 0.148 1.00 x no30 536 536 0 0.210 0.210 1.00 x no30 536 536 0 0.252 0.252 1.00 1010 no40 536 536 0 0.196 0.196 1.00 x no40 536 603 67 0.248 0.296 1.19 640 yes50 536 536 0 0.200 0.200 1.00 120 no50 536 592 56 0.252 0.288 1.14 448 yes60 536 536 0 0.250 0.250 1.00 x no60 536 593 57 0.352 0.405 1.15 884 yes60 536 575 39 0.303 0.328 1.08 640 no70 536 577 41 0.352 0.384 1.09 386 no70 536 586 50 0.403 0.450 1.12 476 yes40 511 511 0 0.810 0.810 1.00 x no


40 511 511 0 1.225 1.225 1.00 x no40 511 511 0 1.414 1.414 1.00 x no40 511 511 0 1.605 1.605 1.00 x no40 511 799 288 2.116 3.749 1.77 820 yes40 511 791 280 2.025 3.424 1.69 850 yes40 511 787 276 1.894 3.239 1.71 879 yes40 511 783 272 1.797 3.030 1.69 910 yes40 511 789 278 1.840 3.113 1.69 880 yes50 511 713 202 1.840 2.667 1.45 684 yes50 511 709 198 1.637 2.343 1.43 718 yes50 511 678 167 1.344 1.812 1.35 925 no50 511 687 176 1.400 1.930 1.38 865 yes60 511 628 117 1.302 1.580 1.21 727 yes60 511 602 91 1.016 1.178 1.16 916 no60 511 609 98 1.058 2.338 2.21 907 no60 511 615 104 1.104 2.394 2.17 851 yes70 511 567 56 1.110 1.221 1.10 810 yes70 511 570 59 1.050 1.157 1.10 722 yes70 511 555 44 1.000 1.066 1.07 849 no30 511 511 0 2.588 2.588 1.00 x no30 517 924 407 1.802 4.405 2.44 535 yes30 517 871 354 1.398 3.441 2.46 610 yes30 517 812 295 0.994 2.240 2.25 775 yes30 517 517 0 0.915 0.915 1.00 x no30 517 517 0 0.945 0.945 1.00 x no40 517 517 0 0.700 0.700 1.00 x no40 517 517 0 0.798 0.798 1.00 950 no40 517 710 193 0.845 1.278 1.51 857 yes50 517 664 147 0.870 1.170 1.34 659 yes50 517 637 120 0.712 0.912 1.28 852 yes50 517 517 0 0.645 0.645 1.00 1020 no60 517 589 72 0.650 0.732 1.13 705 yes60 517 517 0 0.544 0.544 1.00 974 no60 517 581 64 0.605 0.676 1.12 854 yes70 517 559 42 0.646 0.703 1.09 612 no70 517 571 54 0.694 0.772 1.11 536 yes

LPG mixture 2: 40 mol% propane, 30 mol% n-butane and 30 mol%i-butane


60 523 654 131 0.627 0.828 1.32 488 yes60 523 641 118 0.535 0.680 1.27 578 yes60 523 618 95 0.440 0.524 1.19 717 yes60 523 598 75 0.370 0.422 1.14 846 yes

A.0 123

60 523 584 61 0.345 0.380 1.10 948 no60 523 554 31 0.320 0.337 1.05 1058 no60 523 531 8 0.255 0.260 1.02 1500 no70 523 610 87 0.605 0.710 1.17 533 yes70 523 591 68 0.525 0.581 1.11 709 yes70 523 564 41 0.440 0.470 1.07 878 no70 523 546 23 0.395 0.412 1.04 941 no50 523 680 157 0.616 0.860 1.40 798 yes50 523 702 179 0.765 1.137 1.49 644 yes50 523 693 170 0.675 0.956 1.42 758 yes50 523 683 160 0.655 0.914 1.40 813 yes50 523 673 150 0.605 0.830 1.37 900 yes50 523 660 137 0.553 0.714 1.29 1046 no50 523 641 118 0.490 0.602 1.23 1206 no40 523 771 248 0.905 1.615 1.78 827 yes40 523 789 266 1.110 2.095 1.89 606 yes40 523 785 262 1.015 1.880 1.85 676 yes40 523 773 250 0.900 1.610 1.79 812 yes40 523 752 229 0.850 1.500 1.76 869 yes40 523 723 200 0.785 1.340 1.71 960 no40 523 523 0 0.580 0.580 1.00 x no30 523 908 385 1.200 2.990 2.49 746 yes30 523 913 390 1.130 2.860 2.53 583 yes30 523 864 341 1.060 2.553 2.41 630 yes30 523 842 319 1.010 2.380 2.36 666 yes30 523 810 287 0.890 2.038 2.29 766 yes30 523 802 279 0.855 1.920 2.25 863 yes30 523 790 267 0.810 1.790 2.21 931 no

60 523 620 97 0.610 0.720 1.18 1050 no60 523 635 112 0.650 0.780 1.20 916 no60 523 631 108 0.650 0.780 1.20 912 no60 523 672 149 0.930 1.230 1.32 516 yes60 523 635 112 0.680 0.820 1.21 864 yes60 523 629 106 0.645 0.770 1.19 922 no40 523 523 0 1.090 1.090 1.00 x no40 523 776 253 1.100 2.020 1.84 854 yes40 523 802 279 1.320 2.570 1.95 651 yes40 523 792 269 1.240 2.370 1.91 709 yes40 523 776 253 1.150 2.135 1.86 826 yes40 523 765 242 1.050 1.860 1.77 1050 no30 523 523 0 1.130 1.130 1.00 x no30 523 1037 514 1.500 4.320 2.88 620 yes30 523 917 394 1.310 3.390 2.59 599 yes30 523 883 360 1.170 2.920 2.50 659 yes


Methane


60 653 663 10 2.850 2.850 1.00 x no60 653 888 235 2.960 3.596 1.21 965 no60 653 978 325 3.220 4.440 1.38 600 AIT60 653 893 240 2.930 3.560 1.22 975 no60 673 675 2 1.550 1.550 1.00 x no60 673 683 10 1.790 1.790 1.00 x no60 673 873 200 2.080 2.420 1.16 514 AIT60 673 680 7 1.775 1.780 1.00 x no60 673 773 100 1.900 2.040 1.07 750 no60 673 823 150 1.875 2.060 1.10 615 no60 713 723 10 0.860 0.860 1.00 x no60 713 721 8 0.900 0.900 1.00 x no60 713 946 233 1.050 1.600 1.52 62 AIT60 713 721 8 0.930 0.925 0.99 x no60 683 688 5 1.450 1.450 1.00 x no60 683 913 230 1.680 2.060 1.23 348 AIT60 683 691 8 1.540 1.540 1.00 x no60 683 943 260 1.610 2.100 1.30 204 AIT80 683 833 150 1.600 1.825 1.14 77 SC80 683 813 130 1.480 1.650 1.11 98 SC80 683 783 100 1.400 1.475 1.05 115 no80 683 843 160 1.340 1.640 1.22 50 SC80 683 715 32 1.280 1.310 1.02 125 no40 683 683 0 1.270 1.270 1.00 x no40 683 683 0 1.400 1.400 1.00 x no40 683 688 5 1.460 1.460 1.00 x no40 683 688 5 1.720 1.725 1.00 x no40 683 691 8 1.850 1.850 1.00 x no40 683 693 10 2.030 2.030 1.00 x no40 683 945 262 2.275 3.750 1.65 910 no40 683 963 280 2.400 3.550 1.48 1080 no40 683 963 280 2.510 4.100 1.63 928 no40 683 963 280 2.550 4.990 1.96 455 AIT50 683 943 260 2.040 3.475 1.70 248 AIT50 683 943 260 1.920 3.110 1.62 350 AIT50 683 953 270 1.800 2.790 1.55 434 AIT50 683 933 250 1.600 2.100 1.31 755 no50 683 693 10 1.520 1.520 1.00 x no70 683 903 220 1.530 1.890 1.24 106 AIT70 683 873 190 1.420 1.660 1.17 140 SC70 683 843 160 1.275 1.425 1.12 183 SC

A.0 125

70 683 731 48 1.130 1.160 1.03 x no40 713 963 250 1.500 3.400 2.27 32 AIT40 713 1093 380 1.200 2.300 1.92 131 AIT

Appendix B

Chemical kinetics mechanism

In the numerical model of this study a chemical kinetic mechanism for themethane oxidation of Reid et al. (1984) is applied. The total set of species andreactions of this mechanism are presented in the subjoined table.

Reactions Ai βi Eai1 CH4+O2⇔CH3+HO2 9.70E+13 0 234000

Reverse Arrhenius coefficient: 1.00E+12 0 02 CH4+HO2⇔CH3+H2O2 1.50E+13 0 95000

Reverse Arrhenius coefficient: 1.25E+12 0 170003 CH4+OH→CH3+H2O 1.55E+06 2.1 102504 CH4+H⇔CH3+H2 4.22E+14 0 62400

Reverse Arrhenius coefficient: 1.34E+13 0 570005 CH4+O→CH3+OH 2.00E+13 0 378006 CH3+O2⇔CH3O2 4.00E+11 0 0

Reverse Arrhenius coefficient: 1.50E+16 0 1245007 CH3O2+CH4→CH3O2H+CH3 3.00E+12 0 950008 CH3O2+CH2O→CH3O2H+HCO 1.00E+12 0 335009 CH3O2+HO2→CH3O2H+O2 2.00E+11 0 010 CH3O2+CH3O2→CH3O+CH3O+O2 2.60E+11 0 011 CH3O2+CH3→CH3O+CH3O 7.00E+12 0 012 CH3O2H→CH3O+OH 4.40E+16 0 16700013 CH3+HO2→CH3O+OH 2.00E+13 0 450014 CH3O+O2→CH2O+HO2 6.30E+10 0 1090015 CH3O+M→CH2O+H+M 5.01E+13 0 8790016 CH2O+O2→HCO+HO2 2.04E+13 0 16280017 CH2O+HO2→HCO+H2O2 1.00E+12 0 3350018 CH2O+OH→HCO+H2O 3.98E+13 0 600019 CH2O+CH3→HCO+CH4 1.15E+12 0 3020020 CH2O+H→HCO+H2 1.97E+13 0 1540021 CH2O+O→HCO+OH 1.77E+13 0 1280022 HCO+O2→CO+HO2 1.20E+13 0 16600

127

128 Appendix B Chemical kinetics mechanism

23 HCO+M→CO+H+M 1.50E+14 0 6150024 CO+HO2→CO2+OH 1.00E+14 0 9620025 CO+OH→CO2+H 1.26E+07 1.3 -335026 H2O2+O2⇔HO2+HO2 1.55E+13 0 114300

Reverse Arrhenius coefficient: 1.50E+12 0 027 H2O2+M→OH+OH+M 1.20E+17 0 19040028 H2O2+OH→HO2+H2O 4.20E+04 2.5 -700029 H2O2+H→H2O+OH 3.80E+14 0 3740030 H2O2+H⇔H2+HO2 6.30E+12 0 20600

Reverse Arrhenius coefficient: 1.97E+12 0 9000031 H2O2+O→OH+HO2 2.80E+13 0 2660032 CH3+CH3→C2H6 1.70E+13 0 033 C2H6+HO2→C2H5+H2O2 6.00E+12 0 8100034 C2H6+OH→C2H5+H2O 3.60E+12 0 690035 C2H6+H→C2H5+H2 1.32E+14 0 3900036 C2H6+O→C2H5+OH 3.00E+07 2 2140037 C2H6+CH3→C2H5+CH4 5.00E+14 0 9000038 C2H5+O2→C2H4+HO2 8.50E+11 0 1620039 C2H5+M→C2H4+H+M 1.30E+13 0 17100040 C2H4+OH→CH3+CH2O 5.00E+12 0 041 H2+OH→H2O+H 1.28E+08 1.5 1230042 H2+O→H+OH 1.80E+10 1 3720043 HO2+M⇔O2+H+M 5.20E+15 0 203000

Reverse Arrhenius coefficient: 3.00E+12 0 -420044 H+O2→OH+O 1.80E+14 0 7030045 H+HO2→H2+O2 2.80E+13 0 046 H+HO2→OH+OH 2.50E+14 0 790047 HO2+OH→H2O+O2 5.00E+13 0 420048 H2O+O→OH+OH 6.80E+13 0 76800

Table B.1: Reaction mechanism rate coefficients in the form ki=Ai · Tβi · expEaiRT ,

Units are mol, cm3, K and J/mol

Nederlandse samenvatting

129

Invloed van procesconditiesop dezelfontstekingstemperatuurvan gasmengsels

Inhoudsopgave1 Algemene inleiding . . . . . . . . . . . . . . . . . . 1312 Theoretische achtergrond . . . . . . . . . . . . . . . 1323 Experimentele studie . . . . . . . . . . . . . . . . . 1334 Numerieke studie . . . . . . . . . . . . . . . . . . . 1365 Conclusies en aanbevelingen . . . . . . . . . . . . . 138

1 Algemene inleidingVele chemische processen maken gebruik van brandbare gassen en dampen bijverhoogde drukken en temperaturen. Voor een veilige en optimale werkingvan deze processen is het belangrijk om de laagst mogelijke temperatuur tekennen waarbij spontane ontsteking kan optreden. In de literatuur zijn dezelfontstekingstemperaturen (AIT’s) van vele chemische stoffen beschikbaar.Deze zijn bepaald volgens gestandaardiseerde methodes in kleine volumes enbij atmosferische druk. Aangezien de zelfontstekingstemperatuur niet constantis maar daalt bij toenemende druk en toenemend volume zijn deze AIT’s nietrechtstreeks toepasbaar voor industriële condities. Het gebrek aan zelfontste-kingsdata bij verhoogde drukken en grote volumes en het gebrek aan uitgebreidemodellen van het zelfontstekingsproces waren de drijfveren voor deze studie.Deze studie bestaat zowel uit een experimenteel en een numeriek gedeelte.

De experimentele studie (Paragraaf 3) bestaat uit het bepalen van de druk-afhankelijkheid en de concentratieafhankelijkheid van de zelfontstekingstempe-ratuur van verschillende alkaan-lucht mengsels. Eveneens worden de zelfontstek-ingsgrenzen van twee LPG/lucht mengsels bepaald om de invloed van de ver-

131

132 Nederlandse samenvatting

schillende componenten op de zelfontstekingstemperatuur van het mengsel teonderzoeken. In de numerieke studie (Paragraaf 4) wordt een model ontwikkeldvoor de simulatie van het thermo-chemische zelfontstekingsproces van methaan-lucht mengsels bij verhoogde drukken. Enerzijds gaat het model dieper in opde warmteproductie door de vergelijking van verschillende reactiemechanismen.Anderzijds wordt het warmteverlies gemodelleerd door middel van een 0-, 1-en 2-dimensionaal model. Het 2-D model laat toe om de natuurlijke convectiemee in rekening te brengen en de zelfontsteking te simuleren bij reële pro-cescondities. In paragraaf 2 wordt een overzicht gegeven van de verschillendeprocescondities die de zelfontstekingstemperatuur kunnen beïnvloeden.

2 Theoretische achtergrondEen zelfontsteking kan beschouwd worden als een gevolg van het onevenwichttussen de warmteproductie vanwege de chemische reacties en het warmteverliesnaar de omgeving. Twee theorieën die de zelfontsteking beschrijven vanuitthermisch oogpunt zijn de theorieën van Semenov (1935) en Frank-Kamenetskii(1955). Een tweede groep van theorieën beschrijven de zelfontsteking vanuitchemisch oogpunt, zoals het chemisch vertakkingsmodel. Deze twee groepenvan theorieën vormen de basis voor de numerieke modellen ontwikkeld in dezestudie. De zelfontsteking is een zeer complex fenomeen, beïnvloed door veleverschillende factoren. De belangrijke invloedsparameters kunnen opgesplitstworden in drie groepen. Ten eerste zijn er de parameters die afhangen van hetmengsel:

• Druk. Een verhoging van de druk zorgt voor een grotere stijging vanwarmteproductie ten opzichte van de toename van het warmteverlies.Daardoor daalt de AIT bij toenemende druk.

• Brandstof. De zelfontstekingstemperatuur is sterk afhankelijk van debrandstof. In het algemeen daalt de zelfontstekingstemperatuur daalt bijtoenemende ketenlengte en stijgt bij toenemende graad van vertakkingbij alkanen.

• Concentratie. De concentratie met de laagste zelfontstekingstemperatuurkomt meestal niet overeen met de stoichiometrische concentratie, maarde laagste zelfontstekingstemperatuur komt voor bij rijkere mengsels. Indeze studie wordt nagegaan wat de gevoeligste concentratie is voor deverschillende alkaan/lucht mengsels bij de verschillende drukken.

• Additieven. De toevoeging van componenten met een lagere zelfontste-kingstemperatuur zorgt voor een verlaging van de AIT van het gas-mengsel. Een onnauwkeurige voorspelling van de AIT van een mengselis de AIT van de component met de laagste AIT. Sommige additievenkunnen de zelfontsteking bevorderen ondanks dat ze zelf een hogere AIThebben. Bijvoorbeeld ammoniak kan de AIT van methaan/lucht mengselsverlagen, terwijl ammoniak een hogere AIT heeft dan methaan.

3 Experimentele studie 133

• Oxidator. Meestal wordt lucht aangewend als oxidator. Wanneer zuurstofverrijkte lucht als oxidator gebruikt wordt kan dit de zelfontstekingstem-peratuur verlagen.

Ten tweede zijn er de apparaatparameters:

• Volume. De AIT daalt met toenemend volume van het testvat. Aangeziende meeste industriële processen gebruik maken van grote volumes is on-derzoek naar de volumeafhankelijkheid van de AIT heel belangrijk.

• Materiaaleffect. Het materiaal van het testvat kan zowel een bevorderendals remmend effect hebben op de zelfontsteking. Hilado en Clark (1972)hebben aangetoond dat de zelfontstekingstemperatuur 30 K kan dalen alser ijzeroxide (roest) wordt toegevoegd aan het testapparaat.

• Stroming. Een verhoging van de stroomsnelheid en de turbulentie zorgtvoor een grotere warmteafgifte en bemoeilijkt de zelfontsteking. Daardoorstijgt de zelfontstekingstemperatuur. Aangezien de gestandaardiseerdeopstellingen gebruik maken van stationaire mengsels geven ze aanleidingtot conservatieve AIT wat betreft de stromingscondities.

Ten derde zijn er de methodeparameters, zoals het zelfontstekingscriterium.Meestal wordt een visueel criterium toegepast voor de bepaling van een zelf-ontsteking. Bij verhoogde druk is een visuele toegang moeilijk te realiseren.Alternatieve methodes zijn temperatuurs- en drukmetingen of de analyse vanreactieproducten. Deze thesis focust op het ontwikkelen van een aangepastcriterium.

3 Experimentele studie

Experimentele methodeDe experimentele opstelling voor de bepaling van de zelfontstekingsgrenzen bijverhoogde drukken bestaat uit vier delen: de gasmenginstallatie, het buffervat,het explosievat en de meet- en regelapparatuur, zie figuur 1. Het testmengselwordt onder hoge druk opgeslagen in het buffervat. Het explosievat heeft eeninwendig sferisch volume van 8 liter en is bestand tot explosiedrukken van400 bar bij een temperatuur van 550 ◦C. De testprocedure is als volgt. Ini-tieel wordt het explosievat opgewarmd tot de gewenste testtemperatuur. Nahet vacuümzuigen wordt het explosievat gevuld met het buffermengsel tot degewenste begindruk. Het zelfonstekingscriterium is gebaseerd op de tempera-tuursstijging en de drukstijging van het gasmengsel, zie tabel 2. De ontste-kingsuitsteltijd, dit is de tijd na het vullen van het explosievat tot het momentvan ontsteking, bedraagt maximaal 15 min. Door het variëren van de initiëledruk van de opeenvolgende testen wordt de zelfontstekingsgrens bepaald meteen stapgrootte van 0.05 MPa. De zelfontstekingsdrukken zijn gedefinieerd alsde hoogste drukken waarbij geen zelfontsteking optreedt.


explosievat

vacuümpomp

monster-name

spui

perslucht

spui

PV

monstername

spui

MFC A

MFC B

MFC C

vloeistofpomp

PV

ontspanner tegendruk-regelaar filter

spui

debietmeter

mengvat

PI

PV

PV

PV

breekplaat

verdamper

PV

buffervat

spui

thermokoppels drukopnemer(Baldwin)

thermokoppels drukopnemer(Kistler)

Figuur 1: Experimentele testopstelling.

Resultaat Temp.a en rel. drukstijging OntstekingsuitsteltijdGeen reactie < 50 K en < 10% > 15 minZelfontsteking > 50 K of > 10% < 15 min

Tabel 2: Zelfontstekingscriterium voor propaan en butaan mengsels.

Zelfontstekingsgrenzen propaan/n-butaan/i-butaanDe zelfontstekingsgrenzen van propaan, n-butaan en i-butaan in lucht zijn ex-perimenteel bepaald bij begindrukken tot 30 bar en voor een breed concen-tratiegebied. Uit figuur 2 blijkt dat de zelfontstekingstemperaturen (AIT)significant dalen bij toenemende druk. Voor een concentratie van 40 mol%propaan in lucht is de AIT gelijk aan 573 K bij atmosfeerdruk en daalt tot523 K bij een druk van 1.5 MPa. Deze AIT’s zijn veel lager in vergelijkingmet de AIT van propaan (763 K) bepaald volgens de standaard methode EN14522 (2003). De propaanconcentraties met de laagste zelfontstekingsgrenzenzijn rijke concentraties met een equivalentieverhouding van meer als 10. Dezeconcentraties zijn bovendien drukafhankelijk. De aanwezigheid van resterendeverbrandingsproducten en roestvorming in de explosievaten zorgen voor eengrote spreiding tussen de verschillende testreeksen, voornamelijk bij hoge druk,zie figuur 2.

De zelfontstekingsgrenzen van n-butaan/lucht mengsels liggen ongeveer 25K lager in vergelijking met de grenzen van propaan/lucht mengsels, zie figuur3. Dit kan verklaard worden door de hogere ketenlengte van n-butaan ten

3 Experimentele studie 135

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80

Molaire fractie propaan [mol%]

Initi

ële

druk

[MPa

]

523 K Eerste reeks523 K Derde reeks548 K Eerste reeks548 K Derde reeks573 K Eerste reeks

Equivalentieverhouding [-] 0 5 10 20 40

Figuur 2: Overzicht van de zelfontstekingsgrenzen van propaan/lucht mengsels.

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80

Molaire fractie n-butaan [mol%]

Initi

ële

druk

[MPa

]

503 K

511 K

523 K

548 K

Figuur 3: Overzicht van de zelfontstekingsgrenzen van n-butaan/lucht mengsels.

opzichte van propaan waardoor het gemakkelijker is om methylradicalen af tesplitsen. De zelfontstekingsgrenzen van i-butaan/lucht mengsels komen goedovereen met de zelfontstekingsgrenzen van propaan/lucht mengsels. Eveneenszijn de zelfontstekingsgrenzen van twee LPG/lucht mengsels bepaald voor ver-schillende concentraties en begindrukken. Het eerste LPG mengsel bestaat uit50 mol% propaan en 50 mol% n-butaan en het tweede LPG mengsel bestaat uit40 mol% propaan, 30 mol% n-butaan en 30 mol% i-butaan. Figuur 4 toont aandat de minimale zelfontstekingsdrukken van de twee LPG/lucht mengsels goedovereenkomen met de grenzen van de component met de laagste zelfontste-kingstemperatuur, namelijk n-butaan.

De ligging van de zelfontstekingsgebieden geeft een verklaring voor het ver-loop van de bovenste explosiegrenzen van propaan waargenomen door Van denSchoor (2007). De bovenste explosiegrens van propaan/lucht mengsels vertoontbij een druk van 1.0 en 1.5 MPa en bij een temperatuur vanaf 523 K een meerdan lineaire toename (Figuur 5). Deze afwijking kan verklaard worden door denabijheid van het zelfontstekingsgebied.


0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 20 30 40 50 60 70 80

Molaire brandstof fractie [mol%]

Initi

ële

druk

[MPa

]

AIT LPG (40/30/30)

AIT LPG (50/50)

AIT n-butaan

Figuur 4: Vergelijking van de zelfontstekingsgrenzen van 2 LPG/lucht mengsels metde zelfontstekingsgrenzen van n-butaan/lucht mengsels bij een temperatuur van 523K.

0

10

20

30

40

50

60

70

280 330 380 430 480 530 580 630

Temperatuur [K]

Mol

aire

frac

tie C

3H8 [

mol

%]

UFL 3.0 MPa

UFL 2.0 MPa

UFL 1.5 MPa

UFL 1.0 MPa

UFL 0.5 MPa

UFL 0.2 MPa

UFL 0.1 MPa

AIT 1.0 MPa

AIT 1.5 MPa

Figuur 5: Vergelijking van de bovenste explosiegrenzen (UFL) en de zelfontstekings-grenzen (AIT) van propaan/lucht mengsels.

Het laatste gedeelte van de experimentele studie bestaat uit het bepalen vande zelfontstekingsgrenzen van methaan/lucht mengsels bij verhoogde drukken.Deze experimentele data dienen voor de validatie van het numeriek model enzullen in de volgende paragraaf voorgesteld worden.

4 Numerieke studieEen numeriek model van het zelfontstekingsproces moet enerzijds de complexereactiekinetica omvatten en anderzijds de warmteoverdracht goed beschrijven.Omdat het nog niet mogelijk is om de complexe reactiekinetica met honderdenreacties en tientallen stofsoorten te koppelen aan een CFD stromingsmodel-lering, wordt in eerste instantie een 0-D model aangewend om verschillendereactiemechanismen te vergelijken. Uit figuur 6 blijkt dat het methaan reac-

5 Numerieke studie 137

0

1

2

3

4

5

580 600 620 640 660 680 700 720 740

Temperatuur [K]

Zelfo

ntst

ekin

gsdr

uk [M

Pa] NIST

GRI 3.0BGCENSICAIT (deze studie)

Figuur 6: Vergelijking van de zelfontstekingsgrenzen bepaald met het 0-D model enverschillende reactiemechanismen voor een 60 mol% methaan in lucht mengsel.

0

1

2

3

4

5

620 630 640 650 660 670 680 690 700 710 720

Temperature [K]

Pres

sure

[MPa

]

0-D model1-D model2-D modelAIT (deze studie)

Figuur 7: Vergelijking van de zelfontstekingsgrenzen bepaald met het 0-D, 1-D en2-D model en het BGC-mechanisme en de experimentele grenzen voor een 60 mol%methaan in lucht mengsel.

tiemechanisme van de British Gas Corporation (BGC) kwalitatief een goedevoorspelling geeft van de temperatuursafhankelijkheid van de experimentelezelfontstekingsdrukken. Het absolute verschil in de zelfontstekingsdrukken kandeels verklaard worden door de vereenvoudigde 0-D voorstelling van de warm-teoverdracht. Voor een betere modellering van de warmteoverdracht en hetmodelleren van de natuurlijke convectie in het explosievat wordt een 1-D en 2-Dmodel ontwikkeld. Deze modellen maken gebruik van het BGC reactiemecha-nisme (21 stofsoorten en 55 reacties) voor de simulatie van de warmteproductie.De zelfontstekingsgrens bepaald met het 2-D CFD-kinetisch model vertoont eengoede overeenkomst met de experimentele data (figuur 7). Tenslotte wordt het2-D model toegepast om de volumeafhankelijkheid van de zelfontstekingstem-peratuur in sferische en cilindrische volumes te onderzoeken.


5 Conclusies en aanbevelingenDeze studie omvat een theoretisch gedeelte waarin een overzicht is gegeven vande verschillende parameters die de zelfontstekingstemperatuur beïnvloeden enwaarin een aantal bestaande zelfontstekingstheorieën worden beschreven.

De experimentele studie omvat de generatie van een uitgebreide dataset vanzelfontstekingstemperaturen bij verhoogde drukken voor verschillende lagerealkaan/lucht mengsels. Deze data kunnen aangewend worden voor het inschat-ten van het zelfontstekingsrisico in industriële processen en dienen eveneensvoor de validatie van numerieke modellen.

De numerieke studie bestaat uit de ontwikkeling van een model die eenkoppeling maakt tussen de reactiekinetica en de stromingsmodellering, zodateen nauwkeurige voorspelling van de zelfontstekingsgrenzen bekomen wordt.

Ondanks het feit dat deze studie belangrijke stappen verwezenlijkt heeft opexperimenteel en numeriek vlak voor het inschatten van het zelfontstekings-risico bij verhoogde druk, is er nog steeds plaats voor verder onderzoek. Opexperimenteel vlak kunnen experimenten met ethaan/lucht mengsels de reeksvan de lagere alkanen vervolledigen. Verder kan de invloed van de oxidatornagegaan worden door experimenten met zuurstofverrijkte lucht uit te voerenof met andere oxidatoren zoals lachgas (N2O). Eveneens kan de invloed vanandere parameters, zoals de volumeafhankelijkheid, het materiaaleffect en deturbulentie of de ontsteking aan hete oppervlakken nog experimenteel onder-zocht worden.

De numerieke simulaties met propaan/lucht mengsels toonden aan dat ernog veel werk te verrichten op vlak van modellering van de reactiekinetica vande lagere alkanen bij verhoogde drukken. Het ontwikkeld 2-D model van dezestudie kent nog vele toepassingsmogelijkheden, bijvoorbeeld voor zelfontstekingin stromende fluïda of voor de ontsteking aan hete oppervlakken. Het numeriekmodel kan nog uitgebreid worden met oppervlaktereacties aangezien deze eve-neens een invloed hebben op de zelfontstekingstemperatuur van gasmengsels.

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Curriculum vitae 147

Curriculum VitaeFrederik Norman was born in Kortrijk (Belgium) on December 13, 1980. Hegraduated as Burgerlijk Werktuigkundig-Elektrotechnisch Ingenieur, optie Me-chanica, at the Katholieke Universiteit Leuven in 2003. His masters thesis wason the design of a micro compressor and the optimisation of a turbine for thegeneration of mobile electrical energy.

In August 2003 he started his doctoral study on the influence of processconditions on the auto-ignition temperature of gas mixtures, under the super-vision of Prof. dr. ir. Jan Berghmans and Prof. dr. ir. F. Verplaetsen, fundedby the Institute for the Promotion of Innovation by Science and Technology inFlanders (IWT), scholarship (2004-2007). In 2006, he received the award forthe the best student poster on the 13th International Heat Transfer Conference,Sydney, Australia.

List of publications

International journals with reviewNorman, F., Van den Schoor, F. and Verplaetsen, F. (2006), Auto-ignitionand upper explosion limit of rich propane-air mixtures at elevated pressures,Journal of Hazardous Materials 137, 666–671.

Van den Schoor, F., Norman, F. and Verplaetsen, F. (2006), Influence of theignition source location on the determination of the explosion pressure at el-evated initial pressures, Journal of Loss Prevention in the Process Industries19, 459–462.

Van den Schoor, F., Norman, F., Tangen, L., Sæter, O. and Verplaetsen,F. (2007), Explosion limits of mixtures relevant to the production of 1,2dichloroethane (ethylene dichloride), Journal of Loss Prevention in the Pro-cess Industries 20, 281–285.

Proceedings of international symposia with reviewNorman, F., Vandebroek, L., Verplaetsen, F. and Berghmans, J. (2006), Nu-merical Study of the Auto-Ignition in Methane/Air Mixtures, IHTC 13, Syd-ney, Australia.

Norman, F., Vandebroek, L., Verplaetsen, F. and Berghmans, J. (2007), Influ-ence of ammonia on the auto-ignition limits of methane/air mixtures, Pro-ceedings of the 3rd European Combustion Meeting, Chania, Crete, Greece.

Norman, F., Verplaetsen, F. and Berghmans, J. (2007), Experimental valida-tion of auto-ignition models for methane/air mixtures at elevated pressures,

148 Curriculum vitae

Proceedings of the 5th Int. Seminar on Fire and Explosion Hazards, Edin-burgh, United Kingdom.

2008 norman

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