Download Soot Formation Modeling during Hydrocarbon

Soot Formation Modeling during
Hydrocarbon Pyrolysis and Oxidation
behind Shock Waves
DISSERTATION
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of Rupertus Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
M.Sc. Iliyana Ivanova Naydenova
born in Sofia, Bulgaria
Ruprecht-Karls-Universität Heidelberg
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
2007
Soot Formation Modeling during
Hydrocarbon Pyrolysis and Oxidation
behind Shock Waves
DISSERTATION
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of Rupertus Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
M.Sc. Iliyana Ivanova Naydenova
born in Sofia, Bulgaria
Heidelberg, 11.June.2007
Ruprecht-Karls-Universität Heidelberg
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
2007
Soot Formation Modeling during
Hydrocarbon Pyrolysis and Oxidation
behind Shock Waves
Supervisor: Prof. Dr. Dr. h. c. Jürgen Warnatz
Reviewer: Priv. Doz. Dr. Hans-Robert Volpp
Acknowledgement
It is my great pleasure to acknowledge all the people who helped me directly or
indirectly to accomplish this dissertation. First and foremost, I express my deep felt
gratitude towards my supervisor Prof. Dr. Dr. h. c. Jürgen Warnatz for his advice,
encouragement, easy accessibility and freedom of work that leads to the completion
of the thesis.
I am also thankful to Dr. Pavel Vlasov (Institute of Chemical Physics, Russian
Academy of Science) and my colleague Jens Marquetand for the tireless discussions,
useful comments and great support in the development of my work. My special
thanks to Dr. Markus Kraft and Matthew Celnik (Department of Chemical Engineering, University of Cambridge) for their fruitful discussions on the problems
of soot formation modelling. Many thanks to Volkmar Reinhardt for his friendly
helping hand in preparating the results for our colleagues from the SFB-568 Project
(Technical University, Darmstadt).
I acknowledge Deutsche Forschungsgemeinschaft for their financial support.
My sincere thanks to Priv. Doz. Dr. Uwe Riedel for his advices and assistance in
solving the administrative obstacles. Thanks to Volker Karbach for the discussions
on reaction kinetics. I also thank to Ingrid Hellwig for her help in organising the
administrative details and to Jürgen Moldenhauer, Joachim Simon and Jan Pitann
for solving computer related problems. It would have not been possible to complete
the work without the help of my coworkers and friends. Space here would not be
enough to mention them all personally.
Finally, I would like to thank to my entire family for their help, boundless love and
faith in me. I owe a heartfelt gratitude to my husband Alexander for his endless
love, invaluable encouragement, support and assistance in all kind, cheerful sense of
humour and care which has been always important part of my success. Thank you
my friend!
Abstract
In the present work, soot formation was modeled in conditions typical of shock tube
experiments. Two different detailed kinetic models (Model-1 and Model-2) were
developed. The models were validated by means of a suitable numerical technique
(discrete Galerkin method). The gas-phase chemistry of soot precursor and particle
formation was described in terms of different pathways. Accordingly, the formation
and evolution of soot particles differs with respect to the type of the species leading
to soot particle inception.
Based on previously described hypotheses [1, 2], two types of soot precursors were
considered in Model-1, polyyne and PAH. Latest experimental investigations of soot
formation in flames and shock tube [3, 4, 5] confirmed that young soot particles are
built primarily of polycyclic aromatic hydrocarbons, and the reaction of aliphatic
species with pre-existing soot surface can be an important factor for the particle
mass growth. Following these conclusions, another detailed kinetic model was developed (Model-2), where PAH were considered as soot precursors, and aliphatic
species take place only in reactions of surface growth. Both models were validated
against the experimentally obtained concentration profiles of the main gas-phase
species, measured in shock tube experiments. They were further applied for soot
formation simulation during pyrolysis and oxidation of various hydrocarbons and
their mixtures behind shock wave, for a wide range of reaction conditions (temperature, pressure and mixture composition). The calculation results were compared
with the usually measured characteristics of soot formation, e. g., induction delay
time, observable rate of soot particle growth, soot particle concentration, diameter,
and soot yield.
For the application in a multi-dimensional computational fluid dynamics (CFD)
code for turbine combustion simulation, merely simple empirical models with few
variables must be used. Therefore, a two-equation model was developed and implemented in a software package [6] for simulation of time-dependent homogeneous
reaction systems. The model was calibrated by the reaction kinetics of the detailed
chemical mechanisms (Model-1 and Model-2). The complex phenomenon of soot
formation is described in terms of several global steps: inception, growth, coagulation and oxidation, where two differential equations are solved for the temporal
change of soot concentration and soot volume fraction. The simulation results were
compared with the experimentally measured soot characteristics during shock tube
oxidation of various hydrocarbons.
Kurzfassung
Die vorliegende Arbeit beschreibt die Modellierung der Rußbildung unter Bedingungen, die typisch für Stoßwellenexperimente sind. Zwei unterschiedliche, detaillierte kinetische Modelle (Modell-1 und Modell-2) wurden entwickelt und mittels
eines geeigneten numerischen Verfahrens (diskrete Galerkin-Methode) überprüft.
Die Entstehung des Rußvorläufers und die Russteilchenbildung wurde jeweils durch
unterschiedliche Reaktionspfade beschrieben.
Auf der Grundlage bereits beschriebener Hypothesen [1, 2] wurden in Modell-1
zwei verschiedene Arten von Rußvorläufern berücksichtigt: Polyine und polyzyklische aromatische Kohlenwasserstoffe (PAK). Die neuesten experimentellen Untersuchungen der Rußbildung in Flammen und Stoßwellenrohren [3, 4, 5] bestätigen,
dass die Rußteilchen hauptsächlich aus PAK gebildet werden. Die Experimente
deuten daraufhin, dass die Reaktion aliphatischer Spezies mit Rußoberfläche ein
wichtiger Faktor für das Massenwachstum der Teilchen ist. Aufgrund dieser Ergebnisse wurde ein detailliertes kinetisches Modell-2 entwickelt, in welchem die PAK
als Rußvorläufer betrachtet werden. Die aliphatische Spezies sind hier nur an
Oberflächenwachstumsreaktionen beteiligt. Beide Modelle wurden der wichtigsten
Gasphasenspezies Konzentrationsprofile validiert, die in Stoßwellenexperimenten
gemessen worden sind. Ferner wurden die Modelle für Simulation der Rußbildung während der Pyrolyse und der Oxidation verschiedener Kohlenwasserstoffe und
ihrer Mischungen hinter der Stoßwellen für ein breites Spektrum von Reaktionsbedingungen angewandt. Die Ergebnisse der Berechnungen wurden mit Messwerten
(Zündverzugszeit, Bildungsgeschwindigkeit des Rußteilchen, Rußteilchenkonzentration und Durchmesser) verglichen, die üblich bei Experimenten gemessen werden.
Für die mehrdimensionale Simulation der Verbrennung in Gasturbinen kann lediglich
ein einfaches empirisches Russbildungs Modell mit wenigen Variablen verwendet
werden. Hierfür wurde ein Zwei-Gleichungsmodell entwickelt und in ein Softwarepaket [6] für die Simulation zeitabhängiger, räumlich homogener Reaktionssysteme implementiert. Das Modell wurde anhand der Reaktionskinetik der detaillierten chemischen Mechanismen (Modell-1 und Modell-2) kalibriert. Der komplexe
Prozess der Rußbildung wurde mittels einiger globaler Schritte beschrieben: Keimbildung, Wachstum, Koagulation und Oxidation, wobei zwei Differentialgleichungen für die zeitliche Änderung der Rußkonzentration und des Rußvolumenbruchs
gelöst werden. Die Simulationsergebnisse wurden mit der experimentell gemessenen Rußcharakteristika der Oxidation unterschiedlicher Kohlenwasserstoffe in einem
Stoßwellenrohr verglichen.
I
Contents
1 INTRODUCTION
1
1.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Objectives and structure of the thesis . . . . . . . . . . . . . . . . . .
6
2 FUNDAMENTALS OF PHYSICAL CHEMISTRY
2.1
Homogeneous reaction system . . . . . . . . . . . . . . . . . . . . . .
3.2
9
2.1.1
Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2
Chemical kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3
Analysis of reaction mechanisms . . . . . . . . . . . . . . . . . 16
3 SOOT FORMATION
3.1
9
19
Gas phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1
First aromatic ring formation . . . . . . . . . . . . . . . . . . 21
3.1.2
Growth of aromatics by HACA . . . . . . . . . . . . . . . . . 24
3.1.3
Growth of aromatics by other species . . . . . . . . . . . . . . 25
3.1.4
Oxidation of aromatics . . . . . . . . . . . . . . . . . . . . . . 27
Particulate phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
II
3.2.1
Soot particle inception . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2
Soot particle growth . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.3
Soot particle coagulation . . . . . . . . . . . . . . . . . . . . . 31
3.2.4
Soot particle oxidation . . . . . . . . . . . . . . . . . . . . . . 32
3.2.5
Soot agglomeration . . . . . . . . . . . . . . . . . . . . . . . . 33
4 DISCRETE GALERKIN METHOD
35
4.1
Theory of the discrete Galerkin method . . . . . . . . . . . . . . . . . 36
4.2
Program package MACRON
. . . . . . . . . . . . . . . . . . . . . . 39
5 DETAILED KINETIC MODELS OF SOOT FORMATION
5.1
5.2
5.3
5.4
42
Description of Model-1 . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.1.1
Gas-phase reaction mechanism . . . . . . . . . . . . . . . . . . 42
5.1.2
Soot precursors and particle inception, surface growth, coagulation and oxidation . . . . . . . . . . . . . . . . . . . . . . . 44
Results Model-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2.1
Validation of the model . . . . . . . . . . . . . . . . . . . . . . 50
5.2.2
Hydrocarbon pyrolysis behind shock waves . . . . . . . . . . . 59
5.2.3
Hydrocarbon oxidation behind shock waves . . . . . . . . . . . 74
Description of Model-2 . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.1
Gas-phase reaction mechanism . . . . . . . . . . . . . . . . . . 77
5.3.2
Soot precursor and particle inception, growth, coagulation and
oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Results Model-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
III
5.4.1
Validation of the model . . . . . . . . . . . . . . . . . . . . . . 83
5.4.2
Hydrocarbon pyrolysis behind shock waves . . . . . . . . . . . 99
5.4.3
Hydrocarbon oxidation behind shock waves . . . . . . . . . . . 107
6 SIMPLIFIED MODEL OF SOOT FORMATION
6.1
6.2
114
Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.1.1
The temporal change of soot concentration . . . . . . . . . . . 116
6.1.2
The temporal change of the soot volume fraction . . . . . . . 117
6.1.3
Rate laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.1.4
Soot quantities . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7 Conclusion and future prospects
130
Appendix
133
Appendix A. List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Appendix B. List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
1
Chapter 1
INTRODUCTION
1.1
Motivation
Soot formation has been of interest to combustion scientists and engineers at least
since the 19th century. Initially soot was valued for its heat- and light-producing
properties and for its relation to carbon-black manufacturing [7]. The carbon black
is used in the production of automotive tires, as a reinforcing agent for rubbers, to
colour printing ink, painting, paper and plastics. The smoke produced by sooting
flames was only an annoyance until the early 1970s. At that time the dangerous
health effects associated with soot and the polycyclic aromatic hydrocarbons (PAH)
that usually accompany soot formation, came to be known, and soot became an
unwanted by-product of combustion. Longwell [8] pointed out that the interest in
controlling soot emissions was due to the understanding that soot particles can adsorb harmful PAH onto their surfaces. Small soot particles can be breathed deeply
into the lungs, where they can do substantial damage. Combustion related particulate matter is associated with a host of severe impact such as heart attacks, stroke,
cardiovascular death [9] and lung cancer [10] in adults. In children, fine particles
are associated with upper and lower respiratory impact, as well as retardation of
lung growth and crib death [11]. Soot particles from Diesel engines adsorbed onto
their surface metals and toxic substances such as cancer-causing aldehydes and PAH,
while many PAH are known to be carcinogenic or mutagenic. Traffic studies suggest
increased rates of respiratory and cardiovascular disease and risk of premature death
near busy urban streets or highways. Therefore, a great attention was drawn to the
chemistry of soot, PAH and hydrocarbons like 1,3-butadiene, benzene, and toluene
by the scientists allover the world. Thus, the chemistry of rich flames, particularly
1. INTRODUCTION
2
that involved with hydrocarbon growth into PAH and soot, became one of the most
active research areas in combustion chemistry.
In soot formation modeling, several principle proposals are known, which describe
the nature of soot particle inception. According to them, different types of species
are ranged as potential precursors, leading to soot particle inception: polyacetylenes
or polyynes [12, 13, 14, 15, 16, 17, 2, 18], ions [19, 20], and polycyclic aromatic
hydrocarbons [21, 1, 22, 23, 24].
The investigation of the role of acetylene in soot formation dates back to about
hundreds years ago. The reason why many experimentalists suggested the polyacetylenes as contingent soot precursors is that several experimental investigations,
performed in the 1960s and 1970s, showed the existence of hydrocarbons having
molecular mass in excess of 250 g/mol. They appear at the end of the reaction
zone, in the region right before the appearance of the first particles [12] and [25].
Unlike the PAH, these species disappear rapidly during the soot growth, and are
no longer detected at the end of the reaction zone. Some authors suggested that
such species could be polyacetylenes [26, 27, 28]. The development of this idea can
be summarised as follows: Berthelot et al. [29] and Lewes et al. [30] emphasised
the importance of C2 H2 in thermal decomposition reactions. Porter [3] proposed
the hypothesis of carbon formation from acetylene through its simultaneous polymerisation and dehydrogenation. Haynes and Wagner [25] pointed out that the
investigations of the absorption profiles for ”pre-soot” species in pyrolysis and oxidation of different fuels and indicate the presence of species capable of absorbing in
the visible and ultraviolet before soot becomes observable. Cundall et al. [26, 27, 28]
analysed the shape of some spectra and suggested that the absorbers are predominantly polyacetylenes, most probably C10 H2 and C12 H2 . These species have been
measured mass-spectrometrically by Kistiakowsky et al. [31, 32] as products of C2 H2
pyrolysis. They and other authors [33] concluded that the reaction proceeds as:
C2 H2 =⇒ C4 H3 =⇒ C4 H2 =⇒ C6 H2 =⇒ C8 H2 ...
(1.1)
Bohne and Wagner [34] experimentally observed that in premixed flat flames of
C2 H2 , C2 H4 , C3 H8 , C6 H6 , and C2 H5 OH in fuel-rich mixtures higher polyacytylenes
are formed, where such molecules up to C12 H2 have been detected experimentally.
Homann and Wagner [12] investigated the hydrocarbons occurring in the region of
carbon nucleation in acetylene and benzene/oxygen flames and discussed the role
of polyacetylenes and polycyclic aromatics in the process of particle inception. The
authors suggested that the soot precursors can be derived by the following scheme:
C6 H2 + C2 H =⇒ C8 H3 =⇒ C8 H2 + H =⇒ branching =⇒ cyclization =⇒... (1.2)
1. INTRODUCTION
3
Kern et al. [35, 36] measured the product profiles during pyrolysis of acetylene, butadiene, benzene and toluene. The authors found that the the main products are the
polyynes C4 H2 , C6 H2 , C8 H2 . Nevertheless, the polyacetylene hypothesis, describing
the soot inception by means of the formation of long and stable polyacetylene chains,
has not been elaborated further until the work of Krestinin et al. [15]. The authors
developed a detailed kinetic model of soot formation called polyyne model, regarding the high reactivity of these species in polymerisation reactions. The polyyne
model is applied for soot formation simulation during pyrolysis of C2 H2 [16]. A
modified and extended version is further applied for soot formation modeling during pyrolysis of different hydrocarbons in reactive flow experiments [17, 2, 18]. The
model treats soot formation as a process of chemical condensation (polymerisation)
of supersaturated polyyne vapour (C2n H2 ) and describes the formation of young
soot particles and mature soot particles, and the transformation between them. The
authors stated that compared to the rather slow multistage increase in the number
of aromatic rings in the PAH, the polyynes grow in a simple and fast way typically
in reactions like
C2n H2 + C2 H = C2n+2 H2 + H.
(1.3)
Calcote [19] argued that the polyacetylenes did not grow sufficiently rapidly to account for the almost instantaneous formation of soot. He claimed further that the
reactions of neutral species were not fast enough and suggested an ionic mechanism.
In the model chemi-ions are assumed to be the precursors of soot on which free radicals, polyacetylenes, and PAH repeatedly add through fast ion-molecule reactions.
Calcote claimed that H3 O+ was the dominant ion in near-stoichiometric and lean
flames, and C3 H+
3 in rich flames, and proposed a kinetic scheme with the elementary
reactions which produce the primary ions in the system.
Simultaneously with the above described hypotheses, many authors accepted that
the PAH are the only possible soot precursors. Thomas [37] stated that the process
of transformation of precursors to soot particles must involve species that must be
stable enough thermodynamically to survive extreme conditions like high temperature and high pressure combustion environment. In addition to this, they must be
sufficiently reactive to promote the growth of larger molecules on fairly short time
scales (e. g., a few milliseconds in shock tube experiments). Miller [38] pointed
out that the highly reactive criterion can be accommodated by supposing that free
radicals can be formed from stable molecules by abstracting hydrogen atoms. Therefore, a molecular structure is needed, stable enough to grow in flame environments.
Rummel and Veh [39] proposed that the major role of the PAH is due to their thermodynamic stability, whereas Thomas [37] suggested that the essential soot precursors are conjugated polyene radicals that grow into polybenzenoid radicals and soot
1. INTRODUCTION
4
by adding other unsaturated species. Glassman [115] had a similar point of view
and proposed a special role for 1,3-butadiene in the PAH growth. D’Alessio et al.
and Minutolo et al. [40, 41] investigated high molecular mass structured formed
in the main oxidation zone of rich premixed flames and rich flames below the soot
threshold limit. The authors [41] detected the existence of high molecular structures transparent to the visible radiation in both the pre-inception zone of sooting
flames and in flames below the soot formation limit. They stated that the onset of
ultra-violet fluorescence within the main oxidation zone implies that the formation
of these species is a very fast process and can be considered as a polymerisation of
small aromatic groups activated by the presence of oxidising agents.
The modeling of PAH and soot formation and growth in combustion was considerably influenced by the work of Frenklach et al. [13, 21, 1]. The authors suggested
a detailed kinetic mechanism of PAH formation and growth called H-abstractionC-addition (HACA). According to this model, the aromatics grow by a two-step
process of H-abstraction which activates the aromatic molecule, and acetylene addition which propagates molecular growth and cyclisation (see Chapter 3.1.2). The
formation and evolution of soot particles is mathematically described using the
method of moments [1]. As Miller said in his review paper [38], these authors converted the qualitative ideas into a quantitative chemical kinetic model. Fernklach
et al. [13, 42] first considered the soot formation modeling in shock tube pyrolysis
of acetylene. The authors developed a detailed kinetic model of PAH formation and
growth including branching reactions of aliphatics, similar to those showed in scheme
1.2, leading to cyclisation (ring closing reactions), where aromatic compounds are
formed. Furthermore, Frenklach et al. and Wang et al. considerably modified the
existing kinetic scheme and extended the modeling to the pyrolysis and oxidation
of different fuels in flames [43, 21, 1, 44, 45, 46].
In the last decade, the idea supporting the PAH as the principle soot precursors
gains more evidences due to the recent development of the experimental techniques
[4, 47, 48, 49] and the numerical models [50, 51, 52, 24, 53, 54, 55]. This provides the
possibility for an extensive research, providing more details of the different stages
of soot formation.
Kronholm [56] studied the molecular weight growth pathways of fuel-rich combustion and suggested that the distinction between the largest PAH molecules and the
smallest (young) soot particles is arbitrary. In his study, Kronholm assumed the
concept that PAH and soot can be treated analogously in a general formulation of
molecular weight growth. He develop a model of PAH growth and soot nucleation
that treated large PAH similarly to soot aerosols. These aerosols are further lumped
1. INTRODUCTION
5
into average property particles, called BINs, with a molecular weight between 100
amu and 1600 amu. To distinguish large PAH and soot particles, a specific molar
mass of 1600 amu is assumed as upper limit.
This approach was further developed and applied for soot formation simulation
of various combustion systems [57, 24, 53]. Richter et al. [24] proposed a detailed kinetic model of PAH and soot particle formation in a laminar premixed benzene/oxygen/argon low/pressure flame. The authors used the sectional technique to
model the particulate-phase chemistry. They defined large PAH and carbonaceous
particles with diameter up to 70 nm as classes called BINs, covering given mass
ranges. The number of carbon and hydrogen atoms corresponding to their average
mass are assigned to each class. The change of the C/H ratio is calculated with
respect to the particle size. Soot particle inception takes place in reactions of PAH
radicals with PAH molecules and among PAH radicals. The authors stated that at
about 75 % of the final particle mass is due to the process of surface growth, where
the reaction of acetylene with particle radicals is the major growth route. The model
provides information about the size, mass and content (C/H ratios) of the particles,
but cannot predict soot particle structure.
Violi [52] proposed an atomistic model for particle inception, which is a combination
of kinetic Monte-Carlo and molecular dynamic methods. The model is applied to investigate the growth of aromatic compounds up to the nano-size range in chemically
specific way. This approach preserves the atomic scale structures like bonds, bond
angles and dihedral angles as the soot precursors evolve into three-dimensional structures. This technique was applied to aliphatic (C2 H2 ) and aromatic (C6 H6 ) flame
environments. The calculations give information about the similarities and differences of soot precursor structure, morphology and the H/C ratios in aromatic and
aliphatic flames.
Morgan et al. [55] developed a detailed particle model, which simulates the size
distribution of soot particles in laminar flames with the use of stochastic numerical methods. The model is applied to simulate flames with bimodal and unimodal
particle size distribution and provides useful information about the change in morphology between the particles from these two types of flames. These results provide
evidence on the importance of interplay among the processes like nucleation, coagulation and surface growth, which is previously studied by [50, 51, 54]. The authors
stated that the transition of spherical growth in fractial-like objects can be related
to the nucleation, as it provides the appearance of very small, primary soot particles.
Several authors suggested models which combine two different pathways of soot for-
1. INTRODUCTION
6
mation, HACA and polyyne. The model suggested by Vlasov and Warnatz [58]
combines the HACA mechanism of PAH growth [21, 59] with the polyyne model of
soot formation [2], and the model of pure carbon clusters formation [60]. This approach is applied for soot formation simulation in pyrolysis of various hydrocarbons
and their mixtures in conditions typical for shock tube experiments. An extended
version was used for soot formation modeling during shock tube oxidation of different hydrocarbons [61, 62, 63, 64]. This model is in detail described in Chapter
6. Similarly, Wen et al. [65] developed a detailed kinetic model which is again a
combination of both PAH and polyyne pathways of soot formation and simulated
the nano-particle inception and growth in pyrolysis of C6 H6 behind shock waves,
using the sectional technique.
Numerous theoretical models simulate particle formation and evolution in different
types of flames but soot formation modeling in terms of short time scales, e.g.,
the shock tube experiments, takes place in a few milliseconds. This restriction
made it difficult to model soot formation with the use of the traditional HACA
model. It required the investigation and the development of various chemical rection
routes of soot precursor formation and growth together with an adequate kinetic
representation of these processes.
1.2
Objectives and structure of the thesis
Unburned hydrocarbons and soot are typical pollutants formed during combustion,
although these species do not exist in the initial fuel. It is known that the main reason for the appearance of such products is the inappropriate combustion conditions:
time, temperature, and turbulence [66, 67]. Variation of the mixture compositions
and the reaction conditions improve the results for some of the components but
increases the amount of the others. To solve the problem it is necessary to answer
the question, how these compounds are generated and why they were not consumed
during the combustion process.
The goal of the current work is the investigation of the processes and mechanisms
leading to the formation of gas-phase precursors and soot particles. Accordingly,
a detailed kinetic model had to be developed for soot formation simulation during
pyrolysis and oxidation of hydrocarbons and their mixtures at spatially homogeneous
conditions. The model had to be validated against experimentally obtained data,
available in the literature. Furthermore, a simplified model of soot formation had
to be developed and calibrated by the detailed scheme.
1. INTRODUCTION
7
A short historical overview of various hypotheses proposing different types of gasphase species as the potential soot precursors is presented in Chapter 1, together
with a brief description of several basic kinetic mechanisms of soot formation.
The development of a kinetic mechanism is based on the concept of elementary reaction. Therefore, knowledge of the physical and chemical fundamentals are needed
for the adequate description of the reaction systems, in accordance to its thermodynamics, chemical kinetics, and the special features of the combustion facility (see
Chapter 2). In the current work, the soot formation was studied at homogeneous
conditions, in particular shock tube experiments.
The hypothesis regarding the PAH as the most probable soot precursors gains more
evidences in the last decade. Various reaction pathways and mechanisms leading
to PAH formation and growth are presented in Chapter 3, together with a short
description of the physical and chemical processes describing the soot formation:
soot-particle inception, growth and oxidation, coagulation, and agglomeration.
The mathematical representation of the soot formation was performed by a suitable
numerical technique, discrete Galerkin method (see Chapter 4). The method is
previously implemented in a program package, MACRON [68], for the treatment
of large systems of ordinary differential equations, arising from the macromolecular
reaction kinetics. It is initially proposed for simulation of polymerisation reactions,
but is also successfully applied for soot formation modeling in shock tube [69] and
flame experiments [70]. An important feature of this approach is the so called
lumping technique, which describes soot formation analogously to the process of freeradical polymerisation [60, 71, 72]. This technique is based on an approximation of
the distribution function for the degree of polymerisation and a repeating reaction
cycle for the particle growth.
Soot formation modeling usually needs a detailed kinetic scheme, describing the
formation, growth and oxidation of the gas-phase soot precursors, and a soot-particle
model. In Chapter 5, two detailed kinetic mechanisms are presented, which contain
different approaches of the gas-phase precursors formation and the formation and
evolution of the particulate-phase. Both mechanisms are described together with
the literature sources for the relevant kinetic and thermodynamic properties of the
gas-phase species and the reaction kinetics of the macromolecular reactions. The
mechanisms were validated against experimental data available in the literature for
the concentration profiles of various gas-phase species, the induction delay time, soot
growth rate, particle concentration, diameter, and soot yield, measured in shocktube experiments.
1. INTRODUCTION
8
The detailed reaction mechanisms usually consist of thousands of elementary reactions between hundreds of species. Such reaction scheme cannot be directly used
for CFD simulations of three-dimensional systems, because it exceeds available computer capacities. Therefore, reduced reaction mechanisms are needed, which describe
the chemical reaction system using small number of variables. For the application in
a multi-dimensional CFD code for gas-turbine combustion simulation, an empirical
model was developed which describes the complex process of soot particle formation
and evolution in terms of two differential equations (see Chapter 6).
9
Chapter 2
FUNDAMENTALS OF
PHYSICAL CHEMISTRY
2.1
Homogeneous reaction system
According to the macroscopic properties of a system (temperature, pressure, concentrations, viscosity, electro-conductivity etc) it can be characterised as spatially
homogeneous or heterogeneous. If the properties of the system are the same or
change gradually in every point (part), it is defined as homogeneous. Shock wave
reactors are an example of homogeneous reaction system. The shock tubes are used
by many kineticist as a high temperature reactor to obtain rate coefficient data under homogeneous conditions. The shock tube experiment has the advantages that
it provides a nearly one-dimensional flow with practically instantaneous heating of
reactions, high dilution of the reactants by an inert gas and high sensitivity of the
diagnostic techniques employed to monitor species. The main advantage of diluting
the reactants with an inert gas is that the exothermicity or endothermicity of the
reactants involved will not greatly alter the constant temperature conditions during
the investigation. On the other hand, by using very low initial reactant concentrations, the influence of subsequent reactions can be avoided or reduced. This allows
the study of only one or two elementary reactions with high accuracy, without being
strongly disturbed by fast secondary reactions [73, 74].
Soot formation has been studied widely in laminar flames [75, 19, 25, 40, 12, 22, 76,
3, 77, 4, 48, 49], but numerous experiments have been performed behind reflected
shock waves [28, 32, 35, 36, 14, 78, 73, 79, 80, 81, 82, 83, 5]. The shock tube as
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
10
a wave reactor provides an excellent environment for the study of particle nucleation and growth from the vapour phase at high temperatures. It is a convenient
technique to investigate the effect of controlling and varying the initial conditions
like temperature, pressure, and mixture composition on the size and yield of the
produced particles. The observation time is relatively short, usually limited to a
few milliseconds.
A detailed kinetic model of soot formation usually consists of two general parts, a
gas-phase kinetic scheme describing the fuel destruction and soot precursor formation, and a soot model describing the particulate-phase chemistry. Such detailed
kinetic mechanism of hydrocarbon combustion consists of several hundreds or even
thousands of chemical elementary reactions. For each reaction and species included
in the mechanism a set of kinetic and thermodynamic data is needed. Nowadays,
experimentally observed or calculated thermodynamic data of a large number of
species as well as reaction rate coefficients are available in the literature.
2.1.1
Thermodynamics
Thermodynamics studies the different forms of energy transformation, which makes
it possible to analyse quantitatively these phenomenon and gives useful predictions
of the system behaviour. For the needs of numerical simulations the thermodynamic
properties are often stored as polynomials in T . If it is possible these values are based
on experimental data, but most of the data is derived from theoretical calculations
based on number of semi-empirical schemes relating thermodynamic properties to
molecular structure [84].
Heat capacities expressed as NASA polynomials (Stull and Prophet [85], Kee et
al. [84], Burkat [86], Warnatz et al [67] etc.) are used to calculate the enthalpy
4H 0 , the enthropy 4S 0 and the equilibrium constant KC . Usually the molar heat
0
0
0
capacities C p (C p = C V + R) are expressed as polynomials of fourth order in T ,
0
Cp
= a1 + a2 · T + a3 · T 2 + a4 · T 3 + a5 · T 4 .
R
(2.1)
Here a1 , ..., a5 are constants, and R is the gas constant. In addition, two integration
0
constants are needed to compute enthalpies and entropies, where a∗6 · R = H 298 and
0
a∗7 · R = S 298 ,
0
HT
Z
=
a∗6
T
·R+
T 0 =298K
0
C p dT 0
and
0
ST
Z
=
a∗7
T
·R+
T 0 =298K
0
Cp 0
dT .
T0
(2.2)
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
11
The enthalpy at any temperature T follows from integration of the heat capacity,
Eq. (2.1), with an a6 different from a∗6 ,
0
H T (T )
a2
a3
a4
a5
= a6 + a1 · T +
· T2 +
· T3 +
· T4 +
· T 5.
R
2
3
4
5
(2.3)
0
The coefficient a6 can be defined setting T = 298 K and demanding that H (298 K)
is equal to the enthalpy of formation at 298 K.
The entropy at any temperature T follows from integration of the heat capacity
divided by temperature T , with an a7 different from a∗7 ,
0
S T (T )
a3
a4
a5
= a7 + a1 · ln T + a2 · T +
· T2 +
· T3 +
· T 4.
R
2
3
4
(2.4)
The coefficient a7 can be defined by setting T = 298 K and determining that
0
0
S T (298 K) is equal to the entropy at 298 K. Thus seven coefficients define C p ,
0
0
H T , and S T at any temperature T .
2.1.2
Chemical kinetics
Chemical kinetics deals with rates of chemical reactions. It explains how rapidly
reactants are consumed and products formed, how the rate responds to changes
in the conditions or the presence of catalyst, and the step by which a reaction
takes place. The reason for studying the reaction rates is of practical importance
in order to predict how quickly a reaction mixture reaches equilibrium. The study
of reaction rates helps to understand the mechanism of a single reaction as well as
complex reactions. The rate depends on variables under our control such as pressure,
temperature, and presence of catalyst. Therefore, we might be able to control it by
the appropriate choice of conditions.
Rate law and elementary reactions
Detailed reaction mechanisms are based on the concepts of the elementary reaction,
which has the advantages that the reaction order is always constant (in particular,
independent of time and of experimental conditions) and can be easily determined.
It is only necessary to look at the reaction molecularity that denotes the number
of species, which form the reaction complex (the transition state between reactants
and products). In general the molecularity equals the order of elementary reactions.
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
12
A rate law describes an empirical formulation of the reaction rate in particular, the
rate of formation or consumption of a species in a chemical reaction. The reaction
rate of an elementary reaction could be experimentally obtained, but only for a given
temperature range. The rate coefficients beyond that temperature can be calculated
using the Arrhenius equation (Eq. 2.16).
If the equation of an elementary reaction r is given by
S
X
kr
(e)
νrs
As −
→
s=1
S
X
(p)
νrs
As ,
(2.5)
s=1
then the rate law for the formation of species i in reaction r is given by the expression,
µ ¶
S
´Y
³
(e)
∂ci
(p)
(e)
= kr νri − νri
cνsrs .
(2.6)
∂t chem,r
s=1
(e)
(p)
Here νrs and νrs denote stoichiometric coefficients of reactants (educts) and products, and cs , the concentration of the S different species s.
The rate law can always be specified for an elementary reaction mechanism. If the
reaction mechanism is composed of all possible elementary reactions in the system,
then it is a complete mechanism and is valid for all conditions (temperatures and
mixture compositions), but such mechanisms are rarely available.
Relation of forward and reverse reactions
Chemical reactions move towards a dynamic equilibrium in which both educts and
products are present in significant concentrations, but no net change occurs. In such
cases, thermodynamics can be used to predict the equilibrium composition under
any reaction conditions.
For example, the chemical reaction (2.7) runs in both directions,
A + B ­ C + D,
(2.7)
where A and B denote the educts of the reaction, C and D the reaction products,
and kf and kr are the rate coefficients of the forward and reverse respectively. The
reaction rate with respect to the production of the species A is expressed by the
equation
d[A]
= −kr [C]c [D]d .
dt
(2.8)
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
13
At the chemical equilibrium, the forward and reverse reaction have the same rates,
which can be expressed by the equation
kf [A]a [B]b = kr [C]c [D]d ,
(2.9)
or,
[C]c [D]d ,
kf
= .
a
b
[A] [B]
kr
(2.10)
The
expression
on the left hand side corresponds to the equilibrium constant
³
´
kf
Kc = kr of the reaction. For a gas-phase reaction, the equilibrium rate constant
can be expressed by the species partial pressure [87] as
Kp =
pcC · pdD
.
paA · pbB
(2.11)
The equilibrium composition correspond to a minimum in the Gibs energy plotted
against the extent of reaction [67]. If the location of this minimum is established,
the relation between the equilibrium constant and the standard Gibs energy of the
reaction can be derived. In this way, the equilibrium constant Kp can be also
calculated through the thermodynamic data by
³
´
0
Kp = exp − 4R G /RT ,
(2.12)
0
where the standard Gibs free energy 4R G is calculated by the reaction enthalpy
0
0
4H and entropy 4S ,
0
0
0
4G = 4H − T · 4S .
(2.13)
The equilibrium constants Kc and Kp are related by
Kc =
kp
(RT )4v
,
(2.14)
where 4v is the difference between the stoichiometric coefficients of the reaction
(4v = (c + d) − (a + b)) , and R is the ideal gas constant.
Temperature dependence of rate coefficients
It is a characteristic of the chemical reactions that their rate coefficients depend
strongly and in a nonlinear way on the temperature [67]. It is found experimentally
for many reactions that a plot of lnk against 1/T gives a straight line with a slope
that is characteristic of the reaction [87]. The slope is equal to the relation −Ea /RT
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
14
and the interception at 1/T = 0 is equal to natural logarithm of the collision coefficient, lnA. Here, A is defined as the pre-exponential factor or the frequency
factor, the parameter E a is the activation energy. These two parameters are called
Arrhenius parameters and are independent on the temperature. According to this
investigations the rate coefficient is usually expressed by a simple formula called
Arrhenius law,
lnk = lnA −
Ea
,
RT
(2.15)
where after applying antilogarithm the following expression is derived:
µ
¶
Ea
k = A · exp −
.
RT
(2.16)
More recently, accurate measurements showed a temperature dependence of the
pre-exponential factor A, which is usually small in comparison to the exponential
dependence,
µ
¶
Ea
b
k = A T · exp −
.
(2.17)
RT
The activation energy Ea corresponds to the energy barrier to be overcome during
the reaction. Its maximum value corresponds to the bond energies in the molecule
(e.g. for dissociation reaction, the Ea is approximately equal to the bond energy of
the bond, which is split), but it can be much smaller or even zero, if new bonds are
formed simultaneously while the old bonds are breaking. If b in Eq. (2.15) is known,
the Ea can be determined from the slope of the plot of ln(k/T b ) versus 1/T .
Pressure dependence of rate coefficients
The rate coefficients of dissociation (unimolecular) and recombination (trimolecular) reactions are found to be pressure-dependent. This is an indication that these
reactions are not elementary; in fact they are a sequence of reactions. In the simplest case, the pressure dependence can be introduced using the Lindemann model
[88, 67]. According to this model, a unimolecular decomposition is only possible,
if the energy in the model is sufficient to brake the bond. Therefore, it is necessary that before the decomposition energy is added to the molecule by collision
with other molecules (for excitation of the molecule), noticed usually as M. After
that, the excited molecule may decompose into products, or it can deactivated by a
collision,
k
a
A + M −→
A∗ + M
(activation)
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
k−a
A∗ + M −−→ A + M
k
u
A∗ −→
P (roducts)
(deactivation)
15
(2.18)
(unimolecular reaction)
The rate equations for this case are given by
d [P]
= ku [A∗ ]
dt
d [A∗ ]
= ka [A] [M] − k−a [A∗ ] [M] − ku [A∗ ] .
dt
and
(2.19)
Assuming quasistationary concentrations for the highly unstable species, A* is in a
quasi-steady state (d [A∗ ] /dt ≈ 0). Then, the concentration of the activated species
[A*] and the rate of the product P are given by
[A∗ ] =
ka [A] [M]
k−a [M] + ku
and
d [P]
ku ka [A] [M]
.
=
dt
k−a [M] + ku
(2.20)
Two extremes can be distinguished, reaction at very low and very high pressures.
In the low-pressure range, the concentration of the collision partners M is very small
and k −a [M] << k u . The rate law of the reaction appears to be of second order,
d [P]
= ka · [A] [M] = k0 · [A] [M]
dt
(2.21)
with a low pressure rate coefficient usually named k0 . Then, the reaction rate is
proportional to the concentrations of species A and the collision partners M, because
the activation of the A species is slow, it is the rate-limiting process at low pressures.
In the high-pressure range, the collision partner M has a higher concentration and,
therefore k−a [M] >> ku the apparent first order rate law can be obtained,
d [P]
= ka · [A] [M] = k0 · [A] [M]
dt
(2.22)
with a high pressure rate coefficient k∞ . Here, the reaction rate does not depend on
the concentrations of the collision partners, because at high pressures collisions occur
more often then at low pressures, while at high pressures collisions occur very often
and, thus the decomposition of the activated molecule A* is rate-limiting instead of
the activation.
The Lindemann mechanism illustrates the fact that the reaction order of the complex (non-elementary) reactions depends on the chosen conditions. Nevertheless,
between these two extremes exists a wide transition area, which depends also on the
nature of the species. For smaller molecules this area is observed at higher pressures
and is wider than for the bigger species with higher molecular weight. This area
cannot be described by the simple Lindemann theory. More accurately, the pressure dependence of the unimolecular reactions can be obtained using the Theory
of Unimolecular Reactions (Robinson and Holbrook [89], Atkins [87], Golden [90],
Warnatz [67]). This theory takes into account that not only one activated species
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
16
can be defined, but a large number of activated molecules with different levels of
activation (e.g. vibration or rotation).
If the rate law of a unimolecular reaction is written as d[P]/dt = k[A], then the
rate coefficient k depends on the pressure, and the temperature. The theory of
unimolecular reactions yields fall-off curves, which describe the pressure dependence
of k for different temperatures. Usually the logarithm of the rate coefficient is
plotted versus the logarithm of the pressure. The appropriate treatment of pressuredependent reactions is important because many experiments on reaction kinetics are
at atmospheric or lower pressure while many combustion processes run at elevated
pressure. An often used formalism is the F-Center treatment of Troe (Gilbert et al.
[91], Warnatz [67]), where ten parameters are used to determine a rate coefficient
as specified temperature and pressure. One set of coefficients give the high-pressure
modified Arrhenius parameters, another set the low-pressure modified Arrhenius
parameters, and a third set containing four parameters a , T ∗∗∗ , T ∗ , and T ∗∗ which
are used to determine the F-center value (describing the center of the fall-off range),
µ ¶
µ
¶
µ
¶
T
T
T
Fcent = a · exp
+ exp
+ (1 − a) · exp
.
(2.23)
T∗
T ∗∗
T ∗∗∗
The value F is calculated via
(
·
logF = logFcent
logPr + c
1+
n − d · (logPr + c)
¸2 )−1
with
c = −0.4 − 0.67logFcent ,
n = 0.75 − 1.27 logFcent ,
d = 0.14,
Pr =
k0 · [M]
.
k∞
This can then be used to compute the desired result
µ
¶
Pr
· F.
k = k∞ ·
1 + Pr
2.1.3
Analysis of reaction mechanisms
Detailed reaction mechanisms for different hydrocarbons may consist of several thousand elementary reactions. Depending on the system of interest, many of these reactions can be neglected. Thus, analysis methods, which eliminate negligible reactions,
are of particular interest:
• Sensitivity analysis - identifies the rate-limiting steps
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
17
• Reaction flow analysis - determines the characteristic reaction paths.
The information obtained by these methods can be used to reduce the reaction
mechanism by eliminating the unimportant reactions.
Sensitivity analysis
The rate laws for a reaction mechanism consisting of R reactions between S species
can be written as a system of first order ordinary differential equations [67],
dci
= Fi (c1 , ..., cS ; k1 , ..., kR )
dt
i = 1, 2, ..., S
(2.24)
ci (t = t0 ) = c0i .
The time t is the independent variable, the concentrations ci of species i are the
dependent variables, and kr are the parameters of the system; c0i denote the initial
conditions at t0 .
The solution of the differential equation system (2.24) depends on the initial conditions as well as on the parameters of the system. If one of the initial parameters is
changed, i.e., one of the rate coefficients of the elementary reactions, then the solution, i.e., the values of the concentrations at time t, will be influenced. For many of
the elementary reactions, a change in its rate coefficients has nearly no effect on the
time-dependent solution (this shows that quasi-steady state or partial equilibrium
are active). If this reaction has to be included in the mechanism, there is no need
of a highly accurate rate coefficient. On the other hand, for a few of the elementary reactions, changes in its rate coefficients have large effects on the outcome of
the system. Accordingly, accurately obtained rate coefficients are necessary. These
several important reaction steps are called rate-determining or rate-limiting steps.
The dependence of the solution ci on the parameters kr is called sensitivity. The
absolute sensitivity is defined as,
Ei,r =
∂ci
,
∂kr
(2.25)
and the relative sensitivity as,
rel
=
Ei,r
kr ∂ci
∂lnci
=
.
ci ∂kr
∂lnkr
(2.26)
2. FUNDAMENTALS OF PHYSICAL CHEMISTRY
18
Reaction flow analysis
The reaction flow analysis (RFA) shows the percentage of the contribution of reaction r (r = 1, ..., R) to the formation (or consumption) of the chemical species s
(s = 1, ..., S). Thus, a reaction flow diagram can be built, showing the main reaction
paths for the formation (or consumption) of the species of interest. There are two
different types of analysis, the integral and the local reaction flow analysis. The
integral reaction flow analysis considers the overall formation or consumption during the combustion process. The results for homogeneous time-dependent systems
are, e.g., integrated over the whole reaction time. The local reaction flow analysis considers the formation and consumption of species locally. For a homogeneous
time-dependent system the result is calculated with respect to the specific times
[67].
19
Chapter 3
SOOT FORMATION
Due to the incomplete combustion various undesired products like N OX , hydrocarbons including PAH, and soot are formed. The reason for that are the unfavourable
combustion conditions of time, temperature, and turbulence. Because, the present
work is concentrated on the modeling of soot precursors and soot particle formation,
the important stages of these processes will be discussed in the following chapter.
To give an answer to the question, how the gas-phase precursors and soot particles are formed in combustion, every stage starting from the very beginning of the
combustion processes has to be studied until the entire mechanism is completed.
A characteristic time scale of the soot particle formation is tens of milliseconds in
flames and several milliseconds behind shock waves. Examined under an electron
microscope, soot appears as necklace-like agglomerates composed of a selection of
small, basic particles with nearly spherical structure [92, 93]. Individual Diesel soot
particulates vary in shape from clusters of spherules to chains of spherules, where a
soot cluster may contain as many as 4000 spherules. The size of spherules varies in
diameter from 10 to 80 nm, but mostly lies between 15 and 30 nm. The spherules
are called primary soot particles and the cluster- or chain-like soot aggregates are
defined as secondary particles, composed of tends to hundreds of primary spherical
particles [25]. The transmission electron microscopy studies show that the primary
soot particles have a layered structure and consist of numerous concentric crystallites [94]. The X-ray diffraction analysis indicates that the carbon atoms of a
primary soot particle are packed into hexagonal face-centered arrays commonly described as platelets. These platelets are arranged in layers to form crystallites, and
there are typically 2-5 platelets per crystallite. The mean layer spacing is 3.55 nm,
only slightly larger than that of graphite [95]. The thickness of crystallites is about
3. SOOT FORMATION
20
1.2 nm [95], and there are the order of 103 crystallites per primary soot particle.
The crystallites are arranged in a layered structure, parallel to the particle surface.
Dislocation of five- and seven-member rings produce surface wrinkling. The layered structure of soot particles is also characteristic of pyrolytic graphite, which is
though to be responsible for its unusually high resistance to oxidation. Analysed
under high-resolution transmission electron microscopy, two distinct parts of a primary Diesel soot particle can be identified, an outer shell and a inner core [96]. The
platelet model mentioned above applies to the outer shell. However, the inner core
contains fine particles with a spherical nucleus surrounded by carbon networks with
a bending structure. This indicates that the outer shell, composed of graphitic crystallites, is of a rigid structure, while the inner core is chemically less stable due to
the thermodynamic instability of its structure. Heat treatment can alter the internal
microstructure of the particles [25]. Particles produced in situ are quite different
from those formed in exhaust gases [97]. Soot contains at least 10 % by mole or
atomic fraction of hydrogen. The considerable hydrogen content corresponds to an
empirical composition formula of C8 H for soot [92]. The H/C ratio is around 1 for
the young soot particles.
Soot formation is a complex process, which involves many chemical and physical
steps. A detailed kinetic model of soot formation usually contains two general
parts, gas-phase chemistry, initiating the soot precursors, and particulate-phase
model, which is the less explored area in soot formation theory. Several different types of species have been defined as the key gaseous precursors to soot, polyacetylens or polyynes, ionic species and polycyclic aromatic hydrocarbons (see Chapter 1.1). Recent studies stated that the PAH are the most probable soot precursors
[44, 22, 98, 99, 20, 3, 52, 100, 24, 4, 5]. Several authors suggested that particle
inception occurs through formation of aromatic-aliphatic-linked hydrocarbons [101]
or PAH with five membered rings [5], which later graphitise forming more compact
structures. The homogeneous inception of large molecular precursors is a still incompletely studied area. The soot particle size increases in reactions of surface growth
by the active sizes on the particle surface. Coagulation forms larger particles, where
during agglomeration the primary particles stick to each other, forming chain-like
aggregates.
3. SOOT FORMATION
3.1
21
Gas phase
Following the PAH hypothesis, a mechanism of soot formation should consist of
several stages. Starting, e. g., with an aliphatic fuel, the fuel molecules are first
broken down into smaller hydrocarbon molecules and free radicals either by pyrolysis
or oxidation reactions. Then the key step occurs, the formation of the first aromatic
ring in the system, usually benzene or phenyl. This first ring appears as the nucleus
for the formation and growth of PAH, following different mechanisms [95, 13, 43, 99].
If the reaction mechanism is composed of all possible elementary reactions in the
system, this mechanism should be valid for all conditions like temperatures, pressures
and mixture compositions. The construction of such mechanism is a very difficult
task and complete mechanisms are rarely available related to specific problems [67].
3.1.1
First aromatic ring formation
Flame experiments [3, 4, 20, 22, 98, 101] show that the formation and growth of
aromatics bridges the main combustion zone gas-phase molecular chemistry and
soot particle formation. The high temperature chemistry of aromatics received great
attention in the last decades. The primary focus is on the formation of the first
aromatic ring from small aliphatics, because this step is suggested to be the ratelimiting step to higher PAH [13, 43, 102, 1, 103, 104, 46]. Some of the most famous
are the even-carbon-atom pathways as Frenklach showed in his review paper [105],
which involve the addition of acetylene to n-C4 H3 and n-C4 H5 radicals. Frenklach
referred to the reaction
n-C4 H5 + C2 H2 → C6 H6 + H
(3.1)
suggested by Bittner and Howard [106], Weissman and Benson [107], and Cole et
al. [108], as an important cyclisation step, where C6 H6 is benzene. The authors
supposed that such reaction should have one or more intermediate steps, whereas,
at least under flame conditions, the reaction predominantly occurs as written. At
about the same time, but independently of the investigators cited above, Callear and
Smith [19, 109] experimentally showed the viability of Reaction (3.1) as a cyclisation
step. They studied the reaction of H with acetylene at low temperatures and found
large quantities of benzene in the products. The authors suggested that the Reaction
(3.1) is part of a mechanism, which includes Reactions (3.2 and 3.3),
H + C2 H2 → C2 H3
(3.2)
C2 H3 + C2 H2 → n-C4 H5 .
(3.3)
3. SOOT FORMATION
22
The same interpretation was given by Miller et al. [38, 110], and stands till the
present day.
Frenklach et al. [13, 42, 43, 111, 112, 113, 114, 115] stated that cyclisation occurs
primarily through the reaction
n-C4 H3 + C2 H2 → C6 H5
(3.4)
where C6 H5 is phenyl. Reaction (3.4) was suggested as a key step in the formation of the first aromatic ring in a detailed kinetic scheme used for simulation of
pyrolysis of acetylene behind shock waves [13, 42, 43, 111]. The authors confirmed
also the importance of Reaction (3.1) at lower temperatures. Miller and Melius
[116, 102, 117, 113, 38], stated that the Reactions (3.1) and (3.4) occur less probably, because these species should be rapidly transformed to their corresponding
resonantly stabilised isomers, iso-C4 H3 and iso-C4 H5 . Instead, they emphasised on
the importance of resonantly stabilised free radicals (RSFRs), such as propargyl
(C3 H3 ), in forming aromatics and PAH in flames. They proposed an odd-carbonatom pathway via the recombination reaction of two propargyl radicals,
C3 H3 + C3 H3 → C6 H6 (or C6 H5 + H).
(3.5)
The propargyl radical is an exceptionally stable radical and for a long time was
assumed to be the species with the main role in aromatics formation [118, 67].
Miller et al. [119] showed through quantum chemical calculations that the chemical
activation of the educt might be sufficient to overcome the enormous potential energy
barriers to its cyclisation. They explained the stability of the RSFRs as reduced
reactivity, especially with respect to O2 . The RSFRs generally form weaker bonds
than do ordinary free radicals, particularly with stable molecules (O2 ) [120, 38]. The
second factor that makes RSFRs less reactive with O2 is that there is a potential
energy barrier in the entrance channel for the addition of O2 to a RSFR, whereas
the corresponding potentials for the O2 adding to ordinary free radicals are much
lower.
Miller [38] pointed out on the work of Moriarty et al. [121] and Moskaleva et al.
[122] which proposed the reaction
C3 H3 + C2 H2 → c-C5 H5
(3.6)
as an important cyclisation step. Once formed, the cyclopentadienyl radical
(c-C5 H5 ) reacts rapidly to form benzene [123, 104, 124]. Melius et al. [104] suggested
a mechanism of benzene formation through fulvene (C5 H4 CH2 ),
c-C5 H5 + CH3 → ...C5 H4 CH2
(3.7)
3. SOOT FORMATION
C5 H4 CH2 + H → C6 H6 + H.
23
(3.8)
However, Miller [38] stated that Reaction (3.6) is typical of the class of reactions in
which a collisionally stabilised radical is formed as a product from radical + molecule
reactants. It is observed that such reactions shift their equilibria in the 1400 K-1700
K temperature range to favour the reactants, particularly if the radical reactant is
resonantly stabilised.
Flame calculations [57] showed that Reaction (3.6) is actually a source of propargyl,
rather than a source of cyclopentadienyl. The c-C5 H5 is mainly formed from the
oxidative mechanism, discussed in Section 3.1.3 of the same Chapter (Reactions 3.26
and 3.27), and Reaction (3.6) goes in the reverse direction for temperatures above
1500 K. Miller [38] concluded that, at lower temperatures, the potential energy
barrier existing in the inlet channel of such radical-molecule reactions makes them
too slow to be effective. Such equilibrium shifts could have important consequences
for certain steps involved in the growth of PAH, mostly the process of C2 H2 addition
in the periodic sequence of HACA.
Other efficient odd-carbon-atom cyclisation reactions have been suggested in [104,
123, 125, 124, 105]:
c-C5 H5 + CH3 → C6 H6 + H + H
c-C5 H5 + c-C5 H5 → naphthalene + H + H.
(3.9)
(3.10)
Pope and Miller [126] described the reactions
i-C5 H3 + CH3 → C6 H6
(3.11)
→ C5 H4 CH2
(3.12)
→ C6 H5 + H
(3.13)
which could be at least partially responsible for benzene formation.
Marinov et al. [127, 128, 129], investigated different flames and suggested that
reactions involving 2 RSFRs as reactants are primarily responsible for the formation
of the first aromatics containing one or two rings. Particularly prominent is the
Reaction (3.5) and reactions involving radical-substituted propargyls (RCCCH2 ).
The R can be both a small aliphatic or aromatic radical [111, 130].
The reaction between allyl and propargyl discussed in [128, 126],
C3 H3 + C3 H5 → C5 H4 CH2 + H + H,
(3.14)
3. SOOT FORMATION
24
leads to C5 H4 CH2 formation, which is found to play an important role for the PAH
formation in many flames. Reaction (3.14) is actually a short version of a two-step
process, the second of which is a dissociation producing fulvene and a hydrogen
atom. The fulvene produced by Reaction (3.14) can be converted to benzene by
H-atom-assisted isomerisation [104] as described in the Reactions (3.7 and 3.8).
Kazakov et al. [131] showed that the formation of the first aromatic ring via reactions of C6 HX species as well as the ring-ring reactions play a significant role with
increasing the pressure. Such reactions were considered in many kinetic mechanisms
[42, 43, 46, 23, 24].
The formation of single-aromatic-ring compounds is a very common area of investigations, but it may not be the rate-limiting step [132, 105]. Frenklach [105] suggested
that the growth of higher PAH can be initiated by the direct formation of multiring PAH, bypassing the formation of the benzene ring, like, e.g., Reaction (3.10).
Such alternative proposal includes also formation of aromatics from condensation of
polyacetylenes C2n H2 [25], combination of C4 HX species [19], as well as combination
of larger radicals [13, 42].
At present, the most important reactions in forming the first and second
rings in flames of aliphatic fuels appear to be C3 H3 + C3 H3 , C3 H3 + C3 H5 , and
c-C5 H5 + c-C5 H5 [133, 128, 134]. However, except for propargyl recombination, not
enough theoretical or experimental work has been done on these reactions. The
kinetics of reactions involving RSFRs, cyclic species, and unsaturated, conjugated
molecules in general is under investigation [135, 136, 137, 138, 139, 140].
3.1.2
Growth of aromatics by HACA
Stein [141] and Stein and Fahr [142] calculated equilibrium as a function of atomic
structure, temperature, and partial pressures of H2 and C2 H2 . They found that at
high temperature, the most stable species thermodynamically, as the carbon number
is increased, lie in a sequence of peri-fused polybenzenoid molecules with occasional
five-membered rings around the edges. From these results the authors suggested
that such molecules and their radicals are the primary intermediates in the soot
formation process.
The most popular mechanism of PAH growth is the HACA pathway developed by
Frenklach and Wang [21, 1]. The model proposes a repetitive reaction sequence of
two principal steps, 1. Abstraction of an H atom from the reacting hydrocarbon by
3. SOOT FORMATION
25
a gaseous H atom,
Ai + H → Ai- + H2
(3.15)
2. Addition of a gaseous C2 H2 molecule to the radical formed,
Ai- + C2 H2 → products.
(3.16)
The nomenclature of the aromatics is published in [42, 118], where Ai is an aromatic
molecule with i peri-condensed rings, and Ai- is its radical. The key feature of the
first step of HACA is its reversibility. The reverse steps can be the reverse direction
of the H abstraction itself,
Ai- + H2 → Ai + H
(3.17)
or the reaction of combination with a gaseous H,
Ai- + H → Ai .
(3.18)
Frenklach [105] stated that the contribution of Reaction (3.18) as compared to the
Reverse (3.17) increases with pressure and molecular size (e.g., the rate coefficient
of Reaction (3.18) approaches its high-pressure limit). Moreover, the reversibility
of the acetylene addition step (Reaction 3.16) determines whether this step will
contribute to molecular growth. For a simple addition, due to the entropy loss,
the reaction is highly reversible, and often runs in the reverse direction. Forming a
hydrogen atom as a product [105],
Ai- + C2 H2 → products + H,
(3.19)
recovers some of the entropy but, in many cases, the reaction is still highly reversible,
e.g.,
Ai- + C2 H2 → Ai C2 H + H.
(3.20)
Only when, in addition to the recovery in entropy, the decrease in energy is high
enough, the reaction becomes more irreversible, and in the formation of particularly
stable aromatics, called islands of stability [13] or stabilomers [142], the reaction becomes practically irreversible. This coupling between the thermodynamic resistance
of the reaction reversibility and the kinetic driving force is the defining feature of
the HACA model explained in detail in [112].
3.1.3
Growth of aromatics by other species
Glassman [143] suggested that hydrocarbons with conjugated structures and their
derivatives are critical intermediates to soot nucleation. Frencklach [111] showed
3. SOOT FORMATION
26
that in the pyrolysis of benzene the growth of the aromatics is initiated by the
formation of biphenyl,
phenyl + benzene → biphenyl + H,
(3.21)
but the following growth proceeds via acetylene addition,
biphenyl − +C2 H2 → A3 + H.
(3.22)
The same mechanism appears to play an important role for the PAH growth at
different conditions and fuels [111, 118, 131, 105].
The reactions between resonantly stabilised free radicals, e.g., the recombination of
cyclopentadienyl radicals, became one of the most prominent for the formation of
two-ring aromatics, specifically naphthalene [130, 128, 104, 144, 145, 38],
c-C5 H5 + c-C5 H5 → C5 H5 C5 H4 + H
(3.23)
C5 H5 C5 H4 → naphthalene + H.
(3.24)
The reaction of benzyl with propargyl leads directly to the formation of two rings
in the system,
C6 H5 CH2 + C3 H3 → naphthalene + H + H.
(3.25)
Reactions (3.23-3.25), as well as others mentioned above, are not likely to occur as
elementary steps. This problem is discussed in more detail in [146]. Nevertheless,
the cyclopentadienyl needed for the formation of naphthalene through Reactions
(3.23 and 3.24) is found as a by-product of oxidation in most flames. It is generally
formed by
C6 H5 + O2 → C6 H5 O + O
(3.26)
C6 H5 O → c-C5 H5 + CO,
(3.27)
where C6 H5 O is phenoxy. This is an example that the oxygen may also promote
the formation of higher PAH [128, 105]. Marinov et al. [128] described a similar
sequence of steps for modeling the formation of phenanthrene through the reaction
of indenyl with cyclopentadienyl,
naphtoxy = indenyl + CO
(3.28)
indenyl + c-C5 H5 → A3 + H + H.
(3.29)
The advantage of such mechanisms of PAH growth is that they deflect the thermodynamic barriers that exist in forming two- and three-ring aromatics through the
HACA mechanism.
3. SOOT FORMATION
27
Frenklach et al. [147] suggested reaction pathways for aromatic ring growth through
the so called migration reactions. The authors studied theoretically different possible channels, such as enhanced formation of five-member aromatic rings, enhanced
formation of six-member aromatic rings, interconversion of five- and six-member
rings, and migration of the cyclopenta ring along zigzag aromatic edges [105]. All
of these pathways have one critical feature in common: The reaction pathway is induced or assisted by hydrogen atom migration. Moriarty et al.[148] investigated the
kinetics and thermodynamics of several migration reactions by quantum-chemical
calculations. They observed that the derived reaction rates are sufficiently fast for
these reactions to play a role in high-temperature aromatic chemistry. In [149], the
authors studied the five-member ring migration along a graphene edge. They concluded that an important implication of the migration phenomenon is that, while
five-member rings are constantly being formed on the growing edge, they do not
accumulate, but are rather converted to six-member rings.
3.1.4
Oxidation of aromatics
A process parallel to the aromatics growth is their oxidation. Haynes and Wagner
[25] and Neoh et al. [150] considered the hydroxyl radical as the primary oxidising
agent of soot particles.
Frenklach [105] declared that the primary mechanism is the oxidation of aromatic
radicals by O2 , and the oxidation by OH is rather unimportant, at least in laminar
premixed flames [105]. The author further stated that the largest effect in the oxidation of aromatics occurs at the very beginning of their growth, at the phenyl stage.
This is due to the rapidly decreasing concentration of O2 in fuel-rich environments
sustaining aromatics growth. Experimental observations showed that soot inception
appears in the time or space of the main combustion zone, in an environment rich
in H atoms and poor in O2 molecules.
However, the mechanism of PAH and soot oxidation is still not completely understood. Oxidation of aromatics removes carbon mass from further growth, but more
important is the removal of mass at earlier stages, those preceding the PAH formation. Numerical simulations [42, 43] identify oxidation of C2 H3 as the key point
of branching between carbon growth and carbon oxidation. The authors concluded
that the effect of oxidation at this small-molecule level is two-sided. It diverts the
carbon mass from further growth. On the other hand, added in relatively small
quantities in high-temperature pyrolytic environment, molecular oxygen promotes
3. SOOT FORMATION
28
formation of soot by building various radicals, and specifically H atoms.This phenomenon is observed in different experimental studies in shock tubes [13], computational analysis [42], and in diffusion flames [151].
3.2
Particulate phase
In spite of the great effort in understanding the mechanism of hydrocarbons and soot
formation, there are still numerous uncertainties which need to be studied experimentally and theoretically. The formation and evolution of soot particles includes
processes like soot particle inception, surface growth and oxidation, coagulation, and
agglomeration which are briefly described in the following sections.
3.2.1
Soot particle inception
The soot particle inception is a homogeneous process occurring in the gas-phase environment. According to different investigations, it takes place at molecular masses
between 500 a.m.u. [152], 300-700 a.m.u. [153], 1600 a.m.u. [154] and 2000 a.m.u.
[101], discussed in [67]. Above this values the PAH can be interpreted as solid
particles rather than molecules. These first soot particles are roughly spherical in
shape and have a C/H ratio of about 2. Upon aging, they can coalesce into larger
spherical particles, undergo surface reactions, dehydrogenation, oxidation and coagulation. The soot that is emitted from combustion devices typically has a C/H ratio
of approximately 10 and consists of some sort of agglomerates of spherical particles
that have an underlying graphitic-like structure [13].
Two general mechanisms have been proposed in the literature in which homogeneous
particle inception is considered to be a process of physical condensation or a process of chemical (reactive) condensation. The physical condensation suggests that
when the supersaturation of macro-molecular precursors generated by gas-phase reactions become sufficiently high, the partial pressure of the precursors forces the
macromolecules to condense physically into liquid-phase soot [155, 156]. The homogeneous condensation can be approximated by classical nucleation theory, which
gives the number of critical nuclei per unit volume [157, 156]. The chemical (reactive) condensation considers the process of continuous reactions of macro-molecular
precursors as the driving mechanism of homogeneous soot particle inception.
3. SOOT FORMATION
29
Frenklach and Wang [158] studied the reactive coagulation of stable PAH. They
treated the coagulation process, starting form pyrene, in the free molecular regime
and considered the coagulation reactions as irreversible. A size-independent enhancement factor of 2.2 was used in their calculation of collision frequencies. Once
the PAH monomers have reached a certain size they begin to stick to each other during collisions and thus form PAH dimers. These dimers collide with PAH molecules
forming trimers, or with other dimers forming tetramers, and so on. Consequently,
these PAH clusters evolve into solid particles as they increase in size.
Howard [159] and D’Anna et al. [160] emphasised on the role of PAH activation
by hydrogen abstraction. The active sites formed on the PAH provide a chemical
basis for reactive coagulation of polycyclic aromatic compounds with each other and
with small radicals. D’Anna et. al [160] proposed a model in which the chemical
specificity of the reactive coagulation process was studied. They considered the
radical-molecule reactions between the gas-phase PAH having conjugated double
bonds. In these reactions resonantly stabilised radical intermediates are formed
that continue the addition sequence, forming higher mass species.
The polyyne hypothesis assumes that every radical capable of forming polyyne complexes becomes a center of polymerisation. Following a polyyne molecule and radical
or two polyyne molecules react to form the polyyne complex [2].
Experimentally, the particle inception is characterised by the induction period. In
shock-tube experiments, the soot volume fraction, calculated from the extinction of
light, can be plotted versus measurement time. After the clearly visible passage of
incident and reflected shock, soot growth is delayed by a characteristic induction
time, which is specific for the different hydrocarbons. During that period hydrocarbons are transformed into soot particles.
3.2.2
Soot particle growth
The greater part of soot (> 95 %) is formed by surface growth rather than soot
inception [67]. It is assumed that particle growth is similar to the formation of
PAH, and acetylene and PAH are accepted to be the two main potential agents
responsible for soot surface growth. The problem is that surface growth is not a gasphase reaction of small molecules, but a heterogeneous process, where adsorption
and desorption processes at the surface have to be considered as well.
Because of the lack of precise data, phenomenological approaches are used to sim-
3. SOOT FORMATION
30
ulate this process. Mass growth of soot in premixed flames typically rises to an
asymptotic value even though C2 H2 is present and temperatures are high in the
region of no mass growth. Wagner described it through a first order differential
equation [161, 67],
dfV
= ksg (fV∞ − fV ),
dt
(3.30)
where ksg is a fitted surface growth rate coefficient and fV∞ is a fitted parameter
which represents the ultimate volume fraction of soot formed. The temperature
effect for both parameters (ksg and fV∞ ) have been empirically determined [67].
Harris and Weiner [162] studied several premixed acetylene-air flat flames and premixed ethylene/air flames. The authors observed that only C2 H2 satisfies the requirements for a soot growth reactant and proposed a simple model in which soot
mass growth rate is proportional to soot surface area and acetylene concentration
[163, 164, 67],
dfV
= kC2 H2 · pC2 H2 · S,
dt
(3.31)
where S is the soot surface area density (in, e.g., m2 /m3 ) and pC2 H2 is the partial
pressure of the gas-phase acetylene. PAHs were not measured because they were
believed to have insufficient concentrations and could not be counted as possible soot
growth reactants. One of the most important result showed by Harris and Weiner
is that the specific surface growth rate is only weakly dependent on stoichiometry,
compared with the total growth rate. The authors stated that the much higher
total growth rate of soot in richer flames was almost entirely due to the increased
surface area available, while the concentration of growth species was similar in all
of the flames, which is confirmed by Xu and Faeth’s experimental data obtained at
similar condition [165]. Harris and Weiner extended their conclusion and claimed
that there was no depletion of growth species by surface growth. They considered
acetylene as the dominant growth species because its concentration was high enough
to account for the mass increase provided by surface growth. They found that the
PAH concentration changed sharply with stoichiometry, and the PAH concentrations
were at about 100 times higher in benzene flames than in flames of aliphatic fuels
[12], but the soot growth rates in both flames were similar [166].
Behish et al. [167] did not agree with the above conclusions. They believed that
most (95% or more) of the soot growth occurs by PAH addition. The authors
repeated the particular flames investigated by [162] and found that previous soot
concentration profiles for the C/O = 0.79 flame was three times higher than their
experimental results, which was in excellent agreement with interpolated values
3. SOOT FORMATION
31
from optical measurement of Feitelberg [168] in similar rich ethylene flames. They
identified 26 PAHs, which accounted for 49% of the total PAH mass using high
performance liquid chromatography (HPLC). They assumed that PAH growth was
the net effect of acetylene addition to PAH and PAH addition to soot, while soot
growth resulted from addition of acetylene and PAH, ignoring oxidation in view of
the fuel-rich post-flame conditions.
Kazakov and Frenklach [169] numerically analysed the contribution of acetylene and
PAH to soot particle surface growth and concluded that a model with acetylene as
surface growth species is not contradicted by the experiments of Benish et al. [167].
They stated that the difference between the results obtained by [169] and [167] comes
from the different assumptions of the collision efficiencies between acetylene-PAH
and acetylene-soot.
3.2.3
Soot particle coagulation
The coagulation is usually expressed as a process of sticking of two particles, which
are glued together by a common outer shell generated by deposition similarly to
surface growth. Coagulation takes place only for relatively small particles, which
are characterised by high rates of growth (up to a diameter of 10 nm in low pressure
premixed systems [170, 171, 67]. The rate of a sticking process can be calculated by
solving Smoluchowski equation [172], following the assumptions:
1. The soot particles are small in comparison to the gas mean free path,
2. each collision of two particles results in coagulation,
3. all particles are spherical.
∞
X
dnk
1 X
=
Nij −
Nik .
dt
2 i+j=k
i=1
(3.32)
Here, nk represents the number density of new molecules in the size class ’k’, with
mass mk (the molecule of starting class in the molecular size spectrum, e. g., a PAH
monomer), resulting from the collision between two other molecules of different
classes i and j. Nij denotes the rate of collision between molecules of classes i and
j, defined by
Nij = β(mi , mj , ...)ni nj .
(3.33)
3. SOOT FORMATION
32
The collision of two molecules leads to the formation of a new molecule ’k ’, with
the summed mass of the two contributing molecules mk = mi + mj . The rate of
formation of the new molecules ’k’ is
1 X
1 X
Nij =
β(mi , mj )ni nj .
(3.34)
2 i+j=k
2 i+j=k
The molecule ’k’ can lose its identity due to collision with other molecules at the
rate
∞
∞
X
X
Nik = nk
β(mi , mk )ni .
(3.35)
i=1
i=1
β(mi , mj ) is a size-dependent collision frequency factor, which for free-molecular
coagulation is given as,
s
6kB T
(ri + rj )2
µi,j
s
µ
¶1/6 s
´2
3
6kB T
1
1 ³ 1/3
1/3
= 2.2
+
mi + mj
,
4πρ
ρ
mi mj
β(mi , mj ) =
(3.36)
where µi,j = mi mj /(mi + mj ) is the reduced mass, ri is the radius of the molecules
in the classes i and ρ is the density of these molecules.
Graham [173, 67], studied soot coagulation in shock-heated hydrocarbon/argon mixtures and showed a coagulation rate, expressed in terms of the rate of decrease of
the particle number density [n],
µ ¶1/6 µ
¶1/2
dn
5
5
3
6kB T
1/6
11/6
−
= ktheory fV [n] , with ktheory =
· G · α. (3.37)
dt
6
12 4π
ρsoot
Here, fV is the soot volume fraction, kB is the Boltzmann constant, ρ is the condensed particle density, α is a factor related to the polydisperse nature of the system,
and G is a factor accounting for the increase in collision cross-section over the hardsphere value due to electronic and dispersion forces. Graham suggested that G = 2
for spherical particles and for self-preserving size distribution α = 6.55.
3.2.4
Soot particle oxidation
The process of soot particle oxidation is parallel to the surface growth. In fact,
oxidation is also a surface reaction, which in principal should be treated as catalytic
combustion [67]. Potential soot oxidants are O, O2 , OH, and CO2 .
3. SOOT FORMATION
33
Frenklach stated that the major oxidation process occurs at the very beginning of
soot particle growth, which is the soot particle nucleation period, where a rapidly
decreasing concentration of O2 in fuel-rich environments is observed [105].
According to Neoh et al. [174] and Lucht et al. [175], the hydroxyl radical is the
most abundant oxidising species under fuel-rich condition. The authors stated that
OH could suppress soot formation via oxidative destruction of precursors, and OH
concentration might be an important factor in soot precursor kinetics. Lucht et al.
[175] concluded that OH is the limiting oxidative reactant under fuel-rich condition
as the soot decreases with an increase in OH concentration.
Experimental studies performed by Liu et al. [176] showed that CO2 has chemical
dilution, and thermal effects on soot formation reduction. They suggested that the
chemical mechanism of CO2 addition might be to promote the concentrations of
oxygen atom and hydroxyl that in return increase the oxidation of soot precursors
in soot formation regions. Vandooren et al. [177] studied experimentally the CO2
addition to rich but non-sooting CH4 /O2 /Ar premixed flames and showed that the
reaction CO2 + H = CO + OH is responsible for the promoted hydroxyl concentration. They also observed that the concentration of acetylene decreases as a result of
CO2 addition.
However, due to the lack of data on the mechanism of soot particle oxidation, a
one-step treatment is often used, assuming the rate law for the CO formed given as
[67]
d[CO]
= γi · Z i · a s ;
dt
i = O, OH, O2 ,
(3.38)
where γi = reaction probability when molecule i hits the soot surface, Zi = collision
number of molecule i per unit time and area, and as = soot surface per unit volume.
3.2.5
Soot agglomeration
Soot agglomeration takes place in the late phase of soot formation when, due to lack
of surface growth, coagulation is no longer possible [67]. As a result, open structured
aggregates are formed, containing from 10 to 100 primary particles (spherules) and
characterised by a log-normal size distribution [178, 67]. A relationship between the
number N of primary particles and the maximum length L of the aggregates can be
derived as
N = kf · (L/3dp )Df ,
(3.39)
3. SOOT FORMATION
34
where kf is a constant fractal prefactor, dp the primary particle diameter, and Df a
fractal dimension around 1.8 [179, 67]. In the current work, agglomeration was not
considered in the models.
35
Chapter 4
DISCRETE GALERKIN
METHOD
A detailed chemical mechanism of soot formation has to describe the reaction kinetics of both the gas- and the particulate-phase. Usually, the gas-phase chemistry model contains large number of elementary reactions between hundreds of
species. The formation and evolution of the macromolecular species (the heterogeneous, particulate-phase) needs to be treated simultaneously with the gas-phase
chemistry. The temporal change of the gas-phase species concentration and the distribution of the macromolecular species can be calculated by solving an associated
set of differential equations called a countable system of ordinary differential equations (CODEs), where particle size has to be treated separately. The problem is
that such systems have very high or even infinite dimensions, and an efficient numerical solution by standard ODE software is not possible. Standard computational
approaches for solving such systems include several techniques: large scale stiff integration, lumping techniques, statistical moment treatment, and continuous modeling.
Deuflhard and Wulkow [180] suggested the so-called discrete Galerkin method, which
considers a flexible and efficient solution of the kinetics of polymerisation reactions.
In general, two types of polymerisation reactions are considered in the literature,
condensation (step-reaction polymerisation) and addition or chain-reaction polymerisation (free-radical polymerisation). Condensation takes place between two
molecules to form one larger molecule, with a possible elimination of a small species,
e.g., water. The free-radical polymerisation involves chain reactions in which the
chain-carrying species may be a radical or an ion. In a short time, many monomers
are added to the growing chain, and the reaction stops when, e.g., two radicals react
4. DISCRETE GALERKIN METHOD
36
to end each other’s activity.
It has been shown that soot formation can be numerically treated by analogy to the
polymerisation reactions [68, 69, 70, 60, 71] with the use of the discrete Galerkin
method. The addition of a monomer M to the polymer P[S] can be described by
k
r
P[S] + M −
→
P[S + 1], S = 1, ..., N,
(4.1)
where N is the maximum chain length (polymer index, degree) considered in the
model. The size of the truncation index N is initially unknown; usually practical
considerations can limit it up to a given value.
In the current model, the soot formation was modeled by analogy to the process
of free-radical polymerisation, where a variety of macromolecular reactions as initiation, growth, termination, degradation, reverse polymerisation, coagulation and
transformation of the type of the polymer had to be modeled. All macromolecular
processes were treated with the discrete Galerkin method. The method is based on
an error-controlled expansion of the size distribution function of a macromolecule
into orthogonal polynomials of a discrete variable, in particular the polymer degree
or the number of monomers added to the growing macromolecule. It was thoroughly
studied by Sojka and described in [71]. In the present work the previously developed
numerical approach was applied for soot formation simulation during hydrocarbon
pyrolysis and oxidation in homogeneous conditions.
4.1
Theory of the discrete Galerkin method
The Galerkin method is a well known method for converting a differential equation
into a linear algebra problem, or a high-dimensional linear system of equations may
be projected to a lower dimensional system. These small systems are easier to solve,
but their solution is only an approximation to the original problem.
Let us (t) denote the concentration of macromolecules of chain length S at time t.
The sequence u1 (t), u2 (t), ... can be written as distribution u(t) = (us (t), S =
1, 2, ...). As mentioned above, the kinetics of a macromolecular reaction process can
be represented by a countable system of ordinary differential equations (abbreviated
as CODEs) of the form
u0s (t) = (Au(t))S
(4.2)
with a given initial distribution us (0). The key point for the construction of the
discrete Galerkin method [180] is the treatment of the polymer degree (chain length)
4. DISCRETE GALERKIN METHOD
37
S as a discrete variable. Formally, it can be written as
(f, g) :=
∞
X
f (S, ρ) g (S, ρ) ψ (S, ρ) ,
S = 1, 2, ...
(4.3)
S=1
where f and g are functions of the discrete variable S = 1, 2, ... and ψ(S, ρ) is a
given (positive) weight function with a time dependent parameter ρ. This product
induces an associated norm,
kf k := (f, f )1/2 .
(4.4)
and an associated orthogonal basis {lj (S, ρ)}j = 0, 1, 2, ... of polynomials of the
discrete variable S with the following characteristics:
(lj , lk ) =
∞
X
lj (S, ρ) lk (S, ρ) ψ (S, ρ) = γk δjk ,
γk > 0,
j, k = 0, 1, 2, ...
(4.5)
S=1
Here γk depends on the choice of the orthogonal basis, and δk is the Kronecker
symbol.
An unique representation of an unknown distribution P (S, t) of the polymerisation
index S of the polymer P [S] with respect to time is described by Deuflhard and
Wulkow [180, 71]:
P (S, t) := ψ (S, ρ) ·
∞
X
ak (t, ρ) lk (S, ρ) ,
S = 1, 2, ...
(4.6)
k=0
Here, ψ(S, ρ) is the weight function, ak (t, ρ) are the time-dependent coefficients with
a free parameter ρ. Because of the polynomial orthogonality for given P (S, t), the
coefficients ak (t, ρ) can be obtained by
aj (t, ρ) =
1
hlj (S, ρ) , P (S, t)i ,
γj
j = 0, 1, ...
(4.7)
Truncation of the expansion Eq. (4.6) after n terms leads to the so called Galerkin
approximation
P (n) (S, t, ρ) = ψ (S, ρ) ·
n
X
ak (t, ρ) lk (S, ρ) ,
S = 1, 2, ...
(4.8)
k=0
in dependence of the truncation index n. This approximation depends on the parameter ρ as well as on the choice of the truncation index. It is important to notice
that n must be initially given for every type of polymer. This approximation has the
structure of the method of lines [181], an approach used for the treatment of partial differential equations (PDEs). The so-called space discretisation is performed,
4. DISCRETE GALERKIN METHOD
38
which leads to a system of ODEs of fixed dimension. These differential equations are
also stiff and need to be solved by an efficient stiff-stable integrator. The benefit of
the Galerkin method is that the newly arising stiff system has a drastically smaller
dimension than the original one. To achieve this goal, the Galerkin method involves
two important characteristics, which are crucial for the success of the method.
1. A sophisticated choice of the weight function ψ and the parameter ρ provides a
good approximation and decreases n to the needed number. Thus, it is important to
keep n as small as possible. In the case of free-radical polymerisation a reasonable
probability density function is chosen [182], which in the chemical literature is known
¡
¢
as the Schultz-Flory distribution ψ (S, ρ) = (1 − ρ) · ρS−1 , 0 < ρ < 1, S = 1, 2, ... .
The orthogonal polynomials associated with the weight function are the discrete
Laguerre polynomials [71]. There are two natural requirements to normalise a weight
function ψ(S, ρ) such that its zeroth and first order statistical moments v0 and v1
coincide with the corresponding moments µ0, µ1 of an unknown distribution P (S, ρ)
at a fixed time t:
∞
X
a) υ0 (ρ) :=
ψ (S, ρ) = 1
(4.9)
S=1
∞
X
b) υ1 (ρ) :=
Sψ (S, ρ) =
S=1
µ1 (t)
.
µ0 (t)
The normalisation Eq. (4.9 a) ensures that ψ(S, ρ) has a probability distribution,
and condition Eq. (4.9 b) gives an implicit definition of ρ = ρ(t). Thus, the ith
moment µi can be calculated by
∞
® X
µi (t) := S , P (S, t) =
S i P (S, t) ,
­
i
i = 0, 1, ...
(4.10)
S=1
Further development of the S i in the orthogonal function lk (S, ρ)
i
S =
i
X
bik lk (S, ρ) ,
k = 0, ..., i
(4.11)
k=0
leads to a relation between µi and ak (t)
µi (t) =
i
X
bik ak (t) γk .
(4.12)
k=0
As a consequence, the weight function ψ is then time-dependent just as the wanted
distribution P (S, ρ). The conditions Eq. (4.9) imply
a) a0 (t) ≡ µ0 (t)
(4.13)
4. DISCRETE GALERKIN METHOD
39
b) a1 (t) ≡ 0.
2. The quality of the Galerkin approximation is controlled through an error estimation, which is calculated at the end of each simulation. The relative error ²n (t) of
the approximation (4.8) can be calculated by solving
¢2
P∞ ¡ (n)
(S, t, ρ) − P (S, t) /ψ (S, ρ)2
a2n+1 (t) γn+1
S=1 P
²n (t) :=
= Pn+1
.
P∞
2
2
2
S=1 P (S, t) /ψ (S, ρ)
k=0 ak (t) γk
2
(4.14)
As the statistical moments, two of the main characteristics of a polymer, are calculated, the mean chain length Sn and the mean mass Sm of the size distribution
P (S, t) of a polymer P are
Sn (t) =
µ1 (t)
µ0 (t)
and
Sm (t) =
µ2 (t)
.
µ1 (t)
(4.15)
The time variation of the size distribution function P (S, t), which depends on the
chemical kinetics of the macromolecular species, results in a complete system of
ODEs for each coefficient aj (t, ρ). In general, they take the form [180, 71]
¿
À
∞
daj
1
dP (S, t)
1 X
dP (S, t)
= j · lj (S, ρ) ,
= j ·
lj (S, ρ) ·
.
dt
ρ
dt
ρ S=1
dt
4.2
(4.16)
Program package MACRON
The discrete Galerkin technique suggested by Deuflhard and Wulkow [183] for the
solution of ODEs, describing the kinetics of polymerisation reactions, has been successfully applied for the case of free-radical polymerisation [69]. The first software,
that includes the analytical and numerical prerequisites of this method in combination with the solution of the set of ODEs generated by the gas-phase chemical
kinetics, was the so-called program package MACRON (MACROmolecular reaction
kiNetics), proposed by [68]. This package combines the discrete Galerkin techniques
for the simulation of macromolecular reactions with the software environment of
LARKIN [184, 182, 185, 186] for the numerical treatment of large systems of ODEs
arising in chemical reaction kinetics. The gas-phase reactions as well as the macromolecular reaction steps are entered by the user in familiar form, and the preparation
of the Galerkin method (analytical preprocessing) is performed. For this purpose, a
list of typical macromolecular reaction steps (e.g., nucleation, chain addition, transfer reactions, termination process, coagulation) have been implemented [68]. The
extended and revised version of this software [71] is used to model the particle dynamics during thermal decomposition of Fe(CO)5 , pure carbon clusters formation
4. DISCRETE GALERKIN METHOD
40
during pyrolysis of C3 O2 [60, 72], and soot formation in n-heptane rich oxidation
[71]. The size of the chemical system is restricted by the available computer memory. In its current version, it can handle up to 5000 gas-phase elementary reactions
between 500 species and 200 macromolecular reactions. For the interpretation of the
gas-phase elementary reactions, the kinetic parameter field consists of one to three
numbers, which denote the Arrhenius parameters: A, Ea , and n arising from the
Arrhenius equation (k = A · T n · exp(−Ea /RT ), see Chapter 3). The macromolecular reactions are characterised by species, whose empirical formula contains square
brackets (e.g., P[]). A typical example of such a reaction is
A + B ⇒ P[1] + C
(A, Ea , n, p).
Here, the fourth parameter p denotes the number of carbon atoms added to the
polymer species. To define the rate coefficients of the reversible reactions, two
possible descriptions are used:
• A reversible reaction is followed by two kinetic parameter fields, where the
first assigns the forward reaction and the second the reverse reaction.
• If a reaction is written in both directions, the reversible rate coefficient is calculated via the equilibrium constant. This is only possible if thermodynamical
data (included in the THERMO file) is available for all species appearing in
the equation.
The characteristic parameters of the polymer species as the soot volume fraction fV ,
mean particle diameter D and the soot yield Y can be computed from the values of
particle number density N, mean chain length Sn , and the mean mass of the polymer
size distribution Sm .
The total particle number density N is
N = NA ·
NP
X
[P[]i ].
(4.17)
i=1
Here N A is Avogadro’s number, [P[]i ] is the molar concentration of the polymers
P[]i , and NP is the chain length.
The soot volume fraction fV is calculated by
NP
NA X
[P[]i ] · (m0,i + (Sn,i − 1) · mS,i ,
·
fV =
ρ i=1
(4.18)
4. DISCRETE GALERKIN METHOD
41
where ρ is the density of graphite, m0,i is the mass of a monomer from the polymer
P[]i , mS,i is the mass of the smallest momoner added to the polymer P[]i , and Sn,i
is the the mean chain length of the P[]i .
The soot particle diameter D is
r
3 6 fV
D=
.
πN
The soot yield Y can be computed as
PN P
[P[]i ] · (NC,0,i + (Sn,i − 1) · NC,S,i )
Y = i=1 PN HC
,
j=1 [HC]t0,j · NC,HC,j
(4.19)
(4.20)
where NC,0,i denotes the number of C atoms included in a monomer, NC,S,i is the
number of C atoms in a momoner added to the polymer P[]i , NHC is the maximum
number of the fuel molecules, [HC]t0,j is the initial concentration of the fuel, and
NC,HC,j is the number of C atoms in a fuel molecule. Information about the different parameters included in the input blocks as well as the specific subroutines are
described in detail by Sojka in [71].
The advantage of this approach is that it combines the well-known methods to
simulate the reactions of microheterogeneous particles in such a way that the discrete
character of each elementary transformation is preserved. These transformations
are represented as elementary chemical reactions for the particles of all sizes. The
particles react also with the gas-phase species, and, thus a connection between the
gas-phase chemistry and the soot particles is provided during the whole calculation.
In the current work, two different kinetic schemes were introduced in MACRON to
model the formation and evolution of soot particles during pyrolysis and oxidation
of various hydrocarbons and their mixtures behind shock waves at wide range of
reaction conditions [187, 61, 62, 63, 64, 188].
42
Chapter 5
DETAILED KINETIC MODELS
OF SOOT FORMATION
Last decade, the HACA mechanism of polyaromatic hydrocarbons formation and
growth [21, 1] was accepted as the standard model, and many soot formation models
are based on it. The implementation of a specific model in different codes usually
causes modifications of some important characteristics or steps, which may ruin the
basic idea of the original model. Therefore, it is necessary that every mechanism has
to be described in detail, in particular its differences and similarities to the source
mechanism. In this chapter, two different detailed kinetic models of soot formation
are described, as well as their validation and application in homogeneous conditions.
For simplicity, the models are named Model-1 and Model-2, and with these names
they are referred to further in the text.
5.1
5.1.1
Description of Model-1
Gas-phase reaction mechanism
A detailed kinetic model of soot formation during pyrolysis of various hydrocarbons
in shock-tube experiments is developed [58]. The model was further extended with
a part of the mechanism of n-heptane oxidation [189] and applied for soot formation
simulation in CH4 , C3 H8 , and n-C7 H16 rich oxidation behind reflected shock waves
[187, 62]. A set of reactions of C1 to C2 species were also added from the mechanism
of [190]. As a result, the complete detailed kinetic scheme consists of approximately
5. DETAILED KINETIC MODELS OF SOOT FORMATION
43
1850 gas-phase reactions between 186 species and 100 heterogeneous reactions including four ensembles of micro-heterogeneous particles. The gas-phase reaction
mechanism includes a complete set of reactions of polyaromatic hydrocarbon (PAH)
formation, described in [46] for laminar premixed acetylene and ethylene flames with
all modifications presented in [23]. In addition to this, the reaction mechanisms of
acetylene pyrolysis [191, 79], the gas-phase mechanism of polyyne species formation [16, 17, 2], and a set of the gas-phase reactions for small pure carbon clusters
formation up to C30 [60, 192, 72] were included.
The gas-phase kinetic mechanism of polyaromatic hydrocarbon formation describes
the pyrolysis and oxidation of C1 to C2 species, the formation of higher linear hydrocarbons up to C6 species, the formation of benzene and higher PAH up to pyrene and
the oxidation pathways of the aromatic species. Benzene and phenyl molecules are
formed by interaction between C4 HX species with acetylene, by cyclisation of C6 HX
species, and the combination of C3 H3 propargyl radicals (see Chapter 3.1.1). This
reaction was treated as an overall single irreversible step, with the rate coefficient
fitted to the experimental species profiles against which the model was validated
[23]. As mentioned in [23, 105], the kinetic simulations revealed high reversibility of
chemical reactions leading to the formation and growth of the aromatic rings. Only
for particularly stable compounds, like acenaphthalene or pyrene, the formation reactions can be assumed as irreversible. In the kinetic model considered, several evenand odd-carbon-atom paths for polyaromatics formation were implemented together
with a consistent set of kinetic and thermodynamic data. The formation pathway
of PAH starts with benzene and follows the HACA mechanism. The polycyclic aromatic compounds growth up to pyrene by acetylene addition and the ring-forming
addition of vinylacetylene (C4 H4 ) to aromatic radicals. Whereas the vinylacetylene
addition channel contributes mostly to the production of naphthalene (A2 ), phenanthrene (A3 ) is formed by ring-ring condensation reactions in which biphenyl (P2 )
is formed by the addition of benzene (A1 ) to phenyl (A1 -) (see Chapter 3.1.2 and
3.1.3).
The gas-phase mechanism described by Krestinin et al. in [16, 17, 2], as the so
called polyyne pathway, was also implemented into the model. The most important
pathway of polyyne growth is the subsequent increase of the carbon chain by a substitution reaction C2n H + C2m H2 = C2n+2m H2 + H, n, m = 1, 2, ...; n + m < 6,
whose rate coefficients are close to the gas-kinetic collisions. Acetylene and its radical C2 H play the key role in the polyyne growth process. The appropriate chemical
environment, that consists of H, C2 H, C2 H3 and C4 H3 radicals responsible for the
polyyne growth, depends on the type and the structure of the fuel molecules. The
5. DETAILED KINETIC MODELS OF SOOT FORMATION
44
polyyne molecules grow up to C12 H2 and the average size of the polyyne radicals
C2n H increases. Large polyyne radicals react with each other or with higher homologues, forming a variety of aggregates, which are no longer straight and planar and
may contain ring closures. This ring closure results in the appearance of new free
valencies, which enable these aggregates to add still more polyynes. Most of the
small polyyne molecules and radicals react to form higher homologues. Finally, the
radicals necessary to form larger polyynes are consumed. The radicals formed by
molecular dissociation are trapped by the carbon particles. As a result, the radical
concentration reduces, which ends the formation of higher polyynes and diminishes
the rate of soot particle inception. In general, the direct decomposition of acetylene
and small polyynes on the surface of the carbon particles is much slower in comparison to their condensation. These specific steps describe the polyyne submodel of
the gas-phase soot precursor formation and growth of Model-1.
5.1.2
Soot precursors and particle inception,
surface
growth, coagulation and oxidation
The formation and evolution of soot precursors and soot particles is described
within the framework of the discrete Galerkin technique suggested by Deuflhard
and Wulkow [180, 68], which is briefly described in Chapter 4.
A key aspect of the soot formation process is the deposition of soot mass through
reactions of gaseous species with the soot particle surface. Frenklach and Wang
[21], suggested a detailed kinetic mechanism for soot particles surface growth. Their
mechanism is based on the postulate of the chemical similarity between analogous
surface and gas-phase reactions of carbonaceous species. For soot particles this
means that chemical reactions at the soot particle surface are similar to those of
large polycyclic aromatic hydrocarbons (PAH). The essence of this mechanism is
the HACA growth on the armchair edge of PAH [193]. In Model-1, only the basic
mechanism of surface growth presented in [23] was considered. Following [23], the
first precursors are incepted in condensation reactions of pyrene molecules. As an
extention to this process, the reactions among pyrene, phenanthrene and biphenyl
molecules and their radicals [58] were included. Two different types of particles were
considered for the precursors formed from the PAH - particles with dehydrogenated
C* sites (active) and saturated particles with C-H sites (inactive). The formation
and consumption of active sites on the soot particle surface occur in the reactions
with H2 /H and H2 O/OH/O2 species. Surface growth is provided by the reactions of
soot particles with active sites with C2 H2 [23], accompanied by H abstraction, and by
5. DETAILED KINETIC MODELS OF SOOT FORMATION
45
the reactions of pyrene, phenanthrene, and naphthalene condensation on the active
soot particles [58]. The soot particles with active sites participate in coagulation
reactions, where only a free-molecular regime of coagulation was considered.
In the polyyne pathway, the soot precursors are formed in polymerisation reactions
of higher polyynes (C12 H2 , C10 H2 ). In the current model, only the high temperature path of initiation reactions between neutral polyyne molecules and reactions
of particle growth with participation of polyyne molecules and their radicals were
adopted from the original model proposed by Krestinin et al. [16, 17, 2]. Revised thermodynamic data for the polyyne molecules included in the gas-phase part
of the mechanism were taken from the literature [194] or calculated using group
additivity techniques. A complete list of the reactions with participation of microheterogeneous soot precursors and soot particles is presented in Table 5.1. The
surface growth in the polyyne pathway occurs via reactions of soot precursors and
particles with the most reactive gas-phase species: C2 H2 , C2 H, C2 , C4 H2 , C4 H, C4 ,
C6 H2 , C6 H, C6 , C8 H2 , C8 H, C8 , C10 H2 , C10 H, C10 , C12 H2 , C12 H, and C12 . According to the main assumption of the polyyne model, a growing particle generates
active sites in each act of interaction with the gas-phase species. Therefore only
one type of active soot particles was considered in the model. Soot particles formed
through the polyyne pathway react also with PAH and coagulate with each other
(see Table 5.1).
5. DETAILED KINETIC MODELS OF SOOT FORMATION
46
Table 5.1: Mechanism of formation, growth, coagulation and
transformation of soot precursors and soot particles (Model1)
A(a)
Reaction
n(a)
EA
p(b)
Ref.
HACA pathway of soot formation
Soot precursors formation
A4 + A4 → PR[1]
1.558E+13
0.5
0.0
32
(c,d)
A4 + A4 - → P[1]
1.558E+13
0.5
0.0
32
(c,d)
A4 - + A4 - → PR[1]
1.558E+13
0.5
0.0
32
(c,d)
A4 + A3 → PR[1]
1.558E+13
0.5
0.0
30
(c,d)
A4 - + A3 → P[1]
1.558E+13
0.5
0.0
30
(c,d)
A3 + A3 → PR[1]
1.558E+13
0.5
0.0
28
(c,d)
P2 + P2 → PR[1]
1.558E+10
0.0
0.0
24
(c,e)
15.88
2
(f,g)
Growth of soot precursors with active sites
P[N ] + C2 H2 → P[N +1] + H
8.0E+7
1.56
P[N ] + A4 → P[N +1]
4.5E+12
0.5
0.0
16
(f,g)
P[N ] + A3 → P[N +1]
4.5E+12
0.5
0.0
14
(f,g)
P[N ] + A2 → P[N +1]
4.5E+12
0.5
0.0
10
(f,g)
Activation - Deactivation of soot precursors
PR[N ] + H → P[N ] + H2
4.17E+13
0.0
54.34
(h,i)
P[N ] + H2 → PR[N ] + H
3.90E+12
0.0
45.98
(h,i)
PR[N ] + OH → P[N ] + H2 O
1.00E+10
0.73
5.98
(h,i)
P[N ] + H2 O → PR[N ] + OH
3.68E+8
1.14
71.48
(h,i)
P[N ] + H → PR[N ]
2.00E+13
0.0
0.0
(h,i)
P[N ] + O2 → PR[N ] + H2 O +H2 O
2.20E+12
0.0
31.35
(h,i)
Transformation of soot precursors to soot particles
P[N ] → S[N ]
1.0E+6
0.0
0.0
(j,k)
Coagulation of soot precursors with active sites
P[N ] + P[M ] → P[N +M ]
4.50E+12
0,5
0.0
(l)
Polyyne pathway of soot formation
Soot precursors formation
C8 H2 + C8 H2 → C[1]
4.0E+13
0.0
163
16
(m,n)
C10 H2 + C10 H2 → C[1]
4.0E+13
0.0
84
20
(m,n)
C12 H2 + C12 H2 → C[1]
4.0E+13
0.0
17
24
(m,n)
C12 H2 + C12 H2 → C[1]
4.0E+13
0.0
17
22
(m,n)
Growth of soot precursors
C[N ] + C2 H2 → C[N +1] + H
8.0E+7
1.56
15.88
2
(o,p)
C[N ] + C2 H2 → C[N +1] + H2
4.0E+13
0.0
133.1
2
(o,p)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
47
Reaction
A(a)
n(a)
EA
p(b)
Ref.
C[N ] + C2 H → C[N +1] + H
4.0E+13
0.0
0.0
2
(o,p)
C[N ] + C2 H → C[N +1]
4.0E+13
0.0
0.0
2
(o,p)
C[N ] + C2 → C[N +1]
4.0E+13
0.0
0.0
2
(o,p)
C[N ] + C4 H2 → C[N +1] + H2
4.0E+13
0.0
50.2
4
(o,p)
C[N ] + C4 H2 → C[N +1] + H
8.0E+7
1.56
15.88
4
(o,p)
C[N ] + C4 H → C[N +1] + H
4.0E+13
0.0
0.0
4
(o,p)
C[N ] + C4 H → C[N +1]
4.0E+13
0.0
0.0
4
(o,p)
C[N ] + C4 → C[N +1]
4.0E+13
0.0
0.0
4
(o,p)
C[N ] + C6 H2 → C[N +1] + H2
4.0E+13
0.0
33.5
6
(o,p)
C[N ] + C6 H2 → C[N +1] + H
8.0E+7
1.56
15.88
6
(o,p)
C[N ] + C6 H → C[N +1] + H
4.0E+3
0.0
0.0
6
(o,p)
C[N ] + C6 H → C[N +1]
4.0E+13
0.0
0.0
6
(o,p)
C[N ] + C6 → C[N +1]
4.0E+13
0.0
0.0
6
(o,p)
C[N ] + C8 H2 → C[N +1] + H2
4.0E+13
0.0
12.6
8
(o,p)
C[N ] + C8 H2 → C[N +1] + H
8.0E+7
1.56
15.88
8
(o,p)
C[N ] + C8 H → C[N +1] + H
4.0E+13
0.0
0.0
8
(o,p)
C[N ] + C8 H → C[N +1]
4.0E+13
0.0
0.0
8
(o,p)
C[N ] + C8 → C[N +1]
4.0E+13
0.0
0.0
8
(o,p)
C[N ] + C10 H2 → C[N +1] + H2
4.0E+13
0.0
0.0
10
(o,p)
C[N ] + C10 H2 → C[N +1] + H
8.0E+7
1.56
15.88
10
(o,p)
C[N ] + C10 H → C[N +1] + H
4.0E+13
0.0
0.0
10
(o,p)
C[N ] + C10 H → C[N +1]
4.0E+13
0.0
0.0
10
(o,p)
C[N ] + C10 → C[N +1]
4.0E+13
0.0
0.0
10
(o,p)
C[N ] + C12 H2 → C[N +1] + H2
4.0E+13
0.0
0.0
12
(o,p)
C[N ] + C12 H2 → C[N +1] + H
8.0E+7
1.56
15.88
12
(o,p)
C[N ] + C12 H → C[N +1] + H
4.0E+13
0.0
0.0
12
(o,p)
C[N ] + C12 H → C[N +1]
4.0E+13
0.0
0.0
12
(o,p)
C[N ] + C12 → C[N +1]
4.0E+13
0.0
0.0
12
(o,p)
C[N ] + C4 H4 → C[N +1] + H2 + H2
2.0E+12
0.0
115.9
4
(o,p)
C[N ] + A4 → C[N +1]
4.5 E+12
0.5
0.0
16
(q)
C[N ] + A3 → C[N +1]
4.5E+12
0.5
0.0
14
(q)
C[N ] + A2 → C[N +1]
4.5E+12
0.5
0.0
10
(q)
Transformation of soot precursors to soot particles
C[N ] → S[N ]
1.0E+6
0.0
0.0
(k)
0.0
(l)
Coagulation of soot precursors
C[N ] + C[M ] → C[N +M ]
4.50E+12
0.5
Growth of soot particles
S[N ] + C2 H2 → S[N +1] + H
8.0E+7
1.56
15.88
2
(p)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
Reaction
A(a)
n(a)
S[N ] + C2 H2 → S[N +1] + H2
4.0E+13
S[N ] + C2 H → S[N +1] + H
48
EA
p(b)
Ref.
0.0
133.1
2
(p)
4.0E+13
0.0
0.0
2
(p)
S[N ] + C2 H → S[N +1]
4.0E+13
0.0
0.0
2
(p)
S[N ] + C2 → S[N +1]
4.0E+13
0.0
0.0
2
(p)
S[N ] + C4 H2 → S[N +1] + H2
4.0E+13
0.0
50.2
4
(p)
S[N ] + C4 H2 → S[N +1] + H
8.0E+7
1.56
15.88
4
(p)
S[N ] + C4 H → S[N +1] + H
4.0E+13
0.0
0.0
4
(p)
S[N ] + C4 H → S[N +1]
4.0E+13
0.0
0.0
4
(p)
S[N ] + C4 → S[N +1]
4.0E+13
0.0
0.0
4
(p)
S[N ] + C6 H2 → S[N +1] + H2
4.0E+13
0.0
33.5
6
(p)
S[N ] + C6 H2 → S[N +1] + H
8.0E+7
1.56
15.88
6
(p)
S[N ] + C6 H → S[N +1] + H
4.0E+13
0.0
0.0
6
(p)
S[N ] + C6 H → S[N +1]
4.0E+13
0.0
0.0
6
(p)
S[N ] + C6 → S[N +1]
4.0E+13
0.0
0.0
6
(p)
S[N ] + C8 H2 → S[N +1] + H2
4.0E+13
0.0
12.6
8
(p)
S[N ] + C8 H2 → S[N +1] + H
8.0E+7
1.56
15.88
8
(p)
S[N ] + C8 H → S[N +1] + H
4.0E+13
0.0
0.0
8
(p)
S[N ] + C8 H → S[N +1]
4.0E+13
0.0
0.0
8
(p)
S[N ] + C8 → S[N +1]
4.0E+13
0.0
0.0
8
(p)
S[N ] + C10 H2 → S[N +1] + H2
4.0E+13
0.0
0.0
10
(p)
S[N ] + C10 H2 → S[N +1] + H
8.0E+7
1.56
15.88
10
(p)
S[N ] + C10 H → S[N +1] + H
4.0E+13
0.0
0.0
10
(p)
S[N ] + C10 H → S[N +1]
4.0E+13
0.0
0.0
10
(p)
S[N ] + C10 → S[N +1]
4.0E+13
0.0
0.0
10
(p)
S[N ] + C12 H2 → S[N +1] + H2
4.0E+13
0.0
0.0
12
(p)
S[N ] + C12 H2 → S[N +1] + H
8.0E+7
1.56
15.88
12
(p)
S[N ] + C12 H → S[N +1] + H
4.0E+13
0.0
0.0
12
(p)
S[N ] + C12 H → S[N +1]
4.0E+13
0.0
0.0
12
(p)
S[N ] + C12 → S[N +1]
4.0E+13
0.0
0.0
12
(p)
S[N ] + C4 H4 → S[N +1] + H2 + H2
2.0E+12
0.0
115.9
4
(p)
S[N ] + A4 → S[N +1]
4.5E+12
0.5
0.0
16
(q)
S[N ] + A3 → S[N +1]
4.5E+12
0.5
0.0
14
(q)
S[N ] + A2 → S[N +1]
4.5E+12
0.5
0.0
10
(q)
Coagulation of soot particles
S[N ] + S[M ] → S[N +M ]
4.50E+12
0.5
0.0
(l)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
(a)
The rate coefficients are presented by the Arrhenius equation:
k = AT n exp (−EA /RT ), where A (cm3 , mol, s), T (K), and
EA (KJ/mol).
(b) Index p denotes the number of carbon atoms added to a particle in
each act of interaction with carbon-containing gas-phase species.
(c) Notation PR[1] denotes the concentration of the soot precursors
formed through the HACA pathway containing p carbon atoms
(p = 28 − 32) without active sites on their surface. P[1] denotes
the concentration of the PAH precursors with active sites on their
surface (p = 24 − 32).
(d) Rate coefficient is similar to the rate coefficient of soot particle
inception proposed in [23].
(e) This reaction was added to improve the coincidence of the calculated results and experimentally measured values.
(f) Notation P[N ] denotes the concentration of the active soot precursors after N acts of interaction with various carbon-containing
gas-phase species.
(g) The chosen rate coefficient is similar to the rate coefficient of soot
particle growth proposed in [23].
(h) Notation PR[N ] denotes the concentration of the inactive soot precursors, where index N corresponds to the number of interactions of
active soot particles P[N ] with carbon-containing gas-phase species.
(i) The chosen rate coefficient is similar to the rate coefficient of transformation of soot particles proposed in [23].
(j) Notation S[N ] denotes the concentration of active soot particles
formed through the polyyne pathway of soot formation and by
transformation reactions of the P[N ] and C[N ] into S[N ] particles.
(k) The chosen rate coefficient is similar to the rate coefficient of internal transformation of pure carbon clusters into soot-like particles
proposed in [72].
(l) The rate coefficient of coagulation was adopted from [72].
(m) Notation C[1] denotes the concentration of the precursors
formed through the polyyne pathway containing p carbon atoms
(p = 16 − 22) with active sites on their surface.
(n) The rate coefficient was adopted from [16, 17].
(o) Notation C[N ] denotes the concentration of the precursors formed
through the polyyne pathway with active sites on their surface after
N acts of interaction with carbon-containing gas-phase species.
(p) The rate coefficients were adopted from [16, 17, 23].
49
5. DETAILED KINETIC MODELS OF SOOT FORMATION
(q)
5.2
5.2.1
50
The chosen rate coefficient is equal to the rate coefficient of the
coagulation reactions.
Results Model-1
Validation of the model
In the context of the detailed kinetic model (Model-1), the process of soot formation
during acetylene and benzene pyrolysis demonstrates the most pronounced differences with respect to the fuel structure and the reaction pathways included in the
scheme. Kern et al. [35, 36] investigated the pyrolysis of acetylene and benzene and
observed that, although both types of fuel have different chemical structure, the
main gas-phase products are acetylene and several small polyynes. In the current
model the higher polyynes were considered as soot precursors. Thus, to validate
the detailed kinetic model, the calculated results of the concentration profiles of the
species measured in [35, 36] were compared with the experimental measurements
behind reflected shock waves. In Figure 5.1 the concentration profiles of C2 H2 decay
and the main products C2 H2 , C4 H2 , and C6 H2 formed during pyrolysis of a 3.2%
C2 H2 diluted in a (99%Ne/1%Ar) mixture at temperature 2030 K and pressure 0.39
bar are presented. For the case of acetylene pyrolysis, the results of simulations are
in very good agreement with the experiment [35].
Kern et al. [36] studied also the kinetic of benzene thermal decomposition with the
use of three different techniques, time-of-flight mass spectrometry (TOF), atomic
resonant absorption spectroscopy (ARAS), and laser-schlieren density gradient measurements (LS) in shock-tube experiments. Benzene decay profiles measured and
calculated at three different temperatures are plotted in Figure 5.2. The authors
reported that the main species observed in the experiments were C6 H6 , C2 H2 , and
C4 H2 . They described the process of benzene dissociation by means of the reactions C6 H6 → C6 H5 + H and C6 H5 → C2 H2 + C4 H3 , whose rate coefficients were
calculated together with an overall rate of C6 H6 decomposition, occurring by the
direct ring rupture process C6 H6 → C2 H2 + C4 H4 . For the results of calculation
in the case of C6 H6 pyrolysis, a particular difference in the C2 H2 (Figure 5.3) and
C4 H2 (Figures 5.4) formation profiles was observed at high temperatures. Several
additional calculations showed that the agreement improves if the reactions of soot
particle inception and surface growth with participation of polyyne molecules and
radicals are excluded from the kinetic scheme.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
51
Figure 5.1: Concentration profiles of the main gas-phase species measured (closed symbols) [35] and simulated (open symbols and lines) during pyrolysis of 3.2 % C2 H2 /Ne/Ar
mixture, at T = 2030 K, and p = 0.39 bar behind reflected shock waves: (squares) C2 H2 ,
(triangles) C4 H2 · 2, (inverse triangles) C6 H2 · 10.
Figure 5.2: Concentration profiles of C6 H6 decay measured (closed symbols) [36] and
simulated (open symbols and lines) for a mixture of 2.1 % C6 H6 , diluted in argon at p =
0.52 bar for three different temperatures: (circles) 1704 K, (triangles) 1942 K, (squares)
2192 K.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
52
Figure 5.3: Time history of C2 H2 concentration measured (closed symbols) [36] and
simulated (open symbols and lines) at conditions as in Figure 5.2.
Figure 5.4: Time history of C4 H2 concentration measured (closed symbols) [36] and
simulated (open symbols and lines) at conditions as in Fig.5.2.
Integral Reaction Flow Analysis (IRFA) and global sensitivity analysis were performed during pyrolysis for both types of reaction systems, C2 H2 and C6 H6 . The
IRFA diagrams show only the main routes of soot precursor formation, by means of
the different pathways implemented in the kinetic mechanism (HACA and polyyne).
5. DETAILED KINETIC MODELS OF SOOT FORMATION
53
In the case of acetylene pyrolysis, the reaction routes of soot precursor formation
Figure 5.5: Integral reaction flow analysis of the PAH formation pathways during pyrolysis
of a 4.62 % C2 H2 /Ar mixture at T = 2000 K, p = 6.0 bar, and reaction time 0.003 s.
Figure 5.6: Integral reaction flow analysis of the polyyne formation pathways during
pyrolysis of a 4.62 % C2 H2 /Ar mixture at T = 2000 K, p = 6.0 bar, and reaction time
0.003 s.
(PRsoot[1] and Csoot[1] ) are shown in Figures 5.5 and 5.6. The main routes of soot
precursor formation through PAH (HACA pathway) are indicated in Figure 5.5.
Benzene, as the first aromatic ring in the system, is formed at about 50% through
5. DETAILED KINETIC MODELS OF SOOT FORMATION
54
Figure 5.7: Sensitivity analysis with respect to benzene during pyrolysis of acetylene at
conditions as in Figure 5.5.
Figure 5.8: Sensitivity analysis with respect to phenanthrene during pyrolysis of acetylene
at conditions as in Figure 5.5.
the propargyl radical (C3 H3 ) recombination. The rate-determining steps with respect to benzene formation (Figure 5.7) are the vinylacetylene (C4 H4 ) decomposition
and the C3 H3 recombination,
H + C4 H4 = CH3 + C3 H2 ,
(5.1)
C3 H3 + C3 H3 = A1 .
(5.2)
The rate coefficients for both reactions k = 5.0 · 1012 in cm3 mol-1 s-1 were adopted
from [23]. In Model-1, Eq. (5.2) was written as a one-step irreversible reaction.
Phenanthrene is formed preferably through the C2 H2 addition to biphenyl radical,
which is an example for the significant contribution of the ring-ring condensation
reactions in the PAH mass growth. Phenanthrene and pyrene are the main species
engaged in the process of soot precursors formation. Both molecules are mostly
5. DETAILED KINETIC MODELS OF SOOT FORMATION
55
Figure 5.9: Sensitivity analysis with respect to pyrene during pyrolysis of acetylene at
conditions as in Figure 5.5.
Figure 5.10: Sensitivity analysis with respect to C12 H2 during pyrolysis of acetylene at
conditions as in Figure 5.6.
produced following the HACA model. Nevertheless, in the case of acetylene pyrolysis, the PAH route based only on the HACA [46] cannot compete with the polyyne
pathway. The rate-limiting step with respect to phenanthrene (A3 ) and pyrene (A4 )
formation is again Reaction (5.1). Vinylacetylene is one of the key species for the
PAH formation and growth. Important for the PAH growth are also the reactions of
1- and 4-phenanthrene radical formation, which after C2 H2 addition forms pyrene,
and the propargyl radical recombination (see Figures 5.8 and 5.9).
In the case of acetylene pyrolysis, the polyyne pathway of soot formation dominates
(Figure 5.6). Starting from C2 H2 as a parent molecule, the polyyne molecular mass
growth follows the sequence of reactions of substitution described in Section 5.1.1 of
the Chapter. The soot particle precursors are formed in reactions of higher polyyne
polymerisation, like 1,3,5,7,9-decapentayne (C10 H2 ) and 1,3,5,7,9,11-dodecahexayne
5. DETAILED KINETIC MODELS OF SOOT FORMATION
56
(C12 H2 ), which later interact with C2 H2 , C4 H2 and provide the major contribution
in the soot particle surface growth. The sensitivity analysis showed that the ratedetermining reactions with respect to the polyyne molecules participating in the soot
model (C10 H2 and C12 H2 ) are related to the formation of ethynyl radical (C2 H) and
C8 H2 , as these two species play the key role for the the formation of higher polyynes
(Figure 5.10). The reaction
C2 H2 + H = C2 H + H2
(5.3)
was adopted from the C1 -C4 mechanism of hydrocarbon combustion [190], with
the rate coefficient k = 2.0 · 109 T 1.64 exp(−126.788/RT ) in cm3 mol-1 s-1 , with EA in
KJmol-1 .
Figure 5.11: Integral reaction flow analysis of the PAH formation pathways during pyrolysis of a 1.54 % C6 H6 /Ar mixture at T = 2000 K, p = 6.0 bar, and reaction time 0.003
s.
Soot formation starts much earlier in benzene pyrolysis where the PAH route of
soot formation dominates (Figures 5.11 - 5.12). The main reason is the absence of
the rate-limiting cyclisation step with respect to the PAH formation and growth in
comparison to the C2 H2 pyrolysis. During benzene pyrolysis, most of the benzene
molecules are destroyed by analogy to the mechanism described by Kern et al. [36],
but some of them survive the termal decomposition. These are used as a kernel for
PAH growth by HACA.
Critical for the polyyne formation are the benzene dehydrogenation and the phenyl
5. DETAILED KINETIC MODELS OF SOOT FORMATION
57
Figure 5.12: Integral reaction flow analysis of the polyyne formation pathways during
pyrolysis of a 1.54 % C6 H6 /Ar mixture at T = 2000 K, p = 6.0 bar, and reaction time
0.003 s.
Figure 5.13: Sensitivity analysis with respect to biphenyl during pyrolysis of benzene at
conditions as in Figure 5.11.
radical decomposition (Figure 5.12). They are thoroughly studied in [1]. Subsequently, O-benzyne is formed, which decomposes to 1-buten-3-yn-1-yl (n-C4 H3 ) and
C2 H2 . Frenklach and Wang [1] suggested that in rich flames the n-C4 H3 radical is
rapidly consumed to form its resonantly stabilised i-C4 H3 radical.
Paralelly, the polyacetylene mass growth follows the well-known sequence of substitution reactions up to (C10 H2 ) and (C12 H2 ) formation. The global sensitivity
analysis confirmed that the rate-limiting reaction with respect to the C10 H2 and
5. DETAILED KINETIC MODELS OF SOOT FORMATION
58
Figure 5.14: Sensitivity analysis with respect to phenanthrene during pyrolysis of benzene
at conditions as in Figure 5.11.
Figure 5.15: Sensitivity analysis with respect to C12 H2 during pyrolysis of benzene at
conditions as in Figure 5.12.
C12 H2 formation is the phenyl radical decomposition, leading to O-benzyne,
A1 − = H + c-C6 H4 ,
(5.4)
whose ring structure is opened in a propagation reaction with H atom, forming the
linear species 3-hexen-1,5-diyne (l-C6 H4 ),
H + c-C6 H4 = H + l-C6 H4 .
(5.5)
Both steps are described by Wang and Frenklach in [45] and in the model of Appel
et al. [23]. In the current mechanism, the following values for the rate coefficient
(k = 2.4 · 1060 T -13.66 exp(−123.428/RT ) in cm3 mol-1 s-1 , with EA in KJmol-1 [23] and
k = 1.4 · 1054 T -11.7 exp(−144.348/RT ) in cm3 mol-1 s-1 , with EA in KJmol-1 [23]) were
used for the Reactions (5.4) and (5.5) respectively.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
59
Figure 5.16: Sensitivity analysis with respect to C10 H2 during pyrolysis of benzene at
conditions as in Figure 5.12.
5.2.2
Hydrocarbon pyrolysis behind shock waves
Usually, several parameters of soot formation such as induction time (τ ), soot yield
(SY), and soot growth rate coefficient (kf ) are measured from the experimentalists.
They are known to be very sensitive to the chemical structure of the pyrolysed
hydrocarbon. The induction time τ [s] is defined as the intersection point of the
tangent at the inflection point of the soot yield curve with the time axis. The
soot yield is defined as a ratio of the converted to soot carbon to the total carbon
content in the parent mixture. The soot yield profiles, after the inflection point,
can be approximated by an empirically obtained first order rate law, where the
parameter kf [s−1 ] is the soot growth rate coefficient, which can be interpreted as
an effective measure of the active lifetime of soot particles, assuming that they are
losing their reactivity.
A direct comparison of the experimental results with the calculated results for the
induction time, the soot yield and the observable rate of soot growth, obtained by
extinction techniques during pyrolysis of various hydrocarbons and their mixtures,
was performed. Various mixtures were investigated during pyrolysis of methane,
ethylene, acetylene, benzene, benzene/acetylene, and acetylene/hydrogen, diluted
in argon or neon mixtures behind shock waves [195, 81, 82, 78].
5. DETAILED KINETIC MODELS OF SOOT FORMATION
60
Pyrolysis of acetylene and ethylene
The temperature dependences of the soot yield and the Arrhenius-type plots for the
induction delay time during the pyrolysis of C2 H2 /Ar mixtures at a pressure 50.7
bar, and C2 H4 /Ar at a pressure 50.0 bar for different carbon atom concentrations
Figure 5.17: Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of C2 H2 /Ar mixtures at p =
57.0 bar for three different C atom concentrations: (inverse triangles) [C] = 3.8 [mol/m3 ],
(circles) [C] = 1.7 [mol/m3 ], (squares) [C] = 0.9 [mol/m3 ].
Figure 5.18: Induction delay time in measured (closed symbols) [195]and simulated (open
symbols and lines) during pyrolysis of C2 H2 /Ar mixtures at conditions as in Fig. 5.17.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
61
Figure 5.19: Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of C2 H4 /Ar mixtures at p =
50.0 bar for three different C-atom concentrations: (inverse triangles) [C] = 7.4 [mol/m3 ],
(circles) [C] = 4.7 [mol/m3 ], (squares) [C] = 4.0 [mol/m3 ]. Open diamonds denote the
calculated results for C2 H6 /Ar mixture: p = 50.0 bar, [C] = 4.0 [mol/m3 ].
Figure 5.20: Induction delay time measured (closed symbols) [195] and simulated (open
symbols and lines) during pyrolysis of C2 H4 /Ar mixtures at p = 50.0 bar for three different C-atom concentrations: (triangles) [C] = 7.4 [mol/m3 ], (circles) [C] = 4.7 [mol/m3 ],
(squares) [C] = 4.0 [mol/m3 ].
are presented in Figures 5.17 - 5.20. The model predictions are in agreement with
the experimentally measured data. In the case of C2 H2 and C2 H4 pyrolysis, the
5. DETAILED KINETIC MODELS OF SOOT FORMATION
62
polyyne pathway was found to play a dominant role in the soot formation process.
These conclusions were observed by simply excluding one or another submodel from
the soot formation scheme during the calculations. According to these tests, the
kinetic scheme cannot predict the experimentally measured values of the soot yield
if, the polyyne pathway is excluded from the model and only the HACA pathway is
active.
Pyrolysis of methane and benzene
Methane is a fuel with many practical applications, known as one of the major
components of natural gas. Combustion products of methane have the highest
H2 O/CO2 ratio due to its highest H/C ratio. It is also considered to be among
the least-polluting fuels available. However, previous studies showed that even in
non-sooting methane flames the concentration of PAH molecules may be significant
[196].
Tanke [195] studied the soot formation in CH4 /Ar mixtures at different pressures
with the cw-laser extinction technique (Figures 5.21 and 5.22). The model predictions coincide well with the experimentally measured values of the induction time at
low temperatures, whereas at higher temperature both the induction delay time and
the soot yield are overpredicted. Additional investigations showed that in the case
of CH4 pyrolysis the HACA pathway dominates in the soot formation, especially at
low temperatures. With the temperature increase the contribution of the polyyne
pathway in the soot formation becomes equal to the HACA. A similar effect was
observed also in the case of C6 H6 pyrolysis. Two different sets of experiments were
simulated for the case of benzene pyrolysis [195, 81, 82].
In the work of Tanke [195], the conversion of benzene to soot is measured by the
attenuation of the light beam from a HeNe laser (λ = 632.8 nm). The light extinction profiles are converted into soot yield profiles with the help of Beer’s law.
The refractive index and density of soot particles are given as m = 1.57 - 0.56i and
1.86 g/cm3 . The experiments are carried out under elevated pressure, near 50.0 bar,
for various carbon atom concentrations in the initial mixture (4.0, 1.0, 0.8, and 0.4
mol/m3 ) at a reaction time of 1.5 ms. In these experiments, the temperature and
concentration dependences of the soot yield and the induction delay time are quantitatively determined. For these particular cases, the experimentally measured curve
for the maximum soot yield appears at about 1800 K, whereas the kinetic model
predicts this maximum at about 2000 K (Figure 5.23). The calculated induction
5. DETAILED KINETIC MODELS OF SOOT FORMATION
63
Figure 5.21: Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of CH4 /Ar mixtures for several
different carbon atom concentrations: (circles) p = 55.0 bar, [C] = 6.4 [mol/m3 ]; (squares)
p = 55.0 bar, [C] = 3.4 [mol/m3 ]; (inverse triangles) p = 120.0 bar, [C] = 4.0 [mol/m3 ];
(triangles) p = 25.0 bar, [C] = 3.0 [mol/m3 ]; (diamonds) p = 55.0 bar , [C] = 1.7 [mol/m3 ].
Figure 5.22: Induction delay time measured (closed symbols) [195] and simulated (open
symbols and lines) during pyrolysis of CH4 /Ar mixtures at conditions as in Figure 5.21.
times coincide very well with the experimental measurements (Figure 5.24).
5. DETAILED KINETIC MODELS OF SOOT FORMATION
64
Figure 5.23: Temperature dependence of the soot yield measured (closed symbols)
[195] and simulated (open symbols and lines) during pyrolysis of C6 H6 /Ar mixtures at
p = 50.0 bar, and tr = 1.5 ms, for four different C atom concentrations: (circles) [C] =
4.0 [mol/m3 ], (squares) [C] = 1.0 [mol/m3 ]; (triangles) [C] = 0.8, (diamonds) [C] = 0.4
[mol/m3 ].
Figure 5.24: Induction delay time measured (closed symbols) [195] and simulated (open
symbols) during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure 5.23.
Strake et al. [81, 82] measured the formation of soot particles during benzene pyrolysis for four different C6 H6 /Ar mixtures (0.25%, 0.5%, 1%, and 2% C6 H6 ) at
5. DETAILED KINETIC MODELS OF SOOT FORMATION
65
Figure 5.25: Temperature dependence of the soot yield measured (closed symbols) [81, 82]
and simulated (open symbols and lines) during pyrolysis of C6 H6 /Ar mixtures at p =
1.2 bar, tr = 1.3 ms, and for three different reactive mixtures: (squares) 2 %, (circles) 1 %,
(triangles) 0.5 %.
Figure 5.26: Induction delay time, measured (closed symbols) [81, 82] and simulated
(open symbols) during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure 5.25.
pressures 1.0 bar - 1.3 bar behind a reflected shock wave.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
66
For the cw-laser extinction measurements, a conventional 20 mW HeNe laser (λ
= 632.8 nm) is used. The refractive index and density of soot particles are given
as m = 1.90 - 1.0i and 1.86 g/cm3 . The model predictions (Model-1) are in very
good agreement with the experimentally measured soot yield and induction delay
time for all mixtures presented in Figures 5.25 and 5.26. Possible reasons for the
different behaviour of the model with respect to the different sets of experimental
data [81, 195] could be:
• the choice of the refractive indexes ,
• different experimental conditions (pressure),
• insufficient choice of the kinetic data with respect to the pressure dependence
of the rate coefficients included in the model.
It is important to note that the extinction method requires knowledge about the
soot particle refractive index (m), which is subject to large uncertainty. There is
a considerable difference between the refractive indexes used in both experiments
[81, 195]. Smyth and Shaddix [197] studied the influence of the choise of m on the
final results for the amount of soot measured with an extinction technique. They
pointed out that the soot volume fraction may differ by almost a factor of 2, using
different values for m.
The experimentally measured (by the time-resolved LII method), and calculated
temperature dependences of the mean soot particle radius during pyrolysis of benzene/argon mixtures are shown in Figure 5.27 for three different benzene concentrations and tr = 1000 µs. The results of the calculations show the same trend as
the experiment. The particle radius increases with increasing benzene concentration
and follows a bell-shaped curve with respect to the temperature but the maximum
temperature is overpredicted by the model. The time-resolved mean soot particle radius was experimentally studied with the use of the laser induced incandescence (LII)
technique during pyrolysis of various benzene/argon mixtures. A direct comparison
between the experimentally measured data and the simulated values is presented in
Figure 5.28 at p = 1.2 bar and T = 2000 K. A tendency of increasing the mean
particle diameter with increasing the hydrocarbon concentration was observed in
both experiment and calculations. A particular difference between the experimentally measured and calculated values of the mean soot particle radius was observed
at low and high temperatures. At high temperatures, the detailed kinetic model
(Model-1) usually overestimates the soot yield and the mean particle radius. Due to
one of the main assumptions of the model, after a particular time all soot particles
5. DETAILED KINETIC MODELS OF SOOT FORMATION
67
Figure 5.27: Mean particle radius measured (closed symbols) [81, 82] and calculated
(open symbols and lines) during pyrolysis of three different C6 H6 /Ar mixtures: (squares)
2 %, (circles) 1 %, (triangles) 0.5 %, for tr = 1.0 ms at p = 1.2 bar.
Figure 5.28: Time history of the mean particle radius measured (closed symbols) [81,
82] and calculated (open symbols and lines) during pyrolysis of four different C6 H6 /Ar
mixtures: (squares) 2 %, (circles) 1 %, (triangles) 0.5 %, (inverse triangles) 0.25 % at
p = 1.2 bar.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
68
are considered as active which allows them to react with the gas-phase molecules
up to the end of the observation time. In practice, soot particles become inactive
with time and temperature, and their growth is interrupted. To solve this problem
systematically, it is necessary to consider the kinetics of the non-stationary distribution of active sites on the surface of soot particles, which at the current status of
the Galerkin technique was not possible. Therefore, in Model-1 only two extremes
were considered: active and inactive soot particles.
The difference observed at low temperatures cannot be explained only by the insufficient surface growth rate of soot particles in the kinetic model, because the increase
of this rate will result in reduced induction delay times and in increased soot yield.
A rapid heating of soot particles may produce chemical and physical changes of the
soot particle structure: the formation of unusual shell structures, the formation of
pores and porous material in the inner core. These changes in the soot morphology
can alter the heat transfer characteristics of the heated soot, because the pores inside the spheres will reduce their volume and allow the particles to cool faster than
the equivalent solid particles. Implementation of these phenomena in the present
model would improve considerably the predictions, but there is still a great lack of
detailed understanding and interpretation of the soot formation process.
Pyrolysis of benzene/acetylene and acetylene/hydrogen mixtures
Knorre et al. [78] studied the influence of C2 H2 additives on the soot formation
during pyrolysis of C6 H6 at elevated pressure (6.0 bar-60.0 bar) with the cw-laser
extinction technique. In Figure 5.29 the simulated results of the soot formation
time history during pyrolysis of a benzene/acetylene = 3:1 mixture, at pressure
60 bar for four different temperatures, are plotted against the experimentally observed data. The model overestimates the soot yield at high temperatures, but
it clearly demonstrates the tendency of decreasing the induction time with the
temperature increase. This effect was also confirmed in Figure 5.30, where the
Arrhenius-type plots of the experimentally measured and calculated results of the
induction time (τ ) are presented for various benzene/acetylene mixtures and compared to the pure C2 H2 /Ar and C6 H6 /Ar mixtures. A good agreement between
the experimentally measured and calculated values of the induction time for acetylene/argon mixture was observed, and a particular discrepancy for benzene/argon
and benzene/acetylene/argon mixtures. The experimentally determined [78] induction period for the different benzene/acetylene/argon mixtures lies between those
for the pure hydrocarbons. In contrast to the experimentally measured results, the
5. DETAILED KINETIC MODELS OF SOOT FORMATION
69
Figure 5.29: Soot formation time history measured (closed symbols) [78] and simulated
(open symbols and lines) during pyrolysis of a diluted in argon C6 H6 /C2 H2 = 3/1 mixture
([C] = 1.2·10−6 [mol/cm3 ]) at p = 60 bar for various temperatures: (circles) T = 1676 K,
(squares) T = 1789 K, (triangles) T = 1806 K, (inverse triangles) T = 1880 K.
model predictions show that τ for all benzene/acetylene mixtures is shorter than
that obtained for pure benzene/argon mixtures. Interestingly, the acetylene is the
key species in both HACA and polyyne pathway of soot precursor formation and
growth in Model-1.
A direct comparison between the experimentally measured and the calculated results of the normalised soot growth rate coefficient (kf /[C]) for benzene, acetylene,
benzene/acetylene (B/A), and acetylene/hydrogen mixtures at pressure 60 bar is
presented in Figure 5.31. The model properly describes the difference of the kf
values for benzene and acetylene at the low temperatures, but cannot describe
the sharp decrease of the kf values for the pure acetylene/argon and some benzene/acetylene/argon mixtures at high temperatures. As discussed above, these
discrepancies can be described by the fact that an additional approach, describing
the dynamics of the distribution of the active sites on the soot particles surface,
is needed.
The experimentally measured [78] and calculated temperature dependencies of the soot yield in pyrolysis of benzene/argon, acetylene/argon and
benzene/acetylene/argon mixtures are presented in Figures 5.32 to 5.34. The model
overestimates the soot yield for the case of benzene and benzene/acetylene mixtures at the maximum soot yield and higher temperatures, but describes well the
bell-shaped temperature dependence of the soot yield. The influence of acetylene
5. DETAILED KINETIC MODELS OF SOOT FORMATION
70
Figure 5.30: Arrhenius-type plot of the experimentally measured (closed symbols)
[78] and calculated (open symbols) induction time τ for mixtures with various benzene/acetylene ratios (B/A) at pressure 60 bar: (circles) benzene, [C] = 4.0·10−6 mol/cm3 ;
(squares) acetylene, [C]= 4.0 · 10−6 [mol/cm3 ]; (inverse triangles) B/A = 10/1, [C]=
9.0 · 10−6 [mol/cm3 ]; (diamonds) B/A = 1/1, [C]= 5.0 · 10−6 [mol/cm3 ]; (triangles) B/A
= 2.5/1, [C]= 12.0 · 10−6 [mol/cm3 ]; (hexagons) benzene; only the HACA pathway of soot
formation was active, [C]= 4.0 · 10−6 [mol/cm3 ].
additives on the soot formation in benzene/argon mixtures demonstrates a complex,
nonlinear character. The C2 H2 added to benzene results in a decrease of the induction time for all investigated mixtures. The concentration of soot particles and soot
precursors decreased steadily from the maximum value for the pure benzene/argon
mixture to the minimum value for the pure acetylene/argon mixture. The model
does not demonstrate significant pressure dependence of the soot yield, but shows
an essential dependence of the induction delay time, the soot growth rate constant,
and the soot yield on the carbon atom concentration. It predicts properly the induction time for pure benzene/argon mixtures, but considerably overestimates the
soot yield. The maximal soot yield appears at higher temperatures in the case of
pure benzene and benzene/acetylene mixtures. On the other hand, the calculated
values of τ (Figure 5.30) in the case of acetylene pyrolysis differ from the experimentally measured ones, whereas the simulated soot yield is in good agreement with
the experiments.
The temperature dependence of the soot yield was calculated for a pure benzene/argon mixture, when only the HACA route was active, and compared with
5. DETAILED KINETIC MODELS OF SOOT FORMATION
71
Figure 5.31: Temperature dependence of the normalised observable rate of soot particle growth (kf /[C]) measured (closed symbols) [78] and calculated (open symbols) during
pyrolysis of benzene, acetylene, benzene/acetylene (B/A), and acetylene/hydrogen mixtures at pressure 60 bar: (circles) benzene, [C] = 4.0 · 10−6 [mol/cm3 ]; (squares) [C] =
4.0·10−6 [mol/cm3 ]; (inverse triangles) B/A = 10/1, [C]= 9.0·10−6 [mol/cm3 ]; (diamonds)
B/A = 1/1, [C]= 5.0·10−6 [mol/cm3 ]; (triangles) B/A = 2.5/1, [C]= 12.0·10−6 [mol/cm3 ];
(hexagons) C2 H2 /H2 = 1/1, [C]= 2.0 · 10−6 [mol/cm3 ].
Figure 5.32: Temperature dependence of the soot yield measured (closed symbols)
[78] and calculated (open symbols and lines) during pyrolysis of C6 H6 /Ar, [C] = 4.0
·10−6 [mol/cm3 ], and C2 H2 /Ar, [C] = 4.0 ·10−6 [mol/cm3 ] mixtures at p = 6.0 bar.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
72
Figure 5.33: Temperature dependence of the soot yield measured (closed symbols) [78]
and calculated (open symbols and lines) during pyrolysis of C6 H6 /C2 H2 /Ar mixtures,
(triangles) B/A = 2.5/1 [C] = 9.0 ·10−6 [mol/cm3 ], (inverse triangles) B/A = 1/1, [C] =
5.0 ·10−6 [mol/cm3 ], (diamonds) B/A =1/2.5 [C] = 9.0 ·10−6 [mol/cm3 ] at p = 6.0 bar/cm3 .
Figure 5.34: Temperature dependence of the soot yield obtained during pyrolysis of
benzene ([C] = 4.0 · 10−6 mol/cm3 ) at p = 6 bar: (closed circles) the experimental measurements [78], (open circles and line) the calculated results performed with Model-1,
(open hexagons and line) the results of calculation performed with Model-1, when only
the HACA pathway of soot formation (Table 5.1) was active.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
73
Figure 5.35: Temperature dependence of the soot yield measured (closed symbols)
[78] and calculated (open symbols and lines) during pyrolysis of C2 H2 , C2 H4 , and
C2 H2 /H2 diluted in argon mixtures: (squares) C2 H2 , [C] = 4.0·10−6 [mol/cm3 ]; (circles) C2 H4 , [C] = 4.0·10−6 [mol/cm3 ]; (inverse triangles) C2 H2 /H2 = 1/1, [C] = 4.0·10−6
[mol/cm3 ]; (triangles) C2 H2 /H2 = 1/1[mol/cm3 ], [C] = 2.0·10−6 [mol/cm3 ] mixtures at
p = 6.0 bar.
the experimentally measured and simulated results of the soot yield for the same
mixture composition and reaction conditions (Figure 5.34). Within the low temperature range, the pure HACA route considerably underestimates the soot yield,
but describes it quite satisfactory at higher temperatures, whereas Model-1 overestimates the SY. Additional tests showed that the best agreement, between Model-1
and the experimentally measured soot yield can be achieved if the polyyne pathway
is excluded from the surface growth reaction mechanism.
In Figure 5.35 the experimentally measured [78] temperature dependences of the soot
yield in pyrolysis of acetylene/argon, ethylene/argon, and acetylene/hydrogen/argon
mixtures was compared with the calculated results. The model predictions confirmed
the experimentally obtained soot suppression effect on the soot yield of the hydrogen
additives to the acetylene/argon mixtures. As a result, the induction time becomes
longer (Figure 5.30) and the soot yield lower (Figure 5.35) in comparison to the pure
acetylene/argon mixture.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
5.2.3
74
Hydrocarbon oxidation behind shock waves
Oxidation of methane, n-propane and n-heptane
Soot formation is experimentally studied [198] during rich oxidation of CH4 , C3 H8 ,
and n-C7 H16 /Ar mixtures behind shock waves. A combination of extinctionscattering techniques (λ = 488 and 632.8 nm) is used from the authors [198] for
the time-resolved measurements of soot particle diameter and number density, and
a traditional extinction technique is applied to determine the soot yield. In Figure
5.36, the experimentally measured and calculated values for the soot yield of the rich
oxidation of CH4 , C3 H8 , and n-C7 H16 /O2 /Ar mixtures are presented. The mixtures
are selected in such way that the difference in the soot yield for the three hydrocarbons must be insignificant. Nevertheless, the model prediction in the case of propane
oxidation shows different behaviour of the soot yield in comparison to the experimental data [198]. In the case of hydrocarbon combustion, most of the fuel molecules
Figure 5.36: Temperature dependence of the soot yield measured (closed symbols) [198]
and calculated (open symbols and lines) during rich oxidation of CH4 , [C] = 7.6 [mol/m3 ];
C3 H8 [C] = 6.0 [mol/m3 ]; n-C7 H16 [C] = 5.9 [mol/m3 ] at φ= 5 and p = 40 bar.
are destroyed by oxidation or thermal decomposition, and numerous intermediate
species are formed. In this way, a competition between the molecular growth and
oxidative reactions occurs. Although most of the intermediates are oxidised, many
of the carbon-containing species may participate in the molecular growth process.
Oxidative reactions lead to the formation of various oxygen-containing intermedi-
5. DETAILED KINETIC MODELS OF SOOT FORMATION
75
Figure 5.37: Temperature dependence of the experimentally measured (closed symbols) [198] and calculated (open symbols and lines) soot yield during rich oxidation of
n-C7 H16 /Ar mixture (99 % Ar, 0.3125 % C7 H16 , and 0.6875 % O2 ) at constant argon
concentration: (circles) p = 30 bar, (squares) p = 40 bar, (diamonds) p = 50 bar.
ates and products like CO, CO2 , and H2 O. As a result, the soot yield decreases
compared to the case of hydrocarbon pyrolysis.
The influence of the carbon atom concentration on the soot yield was studied experimentally [198] and numerically in n-heptane rich oxidation behind reflected shock
waves. The effect of increased C-atom concentration is presented in Figure 5.37,
where the soot yield is plotted against the temperature for a mixture of 99 % Ar,
0.3125 % C7 H16 , and 0.6875 % O2 , and the pressure is varied from 30 bar, 40 bar,
to 50 bar. The simulations showed the weakest rise of the soot yield at the highest
pressures (p = 50 bar).
5.3
Description of Model-2
Recent progress in the development and understanding of the chemistry of polycyclic aromatic hydrocarbons [52, 24, 199, 200, 160] provided foundation for further
improvement of the kinetic modeling of soot formation.
Violi [52] suggested a theoretical model for PAH growth and soot particle inception
5. DETAILED KINETIC MODELS OF SOOT FORMATION
76
in aliphatic and aromatic flames, using kinetic Monte-Carlo and molecular dynamics
techniques. The authors proposed a model, describing the growth of polycyclic aromatic hydrocarbons, in which the structural parameters like bonds, bond angles, and
dihedral angles are preserved as the soot precursors evolve into three-dimensional
structures. The model is applied in acetylene and benzene premixed flames simulation and describes the differences in the soot precursors born in these systems with
respect to their H/C ratio, particle sphericity, and depolarisation ratio. In this work
[52], two main reaction sequences were considered as possible pathways that contribute to the aromatic growth and soot particle inception. The PAH grow through
the traditional HACA mechanism [46] and a radical-molecule sequence of reactions,
involving five-membered ring PAH, present at large concentrations in the reacting
mixture. In the context of the model [52], soot precursors with different structure are
formed in the case of benzene and acetylene flames. The results of their calculations
showed that the structures formed in aromatic flames are mostly species with 3D
characteristics, whereas the species formed in aliphatic flames have mainly planar
structures, and the contribution of C2 H2 for this case is significant. These results are
in agreement with the findings reported by Homann et al. [20, 3]. The authors [20]
determined experimentally the C/H ratios in both acetylene and benzene flames. In
the case of acetylene flames, the results confirmed that soot nucleation starts with
the formation of PAH structures, while further growth results in the formation of
PAH with unique structures of totally condensed hexagons. Their investigation of
benzene flames [3] shows a variety of possible PAH structures possessing different
C/H ratios. An important conclusion is that either in benzene or acetylene flames
the observed C/H ratios of the hydrocarbon species formed considerably differ from
those that would be observed in the case of fast polymerisation of polyynes.
Frenklach et al. [21, 105] introduced the hypothesis of chemical similarity, confirming
that the surface of soot particles is assumed to look like the edge of a large PAH
molecule covered with C/H bonds. Abstraction of H atom from the surface releases
active sites by forming surface radicals. Richter et al. [57, 24] also described the
formation of active sites on PAH molecules as a result of H atom abstraction. These
sites provide a chemical basis for reactive coagulation of PAH compounds with each
other and with small radicals.
Recent experimental work of Öktem et al. [4] confirmed that the freshly nucleated
soot is built primarily of PAH. The authors observed that the soot nucleation and
the mass growth at the early stage are dominated by the aromatics, and that the
reaction of aliphatic species with pre-existing soot surface must be an important
factor at the later stages of soot mass growth.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
77
The goal of the proposed work was the development of a detailed kinetic model of
soot formation based on the comprehensive models of PAH formation and growth
[57, 24, 23, 42, 201]. The concepts of soot particle nucleation was described through
a combination of different pathways of PAH formation and growth, soot particle
inception published in [52, 24, 199, 200, 160], and the traditional HACA route
of PAH and soot particle growth [21, 1, 23]. The model was initially developed
and applied for soot formation simulation in shock-tube pyrolysis and oxidation of
toluene, n-heptane, and toluene/alcohol mixtures [188]. It was further extended
and applied for soot formation simulation of methane, ethylene, benzene and nheptane pyrolysis and oxidation of methane and propane in conditions typical of
shock tube experiments. The main idea taken from the models listed above is that
the particle mass increases by their reactions with the gaseous species simultaneously
with particle size growth by collision reactions among the PAH species.
5.3.1
Gas-phase reaction mechanism
The developed kinetic model consists of a gas phase reaction mechanism, which
describes the pyrolysis and oxidation of the parent hydrocarbons, and the formation
and growth of PAH through different reaction pathways up to coronene. The gasphase reaction mechanism is a combination of the recently evaluated mechanism of
C1 -C4 hydrocarbon oxidation [190], the C2 mechanism of Appel et al. [23], and a
set of reactions of C3 -, C5 -,C6 - and C7 -hydrocarbons presented in [57, 201, 189].
The formation and growth of polycyclic aromatic hydrocarbons is based on the
HACA model evaluated for laminar premixed acetylene and ethylene flames [1, 46]
with all modifications presented in [23]. The PAH nomenclature from [1, 46, 23]
was adopted in the current mechanism. The abbreviation Ai was use to describe
a PAH, where the index i denotes the number of benzene rings included in the
PAH molecule. Additional reaction paths of PAH formation and growth for PAH
between benzene and pyrene (A1 -A4 ) published in [24], were included in the reaction
scheme. The large polycyclic aromatics up to coronene (A4 -A7 ) were introduced by
several reaction paths, adopted from [24]. As a result, the following pathways of
PAH formation and growth were incorporated in the reaction mechanism:
• the alternating H-abstraction/C2 H2 -addition (HACA) route, resulting in a successive growth of PAH,
• the combination reactions of phenyl with C6 H6 ,
• the cyclopentadienyl recombination,
5. DETAILED KINETIC MODELS OF SOOT FORMATION
78
• the ring-closure reactions of aliphatic hydrocarbons,
• the recombination reactions between Ai R and aliphatic radicals (R is a small
aliphatic radical).
The reaction mechanism contains approximately 2350 direct and reverse elementary reactions between 230 different species. The corresponding thermodynamic
data for all gas-phase species was taken from the available literature sources of the
mechanisms cited above and the thermodata database of Burcat and Ruscic [202].
The main differences between the gas-phase mechanism of Model-2 and the gasphase mechanism of Model-1 (see Sections 5.1.1 and 5.1.2 in this Chapter) are as
follows:
• A set of reactions of polyyne hydrogenation and decomposition [42, 43] was included in Model-2. This strategy provided different behaviour of the polyynes,
whose concentration decreases approximately by one order of magnitude with
increasing number of carbon atoms in the polyyne molecule. The higher
polyynes (C10 H2 and C12 H2 ) were excluded from the scheme because of lack
of thermodynamic data.
• Numerous reactions with participation of aliphatic hydrocarbons (C3 , C5 , C6 ,
C7 , and C8 ) [57, 189, 201, 42, 43] leading to the formation of benzene, phenyl
and higher PAH were included in the model (the reactions in Chapter 3.1.1 3.1.3).
• The variety of reaction paths of PAH formation and growth included in Model2 made it possible to describe the process of soot formation in the case of
pyrolysis and oxidation of hydrocarbons with both aliphatic and aromatic
structures, without necessity to include the polyynes in the particle inception.
5.3.2
Soot precursor and particle inception, growth, coagulation and oxidation
The formation, growth, oxidation and coagulation of soot precursors and soot particles are described with the use of the discrete Galerkin method [180, 68, 71],
described in Chapter 4. The large PAH were considered as soot precursors. Their
mean diameter has value between 1 nm and 2 nm. These values are in agreement with the experiential measurements of young soot particle size reported in
5. DETAILED KINETIC MODELS OF SOOT FORMATION
79
[81, 82, 24, 203, 204]. The C/H ratios of the soot precursors formed during these
reactions are close to the upper boundary of the C-H diagram reported in [3]. In
the present model the precursors are formed mainly by radical-molecule reactions
of different PAH including species with five- and six-membered rings [57, 24, 52].
The radical-radical reactions play a minor role; therefore they were reduced to a
minimum. These reactions result in the formation of polyaromatic molecules (soot
precursors) containing from 24 to 46 carbon atoms, which are stabilised by the formation of new chemical bonds. All reactions with participation of soot precursors
and particles are specified in Table 5.2. The precursors grow by the HACA mechanism, where the initiation of PAH radicals occurs in H-abstraction reactions with H
and OH radicals described in details in [24]. Termination reactions with H atoms,
H2 , and H2 O molecules were also included in the model, whose rate coefficients were
adopted from the literature [24]. The reaction flow analysis showed that more than
70 % of the surface growth is due to C2 H2 addition by the reaction described in
the model of Appel et al. [23], with the same rate coefficient. Species like C2 H2 ,
C4 H2 , C6 H2 , and different PAHs are measured in the pyrolysis and oxidation of
aliphatic and aromatic hydrocarbons [35, 36, 5], and are found in rather high concentrations. Therefore, growth reactions with the participation of those species,
and various PAH molecules and their radicals, were also included in the model. The
particle mass increases by their reactions with the gaseous species, simultaneously
with particle-size growth by collision reactions among the PAH species. Soot precursors are oxidised by O and OH radicals and transformed into soot particles in a
first-order reaction of internal conversion, with the formation of new chemical bonds
[58, 65]. In this transformation reaction, the number of active sites in the reacting
system is preserved. The active soot particles grow by interactions with C2 H2 , C4 H2 ,
and C6 H2 , and with PAH molecules and radicals. All types of particles participate
in coagulation reactions for the case of a free-molecular regime. The soot-particle
oxidation takes place in reactions with O and OH radicals [24]. All reactions with
microheterogeneous particles and the respective rate coefficients are listed in Table
2. The rate coefficients were taken from the literature [23, 24, 61]. They were chosen
to coincide with the reaction classes and the size of the PAH involved in a particular
reaction. No investigation of the thermodynamic properties of the aerosol structures
in this model has been done. Therefore, forward and reverse reactions were written
separately.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
80
Table 5.3: Mechanism of formation, surface growth, coagulation, oxidation and transformation of soot precursors
and soot particles (Model-2)
A(a)
Reaction
n(a)
EA
p(b)
Ref.
Soot precursors formation
Molecule-radical reactions
A2C2HA + A2C2HA* → C-H[1] + H
2.0E+12
0.5
0.0
24
(c)
A2C2HB + A2C2HB-3 → C-H[1] + H
2.0E+12
0.5
0.0
24
(c)
A2R5 + A2R5- → C-H[1] + H
2.0E+12
0.5
0.0
24
(c)
P2 + A2R5- → C-H[1] + H
2.0E+12
0.5
0.0
24
(c)
P2 + A2C2HA* → C-H[1] + H
2.0E+12
0.5
0.0
24
(c)
P2 + HA2R5 → C-H[1] + H
2.0E+12
0.5
0.0
24
(c)
BIPHEN + BIPHENH → C-H[1] + H
2.0E+12
0.0
0.0
24
(c)
A3R5 + INDENYL → C-H[1] + H
2.0E+12
0.0
0.0
25
(c)
A2R5HA + A2R5YNE3-4 → C-H[1] + H
2.0E+12
0.0
0.0
26
(c)
P2 + A2R5YNE3-4 → C-H[1] + H
2.0E+12
0.0
0.0
26
(c)
P2 + A3-1 → C-H[1] + H
2.0E+12
0.0
0.0
26
(c)
P2 + A3-4 → C-H[1] + H
2.0E+12
0.0
0.0
26
(c)
A3 + P2- → C-H[1] + H
2.0E+12
0.0
0.0
26
(c)
P2 + A3R5-7 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A2R5YNE1 + A2R5YN3-4 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A2R5YNE3 + A2R5YN3-4 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A2R5YNE1 + A2R5YN4-3 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A2R5YNE4 + A2R5YN3-4 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A2R5YNE5 + A2R5YN3-4 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A3R5 + A2R5- → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A3C2H + A2R5- → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A3 + A3L-1 → C-H[1] + H
2.0E+12
0.0
0.0
28
(c)
A3 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
30
(c)
P2 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
30
(c)
A4 + P2- → C-H[1] + H
2.0E+12
0.0
0.0
30
(c)
A3 + A3C2H2 → C-H[1] + H
2.0E+12
0.0
0.0
30
(c)
A3R5 + A3R5-7 → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A3LR5 + A3LR5-S → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A4 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A4 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A5 + A3R5-10 → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A3LR5 + A5- → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
81
Reaction
A(a)
n(a)
EA
p(b)
Ref.
A4 + A5- → C-H[1] + H
2.0E+12
0.0
0.0
36
(c)
A4 + A6- → C-H[1] + H
2.0E+12
0.0
0.0
36
(c)
A5 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
36
(c)
A6 + A3R5-10 → C-H[1] + H
2.0E+12
0.0
0.0
38
(c)
A6 + A3R5-10 → C-H[1] + H
2.0E+12
0.0
0.0
38
(c)
A6 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
38
(c)
A5 + A5- → C-H[1] + H
2.0E+12
0.0
0.0
40
(c)
A7 + A3R5-10 → C-H[1] + H
2.0E+12
0.0
0.0
40
(c)
A7 + A4- → C-H[1] + H
2.0E+12
0.0
0.0
40
(c)
A5 + A6- → C-H[1] + H
2.0E+12
0.0
0.0
42
(c)
A6 + A5- → C-H[1] + H
2.0E+12
0.0
0.0
42
(c)
A6 + A6- → C-H[1] + H
2.0E+12
0.0
0.0
44
(c)
A7 + A5- → C-H[1] + H
2.0E+12
0.0
0.0
44
(c)
A7 + A6- → C-H[1] + H
2.0E+12
0.0
0.0
46
(c)
Radical-radical reactions
A3R5-7 + A2R5- → C-H[1] + H
2.0E+12
0.0
0.0
??
(c)
A3R5-7 + A3R5-10 → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A4- + A4- → C-H[1] + H
2.0E+12
0.0
0.0
32
(c)
A5- + A5- → C-H[1] + H
2.0E+12
0.0
0.0
40
(c)
A5- + A6- → C-H[1] + H
2.0E+12
0.0
0.0
42
(c)
A6- + A6- → C-H[1] + H
2.0E+12
0.0
0.0
44
(c)
Soot precursors activation-deactivation
C[N] + H → C-H[1]
0.2E+14
0.0
0.0
(d)
CH[N ] + H → C[N ] + H2
0.417E+14
0.0
54.34
(d)
CH[N ] + 0H → C[N ] + H2O
0.18E+14
0.0
19.14
(c)
C[N ] + H2 → C-H[N ] + H
3.9E+11
0.0
45.98
(e)*
C[N ] + H2O → C-H[N ] + OH
0.199E+11
0.0
43.98
(c)*
Growth of soot precursors
C[N ] + C2H2 → C[N +1] + H
8.0E+07
1.56
15.9
2
(d)
C[N ] + C4H2 → C[N +1] + H2
4.0E+13
0.0
50.2
4
(e)
C[N ] + C6H2 → C[N +1] + H2
4.0E+13
0.0
33.5
6
(e)
C[N ] + A3 → C[N +1]
0.12E+13
0.0
18.03
14
(c)
C[N ] + A4 → C[N +1]
0.12E+13
0.0
18.03
16
(c)
C[N ] + A5 → C[N +1]
0.12E+13
0.0
18.03
20
(c)
C[N ] + A6 → C[N +1]
0.12E+13
0.0
18.03
22
(c)
C[N ] + A7 → C[N +1]
0.12E+13
0.0
18.03
24
(c)
C[N ] + A3- → C[N +1]
0.18E+14
0.0
0.46
14
(c)
C[N ] + A4- → C[N +1]
0.18E+14
0.0
0.46
16
(c)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
82
Reaction
A(a)
n(a)
EA
p(b)
Ref.
C[N ] + A5- → C[N +1]
0.18E+14
0.0
0.46
20
(q)
C[N ] + A6- → C[N +1]
0.18E+14
0.0
0.46
22
(c)
Oxidation of soot precursors
C[N +1] + OH → C-H[N ] + CO + H
0.659E+13
0.5
0.0
1
(c)
C[N +1] + O → C-H[N ] + CO
0.672E+13
0.5
0.0
1
(c)
C[N +1] + OH → C[N ] + CO + H
0.659E+13
0.5
0.0
1
(c)
C[N +1] + O → C[N ] + CO
0.672E+13
0.5
0.0
1
(c)
Coagulation of soot precursors
C[N ] + C[M ] → C[N +M ]
4.50E+12
0.5
0.0
(e)
C-H[N ] + C-H[M ] → C-H[N +M ]
4.50E+12
0.5
0.0
(e)
C[N ] + C-H[M ] → C[N +M ]
4.50E+12
0.5
0.0
(e)
Transformation of soot precursors to soot particles
C[N ] → S[N ]
5.0E+04
0.0
0.0
(e)*
C-H[N ] → S-H[N ]
5.0E+04
0.0
0.0
(e)*
Reactions of soot particles
Soot particles activation-deactivation
S[N ] + H → S-H[N ]
0.2E+14
0.0
0.0
(d)
S-H[N ] + H → S[N ] + H2
0.2E+15
0.0
54.34
(c,d)
S-H[N ] + OH → S[N ] + H2O
0.18E+15
0.0
19.14
(c)
S-H[N ] + H2 → -H[N ] + H
3.9E+11
0.0
45.98
(e)*
S[N ] + H2O → S-H[N ] + OH
0.199E+12
0.0
43.98
(c)*
Growth of soot particles
S[N ] + C2H2 → S[N +1] + H
1.2E+09
1.56
15.88
2
(c,d)*
S[N ] + C4H2 → S[N +1] + H2
4.0E+13
0.0
50.2
4
(e)
S[N ] + C6H2 → S[N +1] + H2
4.0E+13
0.0
33.5
6
(e)
S[N ] + A7 → S[N +1] + H
0.12E+14
0.5
0.0
24
(c)
S[N ] + A6 → S[N +1] + H
0.12E+14
0.5
0.0
22
(c)
S[N ] + A5 → S[N +1] + H
0.12E+14
0.5
0.0
20
(c)
S[N ] + A4 → S[N +1] + H
0.12E+14
0.5
0.0
16
(c)
S[N ] + A3 → S[N +1] + H
0.12E+14
0.5
0.0
14
(c)
S[N ] + A6- → S[N +1] + H
0.18E+14
0.5
0.0
22
(c)
S[N ] + A5- → S[N +1] + H
0.18E+14
0.5
0.0
20
(c)
S[N ] + A4- → S[N +1] + H
0.18E+14
0.5
0.0
16
(c)
S[N ] + A3- → S[N +1] + H
0.18E+14
0.5
0.0
14
(c)
Oxidation of soot particles
SH[N +1] + OH → SH[N ] + CO + H
0.659E+14
0.5
0.0
1
(c)
SH[N +1] + O → SH[N ] + CO
0.672E+14
0.5
0.0
1
(c)
S[N +1] + OH → S[N ] + CO + H
0.659E+14
0.5
0.0
1
(c)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
83
Reaction
A(a)
n(a)
EA
p(b)
Ref.
S[N +1] + O → S[N ] + CO
0.672E+14
0.5
0.0
1
(c)
Coagulation of soot particles
S[N ] + S[M ] → S[N +M ]
4.50E+12
0.5
0.0
(e)
SH[N ] + SH[M ] → SH[N +M ]
4.50E+12
0.5
0.0
(e)
S[N ] + SH[M ] → S[N +M ]
4.50E+12
0.5
0.0
(e)
(a) Rate coefficients are expressed by the Arrhenius equation (k = A ·
T n exp(−EA /RT )) in cm3 mol−1 s−1 , where A (cm3 , mol, s), T (K), and EA (KJ/mol).
(b) Index N denotes the number of carbon atoms, which are incorporated into a
particle in each act of interaction with carbon-containing gas-phase species.
(c) Rate coefficients were adopted from the mechanism of Richter et al. [24].
(d) Rate coefficients were adopted from the mechanism of Appel et al. [23].
(e) Rate coefficients were adopted from Vlasov and Warnatz [58].
* The rate coefficient was modified to provide better representation of the experimental results.
Particles with active sites on the surface were expressed as C[N ] (soot precursors)
and S[N ] (soot particles), CH[N ] and SH[N ] denote the particles without active
sites.
The notation S[N ] shows the concentration of soot particles with active sites after
N acts of interaction with various carbon-containing gas-phase species.
5.4
5.4.1
Results Model-2
Validation of the model
To validate the reaction mechanism (Model-2), the experimentally measured concentration profiles of various gas-phase species formed in pyrolysis and oxidation of
different systems were simulated. An integral reaction flow analysis and a global
sensitivity analysis were performed for the case of toluene and n-heptane oxidation.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
84
The experimentally observed and simulated concentration profiles of H atoms, measured in benzene [205] and phenol [206] thermal decomposition behind reflected
shock waves are presented in Figure 5.38. The kinetic model adequately describes
the concentration profiles and predicts the longer induction delay times at the lower
temperatures.
Figure 5.38: Experimentally measured (closed symbols) and calculated results (open
symbols and lines) of the time-resolved concentration profiles of H atoms measured during
shock-tube pyrolysis of C6 H5 OH [206] and C6 H6 [205].
Vaudevan et al. [207] measured the OH radical concentration during toluene oxidation behind reflected shock wave and extracted the induction delay time values
from the OH profiles. Several concentration profiles obtained in toluene and nheptane oxidation were simulated with Model-2 and presented in Figures 5.39, 5.40
and 5.41. The model clearly predicts the shorter ignition delay times with the temperature increase. Following the observations of Vaudevan et al. [207], three regions
can be distinguished in the OH curves. The first region shows a slight increase in
the OH concentration, followed by the appearance of an intermediate plateau at
low temperatures due to the slower toluene decomposition. In the second region,
the OH concentration rises rapidly due to the chain branching and propagation.
In the third region, the rate of formation of OH comes closer to zero. The reaction flow analysis shows that during toluene oxidation the OH radicals are formed
mainly in the reactions H + O2 = O + OH (51%), HO2 + H = OH + OH (21%) and
O + H2 = H + OH (11%), and are consumed in the reactions CO + OH = CO2 + H
(44%) and OH + H2 = H + H2 O (19%). The first reaction (H + O2 = O + OH) was
investigated in details by several authors [208, 43, 209, 210]. This reaction is reported
5. DETAILED KINETIC MODELS OF SOOT FORMATION
85
as the basic chain-branching step in the high-temperature combustion mechanism of
C1 -C4 hydrocarbon combustion [190], which is also part of the Model-2. The OH
profiles formed in toluene and n-heptane oxidation are shown in Figure 5.41. The
coincidence between the experimentally measured and calculated OH mole fraction
profiles is notable for the toluene oxidation (open squares). In contrast, the model
prediction underestimates the OH concentration in the case of n-heptane oxidation
(open triangles). In the experimental data, a quasistationary level of the OH concentration occurs at approximately 300 µs and 800 µs in n-heptane and toluene
oxidation. The effect is reasonably reproduced by the model and probably caused
by the different times of attaining the maximal concentration of CO which consumes
the OH radicals: 232.8 µs for n-heptane and 678.5 µs for toluene [207].
Kern et al. [35] experimentally measured the product concentration profiles during
pyrolysis of toluene, benzene and acetylene with a time-of-flight mass spectrometer. The main products detected from the reflected shock zone were acetylene and
several polyynes (Figures 5.42, 5.43, and 5.44). The pyrolysis of 3.2 % C2 H2 was
investigated at a temperature 2030 K and a pressure 0.39 bar. The comparison
between the experimentally measured and calculated profiles showed a very good
agreement for the three measured species (Figure 5.42). The authors stated that
the most important observation in this set of experiments are the concentration
Figure 5.39: Concentration profiles of OH radicals measured (closed symbols) [207] and
calculated (open symbols and lines) during toluene oxidation: φ = 1, 0.1 % C6 H5 CH3 , 0.9
% O2 , (circles) T = 1689 K, and (triangles) T = 1586 K and p = 1.9 bar.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
86
Figure 5.40: Concentration profiles of OH radicals measured (closed symbols) [207] and
calculated (open symbols and lines) during toluene oxidation: φ = 1, 0.025 % C6 H5 CH3
+ 0.225 % O2 , (triangles) T = 1783 K, p = 1.84 bar; (inverse triangles) T = 1700 K,
p = 1.89 bar; (squares) T = 1648 K, p = 2.03 bar; (diamonds) T = 1607 K p = 2.03 bar.
Figure 5.41: Concentration profiles of OH radicals measured (closed symbols) [207] and
calculated (open symbols and lines) during n-C7 H16 and C6 H5 CH3 oxidation: (triangles)
130 ppm n-C7 H16 , T = 1640 K, p = 2.0 bar; (squares) 1250 ppm C6 H5 CH3 , T = 1648 K,
p = 2.0 bar.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
87
Figure 5.42: Concentration profiles of the main gas-phase species measured [35] and
simulated in pyrolysis of 3.2 % C2 H2 /Ne/Ar mixture at T = 2030 K and p = 0.39 bar
behind reflected shock waves: (squares) C2 H2 , (triangles) C4 H2 · 2, (inverse triangles)
C6 H2 · 10.
plateaus observed for the investigated species during the 800 µs of observation time
at temperature exceeding 2000 K.
Interestingly, the same species were also detected as the main gas-phase products
in the case of high temperature benzene pyrolysis. In Figure 5.43, the calculated
benzene decay profile is plotted versus time, together with the experimental data
[36]. The model overestimates the consumption of C6 H6 during the first 200 µs. The
simulated concentration profiles of C2 H2 , C4 H2 , and C6 H2 (Figure 5.44) follow the
same tendency with the respective experiments. Their concentration decreases with
increasing the number of C atoms in the polyyne molecule, but there is still some
difference between the calculated results and the experimentally obtained values.
The total carbon concentration and the main gas-phase species, measured [35] and
simulated during pyrolysis of a toluene/neon mixture (1.8% C6 H5 CH3 , T = 1900 K,
and p = 0.4) behind reflected shock waves are presented in Figures 5.45 and 5.46.
The simulated total balance of carbon atoms present in the reaction mixture and
the toluene decay profile are in good agreement with the experimentally measured
values. However, the concentration profiles of the gas-phase species C2 H2 , C4 H2 ,
and C6 H2 are underpredicted at longer reaction times.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
88
Figure 5.43: Concentration decay profiles of the fuel molecule measured (closed symbols)
[36] and simulated (open symbols and lines) during pyrolysis of 2.1 % C6 H6 diluted in
(99% Ne-1% Ar) mixture at T = 2190 K, p = 0.52 bar.
Figure 5.44: Concentration profiles of the main gas-phase species measured (closed symbols) [36] and simulated (open symbols and lines) during pyrolysis of 2.1 % C6 H6 at
conditions as in Figure 5.43.
Another study of the thermal decomposition of toluene was presented by Colket
and Seery in [211]. The authors investigated experimentally and theoretically the
rich gas-phase chemistry occurring during toluene pyrolysis. The experiments are
performed in a single-puls shock tube for temperatures 1200 K to 1850 K, pressure
5. DETAILED KINETIC MODELS OF SOOT FORMATION
89
Figure 5.45: Fuel-decay concentration profiles measured (closed symbols) [35] and simulated (open symbols and lines) during pyrolysis of 1.8 % C6 H5 CH3 at T = 1900 K, p = 0.4
bar.
Figure 5.46: Concentration profiles of the main gas-phase species measured (closed symbols) [35] and simulated (open symbols and lines) during pyrolysis of 1.8 % C6 H5 CH3 at
conditions as in Figure 5.45.
10.013 atm and residence time 600 µs. The pyrolytic products are analysed with a
gas-chromatography technique. In the following Figures (5.47 - 5.52), the toluene
decomposition is shown together with the concentration profiles of hydrogen and
5. DETAILED KINETIC MODELS OF SOOT FORMATION
90
Figure 5.47: Experimentally measured [211] concentration of several aliphatic hydrocarbons and the fuel decay profile detected during pyrolysis of 1 % toluene at pressure 10.013
bar and reaction time 600 µs.
Figure 5.48: Concentration profiles of several aliphatic hydrocarbons and the fuel decay
calculated during pyrolysis of toluene at conditions as in Figure 5.47.
hydrocarbons from methane up to pyrene. For most of the investigated species, the
calculated results are in good agreement with the experimentally measured values.
Nevertheless, there are some discrepancies, especially at temperatures above 1600 K.
The consumption of toluene (A1 CH3 ) is overpredicted (Figure 5.50) at T > 1600 K,
as well as the consumption of ethylbenzene (A1 C2 H5 ) in Figure 5.48 and indene in
5. DETAILED KINETIC MODELS OF SOOT FORMATION
91
Figure 5.49: Experimentally measured [211] concentration profiles of aromatic hydrocarbons detected during pyrolysis of 1 % toluene at pressure 10.013 bar and reaction time
600 µs.
Figure 5.50: Concentration profiles of aromatic hydrocarbons calculated during toluene
pyrolysis at conditions as in Figure 5.49.
Figure 5.52. In the last figure, the phenanthrene (A3 ) concentration is overestimated,
although the concentration of its structural isomer anthracene (A3 L) is close to
the measured values. This effect is caused by the slightly higher concentration
of biphenyl (Figure 5.52) which participates in the main chanel of phenanthrene
formation (see RFA diagram, Figure 5.53).
5. DETAILED KINETIC MODELS OF SOOT FORMATION
92
Figure 5.51: Experimentally measured [211] concentration profiles of various polycyclic
aromatic hydrocarbons detected during pyrolysis of 1 % toluene at pressure 10.013 bar
and reaction time 600 µs.
Figure 5.52: Concentration profiles of various polycyclic aromatic hydrocarbons calculated in toluene pyrolysis at conditions as in Figure 5.51.
Integral reaction flow analysis and sensitivity analysis were carried out for the case
of toluene and n-heptane oxidation at the maximum soot yield temperature. The
reaction flow diagrams (Figures 5.53 and 5.58) show the major reaction routes for
the formation of microheterogenoeus particle.
For the case of toluene oxidation (Figure 5.53), an argon-diluted mixture of 1.5 %
toluene and 1.5 % oxygen was studied at conditions typical of shock tube experiments
(T = 1900 K, p = 2.0 bar, and tr = 2.0 ms). According to these results, toluene is
5. DETAILED KINETIC MODELS OF SOOT FORMATION
93
Figure 5.53: Integral reaction flow analysis of the main pathways of soot precursor inception during C6 H5 CH3 /O2 /Ar oxidation at T = 1900 K, p = 2.0 bar, and reaction time
2.0 ms.
Figure 5.54: Sensitivity analysis with respect to benzene during toluene oxidation at
conditions as in Figure 5.53.
consumed in the reactions
A1 CH2 + H = A1 CH3 (43%)
(5.6)
A1 CH3 + H = A1 CH2 + H2 (41%),
(5.7)
A1 CH3 + H = A1 + CH3 (10%),
(5.8)
where mostly benzyl and a small amount of benzene is formed. The same results
are also observed by Colket and Seery in [211]. Furthermore, benzyl is destructed
to phenyl, which gives benzene, in a hydrogenation reaction
A1 CH2 + H = A1 - + CH3 .
(5.9)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
94
Figure 5.55: Sensitivity analysis with respect to ethynylnaphthalene radical (A2 C2 HB)
during toluene oxidation at conditions as in Figure 5.53.
Figure 5.56: Sensitivity analysis with respect to acenaphthylene (A2 R5 ) during toluene
oxidation at conditions as in Figure 5.53.
The phenyl radical is a key species for the PAH formation and growth in the case
of toluene oxidation. Once formed, it delivers benzene and benzyne to the system,
which start different reaction routes of PAH growth (see Figure 5.53). Phenyl hydrogenation is the major chanel of benzene formation (51 %), through a third body
reaction suggested by Appel et al. [23]. Another possible but less likely pathway in
this particular case is the propargyl radical recombination [23]. Benzyne (c-C6 H4 )
forms biphenylene, which further recombines to acenaphthylene (A2 R5 ), a reaction
sequence suggested by Porter and Steifeld [212], Mebel et al. [213], and Richter
et al. [24]. Simultaneously, biphenyl is formed by the ring-ring condensation between benzene and phenyl, and starts an effective chanel of phenanthrene [23] and
acephenanthrylene (A3 R5 ) production [24].
The sensitivity analysis (Figure 5.54), made with respect to benzene formation,
5. DETAILED KINETIC MODELS OF SOOT FORMATION
95
Figure 5.57: Sensitivity analysis with respect to acephenanthrylene (A3 R5 ) during toluene
oxidation at conditions as in Figure 5.53.
showed that the rate-limiting steps are
A1 CH3 + H = A1 + CH3 ,
(5.10)
and
C2 H2 + c-C5 H5 = A1 CH2 .
(5.11)
Both of them are described by Emdee et al. [214], Richter et al. [215] and Rasmussen
et al. [201], with the rate coefficients k = 1.2 · 1013 exp(−21.55/RT ) in cm3 mol-1 s-1 ,
with EA in KJmol-1 and k = 1.73 · 1017 T -1.89 exp(−42.84/RT ) in cm3 mol-1 s-1 , with
EA in KJmol-1 respectively. The rate coefficient of the Reaction (5.11) has negative temperature dependence. Therefore, with increasing temperature the reverse
reaction will dominate, delivering C2 H2 to the system.
The rate-determining reaction with respect to naphthalene and the ethynylnaphthalene radical (5.55) is the formation of 1-phenyl-1,3-butadienyl (A1 C4 H4 ),
C3 H3 + A1 CH2 = A1 C4 H4 + H,
(5.12)
suggested by Marinov et al. [216] and Rasmussen et al. [201], with k = 2.0 ·
1012 cm3 mol-1 s-1 . The phenylbutadienyl radical then forms naphthalene by
n-A1 C4 H4 = A2 + H,
(5.13)
with a rate coefficient k = 1.0 · 1010 cm3 mol-1 s-1 [42]. Marinov et al. [216] and
Rasussen et al. [201] used a temperature dependent coefficient for that reaction
(k = 5.0 · 1037 T -7.4 exp(−322.08/RT ) in cm3 mol-1 s-1 , with EA in KJmol-1 ). In the
present work, no additional investigation was carried out to determine the role of
5. DETAILED KINETIC MODELS OF SOOT FORMATION
96
the different rate coefficients of Reaction (5.13). Another way to form naphthalene
is the recombination reaction of benzyl and the propargyl radical
C3 H3 + A1 CH2 = A2 + 2H.
(5.14)
This is an effective channel, which in the case of toluene pyrolysis is the fastest step
leading to naphthalene. The reaction is described also by Colket and Seery [211] in
their kinetic study of toluene pyrolysis in shock-tube experiments as the dominant
reaction for naphthalene production with k = 6.3 · 1011 cm3 mol-1 s-1 . Rasmussen
et al. [201] used the same values, whereas Richter et al. [24] reported k = 3.0 ·
1012 cm3 mol-1 s-1 , suggested by D’Anna and Violi [217]. In the present mechanism
the value published by Colket and Seery [211] and Rasmussen et al. [201] was
implemented.
Although acenaphthylene is formed mainly by biphenylene recombination, the reaction with highest sensitivity (Figure 5.56) is
C2 H2 + A2 -1 = A2 R5 + H,
(5.15)
with k = 1.9·1031 T -5.26 exp(−90.374/RT ) cm3 mol-1 s-1 , with EA in KJmol-1 [23]. The
rate-determining step with respect to acephenanthrylene (Figure 5.57) formation is
C2 H2 + A3 -1 = A3 R5 + H,
(5.16)
with k = 1.83 · 1013 T 0.295 exp(−62.51/RT ) cm3 mol-1 s-1 , with EA in KJmol-1 [24].
An integral reaction flow analysis and a global sensitivity analysis were performed
during n-heptane oxidation for a n-C7 H16 /O2 /Ar mixture with [C] = 7.89 [mol/m3 ],
and φ = 5 behind shock wave (T = 1750 K, p = 25.0 bar and tr = 2.0 ms). The
reaction flow diagram (Figure 5.58) shows the major routes of benzene formation,
the PAH growth, and the first particle inception. According to these results, benzene
is generally formed in the reaction of two propargyl radicals, adopted from [23] with
k = 5.0 · 1012 cm3 mol-1 s-1 . Several authors studied the kinetics of this reaction and
the possible products. Scherer [205], e.g., suggested that, depending on the product,
k may vary in a wide range (4.5·1012 ≤ k(2C3 H3 =C6 H6 ) ≤ 9.0·1012 cm3 mol-1 s-1 ). In the
present model, this reaction is written in both directions, whereas in the previously
described model (Model-1) it caused a grate reduction of the soot yield for the case
of acetylene pyrolysis. In the current model another important source of A1 is the
fulvene recombination [201]
C5 H4 CH2 = A1 .
(5.17)
5. DETAILED KINETIC MODELS OF SOOT FORMATION
97
Figure 5.58: Integral reaction flow analysis of the main pathways of soot precursor inception during n-C7 H16 /O2 /Ar rich oxidation, [C] = 7.89 [mol/m3 ], φ = 5, at T = 1750 K,
p = 25.0 bar, and reaction time 2.5 ms.
Figure 5.59: Sensitivity analysis with respect to benzene during n-heptane oxidation at
conditions as in Figure 5.58.
The rate-limiting reaction with respect to benzene is the ethynyl radical decomposition
O2 + C2 H = CH + CO2 ,
(5.18)
as C2 H together with the acetylene are the key species for the PAH formation and
growth [218, 219, 13, 220, 21, 193]. Benzene is oxidised to phenol or phenoxy radical.
The second one decomposes to cyclopentadiene and CO, where the cyclopentadiene
in reactions with O, H and OH is dehydrogenated to the cyclopentadienyl radical
5. DETAILED KINETIC MODELS OF SOOT FORMATION
98
Figure 5.60: Sensitivity analysis with respect to acenaphthylene (A2 R5 ) during n-heptane
oxidation at conditions as in Figure 5.58.
Figure 5.61: Sensitivity analysis with respect to acephenanthrylene (A3 R5 ) during nheptane oxidation at conditions as in Figure 5.58.
c-C5 H5 . The recombination of two c-C5 H5 radicals is an efficient channel of naphthalene formation, with k = 5.0 · 1012 exp(−33.49/RT ) cm3 mol-1 s-1 and EA in KJmol-1 ,
suggested by Richter et al. [24]. In the present reaction mechanism, the growth of
PAH follows several basic pathways. Naphthalene is produced except by the c-C5 H5
recombination, Reactions 5.13 and 5.14, and also in the reaction
A1 − +C4 H4 = A2 + H,
(5.19)
which was adopted from the model of Appel et al. [23] with k = 3.3 ·
1033 T -5.7 exp(−106.692/RT ) in cm3 mol-1 s-1 and EA in KJmol-1 .
The rate-limiting step with respect to acenaphthalene is
A2 -1 + C2 H2 = A2 R5 + H,
(5.20)
with k = 1.9 · 1031 T -5.26 exp(−90.37/RT ) cm3 mol-1 s-1 and EA in KJmol-1 , Appel et
al. [23].
5. DETAILED KINETIC MODELS OF SOOT FORMATION
99
Benzyl and C2 H2 react to form indene (see Figure 5.58) which starts the reaction
route to acephenanthrylene (A3 R5 ). A significant amount of phenanthrene (A3 ) is
produced in from indene and c-C5 H5 . The rate-limiting steps for the acephenanthrylene formation are
A3 -1 + C2 H2 = A3 R5 + H,
(5.21)
c-C5 H5 + INDENYLE = A3 + 2H,
(5.22)
(see [24] and [201]) with the rate coefficients k = 1.83 · 1013 T 0.295 exp(−62.51/RT )
in cm3 mol-1 s-1 , and k = 1.0 · 1013 exp(−33.49/RT ) in cm3 mol-1 s-1 respectively, where
EA in both terms is in KJmol-1 . The same data was implemented in the current
scheme. The analysis showed a competition between A3 R5 and its linear isomer
A3 R5 L, which influences the A3 R5 concentration.
5.4.2
Hydrocarbon pyrolysis behind shock waves
Pyrolysis of ethylene
The temperature dependences of the soot yield and the induction delay time obtained in the pyrolysis of C2 H4 /Ar at pressure 50.0 bar for several different mixtures [195] are presented in Figures 5.62 and 5.63. The calculated results are in
good agreement with the experimentally measured parameters. The model reproduces the typical bell-shape type of the soot-yield curve and the broadening effect
on the soot-yield decay with increasing the C-atom concentration in the mixture.
The simulated values of τ are in good agreement with the experimentally measured
ones for the low temperature range, whereas an increase in τ is observed for the
temperatures above the maximal soot yield. This effect is due to the negative temperature dependence of the rate coefficients of many of the reactions leading to PAH
formation, which decreases the speed of formation of the corresponding species at
the higher temperatures and subsequently increases the τ of the soot particle inception. The same tendency was observed for the τ simulations of all systems studied
with the kinetic scheme Model-2.
Pyrolysis of methane and benzene
The calculated results for the soot yield temperature dependence were compared
with the experimentally measured data (Figure 5.64) in the case of CH4 /Ar pyrolysis at different pressure and carbon atom concentration. The experimentally
5. DETAILED KINETIC MODELS OF SOOT FORMATION
100
Figure 5.62: Temperature dependence of the experimentally measured (closed symbols)
[195] and simulated (open symbols and lines) soot yield during pyrolysis of C2 H4 /Ar
mixtures at p = 50.0 bar for three different C-atom concentrations: (circles) [C] = 7.4
[mol/m3 ], (squares) [C] = 4.7 [mol/m3 ], (inverse triangles) [C] = 4.0 [mol/m3 ].
Figure 5.63: Experimentally measured (closed symbols) [195] and simulated (open symbols) induction delay time during pyrolysis of C2 H4 /Ar mixtures at p = 50.0 bar for
three different C-atom concentrations: (triangles) [C] = 7.4 [mol/m3 ], (circles) [C] = 4.7
[mol/m3 ], (squares) [C] = 4.0 [mol/m3 ].
measured results were obtained for reaction time 1.5 ms, whereas the calculated
results were based on tr = 2.5 ms. A strong dependence of the soot yield on the
carbon atom concentration was observed. However, in the lean mixtures, the model
5. DETAILED KINETIC MODELS OF SOOT FORMATION
101
underestimates the soot yield and the induction delay time.
Figure 5.64: Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of CH4 /Ar mixtures for several
different carbon-atom concentrations: (circles) p = 55.0 bar, [C] = 6.4 [mol/m3 ]; (squares)
p = 55.0 bar, [C] = 3.4 [mol/m3 ]; (inverse triangles) p = 120.0 bar, [C] = 4.0 [mol/m3 ];
(triangles) p = 25.0 bar, [C] = 3.0 [mol/m3 ]; (diamonds) p = 55.0 bar , [C] = 1.7 [mol/m3 ].
The experimental data [195, 81, 82] described in detail in Chapter 5.2.2 were chosen
to model the soot formation in the pyrolysis of benzene. In Figures 5.65 and 5.66,
the calculated values of the soot yield and the induction delay time during pyrolysis of various C6 H6 mixtures at elevated pressure 50 bar were compared with the
experimentally obtained data. The model fairly describes the effect of pressure and
carbon atom concentration on the soot yield although the maximum soot yield is
slightly shifted to the higher temperatures (approximately by 100 K). The shocktube measurements of Starke et al. [81, 82] are performed at a pressure of 1.2 bar
and a wide temperature range (1600 K - 2800K). The best agreement between the
calculated and the experimentally measured soot yield was observed for the lean
mixture (0.5 % C6 H6 ). The model predictions reproduced the strong dependence of
the soot yield on the carbon atom concentration, but underestimated the soot yield
for the rich mixtures. In Figure 5.69, the mean particle radius (MPR) is plotted
versus temperature for three different C-atom concentrations which were measured
and calculated at a pressure 1.2 bar and a reaction time 1 ms. The time-resolved
MPR was also studied with Model-2. The simulated and measured results (T = 2000
K and p = 1.2 bar) are presented in Figure 5.70. The maximum MPR simulated
5. DETAILED KINETIC MODELS OF SOOT FORMATION
102
Figure 5.65: Temperature dependence of the experimentally measured (closed symbols)
[195] and simulated (open symbols and lines) soot yield during pyrolysis of C6 H6 /Ar
mixtures at p = 50.0 bar for four different C-atom concentrations: (circles) [C] = 4.0
[mol/m3 ], (squares) [C] = 1.0 [mol/m3 ]; (triangles) [C] = 0.8 [mol/m3 ], (diamonds) [C] =
0.4 [mol/m3 ].
Figure 5.66: Experimentally measured (closed symbols) [195] and simulated (open symbols) induction delay time during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure
5.65.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
103
Figure 5.67: Temperature dependence of the soot yield measured (closed symbols) [81]
and simulated (open symbols and lines) during pyrolysis of C6 H6 /Ar mixtures at p =
1.2 bar, tr = 1.3 ms for three different reactive mixtures: (squares) 2 %, (circles) 1 %,
(triangles) 0.5 %.
Figure 5.68: Induction delay time, measured (closed symbols) [81] and simulated (open
symbols) during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure 5.67.
with Model-2 is shifted by approximately 200 K (Fig. 5.69) and shows values similar to the calculations performed with Model-1 (see Chapter 5.2.2). Both detailed
kinetic schemes (Model-1 and Model-2) underestimate the experimentally measured
5. DETAILED KINETIC MODELS OF SOOT FORMATION
104
Figure 5.69: Mean particle radius measured (closed symbols) [81] and calculated (open
symbols and lines) during pyrolysis of three different C6 H6 /Ar mixtures: (squares) 2 %,
(circles) 1 %, (triangles) 0.5 %, for a fixed reaction time tr = 1.0 ms, at p = 1.2 bar.
Figure 5.70: Time history of the mean particle radius measured (closed symbols) [81] and
calculated (open symbols and lines) during pyrolysis of four different C6 H6 /Ar mixtures:
(squares) 2 %, (circles) 1 %, (triangles) 0.5 %, (inverse triangles) 0.25 % at p = 1.2 bar.
values of the MPR. Nevertheless, the tendencies of increasing the particle size with
the increase of the carbon-atom concentration were satisfactory reproduced.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
105
Pyrolysis of toluene
The soot formation during pyrolysis of various toluene/argon mixtures was experimentally [221] and numerically studied in a shock tube (Figure 5.71) over a wide
temperature range (1600 K - 2400 K) and at a pressure 3.5 bar. The model describes the temperature dependences of the soot yield in a good way. A strong
influence of the carbon atom concentration on the soot yield was observed in both,
experimentally measured and calculated results.
Figure 5.71: Temperature dependence of the experimentally measured (closed symbols) [221] and calculated (open symbols and lines) soot yield during pyrolysis of three
C6 H5 CH3 /Ar mixtures at tr = 2 ms: (triangles) 1.5 % C6 H5 CH3 , p = 3.5 bar; (squares)
1.0 % C6 H5 CH3 , p = 3.3 bar; (diamonds) 0.5 % C6 H5 CH3 , p = 2.5 bar.
Pyrolysis of n-heptane
The soot formation during pyrolysis of n-heptane has been recently studied in shocktube experiments, using a single-wavelength laser extinction method [222]. The
calculated results were compared with the experimentally measured data of the soot
5. DETAILED KINETIC MODELS OF SOOT FORMATION
106
Figure 5.72: Temperature dependence of the soot yield, measured (closed symbols) [222]
and calculated (open symbols and line) during pyrolysis of 0.1 % n-C7 H16 diluted in argon
mixture at p = 20 bar.
Figure 5.73: Induction delay time, measured (closed symbols) [222] and calculated (open
symbols), during n-C7 H16 pyrolysis at conditions as in Figure 5.72.
yield and the induction delay (Figures 5.72 and 5.73). The model fairly represents
the typical bell-shaped curve, the appearance of both the soot-yield maximum and
the induction delay time, but underestimates the values of the maximum soot yield.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
5.4.3
107
Hydrocarbon oxidation behind shock waves
Oxidation of methane, propane, and n-heptane
The detailed kinetic scheme (Model-2) was applied for soot formation simulation
during CH4 , C3 H8 , and n-C7 H16 rich oxidation behind a reflected shock wave [198]. A
direct comparison of the simulations with the experimentally measured values of the
soot yield is presented in Figure 5.74. The simulated methane profile underestimates
the soot yield at the given conditions. The same problem was observed and discussed
in the case of methane oxidation (see Figure 5.64).
Figure 5.74: Temperature dependence of the soot yield measured (closed symbols) [198]
and calculated (open symbols and lines) during rich oxidation of CH4 , [C] = 7.6 [mol/m3 ];
C3 H8 [C] = 6.0 [mol/m3 ]; and n-C7 H16 [C] = 5.9 [mol/m3 ] , at φ= 5 and p = 40 bar.
The experiments were performed at elevated pressures between 15 and 100 bar and
in a wide temperature range (1500 K - 2200 K). The time-resolved soot yield, the
mean soot particles diameter and the logarithm of soot particle number density
measured and simulated during n-heptane rich oxidation behind shock wave are
plotted in Figures 5.75, 5.76 and 5.77. The coincidence between the simulations and
the experiment is notable. Both experimental and theoretical investigations showed
that an increase of the pressure leads to a subsequent increase of the particle number
density and thus the amount of soot.
The temperature dependences of the experimentally measured [198] and calculated
5. DETAILED KINETIC MODELS OF SOOT FORMATION
108
Figure 5.75: Time-resolved soot yield measured (closed symbols) [198] and calculated
(open symbols and line) during n-C7 H16 rich oxidation, φ= 5, [C] = 7.89 [mol/m3 ], T =
1750 K, p = 25 bar.
Figure 5.76: Time-resolved mean particle diameter measured (closed symbols) [198] and
calculated (open symbols and line) during n-C7 H16 rich oxidation at conditions as in Figure
5.75.
soot yield during rich oxidation of argon diluted n-heptane/oxygen mixtures are
presented in Figure 5.78. The model underestimates the soot yield at the highest
pressure, but adequately reproduces the dependence of the soot yield on the ini-
5. DETAILED KINETIC MODELS OF SOOT FORMATION
109
Figure 5.77: Time-resolved soot particle number density measured (closed symbols) [198]
and calculated (open symbols and line) during n-C7 H16 rich oxidation at conditions as in
Figure 5.75.
Figure 5.78: Temperature dependence of the soot yield measured (closed symbols)
[198] and calculated (open symbols and lines) during shock tube rich oxidation of an
n-C7 H16 /O2 /Ar at constant Ar concentration (0.3125 % C7 H16 , % O2 , and 99 % Ar):
(circles) p = 30 bar, (squares) p = 40 bar, (diamonds) p = 50 bar.
tial hydrocarbon concentration. The experimentalists observed that an increase of
pressure at constant carbon density leads to smaller particle sizes, even though soot
5. DETAILED KINETIC MODELS OF SOOT FORMATION
110
Figure 5.79: The pressure influence of the soot yield measured (closed symbols) [198] and
calculated (open symbols and line) during shock tube rich oxidation of an n-C7 H16 /Ar/O2
mixture, [C] = 5.8 [mol/m3 ], φ= 5 for three different pressures 20 bar, 40 bar and 80 bar.
yield is positively enhanced.
A weak pressure dependence of the soot yield was observed experimentally which is
even less in the calculated results (Figure 5.79), although, the pressure was varied
in a wide range.
Oxidation of toluene, toluene/methanol and toluene/ethanol mixtures
The influence of oxygen and oxygen-containing mixtures on soot formation is experimentally studied in [221]. The authors investigated several toluene/oxygen,
toluene/methanol and toluene/ethanol mixtures in a reflected shock. The simulated results followed the same tendencies as in the experimental observations. The
addition of oxygen to toluene not only suppresses soot formation, but also shifted
the soot yield to lower temperature (Figure 5.80). However, the model overestimates the soot yield, because the contribution of the surface oxidation reactions
with the chosen rate coefficients was very small in comparison to the oxidation in
the gas-phase.
The influence on soot by methanol and ethanol additives to toluene is shown in Figures 5.81 and 5.82, respectively. Both methanol and ethanol suppress soot formation,
5. DETAILED KINETIC MODELS OF SOOT FORMATION
111
and this effect becomes significant if methanol exceeds 50% and ethanol exceeds 70%
of the total fuel mixture to be pyrolysed. At high temperatures methanol suppresses
the soot formation more efficiently than ethanol.
Figure 5.80: Temperature dependence of the soot yield experimentally measured (closed
symbols) [221] and calculated (open symbols and lines) during oxidation of three different
C6 H5 CH3 /O2 /Ar mixtures at tr = 2 ms: (triangles) 1.5 % toluene, p = 3, 5 bar; (squares)
1.5 % toluene + 1.5 % O2 , p = 2.0 bar; (diamonds) 1.5 % toluene + 2.5 % O2 , p = 2.0
bar.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
112
Figure 5.81: Temperature dependence of the soot yield experimentally measured (closed
symbols) [221] and calculated (open symbols and lines) during thermal decomposition of
C6 H5 CH3 /Ar and C6 H5 CH3 /CH3 OH/Ar mixtures at tr = 2 ms: (triangles) 1.0 % toluene,
p = 3, 3 bar; (squares) 1.0 % toluene + 1.0 % methanol, p = 2.7 bar; (diamonds) 1.0 %
toluene + 2.0 % methanol, p = 2.7 bar.
5. DETAILED KINETIC MODELS OF SOOT FORMATION
113
Figure 5.82: Temperature dependence of the experimentally measured (closed symbols)
[221] and calculated (open symbols and lines) soot yield during pyrolysis of C6 H5 CH3 /Ar
and C6 H5 CH3 /C2 H5 OH/Ar mixtures at tr = 2 ms: (triangles) 1.0 % toluene, p = 3, 3 bar;
(inverse triangles) 1.0 % toluene + 1.0 % ethanol, p = 3.0 bar; (squares) 1.0 % toluene +
2.0 % ethanol, p = 3.0 bar; (diamonds) 1.0 % toluene + 3.0 % ethanol, p = 3.0 bar.
114
Chapter 6
SIMPLIFIED MODEL OF SOOT
FORMATION
A direct CD simulation of a real three-dimensional technical system, using detailed
chemical mechanisms, is impossible, because it exceeds the available computer capacities. Therefore, a reduced reaction mechanism is needed, which as accurate as
possible describes the chemical reaction system using a smaller number of variables.
A variety of soot models, including simple empirical correlations, relating the amount
of the particles in the exhaust, to the engine operating parameters, the detailed descriptions of the pre-particle chemistry, and the soot particle dynamics, have been
proposed for engine simulations. Tesner et al. [223] suggested a two-step mechanism
of soot formation, considering the formation of radical nuclei and the soot particles.
The model became significantly popular when several slightly modified versions were
applied to simulate different combustion problems [224, 225]. Hiroyasu et al. [226]
proposed a model in which the net rate of change in soot mass is calculated as the
difference between the rates of soot formation and oxidation. Due to its simplicity,
the model has been widely used in Diesel engine simulations [227, 228, 229]. Kollmann et al. [230] suggested a thermochemical model of soot-formation modeling in
a turbulent ethylene diffusion flame. The authors described the thermochemistry of
the flame in terms of a constrained equilibrium model. Soot formation is described
by means of three processes, nucleation, surface growth and oxidation. The author
introduced a temperature dependence of the surface growth by assuming an Arrhenius expression for the growth rate with a given activation energy. Lindstedt [231]
proposed a four-step mechanism of soot formation, in which soot particle nucleation
occurs in reactions of gas-phase species, like benzene and acetylene. Particle growth
6. SIMPLIFIED MODEL OF SOOT FORMATION
115
is described by the process of acetylene addition to the soot particle mass, where
a surface-area function, corresponding to the rate coefficient, is implemented. Oxidation is introduced by a single reaction of soot particles with molecular oxygen,
and the soot particles growth is expressed by their coagulation. The formation and
oxidation are described by global reaction rates, and the coagulation rate is derived
from the collision theory. Belardini et al. [227], Kazakov and Foster [232] and [233]
used a modified version of the Lindstedt’s model, in which acetylene is assumed to be
both soot precursor and growth species, and applied it for Diesel-engine simulation.
Such simple models are usually valid only for certain geometries, and sometimes
their implementation in other codes is computationally expensive or not warranted
due to uncertainties in the other models involved into the global one.
In the present work, a semi-empirical model of soot formation [234, 235, 71, 236] was
modified for soot formation modeling of shock tube experiments, and implemented
into a program package for spatially homogeneous reaction system simulation HOMREA [6]). The complex process of soot formation is described in terms of several
global steps − nucleation, soot particle growth and coagulation, and particle oxidation. For that purpose two differential equations are solved for the temporal change
of soot particle number density and the soot volume fraction [237].
The goal of the present work is to develop a model that connects the complex
(detailed) hydrocarbon combustion chemistry to such a simple two-equation soot
model and effectively describes the soot formation phenomenon. Such models are
suitable for implementation in the KIVA code of Diesel engine simulation [236] or
CFD codes of turbine combustion simulation. The modeling approach is based on
the implementation of the existing detailed gas-phase chemistry of C1 -C7 hydrocarbons combustion including the variety of reactions pathways of PAH formation,
growth, and oxidation described in details in Model-1 and Model-2 (see Chapter 5).
The simplified soot model has been calibrated by experimental shock-tube data for
methane, propane, n-heptane and toluene oxidation, which were previously studied
with the detailed kinetic schemes (Model-1 and Model-2). In the following Chapter,
the simplified model is described in detail, and the simulations are compared with
the experimentally measured results of the soot characteristics during hydrocarbon
oxidation.
6. SIMPLIFIED MODEL OF SOOT FORMATION
6.1
116
Model description
The simplified model of soot formation is described in terms of two variables, in
particular the soot volume fraction (fV , the volume of soot/total volume), and the
soot concentration (CS in mol/cm3 ). The respective source terms initially presented
by Moss et. al [235] take the following form:
Temporal change of soot concentration
dCS
=α−β
dt
(6.1)
Temporal change of soot volume fraction
dfV
=δ+γ−ε
dt
6.1.1
(6.2)
The temporal change of soot concentration
The source equation for the temporal change of soot concentration is expressed by
the nucleation (α) and coagulation processes (β). A widely accepted theory is that
PAH molecules and their radicals are the soot particle precursors [13, 42, 43, 21, 1,
3, 38, 4, 135, 52]. Therefore, the process of soot particle inception is described by
means of the key step in the PAH formation − the formation of the first aromatic
ring in the system. Coagulation was introduced as a process of sticking of two
particles by which larger particles are formed.
Nucleation
Nucleation increases the number of soot particles, and thus, the soot concentration.
The key step for the soot particle inception was considered to be the propargyl
radical recombination (C3 H3 + C3 H3 = C6 H6 ), which delivers the first aromatic ring
(benzene of phenyl) in the system. The reaction flow analysis confirmed that in
many aliphatic fuels this is the reaction producing the highest amount of benzene.
Therefore, the nucleation term has the form
α = αconst · CC2 3 H3 ,
(6.3)
6. SIMPLIFIED MODEL OF SOOT FORMATION
117
where αconst is the rate coefficient of the gas-phase reaction according to the detailed
kinetic models, Model-1 and Model-2,
αconst = 5.0 · 106
m3
.
mol · s
(6.4)
Coagulation
Coagulation decreases the soot number density and diminishes the concentration.
In the current model, coagulation is described by a collision number β [25, 236] and
the soot particle concentration. This term is derived from the chemical equation −
Csoot (N ) + Csoot (M ) = Csoot (N + M ) and can be expressed as
β = βconst · CS2
(6.5)
with a rate coefficient,
βconst
µ ¶1/2
m3
T
.
= 1.0 · 10
K
mol · s
9
(6.6)
It was assumed in the model that 10 benzene molecules are needed to build one soot
particle. Therefore, the nucleation term α (Eq. 6.1) was reduced by a factor of 10
(a simplified approach for the complex rate calculation). Finally, Eq. (6.1) takes
the form,
dCS
α
=
− β.
dt
10
(6.7)
It was assumed that, in an act of oxidation, a single soot particle is not completely
destroyed and the number of soot particles remains unchanged. Surface growth influences the particle size, but does not change the number of soot particles. Therefore,
the last two processes were not included in the term for the temporal change of soot
concentration.
6.1.2
The temporal change of the soot volume fraction
The temporal change of the soot volume fraction (dfV /dt) consists of the following
terms: nucleation, surface growth and oxidation. Nucleation and surface growth
increase the volume fraction whereas oxidation reduces it. Coagulation has no effect
on the volume fraction therefore; it was not included in the equation.
6. SIMPLIFIED MODEL OF SOOT FORMATION
118
Nucleation
The nucleation process was described by means of the same gas-phase reaction of
propargyl radical recombination (see Eq. 6.3), and the nucleation term is
δ = δconst · CC2 3 H3 ,
(6.8)
with a rate coefficient,
2
δconst
(m3 )
= αconst · VS
.
(mol)2 · s
(6.9)
Here, VS is the volume occupied by a soot particle, formed in the nucleation process,
VS =
Msoot m3
,
ρsoot mol
(6.10)
where Msoot is the molar mass (kg/mol) of a soot particle (taken to be that of
C60 H60 ) and ρsoot is the density of soot (1800 kg/m3 ).
Surface growth
Most of the soot in flames is produced as a result of the surface growth (Chapter 5).
The rate of this process depends on the concentration of the available carbon-bearing
species in the particle neighbourhood, on the temperature and on the reactivity of
the particle surface. Therefore, an empirical correlation between the specific surface
growth rates and the concentration of the growth species is needed. The specific
surface growth rate is the volume of the soot added to a particle per unit aerosol
surface area [230]. Previous investigations [161, 1, 24] and the reaction flow analysis,
made for different reaction systems with the use of the detailed chemistry of Model-1
and Model-2, confirmed that the process of acetylene addition to the soot particle
surface dominates the particle surface growth. According to that, the surface growth
term takes into account the attachment of C2 H2 molecules onto the soot particle
surface (e.g., the reaction: Csoot + C2 H2 = Csoot -H + H [1]. The source term is
derived from the gas kinetic theory and gives a first order growth law suggested in
the literature [87, 25, 236, 71],
γ = σSG · VG · ϑe · (fV,∞ − fV ) /fV,∞
1
s
(6.11)
where
σSG = 1.4 · 10−3 = sticking coefficient of the growth species [71], in particular C2 H2 ,
6. SIMPLIFIED MODEL OF SOOT FORMATION
VG =
mG
ρsoot
119
= volume of an adsorbed growth species [m3 ],
mG = mass of the growth species [kg],
ρsoot = 1800 [kg/m3 ] = soot density [238, 239, 195, 80],
ϑe =
√
PG
2πmG kB T
q
·Asoot =
Asoot = π · DS2 · NS = π ·
[m2 /m3 ],
³
kB T
·NA ·CG ·Asoot
2πmG
6fv
πNS
´2/3
= effusion velocity [(1/s m2 ) · (m2 /m3 )],
2/3
· NS = (36πCS NA )1/3 · fV = soot surface density
CG = concentration of an adsorbed growth species [mol/m3 ],
PG = n · kB · T = partial pressure of a growth species [Pa],
kB = R/NA = Boltzman’s constant [m2 kg/s2 K],
NA = 6.023 · 1023 = Avogadro’s constant [1/mol],
q
DS =
3
6fv
πNS
= soot diameter [m],
NS = soot particle number density [1/m3 ],
CS = soot particle concentration [mol/m3 ],
(fV,∞ − fV ) /fV,∞ = empirically obtained term to preserve unrealistically high values
of fV [-], [71].
After the analytical preprocessing, Eq. (6.11) receives the form
2/3
1/3
γ = γconst · fV · CS
1/3
· NA · (fV,∞ − fV ) /fV,∞ ,
where γconst is the rate coefficient
r
σSG NA R mG
γconst =
· (36π)1/3 · T 1/2 · CC2 H2 .
ρsoot
2π
(6.12)
(6.13)
Finally, the surface growth term can be expressed by
1/3
γ = 58.79 · T 1/2 · CC2 H2 · CS
2/3
· fV · (fV,∞ − fV ) /fV,∞ .
(6.14)
The maximum volume fraction fV,∞ can be estimated with an empirical approach.
A curve fit of the fV values is calculated from the experimental results of the soot
concentration measured in flames for numerous hydrocarbons [240, 71] for wide
6. SIMPLIFIED MODEL OF SOOT FORMATION
120
range of operating conditions (pressure, temperature, and mixture composition). It
gives the maximum volume fraction as a function of the excess C-atom concentration
Csurplus (1018 /cm3 ) in the reacting mixture,
1.7
fV,∞ = 1.45 · 10−6 · Csurplus
.
(6.15)
The excess C-atom concentration ( Csurplus ) can be obtained by computing the excess
£¡ C ¢ ¤
C atoms available over a critical C to O ratio O
. This ratio is a specific
crit
characteristic for every fuel and varies with the pressure [25, 67]. Accordingly, the
Csurplus can be calculated by [71],
µ
µ ¶
¶
C
Csurplus = NA · NC,fuel · [Cfuel ]t0 −
· NO,oxidizer · [Ooxidizer ]t0 ,
(6.16)
O crit
where NC,fuel represents the number of the C atoms in a fuel molecule, NO,oxidiser is
the number of O atoms in an oxidiser molecule, and [Cfuel ]t0 and [Ooxidiser ]to are the
initial concentrations of the fuel and the oxidiser, respectively. The disadvantage of
this approach in this particular case is that the Csurplus is measured in flames and no
¡C¢
detailed information about the O
ratio for the investigated hydrocarbons was
crit
found for shock-tube experiments.
Sojka [71] suggested an empirically obtained value for the maximum volume fraction,
fV,∞ = 1.02 · 10−5 ,
(6.17)
obtained in n-heptane rich oxidation behind shock wave. For the calculations presented in this chapter, the same value was used. This enabled better coincidence
between the experimentally measured and the calculated results of the temporal
change of the soot yield, the particle diameter and the number density in the case
of n-heptane rich oxidation.
Oxidation
The oxidation term is calculated similarly to the surface growth, but in this
case the sticking of OH on the soot particle surface was taken into account instead of C2 H2 . Only one type of oxidation reaction is considered in the model
(Csoot -C + OH → Csoot + CHO) [236]. The oxidation term then is given by
2/3
1/3
ε = εconst · fV · CS
1/3
· NA .
The related rate coefficient is calculated by
r
σOX NA R mOH
εconst =
· (36 · π)1/3 · T 1/2 · COH .
ρsoot
2π
(6.18)
(6.19)
6. SIMPLIFIED MODEL OF SOOT FORMATION
121
In this expression mOH is the mass and COH is the molar concentration of the OH
radicals, respectively. The sticking coefficient of OH is σOX = 0.1 [236, 67]. For the
oxidation term can be obtained by
2/3
1/3
ε = 3.4 · 103 · T 1/2 · COH · fV · CS
1
.
s
(6.20)
The nucleation term for the temporal change of the soot volume fraction was reduced
by a factor of 10, analogous to Eq. (6.7), and finally Eq. (6.2) can be written as
dfV
δ
=
+ γ − ε.
dt
10
6.1.3
(6.21)
Rate laws
The rate laws for the gas-phase species, included in the different terms, are influenced
by the soot formation. Therefore, additional terms for the temporal change of the
concentration of C3 H3 , C2 H2 , and OH were introduced in the model (Eq. 6.22 6.24),
dCC3 H3
dCC3 H3
=
− 2 · α,
dt
dt
(6.22)
dCC2 H2
dCC2 H2
ρsoot
=
−γ
,
dt
dt
mC2 H2 NA
(6.23)
dCOH
ρsoot
dCOH
=
−ε
.
(6.24)
dt
dt
mOH NA
In this way, an interaction between the gas-phase and the particulate phase chemistry is taken into account during the entire simulation.
6.1.4
Soot quantities
The soot volume fraction (fV ), the soot particle concentration (CS ) and the particle
diameter (DS ) are the three characteristics of soot formation usually measured by
the experimentalists. These three parameters are mutually dependent, and each of
them can be calculated if the values of the other two are known [67];
π
fV
= NA · · DS3 .
CS
6
The soot particle diameter can be calculated by [67]
r
6 · fV
DS = 3
,
π · CS · NA
(6.25)
(6.26)
6. SIMPLIFIED MODEL OF SOOT FORMATION
122
In the current model, the particle shape was assumed to be spherical, and the particle
number density was calculated by [67]
NS =
fV · ρsoot · NA
.
MC
(6.27)
Here, MC is the molar mass of a C atom and ρsoot is the soot particle density, taken
to be equal to 1.8 in g/cm3 , the density of graphite [238, 239, 195, 80].
The soot yield expresses the fraction of carbon appearing as soot, which usually is
calculated by
SY =
[C]soot
,
[C]total
(6.28)
where [C]soot is the soot concentration
[C]soot = NS ,
(6.29)
and [C]total is the total carbon atom concentration in the system
[C]total = [Cfuel ]initial · NC,fuel · NA .
(6.30)
Here, [Cfuel ]initial is the initial fuel concentration and NC,fuel is the number of C atoms
in a fuel molecule.
6.2
Results
Rich oxidation of methane, propane and n-heptane
The simplified soot model was applied to predict soot formation in methane,
propane, n-heptane and toluene oxidation for a wide range of operating conditions
(T =1600 K - 2300 K, and p = 2 bar - 40 bar) in shock-tube experiments [198]. The
gas-phase chemistry is modeled with the use of the two detailed kinetic schemes
described in Chapter 5 (Model-1 and Model-2). These mechanisms were validated
against the experimentally measured values of the ignition delay time, the soot yield,
the mean particle diameter, and the concentration profiles of different species during pyrolysis and oxidation of various hydrocarbons in shock-tube experiments for
a wide range of operating conditions (see Chapter 5). The mechanism of C1 -C4 hydrocarbon combustion, introduced in the model, is validated against experimental
measurements of the ignition delay time and flame velocity, measured with different
techniques (shock tube, reactive flow experiments and laminar flat flames) [190].
6. SIMPLIFIED MODEL OF SOOT FORMATION
123
The simulations of the gas-phase chemistry and the simplified soot model are performed simultaneously during the whole reaction time. The results obtained with
the use of the gas-phase chemistry of the detailed kinetic model (Model-1) are described as SSM-1 and those performed with the detailed kinetic model (Model-2) as
SSM-2.
A direct comparison between the model predictions and the experimentally measured
soot characteristics soot yield, mean particle diameter and mean particle number
dencity in the case of n-heptane rich oxidation [198] is presented in Figures 6.1 6.3. Both models describe fairly well the time history of the soot yield (Figure 6.1).
The soot yield simulated with SSM-1 is in better agreement with the experiment
within the longer reaction time. This effect is caused by the higher acetylene concentration (see Figure 6.5). The SSM-2 slightly underestimates the experimentally
obtained soot yield at the longer reaction time (tr = 1 ms - 2.5 ms) because of the
slower surface growth, but better matches the initial data at the early stages of the
soot particle inception (tr = 0.0 ms - 0.5 ms). Similar results were observed for
the simulated particle mean diameter. Although both models (SSM-1 and SSM2) underestimate the experimentally measured particle diameter, the calculations
performed with SSM-2 show better agreement over the whole reaction time.
Figure 6.1: Time-resolved soot yield, measured (closed symbols) [198] and calculated
(open symbols and lines) in n-C7 H16 rich oxidation, [C] = 7.89 [mol/m3 ], φ= 5, T = 1750
K, p = 25 bar and tr = 2.5 ms.
The time-dependent concentration profiles of the nucleation (C3 H3 ), the surface
6. SIMPLIFIED MODEL OF SOOT FORMATION
124
Figure 6.2: Time-resolved mean particle diameter, measured (closed symbols) [198] and
calculated (open symbols and lines) in n-C7 H16 rich oxidation at conditions as in Figure
6.1.
Figure 6.3: Time-resolved soot particle number density, measured (closed symbols) [198]
and calculated (open symbols and lines) in n-C7 H16 rich oxidation at conditions as in
Figure 6.1.
growth species (C2 H2 ) and the oxidation agent (OH), involved in the models, are
presented in Figures 6.4 - 6.6. According to them, the faster rise of the particle
size, observed with SSM-1 at tr = 0.0 ms - 0.5 ms, can be explained with the
faster nucleation rate, influenced by the higher C3 H3 concentration. Although the
C2 H2 concentration is considerably higher in the case of SSM-1, there is no big
6. SIMPLIFIED MODEL OF SOOT FORMATION
125
Figure 6.4: Time-dependent profiles of the C3 H3 concentration, calculated at the conditions as in Figure 6.1: (circles) SSM-1 and (diamonds) SSM-2.
Figure 6.5: Time-dependent profiles of the C2 H2 concentration, calculated at conditions
as in Figure 6.1: (circles) SSM-1 and (diamonds) SSM-2.
influence on the soot particle diameter calculated with the SSM-1, which is even
slightly smaller in comparison to the results of SSM-2. The soot particle oxidation
usually takes place at longer reaction time; therefore in the current calculations the
effect of oxidation is minor. This process will be important in the case of flames or
Diesel-engine simulations.
The soot particle number density is similarly described by both models. It starts
6. SIMPLIFIED MODEL OF SOOT FORMATION
126
Figure 6.6: Time-dependent profiles of the OH concentration, calculated at the conditions
as in Figure 6.1: SSM-1 (circles) and SSM-2 (diamonds).
Figure 6.7: Temperature dependence of the soot yield, measured (closed symbols) [198]
and calculated (open symbols and lines) in rich oxidation of n-C7 H16 [C] = 5.9 [mol/m3 ],
φ= 5, p = 40 bar and tr = 2.5ms: (circles) experiment, (triangles) Model-1 and (diamonds)
Model-2.
with a rapid increase of the particle size due to the fast nucleation at the beginning
of the reaction time. Then the particle concentration shows a smooth decrease
and reaches a plateau after tr = 1 ms due to the drop in the concentration of the
nucleation species (C3 H3 ). The behaviour of the soot particle concentration curves
6. SIMPLIFIED MODEL OF SOOT FORMATION
127
Figure 6.8: Temperature dependence of the soot yield, measured (closed symbols) [198]
and calculated (open symbols and lines) in rich oxidation of C3 H8 [C] = 6.0 [mol/m3 ], φ=
5, p = 40 bar and tr = 2.5 ms: (circles) experiment, (triangles) Model-1 and (diamonds)
Model-2.
Figure 6.9: Temperature dependence of the soot yield, measured (closed symbols) [198]
and calculated (open symbols and lines) in rich oxidation of CH4 [C] = 7.6 [mol/m3 ], φ=
5, p = 40 bar and tr = 2.5 ms: (circles) experiment, (triangles) Model-1 and (diamonds)
Model-2.
follows the shape of the propargyl radical profiles (see Figure 6.4).
6. SIMPLIFIED MODEL OF SOOT FORMATION
128
The temperature dependence of the soot yield was also simulated with the use of
the models described above (SSM-1 and SSM-2). In Figure 6.7, the experimentally
measured and calculated soot yield are compared for the case of n-heptane rich
oxidation ([C] = 5.9 mol/m3 ) at a pressure of 40 bar and in a temperature range
1600 K - 2300 K. In this case, both models shift the maximum soot yield towards
high temperatures (by about 200 K). Nevertheless, SSM-2 matches the maximum
soot yield very well, whereas the SSM-1 overestimates it by about 30 %. This effect
is caused by the higher rates of both nucleation and surface growth with respect
to the higher amount of the reactive species in the gas-phase surrounding of SSM1. Similar calculations were performed in the oxidation of argon-diluted methane
and propane mixtures. The results show the similar tendencies as in the case of
n-heptane oxidation (Figures 6.8 and 6.9).
Toluene oxidation
In the case of toluene oxidation (Figure 6.10), the temperature dependence of the
soot yield was simulated during oxidation of a low-pressure (toluene/O2 = 1/1)
mixture only with the SSM-2. Due to the fact that the detailed kinetic scheme
(Model-1) was not further extended to describe the chemistry of toluene, the Model1 was not considered in this simulations. Accordingly, the experimentally measured
[221] results were plotted against the numerical simulations performed with the
detailed kinetic model (Model-2) with the program package MACRON (see Chapter
5), and the SSM-2 with the modified version of the program HOMREA [237]. Both
models (Model-2 and SSM-2) overestimate the maximum soot yield. In the case of
Model-2, it is caused by the small rate of the soot particle oxidation assumed in the
soot submodel, as it was described in Chapter 5. The soot yield simulated with the
SSM-2 is highly overestimated, and the maximum soot yield is shifted by about 200
K in the high-temperature range. The same effect of shifting the maximum soot
yield towards the high temperatures was found also in the case of methane, propane
and n-heptane oxidation (Figures 6.7, 6.8 and 6.9) in the calculations performed with
both SSM-1 and SSM-2. It is caused by the rate of soot particle surface growth. A
reasonable way to avoid this problem can be the implementation of reverse surface
growth and the effect of the temperature dependence on the process.
6. SIMPLIFIED MODEL OF SOOT FORMATION
129
Figure 6.10: Temperature dependence of the soot yield, measured (closed symbols) [221]
and calculated (open symbols and lines) in oxidation of an C6 H5 CH3 /O2 /Ar mixture (1.5
% toluene + 1.5 % O2 ), p = 2.0 bar and tr = 2 ms: (circles) experiment, (diamonds)
SSM-1 (triangles) Model-2.
130
Chapter 7
Conclusion and future prospects
Two different rection mechanisms (Model-1 and Model-2) were developed and applied for soot formation simulation at homogeneous conditions. Both models differ
with respect to the concepts describing the gas-phase and the particulate-phase
chemistry.
Model-1 involves two different pathways of soot formation (polyyne and HACA),
which required the parallel development of two diverse reaction paths and the corresponding gas-phase environment in the reacting mixture. Soot formation simulation
in a time-dependent system, e.g., a shock tube, needs the kinetic representation of
very fast processes that lead to soot particle nucleation at reaction times of several
milliseconds. The combination between the HACA pathway of PAH and soot particles formation and growth and the process of fast polymerisation of polyyne species
offered an efficient solution to the problem. Nevertheles, there are no thermodynamic data and precise reaction kinetics of the higher polyynes (above C8 H2 ).
Latest experimental studies [99, 3, 100, 4, 5] proposed the PAH as the preferable soot
precursors. Several authors [4, 5] suggested that the aliphatic compounds, including
some polyynes, may play an important role in the earlier stages of soot formation
at the PAH growth as well as in the soot particle mass growth. The role of the
polyynes in the soot formation is not yet clearly understood. They are believed to
be destroyed to smaller species at high temperatures. However, all these conclusions
need further experimental and theoretical investigations.
Following these observations, a new detailed kinetic model of soot formation (Model2) was developed. The polyyne molecules were included in several reaction channels
of aromatic molecules formation and in the soot particle surface growth. Particle
7. Conclusion and future prospects
131
inception occurs in radical-radical and radical-molecule reaction of PAH, including polyaromatics containing five-membered rings, formed through various reaction
pathways. Model-2 was successfully applied for the soot formation simulation in
pyrolysis and oxidation of different hydrocarbons and their mixtures.
Due to the different nature of the soot precursors in Model-1 and Model-2, the soot
yield and the induction delay time simulated with Model-1 were slightly overestimated in some of the cases, whereas Model-2 underestimated them at high temperatures. Additional investigations and improvements are needed, which requires
the implementation of newly obtained kinetic and thermodynamic data of the existing reaction paths, additional pathways of PAH formation and growth, and deeper
investigation and understanding of the complexity of the soot formation process.
It is important to note that all numerical results were obtained while keeping the
reaction mechanisms and the entire sets of rate coefficients unchanged for all calculations performed with Model-1 and Model-2. The calculations were performed for
hydrocarbons with different chemical structures and hydrocarbon mixtures within a
wide range of conditions (with respect to temperature, pressure, mixture composition and reaction time). The comparison between the calculated and experimentally
measured results demonstrated qualitatively and in most cases quantitatively good
agreement for the usually measured parameters of soot formation. The temperature
dependence of the soot yield is described by a bell-shaped curve, usually situated
between 1500 k and 2500 K. This interval varies according to the type of the fuel
and the reaction conditions. The gas-phase soot precursors are formed at temperatures above 1000 K. They go through a maximum at about 1600 K - 1700 K that
is followed by a subsequent decrease in their concentrations at higher temperatures
due to their thermal destruction and oxidation.
An empirical (two-equation) model was applied for soot formation simulation during shock-tube oxidation of various hydrocarbons, with the use of the gas-phase
chemistry of two different detailed kinetic schemes (Model-1, and Model-2). The
gas-phase chemistry and the soot model were simultaneously calculated. The numerical results confirmed that the soot formation strongly depends on the kinetic
representation of the gas-phase chemistry. The different kinetic schemes determined
a distinct behaviour of the gas-phase species chosen as soot precursors, growth or
oxidative reagents. The choice of the reaction kinetics and thermodynamic data
plays a crucial role for the quality of the reaction mechanism, and it is of great
importance to keep these data up to date with respect to the actual experimental
and theoretical results.
7. Conclusion and future prospects
132
In spite of the great effort in understanding the soot formation phenomenon and the
complex processes related to it, there are still lots of uncertainties in the gas-phase
chemistry of the soot precursor formation and growth, the transition between the
gas-phase and the particulate chemistry, and the soot particle surface chemistry.
For the optimisation of theoretical models and combustion facilities with respect to
pollutant formation, it is necessary to study all these processes in detail.
The models described in this work can be improved in the following directions:
• Experimental and theoretical investigations of new reaction channels of PAH
formation and growth.
• Implementation of newly evaluated kinetic and thermodynamic data.
• Validation of the model against experimentally measured data for the gasphase chemistry and the soot characteristics in flames.
• Implementation of the distribution of the active sites on the soot particle
surface.
• Deeper understanding and implementation of the mechanisms of particle inception and growth, in particular the transition of the gas-phase to the liquid
and then to the particulate-phase.
• The simplified soot model needs the implementation of the effect of temperature on the soot particle nucleation and surface growth.
133
List of Figures
5.1
Concentration profiles of the main gas-phase species measured (closed symbols) [35] and simulated (open symbols and lines) during pyrolysis of 3.2
% C2 H2 /Ne/Ar mixture, at T = 2030 K, and p = 0.39 bar behind reflected shock waves: (squares) C2 H2 , (triangles) C4 H2 · 2, (inverse triangles) C6 H2 · 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2
Concentration profiles of C6 H6 decay measured (closed symbols) [36] and
simulated (open symbols and lines) for a mixture of 2.1 % C6 H6 , diluted
in argon at p = 0.52 bar for three different temperatures: (circles) 1704 K,
(triangles) 1942 K, (squares) 2192 K.
5.3
. . . . . . . . . . . . . . . . . . . 51
Time history of C2 H2 concentration measured (closed symbols) [36] and
simulated (open symbols and lines) at conditions as in Figure 5.2. . . . . . 52
5.4
Time history of C4 H2 concentration measured (closed symbols) [36] and
simulated (open symbols and lines) at conditions as in Fig.5.2. . . . . . . 52
5.5
Integral reaction flow analysis of the PAH formation pathways during pyrolysis of a 4.62 % C2 H2 /Ar mixture at T = 2000 K, p = 6.0 bar, and
reaction time 0.003 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.6
Integral reaction flow analysis of the polyyne formation pathways during
pyrolysis of a 4.62 % C2 H2 /Ar mixture at T = 2000 K, p = 6.0 bar, and
reaction time 0.003 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.7
Sensitivity analysis with respect to benzene during pyrolysis of acetylene
at conditions as in Figure 5.5. . . . . . . . . . . . . . . . . . . . . . . . 54
5.8
Sensitivity analysis with respect to phenanthrene during pyrolysis of acetylene at conditions as in Figure 5.5. . . . . . . . . . . . . . . . . . . . . . 54
. LIST OF FIGURES
5.9
134
Sensitivity analysis with respect to pyrene during pyrolysis of acetylene at
conditions as in Figure 5.5. . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.10 Sensitivity analysis with respect to C12 H2 during pyrolysis of acetylene at
conditions as in Figure 5.6. . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.11 Integral reaction flow analysis of the PAH formation pathways during pyrolysis of a 1.54 % C6 H6 /Ar mixture at T = 2000 K, p = 6.0 bar, and
reaction time 0.003 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.12 Integral reaction flow analysis of the polyyne formation pathways during
pyrolysis of a 1.54 % C6 H6 /Ar mixture at T = 2000 K, p = 6.0 bar, and
reaction time 0.003 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.13 Sensitivity analysis with respect to biphenyl during pyrolysis of benzene
at conditions as in Figure 5.11. . . . . . . . . . . . . . . . . . . . . . . . 57
5.14 Sensitivity analysis with respect to phenanthrene during pyrolysis of benzene at conditions as in Figure 5.11. . . . . . . . . . . . . . . . . . . . . 58
5.15 Sensitivity analysis with respect to C12 H2 during pyrolysis of benzene at
conditions as in Figure 5.12. . . . . . . . . . . . . . . . . . . . . . . . . 58
5.16 Sensitivity analysis with respect to C10 H2 during pyrolysis of benzene at
conditions as in Figure 5.12. . . . . . . . . . . . . . . . . . . . . . . . . 59
5.17 Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of C2 H2 /Ar mixtures at p = 57.0 bar for three different C atom concentrations: (inverse
triangles) [C] = 3.8 [mol/m3 ], (circles) [C] = 1.7 [mol/m3 ], (squares) [C]
= 0.9 [mol/m3 ].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.18 Induction delay time in measured (closed symbols) [195]and simulated
(open symbols and lines) during pyrolysis of C2 H2 /Ar mixtures at conditions as in Fig. 5.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
. LIST OF FIGURES
135
5.19 Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of C2 H4 /Ar mixtures at p = 50.0 bar for three different C-atom concentrations: (inverse
triangles) [C] = 7.4 [mol/m3 ], (circles) [C] = 4.7 [mol/m3 ], (squares) [C] =
4.0 [mol/m3 ]. Open diamonds denote the calculated results for C2 H6 /Ar
mixture: p = 50.0 bar, [C] = 4.0 [mol/m3 ]. . . . . . . . . . . . . . . . . . 61
5.20 Induction delay time measured (closed symbols) [195] and simulated (open
symbols and lines) during pyrolysis of C2 H4 /Ar mixtures at p = 50.0 bar
for three different C-atom concentrations: (triangles) [C] = 7.4 [mol/m3 ],
(circles) [C] = 4.7 [mol/m3 ], (squares) [C] = 4.0 [mol/m3 ]. . . . . . . . . . 61
5.21 Temperature dependence of the soot yield measured (closed symbols)
[195] and simulated (open symbols and lines) during pyrolysis of CH4 /Ar
mixtures for several different carbon atom concentrations: (circles) p =
55.0 bar, [C] = 6.4 [mol/m3 ]; (squares) p = 55.0 bar, [C] = 3.4 [mol/m3 ];
(inverse triangles) p = 120.0 bar, [C] = 4.0 [mol/m3 ]; (triangles) p =
25.0 bar, [C] = 3.0 [mol/m3 ]; (diamonds) p = 55.0 bar , [C] = 1.7 [mol/m3 ]. 63
5.22 Induction delay time measured (closed symbols) [195] and simulated (open
symbols and lines) during pyrolysis of CH4 /Ar mixtures at conditions as
in Figure 5.21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.23 Temperature dependence of the soot yield measured (closed symbols) [195]
and simulated (open symbols and lines) during pyrolysis of C6 H6 /Ar mixtures at p = 50.0 bar, and tr = 1.5 ms, for four different C atom concentrations: (circles) [C] = 4.0 [mol/m3 ], (squares) [C] = 1.0 [mol/m3 ];
(triangles) [C] = 0.8, (diamonds) [C] = 0.4 [mol/m3 ]. . . . . . . . . . . . 64
5.24 Induction delay time measured (closed symbols) [195] and simulated (open
symbols) during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure
5.23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.25 Temperature dependence of the soot yield measured (closed symbols)
[81, 82] and simulated (open symbols and lines) during pyrolysis of
C6 H6 /Ar mixtures at p = 1.2 bar, tr = 1.3 ms, and for three different
reactive mixtures: (squares) 2 %, (circles) 1 %, (triangles) 0.5 %. . . . . . 65
. LIST OF FIGURES
136
5.26 Induction delay time, measured (closed symbols) [81, 82] and simulated
(open symbols) during pyrolysis of C6 H6 /Ar mixtures at conditions as in
Figure 5.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.27 Mean particle radius measured (closed symbols) [81, 82] and calculated
(open symbols and lines) during pyrolysis of three different C6 H6 /Ar mixtures: (squares) 2 %, (circles) 1 %, (triangles) 0.5 %, for tr = 1.0 ms at
p = 1.2 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.28 Time history of the mean particle radius measured (closed symbols) [81, 82]
and calculated (open symbols and lines) during pyrolysis of four different
C6 H6 /Ar mixtures: (squares) 2 %, (circles) 1 %, (triangles) 0.5 %, (inverse
triangles) 0.25 % at p = 1.2 bar. . . . . . . . . . . . . . . . . . . . . . . 67
5.29 Soot formation time history measured (closed symbols) [78] and simulated (open symbols and lines) during pyrolysis of a diluted in argon
C6 H6 /C2 H2 = 3/1 mixture ([C] = 1.2·10−6 [mol/cm3 ]) at p = 60 bar
for various temperatures: (circles) T = 1676 K, (squares) T = 1789 K,
(triangles) T = 1806 K, (inverse triangles) T = 1880 K. . . . . . . . . . . 69
5.30 Arrhenius-type plot of the experimentally measured (closed symbols) [78]
and calculated (open symbols) induction time τ for mixtures with various benzene/acetylene ratios (B/A) at pressure 60 bar: (circles) benzene,
[C] = 4.0 · 10−6 mol/cm3 ; (squares) acetylene, [C]= 4.0 · 10−6 [mol/cm3 ];
(inverse triangles) B/A = 10/1, [C]= 9.0 · 10−6 [mol/cm3 ]; (diamonds)
B/A = 1/1, [C]= 5.0 · 10−6 [mol/cm3 ]; (triangles) B/A = 2.5/1, [C]=
12.0 · 10−6 [mol/cm3 ]; (hexagons) benzene; only the HACA pathway of
soot formation was active, [C]= 4.0 · 10−6 [mol/cm3 ]. . . . . . . . . . . . 70
5.31 Temperature dependence of the normalised observable rate of soot particle growth (kf /[C]) measured (closed symbols) [78] and calculated (open
symbols) during pyrolysis of benzene, acetylene, benzene/acetylene (B/A),
and acetylene/hydrogen mixtures at pressure 60 bar: (circles) benzene, [C]
= 4.0 · 10−6 [mol/cm3 ]; (squares) [C] = 4.0 · 10−6 [mol/cm3 ]; (inverse triangles) B/A = 10/1, [C]= 9.0 · 10−6 [mol/cm3 ]; (diamonds) B/A = 1/1, [C]=
5.0 · 10−6 [mol/cm3 ]; (triangles) B/A = 2.5/1, [C]= 12.0 · 10−6 [mol/cm3 ];
(hexagons) C2 H2 /H2 = 1/1, [C]= 2.0 · 10−6 [mol/cm3 ]. . . . . . . . . . . 71
. LIST OF FIGURES
137
5.32 Temperature dependence of the soot yield measured (closed symbols) [78]
and calculated (open symbols and lines) during pyrolysis of C6 H6 /Ar, [C]
= 4.0 ·10−6 [mol/cm3 ], and C2 H2 /Ar, [C] = 4.0 ·10−6 [mol/cm3 ] mixtures
at p = 6.0 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.33 Temperature dependence of the soot yield measured (closed symbols) [78] and calculated (open symbols and lines) during pyrolysis
of C6 H6 /C2 H2 /Ar mixtures, (triangles) B/A = 2.5/1 [C] = 9.0 ·10−6
[mol/cm3 ], (inverse triangles) B/A = 1/1, [C] = 5.0 ·10−6 [mol/cm3 ], (diamonds) B/A =1/2.5 [C] = 9.0 ·10−6 [mol/cm3 ] at p = 6.0 bar/cm3 . . . . . 72
5.34 Temperature dependence of the soot yield obtained during pyrolysis of
benzene ([C] = 4.0 · 10−6 mol/cm3 ) at p = 6 bar: (closed circles) the
experimental measurements [78], (open circles and line) the calculated results performed with Model-1, (open hexagons and line) the results of
calculation performed with Model-1, when only the HACA pathway of
soot formation (Table 5.1) was active. . . . . . . . . . . . . . . . . . . . 72
5.35 Temperature dependence of the soot yield measured (closed symbols)
[78] and calculated (open symbols and lines) during pyrolysis of C2 H2 ,
C2 H4 , and C2 H2 /H2 diluted in argon mixtures:
=
4.0·10−6 [mol/cm3 ];
(squares) C2 H2 , [C]
(circles) C2 H4 , [C] = 4.0·10−6 [mol/cm3 ]; (in-
verse triangles) C2 H2 /H2 = 1/1, [C] = 4.0·10−6 [mol/cm3 ]; (triangles)
C2 H2 /H2 = 1/1[mol/cm3 ], [C] = 2.0·10−6 [mol/cm3 ] mixtures at p = 6.0
bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.36 Temperature dependence of the soot yield measured (closed symbols) [198]
and calculated (open symbols and lines) during rich oxidation of CH4 , [C]
= 7.6 [mol/m3 ]; C3 H8 [C] = 6.0 [mol/m3 ]; n-C7 H16 [C] = 5.9 [mol/m3 ] at
φ= 5 and p = 40 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.37 Temperature dependence of the experimentally measured (closed symbols)
[198] and calculated (open symbols and lines) soot yield during rich oxidation of n-C7 H16 /Ar mixture (99 % Ar, 0.3125 % C7 H16 , and 0.6875 % O2 )
at constant argon concentration: (circles) p = 30 bar, (squares) p = 40
bar, (diamonds) p = 50 bar. . . . . . . . . . . . . . . . . . . . . . . . . 75
5.38 Experimentally measured (closed symbols) and calculated results (open
symbols and lines) of the time-resolved concentration profiles of H atoms
measured during shock-tube pyrolysis of C6 H5 OH [206] and C6 H6 [205].
. 84
. LIST OF FIGURES
138
5.39 Concentration profiles of OH radicals measured (closed symbols) [207] and
calculated (open symbols and lines) during toluene oxidation: φ = 1, 0.1
% C6 H5 CH3 , 0.9 % O2 , (circles) T = 1689 K, and (triangles) T = 1586 K
and p = 1.9 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.40 Concentration profiles of OH radicals measured (closed symbols) [207] and
calculated (open symbols and lines) during toluene oxidation: φ = 1, 0.025
% C6 H5 CH3 + 0.225 % O2 , (triangles) T = 1783 K, p = 1.84 bar; (inverse
triangles) T = 1700 K, p = 1.89 bar; (squares) T = 1648 K, p = 2.03 bar;
(diamonds) T = 1607 K p = 2.03 bar. . . . . . . . . . . . . . . . . . . . 86
5.41 Concentration profiles of OH radicals measured (closed symbols) [207] and
calculated (open symbols and lines) during n-C7 H16 and C6 H5 CH3 oxidation: (triangles) 130 ppm n-C7 H16 , T = 1640 K, p = 2.0 bar; (squares)
1250 ppm C6 H5 CH3 , T = 1648 K, p = 2.0 bar. . . . . . . . . . . . . . . . 86
5.42 Concentration profiles of the main gas-phase species measured [35] and
simulated in pyrolysis of 3.2 % C2 H2 /Ne/Ar mixture at T = 2030 K and
p = 0.39 bar behind reflected shock waves: (squares) C2 H2 , (triangles)
C4 H2 · 2, (inverse triangles) C6 H2 · 10. . . . . . . . . . . . . . . . . . . . 87
5.43 Concentration decay profiles of the fuel molecule measured (closed symbols) [36] and simulated (open symbols and lines) during pyrolysis of 2.1
% C6 H6 diluted in (99% Ne-1% Ar) mixture at T = 2190 K, p = 0.52 bar.
88
5.44 Concentration profiles of the main gas-phase species measured (closed symbols) [36] and simulated (open symbols and lines) during pyrolysis of 2.1
% C6 H6 at conditions as in Figure 5.43. . . . . . . . . . . . . . . . . . . 88
5.45 Fuel-decay concentration profiles measured (closed symbols) [35] and simulated (open symbols and lines) during pyrolysis of 1.8 % C6 H5 CH3 at
T = 1900 K, p = 0.4 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.46 Concentration profiles of the main gas-phase species measured (closed symbols) [35] and simulated (open symbols and lines) during pyrolysis of 1.8
% C6 H5 CH3 at conditions as in Figure 5.45. . . . . . . . . . . . . . . . . 89
5.47 Experimentally measured [211] concentration of several aliphatic hydrocarbons and the fuel decay profile detected during pyrolysis of 1 % toluene
at pressure 10.013 bar and reaction time 600 µs. . . . . . . . . . . . . . . 90
. LIST OF FIGURES
139
5.48 Concentration profiles of several aliphatic hydrocarbons and the fuel decay
calculated during pyrolysis of toluene at conditions as in Figure 5.47. . . . 90
5.49 Experimentally measured [211] concentration profiles of aromatic hydrocarbons detected during pyrolysis of 1 % toluene at pressure 10.013 bar
and reaction time 600 µs.
. . . . . . . . . . . . . . . . . . . . . . . . . 91
5.50 Concentration profiles of aromatic hydrocarbons calculated during toluene
pyrolysis at conditions as in Figure 5.49. . . . . . . . . . . . . . . . . . . 91
5.51 Experimentally measured [211] concentration profiles of various polycyclic
aromatic hydrocarbons detected during pyrolysis of 1 % toluene at pressure
10.013 bar and reaction time 600 µs. . . . . . . . . . . . . . . . . . . . . 92
5.52 Concentration profiles of various polycyclic aromatic hydrocarbons calculated in toluene pyrolysis at conditions as in Figure 5.51. . . . . . . . . . 92
5.53 Integral reaction flow analysis of the main pathways of soot precursor
inception during C6 H5 CH3 /O2 /Ar oxidation at T = 1900 K, p = 2.0 bar,
and reaction time 2.0 ms.
. . . . . . . . . . . . . . . . . . . . . . . . . 93
5.54 Sensitivity analysis with respect to benzene during toluene oxidation at
conditions as in Figure 5.53. . . . . . . . . . . . . . . . . . . . . . . . . 93
5.55 Sensitivity analysis with respect to ethynylnaphthalene radical (A2 C2 HB)
during toluene oxidation at conditions as in Figure 5.53. . . . . . . . . . . 94
5.56 Sensitivity analysis with respect to acenaphthylene (A2 R5 ) during toluene
oxidation at conditions as in Figure 5.53. . . . . . . . . . . . . . . . . . 94
5.57 Sensitivity analysis with respect to acephenanthrylene (A3 R5 ) during
toluene oxidation at conditions as in Figure 5.53. . . . . . . . . . . . . . 95
5.58 Integral reaction flow analysis of the main pathways of soot precursor
inception during n-C7 H16 /O2 /Ar rich oxidation, [C] = 7.89 [mol/m3 ], φ =
5, at T = 1750 K, p = 25.0 bar, and reaction time 2.5 ms. . . . . . . . . . 97
5.59 Sensitivity analysis with respect to benzene during n-heptane oxidation at
conditions as in Figure 5.58. . . . . . . . . . . . . . . . . . . . . . . . . 97
. LIST OF FIGURES
140
5.60 Sensitivity analysis with respect to acenaphthylene (A2 R5 ) during nheptane oxidation at conditions as in Figure 5.58. . . . . . . . . . . . . . 98
5.61 Sensitivity analysis with respect to acephenanthrylene (A3 R5 ) during nheptane oxidation at conditions as in Figure 5.58. . . . . . . . . . . . . . 98
5.62 Temperature dependence of the experimentally measured (closed symbols)
[195] and simulated (open symbols and lines) soot yield during pyrolysis
of C2 H4 /Ar mixtures at p = 50.0 bar for three different C-atom concentrations: (circles) [C] = 7.4 [mol/m3 ], (squares) [C] = 4.7 [mol/m3 ], (inverse
triangles) [C] = 4.0 [mol/m3 ]. . . . . . . . . . . . . . . . . . . . . . . . 100
5.63 Experimentally measured (closed symbols) [195] and simulated (open
symbols) induction delay time during pyrolysis of C2 H4 /Ar mixtures at
p = 50.0 bar for three different C-atom concentrations: (triangles) [C] =
7.4 [mol/m3 ], (circles) [C] = 4.7 [mol/m3 ], (squares) [C] = 4.0 [mol/m3 ]. . 100
5.64 Temperature dependence of the soot yield measured (closed symbols)
[195] and simulated (open symbols and lines) during pyrolysis of CH4 /Ar
mixtures for several different carbon-atom concentrations: (circles) p =
55.0 bar, [C] = 6.4 [mol/m3 ]; (squares) p = 55.0 bar, [C] = 3.4 [mol/m3 ];
(inverse triangles) p = 120.0 bar, [C] = 4.0 [mol/m3 ]; (triangles) p =
25.0 bar, [C] = 3.0 [mol/m3 ]; (diamonds) p = 55.0 bar , [C] = 1.7 [mol/m3 ]. 101
5.65 Temperature dependence of the experimentally measured (closed symbols)
[195] and simulated (open symbols and lines) soot yield during pyrolysis of
C6 H6 /Ar mixtures at p = 50.0 bar for four different C-atom concentrations:
(circles) [C] = 4.0 [mol/m3 ], (squares) [C] = 1.0 [mol/m3 ]; (triangles) [C]
= 0.8 [mol/m3 ], (diamonds) [C] = 0.4 [mol/m3 ]. . . . . . . . . . . . . . . 102
5.66 Experimentally measured (closed symbols) [195] and simulated (open symbols) induction delay time during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure 5.65. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.67 Temperature dependence of the soot yield measured (closed symbols) [81]
and simulated (open symbols and lines) during pyrolysis of C6 H6 /Ar mixtures at p = 1.2 bar, tr = 1.3 ms for three different reactive mixtures:
(squares) 2 %, (circles) 1 %, (triangles) 0.5 %. . . . . . . . . . . . . . . . 103
. LIST OF FIGURES
141
5.68 Induction delay time, measured (closed symbols) [81] and simulated (open
symbols) during pyrolysis of C6 H6 /Ar mixtures at conditions as in Figure
5.67. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.69 Mean particle radius measured (closed symbols) [81] and calculated (open
symbols and lines) during pyrolysis of three different C6 H6 /Ar mixtures:
(squares) 2 %, (circles) 1 %, (triangles) 0.5 %, for a fixed reaction time
tr = 1.0 ms, at p = 1.2 bar. . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.70 Time history of the mean particle radius measured (closed symbols) [81]
and calculated (open symbols and lines) during pyrolysis of four different
C6 H6 /Ar mixtures: (squares) 2 %, (circles) 1 %, (triangles) 0.5 %, (inverse
triangles) 0.25 % at p = 1.2 bar. . . . . . . . . . . . . . . . . . . . . . . 104
5.71 Temperature dependence of the experimentally measured (closed symbols)
[221] and calculated (open symbols and lines) soot yield during pyrolysis
of three C6 H5 CH3 /Ar mixtures at tr = 2 ms: (triangles) 1.5 % C6 H5 CH3 ,
p = 3.5 bar; (squares) 1.0 % C6 H5 CH3 , p = 3.3 bar; (diamonds) 0.5 %
C6 H5 CH3 , p = 2.5 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.72 Temperature dependence of the soot yield, measured (closed symbols) [222]
and calculated (open symbols and line) during pyrolysis of 0.1 % n-C7 H16
diluted in argon mixture at p = 20 bar. . . . . . . . . . . . . . . . . . . 106
5.73 Induction delay time, measured (closed symbols) [222] and calculated
(open symbols), during n-C7 H16 pyrolysis at conditions as in Figure 5.72. . 106
5.74 Temperature dependence of the soot yield measured (closed symbols) [198]
and calculated (open symbols and lines) during rich oxidation of CH4 , [C]
= 7.6 [mol/m3 ]; C3 H8 [C] = 6.0 [mol/m3 ]; and n-C7 H16 [C] = 5.9 [mol/m3 ]
, at φ= 5 and p = 40 bar.
. . . . . . . . . . . . . . . . . . . . . . . . . 107
5.75 Time-resolved soot yield measured (closed symbols) [198] and calculated
(open symbols and line) during n-C7 H16 rich oxidation, φ= 5, [C] = 7.89
[mol/m3 ], T = 1750 K, p = 25 bar. . . . . . . . . . . . . . . . . . . . . . 108
5.76 Time-resolved mean particle diameter measured (closed symbols) [198] and
calculated (open symbols and line) during n-C7 H16 rich oxidation at conditions as in Figure 5.75. . . . . . . . . . . . . . . . . . . . . . . . . . . 108
. LIST OF FIGURES
142
5.77 Time-resolved soot particle number density measured (closed symbols)
[198] and calculated (open symbols and line) during n-C7 H16 rich oxidation
at conditions as in Figure 5.75. . . . . . . . . . . . . . . . . . . . . . . . 109
5.78 Temperature dependence of the soot yield measured (closed symbols) [198]
and calculated (open symbols and lines) during shock tube rich oxidation
of an n-C7 H16 /O2 /Ar at constant Ar concentration (0.3125 % C7 H16 , %
O2 , and 99 % Ar): (circles) p = 30 bar, (squares) p = 40 bar, (diamonds)
p = 50 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.79 The pressure influence of the soot yield measured (closed symbols) [198]
and calculated (open symbols and line) during shock tube rich oxidation of
an n-C7 H16 /Ar/O2 mixture, [C] = 5.8 [mol/m3 ], φ= 5 for three different
pressures 20 bar, 40 bar and 80 bar. . . . . . . . . . . . . . . . . . . . . 110
5.80 Temperature dependence of the soot yield experimentally measured (closed
symbols) [221] and calculated (open symbols and lines) during oxidation
of three different C6 H5 CH3 /O2 /Ar mixtures at tr = 2 ms: (triangles) 1.5
% toluene, p = 3, 5 bar; (squares) 1.5 % toluene + 1.5 % O2 , p = 2.0 bar;
(diamonds) 1.5 % toluene + 2.5 % O2 , p = 2.0 bar. . . . . . . . . . . . . 111
5.81 Temperature dependence of the soot yield experimentally measured (closed
symbols) [221] and calculated (open symbols and lines) during thermal
decomposition of C6 H5 CH3 /Ar and C6 H5 CH3 /CH3 OH/Ar mixtures at
tr = 2 ms: (triangles) 1.0 % toluene, p = 3, 3 bar; (squares) 1.0 % toluene +
1.0 % methanol, p = 2.7 bar; (diamonds) 1.0 % toluene + 2.0 % methanol,
p = 2.7 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.82 Temperature dependence of the experimentally measured (closed symbols)
[221] and calculated (open symbols and lines) soot yield during pyrolysis
of C6 H5 CH3 /Ar and C6 H5 CH3 /C2 H5 OH/Ar mixtures at tr = 2 ms: (triangles) 1.0 % toluene, p = 3, 3 bar; (inverse triangles) 1.0 % toluene + 1.0
% ethanol, p = 3.0 bar; (squares) 1.0 % toluene + 2.0 % ethanol, p = 3.0
bar; (diamonds) 1.0 % toluene + 3.0 % ethanol, p = 3.0 bar. . . . . . . . 113
6.1
Time-resolved soot yield, measured (closed symbols) [198] and calculated
(open symbols and lines) in n-C7 H16 rich oxidation, [C] = 7.89 [mol/m3 ],
φ= 5, T = 1750 K, p = 25 bar and tr = 2.5 ms. . . . . . . . . . . . . . . 123
. LIST OF FIGURES
6.2
143
Time-resolved mean particle diameter, measured (closed symbols) [198]
and calculated (open symbols and lines) in n-C7 H16 rich oxidation at conditions as in Figure 6.1.
6.3
. . . . . . . . . . . . . . . . . . . . . . . . . . 124
Time-resolved soot particle number density, measured (closed symbols)
[198] and calculated (open symbols and lines) in n-C7 H16 rich oxidation at
conditions as in Figure 6.1. . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4
Time-dependent profiles of the C3 H3 concentration, calculated at the conditions as in Figure 6.1: (circles) SSM-1 and (diamonds) SSM-2. . . . . . 125
6.5
Time-dependent profiles of the C2 H2 concentration, calculated at conditions as in Figure 6.1: (circles) SSM-1 and (diamonds) SSM-2. . . . . . . 125
6.6
Time-dependent profiles of the OH concentration, calculated at the conditions as in Figure 6.1: SSM-1 (circles) and SSM-2 (diamonds). . . . . . . 126
6.7
Temperature dependence of the soot yield, measured (closed symbols) [198]
and calculated (open symbols and lines) in rich oxidation of n-C7 H16 [C]
= 5.9 [mol/m3 ], φ= 5, p = 40 bar and tr = 2.5ms: (circles) experiment,
(triangles) Model-1 and (diamonds) Model-2. . . . . . . . . . . . . . . . 126
6.8
Temperature dependence of the soot yield, measured (closed symbols) [198]
and calculated (open symbols and lines) in rich oxidation of C3 H8 [C] =
6.0 [mol/m3 ], φ= 5, p = 40 bar and tr = 2.5 ms: (circles) experiment,
(triangles) Model-1 and (diamonds) Model-2. . . . . . . . . . . . . . . . 127
6.9
Temperature dependence of the soot yield, measured (closed symbols) [198]
and calculated (open symbols and lines) in rich oxidation of CH4 [C] =
7.6 [mol/m3 ], φ= 5, p = 40 bar and tr = 2.5 ms: (circles) experiment,
(triangles) Model-1 and (diamonds) Model-2. . . . . . . . . . . . . . . . 127
6.10 Temperature dependence of the soot yield, measured (closed symbols) [221] and calculated (open symbols and lines) in oxidation of an
C6 H5 CH3 /O2 /Ar mixture (1.5 % toluene + 1.5 % O2 ), p = 2.0 bar and
tr = 2 ms: (circles) experiment, (diamonds) SSM-1 (triangles) Model-2. . . 129
144
List of Tables
5.1
Mechanism of formation, growth, coagulation and transformation of soot
precursors and soot particles (Model-1) . . . . . . . . . . . . . . . . . . 46
5.3
Mechanism of formation, surface growth, coagulation, oxidation and
transformation of soot precursors and soot particles (Model-2) . . . . 80
Eidesstattliche Erklärungen
Ich erkläre hiermit, dass ich die vorgelegte Dissertation selbst verfasst und mich
keiner anderen als der von mir ausdrücklich bezeichneten Quellen und Hilfen bedient
habe.
Heidelberg, 29.03.2007
Iliyana Naydenova
146
Bibliography
[1] M. Frenklach, H. Wang. Detailed kinetic modeling of soot particle formation.
Springer 59, 1994.
[2] A.V. Krestinin. Detailed modeling of soot foormation in hydrocarbon pyrolysis.
Combust. Flame 121, 513–524, 2000.
[3] A. Keller, R. Kovacs, K.-H. Homann. Large molecules, radicals, ions, and
small soot particles in fuel-rich hydrocarbon flames. Part IV: large polycyclic
aromatic hydrocarbons and their radicals in a fuel-rich benzene-oxygen flame.
Phys. Chem. Chem. Phys. 2, 1667–1675, 2000.
[4] B. Öktem, M. P. Tolocka, B. Zhao, H. Wang, M. V. Johnston. Chemical species
associated with the early stage of soot growth in laminar premixed ethyleneoxygen-argon flame. Combust. and Flame 142, 364–373, 2005.
[5] O. Mathieu, G. Frache, N. Djebaili-Chaumeix, C.-E. Paillard, G. Krier, J.-F.
Muller, F. Douce, P. Manuelli. Characterization of adsorbed species on soot
formed behind reflected shock waves. Proc. Comb. Inst. 31, 511–519, 2007.
[6] U. Maas, J. Warnatz. Ignition processes in carbon-monoxide-hydrogen-oxygen
mixtures. Proc. Comb. Inst. 22, 1695–1704, 1988.
[7] G.L. Heller. Vortex reactor for carbon black manufacture.
3,490,869,, 1970.
US Patent
[8] J.P. Longwell. Soot in combustion systems and its toxic properties. Plenum
Press New Yourk and London, 1983.
[9] W.D. Dockery. Epidemiologic evidence of cardiovascular effects of particulate
air pollution. Environ. Health Perspect. 109 (4), 483–486, 2001.
[10] C.A. Pope, R.T. Burnett, M.J. Thun, E.E. Valle, D. Krewski, K. Ito, G.D.
Thurston. Lung Cancer, Cardiopulmonary Mortality, and Long-term Exposure
. BIBLIOGRAPHY
147
to Fine Particulate Air Pollution. American Medical Association (JAMA)
287, 1132–1141, 2002.
[11] W. J. Gauderman, R. Mcconnell, F. Gilliland, S. London, D. Thomas, E. Avol,
H. Vora, K. Berhane, EB. Rappaport F. Lurmann, H. G. Margolis, J. Peters.
Association between air pollution and lung function growth in Southern California children. Am. J. of Resp. and Crit. Care Med. 162, 1383–1390, 2000.
[12] H.K. Homann, H.G. Wagner. Some new aspects of the mechanism of carbon
formation in premixed flames. Proc. Comb. Inst. 11, 371–379, 1967.
[13] M. Frenklach, D.W. Clary, W.C. Gardiner, S.E. Stein. Detailed kinetic modeling of soot formation in shock-tube pyrolysis of acetylene. Proc. Comb. Inst.
20, 887–901, 1985.
[14] J.H. Kiefer, V. Drasek, A. William. The mechanism of the homogeneous pyrolysis of acetylene. Int. J. Chem. Kinet. 22(7), 747–786, 1990.
[15] A.V. Krestinin. Kinetic Model of soot formation from acetylene in different
mixtures at temperatures higher then 1600 K. Chim. Phys. Reports. 6(3),
342–349, 1987.
[16] A.V. Krestinin. For the mechanisms of soot formation from acetylene. Chem.
Phys. Reports 13(1), 121–131, 1994.
[17] A.V. Krestinin. Polyyne model of soot formation process. Proc. Combust. Inst.
27, 1557–1563, 1998.
[18] A.V. Krestinin, A.V. Paevskii M.B. Kislov, O.I. Kolesova, L.N. Stesik. K
Voprosu o mehanizme obrazovanija sajevuie chastic. Kinetics and Katalysis
41(1), 102–111 2000.
[19] H.F. Calcote. Mechanisms of soot nucleation in flames - a critical rewiew.
Combustion and Flame 42(3), 215–242, 1981.
[20] P. Weilmünster, A. Keller, K. H. Homann. Large molecules, radicals, ions,
and small soot particles in fuel-rich hydrocarbon flames. Part I: Positive ions
of polycyclic aromatic hydrocarbons (PAH) in low-pressure premixed flames of
acetylene and oxigen. Combustion and Flame 116, 62–83, 1999.
[21] M. Frenklach, H. Wang. Detailed modeling of soot particle nucleation and
growth. Proc. Comb. Inst. 23, 1559–1566, 1991.
. BIBLIOGRAPHY
148
[22] J. Griesheimer, K.-H. Homann. Large molecules, radicals, ions, and small soot
particles in fuel-rich hydrocarbon flames. Part II: aromatic radicals and intermediate PAHs in a premixed low-pressure naphthalene/oxygen/argon flame.
Proc. Comb. Inst. 27, 1753–1759, 1998.
[23] J Appel, H. Bockhorn, M. Frenklach. Kinetic modeling of soot formation with
detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons.
Combust. and Flame. 121, 122–136, 2000.
[24] H. Richter, S. Granata, W.H. Green, J.B. Howard. Detailed modeling of PAH
and soot formation in a laminar premixed benzene/oxygen/argon low-pressure
flame. Proc. Comb. Inst. 30, 1397–1405, 2005.
[25] B.S. Haynes, H.Gg. Wagner. Soot formation. Prog. Energy Combust. Sci. 7,
229–273, 1981.
[26] R.B. Cundall, D.E. Fussy, A.J. Harrison, D. Lampard. An investigation of the
precursors to carbon particles during the pyrolysis of acetylene and ethylene,.
Int. Shock-tube Symp., Seattle, July 11, 1977.
[27] R.B. Cundall, D.E. Fussy, A.J. Harrison, D. Lampard. Shock tube studies of
the high temperature pyrolysis of acetylene and ethylene. J.C.S. Faraday Trans.
I 74, 1403–1409, 1978.
[28] R.B. Cundall, D.E. Fussy, A.J. Harrison, D. Lampard. Hogh temperature
pyrolysis of ethane and propylene. J.C.S. Faraday Trans. I 75, 1390–1394,
1979.
[29] M.P.E. Berthelot. Theorie des corps pyrogenes. Ann. Chim. Phys. 9, 469–481,
1866.
[30] V.B. Lewes. The action of heat upon ethylene. Proc. Roy. Soc. 55, 90–108,
1894.
[31] J.N. Bradley, G.B.J. Kistiakowsky. Shock wave studies by mass spectrometry.
II. Polymerization and oxidation of acetylene. J. Chem. Phys. 35, 264–270,
1961.
[32] I. D. Gay, G.B. Kistiakowsky, J.V. Michael, H. J. Niki. Thermal decomposition
of acetylene in shock waves. J. Chem. Phys. 43, 1720–1726, 1965.
[33] T. Tanzawa, W. C. Gardiner. Thermal decomposition of acetylene. Proc.
Comb. Inst. 17, 563–573, 1979.
. BIBLIOGRAPHY
149
[34] U. Bonne, H.Gg. Wagner.
Untersuchung des Reaktionsablaufs in fetten Kohlenwasserstoff-Sauerstoff-Flammen 3. Optische Untersuchungen an
russenden Flammen. Ber. Bunsenges. Physik Chem. 69, 35 1965.
[35] R.D. Kern, H.J. Singh, M.A. Esslinger, P.W. Winkeler. Product profiles observed during the pyrolysis of toluene, benzene, butadiene and acetylene. Proc.
Comb. Inst. 19, 1351–1358, 1982.
[36] R.D. Kern, C.H. Wu, G.B. Skinner, V.S. Rao, J.H. Kiefer, J.A. Towers, L.J.
Mizerka. Colaborative shock tube stuties of benzene pyrolysis. Proc. Comb.
Inst. 20, 789–797, 1984.
[37] A. Thomas. Carbon formation in flames. Combust. Flame. 6, 46–62, 1962.
[38] J.A. Miller, M.J. Pilling, J. Troe. Unravelling combustion mechanisms through
a quantitative understanding of elementary reactions. Proc. Comb. Inst. 30,
43–88, 2005.
[39] K. Rummel. Die Strahlung leuchtender Flammen. Arch. Eisenhuttenw. 14,
489–499, 1941.
[40] A. D’Alessio, A. D’Anna, A. D’Orisi, P. Minutolo, R. Barbella, A. Cijalo.
Precursors formation and soot inception in premixed ethylene flames. Proc.
Comb. Inst. 24, 973, 1992.
[41] P. Minutolo, G. Gambi, A. D’Alessio, A. D’Anna. Optical and spectroscopic
characterization of rich premixed flames across the soot formation threshold.
Combust. Sci. Tech. 101, 311–325, 1994.
[42] M. Frenklach, D. W. Clary, T. Yuan, W. C. Gardiner, S. E. Stein. Mechanism
of soot formation in acetylene-oxygen mixtures. Combust. Sci. Tech. 50, 79–
115, 1986.
[43] M. Frenklach, J. Warnatz. Detailed modeling of PAH profiles in a sooting
low-pressure acetylene flame. Combust. Sci. Tech. 51, 265–283, 1987.
[44] H. Wang, M. Frenklach. Transport properties of polycyclic aromatic hydrocarbons for flame modeling. Combust. Flame. 96, 163–170, 1994.
[45] H. Wang, M. Frenklach. Calculations of rate coefficients for the chemically activated reactions of acetylene with vinyl and aromatic radicals. J Phys. Chem.
98, 11465–11489, 1994.
. BIBLIOGRAPHY
150
[46] H. Wang, M. Frenklach. A detailed kinetic modeling study of aromatics formation in laminar premixed acetylene and ethylene flames. Combust. Flame.
110, 173–221, 1997.
[47] B. Bougie, L.C. Ganippa, A.P. Van Vliet, W. L.Meerts, N. J. Dam, J. J. Ter
Meulen. Soot particulate size characterisation in a heavy-duty Diesel engine
for different engine loads by laser-induced incandescence. Proc. Comb. Inst.
31, 685–691, 2007.
[48] P.S. Greenberg, J.C. Ku. Soot volume fraction imaging. Proc. Comb. Inst.
31, 5514–5522, 2007.
[49] D.R. Snelling, K.A. Thomson, G.J. Smallwood, Ö.L. Gülder. Two-dimensional
imaging of soot volume fraction in laminar diffusion flames. Proc. Comb. Inst.
31, 2478–2485, 2007.
[50] P. Mitchell, M. Frenklach. Monte Carlo simulation of soot aggregation with
simultaneous surface growth - why primary particles appear spherical. Proc.
Comb. Inst. 27, 1507–1514, 1998.
[51] P. Mitchell, M. Frenklach. Particle aggregation with simultaneous surface
growth. Phys. Rev. E 67, 061407, 2003.
[52] A. Violi. Modeling of soot particle inception in aromatic and aliphatic premixed
flames. Combust. Flame. 139, 279–287, 2004.
[53] H. Richter, M. Braun-Unkhoff, S. Granada, J. Yu, E. Goos, N. Slavinskaya,
P. Frank, W.H. Green, J.B. Howard. Computational investigation of PAH and
soot formation in premixed ethylene flames. ECM, 2005.
[54] M. Balthasar, M. Frenklach. Detailed kinetic modeling of soot aggregate formation in laminar premixed flames. Combust. Flame. 140, 130–145, 2005.
[55] N. Morgan, M. Kraft, M. Balthasar, D. Wong, M. Frenklach, P. Mitchell.
Numerical simulations of soot aggregation in premixed laminar flames. Proc.
Comb. Inst. 31, 693–700, 2007.
[56] D.F. Kronholm. Molecular weight growth pathways in fuel-rich combustion.
Diplomarbeit, Massachusetts Institute of Technology, Cambridge, MA,, 2000.
[57] H. Richter, J.B. Howard. Formation and consumption of single-ring aromatic
hydrocarbons and their precursors in premixed acetylene, ethylene and benzene
flames. Phys. Chem. Chem. Phys. 4, 2038–2055, 2002.
. BIBLIOGRAPHY
151
[58] P. A. Vlasov, J. Warnatz. Detailed kinetic modeling of soot formation in
hydrocarbon pyrolysis behind shock waves. Proc. Comb. Inst. 29, 2335–2341,
2002.
[59] J. Appel, H. Bockhorn, M. Wulkow. A detailed numerical study of the evolution
of soot particle size distributions in laminar premixed flames. Chemosphere
42, 635–645, 2001.
[60] J. Sojka, J. Warnatz, P. A. Vlasov, I. S. Zaslonko. Kinetic modeling of carbon suboxide thermal decomposition and formation of soot-like particles behind
shock waves. Comb. Sci. Tech. 158, 439–460, 2000.
[61] I. Naydenova, M. Nullmeier, J. Warnatz, P.A. Vlasov. Detailed kinetic modeling of soot formation during shock-tube pyrolysis of C6H6: Direct comparison
with the results of time-resolved laser-induced incandescence (LII) and CWlaser extinction measurements. Comb. Sci. Tech. 176, 1667–1703, 2004.
[62] I. Naydenova, M. Nullmeier, P.A. Vlasov, J. Warnatz. Detailed kinetic modeling of soot formation during shock tube pyrolisis and rich oxidation of various
hydorcarbons, Kapitel Combustion and atmospheric pollution, 183–202. Torus
Press Ltd, Moscow, 2004.
[63] I. Naydenova, P.A. Vlasov, J. Warnatz. Detailed kinetic modeling of soot
formation in pyrolysis of benzene/acetylene/argon mixtures. In ECM, 2005.
[64] I. Naydenova, M. Nullmeier, P.A. Vlasov, J. Warnatz. The role of polyyne and
polyaromatic hydrocarbons in the kinetics of soot formation, Kapitel Plasma,
aerosols, and atmospheric phenomena, 147–161. Torus Press Ltd, Moscow,
2005.
[65] J. Z. Wen, M. J. Thomson, M. F. Lightstone, S. N. Rogak. Detailed Kinetic
Modeling of Carbonaceous Nanoparticle Inception and Surface Growth during
the Pyrolysis of C6H6 behind Shock Waves. Energy Fuels 20 (2), 547–55,9
2006.
[66] G.H. Babcock, S. Wilcox. Steam - Its generation and use. Barberton, 1972.
[67] J. Warnatz, U. Maas, R.W. Dibble. Physical and chemical fundamentals, modeling and simulation, experiments, pollutant formation, 4rd Edition. SpringerVerlag Berlin, Heidelberg, 2006.
[68] J. Ackermann, M. Wulkow. MACRON - A Program Package for Macromolecular Kinetics, Kapitel Preprint SC 90-14. Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1990.
. BIBLIOGRAPHY
152
[69] J. Ackermann, M. Wulkow. The Treatment of Macromolecular Processes with
Chain-Length-Dependent Reaction Coefficients - An Example from Soot Formation, Kapitel SC 91-18. Konrad-Zuse-Tentrum für Informationstechnik,
Berlin, 1991.
[70] J. Appel. Numerische Simulation der Rußbildung bei der Verbrenung von
Kohlenwasserstoffen: Teilchengrößenverteilungen und deren statistische Momente. PhD Thesis, Universität Karlsruhe (TH), 2000.
[71] J. Sojka. Simuation der Rußbildung unter homogenen Verbrennungsbedingungen. PhD Thesis, Ruprecht-Karls-Universität Heidelberg, Interdisziplinäres
Zentrum für Wissenschaftliches Rechnen, 2001.
[72] G.L. Agafonov, M. Nullmeier, P.A. Vlasov, J. Warnatz, I.S. Zaslonko. Kinetic
modeling of solid carbon particle formation and thermal decomposition during
carbon suboxide pyrolysis behind shock waves. Combust. Sci. Tech. 174, 185–
213, 2002.
[73] W. Tsang, A. Lifshitz. Shock tube techniques in chemical kinetics. Annu. Rev.
Phys. Chem. 41, 559–599, 1990.
[74] K.A. Bhaskaran, P. Roth. The shock tube as wave reactor for kinetic studies
and material systems. Prog. Energy Comb. Sci. 28, 151–192, 2002.
[75] U. Bonne, K.H. Homann, H.Gg. Wagner. Carbon formation in premixed
flames. Proc. Comb. Inst. 10, 502–512, 1965.
[76] C. Pels Leusden, H. Pitsch, N. Peters. Rußbildung in einer laminaren Gegenstromflamme. In Verbrennung und Feuerungen 19. Deutscher Flammentag.
VDI, 1999.
[77] B. Zhao, Z. Yang, M.V. Johnston H., Wang, A.S. Wexler, M. Balthasar,
M. Kraft. Measurement and numerical simulation of soot particle size distribution functions in a laminar premixed ethylene-oxygen-argon flame. Combust.
Flame. 133, 173–188, 2003.
[78] V.Gg. Knorre, D. Thanke, T. Thienel, H.Gg. Wagner. Soot formation in
the pyrolysis of Benzene/Acetylene and Acetylene/Hydrogen mixtures at high
carbon concentrations. In Proceedings of the Combustion Institute, Band 26,
2303–2310, 1996.
[79] T. Kruse, P. Roth. Kinetics of C2 reactions during high-temperature pyrolysis
of acetylene. J. Phys. Chem. 101, 2138–2146, 1997.
. BIBLIOGRAPHY
153
[80] F. Douce, N. Djebaili-Chaumeix, C.-E. Paillard, C. Clinard, J.-N. Rouzard.
Soot formation from heavy hydrocarbons behind reflected shock waves. Proc.
Comb. Inst. 28, 2523–2529, 2000.
[81] R. Starke, P. Roth. Soot particle sizing by LII during shock tube pyrolysis of
C6H6. Combust. Flame 127, 1178–2285, 2002.
[82] R. Starke, B. Kock, P. Roth. Nano-particle sizing by laser-induced incandescence (LII) in a shock tube wave reactor. Shock Waves 12, 351–360, 2003.
[83] N. Djebaili-Chaumeix, D. Ladril, C.-E. Paillard. Experimental study on soot
formation from heavy haydrocarbons representative of gasoline fuels. International Symposium on Combustion and Atmospheric Pollution., 2003.
[84] R.J. Kee, F.M. Rupley, J.A. Miller. Chemkin Thermodynamic Database. Sandia Report 87-82153.UC-4, Sandia National Laboratories, Livermore CA Technical Report,, 1987.
[85] D.R. Stull, H. Prophet. JANAF Thermochemical Tables. Department of comerce, Washington DC Technical Report, 1971.
[86] A. Burcat. Kapitel Thermochemical Data for Combustion. Springer-Verlag,
New York, 1984.
[87] P.W. Atkins. Physical chemistry. Oxford University Press, New York, 7th
Eddition, 2002.
[88] F.A. Lindemann. Discussion on ”The radiation theory of chemical action”.
Trans. Farad. Soc. 17, 599, 1922.
[89] P.J. Robinson, K.A. Holbrook. Unimolecular reactions. Wiley-Interscience,
New York, 1972.
[90] D.M. Golden. Gas-phase homogeneous kinetics. In: Low-temperature chemistry of the atmosphere. Springer, Berlin/Heidelberg, 1994.
[91] R.G. Gilbert, K. Luther, J. Troe. Theory of unimolecular reactions in the
fall-off range. Ber. Bunseges. Phys. Chem. 87, 169 1983.
[92] H.B. Palmer, H.F. Cullis. In Chemistry and physics of carbon. , Jr. Vol. 1,
Kapitel The formation of carbon from gases., 265–325. New York, Marsel
Dekker, 1965.
[93] R.A. Dobbin, H. Subramaniasiavam. Soot Formation in Combustion: Mechansims and Models. Ed H. Bockhorn, Springer-Verlag, Heidelberg, 1994.
. BIBLIOGRAPHY
154
[94] R.L. Vander Wal, A.J. Tomasek, T.M. Ticich. Synthesis, laser processing,
and flame purification of nanostructured carbon. Nano Letters 3(2), 223–229,
2003.
[95] O.I. Smith. Fundamentals of soot formation in flames with application to
Diesel engine particulate emmisions. Prog. Energy Combust. Sci. 7, 275–291,
1981.
[96] T. Ishiguro, Y. Takatori, K. Akihama. Microstructure of Diesel soot particles
probed by electron microscopy. First observation of inner core and outer shell.
Combust. Flame. 108, 231–234, 1997.
[97] A.D.H. Clague, J.B. donnet, T.K. Wang, J.C.M. Peng. A comparison of Diesel
engine soot with carbon black. Carbon. 37, 1553–1565, 1999.
[98] J. Ahrens, A. Keller, R. Kovacs, K.-H. Homann. Large molecules, radicals,
ions, and small soot particles in fuel-rich hydrocarbon flames. Part III: REMPI
Mass spectrometry of large flame PAHs and Fullerens and their quantitative
calibration through sublimation. Ber. Bunsenges. Phys. Chem. 102(12), 1823–
1839, 1998.
[99] H. Böhm, H. Jander. PAH formation in acetylene-benzene pyrolysis. Phys.
Chem. Chem. Phys. 1, 3775–3781 1999.
[100] N. Slavinskaya, M. Braun-Unkhoff, P. Frank. Modeling of PAH and polyyne
formation in premixed atmospheric c2H4 / air flames. Proc. European Combustion Meeting ECM, 2005.
[101] A. D’Anna, A. D’Alessio, P. Minutolo. Soot Formation in Combustion. Mechanisms and models., 83. Springer-Verlag, Heidelberg, 1994.
[102] P.R. Westmoreland, A.M. Dean, J.B. Howard, J.P. Longwell. Forming benzene
in flames by chemically activated isomerization. J. Phys. Chem. 93, 8171–
8180, 1989.
[103] M.B. Colket, R.J. Hall. Soot formation in combustion. Mechanisms and models., 442. Springer-Verlag, Heidelberg, 1994.
[104] C.F. Melius, M.E. Colvin, N.M. Marinov, W.J. Pitz, S.M. Senkan. Reaction
mechanisms in aromatic hydrocarbon formation involving the C5H5 cyclopentadienyl moiety. Proc. Comb. Inst. 26, 685–692, 1996.
[105] M. Frenklach. Reaction mechanism of soot formation in flames. Phys. Chem.
Chem. Phys. 4, 2028–2037, 2002.
. BIBLIOGRAPHY
155
[106] J.D. Bittner, J.B. Howard. Composition profiles and reaction mechanisms in
a near-sooting premixed benzene/oxygen/argon flame. Proc. Comb. Inst. 18,
1105–1113, 1981.
[107] M. Weissman, S.W. Benson. Mechanism of soot initiation in methane systems.
Prog. Energy Combust. Sci. 15, 273–285, 1989.
[108] J.A. Cole, J.D. Bittner, J.P. Longwell, J.B. Howard. Formation mechanisms
of aromatic compounds in aliphatic flames. Combust. Flame. 56, 51–70, 1984.
[109] A.B. Callear, G.B. Smith. Addition of atomic hydrogen to acetylene. Chain
reactions of the vinyl radical. Chem. Phys. Lett. 105 (1), 119–122, 1984.
[110] J.A. Miller, S.J. Klippenstein, S.H. Robertson. A theorethical analysis of the
reaction between vinyl and acetylene: Quantum chemistry and solution of the
master equation. J. Phys. Chem. 104, 7525–7536, 2000.
[111] M. Frenklach, D. W. Clary, W. C. Gardiner, S. E. Stein. Effect of fuel structure
on pathways to soot. Proc. Comb. Inst. 21, 1067–1076, 1987.
[112] M. Frenklach. On the driving force of PAH production. Proc. Comb. Inst. 22,
1075–1082, 1989.
[113] J.A. Miller, C.F. Melius. Kinetic and thermodynamic issues in the formation
of aromatic compounds in flames of aliphatic fuels. Combust. Flame. 91,
21–39, 1992.
[114] H. Richter, O.A. Mazyar, R. Sumathi, W.H. Green, J.H. Howard, J.W.
Bozzelly. Detailed kinetic study of the growth of small polycyclic aromatic
hydrocarbons. 1. 1-naphthyl + ethyne. J. Phys. Chem. A 105, 1561–1573,
2001.
[115] T. Yu, M. C. Lin, C. F. Melius. Absolute rate constant for the reaction ofphenyl
radical with acetylene. Int. J. Chem. Kinet. 26, 1095–1104, 1994.
[116] R.D. Kern, H.J. Singh, C.H. Wu. Thermal decomposition of 1,2 butadiene.
Int. J. Chem. Kinet. 20, 731–747, 1988.
[117] S. E. Stein, J. A. Walker, M. M. Suryan, A. Fahr. A new path of benzene in
flames. Proc. Comb. Inst. 23, 85–90, 1991.
[118] M. Frenklach, T. Yuan, M. K. Ramachandra. Soot formation in binary hydrocarbon mixtures. Energy Fuels 2, 462–480, 1988.
. BIBLIOGRAPHY
156
[119] C.F. Melius, J.A. Miller, E.M. Evleth. Unimolecular reaction mechanism involving C3H4, C4H4, and C6H6 hydrocarbon species. Proc. Comb. Inst. 24,
621–628, 1992.
[120] D.K. Hahn, S.J. Klippenstein, J.A. Miller. A theoretical analysis of the reaction
between propargyl and molecular oxygen. Faraday Discuss. 119, 79–100, 2002.
[121] N.W. Moriarty, K. Krokidis, W.A. Lester, Jr.M. Frenklach. The addition
reaction of propargyl and acetylene: pathways to cyclic hydrocarbons. Second
Joint Meeting of the US sections of the Combustion institute, Oakland, CA,,
2001.
[122] L.V. Moskaleva, M.C. Lin.
Unimolecular Isomerization/Decomposition
of Cyclopentadienyl and Related Bimolecular Reverse Process: Ab Initio
MO/Statistical Theory Study. J. Comput. Chem. 21, 415–425, 2000.
[123] L.V. Moskaleva, A.M. Mebel, M.C. Lin. The CH3 + C5H5 reaction: A potential source of benzene at high temperatures. Proc. Comb. Inst 26, 521–526,
1996.
[124] E. Ikeda, R.S. Tranter, J.H. Kiefer, R.D. Kern, H.J. Singh, Q. Zhang. The
pyrolysis of methylcyclopentadiene: isomerization and formation of aromatics.
Proc. Comb. Inst 28, 1725–1732, 2000.
[125] H. Wang, K. Brezinsky. Computational sudy on the thermochemistry of cyclopentadiene derivatives and kinetics of cyclopentadienone thermal decomposition. J. Phys. Chem. 102, 1530–1541, 1998.
[126] C.J. Pope, J.A. Miller. Exploring old and new benzene formation pathways in
low-pressure premixed flames of aliphatic fuels. Proc. Comb. Inst 28, 1519–
1527, 2000.
[127] N.M. Marinov, W.J. Pitz, C.K. Westbrook, M.J. Castaldi, S.M. Senkan. Modeling of aromatic and polycyclic aromatic hydrocarbon formation in premixed
methan and ethane flames. Combust. Sci. Tech. 116-117, 211–287, 1996.
[128] N.M. Marinov, M.J. Castaldi, C.F. Melius, W. Tsang. Aromatic and polycyclic
aromatic hydrocarbon formation in a premixed propane flame. Combust. Sci.
Tech. 128, 295–342, 1997.
[129] M.J. Castaldi, N.M. Marinov, C.F. Melius, J. Huang, S.M. Senkan, W.J. Pitz,
C.K. Westbrook. Experimental and modeling investigation of aromatic and
polycyclic aromatic hydrocarbon formation in a premixed ethylene flame. Proc.
Comb. Inst. 26, 693–702, 1996.
. BIBLIOGRAPHY
157
[130] J.A. Miller. Theory and modeling in combustion chemistry. Proc. Comb. Inst.
26, 461–480, 1996.
[131] A. Kazakov, H. Wang, M. Frenklach. Detailed modeling of soot formation in
laminar premixed ethylene flames at a pressure of 10bar. Combust. Flame.
100, 111–120 1995.
[132] P. Markatou, H. Wang, M. Frenklach. A computational study of sooting limits
in laminar premixed flames of ethane, ethylene, and acetylene. Combust.
Flame 93, 467–482, 1993.
[133] H. Richter, J.B. Howard. Industrial production of fullerenic materials. Prog.
Energy Combust. Sci. 26, 565–608, 2000.
[134] J.A. Miller. Concluding remarks. Faraday Discuss. 119, 461–475, 2001.
[135] A. Violi, A. F. Sarofim, T. N. Truong. Quantum mechanical study of molecular
weight growth process by combination of aromatic molecules. Combust. Flame
126, 1506–1515, 2001.
[136] J.H. Kiefer, R.S. Tranter, H. Wang, A.F. Wagner. Thermodynamic functions
for the cyclopentadienyl radical: The effect of Jahn-Teller distortion. Int. J.
Chem. Kinet. 33, 834–845, 2001.
[137] N.M. Moriarty, M. Frenklach. Ab inition study of naphthalene formation by
addition of vinylacetylene to phenyl. Proc. Comb. Inst. 28, 2563–2568, 2000.
[138] F. Dubnikova, A. Lifshitz. Ring expansion in methylcyclopentadiene radicals.
Quantum chemical and kinetics calculations. J. Phys. Chem. 106, 8173–8183,
2002.
[139] K. Roy, Ch. Horn, P. Frank, V.G. Slutsky, Th. Just. High temperature investigations of the pyrolysis of cyclopentadiene. Proc. Comb. Inst. 27, 329–336,
1998.
[140] R.D. Kern, Q. Zhang, J. Yao, R.S. Jursic, R.S. Tranter, M.A. Greybill, H.J.
Kiefer. Pyrolysis of cyclopentadiene: rates for initial C-H bond fission and the
decomposition of c-C5H5. Proc. Comb. Inst 27, 142–150, 1998.
[141] S. E. Stein. On the high temperature chemical equilibria of polycyclic aromatic
hydrocarbons. J. Phys. Chem. 82, 566–571, 1978.
[142] S. E. Stein, A. Fahr. High-temperature stabilities of hydrocarbons. J. Phys.
Chem. 89, 3714–3725, 1985.
. BIBLIOGRAPHY
158
[143] I. Glassman. Phenomenological Models of Soot Processes in Combustion Systems. Report No. 1450. AFOSR TR, 1979.
[144] M.B. Colket. The pyrolysis of C2H2 and vinylacetylene in a single-pulse shock
tube. Proc. Comb. Inst. 21, 851–864, 1987.
[145] P. Lindstedt, L. Maurice, M. Meyer. Thermodynamic and kinetic issues in the
formation and oxidation of aromatic species. Faraday Discuss. 119, 409–432,
2002.
[146] J.A. Miller, S.J. Klippenstein. The recombination of propargyl radicals and
other reactions on a C6H6 potential. J. Phys. Chem. 107, 7783–7799, 2003.
[147] M. Frenklach, N. M. Moriarty, N. J. Brown. Hydrogen migration in polyaromatic growth. Proc. Comb. Inst 27, 1655–1661, 1998.
[148] N.W. Moriarty, N.J. Brown, M. Frenkalch. Hydrogen migration in the
phenylethen-2-yl radical. J. Phys. Chem. 103, 7127–7135, 1999.
[149] M. Frenklach, C. A. Schuetz, J. Ping. Migration mechanism of aromatic-edge
growth. Proc. Comb. Inst. 30, 1389–1396, 2005.
[150] K. G. Neoh, J. B. Howard, A. F. Sarofim. Particulate Carbon Formation
During Combustion., 261. Plenum Press, New York, 1981.
[151] C. Pels Leusden, N. Peters. Experimental and numerical analysis of the influence of oxygen on soot formation in laminar counterflow flames of acetylene.
Proc. Comb. Inst. 28, 2619–2625, 2000.
[152] L.D. Pfefferle, G. Bermudes, J. Byle. Soot formation in combustion., Kapitel
Benzene and higher hydrocarbon formation during alene pyrolysis. SpringerVerlag, Berlin/Heidelberg, 1994.
[153] M. Frenklach, L. B. Ebert. Comment on the proposed role of spheroidal carbon
clusters in soot formation. J. Phys. Chem. 92, 561–563, 1988.
[154] J.H. Miller. The kinetics of polynuclear aromatic hydrocarbon agglomeration
in flames. Proc. Comb. Inst. 23, 91 1990.
[155] C.A. Amann, D.C. Siegla. Diesel particulates-what they are and why. Aerosol
Science and Technology 1, 73–101, 1982.
[156] T. Feng. Numerical modeling of soot and NOx formation in non-stationary
diesel flames with complex chemistry. Diplomarbeit, Department of Termo
and Fluid Dynamics, Chalmers University of Technology, Göteborg, Sweden,
2003.
. BIBLIOGRAPHY
159
[157] G.W. Smith. Kinetic aspects of diesel soot coagulation. SAE paper, 1982.
[158] M. Frenklach, H. Wang. Detailed kinetic modeling of soot particle nucleation
and growth. Proc. Comb. Inst. 23, 1559–1566, 1990.
[159] J.B. Howard. Carbon addition and oxidation reactions in heterogeneous combustion and soot formation. Proc. comb. Inst. 23, 1107–1127, 1990.
[160] A. D’Anna, A. Violi, A. D’Alessio, A. F. Sarofim. A reaction pathway for
nanoparticle formation in Rich premixed flames. Combust. Flame. 127, 1995–
2003, 2001.
[161] H. Gg. Wagner. Particle carbon formation during combustion., Kapitel Mass
growth of soot. Plenum Press, New York, 1981.
[162] S.J. Harris, A.M. Weiner. Surface growth of soot particles in premixed ethyleneair flames. Combust. Sci. Tech. 31, 155–167, 1983.
[163] J.C. Dasch. Decay of soot surface growth reactivity and its importance in total
soot formation. Combust. Flame. 61, 219–225, 1985.
[164] S.J. Harris, A.M. Weiner. Surface growth and soot particle reactivity. Combust.
Sci. Tech. 72, 67 1990.
[165] F. Xu, G. M. Faeth. Soot formation in laminar acetylene/air diffusion flames
at atmospheric pressure. Combust. Flame. 125, 804–819, 2001.
[166] B.S. Haynes, H. Jander, H.Gg. Wagner. Optical studies of soot formation
processes in premixed flames. Ber. Buns. Gesellschaft. 84(6), 585–592, 1980.
[167] T.G. Benish, A.L. Lafleur, K. Tghizadeh, J.B. Howard. C2H2 and PAH as
surface growth reactants in premixed C2H4-air flames. Proc. Comb. Inst. 26,
2319–2326, 1997.
[168] A. S. Feitelberg, J. P. Longwell, A. F. Sarofim. Metal enhanced soot and PAH
formation. Combust. Flame. 92, 241–253, 1993.
[169] A. Kazakov, M. Frenklach. Brief comunication on the relative contribution
of C2H2 and PAH to soot particle surface growth. Combust. Flame. 112,
270–274, 1998.
[170] K.H. Homann. Carbon formation in premixed flames. Combust. Flame. 11,
265 1967.
[171] J.B. Howard, B.L. Wersborg, G.C. Williams. Coagulation of carbon particles
in premixed fkames. Faraday Symp. Chem. Soc. 7, 109–119, 1973.
. BIBLIOGRAPHY
160
[172] M.V. Smoluchowski. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Loesungen. Z. Phys. Chem. 92, 129–168, 1917.
[173] S.C. Graham. The collisional growth of soot particles at high temperatures.
Proc. Comb. Inst. 16, 663–669, 1976.
[174] K.G. Neoh, J.B. Howard, A.F. Sarofim. Effect of oxidation on the physical
structure of soot. Proc. Comb. Inst. 20, 951–957, 1985.
[175] R.P. Lucht, D.W. Sweeney, N.M. Laurendeau.
Laser-saturated fluorescence measurements of hydroxyl radical in atmospheric pressure
methane/oxygen/nitrogen flames under sooting and non-sooting conditions.
Comb. Sci. Tech. 42, 259–281, 1985.
[176] F. Liu, H. Guo, G.J. Smallwood, O.L. Gülder. The chemical effect of carbon
dioxide as an additive in an ethylene diffusion flame: implications for soot and
NOx formation. Combust. Flame. 125, 778–787, 2001.
[177] J. Vandooren. 20th Task leaders Meeting of the implementing agreement ”Energy Conservation and Emission reduction in Combustion”. 1998.
[178] Ü.Ö. Köylü, G.M. Faeth. Structure of everfine soot in buoyant turbulent diffusion flames at long residence times. Combust. Flame. 89, 140 1992.
[179] Ü.Ö. Köylü, G.M. Faeth, T.L. Farias, M.G. Cavalho. Fractal and projected
structure properties of soot aggregates. Combust. Flame. 100, 62 1995.
[180] P. Deuflhard, M Wulkow. Computational treatment of polyreaction kinetics
by orthogonal polynomials of a discrete variable. Impact Computing Science
Engineering 1, 269–301, 1989.
[181] P. Deufelhard, J. Ackermann. Adaptive discrete Galerkin-methods for macromolecular processes., Kapitel Preprint SC 93-22. Konrad-Zuse-Zentrum für
Informationstechnik Berlin, 1993.
[182] P. Deuflhard, G. Bader, U. Nowak. LARKIN - A software package for the
simulation of large systems arrising in chemical reaction kinetics. In: K. H.
Ebert, P. Deuflhard and W. Jaeger (Hrsg.). Spronger-Verlag, 1981.
[183] P. Deufelhard, M. Wulkow. Simulationsverfahren für die Polymerchemie,
Kapitel Preprint 94-22. Konrad-Zuse-Tentrum für Informationstechnik,
Berlin, 1994.
[184] K.H. Ebert, P. Deuflhard, W. Jäger. Modeling of chemical reaction systems.
Springer Series, Chem. Phys. 18, 1981.
. BIBLIOGRAPHY
161
[185] G. Bader, U. Nowak, P. Deuflhard. An advanced simulation package for large
Chemical reaction systems. University of Heidelberg, SFB 123, Technical Report 149, 1982.
[186] P. Deuflhard. Efficient numerical simulation and identification of large chemical reaction systems. Ber. Bunseges. Phys. Chem. 90, 940–946, 1986.
[187] P.A. Vlasov, J. Warnatz, I. Naydenova. Kinetic Modeling of the soot formation
mechanism during rich oxidation of methane, propane, and n-heptane behind
shock waves. Chim. Phys. Reports 23, 36–43, 2004.
[188] G. L. Agafonov, I. Naydenova, P. A. Vlasov, J. Warnatz. Detailed kinetic
modeling of soot formation in shock tube pyrolysis and oxidation of toluene
and n-heptane. Proc. Comb. Inst. 31, 575–583, 2007.
[189] C. Correa, H. Niemann, B. Schramm, J. Warnatz. Reaction mechanism reduction for higher hydrocarbons by the ILDM mehod. Proc. Comb. Inst. 28,
1607–1614, 2000.
[190] C.I. Heghes. PhD Thesis, C1-C4 hadrocarbon oxidation mechanism. Diplomarbeit, Interdisciplinary Center for Scientific Computing, Ruprecht-karlsHeidelberg Universtity, 2006.
[191] J.H. Kiefer, S.S. Sidhu, R.D. Kern, K. Xie, H. Chen, L. Harding. The homogeneous pyrolysis of acetylene II: The high temperature radical chain mechansim,.
Comb. Sci. Tech. 82, 101–130, 1992.
[192] H. G. Wagner, P. A. Vlasov, K. J. Dörge, A. V. Eremin, I. S. Zaslonko,
D. Tanke. The kinetics of carbon cluster formation during C3O2 pyrolysis.
Kinet. Catal. 42, 645–656, 2001.
[193] M. Frenklach. On surface growth mechanism of soot particles. Proc. Comb.
Inst. 26, 2285–2293, 1996.
[194] A. Burcat. Third Millennium ideal gas and condensed phase thermochemical
database for combustion. Techion Aerospace Engineering (TAE) Report, 2001.
[195] D. Tanke. PhD Thesis. Rußbildung in der Kohlenwasserstoff-Pyrolyse hinter
Stoßwellen. Diplomarbeit, Universität Götingen, 1995.
[196] A Boehm, F. Lacas. On extinctiuon limits and polycyclic aromatic hydrocarbon
formation in straind counterflow diffusion flames from 1 to 6 bar. Proc. Comb.
Inst. 28, 2627–2634, 2000.
. BIBLIOGRAPHY
162
[197] K.C. Smyth, C.R. Shaddix. The elusive history of m=1.57 - 0.56i for the
refractive index of soot. Combust. Flame. 107, 314–320, 1996.
[198] H. Kellerer, A. Müller, H. J. Bauer, S. Wittig. Soot formation in a shock tube
under elevated pressure conditions. Comb. Sci. Tech. 113, 67–80, 1996.
[199] A. Violi, A. F. Sarofim, G. A. Voth. Kinetic Monte Carlo-molecular dynamics
approach to model soot inception. Combust. Sci. Tech. 176, 991–1005, 2004.
[200] A. D’Alessio, A. D’Anna, P. Minutolo, L.A. Sgro, A. Violi. On the relevance
if surface growth in soot formation in premixed flames. Proc. Comb. Inst. 28,
2547–2554, 2000.
[201] M.S. Skjoth-Rasmussen, P. Glarborg, M. Ostberg, J.T. Johannessen, H. Livbjerg, A.D. Jensen, T.S. Christensen. Formation of polycyclic aromatic hydrocarbons and soot in fuel-rich oxidation of methane in a laminar flow reactor.
Combust. Flame 136, 91–128, 2004.
[202] A. Burcat, B. Ruscic. Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with updates from Active Thermochemical Tables. ANL-05/20 and TAE 960. Technion-IIT, Aerospace Engineering,
and Argonne National Laboratory, Chemistry Division, 2005.
[203] S.J. Harris, A.M. Weiner. A picture of soot particle inception. Proc. Comb.
Inst. 22, 333–342, 1988.
[204] J.T. McKinnon, J.B. Howard. The role of PAH and acetylene in soot nucleation and growth. Proc. Comb. Inst. 24, 965–971, 1992.
[205] S. Scherer. Untersuchung pyrolytischer Reactionen der Rußvorläufermoleküls
Propargyl im Stoßwellenrohr. PhD Thesis, Universität Stuttgart, Institut für
Physikalische Chemie der Verbrennung des DLR in Stuttgart, 2001.
[206] C. Horn, P. Frank. High temperature pyrolysis of phenol. In Proceedings of
the 4th International Conference on Chemical Kinetics, NIST. Gaithersburg,
MD, USA, 1997.
[207] V. Vasudevan, D. F. Davidson, R. K. Hanson. Shock tube measurments of
toluene ignition tumes. Proc. Comb. Inst. 30, 1155–1163, 2005.
[208] D.L. Baulch, C.J. Cobos, R.A. Cox, C. Esser, P. Frank, Th. Just, J.A. Kerr,
M.J. Pilling, J. Troe, R.W. Walker, J. Warnatz. Evaluated kinetic data for
combustion modelling. J. Phys. Chem. 21(3), 411 1992.
. BIBLIOGRAPHY
163
[209] V.V. Lissianski, V.M. Zamanski, W.C. Gardiner Jr. Gas-phase combustion
chemistry, Kapitel Combustion Chemistry Modeling. Springer-Verlag, 2000.
[210] M.A. Mallard, F. Westley, J.T. Herron, R.F. Hampson, D.H. Finzzel. NIST
Chemical kinetic database, Verson 6.0. In National Institute of Standarts and
Technology, MD. Gaithersberg, 1994.
[211] M.B. Colket, D.J. Seery. Reaction mechanisms for toluene pyrolysis. Proc.
Comb. Inst. 25, 883–891, 1994.
[212] G. Porter, J.I. Steinfeld. Rate of Dimerisation of Gaseous Benzyne. J. Chem.
Soc. A, 877–878, 1968.
[213] A.M. Mebel, M.C. Lin, T. Yu, K. Morokuma. Theoretical Study of Potential
Energy Surface and Thermal Rate Constants for the C6H5 + H2 and C6H6
+ H Reactions. J. Phys. Chem. 101, 3189–3196, 1997.
[214] J. L. Emdee, K. Brezinsky, I. Glassman. A Kinetic model for the oxidation of
toluene near 1200 K. J. Phys. Chem. 96, 2151–2161, 1992.
[215] H. Richter, W.J. Grieco, J.B.Howard. Formation mechanism of polycyclic
aromatic hydrocarbons and fullerenes in premixed benzene flames. Combust.
Flame. 119, 1–22, 1999.
[216] N.M. Marinov, W.J. Pitz, C.K. Westbrook, A.M. Vincitore, M.J. Castaldi,
S.M. Senkan, C.F. Melius. Aromatic and polycyclic aromatic hydrocarbon formation in a laminar premixed n-butane flame. Combust. Flame. 114, 192–213,
1998.
[217] A. D’Anna, A. Violi. A kinetic model for the formation of aromatic hydrocarbons in premixed laminar flames. Proc. Comb. Inst. 27, 425–433, 1998.
[218] J. Warnatz. Concetration-, pressure-, and temperature-dependence of the flame
velocity in hydrogen-oxygen-nitrogen mixtures. Comb. Sci. Tech. 26, 203–213,
1981.
[219] H. Bockhorn, F. Fetting, H. W. Wenz. Investigation of the formation of high
molecular hydrocarbons and soot in premixed hydrocarbon-oxygen flames. Ber.
Bunsenges. Phys. Chem. 87, 1067–1073, 1983.
[220] K.C. Smyth, J.H. Miller. Chemistry of molecular growth processes in flames.
Science. 236, 1540–1546, 1987.
. BIBLIOGRAPHY
164
[221] A. Alexiou, A. Williams. Soot formation in shock-tube pyrolysis of toluene,
toluene-methanol, toluene-ethanol, and toluene-oxygen mixtures. Combust.
Flame. 104, 51–65, 1996.
[222] C.T. Bowman, D.M. Golden, R.K. Hanson, H. Pitsch, A. Bardos, R. Cook,
Z. Hong, P. Iyengar, Shashank, S. Vasu, K. Walters, R. Malhotra. Optimization of synthetic oxygenated fuels for diesel engines. GCEP Technical Report.,
2006.
[223] P.A. Tesner, T.D. Snegriova, V.G. Knorre. Kinetics of dispersed carbon formation. Combust. Flame. 17, 253–260, 1971.
[224] B.F. Magnussen, B.H. Hjertager. On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Proc. Comb.
Inst. 16, 719–729, 1976.
[225] A.A. Amsden. KIVA-3V: A block-structured KIVA program for engines with
vertical or canted valves. In Los Alamos National Laboratory, Report LA13313-MS, 1997.
[226] H. Hiroyasu, T. Kadota, M. Arai. Development and use of a spray combustion
modeling to predict Diesel engine efficiency and pollutant emissions (Part 1:
Combustion modeling.). In Bulletin of the JSME 26: 569-575, 1983.
[227] P. Belardini, C. Bertoli, C. Beatrice, A. D’Anna, N. Del Giacomo. Application
of a reduced kinetic model for soot formation and burnout in three-dimensional
Diesel combustion computations. Proc. Comb. Inst. 26, 2517–2524, 1996.
[228] S.-C. Kong, Z.Y. Han, R.D. Reitz. The development and application of a
Diesel ignition and combustion model for multidimensional engine simulation.
SAE paper 950278, 1995.
[229] D.K. Mather, R.D. Reitz. Modeling the influence of fuel injection parameters
on Diesel engine emissions. In SAE paper 980789, 1998.
[230] W. Kollmann, I.M. Kennedy, M. Metternich, J.-J. Chen. Soot Formation
in Combustion., Kapitel Application of a soot model to a turbulent ethylene
diffusion flame., 503–526. Springer-Verlag, Berlin,Heidelberg, 1994.
[231] R. P. Lindstedt. Soot formation in Combustion., Kapitel Simplified soot nucleation and surface growth steps for non-premixed flames. Springer-Verlag,
Berlin, 1994.
. BIBLIOGRAPHY
165
[232] A. Kazakov, D.E. Foster. Modeling of soot formation during DI Diesel combustion using a multi-step phenomenological model. In SAE paper 982463,
1998.
[233] F. Tao. Numerical modeling of soot and NOx formation in non-stationary
Diesel flames with complex chemistry. PhD Thesis, Chalmers University of
Technology, Department of Thermo and Fluid Dyanmics, 2003.
[234] J.B. Moss. Soot formation in combustion., Kapitel Modeling soot fomation
for turbulent flame prediction., 551–568. Springer-Verlag, Berlin, Heidelberg,
1994.
[235] J.B. Moss, C.D. Stewart, K.J. Young. Modeling soot formation and burnout
in a high tempertaure laminar diffusion flame burning under oxygen-enriched
conditions. Combust. Flame. 101, 491–500, 1995.
[236] C. Correa. Combustion Simulations in Diesel engines using reduced reaction
mechanisms. PhD Thesis, Ruprecht-Karls-University of Heidelberg, Interdisciplinary Center for Scientific Computing, 2000.
[237] I. Naydenova, J. Marquetand, J. Warnatz. Soot formation simulation of shock
tube experiments with the use of an empirical model. In ECM, 2007.
[238] M. Frenklach, M. K. Ramachandra, R. Matula. Soot formation in shock-tube
oxidation of hydrocarbons. Proc. Comb. Inst. 20, 871–878, 1984.
[239] St. Bauerle, Y. Karasevich, St. Slavov, D. Tanke, M. Tappe, Th. Thienel,
H.Gg. Wagner. Soot formation at elevated pressure and carbon concentrations
in haydrocarbon pyrolysis. Proc. Comb. Inst. 25, 627–634, 1994.
[240] H. Jander. Personal Correspondence., 1998.