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Modeling combustion of single biomass particle
Citation for published version (APA):Haseli, Y. (2012). Modeling combustion of single biomass particle. Technische Universiteit Eindhoven.https://doi.org/10.6100/IR735438
DOI:10.6100/IR735438
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Modeling Combustion of Single Biomass Particle
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
rector magnificus, prof.dr.ir. C.J. van Duijn, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen
op maandag 22 oktober 2012 om 16.00 uur
door
Yousef Haseli
geboren te Orumiyeh, Iran
1
Dit proefschrift is goedgekeurd door de promotor:
prof.dr. L. P. H. de Goey
Copromotor:
dr.ir. J . A. van Oijen
Haseli, Yousef
Modeling Combustion of Single Biomass Particle
A catalogue record is available from the Eindhoven University of Technology Library.
ISBN: 978-9-038-63217-9
Printed in the Netherlands
by Eindhoven University Press
Copyright © 2012 by Yousef Haseli
All rights reserved. Neither this thesis nor any part of it may be reproduced, or stored
in a retrieval system, or transmitted in any form or by any means, electronic or me-
chanical, including photocopying, microfilming, and recording, or by any information
storage, without prior permission in writing from the author.
2
iii
Modeling Combustion of
Single Biomass Particle
Yousef Haseli
3
4
Abstract
Coal fired power plants contribute significantly to greenhouse gas emission, nota-
bly CO2. A novel method to effectively reduce the amount of CO2 emission is to co-
fire a high fraction of biomass and coal at oxygen enriched environments. However,
this technique has not been demonstrated on a large-scale yet. The objective of this
PhD research is to perform a detailed modelling study of combustion of a single bio-
mass particle and to establish reduced models which can be used for describing the
main characteristics of pyrolyzing and combusting single biomass particles to be em-
ployed in design codes of industrial furnaces. To accomplish the goals of this PhD the-
sis, the research has been carried out in two main stages.
First, the sub-processes involved in the biomass combustion are identified and de-
scribed with a one-dimensional mathematical model based on conservation of mass,
energy and momentum. The model encompasses the kinetics of biomass pyrolysis,
homogeneous reactions and heterogeneous char oxidation and gasification reactions,
coupled with transient transport equations. Subsequently, this model is implemented in
an in-house code and a comprehensive numerical study on pyrolysis and combustion
of single biomass particles is conducted. The accuracy of the model is examined by
comparing its predictions with several experimental data obtained from the literature
on pyrolysis and combustion of various types of single biomass particles. The com-
puter code based on the detailed model allows one to observe time and space evolution
of several parameters including biomass and char densities, gaseous species mass frac-
tions, porosity, internal pressure, mass flux of volatiles within the pores of the solid
matrix, and temperature. The model is used for simulation of combustion of particles
of three common shapes; i.e. slab, cylinder and sphere. The results of the detailed
modelling study reveal that the combustion of a single biomass particle at the condi-
tions of industrial furnaces (small particles and high heating conditions) consists of
three main sub-processes: preheating, pyrolysis, and char oxidation. Therefore, any
simplified/reduced particle model should account for these three processes.
In the next stage of the project, simplified models are developed to predict the main
characteristics of pyrolyzing and combusting single biomass particles. Initially, the
preheating stage is modelled using a time and space integral method, which allows one
to convert the partial differential form of the heat transfer equation into an algebraic
equation. This treatment is then applied to model the pyrolysis process. Two possible
regimes are identified: thermally thin and thermally thick particles. A model is estab-
lished for both regimes, which consists of a set of algebraic equations. This treatment
highly simplifies the pyrolysis model so that it can be used in practical applications,
which may involve thousands or even millions of particles. The validation of the sim-
plified preheating and pyrolysis models is carried out using various experiments and
the results of the detailed model based on partial differential equations (PDEs).
The char particle oxidation and gasification processes as the last stages of the parti-
cle combustion process, are modelled using the shrinking core approximation. The ac-
curacy of this model is assessed using the experiments reported in past studies. The
model is used to study the dynamics of biomass char combustion at oxy-fuel condi-
5
vi
tions. The effects of the main process parameters on the maximum particle tempera-
ture and burnout time are examined. It is found that oxy-fuel combustion with an oxy-
gen mass fraction of 0.3 and higher may lead to a considerable reduction in particle
temperature and burnout time compared to the conventional operating case with air as
the gasifying agent. In the last stage of this PhD research, the simplified models of
biomass particle pyrolysis and char combustion are combined to establish a reduced
model for combustion of a single biomass particle. The accuracy of this simplified
combustion model is examined using the measured data available in the literature as
well as the results of the detailed model. As a conclusion, the simplified models devel-
oped in this thesis for pyrolysis and combustion of single biomass particles are effi-
cient enough to capture the main process parameters, and computationally cheaper
than the PDE-based models so that they can be used in the design codes of biomass
furnaces.
6
Acknowledgment
I would like to express my indebtedness to my advisor, Prof. Philip de Goey, for his
excellent guidance, encouragement, and patience, who supported me throughout my
PhD program; to develop and establish my ideas. Despite his extreme activities as the
head of Combustion Technology Group and Dean of Mechanical Engineering De-
partment in TUe, he always offered his support when I needed it. I also thank Dr.
Jeroen van Oijen, the co-promoter of this thesis, whom I had productive discussions
with, and who walked with me from the start of my work at Combustion Technology
group until the completion of this thesis. This research was financially supported by
Dutch Technology Foundation (STW).
I use this opportunity to express my gratitude to all decent individual that I met at
TUe, in particular, Prof. Hans Kuerten, Prof. David Smeulders, Dr. Cees van der Geld,
Dr. Carlo Luijten, Yuri, Evgeniy, Maarten, Manohar, Victor, Emanuele, Mayuri,
Liselotte, Miao, Ulaş, Selim, Maurice, Giel, Michael, Akshay, Sudipto, and Francisco.
I wish them all continuous success in their future careers. Most importantly, I owe my
loving thanks to my family for their unconditional support, love, encouragement and
understanding; without which I would not have reached this point of my life.
Yousef Haseli
August 2012, Eindhoven
7
vi
8
Nomenclature
A Pre-exponential or frequency factor, 1/s
A Surface reaction pre-exponential factor, kg/m2.s.atm
n
Av Specific inner surface, 1/m
Bi Biot number
cP Specific heat, J/kg.K
D Diffusivity coefficient, m2/s
Deff Effective binary diffusion coefficient, m2/s
Dij Binary diffusion coefficient, m2/s
d Pore diameter, m
d Particle diameter, m
E Activation energy, J/mol
e Surface emissivity
H Enthalpy, J
h Convective heat transfer coefficient, W/m2.K
hext External heat transfer coefficient, W/m2.K
hf Enthalpy of formation, J/kg
h Total enthalpy, J/kg
K Permeability, m2
k Thermal conductivity, W/m.K
k Reaction rate, 1/s
k* Effective thermal conductivity, W/m.K
kB Boltzmann constant, J/K
kd Mass transfer coefficient, m/s
L Thickness/length of particle, m
Lcr Minimum particle length for transition from thermally thin to
thermally thick particle, m
M, MW Molecular weight, mol/g
m Mass, kg
m ′′& Decomposition rate per unit surface area, kg/m2.s
vm ′′& Volatiles mass flux per unit surface area, kg/m
2.s
Nu Nusselt number
n Shape factor
n Reaction order (Chapter 7)
9
x
nsto Stoichiometry coefficient
P Pressure, Pa
Pr Prandtl number
Py’ External pyrolysis number
Q~
Source term in energy equation, J/m3.s
qx External heat flux, W/m2
q ′′ Heat flux, W/m2
netq ′′ Net heat flux at particle surface, W/m
2
Rq ′′ Net heat flux at particle surface at the time tR, W/m
2
R Particle radius, m
Rg Universal gas constant, J/mol.K
Re Reynolds number
r Reaction rate, 1/s
r Surface reaction rate (Chapter 7), kg/m2.s
r Radial coordinate
rc Char depth, m
rt Thermal penetration depth, m
S Source term
Sa Specific surface area, m2/kg
Sc Schmidt number
T Temperature, K
Tp Pyrolysis temperature, K
Ts Surface temperature, K
TsL Surface temperature at the time tL, K
TsR Surface temperature at the time tR, K
t Time, s
tb Burnout time, s
tign Time of commencement of pyrolysis at particle surface, s
tL Duration of thermal penetration movement from the front sur-
face to the back face of the slab particle, s
tp Pyrolysis time, s
tpini Time of commencement of pyrolysis at particle surface, s
tR Duration of thermal penetration movement from the front sur-
face to the center of cylindrical/spherical particle, s
u Superficial gas velocity, m/s
X mole fraction
10
xi
x Axial coordinate
xc Char depth, m
xt Thermal penetration depth, m
Y Mass fraction
Greek letters
α Thermal diffusivity, m2/s
ε Porosity
εi, εj Characteristic Lennard-Jones energy, J
θ Dimensionless temperature, Eq. (5.28)
Κ Dimensionless parameter defined in Eq. (5.30)
λ Thermal conductivity, W/m.K
ξ Dimensionless distance, Eq. (5.26)
ρ Density, kg/m3
∆hB-g Enthalpy of Bio → Gas and Bio → Tar reactions, J/kg
∆hB-C Enthalpy of Bio → Char reaction, J/kg
∆hCom Enthalpy of char oxidation reaction, J/kg
∆hGasif Enthalpy of char gasification reaction, J/kg
∆hT-g Enthalpy of tar cracking reaction, J/kg
∆hP Enthalpy of pyrolysis, J/kg
∆hv Specific heat of volatiles combustion, J/kg
µ Viscosity, kg/m.s
σ Stephan-Boltzmann constant
σ Collision diameter (Chapter 7)
τ Dimensionless time
Ω Dimensionless heat flux, Eq. (5.29)
Ω Collision integral (Chapter 7)
ν Mass fraction of gaseous species in light gas
Subscripts
0 Initial condition
∞ Surrounding condition
B Biomass
BC Boundary condition
C Char
ext External
f Final
11
xii
G Light gases
g Gas phase (tar + light gases)
max Maximum
p Pyrolysis/ignition
ph Post-pyrolysis heating up
r Reactor
s Particle surface
surr Surrounding
T Tar
12
Contents
Abstract v
Acknowledgment vii
Nomenclature ix
Chapter 1 Objectives 1
1.1 Introduction 1
1.2 Overview of Recent Fossil Fuel Consumption 2
1.3 Energy From Biomass 8
1.4 Oxy-Fuel Combustion 8
1.5 Objectives 10
1.6 Thesis Outline 12
References 14
Chapter 2 Literature Review 15
2.1 Introduction 15
2.2 Pyrolysis 16
2.2.1 Kinetic Data 17
2.2.1.1 Primary Reactions 18
2.2.1.2 Secondary Reactions 21
2.2.2 Heat of Pyrolysis 21
2.3 Homogeneous Reactions 23
2.4 Heterogeneous Reactions 25
2.5 Past Detailed Modeling Studies 26
2.6 Past Simplified Modeling Studies 27
2.8 Conclusion 28
References 30
Chapter 3 Modeling Biomass Particle Pyrolysis 35
3.1 Introduction 35
3.2 Pyrolysis Model 36
3.2.1 Conservation of Species Mass 38
3.2.2 Conservation of Energy 38
3.2.3 Conservation of Momentum 41
3.2.4 Initial and Boundary Conditions 42
13
xii
3.2.5 Simulation Code 43
3.3 Experimental Validation 44
3.3.1 Comparison with Grønli and Melaaen Data 44
3.3.2 Comparison with Data of Koufopanos et al. 49
3.3.3 Comparison with Data of Rath et al. 56
3.3.4 Conclusion 58
3.4 Pyrolysis Model with an Experimental Correlation for
Heat of Reactions 59
3.5 Conversion Time and Final Char Yield 71
3.6 Pyrolysis Regime at High Heating Conditions 77
3.7 Conclusion 85
References 86
Chapter 4 Modeling Biomass Particle Combustion 91
4.1 Introduction 91
4.2 Modeling Approach 92
4.2.1 Pyrolysis Kinetic Model 92
4.2.2 Homogeneous Reactions 92
4.2.3 Char Gasification and Combustion 93
4.2.4 Transport Equations 94
4.3 Model Validation 98
4.4 Simulation Results 103
4.5 Conclusion 113
References 113
Chapter 5 Simplified Preheating Model 115
5.1 Introduction 115
5.2 Ignition Time of a Wood Slab 118
5.3 Ignition Time of Cylindrical and Spherical Particles 122
5.4 Dimensionless Analysis 126
5.5 Numerical Results and Discussion 131
5.5.1 Ignition Time of a Thermally Thick Particle 131
5.5.2 Transition Criterion 131
5.5.3 Ignition Time of Thermally Thin Particle 136
5.5.4 Comparison with Experiments 140
5.6 Conclusion 141
14
xiii
References 142
Chapter 6 Simplified Pyrolysis Model 145
6.1 Introduction 145
6.2 Description of the Process 148
6.3 Formulation 152
6.3.1 Thermally Thin Particle 152
6.3.1.1 Initial Heating up 152
6.3.1.2 Pre-Pyrolysis Heating up 153
6.3.1.3 Pyrolysis 153
6.3.1.3.1 Double-Temperature Profile 153
6.3.1.3.2 Single-Temperature Profile 156
6.3.1.4 Post-Pyrolysis Heating up 158
6.3.2 Thermally Thick Particle 161
6.3.3 Numerical Solution 164
6.4 Model Validation 164
6.4.1 Thermally Thin Particle 166
6.4.2 Thermally Thick Particle 170
6.5 Discussion 176
6.6 Conclusion 181
References 182
Chapter 7 Simplified Char Combustion Model 185
7.1 Introduction 185
7.2 Modeling Approach 190
7.3 Model Validation 199
7.4 Conclusion 202
References 202
Chapter 8 Simplified Biomass Combustion Model 209
8.1 Introduction 209
8.2 Modeling Approach 212
8.2.1 Heating up Phase 214
8.2.2 Pyrolysis Phase 219
8.2.3 Char Combustion Phase 224
8.3 Model Validation 225
8.3.1 Validation of the Heating up Model 225
15
xiv
8.3.2 Validation of the Pyrolysis Model 226
8.3.3 Validation of the Combustion Model 227
8.4 Effect of Particle Size and Heating Condition 230
8.5 Conclusion 234
References 235
Chapter 9 OxyFuel Combustion of Wood Char Particle 237
9.1 Introduction 237
9.2 Burnout Time 238
9.3 Maximum Particle Temperature 242
9.4 Particle Combustion Dynamics 243
9.5 Useful Relationships 247
9.6 Conclusion 249
References 250
Chapter 10 Conclusion 251
10.1 Detailed Modeling Study 251
10.1.1 Biomass Particle Pyrolysis 251
10.1.2 Biomass Particle Combustion 252
10.2 Simplified Modeling Study 252
10.2.1 Simplified Preheating Model 252
10.2.2 Simplified Pyrolysis Model 253
10.2.3 Simplified Char Combustion Model 253
10.2.4 Simplified Biomass Combustion Model 254
Appendix A Derivation of Heat Transfer Equation 255
Appendix B Makino-Law Theory 259
Appendix C Char Oxidation and Gasification Data 261
Appendix D Derivation of the Simplified Pyrolysis Model Equations 269
16
Chapter 1
Objectives
1.1 INTRODUCTION
We just passed the first decade of the 21st century while we have been fac-
ing serious issues regarding uncertainties over longevity of fossil fuels and in-
creasing concerns about environmental impact of fossil and nuclear energy-
based technologies. Researchers in various parts of the globe have commenced
fundamental investigations about the feasibility of utilization of alternative and
environmental-friendly fuels such as solar, wind, hydrogen and renewable
fuels (e.g. biomass). Unlike solar and wind energy which can be effectively
accessed only in some regions, hydrogen - to be produced by splitting water -
and biomass are believed to be the long term solutions because of their acces-
sibility in most parts of the planet.
In the Netherlands, a research project supported by the Dutch Technology
Foundation STW has been launched with the objective to reduce CO2 emitted
from coal-fired power plants. The proposed technique for achieving this goal
is co-firing of a high fraction of torrefied biomass with coal at high oxygen
concentration. This technique has not been demonstrated on a large scale yet.
In fact, a combination of co-firing at oxy-fuel conditions has the advantages of
increasing the use of biomass of various sources to meet energy demands, and
raising CO2 concentration in the flue gases which would facilitate efficient
capturing of carbon dioxide. The project is a collaborative research between
17
2 Chapter 1
the researchers from Eindhoven University of Technology (TUe) and Twente
University (UT) as well as industrial partners from KEMA, NUON-TSA and
Dutch Utilities Industry.
The ultimate goal of the research is to acquire knowledge and increase
predictive capabilities of torrefied biomass combustion at high co-firing per-
centages under oxy-fuel conditions with respect to emissions, burnout time and
fuel ignition through performing experimental and numerical studies. The
main task of the Combustion Technology Group at Eindhoven University of
Technology (the purpose of this thesis) has been to conduct a detailed numeri-
cal investigation on combustion of single biomass particles, to identify domi-
nant processes during thermo-chemical conversion of a biomass particle at the
conditions similar to those found in industrial furnaces, and to develop an ef-
fective and reduced particle combustion model which can be used in the CFD
codes employed for simulating the thermal performance of biomass combus-
tors.
This chapter is followed by an overview of consumption of fossil fuels in
the world and Netherlands (Sec. 1.2), energy from biomass (Sec. 1.3), the con-
cept of oxy-fuel combustion (Sec. 1.4), objective of this PhD research (Sec.
1.5), and outline of the present thesis (Sec. 1.6).
1.2 OVERVIEW OF RECENT FOSSIL FUEL CONSUMPTION
A statistic survey has been conducted based on the data released by the
Energy Information Administration (EIA) [1] to identify the trend of fossil
fuels (coal, oil and natural gas) consumption and their contribution to the CO2
emissions in the world and in the Netherlands during the first decade of the
21th century. The outcome of this study is presented in Fig. 1.1 through Fig.
1.4.
Figure 1.1 reveals that the consumption of carbon-based fossil fuels has
been globally increasing. The figure shows that the world consumption of coal,
petroleum and natural gas has increased by 58.6%, 11.6% and 29.4%, respec-
tively, within the last decade. This trend is, however, different for the Nether-
lands (Fig. 1.2). In the first three years of the last decade, the consumption of
coal had an increasing trend. It reduced consistently between 2003 and 2006,
but then it increased in 2007, and again decreased until 2009. The consump-
tion of (crude) oil increased 30% in the first seven years of the last decade, af-
18
Modeling Combustion of Single Biomass Particle 3
ter which it decreased until 2009, and then increased in 2010. The consump-
tion of natural gas had an increasing trend between 2000 and 2004. It de-
creased between 2004 and 2007, but it increased by 14.3% until 2010. It can
be realized from Fig. 1.2 that the Netherlands has successfully decreased its
dependence on coal and oil in recent few years, but the need for natural gas
has increased.
Figure 1.1 Overview of world fossil fuel consumption during the first decade of the
21th
century (source of data: Ref. [1]).
19
4 Chapter 1
Figure 1.2 Overview of fossil fuel consumption in the Netherlands during the first
decade of the 21th
century (source of data: Ref. [1]).
20
Modeling Combustion of Single Biomass Particle 5
The history of CO2 emissions from the consumption of fossil fuels in the
world and in the Netherlands during the 2000s is depicted in Fig. 1.3. The ob-
vious and unfortunate message of Fig. 1.3a is that the CO2 emissions have
been continuously increasing globally. Within the first nine years of the 21th
century, the amount of carbon dioxide emissions from the consumption of fos-
sil fuels increased by 27.3%; i.e. on an average basis approximately 3% per
year. With this rate of growth in the amount of CO2 emissions, in about twenty
years (year 2033), the CO2 emissions will be twice as that in the year 2000.
This is a serious threat to our society which requires an immediate cooperation
in a global scale to combat it. In particular, Fig. 1.3a shows that the contribu-
tion of the coal-based energy to total CO2 emissions has been consistently in-
creasing. The amount of CO2 emissions increased 9.6% in the Netherlands
(Fig. 1.3b) within the first six years of the last decade. However, it appears that
from year 2007, the Netherlands was successful to reduce the CO2 emissions
with an average rate of 2.6% per year. This is more likely due to the fact that
the need for coal and petroleum-based energy decreased in the Netherlands
beyond year 2007 (see Fig. 1.2).
On the other hand, data of EIA indicates a considerable increase in elec-
tricity consumption both in the world and the Netherlands (see Fig. 1.4). With-
in the first nine years of the last decade, the world electricity consumption in-
creased by 31.3%. In other words, the need for electricity increased 3.48% per
year on an average basis. With this growth rate, the electricity consumption in
about sixteen years will be twice as that in year 2000. In the Netherlands, the
electricity consumption increased 13.5% within the first eight years of the last
decade; which is equivalent to a 1.69% increase in electricity consumption per
year. Obviously, the consistent increase in electricity consumption requires in-
stallation of more power plants; thereby increasing the need for consumption
of more fuel. From an economical viewpoint, the price of fossil fuels notably
increased during the 2000s (see Fig. 1.5).
The data shown in Figs. 1.1-1.5 lead us to arrive at the conclusion that the
dependence on fossil fuel-based energy will have serious consequences, per-
haps, in a near future. Then, it remains to question: what is the solution? The
first necessary step to reduce our need for fossil fuels is to seek alternative and
environmental friendly fuels. Second, the new energy systems should be de-
signed based on maximum efficiency criterion which guarantees minimization
of energy loss and greenhouse gas emissions. Third, extensive research and
development (R&D) should be conducted to find technological methods for ef-
21
6 Chapter 1
ficient CO2 capture. For instance, new power generation systems need to be
designed based on maximum thermal efficiency criterion, and to operate in
combined configurations such as combined heat and power generation systems
(CHP), and/or combined power cycles. A detailed discussion on optimization
of conventional and integrated gas turbine power plants can be found in Ref.
[2].
(a) (b)
Figure 1.3 History of the CO2 emissions from the consumption of fossil fuels during
the first decade of the 21th
century, (a) world; (b) Netherlands (source of data: Ref.
[1]).
It is believed that hydrogen and biomass, among other alternative fuels,
will be the most attractive energy sources in near future. Because, unlike solar,
wind and geothermal energy that are available only in certain regions of the
world, hydrogen – e.g. to be produced by splitting water via a thermochemical
cycle such as sulfur-iodine and copper-chlorine – and biomass are massively
accessible in many parts of the globe. Although, hydrogen is believed to be a
promising carbon-free energy source, safe storage, transportation and distribu-
tion of hydrogen are yet serious issues which require further R&D on these di-
rections. On the other hand, biomass is a renewable energy source which is al-
ready available on the planet. It does not suffer from the above mentioned
issues. Nevertheless, alike fossil fuels, biomass contains a large fraction of
carbon, so biomass-based energy is expected to emit greenhouse gases. A
combination of biomass-based energy and an efficient carbon dioxide tech-
22
Modeling Combustion of Single Biomass Particle 7
nique seems to be a promising solution in a near future to combat the issues re-
lated to the fossil fuels discussed previously.
(a) (b)
Figure 1.4 History of electricity consumption during the first decade of the 21th
centu-
ry; (a) world; (b) the Netherlands (source of data: Ref. [1]).
Figure 1.5 History of fossil fuel prices for electricity generation during the first dec-
ade of the 21th
century. The prices of coal and natural gas are only for US (source of
data: Ref. [1]).
23
8 Chapter 1
1.3 ENERGY FROM BIOMASS
The representative chemical formula of biomass is CxHyOz. It also contains
a negligible amount of nitrogen, sulfur and chlorine. The term biomass is usu-
ally referred to wood, municipal solid waste (MSW), industrial waste, and al-
cohol fuels (e.g. ethanol). The energy from biomass can be extracted either di-
rectly (e.g. combusting it in the furnace of a power plant for electricity
generation), or indirectly (e.g. converting it via gasification and pyrolysis pro-
cesses for production of syngas and biofuels). The thermal efficiencies of bio-
mass-fired power plants are relatively low, e.g. 20-27% [3], compared to coal-
fired power stations; typically 10 percentage points lower than for coal at the
same installation [4]. Co-firing of biomass in large-scale coal power plants can
boost the thermal efficiency up to 35-40% [4].
A large amount of research has been conducted by means of experimental
and numerical studies on coal combustion and the current state-of-the art of
the thermal conversion of coal is at a mature level. Many numerical models
have been developed to describe combustion, gasification and pyrolysis of
coal. However, these models are not suitable for describing the combustion
characteristics of biomass due to the major differences between coal and bio-
mass. Table 1.1 lists some of the differences in thermo-physical properties of
coal and biomass. A comparison of proximate analysis of a woody biomass
and a typical coal is also provided in Table 1.2. Furthermore, devolatilization
of biomass, oxidation and gasification of biomass char greatly differ from
those of coal. Therefore, mathematical modeling of biomass combustion is ex-
pected to be different from the models already developed for the purpose of
coal combustion simulation. To be able to fully understand the characteristics
of biomass combustion, modeling studies have proven to be a convenient
means to get a deeper insight into the various physiochemical processes in-
volved in biomass combustion in order to optimally use the energy from bio-
mass.
1.4 OXY-FUEL COMBUSTION
Coal-fired power plants, among large scale fossil fuel-based industrial pro-
cesses, discharge huge quantities of carbon dioxide to the atmosphere. Several
technologies are being developed for CO2 capture and sequestration from coal-
fired plants including [7]:
24
Modeling Combustion of Single Biomass Particle 9
Table 1.1 Comparison of coal and biomass properties [5].
Property Coal Biomass
Dry heating value, MJ/kg ~25 ~16
Volatile matter, % 40 80
Adiabatic flame temperature, °C 2100-2200 1800
Fuel density, kg/m3 ~1300 ~500
Particle size, µm ~100 ~3000
Particle shape Spherical Irregular
Table 1.2 Proximate analysis of a typical coal and a woody biomass [6].
Content Coal Biomass
C (% dry) 72.1 48.6
H (% dry) 3.6 4.65
O (% dry) 8.01 42
N (% dry) 1.36 0.09
S (% dry) 0.35 0.093
Cl (% dry) - 0.024
a) CO2 capture from plants of conventional design by scrubbing of the
flue gas,
b) IGCC (Integrated Gasification Combined Cycle gas turbines) with an
air separation unit to provide O2,
c) Oxy-fuel combustion with the oxygen diluted with an external recycle
stream to reduce its combustion temperature,
d) Oxy-combustion with an internal recycle stream induced by the high
momentum oxygen jets in place of external recycle. This technology is
now widely used in the glass industry and, to a lesser extent, in the
steel industry,
e) Chemical looping. This involves the oxidation of an intermediate by
air and the use of the oxidized intermediate to oxidize the fuel.
Oxy-fuel combustion amongst these CO2 capture technologies is a highly in-
teresting method due to the possibility to use advanced steam technology, re-
duce the boiler size and cost and to design a zero-emission power plant [8].
In a conventional coal-fired boiler, air is used for combustion where the ni-
trogen from the air dilutes the CO2 concentration in the flue gas. It is relatively
expensive to capture CO2 from such dilute mixtures using amine stripping. In
an oxy-fuel combustor, a combination of high oxygen concentration (above
95% purity) and recycled flue gas is used for combustion of fuel. Recycling
25
10 Chapter 1
the flue gas leads to the production of a gas consisting mainly of CO2 and wa-
ter which are ready for sequestration without stripping the CO2 from the gas
stream. In order to maintain an adiabatic flame temperature similar to that of
the conventional air combustion, the O2 proportion of the gases passing
through the burner is typically 30%, higher than that for air of 21%, which re-
quires that about 60% of the flue gases need to be recycled [7]. A schematic
presentation of the main flows of mass, heat and electric power in a coal-fired
O2/CO2 recycle combustion power plant is depicted in Fig. 1.6.
Figure 1.6 Schematic diagram of a coal-fired power plant with oxy-fuel combustion
[8].
1.5 OBJECTIVES
The combination of biomass co-firing and oxy-fuel combustion in coal
power plants is believed to be a promising cost-effective technique which of-
fers two advantages over the conventional coal power generation systems: It
provides an opportunity to increase the usage of a renewable fuel (biomass),
26
Modeling Combustion of Single Biomass Particle 11
and facilitates efficient CO2 capture. Nevertheless, as pointed out earlier, ap-
plication of this method has not yet been demonstrated on a large scale.
The BiOxyFuel project sponsored by the Dutch Technology Foundation
STW is a collaborative research, within the Clean Combustion Concepts
(CCC) framework, between the researchers at the Combustion Technology and
Process Technology groups at Eindhoven University of Technology, Laborato-
ry of Thermal Engineering at Twente University and a Dutch-based Industrial
partner (KEMA). The objective of this research project is to increase under-
standing and predictive capability of torrefied biomass combustion under oxy-
fuel conditions at high co-firing percentages. The outcome of this project is
expected to be used by the industrial partners for optimization of biomass/coal
co-firing ratio and future oxy-fuel power plants while minimizing the green-
house gas emissions.
The BiOxyFuel research project is divided into four main tasks.
1. Experimental study. The ignition, combustibility and burnout of bio-
mass/coal mixtures under conventional air-firing and oxy-fuel condi-
tions are studied.
2. Single particle modeling. Detailed numerical simulation of single bio-
mass particle is planned to identify the role of various processes in-
volved in biomass combustion.
3. Particle-laden flow modeling. A model is being developed to account
for interactions between particles of different types and sizes and be-
tween particles and flow.
4. Furnace modeling. An engineering model is planned to be developed
for prediction of burnout of coal, wood and torrefied biomass and the
furnace exit temperatures under oxy-fuel conditions.
The goal of this thesis is to numerically study combustion of single bio-
mass particle (task 2). The main objective of the present thesis is twofold: 1)
numerical simulation of thermo-chemical conversion of single biomass parti-
cles by means of one-dimensional detailed modeling in order to identify the
role of each sub-processes involved in biomass combustion; 2) development of
reduced models for predicting the main characteristics of biomass particle py-
rolysis and char oxidation and gasification at the conditions similar to those
found in industrial furnaces, which can be easily linked with the Computation-
al Fluid Dynamics (CFD) codes. The simplified particle combustion model is
27
12 Chapter 1
planned to be employed by other project partners working on particle-laden
flow modeling (task 3) and furnace modeling (task 4).
1.6 THESIS OUTLINE
This thesis will be continued with the following nine chapters. Chapter 2
provides a general overview and description of various physiochemical pro-
cesses involved in biomass combustion including pyrolysis, homogeneous re-
actions and heterogeneous reactions. Furthermore, a review of the recent state-
of-the art on comprehensive and simplified modeling studies of single-particle
biomass combustion presented in the literature will be given in this chapter.
Chapters 3-9 can be divided into two parts:
a) Detailed modeling study (Chapters 3 and 4),
b) Simplified modeling study (Chapters 5-9).
The detailed modeling study deals with establishment of a one-
dimensional particle model based on conservation of energy, mass and mo-
mentum; and implementing it in CHEM1D. In the first step, pyrolysis of a sin-
gle biomass particle is formulated, coded and validated using several experi-
mental data taken from past studies in Chapter 3. The effects of kinetic data,
heat of pyrolysis, and secondary reactions on the biomass decomposition pro-
cess will be discussed. A numerical study will be subsequently carried out to
establish useful correlations for predicting the conversion time and final char
density of single biomass particles up to 1mm undergoing a pyrolysis process
at high heating conditions.
In Chapter 4, the pyrolysis model of Chapter 3 will be further extended by
accounting for homogeneous gas-phase reactions within and in the vicinity of
the particle as well as heterogeneous surface reactions to complete particle
combustion model. Likewise, the combustion model will be validated using
different experiments reported in the literature. Using the numerical model and
the corresponding computer code developed in CHEM1D, the influence of py-
rolysis kinetic data and gas-phase reactions on the particle combustion process
will be examined. The results of Chapters 3 and 4 will allow us to identify the
main sub-processes during combustion of small size biomass particles at ele-
vated temperatures relevant to those found in practical furnaces.
28
Modeling Combustion of Single Biomass Particle 13
Simplified modeling study will be comprehensively discussed in the sub-
sequent chapters. Chapter 5 presents analytical expressions for predicting the
preheating time, or the time at which particle begins to decompose, of a solid
particle exposed to a hot environment. A particle may be classified into two
groups: thermally thin, and thermally thick. The method of derivation of indi-
vidual expressions and the main parameters influencing the preheating time of
thermally thin and thermally thick particles will also be discussed.
Chapter 6 deals with the development of a simplified model of a
pyrolyzing particle. A time and space integral method is introduced in this
chapter which allows describing the particle pyrolysis with a set of coupled al-
gebraic equations. Two treatments will be presented; one of which can be used
in pyrolysis reactor models while another provides a rather simple method for
estimating the mass loss and surface temperature histories of particle for engi-
neering purposes. Both simplified models will be validated against various ex-
perimental data and computations of the detailed pyrolysis model of Chapter 3.
A reduced model of char combustion and gasification, as the last stage of
the combustion of a biomass particle, will be presented in Chapter 7 by incor-
porating the traditional shrinking core approximation. A survey on char oxida-
tion and gasification kinetic data will be conducted to highlight significant dif-
ference between reactivity of coal char and biomass char. The simplified char
combustion model will be validated and subsequently used to investigate the
effects of kinetic data, initial particle size and surrounding temperature on the
dynamics of combusting single biomass char particles.
By combining the individual simplified models of preheating up, pyrolysis
and char conversion established in Chapters 5-7, a reduced particle combustion
model will be presented in Chapter 8. Its accuracy will be assessed using the
literature experiments and the computations of the detailed combustion model
developed in Chapter 4. The model will be used to study the ignition time and
temperature, preheating time, pyrolysis time, burnout time, surface and mass
loss histories for varying particle size and surrounding temperature.
Due to the importance of combustion behavior at oxy-fuel conditions,
Chapter 9 is devoted to numerically study biomass char combustion at various
O2/CO2 mixtures. For this purpose the char combustion model of Chapter 7 is
used. The particle burning rate, temperature and gaseous species mass frac-
tions will be investigated under oxy-fuel conditions and compared with con-
ventional air-firing condition. Furthermore, the effects of initial particle size,
29
14 Chapter 1
temperature, density, and surrounding temperature and O2/CO2 composition on
the burnout time and maximum particle temperature will be discussed.
Finally, the main conclusion from this thesis will be given in Chapter 10.
RERERENCES
[1] Energy Information Administration, http://www.eia.gov, Accessed on 8
March 2012.
[2] Haseli Y. 2011. Thermodynamic Optimization of Power Plants.
Eindhoven University of Technology, Eindhoven, The Netherlands.
[3] Owning and Operating Costs of Waste and Biomass Power Plants.
www.claverton-energy.com/, Accessed on 12 March 2012.
[4] Biomass for Power Generation and CHP, IEA Energy Technology Es-
sential. http://www.iea.org/techno/essentials3.pdf, Accessed on 12
March 2012.
[5] Baxter L. http://www.et.byu.edu/~larryb/physical.htm, Accessed on 12
March 2012.
[6] Molcan P., Lu G., Bris T. L., Yan Y., Taupin B., Caillat S. 2009. Char-
acterisation of biomass and coal co-firing on a 3 MWth combustion test
facility using flame imaging and gas/ash sampling techniques. Fuel 88:
2328-2334.
[7] Buhre B. J. P., Elliott L. K., Sheng C. D., Gupta R. P., Wall T. F. 2005.
Oxy-fuel combustion technology for coal-fired power generation. Prog
Energ Combust Sci 31: 283-307.
[8] Jordal K., Anheden M., Yan J., Strömberg L. 2005. Oxyfuel combustion for
coal-fired power generation with CO2 capture-Opportunities and challenges.
Greenhouse Gas Cont Technol 7: 201-209.
30
Chapter 2
Literature Review
2.1 INTRODUCTION
Biomass combustion is a complex phenomenon which involves various
physical and chemical processes including virgin biomass heating up (and dry-
ing in case of a wet particle), pyrolysis through which the virgin material de-
composes to volatiles and char, char gasification and combustion, homogenous
gas phase reactions, heat transfer via conduction, convection and radiation
mechanisms, migration of gaseous species through the pores of the solid ma-
trix via diffusion and convection mechanisms, pressure build-up, variation of
thermo-physical properties with composition and temperature, structural
changes and particle shrinkage.
The chapter will be followed by reviewing the well-known kinetic
schemes proposed in the literature for biomass pyrolysis including the kinetic
data of primary and secondary reactions proposed by various researchers and
heat of pyrolysis (Sec. 2.2), possible homogeneous reactions and gas phase
combustion (Sec. 2.3), and heterogeneous surface reactions including char ox-
idation and gasification (Sec. 2.4). Furthermore, the detailed and simplified
modeling approaches of single-particle biomass combustion which have been
previously presented in the literature are reviewed in Sec. 2.5 and Sec. 2.6, re-
spectively. Finally, the key research questions which have not been adequately
addressed in the literature will be raised in the last section of this chapter.
31
16 Chapter 2
2.2 PYROLYSIS
Several kinetic schemes of pyrolysis have been proposed and applied by
different authors. The one-step global model, as the simplest kinetic model,
considers decomposition of biomass into char and volatiles. This is the most
frequently applied model; see for instance Galgano and Di Blasi [1]. An im-
proved version of the one-step model with a single rate constant is a model ac-
cording to which the main constituents of wood (cellulose, hemicelluloses and
lignin) decompose independently into char and volatiles via three parallel reac-
tions.
Another decomposition scheme is the Broido-Shafizadeh model for cellu-
lose decomposition, which assumes that the formation of an intermediate
phase is followed by two competing reactions; in one reaction tar is produced,
while in another, char and light gases are formed. The proposed mechanism of
Koufopanos et al. [2] is similar to the kinetic scheme of Broido-Shafizadeh, in
which the virgin biomass is first converted into an intermediate material (reac-
tion 1) which then decomposes to gases and volatiles (reaction 2), and char
(reaction 3). Shafizadeh and Chin [3] proposed a primary wood degradation
mechanism which suggests three individual competitive reactions forming
light gases, tar and char.
A further kinetic model of biomass degradation assumes that in addition to
the primary reactions proposed by Shafizadeh and Chin [3], tar undergoes ho-
mogeneous degradation producing additional light hydrocarbons and char.
This is referred to as tar cracking or secondary reactions. This model was ap-
plied in detailed pyrolysis simulations conducted by Grønli and Melaaen [4],
Di Blasi [5], Hagge and Bryden [6], Lu et al. [7], and Chan et al. [8]. Moreo-
ver, Koufopanos et al. [9] took into account the nature of secondary reactions
from a different viewpoint. In their model, virgin biomass undergoes primary
reactions to decompose into volatile and gases (reaction 1) and char (reaction
2). The primary pyrolysis products participate in secondary reactions to pro-
duce also volatile, gases and char of different compositions (reaction 3). The
kinetic mechanism of Koufopanos et al. [9] has been applied, for instance, by
Babu and Chaurasia [10] and Sadhukhan et al. [11, 12] to model the pyrolysis
of biomass particles. A summary of the kinetic schemes discussed above is
given in Table 2.1.
32
Modeling Combustion of Single Biomass Particle 17
Table 2.1 Summary of kinetic schemes of biomass pyrolysis proposed in the literature.
One-step global model Biomass Volatiles + Char
Three independent reactions
model
Cellulose Volatiles + Char
Hemicelluloses Volatiles + Char
Lignin Volatiles + Char
Broido-Shafizadeh model Cellulose Intermediate Tar
Intermediate Light gases + Char
Model of Koufopanos et al. Biomass Intermediate Volatiles + Gases
Intermediate Char
Model of Shafizadeh and
Chin
Biomass Light gases
Biomass Tar
Biomass Char
Model of Shafizadeh and
Chin with secondary reactions
Biomass Light gases
Biomass Tar Light gases
Tar Char
Biomass Char
Model of Koufopanos et al.
with secondary reactions
Biomass (Volatiles + Gases)1
Biomass Char1
(Volatiles + Gases)1 + Char1 (Volatiles + Gases)2 + Char2
2.2.1 Kinetic Data
The reaction rate constant of the biomass decomposition models discussed
earlier is usually described by an Arrhenius-type equation as follows.
−=
TR
EAk
g
exp (2.1)
where A is the pre-exponential or frequency factor, E the activation energy, Rg
the universal gas constant, and T the temperature.
A literature survey indicates that a wide range of kinetic data (i.e. A and E)
have been proposed by different researchers for the kinetic schemes summa-
rized in Table 2.1. These kinetic models can be divided into two main groups:
G1) first four kinetic models in Table 2.1; G2) last three kinetic models in Ta-
ble 2.1. Although, all kinetic models given in Table 2.1 have been employed in
several past modelling studies on biomass pyrolysis, the main disadvantage of
the kinetic schemes of G1 is that one needs to know the stoichiometric ratios of
char and volatiles ahead of calculations. On the other hand, pyrolysis models
based on the kinetic schemes of G2 do not suffer from this issue. In other
words, a combination of the models of G2 with transport equations allows one
to compute the yields of char and volatiles.
33
18 Chapter 2
The kinetic mechanism of Shafizadeh-Chin [3] is more comprehensive
than that of Koufopanos et al. [9], because the former model allows evaluation
of the yields of tar and light gases individually, whereas the later scheme pro-
vides only a single yield of volatiles (tar and gas). In the present thesis, the ki-
netic model of Shafizadeh-Chin [3] will be employed in detailed modeling of
biomass pyrolysis and combustion (Chapters 3 and 4). So, the relevant kinetic
constants that have been obtained experimentally by various past researchers
are discussed below.
2.2.1.1 Primary Reactions
According to the kinetic scheme of Shafizadeh-Chin, the decomposition of
biomass occurs via three competing reactions through individual reaction
pathways yielding light gas, tar and char; which are also referred to as primary
reactions. Five different sets of kinetic parameters (i.e. frequency factor and
activation energy) have been proposed in the literature (see Table 2.2).
Table 2.2 Kinetic constants proposed by Chan et al. [8], Thurner and Mann [13], Di
Blasi and Branca [14], and Font et al. [15].
Source Reaction A (1/s) E (kJ/mol)
Chan et al. Bio Gas 1.30×108
140
Bio Tar 2.00×108
133
Bio Char 1.08×107
121
Thurner and Mann Bio Gas 1.44×104
88.6
Bio Tar 4.13×106
112.7
Bio Char 7.38×105
106.5
Di Blasi and Branca Bio Gas 4.38×109 152.7
Bio Tar 1.08×1010
148
Bio Char 3.27×106 111.7
Font et al. Bio Gas 1.52×107
139.3
(Pyroprobe 100) Bio Tar 5.85×106
119
Bio Char 2.98×103
73.4
Font et al. Bio Gas 6.80×108
155.6
(Fluidized bed reactor) Bio Tar 8.23×108
148.5
Bio Char 2.91×102
61.4
34
Modeling Combustion of Single Biomass Particle 19
The kinetic data of primary reactions reported by Chan et al. [8] were used
in their pyrolysis model for predicting experimental results from lodgepole
pine wood devolatilization. These kinetic data were also employed in the py-
rolysis model of Grønli and Melaaen [4] for simulation of spruce wood pyrol-
ysis.
The second set of kinetic constants is of that reported by Thurner and
Mann [13] who studied the pyrolysis of oak sawdust in the temperature range
573-673 K at atmospheric pressure. Hagge and Bryden [11], Bryden and
Hagge [16], and Bryden et al. [17] used these data to validate their pyrolysis
model against experiments of Tran and White [18], who measured temperature
history and char yield of redwood, southern pine, red oak and basswood at
constant radiant heat flux.
Di Blasi and Branca [14] conducted experiments on beech wood to deter-
mine kinetic constants of wood pyrolysis. The weight loss of thin layers of
beech wood power (150µm) was measured for heating rates of 1000 K/min
with reaction temperatures in the range 587-720 K. These data were used by
Park et al. [19] for simulation of maple wood pyrolysis.
The fourth and last set of kinetic constants is the kinetic data of Font et al.
[15], obtained based on a comprehensive experimental study using a fluidized
bed reactor and a Pyroprobe 100 to investigate the kinetics of the flash pyroly-
sis of almond shells and of almond shells impregnated with CoCl2. Experi-
ments were conducted at 673-733 K to study the kinetics of almond shells in a
fluidized bed. For the kinetic study in the Pyroprobe 100 equipment, experi-
ments were carried out at 673-878 K. Despite the apparent discrepancies in the
reported kinetic parameters obtained from two test facilities (see Table 2.2),
the predicted decomposition rate of biomass to individual products, i.e., gas,
tar and char, are approximately the same in both cases. The first set of kinetic
constants was, for example, employed in the model of Lu et al. [7] for simula-
tion of hardwood sawdust particles pyrolysis.
Di Blasi [5] examined data of Chan et al. [8], Thurner and Mann [13], and
(the first set of) Font et al. [15]. A good quantitative agreement was obtained
between the experimental data of Lee et al. [20] and the predicted temperature
profiles along the degrading biomass particle using the kinetic parameters of
Thurner and Mann [13]. However, the author believed that such an agreement
was reached mainly due to the properties of char and biomass used in the nu-
merical simulation, which were those measured in experiments of Lee et al.
35
20 Chapter 2
Thus, no final conclusion was made in Di Blasi’s study concerning the im-
portance of thermo-kinetic data for quantitative predictions.
The rate constants of the primary reactions predicted using the kinetic con-
stants of Chan et al. [8], Thurner and Mann [13], Di Blasi and Branca [14], and
Font et al. [15] are compared in the temperature range 400-900 K. The results
of these observations can be classified in three temperature ranges; 400 < T <
550 K, 550 < T < 700 K, and 700 < T < 900 K, as analyzed below.
400 < T < 550 K. The rate constant of light gases calculated by Thurner and
Mann’s data is higher than those obtained from other three sets. The biomass
decomposition rate to tar is almost the same in all cases. For the char yield, the
data of Font et al. gives higher rates compared to the other cases.
550 < T < 700 K. Di Blasi and Branca’s data overestimate the production rates
of light gases compared to the other data, whereas the other three sets of kinet-
ic constants give almost the same results. Again, the rate of tar production
computed by Di Blasi and Branca’s data are higher than those predicted by da-
ta of the other three groups. All data sets are expected to give approximately
the same results for rate constant of biomass decomposition to char.
700 < T < 900 K. Di Blasi and Branca’s data predicts faster formation of light
gases compared to the other three data sets. The prediction using the data of
Chan et al. and Font et al. are in the same range. Again, the rates for tar pro-
duction computed by Di Blasi and Branca’s data are higher than those predict-
ed by data of other three groups. Computed reaction rate constants of char
formation using Chan et al. and Di Blasi and Branca’s data are in the same
range and higher than those computed by other two groups which produce
compatible results.
Given that several factors such as experimental set up, experiment condi-
tions (high heat flux, low heat flux), biomass composition, etc. may contribute
to the reasons of the discrepancies between various kinetic data, the decision
on which set of kinetic constants must be used in a pyrolysis model, depends
largely upon how well the thermo-kinetic model will predict experimental ob-
servations. The accuracy of the pyrolysis model using the kinetic parameters
suggested by Chan et al., Di Blasi and Branca, Thurner and Mann, and Font et
al. will be examined in Chapter 3.
36
Modeling Combustion of Single Biomass Particle 21
Table 2.3 Kinetic parameters of tar cracking reported in the literature.
Tar Light Gas
Frequency Factor
(1/s)
Activation Energy
(kJ/mol)
Temperature Range
(°C)
Ref.
4.28×106
107.5 460-600 22
1.00×105
93.3 500-800 23
3.26×104
72.8 430-900 24
1.00×105
87.5 > 600 25
2.2.1.2 Secondary Reactions
Vapor phase tar decomposition known as secondary reactions, were inves-
tigated by a number of researchers such as Liden et al. [21], Boroson et al.
[22], Kosstrin [23] and Diebold [24]. Tar cracking was modeled as a homoge-
nous process to give mainly light gas (i.e. char yield is negligible), an assump-
tion which is supported by experimental results [21]. Table 2.3 summarizes the
findings of these researchers on the kinetic constants of tar cracking reaction.
2.2.2 Heat of Pyrolysis
In nearly all past modeling studies of single particle biomass pyrolysis, de-
composition of the virgin biomass to gas, tar and char is assumed to take place
through a series of endothermic reactions, whereas tar cracking through sec-
ondary reactions for additional production of gas and char is considered exo-
thermic. Furthermore, it is commonly assumed that the heat of all three prima-
ry reactions is identical, and so is the one for the secondary tar cracking
reactions.
Literature review indicates a large scatter in the reported values for the
heat of pyrolysis. A survey performed by Milosavljevic et al. [25] revealed
that it may be in the range from –2100 to 2500 kJ/kg. Given the difficulty of
measuring the pyrolysis heat, most of past researchers treated it as an adjusta-
ble parameter which would give reasonable agreement between the results of
simulation and measurements (e.g. a pyrolysis heat of 418 kJ/kg was suggested
by Chan et al. [8]; Grønli [26] assumed a heat of 150 kJ/kg for primary reac-
tions; Park [27] estimated an endothermic heat of 64 kJ/kg for three parallel
reactions). In contrast, there are limited studies which have intended to exper-
imentally (with no aid of parameter fitting in the simulating model) determine
the pyrolysis heat. Havens et al. [28] showed that, based on experiments of dif-
ferential scanning calorimetry (DSC), the heat of pyrolysis reaction for pine
37
22 Chapter 2
and oak is 200 kJ/kg and 110 kJ/kg, respectively. In another effort to measure
the pyrolysis heat of Pinus Pinaster thermal degradation using DSC, Bilbao et
al. [29] reported an endothermic heat of 274 kJ/kg up to a conversion of 60%,
whereas for the remaining conversion of the biomass, the process was ob-
served to be exothermic with a heat of –353 kJ/kg.
An extensive investigation to determine the heat of pyrolysis of dried cy-
lindrical maple particles with 2 cm diameter and 8 cm length was conducted
by Lee et al. [20] at two external heat fluxes of 30 kW/m2 and 84 kW/m
2.
Their results showed that at a low heat flux the pyrolysis layer could be divid-
ed into three zones: an endothermic primary decomposition zone at tempera-
tures up to 250 oC, an exothermic partial char zone between 250
oC and 340
oC, and an endothermic surface char zone at 340
oC < T < 520
oC. The overall
mass weighted heat of reaction was endothermic to the extent of 610 kJ/kg. In
contrast, the overall heat of reaction at the higher heat flux was exothermic,
being greater for perpendicular heating (in the range –1090 kJ/kg to –1720
kJ/kg) than for parallel heating (in the range –105 kJ/kg to –395 kJ/kg). The
authors arrived at the conclusion that the heat of pyrolysis depends upon the
external heating rate, total heating time and anisotropic properties of biomass
and char relative to the internal flow of heat and gas.
Milosavljevic et al. [25] studied the thermo-chemistry of cellulose pyroly-
sis by a combination of DSC and thermogravimetric analysis. They found that
the main thermal degradation pathway was endothermic in the absence of mass
transfer limitations that promoted char formation. They concluded that the
endothermicity, which was estimated to be about 538 kJ/kg of volatiles
evolved, was mainly due to latent heat requirement for vaporizing the primary
tar decomposition products. It was also reported that the pyrolysis could be
driven in the exothermic direction by char forming processes that would com-
pete with tar forming processes. The formation of char, which was favored at
low heating rates, was estimated to be exothermic to the extent of 2000 kJ/kg
of char formed. The authors arrived at the conclusion that the heat of pyrolysis
can be correlated with the char yield at the end of pyrolysis, a result which was
somewhat consistent with findings of Mok and Antal [30] and Rath et al. [31],
who also discovered a linear decrease in the endothermic heat of pyrolysis as
the char yield increased. So, it was concluded that the char yield was the main
factor determining whether the overall pyroysis process is endo- or exother-
mic. Table 2.4 summaries the above discussed values of the pyrolysis heat ob-
38
Modeling Combustion of Single Biomass Particle 23
tained by different researchers either through a fitting procedure or based on
measurements.
From these works, it can be now understood why a wide range of pyrolysis
heat has been reported in the literature. For the purpose of simulating thermal
degradation of a biomass particle, it is of importance that the pyrolysis heat
must be chosen from similar heating and comparable measurement conditions
(such as similar char yield) if it is taken from a referred source. Alternatively,
it should be carefully correlated by comparing the simulation results with
measurements otherwise the predicted parameters of the pyrolysis model may
not be reliable.
Table 2.4 Values of heat of pyrolysis reported in various studies.
Heat of Pyrolysis (kJ/kg) Method Remarks Ref.
418 Fitting with experiments 8
150 Fitting with experiments 26
64 Fitting with experiments 27
255 Fitting with experiments X*<0.95 9
-20 Fitting with experiments X>0.95
200 Measured Pine wood 28
110 Measured Oak wood
274 Measured X<0.60 29
-353 Measured X>0.60
610 Measured Low heat flux 20
–1090 to –1720 (perpen-
dicular heating)
Measured High heat flux
–105 to –395 (parallel
heating)
Measured High heat flux
538 – 2000Yc**
Measured Cellulose 25 * Conversion
** Final char yield
2.3 HOMOGENEOUS REACTIONS
The volatiles released during pyrolysis may react with each other and oxy-
gen within and in the vicinity of the particle. Light gas typically consists of
H2O, CO, CO2, CH4 and H2, whose fractions depend on the heating conditions
and biomass type. However, for engineering applications, a constant composi-
tion is usually assumed; see Table 2.5. For simplicity, an empirical formula in
the form of CxHyOz is considered to represent tar as in past studies. For in-
39
24 Chapter 2
stance, Lu et al. [32] and Johansson et al. [33] used C6H6.2O0.2 for representa-
tion of tar. This formula suggests an oxygen-to-carbon and hydrogen-to-
carbon ratio of 0.0333 and 1.0333, respectively. However, by referring to the
past experimental studies dealt with measurements of byproducts of tar crack-
ing reaction, and performing an elemental analysis, one may realize that the ra-
tios of O/C and H/C are higher than the above values indicating that more at-
oms of oxygen are included in tar compared to the above empirical formula for
tar. For instance, Rath and Staudinger [34] investigated vapor phase cracking
of tar obtained from the pyrolysis of spruce wood by conducting experiments
with small particles (0.5–1 mm) in a thermogravimetric analyzer (TGA) and in
a coupling of the TGA and a consecutive tubular reactor. They measured a dis-
tribution of tar cracking products including CO, CO2, H2O, H2, CH4, C2H6,
C2H4, C2H2 and C3H6. Through an elemental analysis for C, H and O, one may
derive an empirical formula of C3.878H6.426O3.561 for tar giving O/C and H/C ra-
tios of 0.918 and 1.657, respectively, assuming a molecular weight of 110
g/mol for tar [4, 16].
Table 2.5 Mass fraction of light gases released from biomass pyrolysis.
Source H2O CO CO2 H2 CH4
Adams [35] 0.417 0.262 0.105 0.099 0.117
Ragland et al. [36] 0.417 0.305 0.192 0.008 0.078
Yang et al. [37] 0.256 0.422 0.254 0.008 0.06
Di Blasi [38] 0.521 0.156 0.271 0.021 0.031
Gerber et al. [39] 0.256 0.270 0.386 0.032 0.056
Font et al [15], 460 °C 0.554 0.114 0.310 0.003 0.019
Font et al [40], 610 °C 0.419 0.272 0.269 - 0.04
Font et al [40], 710 °C 0.210 0.511 0.195 0.003 0.081
Thunman et al. [41] 0.186 0.414 0.186 0.007 0.207
Grieco and Baldi [42], beech
wood - 0.335 0.567 0.006 0.092
Grieco and Baldi [42], pine
wood - 0.341 0.558 0.006 0.095
The assumption that is usually made in modeling studies is that the rate of
each gas phase reaction can be evaluated through a one-step global reaction
given that the chemistry of gas phase reactions can be a complex phenomenon,
see, for instance, Ref. [43]. The reactions between the gaseous species partici-
pating in the homogeneous reactions are a complex combination of numerous
elementary reactions. The reactions between oxygen and CO, H2 and hydro-
40
Modeling Combustion of Single Biomass Particle 25
carbons include chain mechanisms with elementary steps of stable and unsta-
ble chemical species. In most kinetics used in past modeling studies, the con-
centration exponents are not equal to the corresponding stoichiometric coeffi-
cients [44].
2.4 HETEROGENEOUS REACTIONS
The last stage during biomass combustion is heterogeneous reactions in-
cluding char oxidation and char gasification with carbon dioxide, water vapor
and hydrogen. In most past modeling studies, char obtained from the pyrolysis
process is treated as pure carbon for simplicity. Stimely and Blankenhorn [45]
measured the hydrogen content of the char of four different woods and found
that it decreases with temperature. For instance, for hybrid poplar, their find-
ings revealed that for temperatures above 740 °C – typical case for most com-
bustion applications – char does not contain hydrogen.
Similar to homogeneous reactions, the rate of char oxidation/gasification is
usually described by a one-step global reaction for engineering applications as
follows.
2,222,,:
,:exp
OHOHCOj
onGasificatiOxidationiMn
M
TR
ETAAr
j
jsto
C
g
i
iviρ
−=
(2.2)
where Av is the specific inner surface area of the porous char, Ai is the pre-
exponential factor, M is the molecular weight, nsto is the stoichiometric ratio of
reaction i; and ρj represents the density of gasifying agent j.
Hobbs et al. [46] reviewed the kinetic rate constants of char oxidation and
char gasification with carbon dioxide. They reported that the steam gasifica-
tion rate is the same as the carbon dioxide gasification rate, and the gasifica-
tion rate with hydrogen may be taken three orders of magnitude smaller than
the gasification rate with carbon dioxide.
41
26 Chapter 2
2.5 PAST DETAILED MODELING STUDIES
Unlike biomass pyrolysis which has been extensively investigated numeri-
cally and experimentally by a large number of researchers, limited work has
been carried out with a focus on comprehensive modeling of biomass particle
combustion. Most of these works carried out in recent years have simulated
particle combustion through one-dimensional models. Wurzenberger et al. [47]
presented a combined transient single particle and fuel-bed model. Primary py-
rolysis was described by independent parallel reactions. Secondary tar crack-
ing, homogenous gas reactions and heterogeneous char reactions were mod-
eled using kinetic data obtained from literature. The validation of the particle
combustion model was performed using experimental data of conversion of
spherical beech wood particles. Porteiro et al. [48] reported a mathematical
model to describe thermal conversion of biomass particles. The pyrolysis of
biomass was modeled using three competitive reactions yielding light gases,
tar and char. Additional kinetics considered in their work were combustion of
char yielding carbon monoxide and carbon dioxide, and combustion of hydro-
gen at the surface of the particle. They validated the model using measured
mass loss histories of cylindrical Spanish briquettes. Porteiro et al. [49] used
the model to study the combustion of densified wood particles, and the influ-
ence of structural changes on the heat transfer properties of wood was exam-
ined.
Further comprehensive modeling studies of biomass particle combustion
appeared recently in the literature are those reported by Lu et al. [32] and Yang
et al. [50]. The particle combustion model presented by Lu et al. [32] accounts
for drying, devolatilization, char oxidation and gasification, and gas phase
combustion. The kinetic scheme of Shafizadeh-Chin [3] with secondary reac-
tions was adapted to describe the particle pyrolysis. Heterogeneous reactions
were modeled by accounting for char oxidation and gasification with water
vapor and carbon dioxide. The gas phase reactions considered were oxidation
of hydrogen, carbon monoxide and a lumped hydrocarbon species represented
by the empirical formula C6H6.2O0.2. As discussed previously, this empirical
formula does not represent accurately the hydrocarbons and tar released from
biomass pyrolysis. To validate their combustion model, the predicted mass
loss history and center temperature of spherical poplar particles were com-
pared with their own measured data.
Yang et al. [50] conducted a two-dimensional simulation of single cylin-
drical wood particles. The sub-processes considered in the model were very
42
Modeling Combustion of Single Biomass Particle 27
much similar to those employed in the study of Lu et al. [32], but different
schemes were implemented for describing the chemistry of the particle con-
version. The pyrolysis scheme employed by Yang et al. [50] assumes that bi-
omass decomposes to volatiles and char through a global one-step reaction.
They also applied a different kinetic scheme for gas phase combustion. The
volatiles were characterized by the empirical formula CmHnOl whose combus-
tion produced hydrogen and carbon monoxide. These gaseous species also re-
acted with oxygen. The only heterogeneous reaction considered in the work of
Yang et al. [50] was char combustion. Given that they investigated the effect
of particle size ranging from 0.5 mm to 20 mm in diameter, no validation of
the model was reported.
2.6 PAST SIMPLIFIED MODELING STUDIES
In recent decades, some researchers have tried to come up with rather sim-
ple models for capturing the general behavior (in terms of conversion time,
mass loss and temperature histories) of a combusting particle. The simplified
model introduced by Saastamoinen et al. [51] assumes that devolatilization
takes place uniformly inside particle, and that the char residue burns as a
shrinking particle. The model accounts for simultaneous pyrolysis and char
combustion with partial combustion of volatiles in the mass transfer boundary
layer surrounding the particle. This model has recently been modified by
Saastamoinen et al. [52] by considering a conductive thermal resistance within
the particle and introducing an average particle temperature. In the modified
model, the heat of char combustion, an endothermic heat of pyrolysis, and the
heat received from the flame sheet around the particle are taken into account.
The accuracy of the simplified model presented by Sasstamoinen et al. [52]
was examined by comparing the predicted and measured mass loss history of
polish coal and heartwood particles.
Ouedraogo et al. [53] described a shrinking core model for predicting the
combustion of a moist large wood particle. The formulation was based on the
experimental evidence that large wood specimens inserted into a hot convec-
tive environment lose mass over a relatively thin layer at the particle exterior,
whereas the interior region remains almost undisturbed. They assumed that
when the fuel element is inserted into a hot convective environment, its surface
temperature will instantly reach a quasi-steady state condition with an initial
43
28 Chapter 2
formation of a char layer. They further assumed that the combustion of char
occurs in a diffusion-controlled regime, and the total mass of solid fuel repre-
sents carbon.
A further reduced model of a single large wood particle relevant to various
particle sizes and shapes used in fluidized and fixed bed combustors and
gasifiers was presented by Thunman et al. [54]. The model accounts for the
temperature gradients inside the particle, the release of volatiles, shrinkage,
and swelling. It divides the particle into four layers: moist virgin wood, dry
wood, char residue, and ash. The development of these layers is computed as a
function of time. The model treats the particle in one dimension and the con-
version of the particle is described by heat and mass transfer to the surface of
the particle.
He and Behrendt [55] developed a method by combining a volume reac-
tion model and front reaction approximation for predicting the combustion of a
large moist biomass particle. In their model, drying and char oxidation are
simplified as a front reaction and pyrolysis is described as a volume reaction.
Condensation of water vapor, shrinkage, heat and mass transfer inside the par-
ticle have been also taken into account. The model does not account for any
volatile combustion. They used finite volumes attached to solid materials to
discretize the domain, and an explicit method with variable time steps was
used for the calculations. A kinetics equation for fast pyrolysis was chosen for
the calculation. The simulation results revealed the overlap between drying,
pyrolysis, and char oxidation during conversion of particle.
2.7 CONCLUSION
Limited studies have been performed on detailed and simplified modeling
of single-particle biomass combustion, especially at the conditions of industri-
al biomass combustors (small particle size and high heating conditions). Bio-
mass pyrolysis as an earlier stage during biomass degradation may be de-
scribed by the Shafizadeh-Chin kinetic scheme according to which virgin
material decomposes to light gases, tar and char through three parallel reac-
tions. A comprehensive combustion model should also account for the possi-
bility of homogenous reactions within particle and heterogeneous char oxida-
tion and gasification reactions. The following basic questions have not been
adequately answered yet.
44
Modeling Combustion of Single Biomass Particle 29
1. Which set of kinetic parameters given in Table 2.2 should be used in a
pyrolysis model?
2. What value for the heat of pyrolysis should be assigned as a wide
range of values has been used in previous studies?
3. Do secondary reactions occur within a pyrolyzing particle? In other
words, may inclusion of tar cracking reaction lead to an improvement
of a pyrolysis model?
4. What are the volatiles and char yields obtained from a pyrolysis pro-
cess at the conditions of biomass combustors?
5. Does the pyrolysis process take place homogeneously at the conditions
of industrial furnaces?
6. What is the effect of pyrolysis kinetics on the combustion process?
7. How important are the gas-phase reactions within particle?
8. What are the dominant sub-processes during combustion of small size
particles converting at elevated temperatures?
9. What is the burnout time of millimeter size biomass particles at elevat-
ed temperatures?
The simplified single-particle combustion models presented in the litera-
ture are either applicable to large particles, or have not been adequately vali-
dated for the case of small size particles combusting at the conditions of bio-
mass furnaces. What one may expect from a reduced particle model is that it
should allow accurately prediction of ignition time, ignition temperature,
burnout time, combustion dynamic in terms of time evolution of particle mass
loss (or conversion), rate of volatiles evolved, surface temperature and heat
flux. In particular, the following questions need to be properly answered.
1. What/how sub-processes should be included in a simplified model?
2. What parameters may influence the ignition time and temperature?
3. Should a simplified model account for CO oxidation in the vicinity of
particle during char conversion process?
4. What is the effect of oxy-fuel combustion on particle combustion dy-
namic?
5. What is the effect of oxy-fuel combustion on burnout time and maxi-
mum particle temperature?
6. What is the effect of variable heating rate (pertaining to real furnaces
conditions) on particle combustion dynamic?
The above outlined questions will be the basis of the discussions of the follow-
ing seven chapters.
45
30 Chapter 2
RERERENCES
[1] Galgano A., Di Blasi C. 2003. Modeling wood degradation by the unre-
acted core shrinking approximation. Ind Eng Chem Res 42: 2101-2111.
[2] Koufopanos C. A., Maschio G., Lucchesi A. 1989. Kinetic modeling of
the pyrolysis of biomass and biomass components. Can J Chem Eng 67:
75-84.
[3] Shafizadeh F., Chin P. S. 1977. Thermal deterioration of wood, in: I.S.
Goldstein (Ed.). Wood Technology: Chemical Aspects 43, ACS Symp
Ser 57-81.
[4] Grønli M. G., Melaaen M. C. 2000. Mathematical model for wood py-
rolysis–Comparison of experimental measurements with model predic-
tions. Energ Fuels 14: 791-800.
[5] Di Blasi C. 1996. Heat, momentum and mass transport through a shrink-
ing biomass particle exposed to thermal radiation. Chem Eng Sci 51:
1121-1132.
[6] Hagge M. J., Bryden K. M. 2002. Modeling the impact of shrinkage on
the pyrolysis of dry biomass. Chem Eng Sci 57: 2811-2823.
[7] Lu H., Ip E., Scott J., Foster P., Vickers M., Baxter L. L. 2010. Effects
of particle shape and size on devolatilization of biomass particle. Fuel
89: 1156-1168.
[8] Chan W. C., Kelbon M., Krieger B. B. 1985. Modeling and experi-
mental verification of physical and chemical processes during pyrolysis
of a large biomass particle. Fuel 64: 1505-1513.
[9] Koufopanos C. A., Papayannakos N., Maschio G., Lucchesi A. 1991.
Modeling of the pyrolysis of biomass particles. Studies on kinetics,
thermal and heat transfer effects. Can J Chem Eng 69: 907-915.
[10] Babu B. V., Chaurasia A. S. 2004. Heat transfer and kinetics in the py-
rolysis of shrinking biomass particle. Chem Eng Sci 59: 1999-2012.
[11] Sadhukhan A. K., Gupta P., Saha R. K. 2008. Modeling and experi-
mental studies on pyrolysis of biomass particles. J Anal Appl Pyrolysis
81: 183-192.
[12] Sadhukhan A. K., Gupta P., Saha R. K. 2009. Modeling of pyrolysis of
large wood particles. Bioresour Technol 100: 3134-3139.
46
Modeling Combustion of Single Biomass Particle 31
[13] Thurner F., Mann U. 1981. Kinetic investigation of wood pyrolysis. Ind
Eng Chem Process Des Dev 20: 482-488.
[14] Di Blasi C., Branca C. 2001. Kinetics of primary product formation
from wood pyrolysis. Ind Eng Chem Res 40: 5547-5556.
[15] Font R., Marcilla A., Verdu E., Devesa J. 1990. Kinetics of the pyrolysis
of almond shells and almond shells impregnated with cobalt dichloride
in a fluidized bed reactor and in a pyroprobe 100. Ind Eng Chem Res 29:
1846-1855.
[16] Bryden K. M., Hagge M. J. 2003. Modeling the combined impact of
moisture and char shrinkage on the pyrolysis of a biomass particle. Fuel
82: 1633-1644.
[17] Bryden K. M., Ragland K. W., Rutland C. J. 2002. Modeling thermally
thick pyrolysis of wood. Biomass Bioenerg 22: 41-53.
[18] Tran H. C., White R. H. 1992. Burning rate of solid wood measured in a
heat release rate calorimeter. Fire Mater 16: 197-206.
[19] Park W. C., Atreya A., Baum H. R. 2010. Experimental and theoretical
investigation of heat and mass transfer processes during wood pyrolysis.
Combust Flame 157: 481-494.
[20] Lee C. K., Chaiken R. F., Singer J. M. 1977. Charring pyrolysis of wood
in fires by laser simulation. Proc Combust Inst 16: 1459-1470.
[21] Liden A. G., Berruti F., Scott D. S. 1988. A kinetic model for the pro-
duction of liquids from the flash pyrolysis of biomass. Chem Eng Comm
65: 207-221.
[22] Boroson M. L., Howard J. B., Longwell J. P., Peters W. A. 1989. Prod-
uct yields and kinetics from the vapor phase cracking of wood pyrolysis
tars. AIChE J 35: 120-128.
[23] Kossitrin H. 1980. Direct formation of pyrolysis oil from biomass. Proc.
Spec. Workshop on Fast Pyrolysis of Biomass, Copper Mountain, Co.
105-121.
[24] Diebold J. P. 1985. The cracking of depolymerized biomass vapors in a
continuous, tabular reactor. MSc Thesis, Colorado School of Mines.
[25] Milosavljevic I., Oja V., Suuberg E. M. 1996. Thermal effects in cellu-
lose pyrolysis: relationship to char formation processes. Ind Eng Chem
Res 35: 653-662.
47
32 Chapter 2
[26] Grønli M. G. 1996. A theoretical and experimental study of the thermal
degradation of biomass. PhD Thesis, Norwegian University of Science
and Technology.
[27] Park W. C. 2008. A study of pyrolysis of charring materials and its ap-
plication to fire safety and biomass utilization. PhD Thesis, The Univer-
sity of Michigan.
[28] Havens J. A., Welker J. R., Sliepcevich C. M. 1971. Pyrolysis of wood:
a thermoanalytical study. J Fire Flammability 2: 321-333.
[29] Bilbao R., Mastral J. F., Ceamanos J., Aldea M. E. 1996. Modelling of
the pyrolysis of wet wood. J Anal Appl Pyrolysis 36: 81-97.
[30] Mok W. S. L., Antal M. J., Jr. 1983. Effects of pressure on biomass py-
rolysis. II. Heats of reaction of cellulose pyrolysis. Thermochimica Acta
68: 165-186.
[31] Rath J., Wolfinger M. G., Steiner G., Krammer G., Barontini F.,
Cozzani V. 2003. Heat of wood pyrolysis. Fuel 82: 81-91.
[32] Lu H., Robert W., Peirce G., Ripa B., Baxter L. L. 2008. Comprehen-
sive study of biomass particle combustion. Energ Fuels 22: 2826-2839.
[33] Johansson R. Thunman H., Leckner B. 2007. Influence of interparticle
gradients in modeling of fixed bed combustion. Combust Flame 149:
49-62.
[34] Rath J., Staudinger G. 2001. Cracking reactions of tar from pyrolysis of
spruce wood. Fuel 80: 1379-1389.
[35] Adams T. N. 1980. A simple fuel bed model for predicting particulate
emissions from a wood-waste boiler. Combust Flame 39: 225-239.
[36] Ragland K. W., Aerts D. J., Baker A. J. 1991. Properties of wood for
combustion analysis. Bioresour Technol 37: 161-168.
[37] Yang Y. B., Ryu C., Khor A., Yates N. E., Sharifi V. N., Swithenbank,
J. 2005. Effect of fuel properties on biomass combustion. Part II. Mod-
elling approach-identification of the controlling factors. Fuel 84: 2116-
2130.
[38] Di Blasi C. 2000. Dynamic behavior of stratified downdraft gasifiers.
Chem Eng Sci 55: 2931-2944.
[39] Gerber S., Behrendt F., Oevermann M. 2010. An Eulerian modeling ap-
proach of wood gasification in a bubbling fluidized bed reactor using
char as bed material. Fuel 89: 2903-2917.
48
Modeling Combustion of Single Biomass Particle 33
[40] Font R., Marcilla A., Verdu E., Devesa J. 1986. Fluidized bed flash py-
rolysis of almond shells: temperature influence and catalysts screening.
Ind Eng Chem Prod Res Dev 25: 491-496.
[41] Thunman H., Niklasson F., Johnsson F., Leckner B. 2001. Composition
of volatile gases and thermochemical properties of wood for modeling
of fixed or fluidized beds. Energ Fuels 15: 1488-1497.
[42] Grieco E., Baldi G. 2011. Analysis and modeling of wood pyrolysis.
Chem Eng Sci 66: 650-660.
[43] Westbrook C. K., Dryer F. L. 1984. Chemical kinetic modeling of hy-
drocarbon combustion. Prog Energ Combust Sci 10: 1-57.
[44] Gomez-Barea A., Leckner B. 2010. Modeling of biomass gasification in
fluidized bed. Prog Energ Combust Sci 36: 444-509.
[45] Stimely G. L., Blankenhorn P. R. 1985. Effects of species, specimen
size and heating rate on char yield and fuel properties. Wood Fiber Sci
7: 476-489.
[46] Hobbs M. L., Radulovic P. T., Smoot L. D. 1992. Modeling fixed-bed
coal gasifiers. AIChE J 38: 681-702.
[47] Wurzenberger J. C., Wallner S., Raupenstrauch H., Khinast J. G. 2002.
Thermal conversion of biomass: comprehensive reactor and particle
modeling. AIChE J 48: 2398-2411.
[48] Porteiro J., Miguez J. L., Granada E., Moran J. C. 2006. Mathematical
modeling of the combustion of a single wood particle. Fuel Proc
Technol 87: 169-175.
[49] Porteiro J., Granada E., Collazo J., Patiño D., Morán J. C. 2007. A mod-
el for the combustion of large particles of densified wood. Energ Fuels
21: 3151-3159.
[50] Yang Y. B., Sharifi V. N., Swithenbank J., Ma L., Darvell L. I., Jones J.
M., Pourkashanian M., Williams A. 2008. Combustion of a single parti-
cle biomass. Energ Fuels 22: 306-316.
[51] Saastamoinen J. J., Aho M. J., Linna V. L. 1993. Simultaneous pyrolysis
and char combustion. Fuel 72: 599-609.
[52] Saastamoinen J., Aho M., Moilanen A., Sørensen L. H., Clausen S.,
Berg M. 2010. Burnout of pulverized biomass particles in large scale
boiler-single particle model approach. Biomass Bioenerg 34: 728-736.
49
34 Chapter 2
[53] Ouedraogo A., Mulligan J. C., Cleland J. G. 1998. A quasi-steady
shrinking core analysis of wood combustion. Combust Flame 114: 1-12.
[54] Thunman H., Leckner B., Niklasson F., Johnsson F. 2002. Combustion
of wood particles-a particle model for Eulerian calculations. Combust
Flame 129: 30-46.
[55] He F., Behrendt F. 2011. A new method for simulating the combustion
of a large biomass particle-a combination of a volume reaction model
and front reaction approximation. Combust Flame 158: 2500-2511.
50
Chapter 3
Modeling Biomass Particle Pyrolysis
The content of this chapter is mainly based on the following papers: Haseli Y., van Oijen J. A., de Goey L.
P. H. 2011. Modeling biomass particle pyrolysis with temperature dependent heat of reactions. Journal of
Analytical and Applied Pyrolysis 90: 140-154; Haseli Y., van Oijen J. A., de Goey L. P. H. 2011. Numerical
study of the conversion time of single pyrolyzing biomass particles at high heating conditions. Chemical
Engineering Journal 169: 299-312.
3.1 INTRODUCTION
The thermal characteristics of the pyrolysis process as one of the unavoid-
able steps during thermal decomposition of a biomass particle need to be care-
fully investigated at combustion conditions; even though this phenomenon has
been previously studied theoretically and experimentally by many researchers.
During biomass pyrolysis, several physical and chemical processes take place
including virgin biomass heating up, moisture evaporation and transportation,
kinetics involving the decomposition of biomass to tar, char and light gases,
heat and mass transfer, pressure build-up within the porous medium of the sol-
id, convective and diffusive gas phase flow, variation of thermo-physical
properties with temperature and composition, and change in particle size, i.e.
shrinkage.
The detailed models available in the literature for biomass particle pyroly-
sis are based on coupled time-dependent conservation equations including ki-
netics of the biomass decomposition. In fact, the kinetic model directly influ-
ences the conservation equations. As discussed in Chapter 2, there are
discrepancies in the reported kinetics and thermo-physical data applied in dif-
ferent theoretical investigations for predicting thermal degradation of a bio-
51
36 Chapter 3
mass particle. For instance, the heat of pyrolysis is one of the most important
parameters influencing the pyrolysis process, and has been assigned various
values. So, it remains a question for a pyrolysis modeler what set of kinetic
constants and which value for the heat of reactions must be utilized in the sim-
ulation. Our attempt is to find reasonable answers for these uncertainties in this
chapter.
On the other hand, discrepancies have also been found in measurements
and experimental observations reported in various sources. For instance, the
particle inner temperature showed to exceed the surface temperature of the sol-
id particle before reaching thermal equilibrium in the experimental studies of
Koufopanos et al. [1], Park et al. [2] and Di Blasi et al. [3], whereas this phe-
nomenon was not observed in measurements of other workers such as Larfeldt
et al. [4], Chan et al. [5], Tan and White [6], and Lu et al. [7].
In this chapter, assuming that the biomass decomposition takes place ac-
cording to the Shafizadeh-Chin scheme [8], we investigate the accuracy of the
pyrolysis models when using various kinetic parameters reported in the litera-
ture. The possibility of a tar cracking reaction to produce lighter gases is also
examined. Moreover, it is intended to highlight advantages of an accurate for-
mulation of the conservation of energy that allows computing the enthalpy of
pyrolysis as a function of temperature.
In the upcoming section, a one-dimensional model for pyrolysis of a bio-
mass particle will be presented. The validation of the model will be carried out
in Sec. 3.3. The pyrolysis model employing an empirical correlation for the en-
thalpy of biomass pyrolysis is examined in Sec. 3.4. A numerical study will be
performed in Sec. 3.5 to evaluate the effects of particle shape, size and density
on the conversion (pyrolysis) time and final char yield at high heating rate
conditions. The numerical investigation further aims to find out under what
circumstances (in terms of particle size and density, as well as reactor tempera-
ture) the pyrolysis process may become homogeneous (Sec. 3.6). A summary
of the main findings will be given in Sec. 3.7.
3.2 PYROLYSIS MODEL
The kinetic mechanism employed in the simulation of single particle bio-
mass pyrolysis accounts for three parallel primary reactions with the possibil-
ity of a tar cracking reaction; that is, the virgin biomass decomposes to gas, tar
52
Modeling Combustion of Single Biomass Particle 37
and char, and vapor tar decomposes to yield further gas. As concluded in past
experimental studies [9-11], the main product of the tar cracking reaction is
light gases, and the amount of char yield is negligible.
Despite some past studies [2, 7, 12, 13] that reported the possibility of
cracking tar into lighter gases at elevated temperatures, however, there is no
experimental evidence supporting that this reaction also takes place during
thermal conversion of a biomass particle through a separate path. To the au-
thor’s best knowledge, tar cracking in the form of secondary reactions was first
adapted by Di Blasi [12], who also assumed that char could be formed as a
consequence of tar cracking. Since then, some authors have assumed the sec-
ondary reactions in their pyrolysis models, whereas some others have argued
that the possibility of this reaction directly depends on the residence time of
the volatiles, so that it does not necessarily take place as in the pyrolysis pro-
cess. In a recent study by Park et al. [2], it has been reported that accounting
for the secondary reactions is of minor importance. As a further task of the
present chapter, it is intended to find out whether predictions of the pyrolysis
model with three parallel reactions are sufficient to observe the experiments,
or inclusion of a tar cracking reaction in the model may provide better predic-
tions.
The reaction rates are determined through an Arrhenius type equation.
( ) 4,3,2,1/exp =−= iTREAkgiii
(3.1)
where A is the frequency factor, E the activation energy, Rg the universal gas
constant, and T the temperature.
Biomass Tar
Gas
Char
k1
k2
k3
Gas
k4
53
38 Chapter 3
3.2.1 Conservation of Species Mass
The consumption of biomass (B) and the formation of char (C) can be de-
scribed by the following equations:
( )B
B kkkt
ρρ
321++−=
∂
∂ (3.2)
B
C kt
ρρ
3=
∂
∂ (3.3)
Mass conservation equations of the tar (T) and total gas phase (g) obey
( )TBT
n
n
T kkurrrt
ερρρερ
42
1−=
∂
∂+
∂
∂ (3.4)
( ) ( )Bg
n
n
gkkur
rrtρρ
ερ
21
1+=
∂
∂+
∂
∂ (3.5)
where n denotes a shape factor (n = 0 for flat, n = 1 for cylinder, and n = 2 for
sphere), ε represents the particle porosity, and u is the superficial gas velocity.
During thermal decomposition of biomass, particle porosity increases with
time and it may have different values along the spatial coordinate r.
3.2.2 Conservation of Energy
The main assumptions for the formulation of energy conservation related
to a solid biomass particle undergoing thermal degradation are that the volume
of the particle remains constant during the process, and the solid and the gas
phase are in thermal equilibrium. A proper description of the energy equation
is that it must account for (1) accumulation of energy, (2) conductive heat
transfer through the particle, (3) convective heat transfer due to flow of vola-
tiles through pores. As the problem of study includes the chemical structural
54
Modeling Combustion of Single Biomass Particle 39
changes through various reactions, the enthalpy of each species must be repre-
sented as the summation of sensible and formation enthalpies:
( ) gCBir
Tkr
rrhur
rrh
t
n
ngg
n
ni
i ,,1ˆ1ˆ *
=
∂
∂
∂
∂=
∂
∂+
∂
∂∑ ρρ (3.6)
where h is the total enthalpy, and k* is the effective thermal conductivity
which accounts for thermal conductivity of the biomass, char, gaseous by-
products as well as radiation heat transfer inside the pores (using the Rossland
diffusion approximation for a thick medium). Some mathematical manipula-
tions are required in order to represents the energy equation in terms of tem-
perature as described in Appendix A, so the final form of Eq. (3.6) reads:
( ) Qr
Tkr
rrr
Tcu
t
Tccc
n
nPggPggPCCPBB
~1 *+
∂
∂
∂
∂=
∂
∂+
∂
∂++ ρερρρ (3.7)
where
( ) ( )[ ]
( )[ ]
( )[ ]∫
∫
∫
−+∆
+−+∆
+−+∆+=
−
−
−
dTcchk
dTcchk
dTcchkkQ
GTGTT
CBCBB
gBgBB
4
3
21
~
ερ
ρ
ρ
(3.8)
where ∆hB-g, ∆hB-C, ∆hT-G are, respectively, enthalpies of Bg, BC and
TG reactions at a reference temperature. Notice that ∆hB-g accounts for the
55
40 Chapter 3
enthalpies of both BG and BT reactions according to the assumed kinetic
scheme. The above formulation suggests that the heat of reactions involved in
the pyrolysis process need to be calculated as a function of temperature. How-
ever, in many past studies, Q~
is defined as
( )STPB
hkhkkkQ ∆+∆++=4321
~ερρ (3.9)
where it is assumed that the heat of all three primary reactions are identical
(∆hP), and the heat of secondary reaction is represented by ∆hS.
By comparing Eq. (3.8) with Eq. (3.9), we find
( ) ( )[ ] ( )[ ]∫∫ −+∆+−+∆−=∆−−
dTcchYdTcchYhCBCBCgBgBCP
1 (3.10)
( )∫ −+∆=∆−
dTcchhGTGTS
(3.11)
In Eq. (3.10), YC denotes the fraction of char in the pyrolysis products. So,
in these studies the possibility of evaluating the heat of pyrolysis at different
temperatures and as a function of products yields is taken away. The main is-
sue with the inaccurate formulation of the source term, i.e. Eq. (3.9), in the en-
ergy equation is that an endothermic heat is usually assumed for all three pri-
mary reactions as in many past studies, e.g. 418 kJ/kg [2], 150 kJ/kg [13], and
64 kJ/kg [14]. These values have been obtained by fitting the predictions (usu-
ally mass loss or temperature histories) with the experiments in each individual
study through employing Eq. (3.9) and without accounting for any secondary
reactions. In fact, these studies suggest that heat input is a requirement for the
entire process of biomass decomposition, which is not consistent with experi-
mental observations of Lee et al. [15], Milosavljevic et al. [16] and Bilbao et
al. [17]. The question that may be raised is that, wouldn’t it be better to em-
ploy the accurate version of the source term in the energy equation as repre-
sented in Eq. (3.8), and try to find enthalpy of reactions at a reference tempera-
ture through the same method of fitting of predictions with experiments? We
will further follow this idea in Sec. 3.3 to examine whether with this proposed
method we may still get a variety of reactions heats, or it may be possible to
56
Modeling Combustion of Single Biomass Particle 41
end up with a single value that can be used in the pyrolysis model to reasona-
bly capture various experimental observations.
It can be inferred from Eq. (3.8) that the reaction heats associated with the
formation of volatiles, char and possibly secondary gases become more exo-
thermic as the temperature increases. This is because the specific heat of bio-
mass is usually greater than that of char and that of volatiles, as well as the
specific heat of tar is greater than that of light gases (see the related correla-
tions that are given in Table 3.1). Moreover, Eq. (3.8) shows that the heat of
volatiles release is not necessarily the same as the heat of char formation. The
question that may arise is what would be the physical explanation of the terms
associated with various specific heats appeared in Eq. (3.8)? This term repre-
sents the amount of sensible heat released when species i decomposes to spe-
cies j at a temperature different from the reference one. Alike any chemical re-
action in which a certain amount of energy is released/consumed at a given
temperature, it is possible to estimate the amount of energy (enthalpy of reac-
tion) at another temperature by simply algebraic summation of the enthalpy of
reaction at the reference temperature, and the enthalpy that is equivalent to the
difference in the sensible heats of the products and the reactants.
As a conclusion from this discussion, it is possible that the enthalpy of py-
rolysis may become exothermic at some stages of the pyrolysis depending on
the process conditions, as also confirmed in some studies. In such cases, a py-
rolysis model that uses Eq. (3.9) with constant endothermic heat for the prima-
ry reactions will fail to accurately predict the temperature, and as a conse-
quence the chemistry of the process will be influenced. On the contrary, a
model which employs Eq. (3.8) does not suffer from this issue, since it has a
potential to capture exothermicity of the pyrolysis heat by accounting for the
sensible heat released due the conversion of the biomass to the volatiles and
char. Further demonstration of this idea will be presented in Sec. 3.3.2.
3.2.3 Conservation of Momentum
Darcy law is applied to describe gas phase momentum transfer within the
porous media. Hence, the superficial gas velocity is obtained from
r
pKu
∂
∂−=
µ (3.12)
57
42 Chapter 3
Furthermore, it is assumed that volatiles behave like a perfect gas, so that in-
ternal pressure is determined from
g
g
MW
RTp
ρ= (3.13)
3.2.4 Initial and Boundary Conditions
The numerical solution of the transport equations described above needs to
define five initial and four boundary conditions.
Initial conditions (t = 0)
00000
====== u;TT;;;;inertgTCBB
ρρρρρρ (3.14)
Boundary Conditions (t > 0)
( ) ( )
( ) ( )
−−−−
−+−
=∂
∂=
=∂
∂=
∂
∂=
∂
∂=
∞∞
∞∞
44
44
*:
0;0;0:0
TTeTThq
or
TTeTTh
r
TkRr
r
T
rrr
x
gT
σ
σ
ρρ
(3.15)
Two different types of boundary conditions may be applied to define the
surface temperature. The first one is used for a known reactor temperature so
that heat is transferred to the surface of the particle through radiation and con-
vection. The second boundary condition is suitable when the particle is ex-
posed to a known heating flux qx so that some heat is dissipated from the sur-
face to the environment via radiation and convection. Moreover, in the
simulation code the velocity is initially set to zero as well as that the initial
pressure and pressure at the surface are equal to the surrounding pressure (usu-
ally atmospheric).
58
Modeling Combustion of Single Biomass Particle 43
Table 3.1 Thermo-physical properties used in the simulation
Property Value/Correlation
Specific Heat (J/g.K) cpB = 1.5 + 1.0×10-3
T
cpC = 0.44 + (2×10-3
)T - 6.7×10-7
T2
cpT = -0.162 + (4.6×10-3
)T - 2×10-6
T2
cpG = 0.761 + (7×10-4)T – (2×10-7)T2
cpg = (ρT/ρg)cpT + (1 – ρT/ρg)cpG
Thermal Conductivity (W/cm.K) k* = (ρB/ρB0)kB + (1 - ρB/ρB0)kC + εkg +
13.5σT3d/ω
kg = 0.00026
kc = 0.001 (grain)
kc = 0.007 (radial)
Porosity ε = 1 - (1 – ε0)(ρB + ρC)/ρB0
ε0: biomass dependent
Pore diameter (cm) d = (ρB/ρB0)dB + (1 – ρB/ρB0)dC
dB = 5×10-3
dC = 10-2
Permeability (cm-2
) K = (ρB/ρB0)KB + (1 – ρB/ρB0)KC
KB = 5×10-12
KC = 10-9
Gas Phase Viscosity (kg/m.s) µg = 3×10-5
3.2.5 Simulation Code
The pyrolysis model described above is implemented in CHEM1D to
study thermal conversion of a dry biomass particle. CHEM1D [18] is a com-
puter code developed at the Combustion Technology Group of the Department
of Mechanical Engineering at Eindhoven University of Technology to calcu-
late various flame types. It is capable of solving a set of general time-
dependent 1-D differential equations which includes accumulation, convec-
tion, diffusion and source terms, on the basis of the control volume discretisa-
tion method for specified initial and boundary conditions and known time and
space domains. It uses adaptive gridding and time stepping techniques.
Simultaneous solution of the transport and kinetic equations requires defin-
ing the thermo-physical properties and kinetic constants discussed previously.
Composition-dependence of thermal conductivity, specific heat and solid
phase permeability is taken into consideration. A survey on thermo-physical
properties allowed us to take a fixed value/correlation for most of the parame-
ters, except the thermal conductivity, density and initial porosity of biomass,
and the convective heat transfer coefficient h, which may vary depending upon
59
44 Chapter 3
the type of biomass and process conditions. Table 3.1 lists the required data
and some auxiliary equations which are included in the simulation code. The
presented relationships for the specific heats of char, tar and gas are based on
correlated data of Raznjevic [19].
3.3 EXPERIMENTAL VALIDATION
The accuracy of the developed pyrolysis model and the reliability of the
four different kinetic data are examined by comparing the predictions with ex-
perimental data taken from Gronli and Melaaen [13], Koufopanos et al. [1] and
Rath et al. [20]. The idea is to find out which set of kinetic parameters given in
Table 2.2 may provide a better prediction of the thermal degradation of a sin-
gle biomass particle. Notice that an efficient model must be capable of reason-
ably predicting both heat transfer and kinetics of the process; i.e. mere valida-
tion of heat transfer or mass transport parameters is not sufficient. This has
been taken into consideration in only a few studies [1, 13, 21-23]. The second
idea is to find what value can be obtained for ∆hB-g and ∆hB-C (assuming ∆hB-g
= ∆hB-C) at various experimental conditions when Eq. (3.8) is used as the
source term in the energy equation. Also, we intend to examine whether the
kinetic scheme with three parallel reactions is sufficient enough to capture the
experimental observations, or inclusion of a tar cracking reaction to yield fur-
ther light gases in the model could provide better predictions of the thermo-
kinetics of the pyrolysis process.
3.3.1 Comparison with Gronli and Melaaen Data
In the experimental work of Gronli and Melaaen [13], birch, pine, and
spruce particles were one-dimensionally heated in a bell-shaped glass reactor
using a xenon arc lamp as a radiant heat source. The total times of exposure
(heating times) were 5 and 10 minutes. For validation of their pyrolysis model,
which did not account for particle shrinkage, experimental results of spruce
heated parallel with the grain were chosen which had shown the lowest axial
shrinkage at both low and high heat fluxes compared to pine and birch parti-
cles.
Figure 3.1 shows a comparison between the predicted (obtained from the
simulation code) and measured temperature profiles at five axial positions 0.6,
1.8, 2.2, 2.6 and 3 cm for an external heat flux of 80 kW/m2. A good agree-
60
Modeling Combustion of Single Biomass Particle 45
ment between the predicted and the measured temperatures can be seen using
all sets of kinetic parameters. This agreement was obtained by fitting the pre-
dictions with experimental data for a weighted endothermic reaction heat of 25
kJ/kg; i. e. ∆hB-g = ∆hB-C = 25 kJ/kg, without accounting for the tar cracking
reaction; i . e. k4 = 0. When a possibility of secondary reaction of tar was taken
into consideration, no reasonable match between the measured and the predict-
ed profiles was observed, given that the variety of heat of primary reactions
was tested.
(a) (b)
(c) (d)
Figure 3.1 Comparison of predicted (solid lines) and measured (areas between broken
lines) temperature profiles at five axial positions using kinetic parameters of (a)
Thurner and Mann [24], (b) Di Blasi and Branca [25], (c) Chan et al. [5], (d) Font et al.
[26]. Experimental data are taken from Gronli and Melaaen [13].
61
46 Chapter 3
Table 3.2 Comparison of the predicted and measured biomass conversion and char
yield with experimental data taken from Gronli and Melaaen [13] (T&M: Thurnner
and Mann; C: Chan et al.; D&B: Di Blasi and Branca; F: Font et al.)
Duration Kinetic data
Converted Biomass (%wt) Char Yield (kg/m3)
Measured Predicted ∆% Measured Predicted ∆%
5 mins T&M
25.7 ± 1.63 25.1 -2.3 30.4 33.4 9.9
10 mins 45.5 ± 3.61 41.7 -8.4 58.8 56 -4.8
5 mins C
25.7 ± 1.63 24.3 -5.4 30.4 29.5 -3.0
10 mins 45.5 ± 3.61 39.9 -12.3 58.8 50.4 -14.3
5 mins D&B
25.7 ± 1.63 25.6 -0.4 30.4 19 -37.5
10 mins 45.5 ± 3.61 41.8 -8.1 58.8 35.3 -40.0
5 mins F
25.7 ± 1.63 26 1.2 30.4 62.7 106.3
10 mins 45.5 ± 3.61 44.7 -1.8 58.8 120.5 104.9
As mentioned previously, mere validation against heat transfer parameters
is not sufficient since the process also involves kinetics and mass transport of
various species. The biomass conversion fraction and char yield were also cal-
culated using different kinetic data. In Table 3.2, the predicted and measured
values of these parameters are compared for 5 min and 10 min as the duration
of pyrolysis. The conversion of biomass is well-predicted using all kinetic data
sets at 5 minutes heating duration. The converted biomass is still reasonably
predicted for the 10 minutes heating condition with most under-prediction at-
tributed to the data of Chan et al. [5]. Nevertheless, looking at the predicted
char yields, it is seen that the predictions using the data of Thurner and Mann
[24] and data of Chan et al. [5] are much better than Di Blasi and Branca [25]
and Font et al. [26]. Kinetic constants of Font et al. give a significant over-
prediction of the char yields to the extent of 106%. On the other hand, data of
Di Blasi and Branca leads to a notable under-prediction of char yields to the
extent of 40%.
Figure 3.2 and 3.3 depict typical simulated time and space evolution of
various parameters related to the experimental condition of Gronli and
Melaaen [13]. As the particle with initial temperature of 300K is exposed to a
high heating flux, the surface temperature begins to rise while some heat is
dissipated from the surface to the surrounding due to radiation and convection
heat transfer mechanisms. The heat received by the surface is transferred into
the particle through conduction heat transfer. As the temperature of the particle
62
Modeling Combustion of Single Biomass Particle 47
increases the primary reactions are activated so that the virgin biomass begins
to slightly decompose into three main groups of byproducts at low tempera-
tures according to the kinetic model employed. The rates of conversion be-
come higher as the temperature increases.
Figure 3.2 Time and space evolution of temperature, volatiles mass flux, internal pres-
sure, biomass density, tar density and char density. Simulated time: 10 mins; Different
lines correspond to different times; External heat flux: 80 kW/m2; Horizontal axis: half
thickness of particle (3 cm); Kinetic data: Thurner & Mann.
63
48 Chapter 3
Figure 3.3 Time and space evolution of temperature, volatiles mass flux, internal pres-
sure, biomass density, tar density and char density. Simulated time: 1 min; Different
lines correspond to different times; Applied external heat flux: 80 kW/m2; Horizontal
axis: 0.5 cm inside the particle; Kinetic data Thurner & Mann.
As the gaseous byproducts are generated by continuous decomposition of
biomass, internal non-uniform pressure slightly greater than atmospheric pres-
sure is built up. This causes a flow of volatiles through the pores of the particle
mainly towards the surface of the particle where they escape, but there also ex-
64
Modeling Combustion of Single Biomass Particle 49
ists a flow of gaseous species in the opposite direction which increases the
pressure at the center of the particle. During the initial stages of the process,
the pressure peak takes place near the surface; however, as the process contin-
ues the location of the maximum pressure is shifted to the internal positions.
This is attributed to the higher rate of volatiles generated compared to their lo-
cal velocity. The flux of gaseous flow is dependent on the local permeability
so that the volatiles mass flux is higher in the charred part of the particle than
in virgin part since the permeability of char is higher than that of biomass.
As long as decomposition of the particle surface has not been finalized, the
particle can be divided into two regions: a partial char region where still there
is some biomass to decompose, and a virgin biomass region. In this stage of
the process, maximum formation of volatiles (including tar) and char takes
place at the surface. Soon after all virgin material at the surface has converted
to byproducts a thin layer of char is formed at the surface. As the process of
degradation proceeds, the thickness of the charred region increases and its
front moves towards the particle center. By increasing the thickness of the char
layer, the location of maximum tar yields is shifted to the inside of the particle
and its magnitude increases. In other words, the local density of tar increases
continuously along the axis of the particle up to a point where formation of tar
stops. Beyond this position, the density of tar decreases due to the flow of vol-
atiles towards the surface of the particle.
3.3.2 Comparison with Data of Koufopanos et al.
An isothermal mass-change determination technique was employed in the
work of Koufopanos et al. [1] to measure the pyrolysis rate of dried wood cyl-
inders initially at room temperature at reactor temperatures in the range of
573-873 K. Temperature variations at two positions inside the particles were
also measured during the pyrolysis process. An interesting observation in these
experiments was that the temperature inside the particle exceeded the reactor
temperature, and a peak was observed; with a higher magnitude at a lower re-
actor temperature. To capture this phenomenon, Koufopanos et al. [1] pro-
posed that initial stages of the conversion take place endothermically, but the
rest of process proceeds exothermically. Through fitting the model predictions
with the experiments, they found an endothermic heat of 255 kJ/kg (up to a
conversion of 95%), as well as an exothermic heat of -20 kJ/kg (for the re-
maining stages of the particle conversion). Saduhkhan et al. [27] were also
65
50 Chapter 3
able to model the internal temperature peaks observed in the experiments of
Koufopanos et al. [1] by assuming an exothermic heat of -245 kJ/kg for the en-
tire of the process in their model. They also employed the same kinetic scheme
of Koufopanos et al. [1]. Interesting to note is that, in a subsequent publication,
Saduhkhan et al. [22] used a different value for the pyrolysis heat; i. e., -220
kJ/kg, in order to capture their own experimental data which also included a
temperature peak.
In Fig. 3.4, the predicted center temperature and mass loss are compared
with experiments of Koufopanos et al. [1] at reactor temperatures of 623 K
(top graph) and 773 K (bottom graph). The normalized temperature is defined
as (T-Tr)/(T0-Tr) with T0 and Tr representing the initial and reactor tempera-
tures. Simulations have been performed using all sets of kinetic parameters.
However, the results obtained from data of Font et al. [26] are excluded in Fig.
4 since the pyrolysis rate was significantly overestimated; even though pre-
dicted temperature profiles were satisfactory. In each case, the best match be-
tween the predicted temperature and mass loss profiles with experiment was
achieved with a weighted endothermic heat of 25 kJ/kg; the same value found
in the previous sub-section. These satisfactory agreements between the simula-
tion results and the experimental data were obtained without accounting for tar
cracking reactions, because inclusion of additional gas formation through sec-
ondary reactions did not lead to reasonable results given that various values of
heat of pyrolysis were examined.
The temperature rise at the early stages of the process is predicted to be
faster than the measured data. One possible reason for this is that the value as-
sumed for the convective heat transfer rate in our simulations may be different
from the real one which was not reported in Ref. [1]. Furthermore, thermal
conductivity of the virgin wood can also contribute to the gap between predic-
tions and measurements at the early stage of the process as a single constant
value was chosen in the simulation that may be higher than the actual value of
the biomass thermal conductivity.
Interesting to note is that the presented thermo-kinetic model is capable of
capturing the temperature peak as observed in experiments of Koufopanos et
al. [1], which means that the three parallel reactions yielding gas, tar and char
and the enhanced version of the heat transfer equation are sufficient enough to
predict the temperature peak at the center of the particle. One may argue how
an internal temperature can exceed the surface temperature while the source of
66
Modeling Combustion of Single Biomass Particle 51
thermal energy is external. As discussed in Sec. 3.2.2, the local temperature
can be affected by heat released due to conversion of biomass to products.
Figure 3.4 Comparison of the predicted mass loss and center temperature (lines) with
measurements of Koufopanos et al. [15] (symbols) at two reactor temperatures: 623 K
(top), 773 K (bottom). () measured temperatures; () measured mass losses; () Ki-
netic data of Chan et al.; () Kinetic data of Thurner and Mann; () Kinetic data of
Di Blasi and Branca.
67
52 Chapter 3
Imagine the moment during the pyrolysis process that the center tempera-
ture reaches the surface temperature while thermal degradation of the biomass
at the center of the particle has not yet been finalized. Thus, there is no
heat/energy transfer to the center due to conduction. At this time, the center of
the temperature is at a certain enthalpy level. Since the center temperature is
high enough to cause decomposition of the remaining biomass to char and vol-
atiles, there is a possibility of a local temperature rise because of the reduction
of the local heat capacity in order to satisfy the local conservation of energy. In
fact, this may occur when the rate of particle decomposition is higher than the
rate of heat transfer. The competition between these two processes continues
until the heat transfer rate becomes dominant and therefore the center tempera-
ture begins to drop again (mainly due to conduction) and reaches thermal equi-
librium; the surface temperature. This hypothesis is no longer valid if the par-
ticle decomposition has already been finalized before the center temperature
(or any internal location) reaches the surface temperature. This will be demon-
strated in Sec. 3.3.3.
The above hypothesis is confirmed by the simulated temperature and bio-
mass density profiles in the center and at the surface of the particle as depicted
in Fig. 3.5. It can be seen that the center temperature reaches the surface tem-
perature at around 630 s after initiation of the heating process. At this moment,
over 50% of the biomass in the center still remains to be decomposed. As the
corresponding local temperature is within the range of primary reactions, de-
composition of the remaining biomass continues with a rate higher than the lo-
cal heat transfer rate, which results in a local temperature rise due to the re-
lease of sensible heat by conversion of the virgin material to the byproducts. A
careful observation of the graphs shown in Fig. 3.5 indicates that the tempera-
ture peak takes place at the moment when the rate of biomass decomposition
becomes slower and it is close to finalize. It seems that when there is only a
small amount of virgin material left, the heat transfer rate becomes dominant
compared to the rate of the biomass decomposition so that the local tempera-
ture drops as the remaining biomass undergoes its final stage of conversion.
The ‘temperature-peak’ phenomenon may occur not only at the center of a
pyrolyzing biomass particle but also at any other internal position; for example
at the location of half the radius. Figure 3.6 illustrates an additional compari-
son between the predicted and the measured temperature profiles at the loca-
tion of half the radius. A good agreement is observed between experiments and
our simulation results, especially when using the Thurner and Mann [24] or
68
Modeling Combustion of Single Biomass Particle 53
Chan et al. [5] kinetic data, and the measurements of Koufopanos et al. [1],
which further demonstrates the capability of the presented pyrolysis model in
capturing the behavior of the pyrolyzing particle. Different magnitudes of
temperature peaks are expected at various positions with the highest one taking
place in the center. A possible reason for this is that the rate of heat transfer at
the surface of the particle is the highest. As the flow of heat penetrates inside
the particle the local heat transfer rate decreases as the thermal resistance in-
creases. Thus, in the competition between heat transfer rate and biomass de-
composition rate, the later one is dominant for a longer time at positions closer
to the center. This reasoning can be extended to explain why the magnitude
(and duration) of the temperature peak is lower (and shorter) at a higher reac-
tor temperature as observed in the experiments of Koufopanos et al. [1] and
Park et al. [2]: At higher reactor temperatures the rate of heat transfer becomes
higher and more dominant in the above competition so that there is less oppor-
tunity for the chemical decomposition rate to exceed the heat transfer rate.
From Figs. 3.4 and 3.6, the data of Thurner and Mann [24] give the best
agreement between the experiments and the predictions. Using their data, the
effects of the heat released due to the conversion of biomass to products –
which are represented in terms of differences between the specific heats of
virgin material and those of char and volatiles in Eq. (3.8) – is demonstrated
through generating the center temperature and mass loss profiles without ac-
counting for this term, at various heats of reactions. The results are depicted in
Fig. 3.7 for a reactor temperature of 623 K. Evident from this figure is that by
neglecting the amount of heat released due to the conversion of the virgin
wood to other materials, and by assuming an endothermic heat for the reac-
tions involved, the temperature peak observed in the experiments will not be
predicted. However, this phenomenon can be captured by feeding an exother-
mic heat of reactions into the model. Moreover, the mass loss is remarkably
under-predicted should we only consider an endothermic heat for these reac-
tions.
The phenomena of center temperature peak was also observed in the work
of Park et al. [2] who conducted pyrolysis experiments on moisture free maple
wood particles heated in a vertical tube furnace at temperatures ranging from
638 to 879 K. However, their pyrolysis model with three parallel primary reac-
tions did not allow observation of this phenomenon. This is because they did
not account for the sensible heat released due to the chemical decomposition
of the virgin particle, and an endothermic heat of 64 kJ/kg was assumed for all
69
54 Chapter 3
primary reactions. Therefore, they proposed a kinetic model according to
which the virgin biomass is decomposed to gas, tar and an intermediate solid
as primary reactions, with secondary reactions including conversion of the in-
termediate solid to char and cracking of tar to form additional gas and char.
Despite that this model was not supported by any experimental observations,
however, as an endothermic heat for primary gas and tar formation was used
while an exothermic heat for char generation was considered, they were on a
right track since these considerations were consistent with findings of
Milosavljevic et al. [16].
Figure 3.5 Predicted temperature and biomass density profiles at the center and sur-
face related to the experimental conditions of Koufopanos et al. [1] at reactor tempera-
ture of 623 K.
70
Modeling Combustion of Single Biomass Particle 55
Figure 3.6 Comparison of the predicted temperature (lines) with measurements of
Koufopanos et al. [1] (symbols) at the location of half radius for a reactor temperature
of 673 K; () Kinetic data of Chan et al.; () Kinetic data of Thurner and Mann; ()
Kinetic data of Di Blasi and Branca
Figure 3.7 Comparison of the predicted mass loss and center temperature (lines) with
measurements of Koufopanos et al. [1] (symbols) at a reactor temperatures of 623 K at
three different values for the heat of reaction without accounting for the sensible heat
released due to the conversion of the virgin material to char and volatiles.
71
56 Chapter 3
3.3.3 Comparison with Data of Rath et al.
Further experimental validation of the pyrolysis model is carried out by
comparing the simulation outcome with experimental data of Rath et al. [20],
who measured center and surface temperatures and mass loss profiles of cube-
like 2-cm beech wood particles heated in a muffle furnace maintained at 850 oC. The predicted center temperature and mass loss profiles obtained from var-
ious kinetic parameters are compared with measurements of Rath et al. [20] in
Fig. 3.8. The best match between prediction and measured data related to the
center temperature is achieved using kinetic constants from Thurner and Mann
[24] as well as Font et al. [2]. This agreement is obtained without accounting
for tar cracking reactions and with the same weighted reactions heat of 25
kJ/kg for the primary reactions. Likewise, when the possibility of the second-
ary reaction was considered the results were not as satisfactory as those ob-
tained without tar cracking reaction.
On the other hand, the mass loss over the duration of the pyrolysis process
is overestimated with data of Thurner and Mann [24] and Font et al. [26].
From Fig. 3.8, the best match between the predictions and the experiments is
obtained using the kinetic data of Chan et al. [5], given that the final char yield
is overestimated. Data of Di Blasi and Branca [25] underestimates the mass
loss of the pyrolyzing particle, but the final char yield is slightly closer to the
experimental value than that computed using data of Chan et al. [5]. Overall,
among various groups of kinetic data, the kinetic parameters of Chan et al. [5]
provide the most satisfactory agreement with measurements of Rath et al. [20].
Interesting to note with respect to the experiments of Rath et al. [20] is that
unlike the experiments of Koufopanos et al. [1] and Park et al. [2], the particle
center temperature reached the surface temperature and it remained in thermal
equilibrium without any peak. This can be explained with the same reasoning
discussed previously. The temperature peak did not occur because the biomass
in the center of the particle had completely decomposed before its temperature
reached the surface temperature. This is demonstrated by the numerical results
obtained from the pyrolysis model as shown in Fig. 3.9. As seen from this fig-
ure, the decomposition process at both center and surface of the particle takes
place very rapidly, which can be attributed to the high heating rate. After 110 s
from initiation of the pyrolysis process, conversion of biomass is finalized,
while there is still a considerable difference between the center and the surface
temperature. Thus, beyond this point the charred particle undergoes only the
heating process due to the conduction mechanism as there is no other heat
72
Modeling Combustion of Single Biomass Particle 57
source as the sensible heat related to the conversion of virgin biomass to char
and volatile has been released already.
Figure 3.8 Comparison of the predicted center temperature and mass loss (lines) with
measurements of Rath et al. [20] (symbols); () Kinetic data of Chan et al.; () Ki-
netic data of Thurner and Mann; () Kinetic data of Di Blasi and Branca; () Kinetic
data of Font et al.
73
58 Chapter 3
Figure 3.9 Predicted temperature and biomass density profiles of center and surface
related to the experimental conditions of Rath et al. [20].
3.3.4 Conclusion
Comparison of the simulation results with experimental data of large bio-
mass particles reveals that the pyrolysis model presented in this chapter pro-
vides satisfactory predictions when the kinetic parameters of Chan et al. [5] or
Thurner and Mann [24] are employed. The pyrolysis model with three parallel
reactions yielding tar, gas and char together with an extended version of ener-
74
Modeling Combustion of Single Biomass Particle 59
gy equation sufficiently captures the experimental observations of pyrolyzing
biomass particles, such as the center temperature peak reported in some past
studies. These experimental validations clearly demonstrate the significant in-
fluence of the amount of heat released during the conversion of virgin biomass
on the thermal degradation of the particle. Furthermore, the kinetic model with
three parallel reactions is sufficient to achieve a reasonable agreement between
the predictions and experiments so that any inclusion of secondary reactions is
not needed.
A single value for the heat of primary reactions; i. e. 25 kJ/kg, has been
obtained by assuming ∆hB-g = ∆hB-C and fitting the predictions to the measure-
ments. In fact, it represents a lumped heat of volatiles and char formation at a
reference temperature. Given that a satisfactory agreement between the simu-
lations and experimental data is achieved with the above endothermic heat, in
a more accurate simulation, the endothermic heat of volatiles formation and
exothermic heat of char generation must be treated separately according to
Milosavljevic et al. [16]. Nevertheless, as a consistent value of reactions heat
allowed accurately prediction of the thermal degradation of various biomass
particles at different experimental conditions, this is an essential step towards
better understanding of the pyrolysis heat, noting that a large scatter of values
has been reported in the literature.
The results indicate that it is necessary to account for the release of sensi-
ble heat due to the conversion of virgin biomass to products. It is demonstrated
that a release of this energy, usually overlooked in past works, is responsible
for the temperature peak observed in some past studies. This phenomenon may
occur when the local temperature reaches the surface temperature while the
decomposition of biomass at the corresponding position in not completely fi-
nalized; otherwise the internal local temperature remains in thermal equilibri-
um after it reaches the surface temperature.
3.4 PYOLYSIS MODEL WITH AN EMPIRICAL
CORRELATION FOR HEAT OF REACTIONS
As discussed in Sec. 2.2.2, Milosavljevic et al. [16], Mok and Antal [28],
and Rath et al. [29], among others, found that the pyrolysis heat could be cor-
related as a linear function of the final char yield. The common conclusion
from these works was that the char yield was the main factor determining
75
60 Chapter 3
whether the overall pyroysis process is endothermic or exothermic. In the
work of Rath et al. [29], pyrolysis heat of spruce and beech wood was investi-
gated assuming a kinetic scheme according to which wood decomposes to char
and gas in one pathway and volatiles in a second pathway. They correlated da-
ta of pyrolysis heat in the following form.
( )ccP
YhYhh −∆+∆=∆ 121
(3.16)
where Yc represents final char yield, and ∆hP denotes enthalpy of pyrolysis.
∆h1 and ∆h2 are apparent heats of the two lumped reaction pathways. The re-
sults obtained were ∆h1 = -3525 kJ/kg and ∆h2 = 936 kJ/kg for beech wood;
and ∆h1 = -3827 kJ/kg and ∆h2 = 1277 kJ/kg for spruce wood. ∆h2 is endo-
thermic heat of volatile release, and ∆h1 – ∆h2 is exothermic heat of char for-
mation. On the other hand, Milosavljevic et al. [16] and Mok and Antal [28]
studied heat of cellulose pyrolysis and obtained different values for heat of re-
actions: ∆h1 = -1460 kJ/kg and ∆h2 = 538 kJ/kg [16]; and ∆h1 = -2945 kJ/kg
and ∆h2 = 639 kJ/kg [28].
From these works, it is evident that a pyrolysis model of a woody biomass
particle must account for the exothermic characteristic of the char formation in
the thermochemical process. Thus, thermo-kinetic characteristics of a
pyrolyzing biomass particle are investigated by incorporating Eq. (3.16) into
the pyrolysis model discussed in Sec. 3.2, and using data of Milosavljevic et
al. [16], Mok and Antal [28], and Rath et al. [29] through a comparison of the
model predictions with various experimental data reported in the literature.
To the best knowledge of the author, there is only one study conducted by
Park et al. [2] in which the exothermic nature of char formation is recognized,
which can simultaneously occur with endothermic volatiles generation. In their
model, it is assumed that the wood decomposes through three parallel reac-
tions to gas, tar and an intermediate solid. These primary reactions are fol-
lowed by secondary reactions including cracking of tar into gas and char as
well as conversion of the intermediate solid to char. Through matching the py-
rolysis model predictions with experiments, Park et al. [2] found an endother-
mic heat of 80 kJ/kg for the primary reactions and an exothermic heat of -300
kJ/kg for the char formation reaction through the conversion of the intermedi-
ate solid.
76
Modeling Combustion of Single Biomass Particle 61
The question which remains unanswered is that whether or not the pro-
posed model of Park et al. [2] with the above values of reaction heat would al-
low one to predict the pyrolysis phenomena at other process conditions, since
they performed the experimental validation using only their own measure-
ments. Thus, the present section will not follow the proposed values of Park et
al. [2], as it is aimed to find out whether a pyrolysis model with the kinetic
scheme involving decomposition of wood to char, gas and tar in which the
heat of pyrolysis is computed as function of char and volatiles yields (as in Eq.
(3.16)) would be sufficient to capture a wide range of experimental data. In
this case, the heat of pyrolysis with three parallel reactions is calculated as fol-
lows.
( )PB
hkkkQ ∆++=321
~ρ (3.17)
The accuracy of the pyrolysis model using correlations of Milosavljevic et
al. [16], Mok and Antal [28], and Rath et al. [29] is examined by comparing
the predictions with experimental data reported by Rath et al. [20] and Lu et al.
[7, 30]. Moreover, the experimental validation is carried out using kinetic con-
stants of Chan et al. [5], Thurner and Mann [24], and Di Blasi and Branca [25]
to find out which set of kinetic data may allow the best prediction of the pyrol-
ysis of a biomass particle at high heating conditions, similar to the operational
conditions of industrial furnaces.
Predicted center temperature and mass loss profiles using various correla-
tions of pyrolysis heat are compared with experimental data of Rath et al. [20]
using kinetic data of Chan et al. [5], Thurner and Mann [24], and Di Blasi and
Branca [25] in Figs. 3.10, 3.11 and 3.12, respectively. Notice that the symbols
used in these figures are defined in Table 3.3, in which the various kinetic
mechanisms are represented by the abbreviated names of the corresponding re-
searchers, and subscript numbers 1, 2, 3 and 4 denote, respectively, the corre-
lations of Milosavljevic et al. [16], Mok and Antal [28], Rath et al. [29], and
Eq. (3.8) with k4 = 0. For instance, TM1 refers to the model predictions ob-
tained when the kinetic data of Thurner and Mann [24] and the correlation of
Milosavljevic et al. [16] for computation of the heat of reactions are used in
the simulation.
Shown in these figures are also the profiles obtained using Eq. (3.8) in the
simulation with a weighted heat of 25 kJ/kg. Employing the kinetic data of
77
62 Chapter 3
Thurner and Mann [24] in the simulation results in a relatively good prediction
of center temperature (Fig. 3.10) as well as the conversion time when the cor-
relation of Milosavljevic et al. [16] is employed. However, looking into the
mass loss graphs in Fig. 3.10, the final char yield is over-predicted in all cases.
From Fig. 3.11 which is obtained using kinetic constants of Chan et al. [5] in
the simulation code, the center temperature is also well-predicted with the cor-
relation of Milosavljevic et al. compared to other cases. The mass loss history
is best predicted using Eq. (3.8) with the weighted heat of 25 kJ/kg and the
correlation of Rath et al. [11]. Nonetheless, in all cases, the final char yield is
over-predicted given that the conversion time is best estimated using the corre-
lation of Milosavljevic et al. [16].
From Figs. 3.10 and 3.11, the final char overestimation is 20 % higher with
Thurner and Mann [24] data than using data of Chan et al. [5]. The graphs il-
lustrated in Fig. 3.12 are produced using kinetic data of Di Blasi and Branca
[25]. Prediction of center temperature in this figure is worse compared to Figs.
3.10 and 3.11. The best match between the predicted center temperature and
the experiments in Fig. 3.12 is achieved using the correlation of Mok and
Antal [28] and Eq. (3.8) in the model. On the other hand, the mass loss history
in Fig. 3.12 is better predicted than that in Figs. 3.10 and 3.11. As seen in Fig.
3.12, the simulated mass loss histories using any of the pyrolysis heat correla-
tions are similar. The little differences between the corresponding graphs are
within the experimental uncertainties.
Table 3.3 Nomenclature used in Figs. 3.10-3.12, 3.14 and 3.15
Kinetic Data
Thurner
& Mann Chan et al.
Di Blasi &
Branca
Heat of Pyroly-
sis Correlation
Milosavljevic et al. TM1 C1 DB1
Mok and Antal TM2 C2 DB2
Rath et al. TM3 C3 DB3
Eq. (3.8) TM4 C4 DB4
78
Modeling Combustion of Single Biomass Particle 63
Figure 3.10 Comparison of predicted center temperature and mass loss histories using
various correlations of pyrolysis heat with experiments of Rath et al. [20]. Kinetic da-
ta: Thurner and Mann.
79
64 Chapter 3
Figure 3.11 Comparison of predicted center temperature and mass loss histories using
various correlations of pyrolysis heat with experiments of Rath et al. [20]. Kinetic da-
ta: Chan et al.
80
Modeling Combustion of Single Biomass Particle 65
Figure 3.12 Comparison of predicted center temperature and mass loss histories using
various correlations of pyrolysis heat with experiments of Rath et al. [20]. Kinetic da-
ta:Di Blasi and Branca.
81
66 Chapter 3
As a conclusion from these experimental validations presented in Figs.
3.10-3.12, the kinetic data of Di Blasi and Branca [25] allows accurate predic-
tion of both conversion time and final char yield; which are important parame-
ters for engineering purposes. The best explanation for this, as also discussed
by Di Blasi and Branca [25], is that for the condition of fast pyrolysis in which
the final char yield is below 15% (such as in the experiments of Rath et al.
[20]), data of Di Blasi and Branca, which were obtained at a heating rate of
1000 K/min, provide a better prediction of the kinetics of the process than
those of Thurner and Mann [24] and Chan et al. [5]. On the other hand, one
may wonder why the mechanism of Di Blasi and Branca does not lead to an
accurate prediction of the center temperature as it is well-predicted with either
of Thurner and Mann and Chan et al. mechanism using a pyrolysis heat corre-
lation. This may be attributed to the different values of the pyrolysis heat com-
puted from Eq. (3.16) in which the char yield is obtained from different kinetic
constants.
Shown in Fig. 3.13 are the graphs of the heat of pyrolysis as a function of
reaction temperature, obtained using the correlation of Milosavljevic et al. [16]
in which the char yield is calculated with the aid of various kinetic data. This
figure shows that at low pyrolysis temperature, the heat of reaction is expected
to be exothermic. For the range of temperatures shown in Fig. 3.13, a combi-
nation of Thurner and Mann mechanism and the correlation of Milosavljevic et
al. would lead to an almost neutral pyrolysis heat. However, for the other two
cases, as the reaction temperature increases, the process is expected to be more
endothermic, with values of pyrolysis heat resulted from using the data of Di
Blasi and Branca being greater than those obtained from using the data of
Chan et al. in the simulation.
A careful observation of the measured center temperature history depicted
in Figs. 3.10-3.12 reveals that the decomposition of the virgin biomass begins
at a temperature around 380 ºC and it is terminated at about 480 ºC. Given that
the heating up stage (first 100 seconds) is well-predicted in Figs. 3.10-3.12 us-
ing all kinetic constants and the correlation of Milosavljevic et al., the signifi-
cant difference between the predicted center temperature histories using vari-
ous kinetic constants can be observed in these figures when the decomposition
at the center of the particle begins. Looking into the graphs represented in Fig.
3.13, it can be implied that the main reason for the predicted plateau in center
temperature using the kinetic data of Di Blasi and Branca (Fig. 3.12) is that the
computed pyrolysis heat in this region (380 ºC < T < 480 ºC) is highly endo-
82
Modeling Combustion of Single Biomass Particle 67
thermic compared to the other graphs obtained using the data of Chan et al.
and Thurner and Mann. Hence, the external energy transferred to the center
due to the conduction heat transfer is used to compensate the endothermic heat
of the reaction, thereby resulting in a plateau in the predicted center tempera-
ture at the above temperature region. After the pyrolysis at this position is ter-
minated, the corresponding temperature quickly rises and it eventually reaches
the reactor temperature.
To find out whether the correlated heat of pyrolysis as a function of char
yield may allow acceptable predictions of the thermo-kinetics of a pyrolyzing
particle at various conditions, additional validations are performed using ex-
perimental data of Lu [30] and Lu et al. [7]. In the experiments of Lu [30], cy-
lindrical poplar particles with 9.5 mm diameter were pyrolyzed at a higher re-
actor temperature of 1276 K, and the center and surface temperatures and mass
loss histories were measured at different test runs. Also, Lu et al. [7] carried
out pyrolysis experiments of sawdust particles of 0.32 mm at an even higher
reactor temperature of 1625 K.
Figure 3.13 Variation of heat of pyrolysis with temperature using different kinetic da-
ta.
Comparison of the predicted mass loss profiles with experiments of Lu
[30] using kinetic constants of Chan et al. and Di Blasi and Branca is depicted
83
68 Chapter 3
in Fig. 3.14. Similar to the previous validation case, the kinetic constants of
Chan et al. lead to an overestimation of the final char yield, whereas employ-
ing the data of Di Blais and Branca in the simulation allows rather good pre-
dictions of the final char yield as well as the pyrolysis time. The best agree-
ment between the experiments and the simulation results using data of Di Blasi
and Branca is obtained when the correlation of either Milosavljevic et al. or
Mok and Antal is employed.
The last set of experimental validation is performed by comparing the pre-
diction of the pyrolysis model using the kinetic data of Chan et al. and Di Blasi
and Branca as well as various pyrolysis heat correlations discussed above, with
experiments of Lu et al. [7] related to mass loss history of a 0.32 mm cylindri-
cal sawdust particle, as depicted in Fig. 3.15. Likewise, using the kinetic data
of Di Blasi and Branca in the simulation code allows to fairly predict the py-
rolysis time and to capture the trend of the measured mass loss curve. The final
char yield seems well-predicted with the aid of any of the pyrolysis heat corre-
lations, given that the correlation of Milosavljevic et al. or Mok and Antal al-
lows a relatively better capturing of the experiments than the correlation of
Rath et al. The predicted mass loss curves are steeper than the measured one,
which can possibly arise from the imperfect size and shape distribution of the
sample as pointed out by Lu et al. [7].
From these three different experimental validation cases, which are related
to the pyrolysis of woody biomass particles at relatively high temperatures, it
can be concluded that the pyrolysis model with three parallel reactions with
the kinetic constants of Di Blasi and Branca, and using the empirical correla-
tion (3.16) with the proposed constants of Milosavljevic et al. or Mok and
Antal is capable of accurately predicting the pyrolysis process of a woody bi-
omass particle. Contrary to the past pyrolysis modeling studies, in which a
constant and endothermic heat of pyrolysis has been assumed, an efficient
model in accordance with the experimental findings on the pyrolysis heat,
must account for the endothermic nature of volatiles generation and the
exothermicity of char formation. The empirical correlation (3.16) suggests that
in the absence of char formation, the pyrolysis of the particle would be an en-
dothermic process, and the endothermicity of the process would decrease by
formation of char and increasing its yield. Thus, it is possible that the heat of
reactions becomes exothermic at some stages of the pyrolysis as, for instance,
reported by Bilbao et al. [17].
84
Modeling Combustion of Single Biomass Particle 69
Figure 3.14 Comparison of predicted mass loss histories using various correlations of
pyrolysis heat with experiments of Lu [30]. Kinetic data: Chan et al. (top); Di Blasi
and Branca (bottom).
85
70 Chapter 3
Figure 3.15 Comparison of predicted mass loss histories using various correlations of
pyrolysis heat with experiments of Lu et al. [7]. Kinetic data: Chan et al. (top); Di
Blasi and Branca (bottom).
86
Modeling Combustion of Single Biomass Particle 71
3.5 CONVERSION TIME AND FINAL CHAR YIELD
It is intended to examine the effects of particle size and shape, initial parti-
cle density and external heating conditions on conversion (pyrolysis) time and
final char yield. The simulated conversion time is defined as the time beyond
which the change in the mass loss profile becomes negligible (<0.5%). The
corresponding results are expected to be useful when designing industrial scale
furnaces for the combustion of biomass particles. These results could be used
to have an estimate on total conversion time and char yield if particles with
various shapes, sizes, and densities would undergo only a pyrolysis process. In
the previous section, it was found that the correlation of Milosavljevic et al.
[16] to compute the heat of pyrolysis using Eq. (3.17), together with the kinet-
ic constants of Di Blasi and Branca [25] would allow an accurate prediction of
the pyrolysis time and final char yield. This combination of models is used in
the present section as well.
A parameter study is performed with external heat fluxes in the range of
100–350 kW/m2 for spruce (450 kg/m
3) and beech (700 kg/m
3) wood particles
(to account for the effect of initial biomass density) with three possible geo-
metrical shapes (slab, cylinder, sphere) with radiuses in the range of 0.2–15
mm. Figure 3.16 shows the effects of spruce particle size and shape on the
conversion time and final char concentration for an external heat flux of 100
kW/m2. The results indicate that as the size of the particle increases the final
char density increases. This observation has been frequently confirmed in the
literature. The reason can be explained by the fact that the char yield is favored
at lower and longer heating rates in contrast to the volatile yield which in-
creases at a higher heating condition. For a given external heat flux, an in-
crease in particle size would result in a slower heat transfer across the particle.
On the other hand, it is seen that among three different particle geometries,
the conversion time of a sphere is the shortest; which can be explained by the
highest surface-to-volume ratio of a spherical particle compared to cylindrical
and slab particles. Thus, the rates of heat and mass transfer are expected to be
highest in a spherical particle. This implies that at a given heat flux and parti-
cle size the final char density corresponding to a slab particle is highest where-
as that of a sphere is the lowest with that of a cylindrical particle in between.
The variation of final char density and conversion time with external heat
flux is depicted in Fig. 3.17 for three particle shapes with a diameter of 1 mm.
As expected, by increasing the external heat flux the conversion time and the
87
72 Chapter 3
final char concentration decrease for all three geometries. As mentioned
above, the formation of volatiles is favored at high heating conditions while
the generation of char reduces. These results reveal that in industrial furnaces
operating at relatively high heating conditions, a significant part of the bio-
mass combustion will be due to the homogeneous reactions of various gaseous
species (released from particle devolatilization) with the oxidizing agent.
Figure 3.16 The effects of spruce wood particle half thickness and shape on conver-
sion time and final char concentration; qext = 100 kW/m2.
Figure 3.17 The effects of external heat flux and shape factor on final char concentra-
tion and conversion time of a spruce wood particle with 1 mm thickness.
88
Modeling Combustion of Single Biomass Particle 73
Figure 3.18 The effects of beech wood particle half thickness and shape on conversion
time and final char concentration; qext = 100 kW/m2.
Figure 3.19 The effects of external heat flux and shape factor on final char concentra-
tion and conversion time of a beech wood particle with 1 mm thickness.
Further numerical results include the effects of particle size and shape as
well as external heating flux on conversion time and final char density of a
beech particle, which are illustrated in Figs. 3.18 and 3.19. The results shown
in these figures are qualitatively comparable with those obtained for spruce
represented in Figs. 3.16 and 3.17. However, from a quantitative viewpoint, at
identical process conditions the conversion time and the final char density are
higher for a beech particle than a spruce particle due to the fact that the density
89
74 Chapter 3
of beech wood is higher than that of spruce wood. The data shown in Figs.
3.16-3.19 indicate that a careful selection of the type, size and shape of bio-
mass is a key task as all these parameters could influence design and operation
of biomass combustors.
One important factor when designing pulverized fuel combustors is the
residence time of particles within the reactor. It is of technical importance to
know the time of pyrolysis which is an unavoidable stage during combustion
of a biomass particle. The fuel particles are usually small with diameters up to
1 mm. In practice, the shape of particles is usually aspherical which can be ap-
proximated as cylindrical-like particles. To provide a convenient design tool,
typical graphs as illustrated in Figs. 3.20 and 3.21 are prepared, which should
enable one to estimate the time of pyrolysis and final char density as a function
of initial biomass density and size at a reactor temperature of 1450 K (Fig.
3.20) and 1650 K (Fig. 3.21). An interesting observation from these graphs is
that both the conversion time and the char yield vary as a linear function of bi-
omass initial density. It can be seen that depending on the biomass density, the
pyrolysis time can exceed 1 second – a significant duration considering short
residence time of particles in most industrial furnaces – even for a small parti-
cle with a diameter of 1 mm and a high reactor temperature; e.g. 1650 K (see
Fig. 3.21).
Furthermore, these results have been correlated so that the pyrolysis time
and the final char density can be obtained as functions of particle initial size
and density with the aid of the following relationships.
( ) ( )
( ) ( )
=+
=+
=
KTdd
KTdd
t
rPPB
rPPB
Pyr
1650536.1exp008.0190.2exp0002.0
1450051.2exp01.0966.1exp0003.0
ρ
ρ
(3.18)
=−
=−
=
KTdd
KTdd
rPPB
rPPB
C
16500809.50552.0
14505107.50619.0
2279.02360.0
2004.02308.0
ρ
ρ
ρ (3.19)
90
Modeling Combustion of Single Biomass Particle 75
Figure 3.20 Dependence of conversion time of a cylindrical particle on biomass densi-
ty and size exposed to an environment with a temperature of 1450 K (top) and 1650 K
(bottom).
91
76 Chapter 3
Figure 3.21 Dependence of final char density of a cylindrical particle on biomass den-
sity and size exposed to an environment with a temperature of 1450 K (top) and 1650
K (bottom).
92
Modeling Combustion of Single Biomass Particle 77
3.6 PYROLYSIS REGIME AT HIGH HEATING CONDITIONS
The last part of this chapter is devoted to investigate whether pyrolysis of
biomass fuel may take place homogeneously at high heating conditions. If the
process takes place homogenously, it is possible to treat the particle as a whole
assuming that the entire of particle experiences an isothermal process and the
volatiles formed leave the particle immediately. Thus, the pyrolysis model de-
scribed in terms of PDE’s (partial differential equations) would be reduced to a
set of ODE’s (ordinary differential equation); thereby reducing the complexity
of the model as well as the computational efforts.
The accuracy of a lumped model has been examined, for instance, by
Bharadwaj et al. [31] through comparing the lumped model prediction with
experiments of woody particles with a size less than 1 mm. They found that
such a reduced model would lead to a significant overprediction of pyrolysis
time. In contrast to Bharadwaj et al [31], no such a lumped model will be ex-
amined here, but the idea is to investigate the effects of key parameters includ-
ing particle size, particle initial density and surrounding temperature on intra-
particle gradients. For this purpose, time and space evolution of temperature,
biomass and char densities are numerically studied at various biomass initial
densities and diameters (up to 1 mm) as well as reactor temperature in the
range of 1050 K and 1650 K.
Figure 3.22 shows the transient temperature, biomass and char densities in
a 250µm diameter cylindrical particle at three initial biomass densities with re-
actor temperature of 1450 K. In each case, the simulation results are shown for
the duration of pyrolysis time. Notice that different lines correspond to various
simulation times. Although the particle size is quite small, the gradients in all
parameters are visible. In particular, at a higher biomass initial density, the
profiles of char and biomass densities become steeper. Thus, the assumption of
a homogeneous process in a pyrolysis model for the process conditions related
to Fig. 3.22 could lead to some undesired errors in predictions.
Similar profiles of temperature, biomass and char densities across a cylin-
drical particle with a relatively low initial biomass density; i. e, 300 kg/m3, are
generated at three particle diameters of 250µm, 500µm and 1000µm at a reac-
tor temperature of 1450 K to observe the effect of particle size. The results are
depicted in Fig. 3.23, which reveal that even a less dense and small particle
with a diameter of 500µm or 1000µm could experience significant gradients at
various stages of conversion process when the reactor temperature is high.
93
78 Chapter 3
Hence, as a next step, the transient profiles of temperature, biomass and char
densities of a 250µm particle with an initial density of 300 kg/m3 are investi-
gated at four different reactor temperatures. The simulation results are illus-
trated in Fig. 3.24. As seen, only at a reactor temperature of 1050 K may the
assumption of homogeneous pyrolysis be adapted, given that still small gradi-
ents in the profiles of temperature, biomass and char densities can be observed.
However, as the reactor temperature increases, the profiles of the parameters
become steeper.
(a) (b) (c)
Figure 3.22 Transient temperature, biomass density, and char density along a 250µm
cylindrical particle with initial density of (a) 0.3 g/cm3; (b) 0.5 g/cm
3; (c) 0.7 g/cm
3,
exposed to an environment with a temperature of 1450 K. Note that the simulation is
carried out for half thickness. Different lines correspond to different times increasing
in the direction of the arrows.
94
Modeling Combustion of Single Biomass Particle 79
(a) (b) (c)
Figure 3.23 Transient temperature, biomass density, and char density along a (a)
250µm; (b) 500µm; (c) 1000µm cylindrical particle with an initial density of 0.3
g/cm3, exposed to an environment with a temperature of 1450 K. Note that the simula-
tion is carried out for half thickness. Different lines correspond to different times in-
creasing in the direction of the arrows.
Based on the results shown in Figs. 3.23 and 3.24, additional simulations
are carried out to find out whether at a reactor temperature of 1050 K the parti-
cle size may still lead to notable gradients in the variables. Shown in Fig. 3.25
are the transient profiles of temperature, biomass and char densities along par-
ticles with diameter of 250-1000µm and an initial density of 300 kg/m3. For
the process conditions of Fig. 3.25, an assumption of homogenous pyrolysis of
particle up to 500µm may be roughly adapted. Nevertheless, it is expected that
at particle diameters higher than 500µm, the above assumption may cause con-
siderable calculations errors.
95
80 Chapter 3
(a) (b)
Figure 3.24 Transient temperature, biomass density, and char density along a 250µm
cylindrical particle with an initial density of 0.3 g/cm3, exposed to an environment
with a temperature of (a) 1050 K; (b) 1250 K; (c) 1450 K; (d) 1650 K. Note that the
simulation is carried out for half thickness. Different lines correspond to different
times increasing in the direction of the arrows.
96
Modeling Combustion of Single Biomass Particle 81
(c) (d)
Figure 3.24 (Continued)
97
82 Chapter 3
(a) (b)
Figure 3.25 Transient temperature, biomass density, and char density along a (a)
250µm; (b) 500µm; (c) 750µm; (d) 1000µm, cylindrical particle with an initial density
of 0.3 g/cm3, exposed to an environment with a temperature of 1050 K. Note that the
simulation is carried out for half thickness. Different lines correspond to different
times increasing in the direction of the arrows.
98
Modeling Combustion of Single Biomass Particle 83
(c) (d)
Figure 3.25 (Continued)
99
84 Chapter 3
To provide a better comprehension of the results presented in Figs. 3.22
through 3.25, Biot and External Pyrolysis numbers related to each case are al-
so calculated as given in Table 3.4 and Table 3.5. These dimensionless num-
bers are defined as follows.
B
ext
k
RhBi = (3.20)
Rck
hyP
pBBpyr
ext
ρ=′ (3.21)
where hext represents the external heat transfer coefficient and kpyr is the global
decomposition rate constant.
In a pure transient conduction process, Bi represents the relative signifi-
cance of internal and external heat transfer rates. The relevant error resulted
from thermally thin assumption would be negligible for Bi < 0.1 [32]. Howev-
er, for a particle undergoing thermo-chemical conversion, Bi is not enough to
identify the regime of the process. Under these conditions, the relative rates of
external heating and pyrolysis defined in terms of the external pyrolysis num-
ber, Py’, need to be taken into account. As pointed out by Pyle and Zaror [33],
large values of Py’ correspond to pure kinetic control whilst small values of
Py’ correspond to control by external heat transfer.
According to the figures given in Tables 3.4 and 3.5, in most cases studied,
the process controlling factor is the external heat transfer, since Bi < 0.2 and
Py’ << 1. As mentioned previously, the assumption of thermally thin, kinet-
ically controlled may be valid only for the cases of Figs. 3.25a and 3.25b; or in
terms of Bi and Py’, the process may be assumed homogeneous if Bi < 0.1 and
Py’ > 1.5×10-3
.
As a conclusion from these findings, the pyrolysis of a woody biomass
particle exposed to high heating conditions comparable to those at industrial
furnaces, does not appear to happen homogeneously. Although assuming a
homogeneous pyrolysis process may allow a designer to save substantial cal-
culations efforts, he/she must take into consideration that the accuracy of the
simplified model may not be sufficient in order to establish an optimized de-
sign of the plant.
100
Modeling Combustion of Single Biomass Particle 85
Table 3.4 Biot and Pyrolysis numbers corresponding to Figs. 3.22 (dp = 250 µm) and
3.23 (ρB = 300 kg/cm3). Reactor temperature: 1450 K
dp = 250 µm
ρB [kg/cm3]
300 500 700
Bi 1.50E-01 1.50E-01 1.50E-01
Py' 7.15E-05 4.29E-05 3.07E-05
ρB = 300 kg/cm3
dp [µm]
250 500 1000
Bi 1.50E-01 2.99E-01 5.98E-01
Py' 7.15E-05 3.58E-05 1.79E-05
Table 3.5 Biot and Pyrolysis numbers corresponding to Figs. 3.24 (dp = 250 µm) and
3.25 (Tr = 1050 K). Particle density 300 kg/cm3
dp = 250 µm
Tr [K]
1050 1250 1450 1650
Bi 5.68E-02 9.58E-02 1.50E-01 2.20E-01
Py' 2.98E-03 3.30E-04 7.15E-05 2.36E-05
Tr = 1050 K
dp [µm]
250 500 750 1000
Bi 5.68E-02 1.14E-01 1.70E-01 2.27E-01
Py' 2.98E-03 1.49E-03 9.92E-04 7.44E-04
3.7 CONCLUSION
It is shown that an accurate formulation of energy conservation to model
pyrolysis of a biomass particle needs to account for variations in the heat of
reaction with temperature, usually neglected in most past studies. In particular,
through comprehensive comparisons of the simulation results with various
measurements, a consistent and single value of 25 kJ/kg is obtained as the en-
thalpy of pyrolysis, which represents a lumped heat of volatiles and char for-
mation at a reference temperature.
The improved model of a pyrolyzing biomass particle assumes that virgin
biomass decomposes to light gases, tar and char through three competing
pathways. The kinetic constants proposed in the literature are examined to find
101
86 Chapter 3
out under different process conditions, which set of kinetic data would provide
an accurate prediction of main characteristics of the biomass pyrolysis. The
kinetic parameters of Thurner and Mann [24] and Di Blasi and Branca [25]
provide a reasonable agreement between the model predictions and the exper-
iments, at moderate and high reactor temperatures, respectively.
Given that a satisfactory agreement between the simulations and the exper-
imental data is achieved with the above endothermic heat, in the next step, the
endothermic heat of volatiles formation and the exothermic heat of char gener-
ation are considered using the correlations proposed in three different past
studies. The correlation of Milosavljevic et al. [16] is found to allow even bet-
ter predictions of a wide range of experiments, compared to the case with the
endothermic heat of 25 kJ/kg. Thus, the results of this study clearly demon-
strate that the endo – exothermic nature of the reactions needs to be taken into
consideration when modeling thermo-chemical conversion of woody biomass
particles.
A parametric study is subsequently conducted to investigate pyrolysis time
and final char density of a single biomass particle at high heating environ-
ments. The effect of shape and size and external heat flux on the thermal con-
version of spruce and beech wood particle was examined. The results should
enable furnace designers to estimate the role of pyrolysis in combustion of bi-
omass particles. As the combustion of such fuel particles would be desirable
with diameters up to 1mm, typical informative graphs (Figs. 3.20 and 3.21) are
prepared which can be used for design purposes.
The idea of assuming homogenous pyrolysis of a small biomass particle at
high reactor temperatures was examined. This assumption can result in a more
simplified model with less calculation efforts compared to a complex model
such as employed in this study. The results reveal that a model based on such
an assumption may lead to substantial reduction of the accuracy of the predic-
tion of a pyrolysis model even though the particle size may be in the order of 1
mm.
RERERENCES
[1] Koufopanos C. A., Papayannakos N., Maschio G., Lucchesi A. 1991.
Modeling of the pyrolysis of biomass particles. Studies on kinetics,
thermal and heat transfer effects. Can J Chem Eng 69: 907-915.
102
Modeling Combustion of Single Biomass Particle 87
[2] Park W. C., Atreya A., Baum H. R. 2010. Experimental and theoretical
investigation of heat and mass transfer processes during wood pyrolysis.
Combust Flame 157: 481-494.
[3] Di Blasi C., Branca C., Santoro A., Hernandez E. G. 2001. Pyrolytic be-
havior and products of some wood varieties. Combust Flame 124: 165-
177.
[4] Larfeldt J., Leckner B., Melaaen M. C. 2000. Modelling and measure-
ments of the pyrolysis of large wood particles. Fuel 79: 1637-1643.
[5] Chan W. C., Kelbon M., Krieger B. B. 1985. Modeling and experi-
mental verification of physical and chemical processes during pyrolysis
of a large biomass particle. Fuel 64: 1505-1513.
[6] Tran H. C., White R. H. 1992. Burning rate of solid wood measured in a
heat release rate calorimeter. Fire Mater 16: 197-206.
[7] Lu H., Ip E., Scott J., Foster P., Vickers M., Baxter L. L. 2010. Effects
of particle shape and size on devolatilization of biomass particle. Fuel
89: 1156-1168.
[8] Shafizadeh F., Chin P. S. 1977. Thermal deterioration of wood. in: I.S.
Goldstein (Ed.), Wood Technology: Chemical Aspects, ACS Symp Ser
43: 57-81.
[9] Liden A. G., Berruti F., Scott D. S. 1988. A kinetic model for the pro-
duction of liquids from the flash pyrolysis of biomass. Chem Eng Comm
65: 207-221.
[10] Boroson M. L., Howard J. B., Longwell J. P., Peters W. A. 1989. Prod-
uct yields and kinetics from the vapor phase cracking of wood pyrolysis
tars. AIChE J 35: 120 – 128.
[11] Diebold J. P. 1985. The cracking of depolymerized biomass vapors in a
continuous, tabular reactor. MSc Thesis, Colorado School of Mines,
Golden.
[12] Di Blasi C. 1993. Analysis of convection and secondary effects within
porous solid fuels undergoing Pyrolysis. Combust Sci Technol 90: 315-
340.
[13] Gronli M. G., Melaaen M. C. 2000. Mathematical model for wood py-
rolysis–Comparison of experimental measurements with model predic-
tions. Energ Fuels 14: 791-800.
103
88 Chapter 3
[14] Park W. C. 2008. A study of pyrolysis of charring materials and its ap-
plication to fire safety and biomass utilization. PhD Thesis, The Univer-
sity of Michigan.
[15] Lee C. K., Chaiken R. F., Singer J. M. 1977. Charring pyrolysis of wood
in fires by laser simulation. Proc Combust Symp 16: 1459-1470.
[16] Milosavljevic I., Oja V., Suuberg E. M. 1996. Thermal effects in cellu-
lose pyrolysis: relationship to char formation processes. Ind Eng Chem
Res 35: 653-662.
[17] Bilbao R., Mastral J. F., Ceamanos J., Aldea M. E. 1996. Modelling of
the pyrolysis of wet wood. J Anal Appl Pyrolysis 36: 81-97.
[18] CHEM1D, www.combustion.tue.nl
[19] Raznjevic K., 1976. Handbook of Thermodynamic Tables and Charts.
Hemisphere Publishing Corporation, McGraw-Hill.
[20] Rath J., Steiner G., Wolfinger M. G., Staudinger G. 2002. Tar cracking
from fast pyrolysis of large beech wood particles. J Anal Appl Pyrolysis
62: 83-92.
[21] Bryden K. M., Ragland K. W., Rutland C. J. 2002. Modeling thermally
thick pyrolysis of wood. Biomass Bioenerg 22: 41-53.
[22] Sadhukhan A. K., Gupta P., Saha R. K. 2009. Modeling of pyrolysis of
large wood particles. Bioresour Technol 100: 3134-3139.
[23] Kansa E. J., Perlee H. E., Chaiken R. F. 1977. Mathematical model of
wood pyrolysis including internal forced convection. Combust Flame
29: 311-324.
[24] Thurner F., Mann U. 1981. Kinetic investigation of wood Pyrolysis. Ind
Eng Chem Process Des Dev 20: 482-488.
[25] Di Blasi C., Branca C. 2001. Kinetics of primary product formation
from wood pyrolysis. Ind Eng Chem Res 40: 5547-5556.
[26] Font R., Marcilla A., Verdu E., Devesa J. 1990. Kinetics of the pyrolysis
of almond shells and almond shells impregnated with cobalt dichloride
in a fluidized bed reactor and in a pyroprobe 100. Ind Eng Chem Res 29:
1846-1855.
[27] Sadhukhan A. K., Gupta P., Saha R. K. 2008. Modeling and experi-
mental studies on pyrolysis of biomass particles. J Anal Appl Pyrolysis
81: 183-192.
104
Modeling Combustion of Single Biomass Particle 89
[28] Mok W. S. L., Antal M. J., Jr. 1983. Effects of pressure on biomass py-
rolysis. II. Heats of reaction of cellulose pyrolysis. Thermochimica Acta
68: 165-186.
[29] Rath J., Wolfinger M. G., Steiner G., Krammer G., Barontini F.,
Cozzani V. 2003. Heat of wood pyrolysis. Fuel 82: 81-91.
[30] Lu, H. 2006. Experimental and modeling investigations of biomass par-
ticle combustion. PhD Thesis, Brigham Young University.
[31] Bharadwaj A., Baxter L. L., Robinson A. L. 2004. Effects of
intraparticle heat and mass transfer on biomass devolatilization: experi-
mental results and model predictions. Energ Fuel 18: 1021-1031.
[32] Incropera F. P., Dewitt D. P. 1996. Fundamentals of Heat and Mass
Transfer. 4th edition, Wiley, New York.
[33] Pyle D. L., Zaror C. A. 1984. Heat transfer and kinetics in the low tem-
perature pyrolysis of solids. Chem Eng Sci 39: 147–158.
105
90 Chapter 3
106
Chapter 4
Modeling Biomass Particle Combustion
The content of this chapter is mainly based on the following paper: Haseli Y., van Oijen J. A., de Goey L. P.
H. 2011. A detailed one-dimensional model of combustion of a woody biomass particle. Bioresource Tech-
nology 102: 9772-9782.
4.1 INTRODUCTION
The present chapter aims at describing a detailed model of biomass particle
combustion by accounting for various physical and chemical processes in-
volved in the particle conversion process, to primarily get a deeper insight into
single woody biomass particle combustion by observing time and space evolu-
tion of key parameters such as virgin biomass and char densities. The combus-
tion model presented in this chapter is an extension of the biomass particle py-
rolysis model discussed in Chapter 3.
Special emphasis is given to identify the role of pyrolysis and gas phase
combustion during particle conversion process, which has not been thoroughly
studied in previous works. The modeling methodology will be described in the
upcoming section. It accounts for particle heating up, pyrolysis, char gasifica-
tion and oxidation, and gas phase reactions. Based on the above mentioned ki-
netic schemes, transport equations are developed to compute time and space
evolution of temperature and species mass within the particle. The validation
of the combustion model will be performed in Sec. 4.3. Illustrative simulation
results related to combustion of beech wood particle will be presented and dis-
cussed in Sec. 4.4. The main conclusion from this modeling study will be giv-
en in Sec. 4.5.
107
92 Chapter 4
4.2 MODELING APPROACH
The problem under study is a dry woody biomass particle initially at room
temperature that is exposed to an oxidative hot environment. The particle may
be of three common shapes: sphere, cylinder or slab. The main physical and
chemical processes which take place during combustion of a biomass particle
are heating up, devolatilization, homogenous reactions of gaseous species with
oxygen and with each other, and char gasification and oxidation. Depending
on various parameters such as particle size and density, surrounding tempera-
ture, oxygen concentration in the surrounding flow, the above processes may
take place sequentially or simultaneously.
4.2.1. Pyrolysis Kinetic Model
The pyrolysis kinetic scheme employed in this study assumes that the vir-
gin biomass decomposes to light gases, tar including heavy gases, and char
through three competitive reaction pathways.
R1: Biomass → Light gases
R2: Biomass → Tar
R3: Biomass → Char
The reaction rates are determined through an Arrhenius type equation.
( ) 3,2,1/exp =−= iTREArgiii
(4.1)
It is less likely that tar cracking takes place inside the particle. As demon-
strated in Chapter 3, the kinetic model with three parallel reactions would be
sufficient to achieve a reasonable agreement between predictions and experi-
ments so that any inclusion of secondary reactions would not be needed.
4.2.2 Homogenous Reactions
The gas phase reactions used in this study are
R4: CH4 + 1.5O2 → CO + 2H2O
R5: H2 + 0.5O2 → H2O
R6: CO + 0.5O2 → CO2
108
Modeling Combustion of Single Biomass Particle 93
R7: C3.878H6.426O3.561 + 0.1585O2 → 3.878CO + 3.213H2
R8: CO + H2O ↔ CO2 + H2
The combustion rates of methane (R4), hydrogen (R5) and carbon monox-
ide (R6) are determined using the correlations reported by Dryer and Glassman
[1], de Souza Santos [2], and Howard et al. [3], respectively. The combustion
rate of tar (R7) is assumed to be the same value as CnHm oxidation given by
Smooth and Smith [4]. The correlation used for determination of the water-gas
shift reaction rate (R8) is taken from de Souza Santos [2]. The relationships for
computations of the rates of reactions R4-R8 are given in Table 4.1.
4.2.3 Char Gasification and Combustion
The heterogeneous reactions in terms of char gasification with water vapor
and carbon dioxide, and char combustion with oxygen considered are
R9: C + CO2 → 2CO
R10: C + H2O → CO +H2
R11: C + 0.5O2 → CO
The gasification/combustion rate of carbon in reactions R9-R11 is deter-
mined using
22211109 O,OH,CO:j,,iMn
M
TR
EexpTAAr j
jsto
C
g
i
ivi =
−= ρ (4.2)
where Av is the specific inner surface area (m-1
) of the porous char, Ai is the
pre-exponential factor (m.s-1
.K-1
), M is the molecular weight, nsto is the stoi-
chiometric ratio of reaction i; and ρj represents the density of gasifying agent j.
The reaction constants of char oxidation adapted in most past biomass
combustion models are those reported by Evans and Emmons [5]. The original
form of the expression proposed by Evans and Emmons [5] for the effective
reaction rate of wood charcoal burnt in air is as follows.
( ) [ ]12/9000exp4.25 −−−=′′ scmgTPm
OC& (4.3)
109
94 Chapter 4
Table 4.1 Reaction rates and heat used in the combustion model.
Reaction Heat of reac-
tion [kJ/kg] Reaction rate Source
R4 32460 8.0
O
7.0
CH
10
CH 244CC
T
24157exp10.585.1r
−= Ref. [1]
R5 120900 222 O
5.1
H
5.116
HCC
T
3420expT10159.5r
−×=
− Ref. [2]
R6 10110 5.0
OH
5.0
OCO
7
CO 22CCC
T
16098exp1025.3r
−×= Ref. [3]
R7 41600 2O
5.0
Tar
3.0
TarCCPT
T
12200exp59800r
−= Ref. [4]
R8 1470 OHCOCO 2CC
T
1510exp78.2r
−= Ref. [2]
R9 –14370 2
2
CO
CO
C
vCM
M
RT
15600expT42.3Ar ρ
−= Ref. [6]
R10 –10940 OH
OH
C
vC 2
2M
M
T
15600expT42.3Ar ρ
−= Ref. [6]
R11 9211 2OvC
T
9000expT66.0Ar ρ
−= Ref. [5]
where PO denotes the partial pressure of oxygen in atm. Equation (4.3) can be
represented in the form of Eq. (4.2) using the ideal gas law to describe it in
terms of temperature and oxygen density, and multiplying the resulting expres-
sion by Av. This leads to AO2 = 0.66 m.s-1
.K-1
with the same activation energy
of 9000 kJ/mol. The correlations used in the simulation for calculating the
rates of heterogeneous reactions are provided in Table 4.1.
4.2.4 Transport Equations
To fully describe combustion of a woody biomass particle, the one-
dimensional transport equations are coupled with the kinetic models of pyroly-
sis, homogenous and heterogonous reactions discussed previously. The
transport equations include mass conservation of biomass, char, tar, methane,
hydrogen, carbon monoxide, carbon dioxide, water vapor, oxygen and nitrogen
(considered to be an inert gas), conservation of energy assuming thermal equi-
librium between the gas and solid phases, Darcy’s law to approximate the flow
110
Modeling Combustion of Single Biomass Particle 95
field within the porous matrix of the solid, and the ideal gas law to calculate
the pressure field.
Conservation of biomass and char is described by
( )321
rrrt
B++−=
∂
∂ρ (4.4)
111093rrrr
t
C−−−=
∂
∂ρ (4.5)
Mass fraction of each gaseous species can be obtained from the following
equation
( )
222242,,,,,,,
11
NOTarHOHCHCOCOi
Sr
YDr
rruYr
rrt
Yi
i
gi
n
nig
n
n
ig
=
+
∂
∂
∂
∂=
∂
∂+
∂
∂ρερ
ερ
(4.6)
The source terms in Eq. (4.6) are calculated as follows.
( ) ( )1110987641
2878.3 rrrM
MrrrrMrS
C
CO
COCOCO+++−+−+=ν (4.7)
( )9861
2
222r
M
MrrMrS
C
CO
COCOCO−++=ν (4.8)
41 444rMrS
CHCHCH−=ν (4.9)
( )108541
2
2222 r
M
MrrrMrS
C
OH
OHOHOH−−++=ν (4.10)
( )108751
2
222213.3 r
M
MrrrMrS
C
H
HHH+++−+=ν (4.11)
111
96 Chapter 4
( )117654
2
22
5.01585.05.05.05.1 r
M
MrrrrMS
C
O
OO−+++−= (4.12)
72rMrS
TarTar−= (4.13)
02
=N
S (4.14)
Notice that in the above equations, νi denotes the mass fraction of species i in
light gases released during devolatilization of biomass.
The following equation allows calculation of the gas phase density as func-
tion of time and radial coordinate.
( )gg
n
n
gSur
rrt=
∂
∂+
∂
∂ρ
ερ 1 (4.15)
where n is a shape factor (n = 0 slab; n = 1 cylinder; n = 2 sphere) and the
source term Sg is the summation of the source terms of individual gaseous spe-
cies in Eqs. (4.7)-(4.14).
1110921rrrrrS
g++++= (4.16)
The general from of heat transfer equation deduced from the conservation
of energy is described by
( ) Qr
Tkr
rrr
Tcu
t
Tccc
n
nPggPggPCCPBB
~1 *+
∂
∂
∂
∂=
∂
∂+
∂
∂++ ρερρρ (4.17)
where the source term Q~
includes the heat of pyrolysis, the heat of homoge-
neous reactions, and the heat of heterogeneous reactions.
112
Modeling Combustion of Single Biomass Particle 97
actionsReCharactionsReGasPyrQ~
Q~
Q~
Q~
−−++= (4.18)
Based on the arguments provided in Chapter 3, the heat of pyrolysis is cal-
culated using the correlation of Milosavljevic et al. [7] to account for the
exothermicity of char formation and the endothermicity of volatiles formation.
Hence,
( ) ( )[ ]ccPyr
YYrrrQ~
−−++= 15381460321
(4.19)
The second and the third terms in the right-hand side of Eq. (4.18) are cal-
culated as follows
8877665544hrhrMhrhrhrQ
~TaractionsReGas
∆+∆+∆+∆+∆=−
(4.20)
1111101099hrhrhrQ
~actionsReChar
∆+∆+∆=−
(4.21)
The heats of reactions R4–R11 except R7 are obtained using NIST data [8].
The heat of reaction R7 is taken from Ref. [6].
Initially, the particle with a porosity of ε0 filled with an inert gas (assumed
nitrogen) has a density of ρB0; and it is suddenly exposed to a hot environment
with a temperature of T∞, pressure of P∞, and oxygen mass fraction of YO2,∞ at
the outside. To be able to fully solve the system of partial differential equa-
tions described above two sets of boundary conditions are applied: (1) due to a
symmetry assumption of the particle, the gradients of all species and tempera-
ture are set zero at the position of r = 0; (2) at the outside of the particle, r = R,
the following heat and mass transfer boundary conditions are employed.
( )
( ) ( )44TTeTTh
r
Tk
YYkr
YD
*
i,im
i
i
−+−=∂
∂
−=∂
∂
∞∞
∞
σ
ε
(4.22)
113
98 Chapter 4
where the heat and mass transfer coefficient h and km are determined using ap-
propriate Sherwood and Nusselt number correlations depending on the shape
of the particle. For example, the Nusselt and Sherwood numbers for a spheri-
cal particle are computed using the following correlations.
333050
333050
602
602
..
..
ScRe.Sh
PrRe.Nu
+=
+= (4.23)
Implementation of the biomass combustion model is carried out in
CHEM1D. A distinguished feature of CHEM1D is that it allows one to define
a transient 1-D heat and mass transfer problem in a separate subroutine with a
general partial differential equation form which consists of accumulation, con-
vection, diffusion and source terms. Thus, for the purpose of the present work,
four main subroutines are prescribed in CHEM1D to solve 1) biomass and
char conservation equations; 2) species conservation equations; 3) gas phase
conservation equations; and 4) heat transfer equation. Moreover, some auxilia-
ry equations for computation of thermo-physical properties, pressure (assum-
ing ideal gas law) and velocity are accordingly included in the simulation
code.
4.3 MODEL VALIDATION
Three different sets of experimental data reported in the literature are used
to examine the accuracy of the biomass particle combustion model. The exper-
imental data used for validation of the model are taken from Wurzenberger et
al. [9], Porteiro et al. [10] and Saastamoinen et al. [11]. In each validation
case, the thermo-physical properties are those reported in the related reference.
But in the case of absence of a specific parameter the physical properties and
the correlations given in Table 3.1 are employed.
A comparison of the predicted and the measured mass loss histories are
depicted in Figs.4.1-4.3. The experimental data shown in Fig.4.1 are related to
the combustion of spherical beech wood (700 kg/m3) particles with diameters
of 20 mm and 10 mm in air at a reactor temperature of 1223 K. The mass loss
history illustrated in Fig.4.2 was obtained from burning of cylindrical Laguna
Helada (1480 kg/m3) briquette particles of 50 mm diameter in air at a reactor
114
Modeling Combustion of Single Biomass Particle 99
temperature of 973 K. Figure 4.3 depicts mass loss history of 0.2 mm spheri-
cal-like peat (400 kg/m3) particle burnt in a reactor with a temperature of 1123
K and 19% (vol.) oxygen. In all cases, a very good agreement is achieved be-
tween the model prediction and the experiments, indicating that the combus-
tion model of a woody biomass particle developed in this work can be suffi-
ciently used to numerically investigate combustion of wood particles.
An important task of the present work is the examination of the role of
devolatilization and gas phase reactions and their impact on the conversion of
a single woody biomass particle. In the previous chapter, it was found that the
kinetic rate constants have a significant impact on the accuracy of the predic-
tions of a pyrolysis model. It was concluded that at high reactor temperatures
the kinetic data of Di Blasi and Branca [12], whereas at moderate temperatures
the kinetic constants of Thurner and Mann [13] would provide accurate predic-
tions of the main process parameters.
The effect of kinetic constants of pyrolysis on the combustion of biomass
particles at three experimental conditions outlined above was further exam-
ined. The best fit with measurements of beech wood particles burnt at a reactor
temperature of 1223 K in Fig. 4.1 was obtained using the kinetic data of Di
Blasi and Branca [12]. On the other hand, only with the kinetic constants of
Thuner and Mann [13] was sufficient agreement achieved between model pre-
dictions and experimental data related to the combustion of a Laguna Helada
particle (Fig. 4.2). In the last validation case shown Fig. 4.3, the best agree-
ment between the predicted and measured data was achieved using the kinetic
data of Di Blasi and Branca [12].
The importance of this observation is, in particular, related to the design of
biomass combustors and furnaces. The latter stages of biomass conversion; i.
e., char combustion and gasification, are greatly influenced by the pyrolysis
trend of biomass. In fact, the pyrolysis process of a particle quantifies the rela-
tive contribution of char and volatiles combustion to the total heat released,
and the distribution of temperature and combustion byproducts along the reac-
tor. For a specific application, it is wise to choose the set of devolatilization
kinetic data which would give the best fit with the available experimental data
related to that application. However, in the absence of such data, one may use
the results of this study. That is, based on results of Chapter 3 and the valida-
tion cases shown in Figs. 4.1-4.3, it can be implied that for low to moderate re-
actor temperatures the kinetic constants of Thurner and Man [13]; whereas at
115
100 Chapter 4
higher reactor temperatures the kinetic data of Di Blasi and Branca [12] may
be used in a particle combustion model.
It can be seen from Figs. 4.1 and 4.2 that at the early stage of (large) parti-
cle conversion, the weight loss history has a steep slope (corresponding to the
biomass pyrolysis) up to a point after which the rate of mass loss becomes
slower (corresponding to the char combustion process). This is due to the fact
that the char combustion reaction rate is slower than that of pyrolysis. On the
other hand, Fig. 4.3 shows an almost uniform slope over the combustion pro-
cess, though its slop slightly decreases at the final stage of the process. This
observation indicates that the pyrolysis and char combustion overlap.
The influence of gas phase reactions within and in the vicinity of the parti-
cle on the combustion process has also been investigated. In experimental set-
ups of beech wood and Laguna Helada briquette, the position of the particle
was stationary inside the reactor and the air was flowing with a specific mass
flux. Porteiro et al. [10] carried out simulations of various wood briquettes in-
cluding Laguna Helada, and found a good agreement between their model pre-
dictions and the experiments in terms of mass loss histories. The combustion
model described by Porteiro et al. [10] only accounts for the combustion of
hydrogen at the surface of particle, and no additional gas phase reactions have
been taken into account in their study.
The computer program developed using CHEM1D allows one to turn on
and turn off gas phase reactions. The predicted mass loss in both cases (gas
phase reactions on and gas phase reactions off) did not present a notable dif-
ference. The effect of gas phase reactions R4–R8 was also examined when
simulating beech wood particle combustion (Fig. 4.1); and interestingly the
same result was obtained. This observation is consistent with the findings of
Lu et al. [6] who conducted experiments on combustion of 9.5 mm poplar par-
ticles in conditions similar to the experimental conditions of Wurzenberger et
al. [9] on beech wood. Lu et al. [6] realized that the inclusion of gas phase
combustion in the vicinity of the particle did not yield a considerable differ-
ence in the simulation results. Similar result was also reported by Novozhilov
et al. [14] who examined the effect of volatile combustion on the mass loss
rate. They found that the thermal and radiant heat flux from the flame due to
the volatiles combustion resulted in a very small increase in the mass loss rate,
indicating that the external radiant heat flux is much stronger than the heat flux
generated by flame.
116
Modeling Combustion of Single Biomass Particle 101
Figure 4.1 Comparison of the model prediction with experiments of Wurzenberger et
al. [9] obtained from combustion of spherical beech wood particles in air at a reactor
temperature of 1223 K.
Figure 4.2 Comparison of the model prediction with experiments of Porteiro et al.
[10] obtained from combustion of 50 mm cylindrical Laguna Helada briquettes in air
at a reactor temperature of 973 K.
117
102 Chapter 4
Figure 4.3 Comparison of the model prediction with experiments of Saastamoinen et
al. [11] obtained from combustion of 0.2 mm spherical-like peat particle at a reactor
temperature of 1123 K with oxygen concentration of 19% (vol.).
No or little influence of gas phase reactions on the combustion of a bio-
mass particle corresponding to the above discussed experimental conditions
may be explained by the fact that upon commencement of the pyrolysis pro-
cess, the gaseous species released tend to immediately escape from the surface
of the particle, where they mix with the surrounding air. This outflow of the
volatiles provides a mass transfer resistance against diffusion of oxygen from
the surrounding air, so it seems to be less likely that any significant reaction
between oxygen and gaseous volatiles may take place inside the pores of the
solid particle. On the other hand, due to a continuous flow of surrounding air
passed over the particle, a very thin boundary layer would be formed around
the particle. Thus, the volatiles coming out of the particle have less chance to
mix and react with the oxygen within this boundary layer. This indicates that
the combustion of the major portion of volatiles would occur far from the par-
ticle. As will be discussed in the forthcoming section, the lower rates of gas
phase reactions compared to the char combustion rate is a further reason which
may support the hypothesis that the gas phase reactions appear to be of minor
importance for the previously discussed experimental conditions.
118
Modeling Combustion of Single Biomass Particle 103
4.4 SIMULATION RESULTS
Illustrative simulation results related to combustion of spherical beech
wood particle with diameters of 10 mm and 1 mm corresponding to the exper-
imental conditions of Fig. 4.1, are presented in order to enable one to get a
deeper insight into the complete thermal conversion of a woody biomass parti-
cle.
Figures 4.4-4.6 depict time and space evolution of biomass density, tem-
perature, char and gas phase densities, oxygen mass fraction and porosity dur-
ing the combustion process of a 10 mm particle. Notice that the simulation re-
sults are presented for the half thickness of the particle due to the symmetry
assumption. As the particle, initially at room temperature, is exposed to a reac-
tor temperature of 1223K with air as the surrounding gaseous fluid, the heating
up process begins. Prior to the pyrolysis process, oxygen from the surrounding
diffuses inside the particle and reaches its ultimate amount as in the surround-
ing air. However, upon beginning of the biomass decomposition process after
the temperature reaches a certain level, volatiles and char are formed. Subse-
quently, the mass fraction of oxygen reduces due to the formation of other
gaseous species as well as its partial transference because of the outflow of
volatiles.
As the pyrolysis process continues and a large amount of volatiles is re-
leased, diffusion of oxygen from the outside through the gaseous boundary
layer around the particle experiences a delay. Due to the increasing tempera-
ture inside the particle, the gas phase density decreases. It can be inferred from
the temperature and the porosity graphs that the final stages of the particle py-
rolysis overlaps with the conversion of char at the outer layers of the particle.
This may occur at low mass fluxes of the volatiles at latter stages of the pyrol-
ysis, where there also exists a chance for the oxygen to reach the particle sur-
face at a higher external mass transfer coefficient.
After all virgin biomass has completely converted to char, and the volatiles
have left the particle, the diffusion of the oxygen inside the particle increases.
Due to the high porosity of the remaining char, oxygen may react not only at
the particle surface but also inside the pores. One may recognize from the char
density and the porosity graphs in Figs. 4.6 and 4.4 that the char consumption
proceeds from the outer layers towards the center of the particle indicating that
the size of the particle decreases as the combustion process continues. During
the combustion of char, the particle temperature takes a peak and remains at a
119
104 Chapter 4
certain level (around 1800 K in Fig. 4.5) until complete conversion and disap-
pearance of char, after which the temperature drops to the surrounding temper-
ature and remains in thermal equilibrium. Notice that in the present work, a
negligible percentage of ash is assumed as in most woody biomasses, which
has been regarded to fall off the particle upon its formation.
Figure 4.4 Simulated oxygen mass fraction and gas phase density corresponding to
combustion of a 10 mm spherical beech wood particle burnt in air at a reactor tempera-
ture of 1223 K.
120
Modeling Combustion of Single Biomass Particle 105
Figure 4.5 Simulated temperature and porosity corresponding to combustion of a 10
mm spherical beech wood particle burnt in air at a reactor temperature of 1223 K.
For practical applications such as in power plant furnaces, it is unwise to
utilize large particles with diameters in the order of 10 mm. Due to the short
particle residence time, in the order of a second, smaller particles with diame-
ters less than 1 mm need to be used. From the graphs represented in Figs. 4.4-
4.6, it can be seen that the biomass conversion process takes place non-
121
106 Chapter 4
uniformly due to significant intra-particle heat and mass transfer effects. Addi-
tional simulations have been carried out for a 1 mm spherical beech wood par-
ticle at process conditions corresponding to those in Figs. 4.4-4.6, to observe
the variation of the main parameters with time and radial position; the results
are illustrated in Fig. 4.7-4.9.
Figure 4.6 Simulated biomass and char densities corresponding to combustion of a 10
mm spherical beech wood particle burnt in air at a reactor temperature of 1223 K.
122
Modeling Combustion of Single Biomass Particle 107
Figure 4.7 Simulated oxygen mass fraction and gas phase density corresponding to
combustion of a 1 mm spherical beech wood particle burnt in air at a reactor tempera-
ture of 1223 K.
123
108 Chapter 4
Figure 4.8 Simulated temperature and porosity corresponding to combustion of a 1
mm spherical beech wood particle burnt in air at a reactor temperature of 1223 K.
124
Modeling Combustion of Single Biomass Particle 109
Figure 4.9 Simulated biomass and char densities corresponding to combustion of a 1
mm spherical beech wood particle burnt in air at a reactor temperature of 1223 K.
125
110 Chapter 4
The general trends of the parameters shown in Figs. 4.7-4.9 are similar to
those for a 10 mm particle as given in Figs. 4.4-4.6. A careful observation of
the graphs in Figs. 4.7-4.9 indicates that the sub-processes involved in the par-
ticle conversion process; i. e., heating up, pyrolysis, and char combustion, take
place successively (see the graphs of biomass and char densities and porosity).
Furthermore, particle conversion occurs more uniform at a given instant. This
observation is important, especially when a single particle model is used in
CFD simulations of a large scale combustor; e.g. see Yin et al. [15]. Obvious-
ly, utilization of complex models such as the one described in the present pa-
per for a real industrial application with thousands or even millions of particles
would be extremely time consuming. The uniform trends of the predicted pa-
rameters depicted in Fig. 4.7-4.9 indicate that for practical applications, fair
predictions may be obtained with a reduced particle model, which can be es-
tablished, for example, by including only dominant processes in the model.
As discussed previously, the gas phase reactions do not significantly influ-
ence the conversion process. To allow one to get a deeper insight into the gas
phase reactions, the rates of reactions R4–R8 are compared with that of char
combustion at typical process conditions related to those in Figs. 4.7-4.9.
Shown in Fig. 4.10 are the computed rates of these reactions as a function of
time and radial coordinate. By comparing these graphs it can be realized that
char combustion is the dominant process as it possesses much higher values
compared to the gas phase reactions over the time and space domains repre-
sented in Fig. 4.10. Among the various gas phase reactions, the rate of hydro-
gen combustion is dominant. Perhaps, this can be an explanation why some
other researchers considered only hydrogen oxidation in a biomass particle
model; e.g. Porteiro et al. [10] and Thunman et al. [16], given that the correla-
tion used for computing the hydrogen combustion rate in these works are not
reported.
As a conclusion from the results shown in Fig. 4.10, one may neglect any
effect of gas phase combustion in a particle model at high temperatures with
small particles (< 1 mm). This would certainly lead to a less complex model;
that is, the particle model would only need to account for the pyrolysis and the
char combustion processes. On the other hand, based on the simulation results
presented in Figs. 4.7-4.9, a further simplification may be adapted by assuming
a uniform and isothermal process; thereby treating the particle as a whole and
neglecting the small intra-particle gradients. In this case, the particle model
comprising a system of PDEs (partial differential equations) presented in
126
Modeling Combustion of Single Biomass Particle 111
Sec.4.2.4 would reduce to a system of ODEs (ordinary differential equations).
However, further research needs to be carried out in these directions to ensure
the accuracy of the simplified particle models to be used in CFD models for
simulation and design of industrial furnaces.
Figure 4.10 Computed rates of char, methane, hydrogen, carbon monoxide and tar
combustion, and water-gas shift reaction.
127
112 Chapter 4
By comparing Figs. 4.4-4.6 and 4.7-4.9, one may recognize (specifically
from the graphs of char density) the burnout time of the particle. It can be de-
duced from these graphs that the burnout time of a 10mm particle is about 38
times higher than that of a 1mm particle indicating a quadratic trend. As total
conversion time is a key parameter which greatly influences the design of in-
dustrial reactors, the effect of particle size on burnout time of particles with di-
ameters up to 3mm has been investigated. Typical results related to the com-
bustion of spherical beech wood particles at three reactor temperatures are
shown in Fig. 4.11. The burnout time is referred to as the time needed for
99.5% conversion of the particle. It can be observed from the graphs shown in
Fig. 4.11 that the trend of particle conversion time is exponential with respect
to the particle size. Moreover, it is seen that the burnout time of a particle of
the order of 1 mm at temperatures higher than 1400 K is less than 1 second.
Figure 4.11 Burnout time of a spherical beech particle as a function of size at three
rector temperatures.
128
Modeling Combustion of Single Biomass Particle 113
The results presented in Fig. 4.11 are obtained assuming a constant oxygen
concentration outside the particle and a fixed reactor temperature. However, it
must be noted that in real furnaces, for instance in entrained flow reactors, par-
ticles are not stationary and they move along the reactor. Therefore, solid par-
ticles would experience different oxygen concentrations and temperatures at
various positions within the reactor so that the burnout time would be influ-
enced. Thus, further research needs to be conducted in this area in order to ac-
curately predict the burnout time of biomass particle for industrial applica-
tions.
4.5 CONCLUSION
The presented model of combustion of a biomass particle is capable to
predict a variety of parameters at various stages during the conversion process.
It is validated against three sets of experiments found from the literature. A
correct set of kinetic constants for the pyrolysis process needs to be selected
carefully. The kinetic constants of Thurner and Man [13] can be used for low
to moderate reactor temperatures; whereas the kinetic data of Di Blasi and
Branca [12] may be utilized at higher reactor temperatures; i. e. Tr > 1100 K.
From the validation cases presented, inclusion of gas phase reactions within
and in the vicinity of the particle has a minor influence on the combustion pro-
cess. A reduced particle model comprising only pyrolysis and char combustion
processes may be used in CFD codes for designing furnaces where combustion
of small particles take place.
RERERENCES
[1] Dryer F. L., Glassman I. 1973. High-temperature oxidization of CO and
CH4. Proc Combust Inst 14: 987-1003.
[2] de Souza Santos M. L. 1989. Comprehensive modeling and simulation
of fluidized bed boilers and gasifiers. Fuel 68: 1507-1521.
[3] Howard J. B., Williams G. C., Fine D. H. 1973. Kinetics of carbon
monoxide oxidization in post flame gases. Proc Combust Inst 14: 975-
986.
129
114 Chapter 4
[4] Smoot L. D., Smith, P. J. 1985. Coal Combustion and Gasification. Ple-
num Press, New York.
[5] Evans D. D., Emmons H. W. 1977. Combustion of wood charcoal. Fire
Res 1: 57-66.
[6] Lu H., Robert W., Peirce G., Ripa B., Baxter L. L. 2008. Comprehen-
sive study of biomass particle combustion. Energ Fuel 22: 2826-2839.
[7] Milosavljevic I., Oja V., Suuberg E. M. 1996. Thermal effects in cellu-
lose pyrolysis: relationship to char formation processes. Ind Eng Chem
Res 35: 653-662.
[8] National Institute of Standards and Technology (NIST) Chemistry
WebBook. Available from: http://www.webbook.nist.gov/chemistry/.
[9] Wurzenberger J. C., Wallner S., Raupenstrauch H., Khinast J. G. 2002.
Thermal conversion of biomass: comprehensive reactor and particle
modeling. AIChE J 48: 2398-2411.
[10] Porteiro J., Miguez J. L., Granada E., Moran J. C. 2006. Mathematical
modeling of the combustion of a single wood particle. Fuel Proc
Technol 87; 169-175.
[11] Saastamoinen J. J., Aho M. J., Linna V. L. 1993. Simultaneous pyrolysis
and char combustion. Fuel 72: 599-609.
[12] Di Blasi C., Branca C. 2001. Kinetics of Primary Product Formation
from Wood Pyrolysis. Ind Eng Chem Res 40: 5547-5556.
[13] Thurner F., Mann U. 1981. Kinetic investigation of wood pyrolysis. Ind
Eng Chem Process Des Dev 20: 482-488.
[14] Novozhilov V., Moghtaderi B., Fletcher D. F., Kent J. H. 1996. Compu-
tational fluid dynamics modelling of wood combustion. Fire Safety J
27: 69-84.
[15] Yin C., Kaer S. K., Rosendahl L., Hvid S. L. 2010. Co-firing straw with
coal in a swirl-stablilized dual-feed burner: modeling and experimental
validation. Bioresour Technol 101: 4169-4178.
[16] Thunman H., Leckner B., Niklasson F., Johnsson F. 2002. Combustion
of wood particles-A particle model for eulerian calculations. Combust
Flame 129: 30-46.
130
Chapter 5
Simplified Preheating Model
The content of this chapter is mainly based on the following paper: Haseli Y., van Oijen J. A., de Goey L. P.
H. 2012. Analytical solutions for prediction of the ignition time of wood particles based on a time and space
integral method. Thermochemica Acta, in press.
5.1 INTRODUCTION
When a dry woody biomass particle – initially at room temperature – is
exposed to a hot environment, it begins to undergo a heating up process before
initiation of the thermochemical decomposition and formation of char and vol-
atiles. Wood decomposition takes place at a characteristic temperature, which
will be called ignition or pyrolysis temperature throughout this chapter. In the
absence of oxygen in the surrounding fluid, the volatiles escape from the sur-
face of the particle leaving a char layer behind. In the case of the presence of
oxygen, the volatiles may mix and react with oxygen depending on the exter-
nal heating conditions and oxygen concentration.
Understanding the ignition characteristics of wood and the key parameters
affecting the ignition time are of technical interest. Acquiring sufficient
knowledge on the ignition phenomenon can, for instance, enable a designer of
wood-fired furnaces to estimate how long the ignition of a particle may take
before commencement of the decomposition. Furthermore, it is common prac-
tice in flammability tests to employ measured ignition parameters to evaluate
thermo-physical properties of wood at the time of ignition. The primary goal
of this chapter is to establish a simple method for prediction of the ignition
time of a woody material and to identify what parameters may influence it.
131
116 Chapter 5
There are a large number of publications in the literature on this subject.
Babrauskas [1] presented a very comprehensive review on ignition of wood
and argued that the ignition temperature can be assigned two different values:
one for autoignition or spontaneous ignition, and the other for piloted ignition.
A survey by Babrauskas [1] shows that the values for piloted ignition span
210-497 °C while for autoignition the range is 200-510 °C. Experiments of
Atreya et al. [2] and Thomson et al. [3] showed that the time of ignition is ap-
proximately the same as the time at which the surface of the particle begins to
undergo a pyrolysis process. In the present chapter, the pyrolysis temperature
will be assumed to be equal to the ignition temperature.
Some researchers experimentally studied the ignition characteristics of
various woods; e.g. see [4-8], whereas others used a detailed one-dimensional
model for prediction of the ignition time of a wood particle; e.g. see Refs. [9-
12]. On the other hand, there are limited studies [13, 14] which deal with a
combined simplified modeling and experimental examination of ignition char-
acteristics of woody materials. A common feature of these past works is the
examination of ignition behavior of thermally thick slab particles with the idea
of establishing a graphical or explicit relationship between the ignition time
and the heating conditions (external heat flux or operating temperature) for
practical and engineering applications. The key finding confirmed in these
studies is that the ignition time was found to be proportional to the inverse of
the square of the external heat flux.
Moghtaderi et al. [13] and Spearpoint and Quintiere [14], among others,
presented approximate solutions based on the integral method, which revealed
that the above mentioned relationship between ignition time and external heat
flux exists for a thermally thick slab particle. Here, the regime of thermally
thick is referred to the case that the particle surface temperature attains the crit-
ical ignition temperature while the center (for the case of cylindrical and
spherical particles) or the back face (for the case of a slab) is still at initial
temperature (see Fig. 5.1a). The experimental data of Moghtaderi et al. [13]
showed that the ignition temperature depends on the external heat flux and the
moisture content.
Given that the above cited works provide useful information about the ig-
nition of woody materials, the contribution of the present work is to derive ex-
plicit expressions for the ignition time of both thermally thin and thermal thick
woody materials of various shapes and to identify which process parameters
and in what functional form influence the ignition characteristics. The method
132
Modeling Combustion of Single Biomass Particle 117
used in this work is based on an approximate time and space integration of the
energy equation of the particle described as
2
2
x
T
t
T
∂
∂=
∂
∂α (5.1)
where α = k/(ρcp).
(a) (b)
Figure 5.1 Schematic representation of (a) thermally thick and (b) thermally thin par-
ticles.
According to the Integral Method, a spatial function is assumed for the
temperature along the particle and upon integrating the energy equation over
the space coordinate it is described by an ordinary differential equation (ODE).
q"net
Tign
xc=L
x=L x=0
T0
Ts
q"net
Tign
x=L
T0
x=xt x=0
Ts
133
118 Chapter 5
The result of space integration of Eq. (5.1) is an ODE in terms of the rate of
thermal penetration depth, xt. By applying time integration, as the next step, it
is possible to describe xt in the form of an algebraic equation as a function of
time. This method will be applied to a slab/flat particle in Sec. 5.2 to derive
explicit relationships for predicting the ignition time of thermally thick and
thermally thin particles. The method will be extended to other particle shapes
(cylinder and sphere) in Sec. 5.3. A dimensionless analysis will be carried out
in Sec. 5.4 to identify key parameters influencing the ignition time. Subse-
quently, numerical results together with comparison of the predictions with
some experimental data will be presented in Sec. 5.5. A summary of conclu-
sion will be provided in Sec. 5.6.
5.2 IGNITION TIME OF A WOOD SLAB
Consider a dry wood slab with thickness of L, which is exposed to a hot
environment. The particle is initially at temperature T0 (< Tp), and it is as-
sumed that the pyrolysis begins as soon as the surface temperature reaches the
ignition/pyrolysis temperature Tp. We further assume that 1) the thermo-
physical properties of the wood remain constant; 2) the convective heat trans-
fer between the particle and the surrounding fluid is negligible compared to the
radiant heating; 3) particle does not experience any chemical decomposition
before the surface attains the ignition temperature.
Depending on the particle size, thermo-physical properties and external
heating, the particle may experience two different conversion regimes as noted
earlier and illustrated in Fig. 5.1. Upon exposing the particle to a hot environ-
ment, it begins to heat up so that a thermal wave with a thickness xt measured
from the surface is formed. One possible case is that while the thermal wave is
moving towards the back face of the particle, Ts reaches Tp (see Fig. 5.1a). On
the other hand, a second possibility is that the thermal wave reaches the back
face (assumed to be “insulated” here); i. e., xt equals L, while the surface tem-
perature Ts is still less than Tp (see Fig. 5.1b). The heating up process continues
until Ts becomes Tp. At this moment the surface of the particle decomposes to
volatiles and char residue. In order to avoid any confusion, we intentionally
distinguish between these two situations; the first case will be referred to as
thermally thick particle, and the second one as thermally thin particle.
134
Modeling Combustion of Single Biomass Particle 119
The main basis for the development of the model is that the temperature
along the particle is assumed to obey a quadratic function satisfying the
boundary conditions.
01
2
2φφφ ++= xxT (5.2)
The coefficients of Eq. (5.2) are functions of time. With the aid of the bounda-
ry conditions
( )netx
qx/Tk ′′=∂∂−=0
, ( ) 0=∂∂= txx
x/Tk , 0
TTtxx
==
the coefficients of Eq. (5.2) are obtained so that the temperature profile can be
represented as
2
01
2
−
′′+=
t
t
net
x
xx
k
qTT (5.3)
For a known reactor temperature Tr, the net heat flux is described as
( )44
srnetTTq −=′′ σε (5.4)
On the other hand, for a fixed external radiation heat flux ext
q ′′ , the net heat flux
at the surface of the particle is
( )4
0
4TTqq
sextnet−−′′=′′ σε (5.5)
where it is assumed that the surrounding temperature is the same as the initial
temperature of the particle.
Applying a space integration to Eq. (5.1) from x = 0 to x = xt yields
∂
∂−
∂
∂=−
==∫ 000
xxx
tx
x
T
x
T
dt
dxTTdx
dt
dt
t
α (5.6)
135
120 Chapter 5
Using Eq. (5.3) and the boundary conditions, Eq. (5.6) reduces to
( )nettnet
qxqdt
d′′=′′ α62 (5.7)
Applying approximate time integration to Eq. (5.7) using the assumption
( )tqq.tdqnet
t
net 00
50 ′′+′′=′′′∫ leads to
( ) tq
q+tx
net
t
′′
′′=
013α (5.8)
where 0
q ′′ denotes the net heat flux at t = 0.
Note that the net heat flux is a function of Ts which is obtained from the tem-
perature profile relationship; i. e. Eq. (5.3), with x = 0. Hence,
( )t
net
sx
k
q+TtT
20
′′= (5.9)
The time required for the thermal wave to reach the back face is deter-
mined by inserting xt = L into Eq. (5.8) and rearranging for the time. Hence,
′′
′′=
L
L
q
q+
Lt
0
2
13α
(5.10)
For a thermally thick particle, tL is greater than the ignition time tign. To de-
termine the ignition time of a thermally thick particle tign, one needs to elimi-
nate xt between Eqs. (5.8) and (5.9), rearrange the resulting expression for t
and replace Ts by Tp. Hence,
136
Modeling Combustion of Single Biomass Particle 121
( )
′′
′′
′′
−=
p
p
p
ign
q
q+
k
q
TTt
0
2
2
0
12
3α
, (5.11)
where p
q ′′ is the net surface heat flux at the time of initiation of pyrolysis.
At high external heat fluxes, extp
qqq ′′=′′≈′′0
and Eq. (5.11) can be rewritten as
follows.
( )( )2
2
0
3
2
ext
pp
ignq
TTckt
′′
−=
ρ (5.12)
This result shows that the ignition time (of a thermally thick slab particle) is
proportional to the thermal inertia (kρcp) and the inverse of square of the ex-
ternal heat flux. Similar results have also been reported by Atreya and Abu-
Zaid [15] and Delichatsios et al. [16] who employed different methodologies
for the derivation of an explicit relationship for the ignition time.
For a thermally thin particle, the thermal wave reaches the back face while
Ts is still less than Tp (see Fig. 5.1b). A similar procedure as explained above is
undertaken. That is, the problem is still described by Eq. (5.1) assuming that
the temperature profile can be approximated with Eq. (5.3). Using the bounda-
ry conditions
( )netx
qx/Tk ′′=∂∂−=0
, ( ) 0=∂∂=Lx
x/Tk , sx
TT ==0
the temperature profile takes the following form as a function of x:
2
2x
kL
qx
k
qTT netnet
s
′′+
′′−= (5.13)
Integrating Eq. (5.1) with respect to x along the particle thickness, and insert-
ing Eq. (5.13) into the resulting expression yields
k
qL
k
qLT
dt
d netnet
s
′′=
′′− α
2
3 (5.14)
137
122 Chapter 5
Integrating Eq. (5.14) with respect to time from tL to t, and assuming a mean
value for net
q ′′ equaling (net
q ′′ +L
q ′′ )/2 leads to the following relationship.
( ) ( )( )LLnetLnetsLs
ttqqkLk
LqqTT −′′+′′+′′−′′+=
23
α (5.15)
Notice that the initial condition for this problem is that at tL (to be obtained
from Eq. (5.10)), the surface temperature is TsL, which is calculated using Eq.
(5.9).
To determine the time at which the pyrolysis initiates at the surface, one
needs to solve Eq. (5.15) for t with Ts = Tp. This leads to
( )( )
Lign
LignsLpLignqq
kL
k
LqqTTtt
′′+′′
′′−′′−−+=
α
2
3 (5.16)
where ign
q ′′ is the net heat flux at the time of ignition.
5.3 IGNITION TIME OF CYLINDRICAL AND SPHERICAL
PARTICLES
Let us now consider a cylindrical or spherical particle which experiences
temperature gradients only in r-coordinate as depicted in Fig. 5.2. The proce-
dure for obtaining relationships for the ignition time of a cylindrical/spherical
particle is similar to that explained in the previous section for a slab particle.
That is, the temperature profile and the boundary conditions applied for the
thermally thick and thin regimes can still be employed here (coefficients of Eq.
(5.3) will remain the same but x needs to be replaced by r), and we will per-
form time and space integration of the energy equation described in a general
form as
( )( )
∂
∂−
∂
∂
−=
∂
∂
r
TrR
rrRt
T n
n
1α (5.17)
where for a cylinder n = 1 and for a sphere n = 2.
138
Modeling Combustion of Single Biomass Particle 123
Figure 5.2 Schematic representation of thermally thick cylindrical/spherical particle.
Notice that the particle surface in Fig. 5.2 is denoted by r = 0 and the cen-
ter with r = R. However, a different treatment needs to be employed when ap-
plying space integration. Because if one follows the same procedure of space
integration as we did in Eq. (5.6), it would lead to a singularity. To avoid this
trouble, both sides of Eq. (5.17) are first multiplied by (R – r)n, and the result-
ing expression is integrated with respect to r from r = 0 to r = rt. Hence,
( ) ( )
( )k
qR
r
TR
r
TrR
dt
drTrRdrTrR
dt
d
netn
r
n
rr
n
t
tn
t
r n
t
t
′′=
∂
∂−
∂
∂−
=−−−
==
∫
αα
0
00
(5.18)
R rt
r
r=0
T
T0
Ts > Tp
139
124 Chapter 5
Inserting the quadratic temperature profile into the left hand side of Eq.
(5.18) and performing the integration yields
( ) ( )
( ) ( )251060
1424
222
2
2
=′′
=
+−
′′
=′′
=
−
′′
nk
qRrRrR
k
rq
dt
d
nk
qRrR
k
rq
dt
d
net
tt
tnet
net
t
tnet
α
α
(5.19)
Applying approximate time integration to Eq. (5.19) gives
( )
( )
=
′′
′′+
+−
=
′′
′′+
−
=
2
130
105
1
112
4
02
2234
0
32
n
q
qR
rRRrr
n
q
qR
rRr
t
net
ttt
net
tt
α
α
(5.20)
It is possible to determine the time at which the thermal penetration reach-
es the center of the particle. Thus, inserting rt = R into Eq. (5.20) leads to
( )
( )
=
′′
′′+
=
′′
′′+
=
2
15
1
14
0
2
0
2
n
q
q
R
n
q
q
R
t
R
R
R
α
α
(5.21)
From Eqs. (5.10) and (5.21), one can realize that under identical operational
conditions the following relationship holds.
314151 /:/:/t:t:tSlab,RCylinder,RSphere,R
= (5.22)
140
Modeling Combustion of Single Biomass Particle 125
To determine the ignition time for the thermally thick regime, the thermal
penetration depth rt is first expressed in terms of the surface temperature and
heat flux using Eq. (5.9).
′′
−=
net
s
tq
TTkr 02 (5.23)
Substituting Eq. (5.23) into Eq. (5.20) and replacing Ts with Tp yields
( )
( )
=
′′
′′+
′′
−+
′′
−−
′′
−
=
′′
′′+
′′
−−
′′
−
=
2
115
20208
1
13
24
02
2
02
3
0
4
0
0
3
0
2
0
n
q
qR
q
TTkR
q
TTkR
q
TTk
n
q
qR
q
TTk
q
TTkR
t
p
p
s
p
p
p
p
p
p
p
p
p
ign
α
α
(5.24)
Comparing Eq. (5.24) with Eq. (5.12), one may realize that the ignition
time of a slab particle is proportional to the thermal inertia, whereas this rela-
tion does not hold for cylindrical and spherical particles. In the forthcoming
section, we will further discuss through a dimensionless analysis what parame-
ters may directly influence the ignition time of various shapes.
Likewise, for the case of thermally thin particle, if one undertakes a similar
procedure as explained in Sec. 5.2 with the treatment outlined above, the fol-
lowing expressions result for cylindrical and spherical particles.
( ) ( )
( )
( ) ( )
( )
=′′+′′
′′−′′−−+
=′′+′′
′′−′′−−+
=
215
210
14
4
2
2
nqq
RqqTTkRt
nqq
RqqTTkRt
t
Rp
RpsRp
R
Rp
RpsRp
R
ign
α
α (5.25)
141
126 Chapter 5
5.4 DIMENSIONLESS ANALYSIS
The following dimensionless parameters are defined to consolidate the var-
iables.
R
r=ξ (5.26)
2R
tατ = (5.27)
0T
T=θ (5.28)
4
0T
qext
σε
′′=Ω (5.29)
3
0TR
k
σε=Κ (5.30)
For the case of a known reactor temperature, the net heat flux is calculated
using Eq. (5.4). Substituting for the dimensionless variables in Eqs. (5.11) and
(5.24) leads to the following relationships for non-dimensional ignition time of
thermally thick particles.
Slab
−
−+
−
−Κ
=
44
4
2
44
113
14
pr
r
pr
p
ign
θθ
θ
θθ
θ
τ (5.31)
Cylinder
−
−+
−
−Κ−
−
−Κ
=
44
4
3
44
2
44
113
12
14
pr
r
pr
p
pr
p
ign
θθ
θ
θθ
θ
θθ
θ
τ (5.32)
142
Modeling Combustion of Single Biomass Particle 127
Sphere
−
−+
−
−Κ+
−
−Κ−
−
−Κ
=
44
4
4
44
3
44
2
44
113
1
5
814
14
pr
r
pr
p
pr
p
pr
p
ign
θθ
θ
θθ
θ
θθ
θ
θθ
θ
τ (5.33)
On the other hand, for the case of known external heat flux with radiation
losses the net heat flux at the surface of the particle is obtained from Eq. (5.6).
The ignition time then obeys
Slab
+−Ω
Ω+
+−Ω
−Κ
=
113
1
14
4
2
4
p
p
p
ign
θ
θ
θ
τ (5.34)
Cylinder
+−Ω
Ω+
+−Ω
−Κ−
+−Ω
−Κ
=
113
1
12
1
14
4
3
4
2
4
p
p
p
p
p
ign
θ
θ
θ
θ
θ
τ (5.35)
Sphere
+−Ω
Ω+
+−Ω
−Κ+
+−Ω
−Κ−
+−Ω
−Κ
=
113
1
1
5
8
1
14
1
14
4
4
4
3
4
2
4
p
p
p
p
p
p
p
ign
θ
θ
θ
θ
θ
θ
θ
τ (5.36)
Comparing Eqs. (5.31)-(5.33) with Eqs. (5.34)-(5.36), one may recognize
that 41r
θ≡+Ω . Moreover, when the particle is a slab, the ignition time is pro-
143
128 Chapter 5
portional to the inverse of a quadratic form of the external heat flux. However,
for other particle shapes, the relation between the ignition time and the exter-
nal heating obeys a more complicated functional form.
Similarly, dimensionless expressions can be established for the ignition
time of a thermally thin particle as given in Eqs. (5.37) and (5.38) for the case
of known reactor temperature and know external heat flux.
( ) ( )
( )444
44
2sRpr
sRpsRp
Rignc
ba
θθθ
θθθθττ
−−
−+−Κ+= (5.37)
( ) ( )
( )44
44
22sRp
sRpsRp
Rignc
ba
θθ
θθθθττ
−−+Ω
−+−Κ+= (5.38)
where a, b and c are constant coefficients (see Table 5.1), and the dimension-
less time τR at which the thermal penetration reaches the center of the particle
is obtained using the non-dimensional variables in Eqs. (5.10) and (5.21).
−
−+Γ
=
44
41
1
1
sRr
r
R
θθ
θτ (known reactor temperature) (5.39)
−+Ω
Ω+Γ
=
411
1
sR
R
θ
τ (known external heat flux) (5.40)
where Γ = 3 (slab), Γ = 4 (cylinder), Γ = 5 (sphere).
The dimensionless surface temperature θsR at τR is evaluated using the di-
mensionless form of Eq. (5.23) with ξt = 1. Hence,
( ) 022 44=+Κ−Κ+
rsRsRθθθ (known reactor temperature) (5.41)
( ) 01224=+Ω+Κ−Κ+
sRsRθθ (known external heat flux) (5.42)
144
Modeling Combustion of Single Biomass Particle 129
Table 5.1 Coefficients of Eqs. (5.37) and (5.38).
Shape a b c
Slab 6 2 3
Cylinder 4 1 4
Sphere 10 2 15
The analysis presented above indicates that three variables influence the
ignition time: 1) dimensionless ignition temperature θp, 2) dimensionless ex-
ternal heat flux Ω (or reactor temperature θr), 3) K. The parameter K gives a
measure for the ratio of conduction heat transfer inside the particle to external
radiation heat transfer. Higher values of K are relevant to thermally thin parti-
cles, as the rate of the conductive heat transfer is much higher than the radia-
tion heat transfer rate. In this regime, external heat transfer is the controlling
factor. On the contrary, at lower values for K corresponding to thermally thick
particles, the process is controlled by intra-particle gradients.
Figure 5.3 shows the variation of the dimensionless surface temperature θsR
at the time τR with K at three typical values for the dimensionless reactor tem-
perature (or external heat flux). Notice that θsR is independent of the shape of
the particle. At lower values of K at which conduction heat transfer is compa-
rable with external heat transfer, θsR is much higher than the initial particle
temperature. By increasing K, θsR decreases and approaches unity – independ-
ent of operational temperature – at very high values of K (> 6000). Note that
for higher reactor temperatures, the curve θsR–K approaches the asymptote at
lower values of K. From Eq. (5.39) or Eq. (5.40), it can be implied that when
θsR = 1, τR = 1/(2Γ).
The corresponding graphs of τR versus K for the same values of θr repre-
sented in Fig. 5.3 are depicted in Fig. 5.4. As expected, under identical condi-
tions, τR,Sphere < τR,Cylinder < τR,Slab. This is because the surface-to-volume of a
spherical particle is the highest whereas that of a slab is the lowest with that of
a cylinder in between. So the thermal penetration movement in a spherical par-
ticle is the fastest. It can be further observed in Fig. 5.4 that for K > 290, the
external heating condition has a negligible effect on τR. Similar to the graphs of
θsR–K in Fig. 5.3, the curves of τR – K approach an asymptote depending on
the geometry of the particle as shown in Fig. 5.4. From these results, we may
145
130 Chapter 5
establish a general criterion that at K > 290, τR approaches 0.167, 0.125 and
0.1 for slab, cylinder and sphere, respectively.
Figure 5.3 Variation of θsR with K at three values of θr (or Ω).
Figure 5.4 Variation of τR with K at three values of θr (or Ω).
146
Modeling Combustion of Single Biomass Particle 131
5.5 NUMERICAL RESULTS AND DISCUSSION
The ignition time of a thermally thick particle can be directly calculated
from Eqs. (5.31)-(5.36) for given values of θp, K and θr or Ω. However, for a
thermally thin particle, one needs to first determine θsR from Eq. (5.41) or Eq.
(5.42) and use its value in Eq. (5.37) or Eq. (5.38) for computation of the igni-
tion time. The criterion for distinguishing these two regimes is that the ignition
time of a thermally thick particle is less than τR, whereas that of a thermally
thin particle is greater than τR.
5.5.1 Ignition Time of a Thermally Thick Particle
The non-dimensional ignition times of a thermally thick flat, cylindrical
and spherical particles varying with K and the dimensionless ignition tempera-
ture are illustrated in Figs. 5.5, 5.6, and 5.7, respectively, for two values of di-
mensionless reactor temperature θr. The first observation from Figs. 5.5-5.7 is
that for given values of K, θp and θr, the ignition time of a slab is the longest
and that of a sphere the shortest with that of cylinder in between. In all cases,
the variation of τign with K obeys a polynomial function. It is evident that τign
increases by increasing θp and/or decreasing θr.
Shown in these figures are also the graphs of τR (solid line). Notice that the
range of validity of the ignition time of thermally thick particles in Figs. 5.5-
5.7 is up to the intersection of the curves of τR and τign. If τign happens to be
greater than τR, the ignition time should be calculated from Eq. (5.37) or Eq.
(5.38) instead. In fact, the crossing point of τign with τR denotes the critical val-
ue of K at which transition from thermally thick to thermally thick (or vice
versa) takes place. A subtle observation from these results is that for given
values of θp and θr, Kcr of all geometries is the same. For instance, assume θp =
1.75. The crossing point of τign and τR in Fig. 5.5 (slab), Fig. 5.6 (cylinder) and
Fig. 5.7 (sphere) occurs at Kcr = 48 and Kcr = 410, respectively, for θr = 3 and
θr = 5. These results reveal that Kcr is independent of the shape of the particle
and it merely varies with θp and θr. The reason of this interesting observation is
discussed in the following section.
5.5.2 Transition Criterion
As illustrated in Figs. 5.5-5.7, the transition from the thermally thick re-
gime to the thermally thin regime takes place at a certain K = Kcr at which τign
147
132 Chapter 5
(of a thermally thick particle) equals τR. For example, equating the right-hand
sides of Eqs. (5.34) and (5.39) for the case of a slab yields
−
−+
=
−
−+
−
−Κ
44
4
44
4
2
44
113
1
113
14
sRr
r
pr
r
pr
p
cr
θθ
θ
θθ
θ
θθ
θ
(5.43)
Notice that at the condition of τig = τR, θp is equal to θsR. Thus, Eq. (5.43)
reduces to
11
4
2
44=
−
−Κ
pr
p
crθθ
θ (5.44)
Similarly, for the case of cylinder and sphere we get the following equations.
Cylinder
31
81
16
3
44
2
44=
−
−Κ−
−
−Κ
pr
p
cr
pr
p
crθθ
θ
θθ
θ (5.45)
Sphere
31
201
201
8
2
44
3
44
4
44=
−
−Κ+
−
−Κ−
−
−Κ
pr
p
cr
pr
p
cr
pr
p
crθθ
θ
θθ
θ
θθ
θ (5.46)
From a mathematical point of view, a common root of Eqs. (5.44)-(5.46) is
2
1144
=−
−Κ
pr
p
crθθ
θ (5.47)
Rearranging Eq. (5.47) for Kcr gives
148
Modeling Combustion of Single Biomass Particle 133
12
144
−
−=Κ
p
pr
crθ
θθ (5.48)
This result shows that Kcr is independent of the shape of the particle. Equation
(5.48) reveals that Kcr strictly depends on the dimensionless pyrolysis and re-
actor temperature. In the case of a known external heat flux, Kcr obeys
(a) (b)
Figure 5.5 Dependence of τign (broken lines) and τR (solid lines) of a thermally thick
slab particle on K at varying dimensionless pyrolysis temperature; a) θr = (Ω+1)¼ = 3,
b) θr = (Ω+1)¼ = 5.
(a) (b)
Figure 5.6 Dependence of τign (broken lines) and τR (solid lines) of a cylindrical ther-
mally thick particle on K at varying dimensionless pyrolysis temperature; a) θr =
(Ω+1)¼ = 3, b) θr = (Ω+1)
¼ = 5.
149
134 Chapter 5
(a) (b)
Fig. 7: Dependence of τign (broken lines) and τR (solid lines) of a spherical thermally
thick particle on K at varying dimensionless pyrolysis temperature; a) θr = (Ω+1)¼ = 3,
b) θr = (Ω+1)¼ = 5.
1
1
2
14
−
−+Ω=Κ
p
p
crθ
θ (5.49)
Typical graphical presentations of Kcr versus θp and θr are depicted in Figs.
5.8 and 5.9, respectively. It can be inferred from these graphs that at higher
values of ignition temperature, the transition from one regime to the other may
occur at lower values of K. On the other hand, at higher external heating con-
ditions this transition may take place at higher values of K.
Substituting the dimensionless variables in Eqs. (5.48) and (5.49), we can
establish a transition criterion in terms of a critical particle size as follows.
( )
( )( )
( )
( )( )
−−′′
−
−
−
=
fluxheatexternalknownTTq
TTk
etemperaturreactorknownTT
TTk
R
pext
p
pr
p
cr
4
0
4
0
44
0
2
2
σε
σε (5.50)
For a given process condition, if the size of a particle happens to be less than
Rcr, the particle is thermally thin, otherwise it is thermally thick.
150
Modeling Combustion of Single Biomass Particle 135
Figure 5.8 Variation of Kcr with θp at three different values of θr = (Ω+1)¼.
Figure 5.9 Variation of Kcr with θr = (Ω+1)¼ at three different values of θp.
151
136 Chapter 5
5.5.3 Ignition time of a Thermally Thin Particle
Illustrative numerical results of dimensionless ignition time of a thermally
thin slab, cylinder and sphere versus K at varying dimensionless ignition tem-
perature are depicted in Figs. 5.10, 5.11 and 5.12, respectively, for two values
of non-dimensional reactor temperature. Notice the scale of the ignition time
of thermally thick and thermally thin particles in Figs. 5.5-5.7 and Figs. 5.10-
5.12.
A linear relationship between τig and K is evident from the graphs of Figs.
5.10-5.12, whereas as noted earlier, for the thermally thick regime, τig is pro-
portional to Km with m between 1.8 and 2.0 depending on the shape of particle
(see Figs. 5.5-5.7). In other words, the ignition time of thermally thick or
thermally thin particle increases by increasing the rate of conductive heat
transfer compared to the radiation mechanism. Because, at lower inter-particle
thermal resistances, transportation of the net energy received at the surface of
the particle from the external heating source into the particle is quicker. Thus,
the accumulation of heat at the particle surface takes place with a lower rate,
whereby leading to the slower increase of the surface temperature and attain-
ing the ignition temperature at longer duration.
(a) (b)
Figure 5.10 Dependence of τign of a thermally thin slab particle on K at varying di-
mensionless pyrolysis temperature θp; a) θr = (Ω+1)¼ = 3, b) θr = (Ω+1)
¼ = 5.
152
Modeling Combustion of Single Biomass Particle 137
(a) (b)
Figure 5.11 Dependence of τign of a cylindrical thermally thin particle on K at varying
dimensionless pyrolysis temperature θp; a) θr = (Ω+1)¼ = 3, b) θr = (Ω+1)
¼ = 5.
(a) (b)
Figure 5.12 Dependence of τign of a spherical thermally thin particle on K at varying
dimensionless pyrolysis temperature θp; a) θr = (Ω+1)¼ = 3, b) θr = (Ω+1)
¼ = 5
A further observation is the linear dependence of τign of a thermally thin
particle on θp (notice the approximate identical distances between various lines
corresponding to different values of θp in Figs. 5.10-5.12). But, as shown in
153
138 Chapter 5
Figs. 5.5-5.7, τign of a thermally thick particle obeys a polynomial function
with respect to θp. These observations have been further demonstrated by re-
casting the results and producing τign – θp curves for thermally thin and thick
particles in Figs. 5.13 and 5.14, respectively.
(a)
(b)
(c)
Figure 5.13 Variation of τign of thermally thin particle with θp at different values of K;
a) slab; b) cylinder; c) sphere (θr = 3).
154
Modeling Combustion of Single Biomass Particle 139
(a)
(b)
(c)
Figure 5.14 Variation of τign of thermally thick particle with θp at different values of
K; a) slab; b) cylinder; c) sphere (θr = 3).
155
140 Chapter 5
5.5.4 Comparison with Experiments
In order to examine the accuracy of the relationships derived for prediction
of the ignition time of a woody material, several comparisons are made be-
tween the calculated and measured ignition time of various wood types. The
specification of the wood particles and the external heating condition are given
in Table 5.2. These data are extracted from the studies of Brescianini et al.
[10], Rath et al. [17], Lu et al. [18], Park et al. [19], and Koufopanos et al.
[20]. As denoted in Table 5.2, in some experiments wood specimen were ex-
posed to a constant incident heat flux but in others, the particles were heated
up in a hot reactor maintained at a uniform temperature.
Table 5.2 Specification of various wood types examined in different experiments.
Case
No. Wood type Shape
Size
[mm]
Density
[kg/m3]
Tp [K]
External heating
qext
[kW/m2]
Tr [K]
1 Plywood Slab 11.5 550 673 25 -
2 Plywood Slab 11.5 550 673 35 -
3 Plywood Slab 11.5 550 673 50 -
4 Beech Cube 10 700 760 - 1123
5 Poplar Cylinder 4.75 580 673 - 1276
6 Maple Sphere 12.7 630 630 - 879
7 Wood Cylinder 10 650 600 - 773
Table 5.3 Comparison of the predicted and measured ignition time of various wood
types given in Table 5.2.
Case No. Rtr[mm]
tign [sec]
Source of experiment
Analytical Numerical Measured
1 17.6 133.8 - 113±20
Brescianini et al. [10] 2 10.6 48.2 - 45±4
3 6.6 20.1 - 22±6
4 3.7 9.1 8.8 8.1 Rath et al. [17]
5 1.3 1.6 1.9 2.1 Lu et al. [18]
6 6.2 28.0 28.3 29.0 Park et al. [19]
7 10.0 67.8 67.9 63 Koufopanos et al. [20]
156
Modeling Combustion of Single Biomass Particle 141
Table 5.3 compares the computed ignition time of the various wood types
given in Table 5.2 with the measured values. A further comparison is provided
using the predicted ignition time obtained from the numerical pyrolysis model
discussed in Chapter 3. Shown in Table 5.3 are also the critical particle sizes
for transition from the regime of thermally thin to the regime of thermally
thick. It can be seen that the results of the analytical method compares well
with the measured values and the prediction of the numerical model. Overall,
the comparison provided in Table 5.3 reveals the acceptable predictability of
the explicit relationships of the ignition time of particles with various shapes
for engineering applications. Thus, process engineers and reactor designers
may employ Eqs. (5.31)-(5.38) along with Figs. 5.3-5.14, as a useful tool for
estimating the time to ignition of not only wood particles, but also other solid
particles undergoing a pyrolysis process; e.g. coal and thermoplastics. Fur-
thermore, by measuring the ignition time data at different incident heat flux, it
is possible to evaluate the thermal properties of a specific material such as
thermal inertia at the condition of ignition.
5.6 CONCLUSION
The dimensionless ignition time is found to be a function of three parame-
ters including non-dimensional external heat flux Ω or reactor temperature θr,
ignition temperature θp and the parameter K, which denotes the ratio of inter-
nal heat transfer via conduction mechanism to the external radiation heat trans-
fer. The variation of the ignition time with θp and K is either linear (thermally
thin particle) or polynomial (thermally thick particle). The time τR at which the
thermal penetration reaches the center of the particle also depends on K, exter-
nal heating condition and the particle geometry. It is found that for values of K
> 290, τR approaches an asymptote and becomes independent of the external
heat transfer and K.
Validation of the presented relationships for ignition time is carried out by
comparing the predictions of the analytical model with the results of a numeri-
cal model as well as the measured ignition time of several wood types of vari-
ous shapes at different operational conditions. The satisfactory agreement be-
tween the predictions and the experiments shows that these explicit
expressions can be used by designers for estimating the preheating time of sol-
id particles undergoing a pyrolysis process in industrial reactors. Also, they
157
142 Chapter 5
can be used for determining the thermal properties of a specific material at the
time of ignition by interpreting the ignition data.
RERERENCES
[1] Babrauskas V. 2002. Ignition of wood: a review of the state of the art. J
Fire Protec Eng 12: 163-189.
[2] Atreya A., Carpentier C., Harkleroad M. 1986. Effect of sample orienta-
tion on piloted ignition and flame spread. Fire Safety Sci 1: 97-109.
[3] Thomson H. E., Drysdale D. D., Beyler C. L. 1988. An experimental
evaluation of critical surface temperature as a criterion for piloted igni-
tion of solid fuels. Fire Safety J 13: 185-196.
[4] Delichatsios M., Paroz B., Bhargava A. 2003. Flammability properties
for charring materials. Fire Safety J 38: 219-228.
[5] Liodakis S., Bakirtzis D., Dimitrakopoulos A. 2002. Ignition character-
istics of forest species in relation to thermal analysis data.
Thermochimica Acta 390: 83-91.
[6] Liodakis S., Bakirtzis D., Dimitrakopoulos A. P. 2003. Autoignition and
thermogravimetric analysis of forest species treated with fire retardants.
Thermochimica Acta 399: 31-42.
[7] Delichatsios M. A. 2005. Piloted ignition times, critical heat fluxes and
mass loss rates at reduced oxygen atmospheres. Fire Safety J 40: 197-
212.
[8] Mindykowski P., Fuentes A., Consalvi J. A., Porterie B. 2011. Piloted
ignition of wildland fuels. Fire Safety J 46: 34-40.
[9] Bilbao R., Mastral J. F., Lana J. A., Ceamanos J., Aldea M. E., Betran
M. 2002. A model for the prediction of the thermal degradation and ig-
nition of wood under constant and variable heat flux. J Anal Appl Pyrol-
ysis 62: 63-82.
[10] Brescianini C. P., Delichatsios M. A., Webb A. K. 2003. Mathematical
modeling of time to ignition in the early fire hazard test. Combust Sci
Technol 175: 319-331.
158
Modeling Combustion of Single Biomass Particle 143
[11] Kuo J. T., His C. L. 2005. Pyrolysis and ignition of single wooden
spheres heated in high-temperature streams of air. Combust Flame 142:
401-412.
[12] Lizhong Y., Zaifu G., Yupeng Z., Weicheng F. 2007. The influence of
different external heating ways on pyrolysis and spontaneous ignition of
some woods. J Anal Appl Pyrolysis 78: 40-45.
[13] Moghtaderi B., Novozhilov V., Fletcher D., Kent J. H. 1997. A new cor-
relation for bench-scale piloted ignition data of wood. Fire Safety J 29:
41-59.
[14] Spearpoint M. J., Quintiere J. G. 2001. Predicting the piloted ignition of
wood in the cone calorimeter using an integral model–effect of species,
grain orientation and heat flux. Fire Safety J 36: 391-415.
[15] Atreya A., Abu-Zaid M. 1991. Effect of environmental variables on pi-
loted ignition. Fire Safety Sci 3: 177-186.
[16] Delichatsios M., Panagiotou T. H., Kiley F. 1991. The use of time to ig-
nition data for characterizing the thermal inertia and the minimum (criti-
cal) heat flux for ignition or pyrolysis. Combust Flame 84: 323-332.
[17] Rath J., Steiner G., Wolfinger M. G., Staudinger G. 2002. Tar cracking
from fast pyrolysis of large beech wood particles. J Anal Appl Pyrolysis
62: 83-92.
[18] Lu H., Ip E., Scott J., Foster P., Vickers M., Baxter L. L. 2010. Effects
of particle shape and size on devolatilization of biomass particle. Fuel
89: 1156-1168.
[19] Park W. C., Atreya A., Baum H. R. 2010. Experimental and theoretical
investigation of heat and mass transfer processes during wood pyrolysis.
Combust Flame 157: 481-494.
[20] Koufopanos C. A., Papayannakos N., Maschio G., Lucchesi A. 1991.
Modeling of the pyrolysis of biomass particles. Studies on kinetics,
thermal and heat transfer effects. Can J Chem Eng 69: 907-915.
159
144 Chapter 5
160
Chapter 6
Simplified Pyrolysis Model
The content of this chapter is mainly based on the following papers: Haseli Y., van Oijen J. A., de Goey L.
P. H. 2012. Predicting the pyrolysis of single biomass particles based on a time and space integral method.
Journal of Analytical and Applied Pyrolysis 96: 126-138; Haseli Y., van Oijen J. A., de Goey L. P. H. 2012
A simplified pyrolysis model of a biomass particle based on infinitesimally thin reaction front approxima-
tion. Energy & Fuels 26: 3230-3243.
6.1 INTRODUCTION
In practical applications, the usage of detailed models would be at the cost
of considerable computational efforts and time, in particular, when dealing
with the design of combustors and gasifiers where a large number of particles
undergo thermochemical conversion. For many industrial applications, design-
ers are commonly interested in only a few parameters such as average temper-
ature and/or temperature at the surface of the particle, rate and the amount of
particle mass loss, ignition time at which a particle begins to decompose, and
total duration of the conversion process. To capture the main characteristics of
the pyrolysis of solid fuels with optimized computational efforts requires one
to employ less complex models.
A literature survey reveals several simplified models [1-12] developed by
various researchers for prediction of the main characteristics of a pyrolyzing
particle. The solution methodology and the range of applicability of these sim-
ple models differ from one study to another. A common feature of simplified
modeling studies is to transform the initial partial differential form of transport
equations into a set of ordinary differential equations (ODE). Further, most
past studies on this subject are concerned with thermally thick particles in that
161
146 Chapter 6
pyrolysis begins at the exterior surface of particle before particle center tem-
perature deviates from its initial value. The treatment of a thermally thin parti-
cle (in which pyrolysis begins after the center temperature has started to un-
dergo a heating process) based on the assumption of infinite rate pyrolysis at a
thin reaction front has not been previously discussed in the literature.
In principle, a chemically converting solid particle may ultimately decom-
pose in the following two extreme limits: the regime of shrinking density, and
the shrinking core regime. In the former limit, a particle undergoes an almost
homogenous conversion in the absence of intra-particle gradients, whereas in
the latter extreme limit the reaction takes place at a very thin layer, resulting in
a reaction front that is created at the surface of the particle and moves towards
its center.
Based on the results of Chapter 3, it is unlikely that pyrolysis of biomass in
combustors and gasifiers occurs in the regime of kinetically controlled in the
absence of intra-particle gradients, due to the high operational temperatures
and relatively large particles. It is difficult to mill biomass due to its fibrous
structure, which results in particles of around 1 mm. Moreover, Lu et al. [13]
and Bharadwaj et al. [14] examined the accuracy of a lumped model (treating
the particle as a whole) and found significant errors in the predictions indicat-
ing that the intra-particle effects need to be accounted for in a pyrolysis model.
A recent study by Saastamoinen et al. [15] has also revealed that the intra-
particle gradients of particles of less than a millimeter in practical furnaces can
be significant. Therefore, one needs to account for the temperature gradients
inside a pyrolyzing particle.
Another case is to employ the concept of shrinking core model assuming
that the pyrolysis begins as soon as the surface temperature reaches a charac-
teristics temperature Tp (to be called pyrolysis temperature throughout this the-
sis), thereby yielding a reaction front. A further simplifying assumption is that
the virgin biomass decomposes to char and volatiles at an infinite rate in a very
thin layer dividing the particle into char layer and biomass region. To account
for the temperature gradient inside the particle, one may employ the concept of
integral method that was originally proposed by Goodman [16]. As discussed
in Chapter 5, this method allows one to convert a one-dimensional transient
heat transfer problem described by a partial differential equation (PDE), into
an ordinary differential equation (ODE).
162
Modeling Combustion of Single Biomass Particle 147
The integral method has been used for predicting the pyrolysis of solid
particles in some past studies [4-11]. Although the concept of the shrinking
core model has been commonly employed in these studies, the essential differ-
ences between them are summarized in Table 6.1. Furthermore, the formula-
tion and solution methodology differ from one study to another. Given that the
concept of a fixed pyrolysis temperature Tp may seem to be controversial, it is
a useful simplifying approach, in particular, when dealing with flaming com-
bustion [12]. Moreover, Galgano and Di Blasi [17] assessed the predictions of
a shrinking core model with both finite rate and infinite rate pyrolysis models.
They found that the temperature Tp is not necessarily the same as that predict-
ed by the finite rate model. However, the main conclusion was that the most
important process characteristics could be accurately predicted by assigning a
proper value for Tp.
Table 6.1 The specification of the integral method employed in past studies.
Researcher(s) Temperature profile Particle Validation against
Kanury [4] Linear Charring slab and
cylinder
Experiments
Chen et al. [6] Exponential Charring and non-
charring finite
slab
Analytical solution
Spearpoint and
Quintiere [8]
Linear (char layer) and
quadratic (virgin layer)
Charring semi-
infinite slab
Experiments of dif-
ferent pyrolyzing
woods
Galgano and Di
Blasi [10]
Quadratic Charring cylinder Experiments of wood
Pyrolysis
Weng et al. [11] Linear (char layer) and
quadratic (virgin layer)
Charring semi-
infinite slab
Experiments of wood
pyrolysis with char
oxidation
A careful review of the above cited sources indicates that the concept of
shrinking core model has been used only for predicting the pyrolysis of ther-
mally thick particles in which ignition takes place at the particle surface before
163
148 Chapter 6
thermal penetration reaches the back face. A further possible situation which
has not been fully realized in past studies is the case in which the ignition oc-
curs after thermal penetration has reached the back face; i.e. thermally thin
particle. The present chapter aims to develop simple models for a finite size
wood particle undergoing a pyrolysis process. The main objective is to intro-
duce a novel modeling approach based on a time and space integral method.
Description of the various stages of the pyrolysis process is given in Sec.
6.2, which will be followed by formulation of different stages in Sec. 6.3. Val-
idation of the simplified pyrolysis model will be carried out in Sec. 6.4. The
effect of Tp as the most robust parameter on the process parameters will be dis-
cussed in Sec. 6.5. A summary of conclusion will be given in Sec. 6.6.
6.2 DESCRIPTION OF THE PROCESS
Consider a dry slab biomass particle with a thickness of L that is exposed
to a hot environment. The particle is initially at temperature T0 (< Tp), and it is
assumed that the pyrolysis begins as soon as the surface temperature reaches
the pyrolysis temperature Tp. Depending on particle size, thermo-physical
properties and external heating rate, the particle may experience two different
conversion regimes as depicted in Figs. 6.1 and 6.2. Initially, the particle be-
gins to heat up so that a thermal wave with a thickness xt measured from the
surface is formed. One possible situation is that the thermal wave reaches the
back face (assumed to be insulated in this study); i. e., xt equals L, while the
surface temperature Ts is still less than Tp (see Fig. 6.1b). The heating up pro-
cess continues until Ts becomes Tp; at this moment the surface of the particle
decomposes to volatiles and char residue. On the other hand, a second possi-
bility is that the thermal wave is still moving towards the back face of the par-
ticle while Ts has already reached Tp (see Fig. 6.2b). In order to avoid any con-
fusion, we intentionally distinguish between these two situations; the first case
will be referred to as thermally thin particle, and the second one as thermally
thick particle.
A thermally thin particle undergoes the following four stages:
1. Initial heating up (Fig. 6.1a),
2. Pre-pyrolysis heating up (Fig. 6.1b),
3. Pyrolysis (Fig. 6.1c),
164
Modeling Combustion of Single Biomass Particle 149
Figure 6.1 Schematic representation of a pyrolyzing thermally thin particle.
165
150 Chapter 6
Figure 6.2 Schematic representation of a pyrolyzing thermally thick particle.
166
Modeling Combustion of Single Biomass Particle 151
4. Post-pyrolysis heating up (Fig. 6.1d).
In the first stage of the process, a thermal wave (Fig. 6.1a) is created at the
surface and it moves inside of the particle as the time passes until it reaches the
back face; i. e., xt = L, at the time tL while the surface temperature is still less
than Tp. As shown in Fig. 6.1b, the heating up process continues until Ts reach-
es Tp; whereby initiating the pyrolysis process at the surface of the particle.
The time required for the surface of the particle to reach the pyrolysis tempera-
ture is denoted by tp,ini. From this moment on, the particle is divided into two
regions: the virgin part, which still undergoes the heating up process, and the
char layer with thickness xc (Fig. 6.1c). The pyrolysis front propagates inside
the particle by continuation of the process so that the thickness of the char re-
gion increases until the time tp at which xc equals L. At this moment the virgin
biomass has completely converted to char and volatiles assumed to leave the
particle immediately upon formation. The final stage is the char heating up
(post-pyrolysis stage) as depicted in Fig. 6.1d. So, the problem is a simple
conduction heat transfer. This stage will cease when thermal equilibrium be-
tween the particle and surrounding is established.
As pointed out earlier, for a thermally thick particle the process is a little
different (see Fig. 6.2) in a way that after initiation of the heating up stage
(Fig. 6.2a), the surface temperature increases up to Tp before the thermal wave
reaches the back face. In other words, for a thermally thick particle tL > tp,ini.
Thus, upon initiation of the pyrolysis process, the particle is divided into three
regions: char layer (0 < x < xc), virgin biomass undergoing heating up process
(xc < x < xt), and virgin biomass maintained at the initial temperature (xt < x <
L). By continuation of the pyrolysis process, the thermal wave and the char
front penetrate into the particle until xt reaches the back face. Beyond this
moment, the rest of the process is the same as the thermally thin particle as de-
picted in Figs. 6.2c and 6.3d. In summary, the following processes take place
in a thermally thick particle:
1. Initial heating up (Fig. 6.2a),
2. Heating-pyrolysis (Fig. 6.2b),
3. Pyrolysis (Fig. 6.2c),
4. Post-pyrolysis heating up (Fig. 6.2d).
In the forthcoming section, the formulation of various stages of a
pyrolyzing biomass particle will be presented based on a time and space meth-
od, which was discussed in the preceding chapter.
167
152 Chapter 6
6.3 FORMULATION
As the objective of the present paper is to establish a particle model as
simple as possible which can capture the main characteristics of a pyrolyzing
biomass particle, we need to base our formulation on certain simplifying as-
sumptions. As common in most simplified models; e.g. see Refs. [8-10, 12],
the thermo-physical properties and particle size are assumed to be constant
during the entire process. Worthy of mentioning is that even in comprehensive
modeling studies [18-21] most thermo-physical parameters are treated as con-
stants. Following the works of Peters [18], Sadhukhan et al. [22], Babu and
Chaurasia [23], and Koufopanos et al. [24], the effect of convective flow of
gaseous byproducts on total particle enthalpy balance is not considered here.
This effect may however be implicitly accounted for in the thermo-physical
properties of char. The time and space integral method introduced in Chapter 5
will be used for formulation of all stages of the conversion process depicted in
Figs. 6.1 and 6.2.
6.3.1 Thermally Thin Particle
6.3.1.1 Initial Heating Up
As the particle undergoes a transient conduction process (Figs. 6.1a), the
conservation of energy can be represented as follows
2
2
x
T
t
TB
∂
∂=
∂
∂α (6.1)
where αB = kB/(ρBcpB).
The procedure of derivation of the model equation for the initial heating up
stage is the same as presented in Sec. 5.2 in Eq. (5.2) through Eq. (5.9). The
key equations required for calculation of the history of the surface temperature
and heat flux are Eqs. (5.8) and (5.9).
The net heat flux at the surface of the particle is obtained from
( ) ( )44
∞∞−−−−′′=′′ TTTThqq
ssextnetσε (known external heat flux) (6.2a)
( ) ( )44
srsrnetTTTThq −+−=′′ σε (known reactor temperature) (6.2b)
168
Modeling Combustion of Single Biomass Particle 153
6.3.1.2 Pre-Pyrolysis Heating Up
In the second phase of heating up process, the thermal wave has already
reached the back face while Ts is still less than Tp (see Fig. 6.1b). The problem
is still described by Eq. (6.1) assuming that the temperature profile can be ap-
proximated with Eq. (5.2). Likewise, the analysis presented in Sec. 5.2 in Eq.
(5.13) through Eq. (5.15) can be applied here. The history of surface tempera-
ture and heat flux can be obtained by solving Eqs. (5.15) and (6.2)
6.3.1.3 Pyrolysis
Upon initiation of pyrolysis at the surface of the particle, the particle con-
sists of a char region with thickness xc and a virgin biomass region with length
L – xc (Fig. 6.1c). The temperature at the virgin/char interface, where the py-
rolysis takes place at infinitesimal rate, is Tp. Consistent with the analysis pre-
sented for the heating up stage, the temperature inside the particle is assumed
to obey a quadratic function. Two treatments will be presented: Double-
temperature profile, and single-temperature profile. In the former case, sepa-
rate temperature profiles are considered for biomass and char regions, whereas
in the case of single temperature profile, only one spatial profile is assumed for
temperature through the particle.
6.3.1.3.1 Double-temperature profile
Let us first consider the case of double-temperature profile such that the
temperature profiles in the char and biomass layers are represented as follows.
Char region (c
xx ≤≤0 ): ( ) ( )01
2
2ψψψ +−+−= xxxxT
ccC (6.3)
Biomass region ( Lxxc
≤≤ ): ( ) ( )01
2
2φφφ +−+−=
ccBxxxxT (6.4)
The heat transfer equation in the biomass region is still represented by Eq.
(6.1). A similar equation can be prescribed for the char layer.
2
2
x
T
t
TC
∂
∂=
∂
∂α (6.5)
169
154 Chapter 6
where αC = kC/(ρCcpC).
By applying the following boundary conditions,
BC1: netx
C
Cq
x
Tk ′′=
∂
∂−
=0,
BC2: 0=∂
∂= Lx
B
x
T,
BC3: pxxCxxBTTT
cc==
==,
BC4: pxx
C
Cxx
B
Bhm
x
Tk
x
Tk
cc∆′′+
∂
∂−=
∂
∂−
==& ,
and determining the coefficients i
ψ and i
φ , Eqs. (6.3) and (6.4) are rewritten
as
( ) ( )211
2xx
kx
hmkqxx
k
hmkTT
c
Cc
pBnet
c
C
pB
pC−
∆′′++′′+−
∆′′+−=
&& φφ (6.6)
( )( )
( )21
12
c
c
cpBxx
xLxxTT −
−−−+=
φφ (6.7)
where ∆hp denotes the specific heat of pyrolysis (negative when endothermic
and positive when exothermic), and m ′′& represents the decomposition rate per
unit particle surface area perpendicular to x-coordinate.
t
xm c
B∆
∆=′′ ρ& (6.8)
where ∆t is a very small increment of time.
Initially; i. e. t = tp,ini, xc = 0 and Bini,p
k/q ′′−=1
φ . Integrating Eq. (6.5) with
respect to x between x = 0 and x = xc, and using boundary conditions BC1-BC4
and temperature profile given in Eq. (6.6) yields
170
Modeling Combustion of Single Biomass Particle 155
( )[ ] ( )pBnetCcpBnet
hmkqxhmkqdt
d∆′′++′′=∆′′−−′′ &&
1
2
1622 φαφ (6.9)
Approximate time integration of Eq. (6.9) from tp,ini to t gives
( )ini,p
pBnet
pBnet
Cctt
hmkq
hmkqx −
∆′′−−′′
∆′′++′′=
&
&
223
1
1
φ
φα (6.10)
Note that a mean value for the terms inside the bracket on the right hand side
of Eq. (6.9) is considered when performing the time integration.
Likewise, integrating Eq. (6.1) between x = xc and x = L using Eq. (6.7)
results in
( )[ ]1
2
13 φαφ
BcxL
dt
d−=− (6.11)
After applying approximate time integration from t – ∆t to t and some rear-
rangements, a solution of Eq. (6.11) over a small time increment ∆t is found as
follows.
( ) ( )( )
( ) ( )
−
∆−
−
∆−−∆−=
2
2
11
3
c
B
c
c
xL
texp
txL
ttxLttt
αφφ (6.12)
where ( ) ( )[ ] 2/ttxtxxccc
∆−+= .
At each instant, the surface temperature is determined from Eq. (6.6) with
x = 0. Hence,
c
C
pBnet
psx
k
hmkqTT
∆′′−−′′+=
2
1&φ
(6.13)
171
156 Chapter 6
6.3.1.3.2 Single-temperature profile
Similar to the analysis presented for the initial and pre-pyrolysis heating
up, we assume that the temperature profile throughout the particle is represent-
ed by Eq. (5.2) whose coefficients can be obtained with the appropriate
boundary conditions at the particle surface and back face, and at the location
of xc where the temperature is Tp, thereby resulting in
( ) ( )2
2c
C
net
c
c
C
net
pxx
Lk
qxx
L
xL
k
qTT −
′′+−
−′′−= (6.14)
From conservation of energy for the particle, the net change in the energy
of the particle is equal to the net amount of energy transferred to the particle.
This leads to
pnet
c
ppCC
x
pCC
c
ppBB
L
xpBB
hmqdt
dxTcTdx
dt
dc
dt
dxTcTdx
dt
dc
c
c
∆′′+′′=−++ ∫∫ &ρρρρ0
(6.15)
Substituting Eq. (6.14) into Eq. (6.15) and integrating yields
( )[ ] ( )[ ]pnetccnet
C
pCC
cnet
C
pBBhmqxLxq
dt
d
Lk
cxLq
dt
d
Lk
c∆′′+′′=−′′+−′′− &
32323
63
ρρ (6.16)
Rearranging the above equation and performing approximate time integration
between tp,ini and t, we get
( ) ( )[ ]
( )( )ini,pini,ppnetC
ini,ppBBcnetpBBccnetpCC
ttqhmqLk
LqcxLqcxLxqc
−′′+∆′′+′′=
′′+−′′−−′′
&3
2223 3332ρρρ
(6.17)
Equation (6.17) can further be reshaped to read
172
Modeling Combustion of Single Biomass Particle 157
( ) ( )
( )ini,ppnetC
ini,ppBBcnetpBBccnetpCC
ini,pqhmqLk
LqcxLqcxLxqctt
′′+∆′′+′′
′′+−′′−−′′+=
&3
2223 3332ρρρ
(6.18)
It is possible to estimate the pyrolysis time using Eq. (6.18). The pyrolysis
process ceases when the char penetration depth xc equals L. At this moment,
the mass loss rate is zero. Thus, inserting xc = L and 0=′′m& into Eq. (6.18)
leads to a simple relationship for estimating the pyrolysis time.
( )
( )ini,ppC
ini,ppBBppCC
ini,ppqqk
qcqcLtt
′′+′′
′′+′′+=
3
22ρρ
(6.19)
where p
q ′′ denotes the net surface heat flux at the time of complete conversion
of the particle. To determine its value, one needs to solve Eq. (6.2) together
with an equation for the surface temperature at time tp to be obtained from Eq.
(6.14) with x = 0 and xc = L,
C
p
pspk
LqTT
2
′′+= (6.20)
In Eq. (6.19), tp,ini can be well-estimated using Eq. (5.15) and solving it for
t with Ts = Tp. Hence,
( )( )
Lini,pB
B
B
Lini,psLpLini,pqq
Lk
k
LqqTTtt
′′+′′
′′−′′−−+=
α
2
3 (6.21)
Also, p
q ′′ is calculated from Eqs. (6.2) and (6.20). The rest of the parameters
appearing in Eq. (6.19) are in fact treated as the problem input. In the forth-
coming section, we will discuss that the usefulness of Eq. (6.19) is not limited
to only approximating the pyrolysis time. In fact, it may further allow one to
predict the mass loss history of a particle.
173
158 Chapter 6
Under special circumstances and depending on the operational conditions,
the net surface heat flux may approach zero. In this case, Eq. (6.19) simply re-
duces to
C
pBB
ini,ppk
cLtt
3
2 2ρ
+= (6.22)
Equations (6.19) and (6.22) reveal that the pyrolysis time is proportional to
the biomass density and to the square of the particle size. We arrived at a simi-
lar conclusion in Chapter 3 where it was shown by means of a comprehensive
pyrolysis model that the total conversion time of a pyrolyzing biomass particle
varies linearly with the initial particle density and it changes in a quadratic
functional form with the particle size. From a physical point of view, the high-
er the heat capacitance of the biomass i.e. ρBcpB, the longer the duration of the
char layer movement in order to completely penetrate into the particle. Indeed,
a biomass particle with a higher heat capacitance requires longer time in order
to absorb a certain amount of heat. On the other hand, it can be seen in Eqs.
(6.19) and (6.22) that the pyrolysis time is proportional to the inverse of char
thermal conductivity. This is because at higher values of kC, the heat received
at the surface of the particle rapidly transfers through the char layer so the heat
transfer rate into the biomass layer becomes faster.
6.3.1.4 Post-Pyrolysis Heating Up
Upon completion of the pyrolysis, the particle becomes completely char so
that the problem reduces to a simple conduction heat transfer problem (Fig.
6.1d). Therefore, the solution of the post-pyrolysis process would be identical
to that of the second phase of biomass heating up as described in Sec. 6.3.1.2
with the difference that all thermo-physical properties should be replaced with
those of char. Thus, the temperature profile and the surface temperature are
obtained as follows
2
2x
Lk
qx
k
qTT
C
net
C
net
s
′′+
′′−= (6.23)
174
Modeling Combustion of Single Biomass Particle 159
( ) ( )( )ppnet
C
C
C
pnetspsttqq
Lkk
LqqTT −′′+′′+′′−′′+=
23
α (6.24)
Equation (6.24) can be rearranged as follows.
( )
( )pnet
C
C
C
pnetsps
p
qqLk
k
LqqTT
tt
′′+′′
′′−′′−−
=−
2
3
α (6.25)
At the final moment of the post-pyrolysis heating stage, the surface tempera-
ture is equal to reactor temperature Tr, so there would exist thermal equilibri-
um between the particle and the surrounding; implying a zero net heat flux at
the surface of the particle. Thus, Eq. (6.25) would reduce to
Lk
q
k
LqTT
ttt
C
pC
C
p
spr
pfph
2
3
′′
′′+−
=−=α
(6.26)
where tph denotes the duration of the post-pyrolysis heating up stage.
Eliminating p
q ′′ between Eqs. (6.20) and (6.26), we find
+
−
−=
3
22
psp
spr
C
phTT
TTLt
α (6.27)
It can be inferred from Eq. (6.27) that the minimum duration of the post-
pyrolysis stage would occur if Tsp = Tr. Hence,
C
ph
Lt
α3
2 2
≥ (6.28)
175
160 Chapter 6
It has been observed from detailed numerical models [14, 15, 25] and the
results of Chapter 3 that the trend of mass loss history of small biomass parti-
cles at high temperatures is almost linear. We will later show that the mass loss
history predicted by the double-temperature profile model also approximately
obeys a linear function. Since the final particle density is treated as a known
parameter in the present model (as well as in most simple pyrolysis models;
e.g. a model based on the global one-step kinetics), one may locate the starting
and ending points of mass loss curve in a mass loss-time plot, as illustrated in
Fig. 6.3. The initiation of the pyrolysis would correspond to a mass loss of ze-
ro and the time tp,ini to be estimated using Eq. (6.21). Furthermore, the end
point of the mass loss history graph would correspond to 1 – ρC/ρB, and the
time tp to be obtained from Eq. (6.19). The mass loss versus time would simply
be a line connecting the above two points on a mass loss-time plot. The last
stage of the process; i.e. post-pyrolysis heating, is the location (1 – ρC/ρB, tp +
tph) as depicted in Fig. 6.3. It will be shown later that mass loss graphs ob-
tained from this method are well comparable with those resulted from a com-
prehensive pyrolysis model. Given the simplicity of this method for predicting
the mass loss history, it does not provide a prediction of the mass loss rate his-
tory. Rather, it gives an average rate of mass loss flux throughout the process
defined as ( ) ( )ini,ppfave
tt/mmm −′′−′′=′′0&&& where Lm ρ=′′& represents the particle
mass per external surface area. Hence,
( )( )
( )ini,ppBBppCC
ini,ppcBC
aveqcqcL
qqkm
′′+′′
′′+′′−=′′
ρρ
ρρ
2
3& (6.29)
It is also possible to provide an approximate time evolution of the surface
temperature with a similar procedure. As outlined above, the duration of vari-
ous stages depicted in Fig. 6.1; i.e. tL, tp,ini, tp, tf, can be determined using the
appropriate relationships presented in previous sections. On the other hand, the
corresponding surface temperatures; i.e. TL, Tp, Tsp, Tf, are either already
known (Tp and Tf) or can be determined. Thus, a line connecting (T0, 0), (TsL,
tL), (Tp, tp,ini), (Tsp, tp), (Tf, tf) would provide an approximation of the surface
temperature history (see Fig. 6.4).
176
Modeling Combustion of Single Biomass Particle 161
Figure 6.3 Schematic diagram for predicting the mass loss history based on the single-
temperature profile approach.
6.3.2 Thermally Thick Particle
For a thermally thick particle, all sub-processes are the same as those of a
thermally thin particle except the second phase of the process. Unlike in the
thermally thin particle (Fig. 6.1) where the thermal wave rapidly reaches the
back face of the particle before initiation of the pyrolysis at the front surface,
in the thermally thick particle (Fig. 6.2) the surface temperature attains the py-
rolysis temperature while still xt < L. Therefore, in this section only the formu-
lation of the second stage of a thermally thick particle is presented.
Mas
s lo
ss [
-]
Time
tp,ini
tp
tph
1– ρC/ρB
tf
177
162 Chapter 6
Figure 6.4 Schematic diagram for predicting the surface temperature history based on
the single-temperature profile approach.
The procedure is very much similar to that presented in Sec. 6.3.1.3.1. In
other word, the heat transfer within the char (0 < x < xc) and the biomass (xc <
x < xt) regions are described by Eqs. (6.5) and (6.1), respectively. Furthermore,
the temperature profiles are assumed to be represented by Eqs. (6.3) and (6.4).
One may also use the boundary conditions BC1, BC3 and BC4 given in Sec.
6.3.1.3.1. Two additional boundary conditions need to be defined.
Su
rfac
e te
mp
erat
ure
Time
tL tp,ini tp tf
TsL
Tp
T0
Tsp
Tf
178
Modeling Combustion of Single Biomass Particle 163
BC2: 0=∂
∂= txx
B
x
T
BC5: 0TTtxxB =
=
Thus, the temperature profile within the char layer would be exactly the same
as given in Eq. (6.6). This means that the time and space integration of Eq.
(6.5) would lead to exactly the same result given in Eq. (6.10).
However, with the above two boundary conditions, it can be shown that
the temperature profile in the biomass region undergoing the heating up obeys
the following form.
( ) ( )tc
ct
c
p
ct
c
ppBxxx
xx
xxTT
xx
xxTTTT ≤≤
−
−−+
−
−−−=
2
002 (6.30)
Integrating Eq. (6.1) using Eq. (6.30) leads to (after some algebraic manipula-
tion) the following differential equation.
( )ct
B
tcxx
xxdt
d
−=+
α62 (6.31)
Integrating Eq. (6.31) over a small time increment ∆t gives
( ) ( ) ( ) ( )[ ]ttxtxxx
tttxtx
cc
ct
B
tt∆−−−
−
∆+∆−= 2
6α (6.32)
where t
x and c
x denote mean values of the thermal penetration and the char
layer thicknesses, respectively, over the time increment of ∆t.
Notice that the initial conditions required for solving the second phase of
the thermally thick particle pyrolysis are that at t = tpini, xc = 0 and xt = xt(tpini),
where the thermal penetration depth at the commencement of the pyrolysis is
obtained from the previous stage (initial heating up). To be able to fully solve
179
164 Chapter 6
the pyrolysis problem at this stage, one would need to also use Eqs. (6.2),
(6.8), (6.10) and (6.13), where 1
φ in Eq. (6.13) is obtained from the BCs.
−
−−=
ct
p
xx
TT0
12φ (6.33)
6.3.3 Numerical Solution
The calculation procedure of a thermally thin or thick particle based on the
double-temperature profile method is illustrated in Fig. 6.5. The first step for
numerically solving the equations of the simplified model described in previ-
ous sections is to define whether the particle is thermally thin or thick. Initial-
ly, particle undergoes a heating up process so one needs to simultaneously
solve Eqs. (6.2), (5.8) and (5.9). For a thermally thin particle, the calculations
continue until xt equals L at the characteristic time tL. Upon satisfaction of xt =
L, one needs to solve Eqs. (6.2) and (5.15) to compute the net heat flux and
temperature at the surface of the particle during the pre-pyrolysis heating up
stage. When the surface temperature attains the assigned pyrolysis temperature
at the time tpini, the solution algorithm switches so that Eqs. (6.2), (6.8), (6.10),
(6.12) and (6.13) are solved numerically through a trial-and-error method.
For the thermally thick particle, the solution method is initially the same as
that for the thermally thin particle. That is, one needs to first solve Eqs. (6.2),
(5.8) and (5.9) from time t = 0 until tpini. Beyond this moment, the solution al-
gorithm consists of simultaneously solving Eqs. (6.2), (6.8), (6.10), (6.13) and
(6.32) until thermal penetration reaches the back face at t = tL. Between t = tL
and t = tp, the pyrolysis problem is identical to that of the thermally thin parti-
cle whence a set of Eqs. (6.2), (6.8), (6.10), (6.12) and (6.13) are solved.
6.4 MODEL VALIDATION
The accuracy of the presented models based on an approximate time and
space integral method has been examined by comparing the predictions of the
model against experiments of different wood particles reported in the literature
as well as the computations of a the comprehensive pyrolysis model discussed
180
Modeling Combustion of Single Biomass Particle 165
in Chapter 3. The correlation of Milosavljevic et al. [26] is used for calculating
the enthalpy of pyrolysis.
Figure 6.5 Calculation flowchart.
Input data:
kB, cpB, ρB, kC, cpC, ρC,
T0, T∞, Tp, qext, h, L
Calculate tpini for thermally thin and tL
tL < tpini of
thermally thin?
At each time incre-
ment solve Eqs. (6.2),
(5.8) and (5.9) until xt
equals L
At each time incre-
ment solve Eqs. (6.2)
and (5.15) until Ts
equals Tp
At each time incre-
ment solve Eqs. (6.2),
(6.8), (6.10), (6.12)
and (6.13) until xc
equals L
Yes: Thermally thin No: Thermally thick
At each time incre-
ment solve Eqs. (6.2),
(5.8) and (5.9) until Ts
equals Tp
At each time incre-
ment solve Eqs. (6.2),
(6.8), (6.10), (6.13)
and (6.32) until xt
equals L
At each time increment
solve Eqs. (6.2), (6.8),
(6.10), (6.12) and (6.13)
until xc equals L
181
166 Chapter 6
6.4.1 Thermally Thin Particle
A comparison of the predicted mass loss histories using double- and sin-
gle-temperature profile pyrolysis models with the measured values and the
prediction of the comprehensive pyrolysis model of Lu et al. [25] is shown in
Fig. 6.6. The thermo-physical properties used in the calculation are given in
Table 6.2. The results of both treatments compare very well with the model
prediction of Lu et al. [25]. The trend of mass loss history and the conversion
time reasonably agree with the experiments. All models exhibit a rather steep-
er mass loss history compared to the experimental data, which is likely due to
the imperfect size and irregularity in particle shape, as pointed out by Lu et al.
[25].
In Chapter 3, the effects of particle size and external radiant heat flux on
conversion time and final char yield of beech and spruce particles were studied
by means of a comprehensive pyrolysis model. The conversion times of beech
and spruce wood slab particles predicted by the simplified models of this chap-
ter and the comprehensive model presented in Chapter 3 are illustrated in Figs.
6.7 and 6.8, respectively.
Figure 6.6 Comparison of the prediction of the simple models with the experiment
and the prediction of Lu et al. model [25] (L = 160µm and Tr = 1625 K).
182
Modeling Combustion of Single Biomass Particle 167
(a) (b)
Figure 6.7 Conversion time of beech wood particle predicted by the comprehensive
model and the simplified model, a) conversion time versus particle half thickness qext =
100 kW/m2; b) conversion time of a 1 mm particle versus heat flux.
(a) (b)
Figure 6.8 Conversion time of spruce wood particle predicted by the comprehensive
model and the simplified model, a) conversion time versus particle half thickness qext =
100 kW/m2; b) conversion time of a 1 mm particle versus heat flux.
Figures 6.7a and 6.8a illustrate comparisons between these models for an
incident heat flux of 100 kW/m2 and varying particle size. Simulations were
carried out for the situation that both front surface and back face of particle are
exposed to the above heat flux, so that the calculations were performed for half
of the particle assuming a symmetry condition at the particle center. The com-
parisons shown in Figs. 6.7a and 6.8a reveal the capability of the simplified
183
168 Chapter 6
models for predicting the conversion time of thermally thin particles. In order
to indicate the effect of the external heating condition, another comparison is
made in terms of the conversion time for a 1 mm particle at varying external
heat flux, as depicted in Figs. 6.7b and 6.8b. As can be seen, the simplified
models predictions in both cases are comparable with the computations of the
comprehensive model. These results indicate that the simplified models intro-
duced in this chapter can be effectively used for practical design purposes.
In real furnaces, the shape of particles could be far from a slab and they
may be cylindrical and/or spherical-like. Therefore, it is worth extending the
analysis of the time and space integral method to shapes other than a slab. The
derivation of the key relationships would be very much similar to that present-
ed for a slab particle. However, one should realize that unlike slab particles in
that the heat transfer area is identical along the particle, in a cylindrical and/or
spherical particle the heat transfer area consistently decreases from its maxi-
mum values being at the surface to the center of particle where the surface area
is zero. This has to be accounted for when performing space integration of the
heat transfer equations in all stages of the process described previously. Fur-
ther discussion on this will be presented in Chapter 8.
Table 6.2 Thermo-physical properties used for validations in Figs. 6.6.
Property Value Property Value
Tp [K] 523 ρC [kg/m3] 33
T0 [K] 300 cpB [J/kg.K] 2500
T∞ [K] 1625 cpC [J/kg.K] 1200
kB [W/m.K] 0.2 h [W/m2.K] 15
kC [W/m.K] 0.06 ε 0.95
ρB [kg/m3] 650 L [mm] 0.16
Below, the explicit relationships are presented for computation of time of
initiation of pyrolysis, pyrolysis time and post-pyrolysis heating up duration
suitable for cylindrical/spherical particles. The objective is to provide plant
engineers and designers with simple relationships to help them estimate pre-
heating and pyrolysis time as well as mass loss history. The form of the results
for cylindrical and spherical particles is the same as those of slab, but with dif-
184
Modeling Combustion of Single Biomass Particle 169
ferent numerical constants. In general, the relationships for evaluating the pre-
heating, pyrolysis and post-pyrolysis heating durations are as follows
( ) ( )
( )RpB
RpsRpB
R
B
ini,pqq
RqqC
CTTRkC
q
qC
Rt
′′+′′
′′−′′−−
+
′′
′′+
=α
α
2
1
22
01
2
1
(6.34)
( )
( )ini,ppC
ini,ppBBppCC
ini,ppqqkC
qcCqcRtt
′′+′′
′′+′′+=
1
2
2ρρ
(6.35)
+
−
−=
1
22
2
2 C
C
TT
TTCRt
psp
spr
C
phα
(6.36)
(a) (b)
Figure 6.9 Comparison of the prediction of the simple model with the experiment and
the prediction of Lu et al. model [25]; a) Cylindrical-like particle; b) Spherical-like
particle (deq = 320µm, Tr = 1625K).
185
170 Chapter 6
where for a cylinder (C1 = 4, C2 = 1) and a sphere (C1 = 5, C2 = ⅔). Looking
back into Eqs. (6.19), (6.21) and (6.27) one may realize that for a slab C1 = 3
and C2 = 2. Notice that the relationship for estimating the pyrolysis time; i. e.
Eq. (6.35), is obtained based on the single-temperature profile approach.
The accuracy of the model based on the single-temperature profile ap-
proach for predicting the mass loss of cylindrical and spherical particles is as-
sessed using the data of Lu et al. [25], who investigated the effect of particle
shape on the pyrolysis of small particles. In their study, cylindrical and spheri-
cal-like sawdust particles with equivalent diameter of 320 µm and nearly the
same mass and volume were pyrolyzed at 1625 K. The aspect ratios of the cy-
lindrical-like and spherical-like particles were 6 and 1.65, respectively. Figure
6.9 compares the prediction of the simple model with the experiments and the
model prediction of Lu et al. [25] for both cylindrical and near-spherical parti-
cles. As evident from Fig. 6.9, in both cases the simple model prediction com-
pares well quantitatively and qualitatively with the prediction of a comprehen-
sive model and the measured mass loss history. A further observation from this
figure is that the spherical-like particle pyrolyzes slower than the cylindrical
particle does, which is due to the lower surface area-to-volume of the near-
spherical particle than the cylindrical sawdust species. The measured external
surface area for slab-like, cylindrical and near-spherical particles reported by
Lu et al. [25] was 0.491 mm2, 0.479 mm
2 and 0.344 mm
2, respectively.
6.4.2 Thermally Thick Particle
The first set of validation is carried out using the experiments reported by
Spearpoint and Quintiere [27]. These data are obtained from the pyrolysis of
different wood species of 50 mm thickness exposed to incident heat fluxes of
25–75 kW/m2 with their grain oriented either parallel or perpendicular to the
incident heat flux. Most of the tests were conducted for an exposure time of 25
minutes. All samples were tested in a Cone Calorimeter with horizontal orien-
tation. Table 6.3 lists the thermo-physical data used in the calculations.
Figure 6.10 plots comparisons between the measured and the predicted
burning rates of Douglas fir (Fig. 6.10a), Red oak (Fig. 6.10b) and Redwood
(Fig. 6.10c) slabs with incident heat flux of 75 kW/m2 (Douglas fir and Red
oak woods) and 50 kW/m2 (Redwood) radiated along the grain. Spearpoint and
Quintiere [27] presented only the first 600 seconds of each test for clearly
identifying the growth and decay stages of the conversion process. The predic-
186
Modeling Combustion of Single Biomass Particle 171
tion of the presented simplified model is qualitatively in a good agreement
with the experimental trend of the burning rate history in all three cases. In ad-
dition, the model successfully captures the burning rates at early stages includ-
ing the measured time and amount of the maximum burning rate. The comput-
ed mass loss rate in the decay phase of the conversion is underpredicted. As
outlined by Spearpoint and Quintiere [27], the back face effect may play a role
due to incomplete insulation, but the formulation assumes no heat exchange at
this location with the surrounding. A further alternative reason for the
underprediction of the model in later stages may be the assumption of constant
thermo-physical properties and negligible virgin biomass and char density gra-
dients along the particle, which are not taken into account in the presented
model.
Table 6.3 Thermo-physical properties used for validation in Fig. 6.10.
Property Douglas fir Red Oak Redwood
Tp [K] 657 577 648
T0 [K] 300 300 300
T∞ [K] 400 400 400
kB [W/m.K] 0.4 0.44 0.22
kC [W/m.K] 0.2 0.2 0.2
ρB [kg/m3] 502 753 354
ρC [kg/m3] 50 75 50
cpB [J/kg.K] 3000 3600 3000
cpC [J/kg.K] 1500 1500 1500
h [W/m2.K] 10 10 10
ε 0.95 0.95 0.95
L [mm] 50 50 50
The second validation is carried out using the measured mass loss rate his-
tory reported by Wasan et al. [2]. The data were obtained from pyrolysis test
of a 25.4 mm plywood particle exposed to an external heat flux of 50 kW/m2.
Figure 6.11 compares the predicted mass loss history during the entire decom-
position process with the measured data (see Table 6.4 for the thermo-physical
properties used in the calculation). The model prediction is in a satisfactory
agreement with the experiments both qualitatively and quantitatively. As can
be seen, the mass loss rate takes a peak twice during the particle pyrolysis; first
at the early stage and then in the final stage of conversion. The predicted time
and the quantity of these peaks are within ±5.5% and –4% of the correspond-
ing measured values, respectively.
187
172 Chapter 6
(a)
(b)
(c)
Figure 6.10 Comparison of the predicted and measured burning rate of 50 mm parti-
cle exposed to 75 kW/m2 (a and b) and 50 kW/m
2 (c) heat flux; a) Douglas fir; and b)
Red Oak; c) Redwood.
188
Modeling Combustion of Single Biomass Particle 173
Table 6.4 Thermo-physical properties used for validations in Figs. 6.11-6.13.
Property Fig. 6.11 Fig. 6.12 Fig. 6.13
Tp [K] 648 523 623
T0 [K] 300 300 300
T∞ [K] 400 400 400
kB [W/m.K] 0.6 0.3 0.3
kC [W/m.K] 0.45 0.1 0.15
ρB [kg/m3] 462 450 380
ρC [kg/m3] 60 60 80
cpB [J/kg.K] 4000 2000 1150
cpC [J/kg.K] 2000 1100 1000
h [W/m2.K] 10 15 24
ε 0.95 0.85 1
L [mm] 25.4 30 38
Figure 6.11 Comparison of the predicted and measured mass loss rate of a 25.4 mm
pine particle exposed to 50 kW/m2 heat flux.
189
174 Chapter 6
The accuracy of the model has also been examined by reproducing the
temperature of thick slab particles undergoing pyrolysis at the surface and an
internal location. The first set of data is taken from Grønli and Melaaen [28].
The total times of exposure were 300 and 600 seconds. The experimental re-
sults of spruce particle of 30 mm length were chosen for validation of their py-
rolysis model (which did not account for particle shrinkage).
Shown in Fig. 6.12 are the predicted temperature histories at the surface
and 4 mm below the surface using the simplified model compared with the ex-
perimental values as well as the prediction of the detailed model of Chapter 3
for an exposure time of 600 seconds and an incident heat flux of 80 kW/m2. As
seen, the prediction of the simplified model compares well with the detailed
model, and it is capable of reproducing the time evolution of the temperature
at different positions. In particular, it can be observed that the surface tempera-
ture predicted by the simplified model matches that resulted from the compre-
hensive model. The pyrolysis temperature assigned for producing the graphs
depicted in Fig. 6.12 was chosen 250°C according to the experimental results
of Grønli [29] obtained from the pyrolysis of spruce wood.
To reinsure the capability of the simplified model for reproducing the tem-
perature experiments, another set of data reported by Kashiwagi et al. [30] is
used for additional model validation. They conducted gasification experiments
of thermally thick white pine wood with 38 mm cube samples at three different
atmospheres of nitrogen, 10.5% oxygen/89.5% nitrogen, and air under the
non-flaming conditions at a thermal radiant heat flux of 25 – 69 kW/m2. For
the purpose of comparison of the simplified pyrolysis model, only the meas-
urements obtained in the nitrogen atmosphere are chosen.
A comparison of the predicted and measured temperature history at the
surface and 5 mm beneath the surface of a white pine sample exposed to a 40
kW/m2 external heat flux – parallel to the grain – is shown in Fig. 6.13. The
computed graphs are obtained assuming a pyrolysis temperature of 350°C.
Similar to the previous case (Fig. 6.12), the trend of predicted temperature his-
tories compare well with the experiments. At early stages of the process, the
temperature is overpredicted owing to the moisture content of the sample, as
the model does not account for particle drying. At the later stages of the de-
composition, however, the predicted temperature histories at the surface and
5mm depth match very well with the measured values.
190
Modeling Combustion of Single Biomass Particle 175
Figure 6.12 Comparison of the predicted and measured (area between the broken
lines) spruce particle temperature at the surface and location of 4 mm beneath the sur-
face (L = 30 mm; qext = 80 kW/m2 heat flux).
Figure 6.13 Comparison of the predicted and measured white pine particle tempera-
ture at the surface and at the locations of 5 mm and 10 mm beneath the surface (L = 38
mm; qext = 40 kW/m2).
191
176 Chapter 6
6.5 DISCUSSION
The multiple validations of the simplified model against various experi-
mental data and the prediction of a comprehensive model in terms of main
process parameters lead to the conclusion that the presented model is suffi-
ciently capable of predicting the mass loss (rate), surface temperature and con-
version time. Thus, it can be employed as an effective design tool for predict-
ing the main characteristics of pyrolysis of biomass (and charring solid)
particles of thermally thin and thermally thick. The main advantage of the
simplified model compared to the comprehensive model is that it can be easily
implemented into a reactor model and solved much quicker.
Worth of further discussion is the sensitivity of the model accuracy to
thermo-physical properties and other input parameters; the most rigorous one
being the pyrolysis temperature. A wide range of values has been reported in
the literature for this parameter. Galgano and Di Blasi [17] suggest that it
should be treated as an adjustable parameter leading to results comparable with
experiments or a detailed model based on finite rate kinetics. Past study by
Spearpoint and Quintiere [27] indicates that Tp obtained from experimental
tests is material and orientation dependent. For instance, they determined aver-
age ignition temperatures of 375°C and 204°C for Redwood with the external
heat flux radiating along and across the grain, respectively.
Another study by Moghtaderi et al. [31] revealed that the ignition tempera-
ture depends on the external heat flux and moisture content. They measured
ignition temperatures for Radiata pine wood for incident heat flux of 20-60
kW/m2 and moisture content of 0-30% and found a range of 298°C to 400°C.
Moreover, Yang et al. [32] reported a range of 190°C to 310°C for the ignition
temperature of wood. As a result, a designer needs to carefully select a proper
value for the pyrolysis temperature otherwise it may lead to insufficient accu-
racy of the simplified model predictions. Recently, Park et al. [33] has pro-
posed a correlation for estimating Tp as a function of process parameters such
as external heat flux and particle size, which may be used as a useful tool in
the absence of experimental data. Their results show that at a high heating rate,
the pyrolysis temperature is higher.
The effect of prescribed pyrolysis temperature on model predictions have
further been investigated for both thermally thin and thermally thick beech
wood particle (700 kg/m3) exposed to an incident heat flux of 50 kW/m
2. The
thickness of the thermally thin particle is chosen 1 mm and that of thermally
192
Modeling Combustion of Single Biomass Particle 177
thick particle is assigned 10 mm. In both cases, it is assumed that the final char
density is 70 kg/m3 (90% conversion). The time evolution of burning rate,
mass loss and surface temperature are examined for Tp = 573K, 623K, 673 K,
and 723K. The results are depicted in Figs. 6.14-6.16.
Figure 6.14 illustrates the effect of pyrolysis temperature on burning rate
history. The corresponding mass loss curves are depicted in Fig. 6.15. For a
thermally thick particle (Fig. 6.14a), the trends of the graphs are similar to
those shown in Fig. 6.11. There exist two distinctive maximum mass loss rates
at early and late stages of decomposition. At a lower value of Tp, the global
mass loss peak takes place at the early phase of pyrolysis. By increasing Tp, the
first peak shifts in time, its quantity decreases, and the process becomes long-
er. Also, the global maximum burning rate takes place at the later stage of py-
rolysis at higher values of Tp. In fact, at a higher Tp, the particle regime shifts
towards thermally thin and the initiation time of pyrolysis increases (leading to
an increased preheating phase) and gets closer to the time at which the back
face temperature begins to heat up. When the pyrolysis temperature is lower,
particle decomposition takes place faster than the case with a higher Tp. Based
on the model assumption, the conversion of virgin material would happen as
soon as the temperature reaches Tp. Thus, a higher Tp corresponds to a higher
amount of heat required for virgin material decomposition and the process be-
comes slower.
For a thermally thin particle (Fig. 6.14b), the same general trend can be
observed; that is, by increasing Tp, the process becomes slower and the mass
loss rate reduces. Unlike the thermally thick particle, there exists only one
maximum burning rate which takes place in the first half of the decomposition
process. At higher values of Tp, the burning rate peak occurs later and its quan-
tity becomes lower. Looking into Fig. 6.15, one may realize that the trend of
the mass loss curves for the thermally thin particle is almost linear and the dis-
tance between the mass loss curves is almost the same throughout the process.
On the other hand, for the thermally thick particle, the shape of mass loss
graphs is rather curved. At early decomposition phase, the graphs correspond-
ing to two different values of Tp are close but they deviate from each other as
the process further continues. The above observation may be explained by the
fact that for a thermally thin particle the process is controlled by the external
heat transfer whereas in the regime of thermally thick the intra-particle effects
are important which influence the decomposition of the virgin material.
193
178 Chapter 6
(a)
(b)
Figure 6.14 Effect of pyrolysis temperature on burning rate history of a single (a)
thermally thick particle; (b) thermally thin particle, at an incident heat flux of 50
kW/m2.
194
Modeling Combustion of Single Biomass Particle 179
(a)
(b)
Figure 6.15 Effect of pyrolysis temperature on mass loss history of a single (a) ther-
mally thick particle; (b) thermally thin particle, at an incident heat flux of 50 kW/m2.
195
180 Chapter 6
(a)
(b)
Figure 6.16 Effect of pyrolysis temperature on surface temperature history of a single
(a) thermally thick particle; (b) thermally thin particle, at an incident heat flux of 50
kW/m2.
196
Modeling Combustion of Single Biomass Particle 181
The effect of Tp on the surface temperature is shown in Fig. 6.16. The main
observation is that for the thermally thick particle the surface temperature
reaches thermal equilibrium with the surrounding before completion of the py-
rolysis (Fig. 6.16a), while for the thermally thin particle the surface tempera-
ture still rises after complete conversion of particle (Fig. 6.16b). Again, as
pointed out earlier, this is due to the influence of intra-particle thermal re-
sistances which, in the thermally thick regime, are much greater than those in
the thermally thin regime. This indicates that for the case of thermally thin, the
rate of char penetration depth (dxc/dt) is faster than the rate of surface tempera-
ture rise.
6.6 CONCLUSION
A simple pyrolysis model of a biomass particle is developed based on a
time and space integral method. The model is based on the assumptions of
constant thermo-physical properties, decomposition of biomass according to a
shrinking core model at a thin reaction layer at a prescribed pyrolysis tempera-
ture, and approximating the spatial temperature profile with a quadratic func-
tion. Two different pyrolysis regimes have been identified including thermally
thin and thermally thick. The formulation of various stages of the conversion
process has been presented using the time and space integral method resulting
in transformation of partial differential form of heat transfer equation into an
algebraic equation.
Two different treatments are presented for a thermally thin particle. The
first formulation allows one to compute the history of key process parameters
such as net heat flux at the surface, mass loss rate, char penetration depth and
particle weight loss. This model can, for example, be used in combustor and
gasifier design codes where a large number of biomass particles undergo a
thermal decomposition, since computationally it is cheaper and easier to im-
plement in a CFD code than the comprehensive models. On the other hand, the
second treatment provides rather simple relationships for estimating the dura-
tion of various stages of the process including preheating, pyrolysis and post-
pyrolysis heating. This method can be the interest of plant engineers since it
provides a simple but useful tool to sufficiently predict the mass loss history of
a pyrolyzing particle (see Fig. 6.3). Also, time evolution of the surface temper-
ature can be approximated using the method illustrated in Fig. 6.4.
197
182 Chapter 6
Different validations of the presented formulation with a wide range of ex-
perimental data of as well as the predictions of comprehensive models indicate
that the presented model successfully captures the trend of the main process
parameters. It is capable of predicting mass loss rate, surface and internal tem-
peratures and particle conversion time with sufficient accuracy acceptable for
engineering purposes.
RERERENCES
[1] Wasan S. R., Rauwoens P., Vierendeels J., Merci B. 2010. An enthalpy-
based pyrolysis model for charring and non-charring materials in case of
fire. Combust Flame 157: 715-734.
[2] Wasan S. R., Rauwoens P., Vierendeels J., Merci B. 2010. Application
of a simple enthalpy-based pyrolysis model in numerical simulations of
pyrolysis of charring materials. Fire Mater 34: 39-54.
[3] Saastamoinen J. J. 2006. Simplified model for calculation of
devolatilization in fluidized beds. Fuel 85: 2388-2395.
[4] Kanury A. M. 1972. Rate of burning of wood (A simple thermal model).
Combust Sci Technol 5: 135-146.
[5] Kanury A. M., Holve D. J. 1982. Transient conduction with pyrolysis
(Approximate solutions for charring wood slabs). J Heat Transfer 104:
338-343.
[6] Chen Y., Delichatios M. A., Motevalli V. 1993. Material pyrolysis
properties, Part I: An integral model for one-dimensional transient py-
rolysis of charring and non-charring materials. Combust Sci Technol 88:
309-328.
[7] Moghtaderi B., Novozhilov V., Fletcher D., Kent J. H. 1997. An integral
model for the transient pyrolysis of solid materials. Fire Mater 21: 7-16.
[8] Spearpoint M. J., Quintiere J. G. 2000. Predicting the burning of wood
using an integral model. Combust Flame 123: 308-324.
[9] Galgano A., Di Blasi C. 2003. Modeling wood degradation by the unre-
acted core shrinking approximation. Ind Eng Chem Res 42: 2101-2111.
[10] Galgano A., Di Blasi C. 2004. Modeling the propagation of drying and
decomposition fronts in wood. Combust Flame 139: 16-27.
198
Modeling Combustion of Single Biomass Particle 183
[11] Weng W. G., Hasemi Y., Fan W. C. 2006. Predicting the pyrolysis of
wood considering char oxidation under different ambient oxygen con-
centrations. Combust Flame 145: 723-729.
[12] Jia F., Galea E. R., Patel M. K. 1999. Numerical simulation of the mass
loss process in pyrolizing char materials. Fire Mater 23: 71-78.
[13] Lu H., Robert W., Peirce G., Ripa B., Baxter L. L. 2008. Comprehen-
sive study of biomass particle combustion. Energ Fuels 22: 2826-2839.
[14] Bharadwaj A., Baxter L. L., Robinson A. L. 2004. Effects of
intraparticle heat and mass transfer on biomass devolatilization: experi-
mental results and model predictions. Energ Fuels 18: 1021-1031.
[15] Saastamoinen J., Aho M., Moilanen A., Sørensen L. H., Clausen S.,
Berg M. 2010. Burnout of pulverized biomass particles in large scale
boiler–Single particle model approach. Biomass Bioenerg 34: 728-736.
[16] Goodman T. R. Application of integral method to transient nonlinear
heat transfer. In: Advances in Heat Transfer. Irvine T. F., Hartnelt J. P.
(Eds.), Academic Press: New York, 1964, 51-122.
[17] Galgano A., Di Blasi C. 2005. Infinite versus finite rate kinetics in sim-
plified models of wood pyrolysis. Combust Sci Technol 177: 279-303.
[18] Peters B. 2011. Validation of a numerical approach to model pyrolysis
of biomass and assessment of kinetic Data. Fuel 90: 2301-2314.
[19] Authier O., Ferrer M., Mauviel G., Khalfi A. E., Lede J. 2009. Wood
fast pyrolysis: comparison of Lagrangian and Eulerian modeling ap-
proaches with experimental measurements. Ind Eng Chem Res 48: 4796-
4809.
[20] Sreekanth M., Kolar A. K., Leckner B. 2008. Transient thermal behav-
ior of a cylindrical wood particle during devolatilization in a bubbling
fluidized bed. Fuel Process Technol 89: 838-850.
[21] Di Blasi C. 2000. Modeling the fast pyrolysis of cellulosic particles in
fluid-bed reactors. Chem Eng Sci 55: 5999-6013.
[22] Sadhukhan A. K., Gupta P., Saha R. K. 2008. Modeling and experi-
mental studies on pyrolysis of biomass particles. J Anal Appl Pyrolysis
81: 183-192.
[23] Babu B. V., Chaurasia A. S. 2004. Heat Transfer and kinetics in the py-
rolysis of shrinking biomass particle. Chem Eng Sci 59: 1999-2012.
199
184 Chapter 6
[24] Koufopanos C. A., Papayannakos N., Maschio G., Lucchesi A. 1991.
Modeling of the pyrolysis of biomass particles. Studies on kinetics,
thermal and heat transfer effects. Can J Chem Eng 69: 907-915.
[25] Lu H., Ip E., Scott J., Foster P., Vickers M., Baxter L. L. 2010. Effects
of particle shape and size on devolatilization of biomass particle. Fuel
89: 1156-1168.
[26] Milosavljevic I., Oja V., Suuberg E. M. 1996. Thermal effects in cellu-
lose pyrolysis: relationship to char formation processes. Ind Eng Chem
Res 35: 653-662.
[27] Spearpoint M. J., Quintiere J. G. 2000. Predicting the burning of wood
using an integral model. Combust Flame 123: 308-324.
[28] Grønli M. G., Melaaen M. C. 2000. Mathematical model for wood py-
rolysis-comparison of experimental measurements with model predic-
tions. Energ Fuels 14: 791-800.
[29] Grønli M. G. 1996. A theoretical and experimental study of the thermal
degradation of biomass. PhD Dissertation, Norwegian University of
Science and Technology, Trondheim.
[30] Kashiwagi T., Ohlemiller T. J., Werner K. 1987. Effects of external ra-
diant flux and ambient oxygen concentration on nonflaming gasification
rates and evolved products of white pine. Combust Flame 69: 331-345.
[31] Moghtaderi B., Novozhilov V., Fletcher D., Kent J. H. 1997. A new cor-
relation for bench-scale piloted ignition data of wood. Fire Safety J 29:
41-59.
[32] Yang L., Chen X., Zhou X., Fan W. 2003. The pyrolysis and ignition of
charring materials under an external heat flux. Combust Flame 133:
407-413.
[33] Park W. C., Atreya A., Baum H. R. 2009. Determination of pyrolysis
temperature for charring materials. Proc Combust Inst 32: 2471-2479.
200
Chapter 7
Simplified Char Combustion Model
The content of this chapter is partially from the following paper: Haseli Y., van Oijen J. A., de Goey L. P. H.
2012. A quasi-steady analysis of oxy-fuel combustion of a wood char particle. Combustion Science and
Technology, in press.
7.1 INTRODUCTION
A literature survey reveals that a large number of studies have been carried
out on combustion of char particles. Table 7.1 lists the main features of the
relevant past studies. This table shows that the focus of most previous works
has been on coal char and limited research has been carried out on the exami-
nation of biomass char combustion. Aside from the structural differences be-
tween coal char and biomass (e.g. wood) char, the reactivity of biomass char is
different from that of coal char. Furthermore, the density of the biomass char is
much less than that of coal char. The results of Chapter 3 indicates that the
density of biomass char obtained from a pyrolysis process at high operating
temperatures (e.g. 1450K) varies between 30 kg/m3 and 120 kg/m
3 depending
upon the initial particle size and density. Furthermore, the size of biomass par-
ticles is usually bigger than that of coal particles since it is difficult to mill bi-
omass due to its fibrous structure [50]; which results in particles of 250–1000
µm, considerably larger than pulverized coal particles of around 100 µm. Sec-
tion 7.2 describes a simple model for combustion of a small (< 1mm) size sin-
gle char particle based on the shrinking core approximation. The accuracy of
the model will be examined in Sec. 7.3. The main conclusions will be present-
ed in Sec. 7.4.
201
186 Chapter 7
Table 7.1 Survey of past studies on char combustion.
Researchers/Ref. Char type Approach Remarks
Field/Ref. [1] Low-rank
coal char Experimental
A reaction rate correlation was pro-
posed.
Smith/Ref. [2] Semi-
anthracite Experimental
A reaction rate correlation was pro-
posed.
Hamor et al./Ref.
[3]
Brown coal
char Experimental
A reaction rate correlation was pro-
posed.
Ubhayakar/Ref.
[4] Carbon
Analytical
modeling
The model incorporated quasi-steady
assumption.
Ubhayakar and
Williams/Ref. [5]
Electrode
carbon
Experimen-
men-
tal/Modeling
The model is an extension of
Ubhayakar’s Ref. [13] model. The
experiments were related to the parti-
cle extinction.
Evans and Em-
mons/Ref. [6]
Basswood
char
Theoreti-
cal/Experimen
tal
Correlations for char burning rate and
the molar CO/CO2 ratio were derived.
Libby and
Blake/Ref. [7] Carbon
Theoretical
modeling
Two different treatment were present-
ed: Frozen-flow analysis, and Equi-
librium chemical behavior analysis
Mitchell and
Madsen/Ref. [8]
Bituminous
coal char
Experimen-
men-
tal/Theoretical
Measurements were coupled with a
single-film model and a reaction rate
correlation was proposed for pulver-
ized coal char.
Makino and
Law/Ref. [9] Carbon
Theoretical
analysis
The analysis is a combination of ana-
lytical and numerical treatment. Ex-
plicit relations were given for limiting
cases.
Bar-Ziv et al./Ref.
[10]
Synthetic
char-
Spherocarb
Experimental
The kinetics of oxidation of 140-200
µm particles was studied. The meas-
urements of particle density, diameter
surface area and temperature were
conducted.
Makino/Ref. [11] Coal char
Experimen-
men-
tal/Theoretical
Effects of gas-phase and surface
Damköhler numbers, surface tem-
perature, CO2 mass fraction in the
surrounding on the burning rate were
examined.
Makino and
Law/Ref. [12] Carbon rod
Analytical
modeling
Explicit criteria were established for
ignition and extinction of CO flame
around particle.
Ha and
Yavuzkurt/Ref.
[13]
Coal char 2D numerical
modeling
The effects of high-intensity acoustic
field on combustion of single spheri-
cal particle were studied.
Tognotti et
al./Ref. [14] Spherocarb Experimental
The molar CO2/CO ratio and tem-
perature were measured. Particles
were ignited with laser irradiation.
The CO2/CO ratio was found to be
proportional to the oxygen partial
pressure.
202
Modeling Combustion of Single Biomass Particle 187
Table 7.1 (Continued)
Researchers/Ref. Char type Approach Remarks
Mitchell et
al./Ref. [15] Coal char
Numerical
modeling
The model incorporates elementary,
finite rate chemistry in the gas phase
and at the particle surface. The extent
of conversion of CO to CO2 in the
boundary layer was examined.
Makino/Ref. [16] Carbon Analytical
modeling
Explicit relationship for the combus-
tion rate of particle was derived. Val-
idation was done using the petroleum
coke and coal char.
Dámore et al./Ref.
[17] Spherocarb Experimental
Char oxidation kinetics was obtained
using an electrodynamic balance
(EDB) at various O2 concentrations.
Ha and Choi/Ref.
[18] Coal char
2D numerical
modeling
The effects of entrainment, particle
size, gas velocity, oxygen concentra-
tion in the surrounding, and kinetic
constants on particle combustion were
examined.
Makino et al./Ref.
[19] Graphite rod Experimental
The combustion rate and the tempera-
ture of CO flame establishment were
measured. An earlier model of
Makino [18] was employed for esti-
mation of kinetic parameters.
Lee et al./Ref.
[20] Carbon
Numerical
modeling
The model consists of transient
transport equations coupled with de-
tailed gas-phase reaction and a five-
step heterogeneous surface reaction
mechanisms.
Chelliah et
al./Ref. [21] Graphite rod
Numerical
modeling
Detailed homogenous and semiglobal
heterogeneous reaction mechanisms
were adapted in the simulation.
Chen and Koji-
ma/Ref. [22]
Sunagawa
subbitumi-
nous coal
Experimen-
men-
tal/Numerical
modeling
The model is based on unreacted
shrinking core and quasi-steady as-
sumptions. The effect of ash content
on particle burning was investigated
Lee et al./Ref.
[23] Carbon
Numerical
modeling
An earlier model of Lee et la. [25]
was employed to simulate the com-
bustion experiments of Bar-Ziv et al.
[18] and Tognotti et al. [21].
Zeng and Fu/Ref.
[24] Carbon
Experimen-
men-
tal/Theoretical
A relationship was derived for the
molar ratio of CO/CO2, which was
found to be a function of both oxygen
mass fraction and temperature at the
surface of the particle.
Biggs and
Agarwal/Ref. [25]
Petroleum
coke
Numerical
modeling
The molar ratio CO/CO2 at the sur-
face of 1 and 5 mm particles was
evaluated.
203
188 Chapter 7
Table 7.1 (Continued)
Researchers/Ref. Char type Approach Remarks
Hurt et al./Ref.
[26]
Various coal
chars
Experimen-
men-
tal/Numerical
modeling
High-temperature kinetic data of five
coal chars were measured. A kinetic
model combining the single-film
model, thermal annealing, statistical
kinetics, statistical densities, and ash
inhibition was presented.
Kulasekaran et
al./Ref. [27] Carbon
Numerical
modeling
A single particle model was estab-
lished for combustion of a porous
char by incorporating the features of
single- and double-film models.
Henrich et al./Ref.
[28]
Municipal
waste, elec-
tronic scrap,
wood and
straw chars
Experimental
Reaction rate measurements with O2
and CO2 were carried out at low tem-
peratures using a thermobalance, a
differential flow reactor and a fluid-
ized bed of sands.
Blake/Ref. [29] Carbon Theoretical
Analytical expressions were estab-
lished for particle mass loss rates. The
treatment was presented for frozen
and equilibrium gas phase chemistry.
Meesri and
Moghtaderi/Ref.
[30]
Pine saw-
dust char
Experimen-
men-
tal/Numerical
modeling
Combustion rate, burn-off and tem-
perature of 125 µm particles were
measured using a drop tube furnace.
A 2D model was developed and a re-
action rate correlation was proposed
He et al./Ref. [31]
Yongcheng
and Luo-
yang chars
Theoretical
A simple model was used for predict-
ing of pulverized char particles. An
optimum particle size requiring a
minimum conversion time was
demonstrated.
Bejarano and
Levendis/Ref.
[32]
Bituminous
coal char Experimental
Measurements of particle temperature
and burnout time were conducted at
oxygen-enriched environments in a
drop-tube furnace.
Gupta et al./Ref.
[33]
Carbon and
lignite char
Numerical
modeling
The existence of CO flame beyond a
critical bulk temperature and particle
size, and an optimum particle size
giving a minimum burnout time were
demonstrated.
Makino and
Umehara/Ref.
[34]
Graphite
Experimen-
men-
tal/Theoretical
Measurements of combustion rates
were conducted to investigate the ef-
fects of water vapor content in air.
Cano et al./Ref.
[35]
Sewage
sludge char
Numerical
modeling
A model was developed for fluidized
bed combustion of single particle
fuels characterized by coherent ash
skeletons.
Higuera/Ref. [36] Coal char Numerical
modeling
Burning rate, surface temperature,
drag and extinction conditions of a
particle moving in a gas were studied.
204
Modeling Combustion of Single Biomass Particle 189
Table 7.1 (Continued)
Researchers/Ref. Char type Approach Remarks
Kaushal et al./Ref.
[37]
Biomass
char
Numerical
modeling
A 1-D model for steady-state com-
bustion and gasification of biomass
char in a fast fluidized bed was de-
veloped.
Manovic et
al./Ref. [38]
Lignite and
Brown coal
chars
Experimen-
men-
tal/Numerical
modeling
A 1-D model was developed to pre-
dict measured temperature history of
large particles (5-10 mm)in fluidized
bed
Makino and
Law/Ref. [39] Carbon
Numerical
modeling
The model is an extended version of
the earlier formulations given in Ref.
[21, 37], which accounts for three sur-
face and two gas phase reactions.
Stauch and
Maas/Ref. [40] Graphite
Numerical
modeling
The model is based on detailed gas
phase reactions and surface reactions
mechanisms. Two different surface
reaction mechanisms were examined.
Sadhukhan et
al./Ref. [41]
Sub-
bituminous
Coal char
Experimen-
men-
tal/Theoretical
analysis
The BET surface area, micropore sur-
face area and porosity were deter-
mined at various burn-off levels.
Random pore model was applied to fit
experimental data.
Sadhukhan et
al./Ref. [42] Coal char
Numerical
modeling
A 1-D model was developed to study
the conversion of large particles (3
mm) at elevated pressures.
Scala and
Chirone/Ref. [43]
Snibston
bituminous
coal char
Experimental
Combustion rates of large particles
(6-7 mm) and CO and O2 concentra-
tions were measured in O2/CO2 mix-
tures with low O2 concentrations (<
10 %)
Scala/Ref. [44] Carbon Theoretical
analysis
Analytical solution was given to the
set of Stefan-Maxwell equations with
the assumption of negligible gas
phase reaction in the boundary layer.
Brix et al./Ref.
[45] Coal char
Experimen-
men-
tal/Numerical
modeling
Experiments were carried out in
O2/N2 and O2/CO2 mixtures using an
entrained flow reactor at temperatures
up to 1673K and O2 concentration up
to 28%. A detailed model was devel-
oped to capture the experiments.
Fei et al./Ref. [46] Coal char
Experimen-
men-
tal/Theoretical
analysis
TGA experiments were conducted in
the mixture of O2/CO2. The combus-
tion of char was investigated using a
two-stage random pore model.
Hecht et al./Ref.
[47]
Bituminous
Coal char
Numerical
modeling
Oxy-fuel combustion was studied by
accounting for detailed surface reac-
tion. The results of complete chemis-
try of the gas phase and single-film
model were compared
205
190 Chapter 7
Table 7.1 (Continued)
Researchers/Ref. Char type Approach Remarks
Rangel and
Pinho/Ref. [48]
Nut pine
and cork
oak wood
chars
Experimen-
men-
tal/Theoretical
analysis
Combustion of batches of wood char
was studied in a lab scale fluidized
bed. A simple model was used to as-
sess kinetics of the combustion.
Chern and
Hayhurst/Ref.
[49]
Coal char Experimental
Measurements of 13-14 mm coal par-
ticle devolatilization and char residue
combustion were conducted.
7.2 MODELING APPROACH
The problem of interest is the transient combustion of a spherical wood
char particle having initial temperature T0 and diameter d0, which is suddenly
exposed to a hot environment with temperature T∞. The surrounding fluid is
assumed to consist of oxygen, nitrogen and carbon dioxide with mass fractions
YO2,∞, YN2,∞, and YCO2,∞, respectively. Under these conditions, the most relevant
heterogeneous reactions include oxidation of char to produce CO and CO2, and
char gasification with CO2 to yield additional CO.
( ) ( )22
1212 COCOOC −+−→+ ννν (7.1)
COCOC 22
→+ (7.2)
The carbon monoxide produced due to the heterogeneous reactions (7.1)
and (7.2) may react with the oxygen in the gas phase outside of the particle to
produce additional carbon dioxide.
222
1COOCO →+ (7.3)
It is however a subject of debate whether reaction (7.3) occurs within or
outside of the gaseous boundary layer around the particle. In accordance with
the arguments provided by Ubhayakar [4], Mitchell et al. [15], Bejarano and
Levendis [32], Rangel and Pinho [48], Chern and Hayhurst [49], Hayhurst
206
Modeling Combustion of Single Biomass Particle 191
[51], Huang and Scaroni [52], it will be assumed that the carbon monoxide
formed at the particle surface diffuses through the boundary layer around the
particle and reacts with oxygen in the gaseous stream sufficiently far from the
particle.
In the experimental study of Ubhayakar and Williams [5], electrode carbon
particles (50-200 µm) were ignited by a laser and dropped (with falling veloci-
ty in the range 5-50 cm/s in quiescent mixtures of O2 and N2 maintained at
room temperature. They observed that the burning zone was restricted to the
particle surface, implying that no gas-phase reaction between CO and O2 took
place outside the particle. Huang et al. [53] reported that no intensive exo-
thermic reaction was observed in the boundary layer of a burning char particle
and concluded the absence of CO oxidation. In a numerical study by Gupta et
al. [33], it was demonstrated that depending on particle size and surrounding
temperature, a CO flame sheet could exist surrounding a lignite char particle.
For instance, they showed that at a bulk temperature of 1173K, the homogene-
ous reaction (7.3) would be suppressed for a particle size less than 850 µm.
In the case of combustion of a motionless particle in a quiescent atmos-
phere, Makino and Law [12, 39] developed a criterion for the existence of a
CO flame sheet (see Appendix B). For a given set of physicochemical parame-
ters and process conditions, the theory allows one to determine the critical par-
ticle diameter beyond which the CO flame exists outside a burning char parti-
cle. For instance, Makino and Law [39] showed that for a coal char particle
burning in air maintained at 1300K, the critical diameter would be 600 µm.
Makino and Law’s theory is employed to determine the critical size of a
wood char particle burning in air. According to the Makino and Law ignition
criterion [12], the critical particle diameter is found to be 720 µm and 500 µm
at a surrounding temperature of 1273 K and 1473 K, respectively. The theory
also predicts a critical diameter of 240 µm for a wood char particle burning in
pure oxygen maintained at 1273 K. As a conclusion, the ignition criterion of
Makino and Law [12] suggests that for pulverized fuels combusting in en-
trained-flow reactors where the fluid flow regime can be treated as a quiescent
atmosphere the gas-phase reaction between CO and O2 is suppressed in the
boundary layer. Thus, the analysis of this chapter does not account for any re-
action between CO and O2 in the gas phase around the particle.
The formulation of the particle burning rate is based on the traditional
shrinking core approximation. This means that during the char conversion pro-
207
192 Chapter 7
cess reactions (7.1) and (7.2) occur at the surface of the particle forming a re-
action front which moves towards the particle center as the combustion pro-
cess continues, thereby resulting in a decreasing particle size while its internal
density remains unaltered throughout the conversion process. The conservation
of particle mass can therefore be represented as follows.
( )21
24 rrRdt
dmc
c+−= π (7.4)
where mc denotes the mass of particle, Rc represents the particle radius at a
given instant t, r1 and r2 are the rates of surface reactions (7.1) and (7.2).
Using the relationship mc = ρcVc, Eq. (7.4) can be rearranged to give the
time evolution of the particle radius. Hence,
( )21
1rr
dt
dR
c
c+−=
ρ (7.5)
where ρc is the char density.
The rates of surface reactions (7.1) and (7.2) are described by an Arrhenius
law as follows.
2,1exp , =
−= iP
TR
EAr in
si
sg
i
ii (7.6)
The molar ratio of CO/CO2 in reaction (7.1) depends on the temperature
through an Arrhenius-type equation as follows [6, 14, 25].
−=
sg
COCO
COCOTR
EA
CO
CO2
2
/
/
2
exp (7.7)
In Eqs. (7.6) and (7.7), A is the pre-exponential factor, E the activation energy,
R the universal gas constant, and Ts the particle surface temperature, n the re-
208
Modeling Combustion of Single Biomass Particle 193
action order, and Ps the partial pressure of the gasifying agent (i.e. O2 , CO2)
at the particle surface.
A necessary step when modeling burning of a char particle is to select ap-
propriate kinetic constants (i.e. A, E and n). A wide range of data has been
proposed by various past researchers for both char oxidation and char gasifica-
tion reactions (see Table 7.2 and Table 7.3). A careful review of these data in-
dicates that they are material dependent. Of course, experimental conditions
could also lead to the discrepancies between various sets of kinetic data. It can
be inferred from Table 7.2 and Table 7.3 that unlike coal char, limited studies
have dealt with determination of the kinetics of biomass char oxidation and
gasification.
The partial pressures of O2 and CO2 at the surface of particle need to be de-
termined for calculation of the surface reaction rates. Using a quasi-steady as-
sumption, the conservation of mass of O2 and CO2 yields
( ) ( )121
2
2222r
M
MYrrYYk
c
O
sOsOOO,dgνρ =+−−
∞ (7.8)
( ) ( ) ( )[ ]1221
122
2222rr
M
MYrrYYk
c
CO
sCOsCOCOCO,dg−−=+−−
∞νρ (7.9)
where ρg is the gas density, kd the mass transfer coefficient, Y the mass frac-
tion, and M the molecular weight. The first terms on the left hand side of Eqs.
(7.8) and (7.9) represent the mass flux due to the diffusion through the bounda-
ry layer around the particle. The second terms on the left hand side of these
equations denote the mass flux due to the convective flow of gaseous species
leaving the particle. The terms on the right hand side of Eqs. (7.8) and (7.9)
represent the net mass flux consumption due to the surface reactions.
The corresponding partial pressures are determined from
sOg
O
g
O,sYP
M
MP
2
2
2= (7.10)
209
194 Chapter 7
Table 7.2 Char oxidation kinetic data reported in the literature.
Char type
Pre-
exponential
factor
kg.m-2
.s-
1.atm
-n
Activation
energy
kJ.kmol-1
Reaction or-
der, n Source
Coal char 87100 149450 1 Ref. [1]
Semi-anthracite char 204 79540 1 Ref. [2]
Brown coal char 93 67820 0.5 Ref. [3]
Basswood char 254 74830 1 Ref. [6]
Bituminous coal char 284 83730 0.5 Ref. [8]
Pine sawdust char 25 ± 44 69200 ±
14000 0.4 Ref. [30]
Wide range of carbons 3050 179400 0 Ref. [54]
Petroleum coke 70 82470 0.5 Ref. [55]
Swelling bituminous coal char 6358 142330 1 Ref. [55]
Swelling bituminous coal char 1113 100890 1 Ref. [55]
Non-swelling sub-bituminous
coal char 156 73260 0.5 Ref. [55]
Non-swelling sub-bituminous
coal char 703 90000 1 Ref. [55]
Non-swelling sub-bituminous
coal char 504 74100 1 Ref. [55]
Swelling sub-bituminous coal
char 41870 142330 0.17 Ref. [55]
Swelling sub-bituminous coal
char 63370 142750 0.17 Ref. [55]
Bituminous coal char 0.0821 18500 0.5 Ref. [55]
Sub-bituminous coal char 0.244 36660 0.5 Ref. [56]
Sub-bituminous coal char 9.2 71180 0.5 Ref. [56]
Beech wood char 0.0856 16600 0.5 Ref. [56]
Sewage sludge char 0.126 29800 0.5 Ref. [56]
Sub-bituminous C coal char 1450 83600 1 Ref. [57]
332 95300 1 This study*
High volatile C bituminous coal
char
600 71800 1 Ref. [57]
382 70180 1 This study*
High volatile A bituminous coal
char
660 85230 1 Ref. [57]
941 98480 1 This study*
Texas lignite char 460 86815 1 Ref. [58]**
Montana subbituminous coal char 421 109545 1 Ref. [58]**
Alabama high volatile bituminous
coal char 644 96168 1 Ref. [58]**
Pennsylvania anthracite char 40 74820 1 Ref. [58]**
Biomass char 465 68000 0 Ref. [59]
* Kinetic data are obtained by analyzing all data given in Ref. [57]; see Appendix C.
** Two sets of kinetic constants were obtained by Nasakala et al. [58] using measured
gas temperature (Method 1) and calculated particle surface temperature (Method 2).
The kinetic constants given here are the average of the values corresponding to Meth-
od 1 and Method 2.
210
Modeling Combustion of Single Biomass Particle 195
Table 7.3 Char gasification kinetic data reported in the literature.
Char type
Pre-
exponential
factor
kg.m-2
.s-1
.atm-n
Activation
energy
kJ.kmol-1
Reaction
order, n Source
Coal char 2470 175090 1 Ref. [7]
Non-porous graphite 9000 285100 1 Ref. [21]
Sub-bituminous C coal char 10400 177800 1 Ref. [57]
610 154680 1 This study*
High volatile C bituminous coal char 129500 235940 1 Ref. [57]
362 165050 1 This study*
High volatile A bituminous coal char 13900 224800 1 Ref. [57]
337 178960 1 This study*
Lignite A char 6600 165320 1 Ref. [57]
42160 197790 1 This study*
* Kinetic data are obtained by analyzing all data given in Ref. [57]; see Appendix C.
sCOg
CO
g
CO,sYP
M
MP
2
2
2= (7.11)
Likewise, the conservation of CO at the particle surface reads
( ) ( ) ( )[ ]2121
212 rrM
MYrrYYk
c
CO
COsCOCOsCO,dg+−=++−
∞νρ (7.12)
The mass fraction of nitrogen is therefore found from
COssCOsOsNYYYY −−−=
2221 (7.13)
The temperature history of the particle is obtained from conservation of
energy by assuming a uniform temperature inside the particle during the con-
version process [39, 60], as the focus of this chapter is on small size particles
(< 1mm). The net heat flux at the particle surface is the sum of convective and
radiant heat transfer between particle and the surrounding, exothermic char ox-
idation heat, and endothermic char gasification heat. Thus, the net change in
the enthalpy of particle per unit external surface area is equal to the net heat
flux at the surface. Hence,
211
196 Chapter 7
( ) ( ) ( )GasifCombcc
c
pccchrhrTTTTh
dt
dTcR ∆+∆+−+−=
∞∞ 21
44
3
1σερ (7.14)
where cpc is the char specific heat, h the convective heat transfer coefficient be-
tween particle and the surrounding fluid, σ the Stephan-Boltzmann constant, ε
the emissivity, ∆hCom the specific enthalpy of char oxidation reaction, and
∆hGasif the specific enthalpy of char gasification reaction.
Equations (7.5)-(7.14) form a system of eight algebraic and two differen-
tial equations which need to be solved simultaneously for computation of dy-
namic of particle combustion.
The heat and mass transfer coefficients are calculated using the following
well-established correlations for a spherical particle.
+= 3
1
2
1
6022
PrRe.R
hc
gλ
(7.15)
2223
1
2
1
6022
N,CO,COOiScRe.R
Dk
,
c
i
i,d=
+= (7.16)
where λg is the thermal conductivity of the gas, Re the Reynolds number, Pr
the Prandtl number, Sc the Schmidt number, and Di the effective binary diffu-
sion coefficient of species i defined as [61]
∑≠
−=
ij
ijj
i
iD/X
XD
1 (7.17)
where Xi is the mole fraction of species i and Dij denotes the binary diffusion
coefficient to be obtained from [61],
Dij
.
ij
.
ijPM
T.D
Ω=
250
5102660
σ (7.18)
212
Modeling Combustion of Single Biomass Particle 197
1
112
−
+=
ji
ijMM
M (7.19)
2
ji
ij
σσσ
+= (7.20)
( ) ( ) ( )
( )*
**.*D
T.exp
.
T.exp
.
T.exp
.
T
.
894113
764741
529961
035871
476350
193000060361156100
+++=Ω
(7.21)
ji
B* TkT
εε= (7.22)
where σij represents the collision diameter, ΩD is the collision integral, kB and ε
stand for the Boltzmann constant and the characteristic Lennard-Jones energy,
respectively.
As the present study deals with four gaseous substances O2, CO2, CO and
N2, simple relationships are derived for binary diffusion of six molecular pairs
using Eqs. (7.18)-(7.22) as functions of temperature (in Kelvin) and pressure
(in Pascal).
[ ]s/mP
TCD
C
ij
2
1
2
= (7.23)
where the constants C1 and C2 are given in Table 7.4.
Additional thermo-physical properties required for calculation of Reynolds
(=2RcρV/µ), Prandtl (=cpµ/k), and Schmidt (=µ/ρD) numbers are the gaseous
mixture density, thermal conductivity, viscosity and specific heat. Hence,
RT
MPgg
g=ρ (7.24)
222222 NsNCOCOsCOsCOOsOgYYYY λλλλλ +++= (7.25)
213
198 Chapter 7
Table 7.4 Coefficients of Eq. (7.23) for six molecular pairs considered in this study.
Molecular pair C1 C2
O2–N2 0.0001630 1.664
CO2–N2 0.0001175 1.676
CO–N2 0.0001627 1.663
O2–CO2 0.0001099 1.688
O2–CO 0.0001599 1.669
CO2–CO 0.0001128 1.683
222222 NsNCOCOsCOsCOOsOgYYYY µµµµµ +++= (7.26)
222222 N,psNCO,pCOsCO,psCOO,psOpgcYcYcYcYc +++= (7.27)
The molecular weight of the gaseous mixture is obtained from
1
2
2
2
2
2
2
−
+++=
N
sN
CO
COs
CO
sCO
O
sO
gM
Y
M
Y
M
Y
M
YM (7.28)
The thermal conductivity, viscosity and specific heat of individual gaseous
species are obtained from NIST data [62], which allowed derivation of appro-
priate correlations as given in Table 7.5. Lastly, the specific heat of char is de-
termined using the correlation given in Table 3.1.
Table 7.5 Correlations of thermo-physical properties obtained from NIST data [62].
Substance Thermal conductivity
(W/m.K)
Viscosity
(kg/m.s)
Specific heat
(J/kg.K)
Oxygen 915.04 T10− 704.07 T1081.3 −
× T2.09.852 +
Carbon dioxide 162.15 T102 −
× 794.07 T1072.1 −
× T4.02.794 +
Carbon monoxide 761.04 T103 −
× 714.07 T1003.3 −
× T1.08.1006 +
Nitrogen 778.04 T103 −
× 664.07 T102.4 −
× T2.08.996 +
214
Modeling Combustion of Single Biomass Particle 199
7.3 MODEL VALIDATION
Validation of the model is carried out by comparing its predictions against
computations of a detailed numerical model and experimental data found from
the literature. Figure 7.1 compares the predictions of the model with the out-
come of a detailed model presented by Ha and Choi [18]. The simulation is
performed for a carbon particle with a density of 1500 kg/m3 and initial diame-
ter of 100 µm and 150 µm in a quiescent environment consisting of an O2/N2
mixture with a surrounding temperature of 1500 K at an O2 mass fraction of
0.2. The kinetic data of char oxidation and gasification given in Refs. [2] and
[7], respectively (see Tables 7.2 and 7.3), which were used by Ha and Choi
[18], are also employed in the simulation. The discrepancy between the results
of two models is due to the different heat transfer coefficients considered in
this study and in Ref. [18]. Considering the simplicity of the presented zero-
dimensional model compared to the detailed 2-D model of Ha and Choi [18],
the agreement between these two models is fairly good.
(a) (b)
Figure 7.1 Comparison between the predictions of the models of this chapter and Ha
and Choi [18]; a) particle temperature history; b) particle size history (surrounding flu-
id: O2/N2 mixture, R0 = 50 µm, T∞ = 1500 K).
215
200 Chapter 7
Figure 7.2 Comparison between the predictions and the experiments of Mulchay and
Smith [63]; Variation of burnout time with initial particle diameter in pure oxygen.
The accuracy of the model is further examined by comparing the predic-
tions with the experiments of Mulcahy and Smith [63] who measured the
burnout time of a wide variety of carbon particles (e.g. electrode carbon, bitu-
minous coal char, graphite) burning in pure oxygen. The comparison between
the prediction and data is depicted in Fig. 7.2. The region enclosed with the
dashed lines is the range of experimental data. The main reason for the wide
scatter of the measured data is believed to be due to the different reactivity of
chars of different materials. It can be seen that the predicted burnout time ver-
sus particle initial diameter is within the range of the measured values.
Overall, the above validations reveal the sufficient accuracy of the present-
ed model. Although the validation cases are related to the coal char particles
while the focus of the present study has been on biomass char particles com-
bustion, the attempt to find suitable experimental data related to the combus-
tion of biomass char particles has not been successful. The key differences be-
tween these two types of char, as mentioned earlier, are their different
reactivity (implying that one would have to use an appropriate set of kinetic
data) and thermo-physical properties, which can be accordingly taken into ac-
count in the present formulation.
216
Modeling Combustion of Single Biomass Particle 201
Figure 7.3 Effect of four different char oxidation kinetic constants on temperature his-
tory of a particle burning in air (R0 = 200 µm; ρc = 60 kg/m3; T0 = 600 K; T∞ = 1373
K).
To highlight the effect of char oxidation kinetic parameters, an illustrative
comparison is made between the predicted particle temperatures using Evans
and Emmons [6] data related to Basswood char, and three other sets of kinetic
constants of coal char oxidation given by Goetz et al. [57], Smith [2] and Field
et al. [1], as shown in Fig. 7.3. The kinetic constants of Evans and Emmons [6]
and Goetz et al. [57] provide approximately the same temperature history even
though different char types were examined by these two research teams. The
highest temperature and the shortest combustion duration are obtained using
the data of Field et al. [1], whereas the lowest temperature and the longest
conversion time are resulted using the kinetic parameters of Smith [2].
Furthermore, the effect of char gasification kinetic data was also examined
by comparing the predicted mass loss histories obtained using the data report-
ed by Goetz et al. [57] (for a lignite char) and Dobner as given in Ref. [7] (for
a coal char). In both cases, the temperature rapidly increased up to around the
surrounding temperature and remained at this level until the end of process.
The conversion time (the time at which 99.5% mass is burnt) was about 5.2
217
202 Chapter 7
sec using the data of Goetz et al., whereas the data of Dobner led to a conver-
sion time of 29.5 sec. The calculations were performed for the same conditions
of Fig. 7.4 in a CO2/N2 mixture with CO2 mass fraction of 0.7. The substantial
difference in burnout time in two cases is due to different reactivity of lignite
char and coal char under identical gasification conditions. A further likely rea-
son is that the data of Goetz et al. [57] implicitly include the effects of pore
diffusion.
7.4 CONCLUSION
A simple zero-dimensional model is presented for simulating combustion
of a small size single char particle. The model is based on the traditional
shrinking core approximation and the assumption of uniform temperature in-
side the particle throughout the process. The model is validated against com-
putations of a detailed 2-D model and experimental data taken from past stud-
ies. It is demonstrated that the model is capable of capturing particle
temperature and conversion with reasonable accuracy. Furthermore, it is noted
that the kinetic data of char oxidation and gasification play an important role
when modeling the combustion dynamic of a burning particle. The model pre-
sented in this chapter will be used in a simplified combustion model of a bio-
mass particle (Chapter 8), and investigating the burning characteristics of sin-
gle biomass char particle combusting under oxy-fuel conditions (Chapter 9).
RERERENCES
[1] Field M. A. 1969. Rate of combustion of size-graded fractions of char
from a low-rank coal between 1200K and 2000K. Combust Flame 13:
237-252.
[2] Smith I. W. 1971. The kinetics of combustion of pulverized semi-
anthracite in the temperature range 1400-2200 K. Combust Flame 17:
421-428.
[3] Hamor R. J., Smith I. W., Tyler R. J. 1973. Kinetics of combustion of
pulverized Brown coal char between 630 and 2200 K. Combust Flame
21: 153-162.
218
Modeling Combustion of Single Biomass Particle 203
[4] Ubhayakar S. K. 1976. Burning characteristics of a spherical particle re-
acting with ambient oxidizing gas at its surface. Combust Flame 26: 23-
34.
[5] Ubhayakar S. K., Williams F. A. 1976. Burning and extinction of a la-
ser-ignited carbon particle in quiescent mixtures of oxygen and nitrogen.
J Electrochem Soc 123: 747-756.
[6] Evans D. D., Emmons H. W. 1977. Combustion of wood charcoal. Fire
Res 1: 57-66.
[7] Libby P. A., Blake T. R. 1979. Theoretical study of burning carbon par-
ticle. Combust Flame 36: 139-169.
[8] Mitchell R. E., Madsen O. H. 1988. Experimentally determined overall
burning rates of pulverized-coal chars in specified O2 and CO2 environ-
ments. Proc Combust Inst 21: 173-181.
[9] Makino A., Law C. K. 1988. Quasi-steady and transient combustion of a
carbon particle: theory and experimental comparison. Proc Combust
Inst 21: 183-191.
[10] Bar-Ziz E., Jones D. B., Spjut R. E. 1989. Measurment of combustion
kinetics of single char particle in an electrodynamic thermogravimetric
analyzer. Combust Flame 75: 81-106.
[11] Makino A. 1990. A theoretical and experimental study of carbon com-
bustion in stagnation flow. Combust Flame 81: 166-187.
[12] Makino A., Law C. K. 1990. Ignition and extinction of CO flame over a
carbon rod. Combust Sci Technol 73: 589-615.
[13] Ha M. Y., Yavuzkurt S. 1991. Combustion of single carbon or char par-
ticle in the presence of high-intensity acoustic fields. Combust Flame
86: 33-46.
[14] Tognotti L., Longwell J. P., Sarofim A. F. 1991. The products of the
high temperature oxidation of a single char particle in an electrodynamic
balance. Proc Combust Inst 23: 1207-1213.
[15] Mitchell R. E., Kee R. J., Glarborg P., Coltrin M. E. 1991. The effect of
CO conversion in the boundary layers surrounding pulverized-coal char
particles. Proc Combust Inst 23: 1169-1176.
[16] Makino A. 1992. An approximate explicit expression for the combus-
tion rate of a small carbon particle. Combust Flame 90: 143-154.
219
204 Chapter 7
[17] D’more M., Tognotti L., Sarofim A. F. 1993. Oxidation rates of a single
char particle in an electrodynamic balance. Combust Flame 95: 374-
382.
[18] Ha M. Y., Choi B. R. 1994. A numerical study on the combustion of a
single carbon particle entrained in a steady flow. Combust Flame 97: 1-
16.
[19] Makino A., Araki N., Mihara Y., Combustion of artificial graphite in
stagnation flow: estimation of global kinetic parameters from experi-
mental results. Combust Flame 96: 261-274.
[20] Lee J. C., Yetter R. A., Dryer F. L. 1995. Transient numerical modeling
of carbon particle ignition and oxidation. Combust Flame 101: 387-398.
[21] Chelliah H. K., Makino A., Kato I., Araki N., Law C. K. 1996. Model-
ing of graphite oxidation in a stagnation-point flow field using detailed
homogeneous and semiglobal heterogeneous mechanisms with compari-
sons with experiments. Combust Flame 104: 469-480.
[22] Chen C., Kojima T. 1996. Single char particle combustion at moderate
temperature: effects of ash. Fuel Proc Technol 47: 215-232.
[23] Lee J. C., Yetter R. A., Dryer F. L. 1996. Numerical simulation of laser
ignition of an isolated carbon particle in quiescent environment. Com-
bust Flame 105: 591-599.
[24] Zeng T., Fu W. B. 1996. The ratio of CO/CO2 of oxidation on a burning
carbon surface. Combust Flame 107: 197-210.
[25] Biggs M. J., Agarwal P. K. 1997. The CO/CO2 product ratio for a po-
rous char particle within an incipiently fluidized bed: a numerical study.
Chem Eng Sci 52: 941-952.
[26] Hurt R., Sun J-K, Lunden M. 1998. A kinetic model of carbon burnout
in pulverized coal combustion. Combust Flame 113: 181-197.
[27] Kulasekaran S., Linjewile T. M., Agarwal P. K., Biggs M. J. 1998.
Combustion of a porous char particle in an incipiently fluidized bed.
Fuel 77: 1549-1560.
[28] Henrich E., Bürkle S., Meza-Renken Z. I., Rumple S. 1999. Combustion
and gasification kinetics of pyrolysis chars afrom waste and biomass. J
Anal Appl Pyrolysis 49: 221-241.
[29] Blake T. R. 2002. Low Reynolds number combustion of a spherical car-
bon particle. Combust Flame 129: 87-111.
220
Modeling Combustion of Single Biomass Particle 205
[30] Meesri C., Moghtaderi B. 2003. Experimental and numerical analysis of
sawdust char combustion reactivity in a drop tube reactor. Combust Sci
Technol 175: 793-823.
[31] He R., Suda T., Fujimori T., Sato J. 2003. Effects of particle sizes on
transport phenomena in single char combustion. Int J Heat Mass Transf
46: 3619-3627.
[32] Bejarano P. A., Levendis Y. A. 2007. Combustion of coal chars in oxy-
gen-enriched atmospheres. Combust Sci Technol 179: 1569-1587.
[33] Gupta P., Sadhukhan A. K., Saha R. K. 2007. Analysis of the combus-
tion reaction of casrbon and lignite char with ignition and extinction
phenomena: shrinking sphere model. Int J Chem Kinet 39: 307-319.
[34] Makino A., Umehara N. 2007. Combustion rates of graphite rods in the
forward stagnation field of the high-temperature, humid airflow. Proc
Combust Inst 31: 1873-1880.
[35] Cano G., Salatino P., Scala F. 2007. A single particle model of the fluid-
ized bed combustion of a char particle with coherent ash skeleton: ap-
plication to granulated sewage sludge. Fuel Proc Technol 88: 577-584.
[36] Higuera F. J. 2008. Combustion of a coal char particle in a stream of dry
gas. Combust Flame 152: 230-244.
[37] Kaushal P., Proll T., Hofbauer H. 2008. Model for biomass char com-
bustion in the riser of a dual fluidized bed gasification unit: Part 1-
model development and sensitivity analysis. Fuel Proc Technol 89: 651-
659.
[38] Manovic V., Komatina M., Oka S. 2008. Modeling the temperature in
coal char particle during fluidized bed combustion. Fuel 87: 905-914.
[39] Makino A., Law C. K. 2009. An analysis of the transient combustion
and burnout time of carbon particles. Proc Combust Inst 32: 2067-2074.
[40] Stauch R., Maas U. 2009. Transient detailed numerical simulation of the
combustion of carbon particles. Int J Heat Mass Transf 52: 4584-4591.
[41] Sadhukhan A. K., Gupta P., Saha R. 2009. Characterization of porous
structure of coal char from a single devolatilized coal particle: coal
combustion in a fluidized bed. Fuel Proc Technol 90: 692-700.
[42] Sadhukhan A. K., Gupta P., Saha R. 2010. Modelling of combustion
characteristics of high ash coal char particles at high pressure: shrinking
reactive core model. Fuel 89: 162-169.
221
206 Chapter 7
[43] Scala F., Chirone R. 2010. Combustion of single coal char particles un-
der fluidized bed oxyfiring conditions. Ind Eng Chem Res 49: 11029-
11036.
[44] Scala F. 2010. Calculation of the mass transfer coefficient for the com-
bustion of a carbon particle. Combust Flame 157: 137-142.
[45] Brix J., Jensen P. A., Jensen A. D. 2011. Modeling char conversion un-
der suspension fired conditions in O2/N2 and O2/CO2 atmospheres. Fuel
90: 2224-2239.
[46] Fei H., Sun L., Hu S., Xiang J., Song Y., Wang B., Chen G. 2011. The
combustion reactivity of coal chars in oxyfuel atmosphere: comparison
of different random pore models. J Anal Appl Pyrolysis 91: 251-256.
[47] Hecht E. S., Shaddix C. R., Molina A., Haynes B. S. 2011. Effect of
CO2 gasification reaction on oxy-combustion of pulverized coal char.
Proc Combust Inst 33: 1699-1706.
[48] Rangel N., Pinho C. 2011. Kinetic and diffusive data from batch com-
bustion of wood chars in fluidized bed. Biomass Bioenerg 35: 4124-
4133.
[49] Chern J-S., Hayhurst A. N. 2012. Fluidised bed studies of: (i) reaction-
fronts inside a coal particle during its pyrolysis or devolatilisation, (ii)
the combustion of carbon in various coal chars. Combust Flame 159:
367-375.
[50] Gubba S.R., Ma L., Pourkashanian M., Williams A. 2011. Influence of
particle shape and internal thermal gradients of biomass particles on
pulverised coal/biomass co-fired flames. Fuel Proc Technol 92: 2185-
2195.
[51] Hayhurst A. N. 1991. Does carbon monoxide burn inside a fluidized
bed? A new model for the combustion of coal char particles in fluidized
beds. Combust Flame 85: 155-168.
[52] Huang G., Scaroni A. W. 1992. Prediction and measurement of the
combustion time of single coal particles. Fuel 71: 159-164.
[53] Huang G., Vastola F. J., Scaroni A. W. 1988. Temperature gradients in
the gas phase surrounding pyrolyzing and burning coal particles. Energ
Fuels 2: 385-390.
[54] Smith I. W. 1978. The intrinsic reactivity of carbons to oxygen. Fuel 57:
409-414.
222
Modeling Combustion of Single Biomass Particle 207
[55] Smith I. W. 1982. The combustion rates of coal chars: a review. Proc
Combust Inst 19: 1045-1065.
[56] Winter F., Prah M. E., Hofbauer H. 1997. Temperatures in a fuel parti-
cle in a fluidized bed: the effect of drying, devolatilization, and char
combustion. Combust Flame 108: 302-314.
[57] Goetz G. J., Nsakala N. Y., Patel R. L., Lao T. C. 1982. Combustion and
Gasification Characteristics of Chars from Four Commercially Signifi-
cant Coals of Different Rank. Report No. EPRI-AP-2601, Electric Pow-
er Research Institute.
[58] Nsakala N. Y., Goetz G. J., Patel R. L., Lao T. C. 1985. Pyrolysis and
combustion characterization of pulverized coals for industrial applica-
tions. Am Chem Soc 30: 221-230.
[59] Saastamoinen J. J., Aho M. J., Linna V. L. 1993. Simultaneous pyrolysis
and char combustion. Fuel 72: 599-609.
[60] Law C. K., Sirignano W. A. 1977. Unsteady droplet combustion with
droplet heating–II: combustion limit. Combust Flame 28: 175-186.
[61] Turns S. R. 2011. An Introduction to Combustion: Concepts and Appli-
cations. McGraw-Hill, USA.
[62] National Institute of Standards and Technology (NIST) Chemistry
WebBook. Available from: http://www.webbook.nist.gov/chemistry/.
[63] Mulcahy M. F. R., Smith I. W. 1969. Rev Pure Appl Chem 19: 81-108.
223
208 Chapter 7
224
Chapter 8
Simplified Biomass Combustion Model
8.1 INTRODUCTION
The primary aim of the present chapter is to establish a reduced but effi-
cient mathematical model for predicting the main characteristics of combus-
tion of a single biomass particle at the conditions of biomass combustors,
where particles in the order of less than millimeter undergo a complete ther-
mo-chemical conversion process. Experimental observations [1, 2] indicate
that the combustion of small size biomass particles (< 1mm) at high tempera-
tures (> 1100 K) consists of three main stages including heating up, pyrolysis
and char oxidation and gasification. Figure 8.1 depicts the trends of mass loss
and temperature histories of a dry biomass particle during the above three dis-
tinguished conversion stages. Of course, depending upon process conditions,
the pyrolysis and the char consumption phases may partly overlap.
The various stages of a combusting spherical particle with initial radius of
R are schematically illustrated in Fig. 8.2. The particle initially at temperature
T0 is suddenly exposed to a hot oxidative environment characterized with tem-
perature T∞ and a given oxygen fraction in the surrounding fluid passing over
the particle. The problem is assumed to be described only with a radial coordi-
nate. As first stage of the particle conversion, heat is transferred from the sur-
rounding to the surface of the particle via convection and radiation mecha-
225
210 Chapter 8
nisms. The heating up process continues until the particle temperature reaches
a certain level beyond which the virgin biomass begins to decompose to vola-
tiles and char residue. At this stage, a thin char layer is formed at the exterior
surface of the virgin material.
Upon generation of the volatiles, they move through the pores of the solid
matrix towards the particle surface where they leave the particle behind. This
flow of the volatiles escaping from the surface of the particle causes a re-
sistance against the diffusion of the surrounding oxygen to reach the particle
surface and to react with the char formed during the pyrolysis process. The
amount of oxygen mass transfer from the surrounding to the surface of the par-
ticle depends on factors such as its concentration in the surrounding stream,
the mass flux of the volatiles leaving the particle, the Reynolds number repre-
senting the flow regime around the particle, and the rate of combustion of vol-
atiles with oxygen. Thus, oxidation of char may or may not take place simulta-
neously with pyrolysis. After all volatiles have been completely released the
remaining material is the char residue and the final stage of the conversion is
char oxidation and gasification.
Figure 8.1 Schematic representation of mass loss (blue line) and temperature (red line)
histories during combustion of a thermally thin particle. The three distinguished phas-
es include (1) heating up (0 ≤ t ≤ tpini), (2) pyrolysis (tpini < t ≤ tp), (3) char combustion
and gasification (tp < t ≤ tb).
226
Modeling Combustion of Single Biomass Particle 211
Figure 8.2 Schematic representation of thermo-chemical conversion of a biomass par-
ticle.
Virgin
biomass YO2,∞
T∞
r = R r = 0 Radial coordinate
Time
YO2,∞
T∞
Volatiles
YO2,∞
T∞
Volatiles
CO
CO2
YO2,∞
T∞
Char layer
227
212 Chapter 8
Detailed numerical models, e.g. the model presented in Chapter 4, allow
one to predict time and space evolution of various process parameters (e.g. bi-
omass and char densities, porosity, temperature, velocity of gaseous flow with-
in the pores, pressure gradient, mass fraction of various gaseous species such
as H2O, CO, CO2, tar) during combustion of a single particle. In fact, the com-
prehensive models provide a useful tool to get a deeper inside into the complex
physics of thermo-chemical conversion of single solid particles. Nevertheless,
simulations using these models would be at the expense of significant compu-
tational time and programming efforts since they consist of a set of strongly
coupled partial differential equations based on the conservation of mass, mo-
mentum and energy. The question of interest is how one may establish a re-
duced model based on the basic conservation laws in order to predict the main
characteristics of combustion of a single thermally thin biomass particle per-
taining to the conditions of biomass combustors?
In the present chapter, a simplified combustion model of a thermally thin
solid fuel particle is developed. The definition of thermally thin particle is ex-
plained in Chapter 5 and Chapter 7. The formulation will be presented in Sec.
8.2 for the three main phases of the combustion process of a spherical particle
as depicted in Fig. 8.1 (i.e. heating up, pyrolysis, and char conversion). The
heating up and the pyrolysis stages are modeled using an integral method
whereas the char combustion phase is formulated according to the shrinking
core approximation taking into account finite-rate kinetics of surface reactions.
The accuracy of the proposed model and its sub-models will be examined in
Sec. 8.3. Subsequently, the model will be used to study the effects of particle
size and heating conditions on combustion dynamics in Sec. 8.4. The conclu-
sion from this study will be given in Sec. 8.5.
8.2 MODELING APPROACH
Let us consider a dry spherical biomass particle that combusts in an oxida-
tive hot environment. We divide the combustion process to the following three
distinguished phases: 1) Heating up, 2) Pyrolysis with partial combustion of
volatiles in the boundary layer around the particle, 3) Char combustion.
The pyrolysis process may overlap partially with char combustion if the
oxygen in the surrounding stream can sufficiently reach the particle, or it may
occur without char combustion in the case that oxygen cannot sufficiently dif-
228
Modeling Combustion of Single Biomass Particle 213
fuse through the boundary layer because of the large outgoing flow of vola-
tiles. The criterion to determine whether the pyrolysis phase may overlap with
char combustion, as outlined by Peters [3], is that if the convective outflow
flux of volatiles becomes smaller than the incoming diffusive flux of oxygen,
char combustion will occur simultaneously with the pyrolysis process.
Overlapping pyrolysis and char combustion processes may happen in the
case of slow pyrolysis, where the rate of volatiles generation is not as high as
that in the case of flash pyrolysis. It is unlikely that the pyrolysis and char
combustion occur simultaneously at the condition of entrained flow reactors
with a nearly laminar flow regime around the particle (Re 0), and at operat-
ing temperature of above 1200 K, where the biomass decomposition takes
place at a high rate producing a large mass transfer resistance (due to the large
volatiles flow) against the diffusing oxygen. The results of a recent study by
Saastamoinen et al. [2] indicate near zero oxygen concentration at the surface
of a particle combusting at elevated temperatures.
Furthermore, a flame sheet may exist due to the volatiles combustion
around the particle, again, depending upon the process condition such as the
thickness of the boundary layer (function of Reynolds number) and oxygen
concentration in the surrounding fluid. Lu et al. [10] studied the combustion of
a near-spherical 9.5 mm poplar particle in a reactor temperature of 1276 K.
The particle was sustained in the reactor while the preheated air was blown
from the bottom of the reactor at a velocity of around 0.5 m/s. Their numerical
results revealed a negligible effect of volatiles combustion on the particle con-
version process; indicating the absence of combustion of volatiles in the
boundary layer surrounding the particle. In Chapter 4, the effect of gas-phase
reactions in the vicinity of spherical large beech wood particle (10 mm and 20
mm) combusting under similar operational conditions of the experiments of Lu
et al. [10] was investigated and revealed the same conclusion. The absence or
negligible volatiles combustion in the vicinity of the particle is mainly due to
the thin boundary layer and the large outflow of gaseous species which lead to
a large mass transfer resistance against the diffusion of oxygen, thereby retard-
ing the mixing and reaction of volatiles with oxygen adjacent to the particle.
The situation may however be different if the slip velocity between the
surrounding stream and oxygen is near zero such as in entrained flow reactors.
In this case, the boundary layer around the particle is thicker than the case with
a high slip velocity so that the volatiles have a better chance to mix and react
with the surrounding oxygen. So, any thermal effect resulted from existence of
229
214 Chapter 8
a flame formed due to volatiles combustion on the particle conversion process
need to be carefully taken into account. This discussion will be further elabo-
rated in Sec. 8.2.2. The model to be present in this chapter will account for the
various stages of the combustion process as explained above.
It is assumed that the pyrolysis process begins as soon as the particle sur-
face temperature attains a characteristics pyrolysis temperature Tp (> T0) at the
time tpini. As the problem of interest is combustion of particles of less than a
millimeter at high heating conditions (above 1100 K corresponding to the con-
ditions of existing coal and biomass furnaces), the particle is characterized as
“thermally thin” (see Fig. 8.3). Under these circumstances, it can be reasona-
bly assumed that the decomposition of virgin material into volatiles and char
residue takes place under flash pyrolysis condition with a high conversion rate.
Thus, we further assume that the pyrolysis takes place with an infinite rate at a
characteristic pyrolysis temperature.
8.2.1 Heating up Phase
The conservation of energy during the heating up phase is described as
( )( )
∂
∂−
∂
∂=
∂
−∂
r
TrR
rk
t
TrRc
BpBB
2
2
ρ (8.1)
where ρB, cpB, and kB represent, density, specific heat and thermal conductivity
of biomass, respectively.
In a thermally thin particle (see Fig. 8.3), the heating up process consists of
two sub-phases. In the first phase, a thermal wave with the length rt is formed
soon after the particle is exposed to a hot environment. It moves towards the
center of the particle (Fig. 8.3a). It reaches the center at time tR at which the
surface temperature Ts is still less than the pyrolysis temperature Tp. Beyond tR,
the heating up continues (Fig. 8.3b) until the surface temperature attains Tp at
time tpini, which represents the time of initiation of pyrolysis at the particle sur-
face; or the duration of the heating up phase.
The boundary conditions at the first phase of the heating up process are:
( )netrB
qrTk ′′=∂∂−=0
/ , ( ) 0/ =∂∂= trrB
rTk , and 0
TTtrr
==
230
Modeling Combustion of Single Biomass Particle 215
(a)
(b)
Figure 8.3 Schematic representation of a thermally thin particle; a) initial heating up
phase, b) pre-pyrolysis heating up phase.
231
216 Chapter 8
whereas for the second phase of the hating up process, the prescribed boundary
conditions are:
( )netrB
qrTk ′′=∂∂−=0
/ , ( ) 0=∂∂=RrB
r/Tk
The parameters of interest are Ts and the net heat flux at the particle surface
netq ′′ defined as
( ) ( )44
ssnetTTTThq −+−=′′
∞∞σε (8.2)
where h is the convective heat transfer coefficient, T∞ the surrounding temper-
ature, σ the Stephan-Boltzmann coefficient, and ε the emissivity.
To simplify the partial differential (PD) form of the heat transfer equation
given by Eq. (8.1), we employ an integral method allowing us to convert Eq.
(8.1) into an ordinary differential equation (ODE); see Appendix D for de-
tailed model derivation. The temperature gradient inside the particle in Fig. 8.3
can be approximated with various mathematical functions; e.g. exponential,
power, or polynomial. We choose a quadratic function to represent the temper-
ature profile since it can satisfy the boundary conditions given above in both
phases of the heating up stage. This assumption will be verified in Sec. 8.3.1.
Let us first solve the problem for the first phase of the heating up stage
(Fig. 8.3a). In this case, the temperature profile obeys
2
01
2
−
′′+=
t
t
B
net
r
rr
k
qTT (8.3)
The surface temperature is obtained from Eq. (8.3) with r = 0. Hence,
t
B
net
sr
k
qTT
20
′′+= (8.4)
Substituting Eq. (8.3) into Eq. (8.1) and applying a space integration between r
= 0 and r = rt yields,
232
Modeling Combustion of Single Biomass Particle 217
( )B
net
Btt
B
tnet
k
qRrRrR
k
rq
dt
d ′′=
+−
′′α
222
2
51060
(8.5)
Equation (8.5) may be further simplified by assuming
( )tqqdtqnet
t
net 00
5.0 ′′+′′=′′∫
and integrating Eq. (8.5) from time zero to time t. This results in the following
relationship for the length of the thermal penetration depth:
tq
qRrRRrr
net
Bttt
′′
′′+=+−
022234 130105 α (8.6)
where
( ) ( )4
0
4
00TTTThq −+−=′′
∞∞σε (8.7)
Equations (8.2), (8.4) and (8.6) form a system of three algebraic equations
which should be solved simultaneously from t = 0 until t = tR (at which rt = R,
and Ts = TsR) to give the histories of the surface temperature and heat flux. The
above solution is no longer valid for t > tR. Indeed, in the second phase of the
heating up process (piniR
ttt ≤≤ ), the temperature profile is represented as fol-
lows.
2
2r
Rk
qr
k
qTT
B
net
B
net
s
′′+
′′−= (8.8)
Applying a space integration to Eq. (8.1) using Eq. (8.8) between r = 0 and r =
R gives
233
218 Chapter 8
( )net
B
netBsq
RRqkT
dt
d′′=′′−
α155 (8.9)
Using the approximation
( )( )RRnet
t
tnet
ttqq.dtqR
−′′+′′=′′∫ 50
and integrating Eq. (8.9) from tR to t leads to a relationship for the surface
temperature. Hence,
( ) ( )( )RRnet
B
B
Rnet
B
sRsttqq
Rkqq
k
RTT −′′+′′+′′−′′+=
2
3
5
α (8.10)
A solution of Eqs. (8.2) and (8.10) at each instant t between t = tR and t =
tpini allows one to determine the surface temperature and heat flux. After Ts has
reached the characteristic pyrolysis temperature at tpini, the second phase of the
heating up process will end, and the pyrolysis process will begin.
The surface temperature corresponding to time tR is obtained from Eq.
(8.4). Hence,
Rk
qTT
B
R
sR2
0
′′+= (8.11)
where
( ) ( )44
sRsRRTTTThq −+−=′′
∞∞σε (8.12)
Indeed, one would have to solve Eqs. (8.11) and (8.12) simultaneously to de-
termine the surface temperature and the surface heat flux at the time tR. In a
thermally thin particle, the particle radius is less than a critical particle size,
234
Modeling Combustion of Single Biomass Particle 219
Rcr, at which TsR equals Tp. So, rearranging Eq. (8.11) and replacing TsR with
Tp, we get
p
p
Bcrq
TTkR
′′
−=
02 (8.13)
Rcr denotes the minimum size of the particle for transition from thermally thin
to thermally thick regime. In fact, Eq. (8.13) allows one to identify whether a
particle is thermally thin or thermally thick.
Typically, thermal conductivity of various biomass types is between 0.2-
0.4 W/m.K, the pyrolysis temperature varies in the range 523-773 K, and the
reactor temperature is above 1200 K. For instance, assume Tp = 673 K, T0 =
300 K, kB = 0.25 W/m.K, Tr = T∞ = 1273 K, h = 15 W/m2.K. Using Eq. (8.2),
the net heat flux at the surface of the particle at the time of initiation of pyroly-
sis is 146 kW. Inserting the above values in Eq. (8.13) gives Rcr = 1.3 mm,
which is equivalent to a particle diameter of 2.6 mm. In practice, such as in
power plant furnaces, the particle thickness is usually less than 1mm for raw
biomass particles. In the case of torrefied biomass, the particle size is expected
to be even smaller; e.g. less than 0.5 mm. This sample calculation indicates
that the regime of particle pyrolysis in real combustors is thermally thin since
the particle size is less than its critical value. It is obvious that depending on
ignition temperature, thermal conductivity and heating condition, the value of
Rcr would be different. Typical values of the critical radius of a particle are de-
picted in Fig. 8.4, which supports the idea that the pyrolysis of (raw and torre-
fied) biomass particles in many real furnaces occurs in a thermally thin regime.
8.2.2 Pyrolysis Phase
The main assumption employed in the formulation of the pyrolysis phase
is that the decomposition of biomass into volatiles and char residue occurs at
an infinitely thin reaction front at a constant pyrolysis temperature Tp (see Fig.
8.5). In reality, of course, decomposition may take place with different degrees
inside a pyrolyzing particle. Implication of a thin reaction front is based on the
assumption that the volume integration of biomass pyrolysis at each instant
takes place at a single thin front dividing the particle into biomass and char re-
gions as depicted in Fig. 8.5.
235
220 Chapter 8
(a)
(b)
Figure 8.4 Critical particle size versus pyrolysis temperature at varying thermal con-
ductivity at a reactor temperature of a) 1273K, and b) 1473 K.
236
Modeling Combustion of Single Biomass Particle 221
Figure 8.5 Schematic representation of the pyrolysis phase.
Similar to the analysis presented in Chapter 6 (see Eqs. (6.3) and (6.4)), the
temperature profiles in the biomass and char regions are approximated with
quadratic functions. The boundary conditions at this stage of the problem un-
der study are:
BC1: ( )netrCC
qrTk ′′=∂∂−=0
/ ; BC2: ( ) 0/ =∂∂=RrB
rT ; BC3: prrCrrBTTT
cc==
==;
BC4: ( ) ( )prrCCrrBB
hmrTkrTkcc
∆′′+∂∂−=∂∂−==
&// .
Thus, it can be shown that the temperature profiles obey
( ) ( )( )
( )21
12
,c
c
cpBrr
rRrrTrtT −
−−−+=
φφ (8.14)
R rc
r
r=0
T
Tc
Ts Pyrolysis reaction
front
Char region
Tp
237
222 Chapter 8
( ) ( ) ( )211
2, rr
kr
hmkqrr
k
hmkTrtT
c
Cc
pBnet
c
C
pB
pC−
∆′′++′′+−
∆′′+−=
&& φφ (8.15)
where rc is the char penetration depth, ∆hp represents the pyrolysis heat, and
m ′′& denotes the rate of biomass decomposition flux defined as
dt
drm c
Bρ=′′& (8.16)
Based on the results of Chapter 3, we assume that the volatiles generated
with rate
( ) ( )B
Cc
CBvm
dt
drm
ρ
ρωωρρ =′′−=−=′′ && 1 (8.17)
move towards the surface of the particle where they escape.
The heat transfer equation of the biomass region can still be represented
with Eq. (8.1). Substituting Eq. (8.14) into Eq. (8.1) and performing space in-
tegration from r = rc to r = R and some algebraic manipulation results in the
following ODE.
( )2
111154
c
Bc
c rRdt
dr
rRdt
d
−−
−=
φαφφ (8.18)
The heat transfer equation of the char region is described as follows.
( )[ ] ( ) ( ) ( )
∂
∂−
∂
∂=
∂
∂−′′−−−
∂
∂
r
TrR
rk
r
TrRcmTrR
tc
CcpvpCC
2221 &ωρ (8.19)
where cpv denotes the specific heat of volatiles.
238
Modeling Combustion of Single Biomass Particle 223
Likewise, inserting Eq. (8.15) into Eq. (8.19) and applying space integration
between r = 0 and r = rc lead us to another ODE. Hence,
( )( ) ( )[ ]
( ) ( ) ( ) ( ) ( )[ ]pscpvnetpBcC
cccnetcccpB
TTrRcmqRhmkrR
rRrRrqrRrRrhmkdt
d
−−′′−−′′+∆′′+−
=+−′′+−−∆′′+
22
1
2
43222243
1
160
51020415
&&
&
ωφα
φ
(8.20)
As discussed in the preceding section, the volatiles leaving the particle
may interact with oxygen in the surrounding stream and form a flame sheet
around the particle. In this case, the net heat flux at the surface of the particle
is determined from
( ) ( )44
ssfeffnetTTTThq −+−=′′
∞σε (8.21)
where Tf represents a flame temperature, and heff denotes an effective heat
transfer coefficient between flame and the particle surface.
To obtain the flame temperature, one would have to solve the conservation
equations of the gas-phase outside the particle. Existence of a flame around the
particle would provide a thermal source. Saastamoinen et al. [1, 2] propose the
following relationship to determine the effective flame temperature.
pvOvvfcYfhTT /
,2 ∞∞∆+= (8.22)
where ∆hv is the specific enthalpy of volatiles combustion, and fv denotes the
stoichiometric volatiles/oxygen ratio.
At this stage of the conversion, five unknowns including char penetration
depth, biomass decomposition flux, temperature and heat flux at the particle
surface and parameter φ1 should be determined at every time increment. A re-
lation can be established between Ts and other parameters using Eq. (8.15).
c
C
pBnet
psr
k
hmkqTT
2
1∆′′−−′′
+=&φ
(8.23)
239
224 Chapter 8
8.2.3 Char Combustion Phase
Upon release of all volatiles and complete conversion of biomass to char,
the oxygen from surrounding diffuses through the boundary layer and reaches
the particle surface where it reacts heterogeneously with char according to the
surface reaction (7.1); see Chapter 7. A further heterogeneous surface reaction
considered is the gasification of char with carbon dioxide; i.e. reaction (7.2).
The formulation of char combustion process is the same as the model present-
ed in Chapter 7. The reactions rates of char oxidation and gasification are ob-
tained from Eq. (7.6).
In the case of reaction order of unity; i.e. n = 1in Eq. (7.6), it is possible to
further simplify the char combustion model. Eliminating partial pressure of
oxygen between Eqs. (7.6) and (7.10) yields
sOg
O
g
sg
YPM
M
TR
EAr
2
2
1
11 exp
−= (8.24)
Equation (7.8) can be reshaped to read
( )21,
1,
2
2
22
2 rrk
rM
MYk
YOdg
c
O
OOdg
sO++
−
=
∞
ρ
νρ
(8.25)
Substituting Eq. (8.25) into Eq. (8.24) and rearranging for r1 results in a quad-
ratic equation whose solution gives
( )
( )
( )
−++−
−
+
−++
=
∞
c
g
gsgOdg
OOdg
O
g
gsg
c
g
gsgOdg
M
MPTREArk
YkM
MPTREA
M
MPTREArk
r
/exp2
1
/exp4
/exp
2
1
112,
2
1
,11
2
112,
1
2
22
2
2
νρ
ρ
νρ
(8.26)
240
Modeling Combustion of Single Biomass Particle 225
By performing a similar analysis, it can be shown that the rate of gasifica-
tion reaction is obtained from
( )
−++−
−+
−
+
−++
=
∞
c
g
g
sg
COdg
c
CO
COCOdg
CO
g
g
sg
c
g
g
sg
COdg
M
MP
TR
EArk
rM
MYk
M
MP
TR
EA
M
MP
TR
EArk
r
2
21,
2
1
1,
2
2
2
2
21,
2
exp2
1
12exp4
exp
2
1
2
2
22
2
2
ρ
νρ
ρ
(8.27)
8.3 MODEL VALIDATION
The assessment of the accuracy of the presented model is carried out in
three stages: 1) validation of the heating up phase model by comparing its pre-
dictions to the computation of a PDE model; 2) validation of the pyrolysis
model using measured data; 3) validation of the complete combustion model
using the experiments of wood particles. The thermo-physical properties em-
ployed for the purpose of model validation are listed in Table 8.1.
8.3.1 Validation of the Heating up Model
The predicted surface temperature of a spherical particle undergoing a
heating up process using the simplified model described in Sec. 8.2.1 is com-
pared with the results of a PDE model, i.e. the numerical solution of Eq. (8.1),
in Fig. 8.6. The calculations are performed using the thermo-physical data giv-
en in Table 8.1 for two surrounding temperatures 1273 K (Fig. 8.6a) and 1473
K (Fig. 8.6b). The surface temperature is computed using both models up to
typical pyrolysis temperatures 623 K (Fig. 8.6a) and 523 K (Fig. 8.6b). The se-
lected values for the pyrolysis temperature fall within the range reported in the
literature [4, 5]. The agreement between the predicted surface temperatures us-
ing the simplified and PDE models is excellent in both cases in Figs. 8.6a and
8.6b. This indicates that the approximation of the spatial temperature profile
with a quadratic function and assuming linear dependence of the surface heat
flux on time do not lead to considerable errors in the calculation of Ts.
241
226 Chapter 8
Table 8.1 Thermo-physical data used in the model validation (Figs. 8.6-8.9).
Parameter Heating up model Pyrolysis model Combustion model
Tp [K] - 573 453
kB [W/m.K] 0.25 0.25 0.25
ρB [kg/m3] 500 650 500
cpB [J/kg.K] 2500 2500 2500
kC [W/m.K] - 0.15 0.15
ρC [kg/m3] - 50 80
cpC [J/kg.K] - 1100 1100
(a) (b)
Figure 8.6 Validation of the heating up model. Predicted surface temperature versus
time; a) T∞ = 1273 K and Tp = 623 K; b) . T∞ = 1473 K and Tp = 523 K (R = 125 µm).
8.3.2 Validation of the Pyrolysis Model
The experiment data of mass loss history of pyrolyzing sawdust particles
reported by Lu et al. [6] is used to examine the accuracy of the pyrolysis mod-
el. The enthalpy of pyrolysis is determined using the correlation of
Milosavljevic et al. [7]; and the char density is set to the measured value (8%
of sawdust density). Figure 8.7 compares the prediction of the pyrolysis model
with the measured data as well as the predictions of the detailed model of Lu et
al. [6]. The duration of the heating up and the pyrolysis time are predicted well
with the presented model. Moreover, the computed mass loss history is quanti-
242
Modeling Combustion of Single Biomass Particle 227
tatively and qualitatively comparable with the measured data (especially up to
300 msec) as well as the prediction of the model of Lu et al. [6].
Figure 8.7 Comparison of the prediction of the pyrolysis model with experiment and
prediction of the detailed pyrolysis model of Lu et al. [6]. Pyrolysis of near-spherical
single sawdust particles: Equivalent diameter: 0.32 mm; aspect ratio: 1.65; reactor
temperature 1625 K.
8.3.3 Validation of the Combustion Model
The experiments of mass loss histories of biomass particles reported by
Saastamoinen et al. [2] are employed to assess the predictability of the reduced
combustion model (heating up, pyrolysis, and char combustion). The experi-
mental data given in Ref. [2] are related to the combustion of heartwood and
straw particles (d = 180-315 µm) in O2/N2 mixtures with different amounts of
oxygen content. Figure 8.8 depicts a comparison between the predicted and
measured mass loss histories of single particles combusting in an O2/N2 mix-
ture with 10% (volume based) oxygen concentration in the surrounding
stream. Shown in this figure is also the computed particle surface temperature
normalized with the reactor temperature (i.e. 1273 K). The ignition (see Fig.
8.1 for the definition of ignition temperature and time) of the particle occurs at
about 80 msec, at which the pyrolysis process is almost completed. The sur-
243
228 Chapter 8
face temperature during the quasi-steady combustion process is around 1600
K. The predicted transient mass loss in the last stage of the particle conversion
matches with the measured data. The durations of heating up, pyrolysis and fi-
nal conversion (when 99.5% of mass is burnt) predicted by the model are 40
msec, 80 msec, and 185 msec, respectively.
Figure 8.8 Comparison of the predicted (line) and measured (symbols) mass loss his-
tory of single sawdust particles combusting in an O2/N2 mixture (10% vol. O2) with a
reactor temperature of 1273K, and predicted particle surface temperature normalized
with reactor temperature.
Another model-experiment comparison is depicted in Fig. 8.9 related to
the combustion of sawdust and straw particles in an O2/N2 mixture with 5%
(volume based) oxygen concentration. The experiments of straw are obtained
at a reactor temperature of 1123 K. The predicted surface temperature (nor-
malized with the reactor temperature) is also depicted in Fig. 8.9. As expected,
the conversion time lasts longer at O2 concentration of 5% compared to the
case with O2 concentration of 10%. Furthermore, notice the magnitude of the
surface temperature in Fig. 8.9 (around 1400 K), which is 200 K lower than
the case in Fig. 8.8. The durations of heating up, pyrolysis and final conversion
computed by the model are 40 msec, 80 msec, and 325 msec, respectively.
244
Modeling Combustion of Single Biomass Particle 229
Figure 8.9 Comparison of the predicted (line) and measured (symbols) mass loss his-
tory of single sawdust (circle symbols) and straw (triangle symbols) particles combust-
ing in an O2/N2 mixture (5% vol. O2), and predicted particle surface temperature nor-
malized with reactor temperature. The rector temperature in the case of sawdust is
1273 K, whereas it is 1123 K in the case of straw.
The underprediction of the mass loss history by the presented model is due
to several factors. First, a single value of 230 µm is assumed for the particle
size in the calculations while the experimental data are obtained from the
combustion of particles of various sizes ranging from 180 µm to 315 µm. Se-
cond, based on the assumption of Saastamoinen et al. [2], the final char density
is assumed to be 80 kg/m3 (16% of the biomass density). However, according
to the findings of Chapter 3, the final char density obtained from the pyrolysis
of small biomass particles at high temperatures is anticipated to be less than 10
percent. Thus, accounting for these factors, the agreement between the model
predictions and the measured values in Figs. 8.8 and 8.9 is reasonably fair.
In the last validation case, the simplified model predictions are compared
with the computations of the detailed particle combustion model presented in
Chapter 4, in terms of the conversion time of spherical beech wood particles of
three different diameters (250 µm, 500 µm, 1000 µm) at reactor temperatures
in the range 1200-1600 K (see Fig. 8.10). The average error between the pre-
dictions of the simplified and detailed PDE models is -8% with a standard de-
245
230 Chapter 8
viation of 9.5%. For each particle size, the conversion time is computed for
five operating temperatures 1200K, 1300K, 1400K, 1500K, and 1600K. It is
obvious that a higher reactor temperature leads to a shorter conversion time. A
key observation from Fig. 8.10 is that the burnout time of particles with diame-
ters 500 µm and less burning at reactor temperatures of 1200K and higher
(corresponding to the condition of industrial furnaces) is less than 0.8 sec as
predicted by both simplified and detailed particle combustion models.
Figure 8.10 Comparison of the predictions of the simplified model and the detailed
combustion model of Chapter 4 in terms of burnout time (values on axes are in se-
conds) of single beech wood particles of three different sizes at reactor temperatures
1200-1600 K.
8.4 EFFECT OF PARTICLE SIZE AND HEATING CONDITION
As it is difficult to mill biomass due to its fibrous structure, the size of bi-
omass particles combusting in the furnaces of industrial power plants is gener-
ally larger than that of coal particles. Furthermore, surrounding temperature
varies within combustors implying that the particles experience different heat-
ing conditions as they burn within the furnace. Therefore, this section is devot-
246
Modeling Combustion of Single Biomass Particle 231
ed to examine how the initial size of particle and the surrounding temperature
may influence the combustion dynamics of a biomass particle burning in air.
Figure 8.11 illustrates the effect of initial particle size on the surface tem-
perature history of single sawdust particles undergoing a combustion process
at two surrounding temperatures. The corresponding mass loss histories are
depicted in Fig. 8.12. The main observation from these figures is that an in-
crease in the particle size results in increasing burnout time (99.5% mass loss),
ignition time and ignition temperature. For a given particle size, the ignition
time at the surrounding temperature of 1573 K is shorter than that at the sur-
rounding temperature of 1273 K, whereas the ignition temperature is higher at
1573 K than that in 1273 K. Furthermore, it can be deduced from Figs. 8.11
and 8.12 that the burnout time, an important design parameter, is less than 1
second for particles smaller than 650 µm burning at a reactor temperature of
1273 K and higher.
A question that can be subsequently raised is what would be the duration
of each phase of the particle combustion process? Figure 8.13 depicts preheat-
ing time, ignition time and burnout time versus initial particle size at surround-
ing temperatures of 1273 K (solid lines) and 1573 K (broken lines). An in-
crease in particle diameter leads to a higher preheating, ignition and burnout
time. On the other hand, a higher surrounding temperature results in reduction
of these parameters. The results in Fig. 8.13 are recast to identify the longest
and shortest sub-processes as function of particle size. Figure 8.14 shows the
ratio of duration of each main sub-process (heating up, pyrolysis and char
combustion) to the total burnout time for varying initial particle size and two
surrounding temperatures.
Several important conclusions can be drawn from Fig. 8.14. First, the ratio
of the heating up phase duration to the total burnout time decreases whereas
those of the pyrolysis and char combustion processes increase with increasing
particle size. The same trend can also be observed at increased surrounding
temperature. Second, the char combustion process is the shortest stage for a
surrounding temperature of 1273 K, and the dominant process is the pyrolysis
phase for particles larger than 300 µm. Also, the longest and predominant pro-
cess at the surrounding temperature of 1573 K is the pyrolysis phase owing to
50% of the total burnout time. For particles smaller than 460 µm, the shortest
process is the char combustion stage. However, for particles larger than 460
µm, the heating up phase is predicted to be the shortest process.
247
232 Chapter 8
(a) (b)
Figure 8.11 Predicted surface temperature history at various particle sizes (increasing
in the direction of arrows with 0.05mm increment) and surrounding temperature of (a)
1273 K and (b) 1573 K.
(a) (b)
Figure 8.12 Predicted mass loss history for various particle sizes (increasing in the di-
rection of arrows with 0.05mm increment) and surrounding temperature of (a) 1273 K
and (b) 1573 K.
The effect of varying surrounding temperature on the combustion dynam-
ics is depicted in Fig. 8.15 at three different heating conditions: constant sur-
rounding temperature, surrounding temperature increasing with 250 K/s and
500 K/s. The initial surrounding temperature in all three cases is 1273 K. The
results in Fig. 8.15 are presented for two values of the initial particle diameter.
Compared to the case with a uniform surrounding temperature, i.e. the graphs
248
Modeling Combustion of Single Biomass Particle 233
corresponding to 0 K/s rate, it is seen that the combustion dynamics under var-
ying operating temperature (which is the case in real furnaces) is considerably
different from the situation with a uniform surrounding temperature. The re-
sults indicate that a higher heating rate leads to a higher ignition temperature
but a shorter ignition time. Moreover, the total burnout time and maximum
surface temperature are significantly influenced under the conditions of vary-
ing heating conditions.
Figure 8.13 Computed preheating time, ignition time, and burnout time versus particle
initial size at a surrounding temperature of 1273 K (solid lines) and 1573 K (broken
lines).
Figure 8.14 Duration fraction of various stages of the combustion process (normalized
with total burnout time) versus particle initial size at a surrounding temperature of
1273 K (solid lines) and 1573 K (broken lines).
249
234 Chapter 8
Figure 8.15 Effect of varying surrounding temperature on the transient particle surface
temperature for two values of the particle initial diameter and three heating rates (ini-
tial surrounding temperature is 1273 K).
8.5 CONCLUSION
A reduced model is developed for predicting transient combustion of
thermally thin single biomass particles which can capture the main characteris-
tics of a burning particle. The model can be used in the CFD codes of biomass
combustors. The formulation takes into account the various stages of the com-
bustion process including heating up, pyrolysis and char combustion. The
model is validated against recent experimental data reported in the literature as
well as the computations of detailed numerical models. The effects of particle
size and heating conditions on combustion dynamics of single biomass parti-
cles are investigated using the developed model.
The burnout time is found to be less than 1 second for particles smaller
than 650 µm burning in air at reactor temperatures of 1273 K and higher.
Larger particles lead to higher ignition temperature but longer ignition time.
The results reveal that the predominant process during combustion of a ther-
mally thin single biomass particle is the pyolysis phase; 40-50% of the dura-
tion of the entire combustion process is due to the particle pyrolysis. The in-
fluence of varying surrounding temperature on the combustion process is also
investigated. It is found that the ignition time and temperature and the total
burnout time can significantly be affected by variable heating conditions.
250
Modeling Combustion of Single Biomass Particle 235
RERERENCES
[1] Saastamoinen J. J., Aho M. J., Linna V. L. 1993. Simultaneous pyrolysis
and char combustion. Fuel 72: 599-609.
[2] Saastamoinen J., Aho M., Moilanen A., Sørensen L. H., Clausen S.,
Berg M. 2010. Burnout of pulverized biomass particles in large scale
boiler-single particle model approach. Biomass Bioenerg 34: 728-736.
[3] Peters B. 2002. Measurements and application of discrete particle model
(DPM) to simulate combustion of a packed bed of individual fuel parti-
cles. Combust Flame 131: 132-146.
[4] Galgano A., Di Blasi C. 2005. Infinite versus finite rate kinetics in sim-
plified models of wood pyrolysis. Combust Sci Technol 177: 279-303.
[5] Yang L., Chen X., Zhou X., Fan W. 2003. The pyrolysis and ignition of
charring materials under an external heat flux. Combust Flame 133:
407-413.
[6] Lu H., Ip E., Scott J., Foster P., Vickers M., Baxter L. L. 2010. Effects
of particle shape and size on devolatilization of biomass particle. Fuel
89: 1156-1168.
[7] Milosavljevic I., Oja V., Suuberg E. M. 1996. Thermal effects in cellu-
lose pyrolysis: relationship to char formation processes. Ind Eng Chem
Res 35: 653-662.
251
236 Chapter 8
252
Chapter 9
OxyFuel Combustion of Wood Char Particle
Some of the content of this chapter is taken from the following paper: Haseli Y., van Oijen J. A., de Goey L.
P. H. 2012. A quasi-steady analysis of oxy-fuel combustion of a wood char particle. Combustion Science
and Technology, in press.
9.1 INTRODUCTION
Given that several modeling studies have been conducted on single
char/carbon particles (see Table 7.1), limited numerical studies are reported in
the literature related to oxy-combustion of char particles, e.g. see Refs. [1, 2].
The common interest of these past studies has been on coal char particles,
while to the authors best knowledge, no study has so far been reported with re-
spect to oxy-fuel combustion of small biomass char particles (less than 1mm)
at conditions corresponding to those found in real furnaces. Due to the increas-
ing interest in co-combustion of biomass and coal at oxy-fuel conditions, it is
important to understand the burning characteristics and burnout time of bio-
mass char at high temperatures and under oxy-fuel conditions. This chapter
aims to conduct a comprehensive numerical study of the conversion of single
wood char particles in various O2/CO2 surrounding mixtures. For this purpose,
the char combustion model introduced in Chapter 7 is used.
In the present numerical analysis, the kinetic data proposed by Evans and
Emmons [3] will be used for calculation of the char oxidation rate (see Table
7.2). Also, the kinetic constants of lignite char gasification obtained by corre-
lating the data of Goetz et al. [4] are selected in the present numerical study to
determine the particle gasification rate (see Table 7.3). The base case of simu-
253
238 Chapter 9
lation and the range of parameters of interest are given in Table 9.1. This chap-
ter will be followed by examination of the burnout time of a char particle in air
and under oxy-fuel conditions (Sec. 9.2). The maximum particle temperature
will be discussed in Sec. 9.3. Typical numerical results related to the combus-
tion dynamics of single char particles in O2/N2 and O2/CO2 mixtures will be
presented and discussed in Sec. 9.4. Based on the results of Sec. 9.2 and Sec.
9.3, a set of explicit relationships will be presented in Sec. 9.5 for estimating
the burnout time and maximum temperature of a char particle. Finally, the
conclusion from this study will be summarized in Sec. 9.6.
9.2 BURNOUT TIME
The effect of the surrounding temperature on the burnout time of particles
of different initial diameters combusting in air is depicted in Fig. 9.1. Within
the range of the parameters shown in Fig. 9.1, the burnout time decreases with
increasing the surrounding temperature and/or reducing the particle initial size.
From this figure, one can realize that the conversion time of a particle at the
base case conditions is 130 msec. For an initial particle diameter of 200 µm
(half of the size in the base case), the burnout time is 40 msec; implying that
the conversion time is over three times faster than the base case. On the other
hand, when the initial particle size becomes one-and-half times larger (i.e. 600
µm) than the base case, the conversion is estimated to last twice longer as the
corresponding burnout time from Fig. 9.1 is around 270 msec. These sample
calculations reveal that the burnout time α
cbdt ∝ with α between 1.7 and 1.8.
A similar observation can also be made with respect to the effect of surround-
ing temperature on the burnout time. That is, the particle burnout time may be
assumed to be proportional to the surrounding temperature by a power-law.
Figure 9.2 compares the burnout time versus initial diameter of particles
burning in air and O2/CO2 mixtures. The same power-law dependence of burn-
out time on particle size discussed for the case of combustion in air (Fig. 9.1)
can be observed for particles burning at oxy-fuel conditions. Only in the case
of oxygen mass fraction of 0.1 would the particle conversion last longer com-
pared to the base case with air as the oxidizing agent. Figure 9.2 exhibits ap-
proximately identical burnout time for the base case and an O2/CO2 mixture
with an oxygen mass fraction of 0.2. On the other hand, the burnout time of a
particle in the remaining two cases of O2/CO2 mixtures with higher O2 mass
254
Modeling Combustion of Single Biomass Particle 239
fraction (i.e. 0.3 and 0.4) is found to be shorter than the base case over the par-
ticle diameters shown in Fig. 9.2. This is an interesting result indicating that
the particle consumption would occur faster under oxy-fuel conditions at oxy-
gen mass fraction of around 0.3 and higher, even though the char gasification
is an endothermic reaction which results in the reduction of the particle tem-
perature and the oxidation rate.
Table 9.1 The range of parameters considered in the parameter study.
Parameter Base case Considered range for
parameter study
Gasifying gas Air (YO2 = 0.232) O2/CO2 with YO2 be-
tween 0.1 and 0.4
Surrounding temperature, K 1373 1200–1800
Surrounding pressure, atm 1 1
Particle density, kg/m3 60 40–120
Particle diameter, µm 400 200–800
Initial temperature, K 600 400–900
AO2, kg/m2.s.atm 254 254
EO2, kJ/kmol 74830 74830
ACO2, kg/m2.s.atm 42160 42160
ECO2, kJ/kmol 197790 197790
Figure 9.1 Effect of surrounding temperature on burnout time at varying particle size.
A further comparison is represented in Fig. 9.3 to examine the effect of
oxy-fuel combustion on the burnout time at varying surrounding temperature
for fixed values of other process parameters as given in Table 9.1. An increase
255
240 Chapter 9
in surrounding temperature leads to a decrease in the burnout time in all cases
shown in Fig. 9.3. The reduction in burnout time is sharper when the oxygen
content in the surrounding fluid is lower. Over the temperature range shown in
Fig. 9.3, the conversion time of a char particle burning in air is found to be
lower than that in an O2/CO2 mixture with YO2 = 0.1. However, by increasing
the surrounding temperature the difference between the burnout times in these
two cases vanishes. For the case of oxy-fuel combustion with O2 mass fraction
of 0.2, it can be seen that the burnout time in air is shorter than in oxy-fuel
case up to a surrounding temperature of 1440 K, at which the burnout times at
these two cases become equal. Beyond 1440 K, the combustion in O2/CO2
mixture is predicted to be faster than in air. An additional observation from
Fig. 9.3 is that oxy-fuel combustion of a char particle at higher O2 mass frac-
tions (i.e. 0.3 and 0.4) is anticipated to last notably shorter than the case in air
over the temperature range represented in Fig. 9.3.
Figure 9.2 Effect of initial particle diameter on burnout time at different oxidizing
mixtures.
Next, we examine the effect of initial particle temperature and density on
the particle burnout time at various gasifying mixtures as shown in Figs. 9.4
and 9.5, respectively. It can be seen from Fig. 9.4 that the influence of particle
initial temperature on the burnout time is negligible indicating that the duration
of the heating up stage before ignition is shorter than the time needed for a par-
ticle to undergo the complete conversion process. On the contrary, Fig. 9.5 re-
veals that the burnout time linearly increases with an increase in the particle
256
Modeling Combustion of Single Biomass Particle 241
density in all gasifying mixtures. This linear-dependence of the conversion
time on density was also observed in Chapter 3 where the effect of initial den-
sity of a biomass particle on the pyrolysis time was examined. Over the range
of particle density investigated in this study, it can be observed from Fig. 9.5
that the burnout time in air is considerably shorter than the case in O2/CO2
mixture with YO2 = 0.1, it is slightly less than the case with YO2 = 0.2, whereas
it is notably longer than the other oxy-fuel scenarios with O2 mass fraction 0.3
and 0.4.
Figure 9.3 Effect of surrounding temperature on burnout time at different oxidizing
mixtures.
Figure 9.4 Effect of initial particle temperature on burnout time at different oxidizing
mixtures.
257
242 Chapter 9
Figure 9.5 Effect of particle density on burnout time at different oxidizing mixtures.
9.3 MAXIMUM PARTICLE TEMPERATURE
A further important parameter to be discussed is the particle temperature
which is expected to be lower in oxy-fuel combustion (due to the
endothermicity of the char gasification reaction) than in air. The effects of par-
ticle initial size, density and initial temperature were found to negligibly influ-
ence the predicted maximum particle temperature. However, the oxygen con-
tent in the bulk stream and the surrounding temperature can significantly affect
it. Figure 9.6 depicts the computed maximum particle temperature during
combustion versus surrounding temperature in air and various O2/CO2 mix-
tures. It is seen that Tmax of a particle burning in air is higher than that in all
oxy-fuel combustion cases, except for a surrounding temperature less than
1300K in the case of O2/CO2 mixture with YO2 = 0.4. In the case of oxy-fuel
combustion, the maximum temperature is higher for a higher O2 mass fraction.
This is because at a lower CO2 content the net heat of reactions tends to be
more exothermic resulting in a higher particle temperature.
A further subtle observation in Fig. 9.6 is that the difference between the
maximum particle and surrounding temperatures decreases by an increase in
the surrounding temperature in the case of oxy-fuel combustion. However, the
difference between the maximum particle and surrounding temperatures in-
creases with the surrounding temperature in the case of combustion in air. In
258
Modeling Combustion of Single Biomass Particle 243
the case of oxy-fuel combustion, an increase in the surrounding temperature
leads to an increase in contribution of gasification reaction thereby resulting in
a decrease in net heat of surface reactions. On the other hand, increasing the
surrounding temperature in the case of combustion in air, leads to the augmen-
tation of burning rate and the rate of char oxidation reaction. Thus, the rate of
energy release becomes faster than the rate of heat transfer to the surrounding;
this boosts heating up the particle and yields a higher particle temperature.
Figure 9.6 Variation of maximum particle temperature with surrounding temperature
at different oxidizing mixtures.
9.4 PARTICLE COMBUSTION DYNAMICS
The temperature and burning rate histories of a char particle combusting in
O2/N2 and O2/CO2 mixtures with various composition of gasifying substances
in the surrounding stream is depicted in Fig. 9.7. In both environments, the
calculations were performed for three different O2 mass fractions in the sur-
rounding with balanced mass fraction of N2 (green lines in Fig. 9.7) or CO2
(blue lines in Fig. 9.7). As expected, an increase in O2 mass fraction in both
environments leads to the augmentation of particle temperature and a reduc-
tion of conversion time. The general trend of particle consumption in O2/N2
and O2/CO2 (Fig. 9.7b) is similar, and they follow the global trend of the parti-
cle temperature history in Fig. 9.7a.
259
244 Chapter 9
(a) (b)
Figure 9.7 Comparison of burning characteristics of a wood char particle in two dif-
ferent environments; (a) particle temperature history; (b) burning rate history.
Two further important observations can be made from Fig. 9.7. First, the
particle temperature notably reduces by replacing N2 with CO2, which is due to
the endothermicity of the char gasification reaction with a specific enthalpy of
-14.23 MJ/kg. Second, despite that this effect leads to a reduction in the tem-
perature and oxidation rate, the char gasification reaction plays an important
role at relatively high fractions of CO2 in the surrounding fluid, which boosts
the overall particle conversion rate. Only in the case of an O2 mass fraction of
0.3 is the conversion time almost identical in both environments. In this case,
the char combustion rate due to the gasification reaction is offset by the de-
creased oxidation rate resulting from the reduced particle temperature. This is
an interesting observation which reveals that whether the combustion occurs in
an oxy-fuel condition or in an O2/N2 environment with an enriched oxygen
concentration (compared to air), the duration of the conversion process would
not be significantly influenced. In this case, the only global effect of oxy-fuel
environment compared to that of O2/N2 mixture would be a remarkable reduc-
tion in the particle temperature during the combustion process. However, no-
tice that in this particular case; i.e. O2 mass fraction of 0.3, the particle resi-
dence time would be shorter than that in a furnace operating with air. From
Fig. 9.7, the burnout time of particle burning in O2/CO2 environment is about
100 msec, while the burnout time of a particle combusting in air in Fig. 9.1 is
about 135 msec. This indicates that oxy-fuel combustion allows 25.9% reduc-
tion in particle residence time compared to the conventional combustion in air.
260
Modeling Combustion of Single Biomass Particle 245
Figure 9.8 Effect of surrounding temperature on particle temperature history at two
different environments. Green lines: O2/N2 mixture with YO2 = 0.3; b) Blue lines:
O2/CO2 mixture with YO2 = 0.3.
To examine whether the above conclusion may be extended to a wider
range of operational conditions, the histories of particle temperature in O2/N2
and O2/CO2 environments with YO2 = 0.3 at three different surrounding tem-
peratures are compared in Fig. 9.8. The general observations discussed earlier
can also be made from Fig. 9.8. It can be inferred from Fig. 9.8 that the re-
placement of N2 with CO2 leads to a considerable reduction in particle temper-
ature, and slightly decrease in the conversion time; except in the case of sur-
rounding temperature of 1273 in that the conversion time remains almost
unaffected by the presence of CO2.
A similar comparison is also made for particles with an initial particle ra-
dius 150 µm, 200 µm and 250 µm to assess the influence of particle size on the
combustion process. Figure 9.9 compares the computed temperature histories
for two gasifying environments at three different initial particle radiuses. It can
be seen that only for a particle radius of 250 µm the conversion time decreases
(9%) in the oxy-fuel atmosphere compared to the O2/N2 environment, but in
the case of a smaller particle the duration of combustion process is approxi-
mately the same irrespective of the gasifying substance.
261
246 Chapter 9
Figure 9.9 Effect of particle size on temperature history at two different environments.
Green lines: O2/N2 mixture with YO2 = 0.3; b) Blue lines: O2/CO2 mixture with YO2 =
0.3.
The final results are related to the species mass fractions at the surface of a
particle combusting under identical process conditions but at two different en-
vironments. Figure 9.10 shows the transient variations of O2, CO2 and CO
mass fractions at the surface of a char particle combusting in air and O2/CO2
mixture with YO2 = 0.3, respectively. Note that in Fig. 9.10a (combustion in
air) the sum of the species mass fractions is balanced with nitrogen mass frac-
tion. The O2 mass fraction is initially the same as its value in the surrounding
air. Upon ignition of the particle, the oxygen content on the surface drastically
drops. This is due to the production of mainly carbon monoxide (notice the
negligible mass fraction of CO2 in Fig. 9.10a) assumed to leave the particle
upon its formation. This causes a mass transfer resistance against the diffusive
flow of the oxygen from the bulk stream to the particle surface. During the
steady combustion stage, around 27% (mass basis) of the gaseous mixture on
the particle surface is carbon monoxide. By continuation of the particle com-
bustion, its size and the flux of outgoing combustion products decrease so that
the diffusion flux of oxygen increases. At the final stage of the conversion
process, the oxygen diffusion becomes dominant so oxygen can completely
262
Modeling Combustion of Single Biomass Particle 247
penetrate through the boundary layer around the particle to reach the particle
surface.
Similar calculations have been carried out to observe species mass frac-
tions on the particle surface in an oxy-fuel environment with YO2 = 0.3 (Fig.
9.10b). The trends of O2 and CO mass fractions are qualitatively the same as
those in Fig. 9.10a. The CO content in the gas phase at the particle surface is
notably higher than that in the case of combustion in air (Fig. 9.10a). This is
obviously due to the contribution of the gasification reaction in the case of
oxy-fuel combustion with a high fraction of CO2 in the gasifying mixture. The
trend of CO2 mass fraction is similar to that of O2. The same reasoning given
above for explanation of the O2 mass fraction variation during the combustion
in air is also valid for justification of the transient behavior of O2 and CO2
mass fractions in Fig. 9.10b.
9.5 USEFUL RELATIONSHIPS
To provide a convenient means for designers and plant engineers to direct-
ly estimate burnout time and maximum particle temperature of a biomass char
particle burning in air and oxy-fuel conditions, explicit relationships have been
derived using the results of Figs. 9.1-9.6. Indeed, it is found that the burnout
time tb is a function of the particle density, initial size, surrounding tempera-
ture and oxygen content in the bulk stream, whereas the maximum particle
temperature is dependent only upon the surrounding conditions (temperature
and oxygen content).
For the case of a char particle burning in air, the results of Figs. 9.1 and 9.6
allows one to establish the following relationships.
( )[ ]surrcccb
Tddt 0174.01.1633.72exp 493.032.0+−=
−−ρ (9.1)
4210739.1max
+=surr
TT (9.2)
The average error and standard deviation of the burnout time estimated from
Eq. (9.1) are -1.4% and 11.4%, respectively. These figures for maximum tem-
perature computed from Eq. (9.2) are 0 and 0.4%.
263
248 Chapter 9
(a)
(b)
Figure 9.10 Predicted species mass fractions at the surface of a char particle combust-
ing in (a) air, (b) an O2/CO2 mixture with YO2 = 0.3
Furthermore, based on the results of Figs. 9.2-9.6, the corresponding rela-
tionships giving the particle burnout time (for two surrounding temperatures)
and maximum particle temperature are obtained as follows.
264
Modeling Combustion of Single Biomass Particle 249
( )( )
( )( )
=×
=×=
+−
+−
KTd
KTdt
surrcc
surrcc
b
1473Y 9.16-exp109.0
137310.58Y-exp102
1.463 0.77Y
O
3
1.377 0.91Y
O
3
2O
2
2O
2
ρ
ρ (9.3)
( ) 13021325864.087.022max
++−=OOsurr
YYTT (9.4)
The average error and standard deviation of the burnout time estimated from
Eq. (9.3) are 3.7% and 12.9% (at a surrounding temperature of 1373 K), and
4.8% and 11.4% (at a surrounding temperature of 1473 K), respectively. These
figures for maximum temperature computed from Eq. (9.4) are 3.1% and 2%.
Notice that in Eqs. (9.1)-(9.4), the units of burnout time, density, diameter and
temperature are in [msec], [kg/m3], [µm], and [K], respectively.
9.6 CONCLUSION
The parameter analysis of single biomass char particles combusting under
oxy-fuel conditions reveals several conclusive guidelines. The results show
that the particle density and initial size, operating temperature and oxygen con-
tent in the surrounding gas are predominant factors influencing the burnout
time of a char particle. The maximum particle temperature is affected only by
surrounding conditions; i.e. temperature and oxygen content. Over the range of
parameters considered in this study corresponding to char particles obtained
from devolatilization of biomass at high temperatures, oxy-fuel combustion
with oxygen mass fraction of 0.3 and higher (in the surrounding stream) leads
to a notable reduction in maximum particle temperature and burnout time
compared to the case with air as the conventional oxidizing agent. For the op-
erating conditions in the base case (see Table 9.1), as an example, the burnout
time of a char particle combusting in an O2/CO2 mixture with O2 mass fraction
of 0.3 is found to be 25.9% less than that in air. Further, the reduction in parti-
cle maximum temperature is expected to be around 185 K (see Fig. 9.6).
Illustrative numerical results were presented to compare dynamic charac-
teristics of single wood char particles combusting in O2/N2 and oxy-fuel envi-
ronments at the conditions similar to those found in power plants furnaces. It
was found that the replacement of N2 with CO2 would result in a considerable
reduction in particle temperature. It could also lead to a reduction in burnout
265
250 Chapter 9
time at low O2 mass fractions (e.g. 0.1). At O2 mass fraction of 0.3 in the sur-
rounding stream, the burnout time remained almost unaffected irrespective of
the gasifying agent, while it was found to be shorter than that in a case with
air. The scenario to be established in industrial biomass furnaces with the gasi-
fying substance is a mixture of O2/CO2 with an approximately 30%/70% com-
position ratio. Thus, based on the results of this study, the particle residence
time in oxy-fuel combustion is expected to be shorter than that in conventional
combustors operating with air.
RERERENCES
[1] Hecht E. S., Shaddix C. R., Molina A., Haynes B. S. 2011. Effect of
CO2 gasification reaction on oxy-combustion of pulverized coal char.
Proc Combust Inst 33: 1699-1706.
[2] Brix J., Jensen P. A., Jensen A. D. 2011. Modeling char conversion un-
der suspension fired conditions in O2/N2 and O2/CO2 atmospheres. Fuel
90: 2224-2239.
[3] Evans D. D., Emmons H. W. 1977. Combustion of wood charcoal. Fire
Res 1: 57-66.
[4] Goetz G. J., Nsakala N. Y., Patel R. L., Lao T. C. 1982. Combustion and
Gasification Characteristics of Chars from Four Commercially Signifi-
cant Coals of Different Rank. Report No. EPRI-AP-2601, Electric Pow-
er Research Institute.
266
Chapter 10
Conclusion
10.1 DETAILED MODELING STUDY
The first phase of this thesis dealt with one-dimensional modeling of a sin-
gle biomass particle pyrolysis and combustion. The main findings from this
part can be summarized as follows.
10.1.1 Biomass Particle Pyrolysis
Employing empirical correlations of pyrolysis heat proposed by
Milosavljevic et al. (Ind Eng Chem Res 35: 653-662) and Mok and Antal
(Thermochimica Acta 68: 165-186) together with kinetic constants of Di Blasi
and Branca (Ind Eng Chem Res 40: 5547-5556) in the pyrolysis model allow
reasonable predictions of conversion time of a single biomass particle and final
char density at high heating conditions
The correlations obtained from the parametric study presented in Sec. 3.5
(see Eqs. (3.18) and (3.19)) should enable designers to estimate the pyrolysis
time and final char density of a biomass particle undergoing thermochemical
conversion at the conditions of industrial combustors.
Adaption of a homogenous process in a particle conversion model for sim-
ulation of thermal conversion of small particles ( < 1 mm) exposed to non-
oxidative environments with high temperature may result in undesired reduc-
tion of the accuracy of the predictions.
267
252 Chapter 10
10.1.2 Biomass Particle Combustion
The reasonable agreement obtained between the predictions and the differ-
ent experiments indicates that the biomass combustion model and the related
code developed using CHEM1D can be used with sufficient accuracy to study
combustion of wood particles.
A correct set of kinetic constants for the pyrolysis process needs to be se-
lected carefully, since the later stages of the combustion process are greatly
dependent on the amount of char and volatiles released during particle pyroly-
sis. In the case of absence of experimental data for a specific application, the
kinetic constants of Thurner and Man (Ind Eng Chem Process Des Dev 20:
482-488) can be used for low to moderate reactor temperatures; whereas the
kinetic data of Di Blasi and Branca (Ind Eng Chem Res 40: 5547-5556) may
be utilized at higher reactor temperatures; i. e. Tr > 1100 K.
Based on the experimental validation, it appears that inclusion of gas phase
reactions within and in the vicinity of the particle has a minor influence on the
combustion process, so that they could be removed from the particle model,
thereby reducing the complexity of the model.
10.2 SIMPLIFIED MODELING STUDY
In the second phase of this thesis, the idea was to develop simplified mod-
els for predicting the main characteristics of pyrolyzing and combusting single
biomass particles. For this purpose, individual models were established for
particle preheating, pyrolysis and char combustion. These models were then
combined to establish a simplified model for combustion of a thermally thin
biomass particle. The main results are given below.
10.2.1 Simplified Preheating Model
Analytical expressions are derived providing a useful design tool to com-
pute the ignition time of solid particles undergoing a pyrolysis process. The
dimensionless ignition time is found to be a function of non-dimensional ex-
ternal heat flux Ω or reactor temperature θr, ignition temperature θp and pa-
rameter K, which denotes the ratio of internal heat transfer via conduction
mechanism to the external radiation heat transfer.
268
Modeling Combustion of Single Biomass Particle 253
The variation of the ignition time with θp and K is either linear (thermally
thin particle) or polynomial (thermally thick particle). It is found that for val-
ues of K > 290, τR approaches an asymptote and becomes independent of the
external heat transfer and K.
10.2.2 Simplified Pyrolysis Model
Two different treatments are considered. The first formulation allows one
to compute the history of key process parameters such as net heat flux at the
surface, mass loss rate, char penetration depth and particle weight loss. This
model can be used in combustor and gasifier design codes where a large num-
ber of biomass particles undergo a thermal decomposition, since computation-
ally it is cheaper and easier to implement in a CFD code than the comprehen-
sive pyrolysis models.
The second treatment provides rather simple relationships for estimating
the duration of various stages of the process including preheating, pyrolysis
and post-pyrolysis heating. This method can be the interest of plant engineers
since it provides a simple but useful tool to sufficiently predict the mass loss
and surface temperature histories of a pyrolyzing particle.
The key conclusion is that if the thermo-physical properties are assigned
proper values, the pyrolysis models based on double- and single-temperature
profile can be effectively used in practical applications.
10.2.3 Simplified Char Combustion Model
The first necessary step when simulating combustion of char particles is to
properly select the kinetic parameters for oxidation and gasification reactions.
It is found that the replacement of N2 with CO2 would result in a considerable
reduction in particle temperature. It could also lead to a reduction in burnout
time at low O2 mass fractions (e.g. 0.1).
At O2 mass fraction of 0.3 in the surrounding stream, the burnout time re-
mained almost unaffected irrespective of the gasifying agent, while it was
found to be shorter than that in a case with air. As the scenario to be estab-
lished in industrial biomass furnaces is a mixture of O2/CO2 with an approxi-
mately 30%/70% composition ratio, the results of this study indicate that the
particle residence time in oxy-fuel combustion is expected to be shorter
(around 26%) than that in conventional combustors operating with air.
269
254 Chapter 10
10.2.4 Simplified Biomass Combustion Model
Based on the simplified models of preheating, pyrolysis and char combus-
tion, a simplified model was established for predicting a thermally thin single
biomass particle. The effects of particle size and heating conditions on com-
bustion dynamics of single biomass particles were investigated using the de-
veloped model.
The burnout time is found to be less than 1 second for particles smaller
than 650 µm burning in air at reactor temperatures of 1273 K and higher. The
results revealed that the predominant process during combustion of a thermally
thin single biomass particle is the pyolysis phase; 40-50% of the duration of
the entire combustion process is due to the particle pyrolysis. It was found that
the ignition time and temperature and the total burnout time can significantly
be affected by variable heating conditions.
270
Appendix A
Derivation of Heat Transfer Equation
Conservation of energy for a solid particle undergoing thermal degradation
assuming a constant volume during the process, and thermal equilibrium be-
tween solid and gas phases can be expressed as below in terms of total enthal-
py which accounts for enthalpy of formation and sensible enthalpy.
( ) gCBir
Tkr
rrhur
rrh
t
n
ngg
n
ni
ii ,,1ˆ1ˆ *
=
∂
∂
∂
∂=
∂
∂+
∂
∂∑ ρρ (A.1)
The derivation is presented assuming that decomposition of the biomass parti-
cle takes place according to only three primary reactions.
The first term in Eq. (A.1) is expanded as follows.
[ ]ggCCBB
all
i
hhht
ht
ˆˆˆˆ ερρρρ ++∂
∂=
∂
∂∑
( )t
ht
h
t
hB
B
B
B
BB
∂
∂+
∂
∂=
∂
∂ ρρ
ρ ˆˆˆ
271
256 Appendix A
( )t
ht
h
t
h C
C
C
C
CC
∂
∂+
∂
∂=
∂
∂ ρρ
ρ ˆˆˆ
( )t
ht
h
t
hg
g
g
g
gg
∂
∂+
∂
∂=
∂
∂ ερερ
ρ ˆˆˆ
Hence,
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂=
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂=
∂
∂∑
th
th
th
t
Tc
t
Tc
t
Tc
th
t
h
th
t
h
th
t
hh
t
g
g
C
C
B
BggCCBB
g
g
g
g
C
C
C
C
B
B
B
B
all
i
ερρρερρρ
ερερ
ρρ
ρρρ
ˆˆˆ
ˆˆ
ˆˆ
ˆˆ
ˆ
(A.2)
We also expand the second term in Eq. (A.1).
( ) ( )
( )g
n
nggg
g
n
g
g
g
n
ngg
n
n
urrr
hr
Tcu
urr
hr
hur
rhur
rr
ρρ
ρρρ
∂
∂+
∂
∂=
∂
∂+
∂
∂=
∂
∂
1ˆ
ˆˆ1ˆ1
(A.3)
Combination of Eqs. (A.2) and (A.3) gives
( )
( )
( )
( )
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂++
=∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂+
∂
∂=
∂
∂+
∂
∂∑
g
n
n
g
g
C
C
B
BggggCCBB
g
n
nggg
g
g
C
C
B
B
ggCCBBgg
n
n
all
i
urrrt
h
th
th
r
Tcu
t
Tccc
urrr
hr
Tcu
th
th
th
t
Tc
t
Tc
t
Tchur
rrh
t
ρερ
ρρρερρρ
ρρερρρ
ερρρρρ
1ˆ
ˆˆ
1ˆˆˆˆ
ˆ1ˆ
(A.4)
272
Modeling Combustion of Single Biomass Particle 257
With the aid of the mass conservation equations of different species, i. e.
Eqs. (3.2), (3.3) and (3.5), the last three terms of Eq. (A.4) are expressed as
( )
( ) ( ) ( )BgBCBB
g
n
n
g
g
C
C
B
B
kkhkhkkkh
urrrt
ht
ht
h
ρρρ
ρερρρ
213321ˆˆˆ
1ˆˆˆ
+++++−
=
∂
∂+
∂
∂+
∂
∂+
∂
∂
(A.5)
Inserting Eq. (A.5) into Eq. (A.4), and then substituting it into Eq. (A.1), we
get
( ) Qr
Tkr
rrr
Tcu
t
Tccc
n
nggggCCBB
~1 *+
∂
∂
∂
∂=
∂
∂+
∂
∂++ ρερρρ (3.7)
where
( ) ( ) ( )
( ) ( )
( )( ) ( )BCBBgB
BgBCBBBB
BgBCBB
khhkkhh
kkhkhkhkkh
kkhkhkkkhQ
ρρ
ρρρρ
ρρρ
321
213321
213321
ˆˆˆˆ
ˆˆˆˆ
ˆˆˆ~
−++−=
+−−++=
+−−++=
(A.6)
Equation (A.6) can be reshaped using ∫+= dTchhpf
ˆ to read
( ) ( )[ ] ( )[ ]∫∫ −+∆+−+∆+=−−
dTcchkdTcchkkQCBCBBgBgBB
ρρ321
~ (A.7)
If tar cracking reaction was also taken into account, Eq. (A.7) would be as fol-
lows.
( ) ( )[ ] ( )[ ]
( )[ ]∫
∫∫
−+∆
+−+∆+−+∆+=
−
−−
dTcchk
dTcchkdTcchkkQ
GTGTT
CBCBBgBgBB
4
321
~
ερ
ρρ
(3.8)
273
258 Appendix A
274
Appendix B
Makino-Law Theory
The criterion for the existence of a CO flame sheet developed by Makino
and Law states that the gas-phase reaction between CO formed due to the het-
erogeneous reactions and O2 in the surrounding gas takes place only if a re-
duced gas-phase Damköhler number defined as
( )5.0
5.125.02
~
~
~
~
~~
~
~~
~
exp2
2 s
Fs
gs
s
s
g
CO
gpg
T
Y
aT
T
TT
T
mT
aT
WD
rB
λ
βρ
−
−
=∆
∞
∞
∞
∞
(B.1)
exceeds an ignition Damköhler number given by
( ) ( )( )
15.0
5.0
5.0
5.0
2exp1
1exp
22
1−
−
−++=∆
O
OOOiF
erfcη
ληη
πη
λ (B.2)
where
qTcTpF
/~
α= (B.3)
( )qREcaTggpFg
/~
α= (B.4)
275
260 Appendix B
( ) 5.0
, 22/
OHOHgggWYBB
∞′= ρ (B.5)
( ) ( )βπρ +==∞∞
1ln4/~0,pg
rDmm (B.6)
+
+
++
+=
∞
∞∞
,
,
,
,
,
,
,
,
,
2
22
2
2
22
2
2
22
2
1
1
2
1
OH
OH
C
OHs
OHs
CO
O
C
COs
COs
O
O
C
Os
Os
YW
W
A
A
YW
W
A
AY
W
W
A
Aβ
(B.7)
OHCOOiT
Ta
T
T
D
rBA
s
is
s
pis
is 222
,,
,,,exp =
−
=
∞
∞
(B.8)
∞
∞
−=
T~
T~Y~
s
,Oλ (B.9)
2
~OOO
YY α= (B.10)
COCOCOCOFWW υυα /
22= (B.11)
2222/
OOCOCOOWW υυα = (B.12)
( )
−
++=
∞
λλββη
2
,
,
~
~1
1~/1
~
2 s
g
Os
O
OT
aT
mA
Y (B.13)
( )( )
−
+++
+
+−=
∞∞
λβββ
δβ 11~/1
~
1
2~
~
2,
,,
mA
YYY
Os
OO
sF (B.14)
( )32
350120210560
λλλλ
....F +−+= (B.15)
Note that g
B′ and Eg denote the frequency factor and the activation energy
of CO oxidation reaction. Further, Bs,i and and Tas,i represent the frequency
factor and the activation temperature of the surface reaction. δ is defined as the
ratio of WCO2 to WC.
276
Appendix C
Char Oxidation and Gasification Data
In 1982, Goetz et al. investigated experimentally the combustion and gasi-
fication kinetics of four size graded coal chars in a Drop Tube Furnace System
(DTFS). The chars were prepared in the DTFS from commercially significant
coals representing a wide range of rank including a Pittsburgh No. 8 Seam
coal, an Illinois No. 6 Seam coal, a Wyoming Sub C, and Texas Lignite A.
The ASTM ranks of these coals are, respectively, High Volatile A Bituminous
Coal, High Volatile C Bituminous Coal, Subbituminous C Coal, and Lignite
A. The corresponding designated codes of these coals were PSC, ILC, JRC
and TXL, respectively.
The combustion experiments of JRC, ILC and PSC chars were conducted
in the temperature range 1221-1725 K, whereas the gasification tests of all
coal chars were carried out in the temperature range 1294-1724 K. As denoted
in Tables 7.2 and 7.3, the kinetic data of combustion and gasification reported
by Goetz et al. are based on selected measured data. It is unclear why they did
not use all measured values for derivation of kinetic parameters (no explana-
tion is given in their report). The reaction rate constants of char oxidation and
gasification measured as function of temperature reported by Goetz et al. are
reported in Tables C.1-C.7. By analyzing all these data, it is found that the ki-
netic parameter in terms of pre-exponential factor and activation energy nota-
bly differ from those obtained by Goetz et al. The new sets of kinetic parame-
ters given in Tables 7.2 and 7.3 are obtained based on all measured values.
277
262 Appendix C
Table C.1 Reaction rate constant from oxidation of PSC char.
T [K] K [g/cm.s.atm] O2 [atm]
1227 0.0084 0.03
1257 0.01123 0.03
1259 0.02118 0.03
1258 0.02357 0.03
1365 0.00059 0.03
1381 0.00848 0.03
1409 0.00707 0.03
1449 0.06005 0.03
1481 0.07655 0.03
1491 0.10114 0.03
1594 0.00523 0.03
1635 0.09267 0.03
1679 0.12611 0.03
1713 0.17151 0.03
1725 0.17698 0.03
1566 0.06184 0.03
1594 0.02551 0.03
1635 0.04107 0.03
1679 0.08329 0.03
1713 0.06942 0.03
1725 0.07547 0.03
1635 0.00777 0.01
1679 0.08028 0.01
1713 0.14625 0.01
1725 0.21217 0.01
1566 0.08617 0.05
1594 0.04968 0.05
1635 0.12046 0.05
1679 0.13292 0.05
1713 0.15401 0.05
1725 0.14336 0.05
278
Modeling Combustion of Single Biomass Particle 263
Table C.2 Reaction rate constant from oxidation of ILC char.
T [K] K [g/cm.s.atm] O2 [atm]
1221 1.81601 0.03
1227 0.27163 0.03
1242 0.13451 0.03
1257 0.18538 0.03
1259 0.12574 0.03
1258 0.14258 0.03
1679 0.76258 0.03
1713 0.64748 0.03
1725 0.69176 0.03
1227 0.0054 0.03
1242 0.00277 0.03
1257 0.02647 0.03
1259 0.06783 0.03
1258 0.07989 0.03
1365 0.01016 0.03
1381 0.01804 0.03
1409 0.13971 0.03
1449 0.30481 0.03
1481 0.25937 0.03
1491 0.27893 0.03
1566 0.02926 0.03
1594 0.14412 0.03
1635 0.24737 0.03
1679 0.2937 0.03
1713 0.40921 0.03
1725 0.39119 0.03
1566 0.03016 0.03
1594 0.13553 0.03
1635 0.16992 0.03
1679 0.24063 0.03
1713 0.20537 0.03
1725 0.17109 0.03
279
264 Appendix C
Table C.3 Reaction rate constant from oxidation of JRC char.
T [K] K [g/cm.s.atm] O2 [atm]
1221 0.15376 0.03
1227 0.18426 0.03
1242 0.18916 0.03
1257 0.23948 0.03
1259 0.19911 0.03
1258 0.22491 0.03
1725 0.6324 0.03
1221 0.04273 0.03
1227 0.0177 0.03
1242 0.01019 0.03
1257 0.04484 0.03
1259 0.07871 0.03
1258 0.08981 0.03
1365 0.05112 0.03
1381 0.03599 0.03
1409 0.1111 0.03
1449 0.12362 0.03
1481 0.20348 0.03
1491 0.19479 0.03
1566 0.2031 0.03
1594 0.17227 0.03
1635 0.26113 0.03
1679 0.48106 0.03
1713 0.5259 0.03
1725 0.39209 0.03
280
Modeling Combustion of Single Biomass Particle 265
Table C.4 Reaction rate constant from gasification of PSC char.
T [K] K [g/cm.s.atm] CO2 [atm]
1485 0.00001 0.3
1498 0.00003 0.3
1488 0.00003 0.3
1574 0.00004 0.3
1603 0.00004 0.3
1613 0.00007 0.3
1616 0.00007 0.3
1617 0.00009 0.3
1660 0.00004 0.3
1698 0.00008 0.3
1721 0.00016 0.3
1724 0.00024 0.3
1720 0.0003 0.3
1660 0.00003 0.3
1698 0.00007 0.3
1721 0.00012 0.3
1724 0.00017 0.3
1720 0.0002 0.3
1698 0.00003 0.3
1721 0.00011 0.3
1724 0.00011 0.3
1720 0.00011 0.3
1660 0.00004 0.15
1698 0.00011 0.15
1721 0.00009 0.15
1724 0.00022 0.15
1720 0.00028 0.15
1721 0.00006 0.6
1724 0.00012 0.6
1720 0.00024 0.6
281
266 Appendix C
Table C.5 Reaction rate constant from gasification of ILC char.
T [K] K [g/cm.s.atm] CO2 [atm]
1485 0.00006 0.3
1498 0.00008 0.3
1488 0.00008 0.3
1574 0.00005 0.3
1603 0.00008 0.3
1613 0.00026 0.3
1616 0.00028 0.3
1617 0.00032 0.3
1660 0.00009 0.3
1698 0.00027 0.3
1721 0.00081 0.3
1724 0.00108 0.3
1720 0.001 0.3
1660 0.00013 0.3
1698 0.00013 0.3
1721 0.00024 0.3
1724 0.0002 0.3
1720 0.00028 0.3
282
Modeling Combustion of Single Biomass Particle 267
Table C.6 Reaction rate constant from gasification of JRC char.
T [K] K [g/cm.s.atm] CO2 [atm]
1294 0.00004 0.3
1333 0.0002 0.3
1365 0.00016 0.3
1464 0.00005 0.3
1485 0.00046 0.3
1498 0.00071 0.3
1488 0.00087 0.3
1574 0.00007 0.3
1603 0.00014 0.3
1613 0.00148 0.3
1616 0.00196 0.3
1617 0.00219 0.3
1660 0.00011 0.3
1698 0.00137 0.3
1721 0.00579 0.3
1724 0.00577 0.3
1720 0.00461 0.3
1660 0.00043 0.3
1698 0.00077 0.3
1721 0.00165 0.3
1724 0.00206 0.3
1720 0.00165 0.3
1428 0.00026 0.3
1442 0.00013 0.3
1464 0.00007 0.3
1485 0.00003 0.3
1498 0.00007 0.3
1488 0.00008 0.3
1721 0.00052 0.3
1724 0.00039 0.3
1720 0.00107 0.3
283
268 Appendix C
Table C.7 Reaction rate constant from gasification of TXL char.
T [K] K [g/cm.s.atm] CO2 [atm]
1294 0.00003 0.3
1333 0.00003 0.3
1365 0.00019 0.3
1442 0.00017 0.3
1464 0.00027 0.3
1485 0.00098 0.3
1498 0.00152 0.3
1488 0.00188 0.3
1660 0.00045 0.3
1698 0.00167 0.3
1721 0.00578 0.3
1724 0.00548 0.3
1720 0.00582 0.3
284
Appendix D
Derivation of the Simplified Pyrolysis Model
Equations
The procedure for derivation of the model equations of a pyrolyzing spher-
ical thermally thin particle presented in chapter 8 is described here.
Phase 1: Initial heating up
The heat transfer equation is
( )( )
∂
∂−
∂
∂=
∂
−∂
r
TrR
rk
t
TrRc
BpBB
2
2
ρ (8.1)
The following boundary conditions are applied for the initial heating up
phase; see Fig. 8.3a.
BC1: ( )netrB
qr/Tk ′′=∂∂−=0
BC2: ( ) 0/ =∂∂= trrB
rTk
BC3: 0TT
trr=
=
285
270 Appendix D
Let us assume that the temperature profile inside the particle at each time
instant can be represented with a quadratic profile as follows.
( ) 2
210rrr,tT φφφ ++= (D.1)
Using the above boundary conditions, we get
B
tnet
k
rqT
200
′′+=φ (D.2)
B
net
k
q ′′−=
1φ (D.3)
tB
net
rk
q
22
′′=φ (D.4)
Substituting Eqs. (D.2)-(D.4) into Eq. (D.1) yields
( ) ( )2
02
rrrk
qTr,tT
t
tB
net−
′′+= (D.5)
In the next step, we apply space integration to Eq. (8.1) from r = 0 to r = rt.
( )( ) ⇒
∂
∂−
∂
∂=
∂
−∂
∫∫tt r
B
r
pBBdr
r
TrR
rkdr
t
TrRc
0
2
0
2
ρ
( ) ( )
( )
∂
∂−
∂
∂−
=−−−
==
∫
0
22
0
2
0
2
rrr
tB
t
t
r
r
TR
r
TrR
dt
drTrRdrTrR
dt
d
t
t
α
(D.6)
From BC1 and BC2, the right-hand-side of Eq. (D.6) becomes
286
Modeling Combustion of Single Biomass Particle 271
( )B
net
B
rrr
tBk
qR
r
TR
r
TrR
t
′′=
∂
∂−
∂
∂−
==
2
0
22αα (D.7)
We now calculate the first integral on the left-hand-side of Eq. (D.6) with
the aid of the temperature profile given in Eq. (D.5).
( ) ( ) ( )
( ) ( )( )4444444 34444444 21
444 3444 21
2
1
0
2222
0
22
0
0
2
0
2
0
2
222
2
2
I
r
tt
tB
net
I
r
r
t
tB
netr
drrrrrrrRRrk
qdrrrRRT
drrrrk
qTrRdrTrR
tt
tt
∫∫
∫∫
+−+−′′
++−
=
−
′′+−=−
(D.8)
( )
+−=+−= ∫ 3
23
22
00
22
01
t
tt
r rRrrRTdrrrRRTI
t
(D.9)
( )( )
+−
′′=
+−+−′′
= ∫
1026
222
43
22
0
2222
2
tt
t
B
net
r
tt
tB
net
rRrrR
k
q
drrrrrrrRRrk
qI
t
(D.10)
Using Eqs. (D.8)-(D.10), the left-hand-side of Eq. (D.6) reads
( ) ( )
( )
( ) ( ) =−−
+−
′′+−
=−−
+−
′′+
+−
=−−−∫
dt
drTrR
rRrrR
k
q
dt
d
dt
drTrR
dt
drTrR
rRrrR
k
qrRrrRT
dt
d
dt
drTrRdrTrR
dt
d
t
t
tt
t
B
nett
t
t
t
tt
t
B
nett
tt
t
t
rt
0
243
22
0
2
0
243
22
3
22
0
0
2
0
2
1026
10263
+−
′′
1026
43
22 tt
t
B
netrRr
rRk
q
dt
d (D.11)
287
272 Appendix D
Thus, substituting Eqs. (D.7) and (D.11) into Eq. (D.6), we get
netB
tt
tnetqR
rRrrRq
dt
d′′=
+−′′ α
2
43
22 6102
(D.12)
Next, approximate time integration is applied in order to transform the
ODE form of Eq. (D.12) to an algebraic equation. For this, it is assumed that
( ) ( )
2
0netnet
net
qtqq
′′+′′≈′′ (D.13)
Integrating Eq. (D.13) from t = 0 to any given instant t yields
( ) ( ) ⇒′′+′′=+−′′
⇒′′=
+−′′ ∫
tqqRrRrrRq
dtqRrRr
rRqd
netBtttnet
t
netB
tt
tnet
0
24322
0
2
43
22
30510
6102
α
α
tq
qRrRRrr
net
Bttt
′′
′′+=+−
022234 130105 α (D.14)
Phase 2: Pre-pyrolysis heating up
The heat transfer equation can still be represented with Eq. (8.1) during the
pre-pyrolysis heating up stage; see Fig. 8.3b. Moreover, the temperature pro-
file inside particle is assumed to be a quadratic function as given in Eq. (D.1).
The following boundary conditions are employed to obtain the coefficients of
Eq. (D.1).
BC4: ( )netrB
qr/Tk ′′=∂∂−=0
BC5: ( ) 0=∂∂=RrB
r/Tk
BC6: srTT =
=0
288
Modeling Combustion of Single Biomass Particle 273
sT=
0φ (D.15)
B
net
k
q ′′−=
1φ (D.16)
Rk
q
B
net
22
′′=φ (D.17)
Thus, substituting Eqs. (D.15)-(D.17) into Eq. (D.1) results in
2
2r
Rk
qr
k
qTT
B
net
B
net
s
′′+
′′−= (D.18)
Next, Eq. (8.1) is spatially integrated from r = 0 to r = R. Hence,
( ) ( )B
net
B
rRr
B
R
k
qR
r
TR
r
TRRdrTrR
dt
d ′′=
∂
∂−
∂
∂−=−
==
∫2
0
22
0
2αα (D.19)
To calculate the integral in Eq. (D.19), Eq. (D.18) is employed.
( ) ( )
⇒
′′−+
′′−−
′′−
=
′′+
′′−
+
′′+
′′−−
′′+
′′−
=
′′+
′′−−=−
∫
∫∫
∫∫
4
3
4343
0
432
0
32
0
222
0
22
0
2
20
3
312
5
3
2
222
2
Rk
qRTR
k
qTRR
k
qTR
drrRk
qr
k
qrT
drrk
qr
k
qRrRTdrr
k
qRrR
k
qTR
drrRk
qr
k
qTrRdrTrR
B
nets
B
net
s
B
net
s
R
B
net
B
net
s
R
B
net
B
net
s
R
B
net
B
net
s
r
B
net
B
net
s
R t
( ) 4
3
0
2
153R
k
qRTdrTrR
B
netsR ′′
−=−∫ (D.20)
289
274 Appendix D
A combination of Eqs. (D.19) and (D.20) yields
( )netBnetBs
qqRRkTdt
d′′=′′− α155 2 (D.21)
Equation (D.21) is integrated from tR to t using the following approximation
( ) ( )
2
Rnetnet
net
tqtqq
′′+′′≈′′ (D.22)
Hence,
( )
( ) ( ) ( )
( ) ( ) ( )⇒−′′+′′
+′′−′′=−
⇒−′′+′′
=′′−−′′−
⇒′′=′′− ∫
R
Rnet
BRnetsRsB
R
Rnet
BRBsRnetBs
t
tnetBnetBs
ttqq
RqqTTRk
ttqq
qRRkTqRRkT
dtqqRRkTdR
2155
21555
155
2
22
2
α
α
α
( )( )( )
RRnet
B
B
B
Rnet
sRsttqq
Rkk
qqRTT −′′+′′+
′′−′′+=
2
3
5
α (D.23)
Phase 3: Pyrolysis
Let us consider Fig. 8.5. The temperature profiles within the char and the
biomass regions are assumed to be represented as follows.
Char region (c
rr ≤≤0 ): ( ) ( )2
210rrrrT
ccC−+−+= ψψψ (D.24)
Biomass region ( Rrrc
≤≤ ): ( ) ( )2
210 ccBrrrrT −+−+= φφφ (D.25)
Using the boundary conditions BC1-BC5 given in page 221, we find
pT=
0ψ (D.26)
290
Modeling Combustion of Single Biomass Particle 275
C
pB
k
hmk ∆′′+−=
&1
1
φψ (D.27)
Cc
pBnet
kr
hmkq
2
1
2
∆′′++′′=
&φψ (D.28)
pT=
0φ (D.29)
( )c
rR −−=
2
1
2
φφ (D.30)
Thus, the temperature profiles given by Eqs. (D.24) and (D.25) are rewritten as
follows.
( ) ( )211
2rr
kr
hmkqrr
k
hmkTT
c
Cc
pBnet
c
C
pB
pC−
∆′′++′′+−
∆′′+−=
&& φφ (D.31)
( )( )
( )21
12
c
c
cpBrr
rRrrTT −
−−−+=
φφ (D.32)
The heat transfer equation for the biomass region can still be represented
with Eq. (8.1). As the next step, it is integrated from r = rc to r = R. Hence,
( )( ) ⇒
∂
∂−
∂
∂=
∂
−∂
∫∫R
rB
R
rpBB
cc
drr
TrR
rkdr
t
TrRc
2
2
ρ
( ) ( )
( ) ( )
( )1
222
22
1
φαα
φ
cB
rr
c
Rr
B
c
pc
R
r
rRr
TrR
r
TRR
dt
drTrRdrTrR
dt
d
c
c
−−=
∂
∂−−
∂
∂−
=−+−
=
=
∫
(D.33)
The integral on the left-hand-side of Eq. (D.33) is determined using Eq.
(D.32). Hence,
291
276 Appendix D
( ) ( ) ( )( )
( )
( ) ( )( )
( )( )( )drrrrrrRrR
rR
drrrrRrRdrrRrRT
drrrrR
rrTrRdrTrR
R
rcc
c
R
rc
R
rp
R
rc
c
cp
R
r
c
cc
cc
∫
∫∫
∫∫
+−+−−
−
−+−++−
=
−
−−−+−=−
22221
22
1
22
21
1
22
222
22
2
φ
φ
φφ
(D.34)
where
( ) ( )322
32
c
pR
rp
rRT
drrRrRTc
−=+−∫ (D.35)
( )( ) ( )
=
−+−+−
=−+−+−=−+− ∫∫R
r
c
cc
R
rccc
R
rc
c
cc
rrRrrrRr
rRrrR
drrrRrrRrrRrrRdrrrrRrR
343
2
2
222
3
22
4322
1
22322
1
22
1
φ
φφ
( ) ( )414322341
12464
12ccccc
rRrRrrRRrR −=+−+−φφ
(D.36)
( )( ) ( )
( ) ( )drrrrRrRrdrrRrrRr
drrRrRrdrrrrrrRrR
R
rccc
R
rc
R
r
R
rcc
cc
cc
∫∫
∫∫
+−++−−
+−=+−+−
22222322
43222222
222
222
( ) ( )543254322 6151030
12
ccc
R
rrRrrRRdrrRrRr
c
−+−=+−∫
( ) ( )54324322 3866
122
cccc
R
rc
rRrrRRrdrrRrrRrc
−+−=+−∫
( ) ( )54233222222 333
12
cccc
R
rccc
rRrRrRrdrrrrRrRrc
−+−=+−∫
Hence,
292
Modeling Combustion of Single Biomass Particle 277
( )( )
( )( )
30510105
30
1
22
5
54233245
2222
c
ccccc
R
rcc
rRrRrRrRrRrR
drrrrrrRrRc
−=−+−+−
=+−+−∫ (D.37)
Combining Eqs. (D.34)-(D.37) results in
( ) ( ) ( )( )
( )
( ) ( )413
5
14132
153
302123
cc
p
c
c
cc
pR
r
rRrRT
rR
rRrRrR
TdrTrR
c
−+−=
−
−−−+−=−∫
φ
φφ
(D.38)
Finally, we substitute Eq. (D.38) into Eq. (D.33). Hence,
( ) ( ) ( ) ( ) ⇒−−=−+
−+−
1
22413
153φα
φcB
c
pccc
prR
dt
drTrRrR
dt
drR
dt
dT
( )[ ] ( )
( ) ( ) ( ) ⇒−−=−−−
⇒−−=−
1
2
1
314
1
24
1
154
15
φαφφ
φαφ
cB
c
cc
cBc
rRdt
drrR
dt
drR
rRrRdt
d
( )2
111154
c
Bc
c rRdt
dr
rRdt
d
−−
−=
φαφφ (D.39)
The heat transfer equation for the char region including the convective
flow of the volatiles is described as follows.
( )[ ] ( ) ( ) ( )
∂
∂−
∂
∂=
∂
∂−′′−−−
∂
∂
r
TrR
rk
r
TrRcmTrR
tc
CcpvpCC
2221 &ωρ (D.40)
Equation (D.40) is integrated from r = 0 to r = rc. Hence,
293
278 Appendix D
( ) ( )( ) ( )
( )
∂
∂−
∂
∂−
=∂
∂−′′−−−−−
==
∫∫
0
22
0
2
2
0
2 1
rrr
cC
r
pCC
cpvc
pc
r
r
TR
r
TrR
drr
T
c
rRcm
dt
drTrRTdrrR
dt
d
c
cc
α
ρ
ω &
(D.41)
The derivative of temperature at r = 0 and r = rc is determined from Eq.
(D.31). Hence,
C
pB
rr k
hmk
r
T
c
∆′′+=
∂
∂
=
&1φ
(D.42)
C
net
r k
q
r
T ′′−=
∂
∂
=0
(D.43)
Next, we calculate the first integral on the left-hand-side of Eq. (D.41)
with the aid of Eq. (D.31).
( )
( ) ( ) ( ) =
−
∆′′++′′+−
∆′′+−−
=−
∫
∫c
c
r
c
Cc
pBnet
c
C
pB
p
r
drrrkr
hmkqrr
k
hmkTrR
TdrrR
0
2112
0
2
2
&& φφ
( ) ( )( )
( )( )[ ] ⇒+−+−∆′′++′′
+−+−∆′′+
−+−
∫
∫∫
c
cc
r
cc
Cc
pBnet
r
c
C
pBr
p
drrrrrrRrRkr
hmkq
drrrrRrRk
hmkdrrRrRT
0
22221
0
221
0
22
222
22
&
&
φ
φ
where
( ) ( )322
0
22 333
12
ccc
r
rRrrRdrrRrRc
+−=+−∫
( )( ) ( )4322
0
22 4612
12
ccc
r
crRrrRdrrrrRrR
c
+−=−+−∫
294
Modeling Combustion of Single Biomass Particle 279
( )( )[ ] ( )3245
0
2222 10530
122
ccc
r
ccrRRrrdrrrrrrRrR
c
+−=+−+−∫
Hence,
( ) ( )
( )
( )32451
43221
322
0
2
10560
4612
333
ccc
Cc
pBnet
ccc
C
pB
ccc
pr
rRRrrkr
hmkq
rRrrRk
hmk
rRrrRT
TdrrRc
+−∆′′++′′
++−∆′′+
−+−=−∫
&
&
φ
φ (D.44)
Substituting Eqs. (D.42)-(D.44) into Eq. (D.41) yields
( ) ( )
( ) ( )
( ) ( )( ) ⇒
′′+
∆′′+−=
∂
∂−′′−
−−−
+−
∆′′++′′
+
+−
∆′′+−+−
∫C
net
C
pB
cC
r
pCC
cpv
c
pcccc
Cc
pBnet
ccc
C
pB
ccc
p
k
qR
k
hmkrRdr
r
T
c
rRcm
dt
drTrRrRRrr
kr
hmkq
dt
d
rRrrRk
hmk
dt
drRrrR
dt
dT
c 212
0
2
232451
43221322
1
10560
4612
333
&&
&
&
φα
ρ
ω
φ
φ
( )( )[ ]
( )( )[ ]
( ) ( ) ( ) ( ) ( )[ ]⇒−−′′−−′′+∆′′+−=
++−∆′′+
−+−∆′′++′′
pscpvnetpBcC
cccpB
cccpBnet
TTrRcmqRhmkrR
rRrrRhmkdt
d
rRRrrhmkqdt
d
22
1
2
4322
1
2234
1
160
4655
105
&&
&
&
ωφα
φ
φ
( ) ( )( )[ ]
( ) ( ) ( ) ( ) ( )[ ]pscpvnetpBcC
cccpBcccnet
TTrRcmqRhmkrR
rRrRrhmkrRRrrqdt
d
−−′′−−′′+∆′′+−=
−−∆′′+++−′′
22
1
2
2243
1
2234
160
20415105
&&
&
ωφα
φ
(D.45)
295
280 Appendix D
296
Author: Yousef Haseli
Edition: 1st edition (2011)
Chapters: 7 chapters
Pages: 230pp
ISBN-13: 978-9-038-62522-5
Illustrations: 55 ills. (3 in color)
Thermodynamic Optimization of Power Plants aims to establish and illustrate com-
parative multi-criteria optimization of various models and configurations of power
plants. It intends to show what optimization objectives one may define on the basis of
the thermodynamic laws, and how they can be applied for optimization of heat en-
gines. By examination of a variety of power plant models, the operational regimes at
maximum work output, maximum thermal efficiency and minimum entropy genera-
tion have been examined and compared. The discussions covered in this book include:
• Explanation of the concept of entropy and its generation,
• Relationship between entropy generation and exergy destruction,
• Review of Sadi Carnot’s principles, and explaining under what conditions
Carnot cycle can be considered as the most efficient engine,
• Stirling and Ericsson cycles operating with nonideal gas,
• Examination of performance of different endoreversible power plants at max-
imum work and minimum entropy generation,
• Multi-objective optimization of conventional gas turbine engines,
• Thermodynamic performance of a combined gas turbine and solid oxide fuel
cell power cycle.
This is a promising supplementary book for advanced undergraduate and graduate
students of thermodynamics, energy systems, and thermal design. It can be also used
by engineers and researchers working in the field of power plant technology.
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