modeling combustion of single biomass particle

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

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

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


6.2 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


6.4.1 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




7.4 Conclusion 202

References 202

Chapter 8 Simplified Biomass Combustion Model 209



8.2.1 Heating up Phase 214

8.2.2 Pyrolysis Phase 219

8.2.3 Char Combustion Phase 224


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


9.2 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


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


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


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


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


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


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


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


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


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



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


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


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


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

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moisture and char shrinkage on the pyrolysis of a biomass particle. Fuel

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[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.

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in fires by laser simulation. Proc Combust Inst 16: 1459-1470.

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[24] Diebold J. P. 1985. The cracking of depolymerized biomass vapors in a

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[26] Grønli M. G. 1996. A theoretical and experimental study of the thermal

degradation of biomass. PhD Thesis, Norwegian University of Science

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a thermoanalytical study. J Fire Flammability 2: 321-333.

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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

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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,

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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-

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48


[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


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


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


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


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


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


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


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


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


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


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


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


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


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


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



ta: Chan et al.

80




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


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


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


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


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


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


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


(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


(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


(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


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




102





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havior and products of some wood varieties. Combust Flame 124: 165-

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[4] Larfeldt J., Leckner B., Melaaen M. C. 2000. Modelling and measure-

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[5] Chan W. C., Kelbon M., Krieger B. B. 1985. Modeling and experi-

mental verification of physical and chemical processes during pyrolysis

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[6] Tran H. C., White R. H. 1992. Burning rate of solid wood measured in a

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[8] Shafizadeh F., Chin P. S. 1977. Thermal deterioration of wood. in: I.S.

Goldstein (Ed.), Wood Technology: Chemical Aspects, ACS Symp Ser

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[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

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[10] Boroson M. L., Howard J. B., Longwell J. P., Peters W. A. 1989. Prod-

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[11] Diebold J. P. 1985. The cracking of depolymerized biomass vapors in a

continuous, tabular reactor. MSc Thesis, Colorado School of Mines,

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[12] Di Blasi C. 1993. Analysis of convection and secondary effects within

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[14] Park W. C. 2008. A study of pyrolysis of charring materials and its ap-

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from fast pyrolysis of large beech wood particles. J Anal Appl Pyrolysis

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[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


[25] Di Blasi C., Branca C. 2001. Kinetics of primary product formation

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[26] Font R., Marcilla A., Verdu E., Devesa J. 1990. Kinetics of the pyrolysis

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[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.

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Cozzani V. 2003. Heat of wood pyrolysis. Fuel 82: 81-91.

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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


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


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


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


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


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


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


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


122


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


124


Figure 4.9 Simulated biomass and char densities corresponding to combustion of a 1


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


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


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.


sive study of biomass particle combustion. Energ Fuel 22: 2826-2839.



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.



[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


[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


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


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


( )

′′

′′

′′

−=

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


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


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


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


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


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


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


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


(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


(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


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.

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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.



89: 1156-1168.







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


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


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


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


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


( )[ ] ( )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


( ) ( )

( )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


( ) ( )( )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


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


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.


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


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-


(6.8), (6.10), (6.12)

and (6.13) until xc

equals L

Yes: Thermally thin No: Thermally thick

At each time incre-


(5.8) and (5.9) until Ts

equals Tp

At each time incre-


(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


(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


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


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


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


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


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


(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


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.

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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).

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[5] Kanury A. M., Holve D. J. 1982. Transient conduction with pyrolysis

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[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

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[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

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198


[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.


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.



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

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89: 1156-1168.



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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


posed.

Hamor et al./Ref.

[3]

Brown coal

char Experimental


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


Table 7.1 (Continued)


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



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




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



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.


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


[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


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]


coal char 703 90000 1 Ref. [55]


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


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


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



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


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).

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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


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.


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


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


(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


( )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


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


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


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


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)


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


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


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


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


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


RERERENCES





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.



89: 1156-1168.



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


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


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


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


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


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


( )( )

( )( )

=×

=×=

+−

+−

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.


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


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


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


Table C.2 Reaction rate constant from oxidation of ILC char.


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.


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


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.


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


Table C.6 Reaction rate constant from gasification of JRC char.


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.


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


( )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


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


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


( )( )

( )( )

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


( )( )[ ] ( )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.

www.haselinnovation.com

Thermodynamic Optimization of Power Plants

297

vi

298

modeling combustion of single biomass particle

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