SIMULATION OF MACROSCOPIC MASS LOSS RATE BEHAVIOR
AS A FUNCTION OF TEMPERATURE AND HEATING RATE FOR
THE PYROLYSIS OF WASTE TIRE RUBBER PARTICULATE
MATTER
Thesis
By
MANUEL FELIPE NAVARRETE RODRIGUEZ
Submitted to the office of Undergraduate studies of Universidad de Los Andes
In fulfillment of the requirements for the degree of
B. SC. CHEMICAL ENGINEERING
January 2015
Simulation of macroscopic mass loss rate behavior as a function of temperature and heating rate for the pyrolysis of waste tire rubber particulate matter
SIMULATION OF MACROSCOPIC MASS LOSS RATE BEHAVIOR
AS A FUNCTION OF TEMPERATURE AND HEATING RATE FOR
THE PYROLYSIS OF WASTE TIRE RUBBER PARTICULATE
MATTER
Thesis
By
MANUEL FELIPE NAVARRETE RODRIGUEZ
Submitted to the office of Undergraduate studies of Universidad de Los Andes
In fulfillment of the requirements for the degree of
B. SC. CHEMICAL ENGINEERING
Approved by:
Chair of committee, Rocío Sierra Ramírez, PhD.
Committee Members, Nicolas Ríos Ratkovich, PhD.
John Jairo Ortíz Martínez, B.Sc.
Head of department Oscar Alvarez Solano, PhD.
January 2015
ABSTRACT
Simulation of macroscopic mass loss rate behavior as a function of temperature and heating rate for
the pyrolysis of waste tire rubber particulate matter (January 2015)
Manuel Felipe Navarrete Rodriguez, Universidad de Los Andes, Colombia
Advisor: Rocío Sierra Ramírez, PhD Co-Advisor: John Jairo Ortíz Martínez, B.Sc
The pyrolysis of waste tire rubber (WTR) is an important process by which the recovery of
energy from waste tires becomes feasible by enabling its conversion into tire derived fuels (TDF).
Careful considerations of the effect of key variables which govern the process must be taken in
order to properly model the pyrolysis of WTR. The aim of this work is to simulate the macroscopic
behavior of mass loss rate in the pyrolysis of waste tire rubber as a function of temperature and
heating rate of the feed, through an adequate mathematical model which considers mass and heat
transfer limitations in concurrence with their importance as key limiting phenomena which govern
the process depending on the heating rate and final temperature of the pyrolysis of WTR for chips
sizes up to 2.5cm. An experimental validation of the simulated results supports the chosen model
which shows good fit and accurate WTR pyrolysis behavior prediction for heating rates up to
40K/min without curve fitting.
RESUMEN
Simulación del comportamiento macroscópico de rata de pérdida de masa como función de la
temperatura y rata de calentamiento en la pirolisis de caucho de llanta (Enero 2015)
Manuel Felipe Navarrete Rodríguez, Universidad de Los Andes, Colombia
Asesor: Rocío Sierra Ramírez, PhD Co-Asesor: John Jairo Ortíz Martínez, B.Sc
La pirolisis de caucho de llanta (WTR por sus siglas en inglés) es un proceso importante por
medio del cual se hace factible la recuperación de energía a partir de llantas usadas a través de su
conversión en combustibles derivados de las llantas. Se deben tomar consideraciones cuidadosas de
las variables principales que gobiernan el proceso con el fin de modelar adecuadamente la pirolisis
de WTR. El objetivo de este trabajo es simular el comportamiento macroscópico de la rata de
pérdida de masa durante el proceso de pirolisis de caucho de llanta, como función de la temperatura
y rata de calentamiento. Esto se hace a través de un modelo matemático que considera las
limitaciones de transferencia de masa y calor en línea con su importancia como fenómenos
limitantes claves que gobiernan el proceso de pirolisis dependiendo de la temperatura y rata de
calentamiento efectiva en chips de hasta 2.5cm. Se ha comparado el modelo escogido en este
trabajo con resultados experimentales obtenidos en trabajos citados que indican un ajuste preciso al
comportamiento del proceso de pirolisis hasta ratas de calentamiento de 40 K/min sin realizar
ajustes de parámetros.
Palabras claves: Pirolisis, rata de calentamiento, caucho de llanta (WTR), combustibles derivados, rata de pérdida de masa.
AKNOWLEDGEMENTS
This work is dedicated to my mother, Maria Antonieta Rodriguez for her unconditional support
along my life and particularly throughout the development of my major studies towards achieving a
chemical engineering degree. I would also like to thank my family and friends for accompanying
and supporting me through this journey. Special thanks to Dr. Rocío Sierra for her guidance,
patience, mentorship and enthusiasm during the development of this entire work. Last but not least,
I would like to thank the people who helped me during this project whom I could not have done this
NOMENCLATURE
𝑎𝑖 Mass loss conversion of reaction i 𝛼 Total mass loss fraction
𝐴𝑖 Preexponential factor (s−1)
𝐴𝑐𝑗 Preexponential factor for exothermic reaction j (s−1)
𝐸𝑎𝑖 Activation energy (J/mol)
𝐸𝑐𝑗 Activation energy for exothermic reaction j (J/mol) 𝑖 Mass loss reaction index
𝑗 Exothermic reaction index
𝑘𝑐𝑗 Rate constante of exothermic reation j (s−1)
𝑘𝑖 Rate constant of reaction i (s−1)
𝑛𝑐𝑗 Reaction order of exothermic reaction j 𝑛𝑖 Reaction order of reaction i
𝑅 Gas constant (J/mol − K) 𝑡 Time (s)
𝑇 Temperature (K)
𝑤𝑖 Coefficient of mass loss contribution due to reaction i 𝑊0 Initial tyre particle mass
𝑊 Tyre particle mass
TABLE OF CONTENTS
ABSTRACT ... iv
RESUMEN ... v
NOMENCLATURE ... vii
TABLE OF CONTENTS ... viii
LIST OF FIGURES ... ix
LIST OF TABLES ... xi
1. INTRODUCTION ... 1
1.1. Pyrolysis ... 2
1.1.1. Slow pyrolysis ... 3
1.1.2. Fast pyrolysis ... 4
1.2. Rubber tire composition ... 5
1.3. Mathematical Models for Pyrolysis ... 6
1.3.1. Mathematical model for exothermic kinetics ... 14
1.3.2. Coupled Mathematical model for heat flow ... 15
2. OBJECTIVES ... 16
3. METHODOLOGY ... 17
3.1. Algorithm for solution ... 17
3.2. Assumptions ... 18
4. RESULTS AND DISCUSSION ... 20
4.1. Kinetic Model definition & selection ... 20
4.1.1. Comparison with other models... 20
4.2. Simulated Results ... 24
4.3. Experimental comparison of results ... 30
5. CONCLUSIONS ... 32
BIBLIOGRAPHY ... 33
APPENDIX 1. SIMULATION RESULTS COMPARISON OF KINETIC MODELS AT DIFFERENT HEATING RATES... 35
LIST OF FIGURES
Figure 1. Product spectrum from pyrolysis. (Bridgwater, 2012) ... 3
Figure 2. Behavior of mass loss rate profiles as a function of heating rate in a DTG analysis. (JD, 2013) ... 5
Figure 3. Rubber monomers in tires. Taken from (Quek & Balasubramanian, 2012) ... 6
Figure 4. DTG profiles at different heating rates of 1mm samples. (Senneca, Salatino, & Chirone, 1999) ... 8
Figure 5. Deconvolution of different components of rubber tire pyrolysis. (Quek A. B., 2008) ... 11
Figure 6. Multi-reaction Pyrolysis Kinetic Framework. (Cheung, Lee, Lam, Lee, & Hui, 2010) .... 12
Figure 7. DTG curve for heating rate 15 K/min. (González, Encinar, Canito, & Rodríguez, 2001) 13 Figure 8. Methodology to best approximate WTR Pyrolysis by mathematical modeling and simulation ... 17
Figure 9. Algorithm for solution using finite difference method ... 18
Figure 10. Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al and experiments at heating rate 20K/min. Particle size 7mm. ... 21
Figure 11.Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 20K/min. Particle size 25mm. ... 22
Figure 12. Mass loss kinetics model comparison at heating rate 20K/min vs experimental data ... 23
Figure 13. Comparison of experimental and simulated results of DTG at Heating rate 20K/min based on Aylon et Al Kinetics Model. Particle size 25mm. ... 24
Figure 14. Derivative Mass Loss profiles for heating rates β= 2K/min - 20K/min ... 25
Figure 15. Derivative mass loss radial profiles for heating rates 2K/min – 20K/min ... 26
Figure 16. Derivative mass loss radial profile for heating rate 20K/min ... 27
Figure 17. Comparison of Derivative mass loss at surface and center of the particle for B=2K/min and 20K/min ... 28
Figure 18. Temperature radial profiles for heating rates 2K/min – 20K/min ... 29
Figure 19. Total Mass Loss profiles for heating rates 2 K/min – 20K/min ... 29
Figure 20. Experimental data results obtained by TGA analysis. ... 30
Figure 21. Comparison of experimental and simulated results of DTG at Heating rate 10K/min. ... 31
Figure 22 Comparison of experimental and simulated results of DTG at heating rate 20K/min ... 31
Figure A1. 1 Mass loss kinetics model results comparison of Aylon et al at heating rate 10K/min vs experimental data. ... 35
Figure A1. 2 Mass loss kinetics model results comparison of Cheung et al at heating rate 10K/min vs experimental data. ... 35
Figure A1. 3 Mass loss kinetics model results comparison of Queck et al at heating rate 10K/min vs experimental data. ... 36
Figure A1. 4 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 10K/min. Particle size 7mm. ... 36
Figure A1. 5 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 10K/min. Particle size 25mm. ... 37
Figure A1. 6 Mass loss kinetics model results comparison of Aylon et al at heating rate 20K/min vs experimental data. ... 37
Figure A1. 7 Mass loss kinetics model results comparison of Cheung et al at heating rate 20K/min vs experimental data. ... 38 Figure A1. 8 Mass loss kinetics model results comparison of Quekc et al at heating rate 20K/min vs
experimental data. ... 38 Figure A1. 9 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck
et al at heating rate 20K/min. Particle size 7mm. ... 39 Figure A1. 10 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck
et al at heating rate 20K/min. Particle size 25mm. ... 39 Figure A1. 11 Mass loss kinetics model results comparison of Aylon et al at heating rate 30K/min
vs experimental data. ... 40 Figure A1. 12 Mass loss kinetics model results comparison of Cheung et al at heating rate 30K/min
vs experimental data. ... 40 Figure A1. 13 Mass loss kinetics model results comparison of Queck et al at heating rate 30K/min
vs experimental data. ... 41 Figure A1. 14 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck
et al at heating rate 30K/min. Particle size 7mm. ... 41 Figure A1. 15 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck
et al at heating rate 30K/min. Particle size 25mm. ... 42 Figure A1. 16 Mass loss kinetics model results comparison of Aylon et al at heating rate 40K/min
vs experimental data. ... 42 Figure A1. 17 Mass loss kinetics model results comparison of Cheung et al at heating rate 40K/min
vs experimental data. ... 43 Figure A1. 18 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, at heating
rate 40K/min. Particle size 7mm. ... 43 Figure A1. 19 Mass loss kinetics model results comparison of Aylon et al at heating rate 100K/min
... 44 Figure A1. 20 Mass loss kinetics model results comparison of Cheung et al, Aylon et al at heating
LIST OF TABLES
Table 1. Elemental and proximate analysis of different tires reported in literature. (JD, 2013) ... 9 Table 2. Mass loss kinetic parameters (Cheung, Lee, Lam, Lee, & Hui, 2010) ... 11 Table 3. Dynamic kinetic parameters for heating range 5-60 K/min. (González, Encinar, Canito, &
Rodríguez, 2001) ... 13 Table 4. Model prediction range comparison ... 24
1. INTRODUCTION
Around the globe, rubber tire production is one of the greatest sources of non-biodegradable
waste, estimated at 1.5 billion units per year. Currently, an estimated 4 billion waste tires are
deposited in landfills and stockpiles worldwide and in Europe alone, more than 3.3 million tons of
used tires are discarded annually (JD, 2013). Waste tire rubber management thus presents both a
great challenge in the current panorama of waste disposal in terms of pollution control and an
opportunity in energy recovery from waste sources (United Nations, 2011). Due to the large scale
production and annual disposal of used rubber tires, this product has become a potentially valuable
source of alternative energy, granted its valuable chemical composition and high calorific value of
25-35 GJ/ton, in comparison to an average of 27 GJ/ton present in coal/carbon
(EuropeanTyre&RubberManufacturers’Association, 2011).
Many efforts have been made throughout the years to reduce the impact of waste tire disposal
around the world. Such efforts include both physical and chemical treatments to reuse or recover
energy from waste tires and prevent landfills from stocking up with this non-biodegradable material
which poses a serious risk for the pollution of water streams and air in case of combustion.
Additionally, CO2 emissions from tire rubber combustion are comparable to that of carbon, thus
making it an unfeasible option to dispose of this waste by this method. Nevertheless, for the past
three decades scientists and engineers have worked on the application and modeling of pyrolysis
(Quek & Balasubramanian, 2012) aiming toward establishing a better way to reuse the energy from
waste tires and prevent the pollution inherently coming from its disposal by traditional methods.
Due to the physical properties of scrap tires, thermochemical processes such as pyrolysis have
gained high interest because not only valuable products can be obtained, but low emissions are also
provide the internal energy demand. (Aylón, Fernández-Colino, Murillo, Navarro, García, &
Mastral, 2009).
Mathematical modeling and simulation is chosen as a complementary method over
experimental characterization of the process as it presents an important advantage in terms of
experimental costs. Furthermore, the ability to understand the contributions of the different
phenomena which take place during the pyrolysis reactions through modeling and simulation at a
macroscopic level allow for a better identification of the processes governing limitations which
enable the prediction of the behavior of the WTR pyrolysis system at different operation conditions.
Nevertheless, validation versus experimental results is a key final stage of such simulation and
modeling procedure, as it confirms the usefulness of the chosen mathematical model.
1.1.
Pyrolysis
Pyrolysis is a thermochemical process which allows breaking apart chemical bonds in organic
materials which are decomposed into simpler constituent components when subjected to high heat
in an inert or oxygen free atmosphere (JD, 2013). The main products obtained from this thermal
devolatization of organic materials are char and volatiles (Bellais, 2007). Temperature and heating
rate are two of the main operation variables which determine the stability of the products obtained,
along with the kinetics of several chemical reactions that may occur simultaneously and the limiting
phenomena which drive such reactions (Sanchez, 2013). Concurrently, several authorities and
investigators of the field of WTR pyrolysis agree on the main limiting phenomena of the process
which primarily depend on the operating conditions of the process. Such phenomena are mainly the
kinetics of occurring chemical reactions, the internal heat transfer by conduction and the external
heat transfer by convection from the mass subjected to a high heating rate (Bellais, 2007).
It is thoroughly accepted by researchers that pyrolysis temperature is the main variable to
separated (Bridgwater, 2012). For instance, Biomass pyrolysis takes place from 573K to 923K and
WTR pyrolysis is in the range between 673K to 873K.This is due to the differences of the organic
tissue found in Biomass versus the composition of WTR. Operation temperature has a great impact
on the type of products obtained during pyrolysis, ranging from char to gases and tar. Nevertheless,
it has been found that the heating rate at which the pyrolysis occurs, greatly determines the yield
proportion of such products as it can be observed in Figure 1. The heating rate of the feed is thus a
key variable and depending on it, pyrolysis can be categorized as slow or fast pyrolysis (Sanchez,
2013).
Figure 1. Product spectrum from pyrolysis. (Bridgwater, 2012)
1.1.1.
Slow pyrolysis
Slow pyrolysis occurs if the heating time is longer than the characteristic reaction time. Such
characteristic time is related to the kinetic rate constant for the specific pyrolysis taking place
(Sanchez, 2013). Slow pyrolysis normally occurs at heating rates ranging from 0.1 K/min to 20
slow pyrolysis favors the production of char due to lower process temperatures and longer vapor
residence times. (Bridgwater, 2012)
In the case of WTR, slow pyrolysis greatly differs from fast pyrolysis due to the composition of
rubber tires. According to Senneca et al. at low heating rates, the pyrolysis of WTR can be divided
into two main stages (Senneca, Salatino, & Chirone, 1999). The primary stage is the
depolymerization of rubber components and the secondary stage is the cyclization and crosslinking
of chemical compounds produced by the high temperature of the system during extended periods of
time (Quek & Balasubramanian, 2012).
1.1.2.
Fast pyrolysis
Fast or flash pyrolysis occurs at high heating rates in which the conservation of energy in the
final product is favored; approximately 60% of the total energy contained in the original substrate is
recovered (Bellais, 2007). For WTR, fast pyrolysis does not follow the two stage model presented
by Senneca et al. since the internal heat conduction becomes the new governing phenomena and it
is not accounted for within such model (Senneca, Salatino, & Chirone, 1999). Figure 2 depicts the
effect of rising heating rate on the behavior of mass loss rate versus temperature. From this figure it
can be established that at higher heating rates the reaction temperature raises, thus favoring liquid
yields as reported by Martinez et al. (JD, 2013).
The fast pyrolysis process usually requires feedstock in small particles and devices which can
allow a fast removal of vapors in order to prevent secondary reactions to take place (Bridgwater,
2012). Such secondary reactions lead to a higher yield of char, due to a possible nucleation in
existing char particles. Nevertheless, if controlled properly, fast pyrolysis can lead to the recovery
of TDF at higher yields (around 50-60% wt. for rubber feedstock) and is recognized as an effective
production route for liquid fuels (Sanchez, 2013). The heating rate conditions at which fast
called superfast pyrolysis can take place at heating rates up to 900K/min but the residence times of
the volatiles should be lower than 2s (Senneca, Salatino, & Chirone, 1999).
Figure 2. Behavior of mass loss rate profiles as a function of heating rate in a DTG analysis. (JD, 2013)
1.2.
Rubber tire composition
Rubber tire is a mix of polymers composed mainly of vulcanized isoprene (natural rubber
(NR)), butadiene rubber (BR) and Stirene-Butadiene Rubber (SBR). These compounds are shown in
Figure 3. In addition to these, other chemicals and materials added during the tire manufacturing
process include vulcanization accelerators and retarders, fillers, softeners and extenders,
Figure 3. Rubber monomers in tires. Taken from (Quek & Balasubramanian, 2012)
The rubber tire composition is best described by both an elemental analysis and a proximate
analysis to find its amount of moisture, volatile matter, fixed carbon and ash. In Table 1 the
elemental analysis of rubber tires from multiple sources show that Carbon is the main component
followed by hydrogen, ashes and oxygen. Table 1 also shows that volatile material represents more
than 60% of the mass constituent of rubber tire. A study conducted by Conesa et. Al. shows that
rubber tire pyrolysis yields over seventeen different types of volatiles including methane, ethane,
ethylene, propylene, acetylene, among other molecules (Conesa, Fullana, & Font, 2000).
1.3.
Mathematical Models for Pyrolysis
Based on the previous works of Aylon, et al. Cheung et al., Senneca, et al. and Quek et al,
among other relevant works cited in their studies, it is possible to establish a set of mathematical
models which best describe the results found experimentally and in literature depending on the
As a first approach, pyrolysis models assume a kinetic rate-limiting type of reaction and do not
consider heat or mass transfer phenomena in the process at any given heating rate or temperature
conditions. Such a model is of the form presented in Equation 1:
𝑟 = 𝐴𝑒−𝐸𝑎/𝑅𝑇𝐶𝑛 (1)
Where C is the mass concentration of the reactant, R is the molar gas constant (8,314 J mol-1K
-1
), T the temperature of the particular data point, A is the pre-exponential factor [min-1], and Ea is
the activation energy of reaction [J/mol] using an Arrhenius type reaction model constant. In this
case C may be substituted by X, which is the normalized mass fraction of the tire sample
decomposed in terms of the initial mass of the tire sample, mo, the final mass after complete
pyrolysis, 𝑚∞, and the mass at any time m as shown in Equations 2 and 3 for isothermal conditions (Quek & Balasubramanian, 2012).
𝑋 = 𝑚𝑜−𝑚
𝑚𝑜−𝑚∞ (2)
𝑑𝑋
𝑑𝑇= 𝐴𝑒−𝐸𝑎/𝑅𝑇(1 − 𝑋)𝑛 (3) For non-isothermal conditions where the heating rate dT/dt = 𝛽 is constant, Equation 4 applies: (Quek & Balasubramanian, 2012).
𝑑𝑋 𝑑𝑇=
1 𝛽𝐴𝑒
−𝐸𝑎/𝑅𝑇(1 − 𝑋)𝑛 (4)
Another approach is a multi-stage model presented by Senneca et al. which addresses the
kinetics and mechanisms of pyrolysis of WTR by fitting straight lines on Arrhenius plots obtained
experimentally at four different heating rates (5, 20, 100 and 900 K/min). The model considers two
pyrolysis stages which are divided into depolymerization and degradation of cyclization products
(Senneca, Salatino, & Chirone, 1999). The model can be supported by the fact that the mass rate
loss shows two different peaks at heating rates between 5 and 20 K/min, which can be observed in
the extensive use of logarithm involving the Arrhenius rate equation which leads toward the fact
that this mathematical method might conceal errors (Conesa, Marcilla, Caballero, & Font, 2001).
Furthermore, Quek et al. (Quek & Balasubramanian, 2012) have developed a model which
includes both the kinetic rate-limiting behavior and the effects of the thermal lag associated to
internal heat conduction limitations and mass transfer limitations found in the tire pyrolysis process
at higher heating rates.
Table 1. Elemental and proximate analysis of different tires reported in literature. (JD, 2013)
Elemental analysis on dry basis (wt.%) Proximate analysis on as received basis (wt.%)
Sample C H N S O A A VM FC M
1 81.72 6.54 0.55 1.87 2.68 6.64 6.64 62.58 30.07 0.71
2 83.80 6.90 0.60 2.00 2.30 4.40 4.30 63.40 30.40 1.90
3 83.80 7.60 0.40 1.40 3.10 3.70 3.70 67.30 28.50 0.50
4 82.36 6.92 0.30 1.40 2.03 5.00 4.95 73.74 20.22 1.09
5 85.90 8.00 0.40 1.00 2.30 2.40 2.40 66.50 30.30 0.80
6 84.33 7.81 0.49 1.66 3.32 2.40 7.10 62.20 29.40 1.30
7 82.80 7.60 0.50 1.30 4.50 3.30 3.30 68.70 27.20 0.80
8 86.70 8.10 0.40 1.40 1.30 2.10 8.00 61.90 29.50 0.70
9 80.29 7.25 0.31 1.84 4.90 5.41 5.30 67.50 25.20 2.10
10 85.05 6.79 0.50 1.53 1.75 4.40 4.35 62.24 32.28 1.14
11 81.50 7.10 0.50 1.40 3.40 6.10 6.07 64.87 28.56 0.50
12 86.09 6.74 0.19 1.93 1.35 3.70 3.70 65.50 29.40 0.90
13 86.70 6.90 0.30 1.90 0.90 3.30 4.40 64.00 30.70 0.90
14 83.92 6.83 0.78 0.92 3.39 4.16 4.16 64.97 30.08 0.75
15 85.25 7.94 0.41 1.38 1.19 3.83 3.83 64.09 31.14 0.94
16 83.00 6.79 0.32 1.37 3.46 5.06 5.00 64.10 29.70 1.20
17 81.79 7.99 0.48 1.81 3.04 4.90 4.88 65.74 28.98 0.40
18 84.00 7.19 0.49 1.42 3.30 3.60 3.60 65.60 30.00 0.80
19 83.15 6.78 0.28 1.77 0.84d 7.10 7.10 61.90 29.90 1.10
AVG 83.80 7.25 0.43 1.54 2.68 4.29 4.88 65.10 29.03 0.98 STD.
DEV 1.79 0.50 0.13 0.30 1.10 1.35 1.45 2.82 2.54 0.42 A-Ash VM- Volatile Matter FC - Fixed Carbon M - Moisture
In comparison to the previously mentioned models, this provides a more robust approach as it
considers such limitations and assumes that each of the components in the tire pyrolysis system
degrades at their own independent rate and follows the basic Arrhenius-type rate equation as shown
in Figure 6. This model assumes that the activation energies are fixed and unique to each
component; using values obtained by Yang et al. shown in Table 3 (Yang, Kaliaguine, & Roy,
1993). The components considered are extender oil, natural rubber (NR) and manufactured rubbers
(BR, SBR) (Quek A. B., 2008). The overall equation is shown in Equation 5:
𝑑𝑀
𝑑𝑇 = ∑ 𝑚𝑖𝑘𝑖 𝑁
𝑖=1 (5)
Where dM/dT is the rate of change of the total mass of tire sample, N is the number of
components, 𝑚𝑖𝑘𝑖 is the reaction rate of the ith component, where 𝑘𝑖 is an Arrhenius type coefficient for each component, dependent on the inverse of the heating rate dt/dT, as shown in
Equation 6:
𝑘𝑖=𝑑𝑇𝑑𝑡𝐴𝑖𝑒−𝐸𝑎,𝑖𝑅𝑇 (6)
The thermal lag which occurs at high heating rates is modeled by a simplified form of Newton´s
heat transfer equation (Equation 7) as a function of furnace temperature Tf. and the characteristic
time constant r. The mass transfer limitation is modeled by the third order Avrami-Erofe´ev
equation for bubble growth, where xi is the mass fraction of component i in Equation 8: (Quek A.
B., 2008)
𝑇(𝑡) = 𝑇𝑓+ (𝑇(0) − 𝑇𝑓)𝑒−𝑟𝑡 (7)
𝑚𝑖 = 𝑚𝑖,𝑜4(𝑥𝑖)[− ln(𝑥𝑖)]3/4 (8)
𝑚𝑖 = 𝑚𝑖,𝑜+𝑑𝑚𝑖
𝑑𝑇 ∆𝑇 (9)
Where ∆𝑇 is the difference in the temperatures between the two points evaluated during the devolatization of each component.
Figure 5. Deconvolution of different components of rubber tire pyrolysis. (Quek A. B., 2008)
Another approach which considers the effects of heat transfer during the pyrolysis reactions is
based on Senneca et al. multi-stage model with a coupled heat modeling presented by Aylon et al.
and Cheung et al. The proposed model follows the pyrolysis mechanism shown on Figure 6 which
divides the pyrolysis process in 5 main reactions with different parameters for each (Cheung, Lee,
Lam, Lee, & Hui, 2010).
Table 2. Mass loss kinetic parameters (Cheung, Lee, Lam, Lee, & Hui, 2010)
Reaction 1 Reaction 3a Reaction 3c
Pre-exponential factor (A (s-1)) 7.70x104 8.38x106 2.07x107
Activation energy (Ea J/mol) 6.97 x104 1.18 x105 1.29 x105
Reaction order (n) 2.26 0.93 0.9
Coefficient of mass loss (w)
Heating rate (B) 2 K/min 0.0481 0.2065 0.3154
5 K/min 0.0481 0.2216 0.2701
10 K/min 0.0481 0.2422 0.265
Figure 6. Multi-reaction Pyrolysis Kinetic Framework. (Cheung, Lee, Lam, Lee, & Hui, 2010)
According to the study by Aylon et al., the total mass loss is calculated by summing up the
mass loss contributions by individual mass loss reactions. There are three mass loss reactions
involved in the pyrolysis framework, the reactions R1, R3a and R3c. The mass loss kinetics can be
expressed by Equations 10 - 13 (Aylón, Callén, Lopez, & Mastral, 2005).
𝑑𝛼𝑖
𝑑𝑡 = 𝑘𝑖(1 − 𝛼𝑖)
𝑛𝑖 (10)
𝑘𝑖 = 𝐴𝑖exp (−𝐸𝑎𝑖
𝑅𝑇) (11)
𝛼 = ∑ 𝑤𝑖 𝑖𝑎𝑖 (12)
𝛼 =𝑊0−𝑊
𝑊0 (13)
According to Cheung et al (Cheung, Lee, Lam, Lee, & Hui, 2010), prior studies suggest that
different heating rates would result in different mass loss kinetics parameters. However, according
to the authors, it is assumed that the heating rates should not affect the kinetics parameters directly.
Instead, the heating rate influences the extensions of the contributions of each mass loss reaction in
the overall pyrolysis process. This is said to be more significant for reactions R3a and R3b in the
proposed pyrolysis framework, as TA is more ready for decomposition according to the authors.
different heating rates although the mass loss contributions of reactions R3a and R3c (ω3a, ω3c) are
varied by the heating rate (Cheung, Lee, Lam, Lee, & Hui, 2010). Additionally, a study presented
by González et al. supports these findings experimentally and provide a similar model for both
isothermal and dynamic experiments. The dynamic model presented by González et al. shows the
same behavior observed by the aforementioned authors (see Figure 7) and provides a table of results
(Table 3) which is very useful to set the kinetic parameters for modeling along different heating
ranges. (González, Encinar, Canito, & Rodríguez, 2001)
Table 3. Dynamic kinetic parameters for heating range 5-60 K/min. (González, Encinar, Canito, & Rodríguez, 2001)
Heating rate
(K/min) Activation energy Ea (J/mol) Pre-exponential factor ko (1/min)
Region 1 Region 2 Region 3 Region 1 Region 2 Region 3
5 - 20, 66.8 44.8 32.9 1 x105 3 x104 756
40 - 50, 93.4 78.4 61.1 2.9 x107 2.2 x106 6.1 x104
10 - 60, 52.5 164.5 136.1 2 x104 6.3 x1013 2.3 x109
- 42 195 204 1436 2.1 x1015 2.0 x1013
30 125.7 178.5 243.7 2.7 x1011 6.8 x1013 2.8 x1017
In this manner, Cheung et al.’s model proves to be useful since heat transfer is a significant
variable inside larger particles where Biot numbers and Fourier numbers are greater and
non-uniformity on the temperature distribution along the particle may be found (Incropera & Dewitt,
2009). Therefore, the heat flow inside the tire particle, evidenced by the change of tire specific heat
capacity, the heat of exothermic reactions, and the heat of vaporisations during the pyrolysis is
included in a mathematical model for exothermic kinetics. Such heat transfer model may be
compared to the analytical solution for a one- dimensional semi-infinite heat transfer problem with
convection boundary condition to validate coherent results considering the assumptions for the
iterative solution (Azevedo, Braga, & Mantelli, 2005). This approach thus further increases the
ability of modeling larger particles of up to 2.5cm according to Cheung et al (Cheung, Lee, Lam,
Lee, & Hui, 2010).
1.3.1.
Mathematical model for exothermic kinetics
The exothermic reactions involved in the proposed kinetic framework are reactions R2 and R3a
as shown on Figure 6. Since these reactions are different from the mass loss reactions, the set of
equations used to describe differs and are modeled by Equations 14 and 15 (Cheung, Lee, Lam,
Lee, & Hui, 2010).
𝑑𝛾𝑗
𝑑𝑡 = 𝑘𝑐𝑗(1 − 𝛾𝑗) 𝑛𝑐𝑗
(14)
𝑘𝑐𝑗 = 𝐴𝑐𝑗exp (−𝐸𝑐𝑗
1.3.2.
Coupled Mathematical model for heat flow
Based on the contributions of the mass loss kinetics, the exothermic kinetics, and heat flow of
the pyrolysis system, Cheung et al present an integrated mathematical model which simulates the
pyrolysis of a single WTR particle (Cheung, Lee, Lam, Lee, & Hui, 2010). Such model considers
the enthalpy contributions which are of great importance for high heating rate processes where
chemical reactions do not control the process but rather heat and mass transfer limitations are
present (González, Encinar, Canito, & Rodríguez, 2001).
𝛿𝑇 𝑑𝑡 =
𝜆 𝜌𝐶𝑝∗
𝛿2𝑇 𝛿𝑟2+
2 𝑟∗ 𝜆 𝜌𝐶𝑝∗ 𝛿𝑇 𝛿𝑟+ 1
𝐶𝑝∗ ∑ (ℎ𝑐𝑗∗ 𝑑𝛾𝑗
𝑑𝑡) − 1
𝐶𝑝∑ (ℎ𝑔𝑖∗ 𝛿𝛼𝑖
𝛿𝑡 ∗ 𝑤𝑖) 𝑖
𝑗 (16)
𝜆 = (1 − 𝛼) ∗ 𝜆𝑡𝑖𝑟𝑒+ 𝛼 ∗ 𝜆𝑐𝑎𝑟𝑏𝑜𝑛 (17)
𝐶𝑝 = 𝛼 ∗ 𝐶𝑝𝑡𝑖𝑟𝑒+ (1 − 𝛼) ∗ 𝐶𝑝𝑐𝑎𝑟𝑏𝑜𝑛 (18) Boundary Conditions:
−𝜆 ∗𝛿𝑇𝛿𝑟]
𝑟=𝑅 = 𝑈 ∗ (𝑇]𝑟=𝑅− 𝑇∞) (19) 𝛿𝑇
2. OBJECTIVES General Objective
Simulate the macroscopic mass loss rate behavior as a function of temperature and heating rates for
the thermal degradation (Pyrolysis) of waste tire rubber particulate matter.
Specific Objectives
1. Define an adequate mathematical model to describe the mass loss rate phenomenon present
in the pyrolysis of waste tire rubber based on pyrolysis theory and reported results of
experimental work found in literature.
2. Simulate the proposed mathematical model by numerical methods in order to predict results
at different temperatures and heating rate conditions.
3. Validate the simulated results with the theoretical and experimental results found in reports
3. METHODOLOGY
The methodology proposed in order to perform a correct simulation of the WTR pyrolysis is
shown in Figure 8. The steps described aim toward finding the best model and algorithm of solution
for the different limitations which govern WTR pyrolysis in order to avoid errors concealed by
solely changing parameters to fit the mass loss rate curves as a function of temperature and heating
rates.
Figure 8. Methodology to best approximate WTR Pyrolysis by mathematical modeling and simulation
3.1.
Algorithm for solution
The algorithm proposed for solving the multi-reaction model is based on the approach presented
by Cheung et al (Cheung, Lee, Lam, Lee, & Hui, 2010) and will be applied to this study in order to
leverage on the results found by previous experiments to validate the simulation of the WTR
pyrolysis. A vectorial solution finite difference approach was taken to solve the differential
equations presented in the model. Through this method, MATLAB® fsolve function was used in a
loop for every time lapse dt and radius step dr in order to find the solution numerically. This
provides an advantage in simulation time and troubleshooting for parameter issues as every time
Figure 9. Algorithm for solution using finite difference method
3.2.
Assumptions
The assumptions which were taken into consideration to successfully apply the model and
simulate coherent results compared to the results found in literature and experimentally are:
The reaction rate function, representing the rate of mass loss, follows an order of reaction n which is reported in literature for each model independently.
The orders of the reaction for the systems are adopted from the results reported by Cheung
The devolatized vapors and liquids leave the pyrolysis process immediately and no secondary nucleation reactions are considered for the purpose of this study. (Cheung, Lee,
Lam, Lee, & Hui, 2010)
The activation energies and kinetic parameters of the main pyrolysis reactions of the system
are fixed for each reaction as shown in Table 2 and were obtained from Cheung et al.
(Cheung, Lee, Lam, Lee, & Hui, 2010)
The tire particle is spherical and has radius R ≤2.5cm. (Cheung, Lee, Lam, Lee, & Hui, 2010)
Heat is transferred by conduction only inside the particle. (Cheung, Lee, Lam, Lee, & Hui,
2010)
Density of tire particle is assumed constant. (Cheung, Lee, Lam, Lee, & Hui, 2010)
The reactor temperature is assumed to be the same as the pyrolysis gas temperature. (Aylón,
Callén, Lopez, & Mastral, 2005)
The tire particle is heated by convection by the pyrolysis gas. (Senneca, Salatino, & Chirone, 1999)
4. RESULTS AND DISCUSSION
The approach taken to define an adequate mathematical model and algorithm to describe WTR
pyrolysis was performed based on a comparison among four reported models by various authors on
WTR pyrolysis such as Queck et al. (Quek & Balasubramanian, 2012), Senneca et al. (Senneca,
Salatino, & Chirone, 1999), Cheung et al. (Cheung, Lee, Lam, Lee, & Hui, 2010) and Aylon et al.
(Aylón, Callén, Lopez, & Mastral, 2005). The results shown in this study were obtained by
recreating the proposed mathematical models through finite differences simulation on MATLAB®
Software. These were subsequently validated through a comparison between the simulated results,
the results reported by the aforementioned authors, and experimental data provided by Dr. Rocío
Sierra et al. measured on a TGA experimental device for WTR samples at different heating rates.
4.1.
Kinetic Model definition & selection
The model developed by Cheung et al. (Cheung, Lee, Lam, Lee, & Hui, 2010) is chosen as the
best mathematical model used in this study in order to predict the macroscopic behavior of mass
loss rate in the pyrolysis of waste tire rubber at desired temperatures and heating rates between
300K to 800K and 2K/min to 30K/min respectively. This model considers key factors such as
integrated heat and mass transfer equations as functions of temperature and heating rate of the feed.
These considerations allow for a modeling of larger particle sizes of up to 2.5cm, in concurrence
with the physical modeling limitations which are best described by the Biot and Fourier numbers to
account only for the effects of conductive heat flow throughout the WTR chips. The model is
described by Equations (10 -20).
4.1.1.
Comparison with other models
The mathematic models proposed by Queck et al (Quek A. B., 2008) , Cheung et al (Cheung,
Lee, Lam, Lee, & Hui, 2010) and Aylon et al (Aylón, Callén, Lopez, & Mastral, 2005) have been
in the results obtained can be justified from a theoretic stand since these models consider different
variables and limiting factors as described in section 1.3. The main criteria used to establish which
of the models is more useful for the purpose of this study was to compare the models´ accuracy at
predicting the behavior of the data obtained by Dr. Rocio Sierra et al. without fitting the parameters
to the experimental data by keeping the same pyrolysis conditions applicable to all models as base
study cases.
Figure 10. Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al and experiments at heating rate 20K/min. Particle size 7mm.
Figures 10 and 11 show a comparison graph of the results obtained from the evaluation of the
models at specific conditions taken as a standard base case: heating rate 20K/min, pyrolysis
all of the models predict a similar behavior for the mass loss rate of WTR pyrolysis as a funcion of
temperature with slight differences in terms of pyrolysis peak activation temperature ranges and
mass loss rates below 10%. The main difference in pyrolysis activiation temperature is due to the
rubber tire’s characteristic devolatisation behavior which has 2 peaks due to the main compound
activation energies as mentioned by Gonzalez et al. (González, Encinar, Canito, & Rodríguez,
2001)
Figure 11.Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 20K/min. Particle size 25mm.
Nonetheless, it is important to highlight that the results observed from the models present a
difference in terms of pyrolysis temperature ranges i.e. the temperature range at which the main
pyrolysis reaction occurs. Specifically, the models presented by Aylon et al. and Queck et al.
occurring while the model presented by Cheung et al. predicts a temperature range between 600K to
750K. These predictions were contrasted to the temperature range obtained experimentally by TGA
analysis and it was found that there is a better fit between the results obtained from Cheung´s et al.
model in this aspect.
Figure 12. Mass loss kinetics model comparison at heating rate 20K/min vs experimental data
The second main difference is the maximum pyrolysis rate achieved during the entire process.
In this aspect, there is a broad range of results predicted by each model ranging from a minimum of
0.12% up to a maximum of 0.6%of total mass loss per second. The specific case of the model
proposed by Cheung et al. shows a difference of 0.25% vs the experimental data in terms of max
pyrolysis peak and 6% in terms of pyrolysis temperature precision for such peak. These results are
the best fit above all other models studied as shown on Figure 12 for the base study case and
Appendix A for all other study cases evaluated. The model’s prediction ranges and peak mass loss
Table 4. Model prediction range comparison
Heating rate
(K/min) Temperature (K)
Mass loss rate peak (%/sec)
Particle size (mm) Cheung et Al 2- 40, 450 - 740 0.43 @ 40K/min 7 - 25, Aylon et Al 10 - 20, 650 -760 0.28 @ 40K/min 0 - 7, Queck et Al 10 - 30, 700 - 800 0.68 @ 40K/min 25
Figure 13. Comparison of experimental and simulated results of DTG at Heating rate 20K/min based on Aylon et
Al Kinetics Model. Particle size 25mm.
4.2.
Simulated Results
Figure 14 shows the total derivative mass loss per second in the pyrolysis system for a base
study case consisting of a spherical WTR chip of radius 75mm subject to a range of heating rates
from 2K/min to 20K/min. From these results it is possible to establish that there is a strong
important fact which can be obtained from the model is the temperature range at which WTR
Pyrolysis occurs. It can be observed that the mass loss process occurs in greater degree at a range of
600K -750K, which is clearly dependent on the heating rate applied. This fact is relevant because it
is a good prediction of the experimental temperatures where the actual process occurs throughout a
range of various heating rates.
Figure 14. Derivative Mass Loss profiles for heating rates β= 2K/min - 20K/min
The derivative mass loss radial profiles depicted on Figure 15 shows how the behavior of WTR
pyrolysis process varies radially in terms of mass loss rates due to the changes on the heating rates.
(16-18) which contribute to a greater degree of radial mass loss change on study cases with higher
heating rates (10K/min – 20K/min). This is due to the changes in thermal conductivity and heat
capacity as particles devolatize and char remains. This fact can be seen on Figure 11, where the
behavior of the profile at a heating rate of 20K/min changes up to 12% from the highest derivative
mass loss percentage at the surface (dr=20) and the lowest point within the particle (dr=10).
Figure 16. Derivative mass loss radial profile for heating rate 20K/min
To further emphasize the importance of modeling the changes in internal heat flow at higher
heating rates, Figure 16 shows a comparison of two study cases (β=2K/min and β=20K/min) where
the derivative mass loss profiles do not vary significantly at β=2K/min along the particle but do so
at β=20K/min regardless of the fact that the particle modeled is the same size (R=2.5cm). This
clearly supports the idea that at higher heating rates, the effects of heat flow are of great importance
Figure 17. Comparison of Derivative mass loss at surface and center of the particle for B=2K/min and 20K/min
Regarding the effect of heat flow and heating rates on the radial temperature profile of the
particle, it can be observed that at lower heating rates the profile remains linear along changes in the
radius (dr=0-20). Accordingly, as heating rates increase, a similar effect to the one which was
observed in the derivative mass loss radial profiles can be evidenced along the temperature profiles
where at a single time, different temperatures along the particle can be found. This is an important
effect for larger particles (2mm-25mm) but can be disregarded at sizes ranging from dust particles
Figure 18. Temperature radial profiles for heating rates 2K/min – 20K/min
Nevertheless, it is important to note that the final conversion (percentage of total mass loss) is
not radically affected by the changes studied in this case. All of the profiles in Figure 19 indicate
that the maximum level of mass devolatization lies at approximately 55-57% of the total initial
mass which is in agreement with the results reported by Senneca et al. (Senneca, Salatino, &
Chirone, 1999)
4.3.
Experimental comparison of results
The results presented were validated from an experimental standpoint through a comparison of
the predictions obtained by Cheung et al.’s model and TGA experimental data at heating rates
10K/min and 20K/min. The experimental data used for this validation was provided by Dr. Rocío
Sierra et al. as it was measured on a TGA experimental device for WTR samples at different heating
rates as presented on Figure 20.
Figure 20. Experimental data results obtained by TGA analysis.
After a thorough comparison of the predicted results obtained by the different kinetic models at
different heating rates (See Appendix A of the present document), it can be established that the
simulated results obtained through the model developed Cheung et al. are in strong agreement with
the experimental data as shown in Figures 19 and 20. Furthermore, it is important to consider that
the parameters used for the simulation were kept as reported on the original model and not altered
to fit the experimental data. This is of great importance as the model can be further adjusted by
important to note that a better fitting may be obtained by considering the enthalpy changes due to
particle size differences between the experimental data and the simulated results.
Figure 21. Comparison of experimental and simulated results of DTG at Heating rate 10K/min.
Figure 22 Comparison of experimental and simulated results of DTG at heating rate 20K/min
From Figures 21 and 22, it can be observed that the model successfully predicts the behavior of
the mass loss rate as a function of temperature whereby the main changes of the mass loss rate are
accurately predicted throughout the entire starting phase of the pyrolysis process (i.e. the rise of
mass loss rate) and the final phase is also accurately predicted as the decline of the mass loss rate
5. CONCLUSIONS
After evaluating several models proposed in the literature regarding WTR pyrolysis, it has been
found that the model presented by Cheung et al. (Cheung, Lee, Lam, Lee, & Hui, 2010) provides
the most accurate predictions for WTR pyrolysis behavior in comparison with the models presented
by Queck et al. (Quek & Balasubramanian, 2012), Aylon et al. (Aylón, Callén, Lopez, & Mastral,
2005), and Seneca et al. (Senneca, Salatino, & Chirone, 1999) versus the experimental results
reported on section 3.5 of this document. This is supported by the fact that the predicted behavior
of WTR pyrolysis resulting from this model shows a good fit in comparison to the experimental
data for both of the main measurable variables of the system: mass loss rate and pyrolysis
temperature ranges. Regarding the mass loss rate prediction, the model is the most precise at
estimating the peak mass loss rate versus experimental results.
Additionally, the variation found between the simulated results and experimental data are due to
the changing enthalpy values which were taken as parameters directly from the proposed model and
as such values are fitted to the real conditions of the particles studied by the TGA analysis the fit
between the data and the predictions can be improved.
It has also been proven that considering the effect of heat transfer at different heating rates and
final pyrolysis temperatures does have an impact on the mass loss rate of WTR during pyrolysis.
Such impact is higher on cases where the heating rate exceeds 10K/min and at particle sizes above
7mm due to the internal heat conduction phenomenon which is accounted for through the heat
transfer equation shown in Equation 16, included in the modeling of this process. In cases where the
heating rate is lower than 10K/min and the WTR chips are as large as 2.5cm the effect of heat
transfer is minimized and the heat distribution profile remains constant across the chip. The
modeling of such effect proves to be useful since additional variables such as change in
conductivity and heat capacity can be taken into consideration where as other models ignore these
BIBLIOGRAPHY
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Aylón, E., Fernández-Colino, A., Murillo, R., Navarro, M. V., García, T., & Mastral, A. M. (2009).
Valorisation of waste tyre by pyrolysis in a moving bed reactor. Waste Management 30,
1220-1224.
Azevedo, J., Braga, W. F., & Mantelli, M. B. (2005). Analytical solution for one-dimensional semi-infinite heat transfer problem with boundary condition. AIAA.
Bellais, M. (2007, Jun). Modelling of the pyrolysis of large wood particles. Stockholm, Sweden.
Bridgwater, A. (2012). Review of fast pyrolysis of biomass and product upgrading. Biomass and
Bioenergy 38 , 68-94.
Cheung, K.-Y., Lee, K.-L., Lam, K.-L., Lee, C.-W., & Hui, C.-W. (2010). Integrated kinetics and heat flow modelling to optimise waste tyre pyrolysis at different heating rates. Hong Kong: El Sevier.
Conesa, J. A., Fullana, A., & Font, R. (2000). Tire Pyrolysis: Evolution of volatile and semivolatile compounds. Energy & Fuels 14, 409-418.
Conesa, J. A., Marcilla, A., Caballero, J. A., & Font, R. (2001). Comments on the validity and utility of the different methods for kinetic analysis of thermogravimetric data. J. Anal. Appl. Pyrolysis 58–59 (2001) 617–633.
EuropeanTyre&RubberManufacturers’Association. (2011). End-of-life tyres management report 2011. Retrieved Mar 2014, from
http://www.etrma.org/uploads/Modules/Documentsmanager/brochure-elt-2011-final.pdf
González, J., Encinar, J. M., Canito, J. L., & Rodríguez, J. J. (2001). Pyrolysis of automotive tyre waste. Influence of operating variables and kinetics study. Journal of analytical and applied Pyrolysis, 667-683.
Haydary, J., Jelemenský, L., & Gasparovic, J. M. (2012). Influence of particle size and kinetic parameters on tire pyrolysis. Journal of Analytical and Applied Pyrolysis, 73-79.
Incropera, F. P., & Dewitt, D. P. (2009). Fundamentals of Heat and Mass Transfer (5th Edition ed.). Wiley.
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Quek, A. B. (2008, Nov 21). An Algorithm for the kinetics of tire pyrolysis under different heating rates. Singapore, Singapore: Journal of Hazardous Materials 166 (2009) 126-132.
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Sanchez, D. (2013, May). Synthetic diesel production through catalytic pyrolysis of biomass-waste tire mixtures. Bogotá.
Senneca, O., Salatino, P., & Chirone, R. (1999). A fast heating rate thermogravimetric study of the pyrolysis of scrap tyres. Naples, Italy: Fuel 78 (1999) 1575 - 1581.
United Nations. (2011, Nov 11). Revised technical guidelines for the environmentally sound management of used and waste pneumatic tyres. Cartagena, Colombia. Retrieved Mar 7, 2014, from
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Yang, J., Kaliaguine, S., & Roy, C. (1993). Improved quantitative determination of elastomers in tire rubber by kinetic simulation of DTG curves. Rubber Chem. Technol.66.
APPENDIX 1. SIMULATION RESULTS COMPARISON OF KINETIC MODELS
AT DIFFERENT HEATING RATES.
Figure A1. 1 Mass loss kinetics model results comparison of Aylon et al at heating rate 10K/min vs experimental data.
Figure A1. 2 Mass loss kinetics model results comparison of Cheung et al at heating rate 10K/min vs experimental data.
Figure A1. 3 Mass loss kinetics model results comparison of Queck et al at heating rate 10K/min vs experimental data.
Figure A1. 4 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 10K/min. Particle size 7mm.
Figure A1. 5 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 10K/min. Particle size 25mm.
Figure A1. 6 Mass loss kinetics model results comparison of Aylon et al at heating rate 20K/min vs experimental data.
Figure A1. 7 Mass loss kinetics model results comparison of Cheung et al at heating rate 20K/min vs experimental data.
Figure A1. 8 Mass loss kinetics model results comparison of Quekc et al at heating rate 20K/min vs experimental data.
Figure A1. 9 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 20K/min. Particle size 7mm.
Figure A1. 10 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 20K/min. Particle size 25mm.
Figure A1. 11 Mass loss kinetics model results comparison of Aylon et al at heating rate 30K/min vs experimental data.
Figure A1. 12 Mass loss kinetics model results comparison of Cheung et al at heating rate 30K/min vs experimental data.
Figure A1. 13 Mass loss kinetics model results comparison of Queck et al at heating rate 30K/min vs experimental data.
Figure A1. 14 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 30K/min. Particle size 7mm.
Figure A1. 15 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, and Queck et al at heating rate 30K/min. Particle size 25mm.
Figure A1. 16 Mass loss kinetics model results comparison of Aylon et al at heating rate 40K/min vs experimental data.
Figure A1. 17 Mass loss kinetics model results comparison of Cheung et al at heating rate 40K/min vs experimental data.
Figure A1. 18 Mass loss kinetics model results comparison of Cheung et al, Aylon et al, at heating rate 40K/min. Particle size 7mm.
Figure A1. 19 Mass loss kinetics model results comparison of Aylon et al at heating rate 100K/min
APPENDIX 2. MATLAB BASE CODES FOR SOLUTION
The code presented below is a general version of the main code used for this simulation which
allows varying parameters such as heating rates, final temperatures, and kinetic parameters in order
to model WTR pyrolysis under diverse assumptions including accounting for heat transfer
contributions.
function CheungFinalCp
%% Cyclic solver base code
%Initialize clean variables clear all
clc
global dr Nr Nt dt B w z iter lda cp
Bmin=20;% desired heating rate C/min
B=Bmin/60;% conversion to units C/s
%Parameters by Heating rate (see table 2)
if B==2/60 z=1;
elseif B==5/60
z=2;
elseif B==10/60
z=3;
else
z=4;
end
r=2.5/100;% Radius (m)
dr = (.125)/100; % radius step (m)
Nr = floor(r/dr); % number of radius steps
t=2000;% time (s)
dt=1;%time step (s)
Nt = floor(t/dt); % number of time steps
Tfur=510+273.15;%Furnace temperature (K)
Tfurpre=200+273.15;% preheat Furnace temperature (K)
T0=zeros(Nr,1) + 298.15+5;% Temperature initializing @30 Celsius
A0=zeros(Nr,3);%Conversion initialization vector -0- No conversión @time 0
Gam0=zeros(Nr,2)+0.0001; Tamb=30+273.15;%Temperature
M0=[T0,A0,Gam0];%Initialization matrix
options=optimset('Algorithm','levenberg-marquardt'); xmax=Nt;
%Initialization of vectors @0
M=M0; tol=100; A1prev=zeros(Nr,xmax); A2prev=zeros(Nr,xmax); A3prev=zeros(Nr,xmax); Gam1prev=zeros(Nr,xmax); Gam2prev=zeros(Nr,xmax); Temperatura=zeros(Nr,xmax); A1=zeros(Nr,xmax); A2=zeros(Nr,xmax); A3=zeros(Nr,xmax); Gam1=zeros(Nr,xmax); Gam2=zeros(Nr,xmax);
%Variable estimation cycle @ time x
for x=1:xmax iter=x
Tinf=B*dt*(x-1)+Tfurpre; if Tinf >=Tfur;
Tinf=Tfur; end
Tt(x)=Tinf;
[rta,Fval]=fsolve(@(M1)cheung(M1,M,Tinf),M,options); difT=(rta(Nr,1)-M(Nr,1));
if abs(difT)>=tol break
end
%Store estimated variables in vectors for graphs and results at each time step A1prev(:,x)=M(:,2); A2prev(:,x)=M(:,3); A3prev(:,x)=M(:,4); Gam1prev(:,x)=M(:,5); Gam2prev(:,x)=M(:,6); M=real(rta);
Temperatura(:,x) = M(:,1); A1(:,x)=M(:,2);
A2(:,x)=M(:,3); A3(:,x)=M(:,4); Gam1(:,x)=M(:,5); if Gam2prev(1,x)>=1 M(:,6)=1; end Gam2(:,x)=M(:,6); slda(:,iter)=lda'; scp(:,iter)=cp'; end
%differential variable estimation between time steps (variables changes)
dA2=A2-A2prev; dA3=A3-A3prev; dGam1=Gam1-Gam1prev; dGam2=Gam2-Gam2prev; dA4=real(w(z,1).*dA1+w(z,2).*dA2+w(z,3).*dA3); A4=real(w(z,1).*A1+w(z,2).*A2+w(z,3).*A3);
%vector variable storage in workspace base
assignin('base', 'slda', slda); assignin('base', 'scp', scp); assignin('base', 'Tinf', Tt);
assignin('base', 'Temperatura', Temperatura); assignin('base', 'dA1', dA1);
assignin('base', 'dA2', dA2); assignin('base', 'dA3', dA3); assignin('base', 'dGAM1', dGam1); assignin('base', 'dGAM2', dGam2); assignin('base', 'dA4', dA4);
assignin('base', 'A1', A1); assignin('base', 'A2', A2); assignin('base', 'A3', A3); assignin('base', 'GAM1', Gam1); assignin('base', 'GAM2', Gam2); assignin('base', 'A4', A4);
function eq = cheung(M1,M,Tinf)
%%Cheung model base case code for rubber tire pyrolysis
%%Parameters
global dr Nr Nt dt B w z iter lda cp
R=8.314; cptire=1230; cpchar=1800; ldatire=0.38; ldachar=0.20; U=50;%J/m2 K s
rho = 1100; % tire density kg/m3
% Endothermic reaction Parameters – Mass consumption modeling
N=3;%Number of endothermic reactions
Ea =[69.73e3 118.04e3 128.92e3]; % Activation Energy per reaction
ko=[7.7e4 8.38e6 2.07e7];%Preexponential factor per reaction (Aylon.2005)
n=[2.26 0.93 0.9];%Order of reaction
w=[0.0481 0.2065 0.3154 0.0481 0.2216 0.2701 0.0481 0.2422 0.2650
0.0481 0.5098 0.0001];%Reaction parameter matrix -3 reactions & 4 heating rates
hg=[481.42 90.84 222.76 546.42 198.21 265.71 481.42 253.46 701.9
496.42 521.95 627.7];%3 reacciones y 4 heating rates
%% Endothermic reaction Parameters – heat transfer modeling
Nex=2;% Number of exothermic reactions
Acj=[4.12e6 9.09e6]; Ec=[88.02e3 103.95e3]; nc=[1.74 0.89]; hc=[95.34 372.4 166.04 159.07 42.48 195.57
41.62 72.88];%2 reacciones y 4 heating rates
%Initialize vectors T=M(:,1); A=M(:,2:4); Gam=M(:,5:6); T1=real(M1(:,1)); A1=real(M1(:,2:4)); Gam1=real(M1(:,5:6)); eq=zeros(Nr,7);
%% Estimate Heat contribution @ Variable Lda & Cp
exo=zeros(Nr,Nex); endo=zeros(Nr,N); alfaW=zeros(Nr,N); sumExo=zeros(Nr); sumEndo=zeros(Nr); alfa=zeros(Nr,1);
%%mass loss modeling @ring m due to x reaction
for m=1:Nr for x=1:Nex
exo(m,x)=hc(z,x)*((Gam1(m,x)-Gam(m,x))/dt); end
for x=1:N
endo(m,x)=hg(z,x)*w(z,x)*((A1(m,x)-A(m,x))/dt); alfaW(m,x)=w(z,x)*A(m,x); alfaWT(m,x)=w(z,x)*A(m,x)/B; end sumExo(m)=sum(exo(m,:)); sumEndo(m)=sum(endo(m,:)); alfa(m,1)=sum(alfaW(m,:)); alfaT(m,1)=sum(alfaWT(m,:)); end lda=zeros(Nr,1); cp=zeros(Nr,1);
for m=1:Nr
lda(m)=(1-alfa(m,1))*ldatire+alfa(m,1)*ldachar; cp(m)=alfaT(m,1)*cptire + (1-alfaT(m,1))*cpchar;
end
%% Mathematical model equations to be solved using fsolve
eq(1,1)= 0-((T1(1+1)-T1(1))/dr);
eq(Nr,1)=U*(T1(Nr)-Tinf)+lda(Nr)*((T1(Nr)-T1(Nr-1))/dr);
for j=1:N
eq(1,j+1)= (A1(1,j)-A(1,j))/dt-ko(j)*exp(-Ea(j)/(R*T(1)))*(1-A(1,j))^(n(j));
eq(Nr,j+1)= ((A1(Nr,j)-A(Nr,j))/dt)-ko(j)*exp(-Ea(j)/(R*T(Nr)))*(1-A(Nr,j))^(n(j));
for i=2:Nr-1
%% Model to estimate alfa
eq(i,j+1)= (A1(i,j)-A(i,j))/dt-ko(j)*exp(-Ea(j)/(R*T(i)))*(1-A(i,j))^(n(j));
%% model to estimate gamma at boundary conditions %Exothermic reaction kinetics model
if j <=2
eq(1,j+N+1)=(Gam1(1,j)-Gam(1,j))/dt -Acj(j)*exp(-Ec(j)/(R*T(1)))*(1-Gam(1,j))^(nc(j));
eq(Nr,j+N+1)=(Gam1(Nr,j)-Gam(Nr,j))/dt -Acj(j)*exp(-Ec(j)/(R*T(Nr)))*(1-Gam(Nr,j))^(nc(j));
eq(i,j+N+1)=(Gam1(i,j)-Gam(i,j))/dt - Acj(j)*exp(-Ec(j)/(R*T(i)))*(1-Gam(i,j))^(nc(j));
end
%% Estimate T, Lda & cp variable considering heat transfer contribution eq(i,1)=(lda(i)/(rho*cp(i)))*((T(i+1)-2*T(i)+T(i- 1))/dr^2)+(2/(i*dr))*(lda(i)/(rho*cp(i)))*((T(i+1)-T(i))/dr)+(1/cp(i))*sumExo(i)-(1/cp(i))*sumEndo(i)-(T1(i)-T(i))/dt; end end end
