Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Contents lists available at ScienceDirect
Journal of Analytical and Applied Pyrolysis
journal homepage: www.elsevier.com/locate/jaap
Review
Biomass pyrolysis kinetics: A comparative critical review with relevant
agricultural residue case studies
John E. White a,∗ , W. James Catallo b,1 , Benjamin L. Legendre a
a
b
Audubon Sugar Institute, Louisiana State University AgCenter, 3845 Hwy 75, St. Gabriel, LA 70776, USA
Laboratory for Ecological Chemistry, Comparative Biomedical Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA 70803, USA
a r t i c l e
i n f o
Article history:
Received 21 March 2009
Accepted 8 January 2011
Available online 14 January 2011
Keywords:
Agricultural residues
Biomass
Kinetic models
Kinetic triplet
Nutshells
Pyrolysis kinetics
Sugarcane bagasse
Thermal decomposition
a b s t r a c t
Biomass pyrolysis is a fundamental thermochemical conversion process that is of both industrial and ecological importance. From designing and operating industrial biomass conversion systems to modeling the
spread of wildfires, an understanding of solid state pyrolysis kinetics is imperative. A critical review of
kinetic models and mathematical approximations currently employed in solid state thermal analysis is
provided. Isoconversional and model-fitting methods for estimating kinetic parameters are comparatively evaluated. The thermal decomposition of biomass proceeds via a very complex set of competitive
and concurrent reactions and thus the exact mechanism for biomass pyrolysis remains a mystery. The
pernicious persistence of substantial variations in kinetic rate data for solids irrespective of the kinetic
model employed has exposed serious divisions within the thermal analysis community and also caused
the broader scientific and industrial community to question the relevancy and applicability of all kinetic
data obtained from heterogeneous reactions. Many factors can influence the kinetic parameters, including process conditions, heat and mass transfer limitations, physical and chemical heterogeneity of the
sample, and systematic errors. An analysis of thermal decomposition data obtained from two agricultural
residues, nutshells and sugarcane bagasse, reveals the inherent difficulty and risks involved in modeling
heterogeneous reaction systems.
© 2011 Published by Elsevier B.V.
Contents
1.
2.
3.
4.
5.
6.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fundamentals of thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.
Concise history of thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.
Experimental kinetic analysis techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.
Arrhenius rate expression and the significance of the kinetic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Biomass pyrolysis kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.
Kinetic expressions for biomass thermal decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.
Biomass pyrolysis kinetic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.
Multiple-step models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.
Isoconversional techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.
Comparative evaluation of integral and differential isoconversional techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.
Other kinetic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis of kinetic data obtained from various nutshells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Biomass thermal decomposition mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Influence of experimental conditions on biomass reaction kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.
Heat and mass transport models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.
Heating rate and particle size effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∗ Corresponding author. Present address: USDA, ARS, Pacific Basin Agricultural Research Center, 64 Nowelo St., Hilo, HI 96720, USA. Tel.: +1 808 932 2177;
fax: +1 808 959 5470.
E-mail address: John.White2@ars.usda.gov (J.E. White).
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Deceased.
0165-2370/$ – see front matter. © 2011 Published by Elsevier B.V.
doi:10.1016/j.jaap.2011.01.004
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J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
6.3.
Significance of surrounding atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.
Catalytic effect of inorganic material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.
Variations in kinetic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.
Systematic errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.
Temperature gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.
Temperature lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.
Kinetic compensation effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.
Sugarcane bagasse case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.
Sugarcane bagasse – background and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.
Review of sugarcane bagasse pyrolysis studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.
Analysis of published kinetic data for sugarcane bagasse pyrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.
Suggestions for mitigating inconsistencies in kinetic triplet data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5.
Evaluation of kinetic compensation effect for sugarcane bagasse data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.
Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
Increased volatility in traditional fossil fuel markets has revived
interest in the production of alternative fuels from biomass. Renewable energy derived from biomass reduces reliance on fossil fuels
and it does not add new carbon dioxide to the atmosphere [1].
Pyrolysis is a fundamental thermochemical conversion process that
can be used to transform biomass directly into gaseous and liquid
fuels. Pyrolysis is also an important step in combustion and gasification processes. In this regard, a thorough understanding of pyrolysis
kinetics is vital to the assessment of items including the feasibility,
design, and scaling of industrial biomass conversion applications
[2,3]. An awareness of pyrolysis kinetics can also be useful in modeling the propagation of wildfires [4], which ravage 550 million ha
worldwide annually [5].
Vegetative biomass, also known as phytomass, is comprised
primarily of cellulose, hemicellulose, and lignin along with lesser
amounts of extractives (e.g., terpenes, tannins, fatty acids, oils, and
resins), moisture, and mineral matter [6]. Cellulose is the most
abundant organic compound in nature, comprising up to 50 wt%
of dry biomass [7,8]. It is a linear polysaccharide formed from
repetitive ␤-(1,4)-glycosidic linkage of d-glucopyranose units. Cellulose from different biomass types is chemically indistinguishable
except for its degree of polymerization (DP), which can range
from 500 to 10,000 depending on the type of biomass [9]. Strong
hydrogen bonding between the straight chains imparts a crystalline structure to the cellulose, making it highly impervious
to dissolution and hydrolysis using common chemical reagents
[9,10]. Unlike cellulose, the composition of hemicelluloses and
lignin is heterogeneous and can vary greatly even within a given
biomass species. Hemicelluloses have an amorphous structure
and display branching in their polymer chains. Several sugar
monomers are contained in hemicellulose, including xylose, mannose, galactose, and arabinose. Lignin accounts for almost 30%
of terrestrial organic carbon and provides the rigidity and structural framework for plants [11]. The lignin biopolymer consists
of a complex network of cross-linked aromatic molecules, which
serves to inhibit the absorption of water through cell walls. The
structure and chemical composition of lignin are determined by
the type and age of the plant from which the lignin is isolated
[12]. Studies addressing the transformation kinetics of biomass
must account for the intrinsically heterogeneous nature of the substrate. In this regard, the frequent practice of typifying the overall
kinetic behavior of a particular biomass substrate based on the
kinetic results from just a single benchmark component is troublesome.
Pyrolysis of solid state materials, such as biomass, can be classified as a heterogeneous chemical reaction. The reaction dynamics
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25
27
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and chemical kinetics of heterogeneous processes can be affected
by three key elements [13], i.e., the breakage and redistribution of
chemical bonds, changing reaction geometry, and the interfacial
diffusion of reactants and products. Unlike homogeneous reactions, concentration is an inconsequential parameter that cannot
be used to monitor the progress of heterogeneous reaction kinetics because it can vary spatially [13–16]. Heterogeneous reactions
usually involve a superposition of several elementary processes
such as nucleation, adsorption, desorption, interfacial reaction, and
surface/bulk diffusion, each of which may become rate-limiting
depending on the experimental conditions. The initiation step in
solid state decomposition reactions frequently involves a “random
walk” of defects and vacancies within the crystal lattice which gives
rise to nucleation growth [17]. Equally significant is the concept
of a “reaction interface”, which is defined as the boundary surface between the reactant and the product. This representation has
been used extensively to model the kinetics of solid state reactions
[18].
The only extant review of sugarcane pyrolysis was published
more than thirty years ago [19]. Solid state kinetic theory was in
a state of considerable disarray during this era and decomposition
mechanisms for cellulose pyrolysis were in their formative stages.
Understanding of the reaction dynamics involved in pyrolytic processes has evolved substantially since then, and the corresponding
kinetic schemes have been refined to encompass the entire lignocellulosic substrate. In light of this, the original intent of this paper
was to provide a succinct overview of modern biomass pyrolysis
kinetics supported by an analytical survey of rate data obtained
from a particular biomass species (i.e., sugarcane bagasse). However, considering the uncertainty and flux that continue to envelop
the field of thermal analysis, it was decided that an experimental
case study isolated from a contextual discourse on the current state
of affairs in heterogeneous kinetics might only add to the existing
turmoil. Therefore, the objective of this critical review is to not only
expose the nature and origin of the rampant inconsistencies in published biomass kinetic data but also emphasize the urgent need to
dispense with the “. . .hundreds of cute and clever mathematical
manipulations [that] were performed on variations of three (highly
stylized) equations” [i.e., the degree of conversion rate equation
(Eq. (2)), the Arrhenius expression (Eq. (1)), and the temperature
integral (Eq. (11))], and instead focus on the reexamination of fundamental solid state reaction kinetic theory as it applies to biomass
pyrolysis. After a précis of experimental kinetic techniques and fundamental rate equations, various biomass degradation models and
process parameters that impact rates of biomass degradation are
examined. This treatment is then followed by an analytical evaluation of experimental studies on the kinetics of sugarcane bagasse
pyrolysis.
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Nomenclature
A
a,b
C
Ea
f(˛)
g(˛)
I(Ea ,T˛ )
k
k(T)
n
p(x)
r
R
t
T
Vi
Vi *
v
w
x
y
z
frequency factor (s−1 )
correlation parameters in the linear compensation
effect relation
constant of integration
apparent activation energy (kJ mol−1 )
reaction model (function expressing the dependence of the reaction rate on the conversion)
integrated reaction model
equivalent function for p(x)
reaction rate constant (s−1 )
temperature-dependent rate constant (s−1 )
reaction order
temperature integral
reaction initiation parameter
universal gas constant (8.3144 × 10−3 kJ mol−1 K−1 )
time (s)
absolute temperature (K)
cumulative mass of released volatiles corresponding
to fraction i through time t
effective volatile content for fraction i
volatile mass at time t
substrate mass at time t
equivalent to Ea /RT
unreacted fraction of substrate
activity of solid
Greek letters
˛
extent of reaction (degree of conversion)
ˇ
heating rate (◦ C s−1 )
minimization function
deactivation rate constant
Superscripts
c, d, e
adjustable reaction exponents in the SB equation
n
reaction order
q
number of experiments
s
adjustable nucleation parameter used in the modified Prout–Tompkins model
Subscripts
0
initial
a
apparent
f
final
iso
isokinetic
i
volatile fraction
j
ordinal number of experiment
k
ordinal number of experiment
m
maximum
2. Fundamentals of thermal analysis
2.1. Concise history of thermal analysis
The storied field of thermal analysis is no stranger to disagreement and uncertainty. Thus it should come as no surprise that
even the origins of modern thermal analysis remain blurred in
controversy. Although Le Chatelier is frequently credited with having initiated thermal analysis in 1887 [20–23], Jakob Rudberg had
already employed a crude form of thermal analysis in 1829 to obtain
rate data for various metals and their alloys [22], and as early as
1780, Bryan Higgins had observed the effect of heating chalk and
limestone at various temperatures [24]. Likewise, dissent has pre-
3
vented the adoption of a mutually acceptable definition for thermal
analysis methods. Thermal analysis has been formally defined by
the International Confederation for Thermal Analysis and Calorimetry (ICTAC) as “a group of techniques in which a property of the
sample is monitored against time or temperature while the temperature of the sample, in a specified atmosphere, is programmed”
[25]. The ICTAC definition has been criticized [26] for being too
constrictive (i.e., “monitoring” does not adequately reflect the elements of evaluation and experimental investigation that comprise
“thermal analysis”) or immaterial (i.e., a “specified atmosphere” is
a unique, local operational factor that is inappropriate for a global
definition). It has been proposed that the essence of thermal analysis can be summarized “as the measurement of a change in a sample
property, which is the result of an imposed temperature alteration”
[26].
2.2. Experimental kinetic analysis techniques
Kinetic data from solid state pyrolysis reactions has traditionally been obtained using discrete isothermal methods of
analysis. Isothermal kinetic data usually is acquired by performing several experiments under isothermal conditions at different
temperatures. Additionally, isothermal experiments still possess an
element of non-isothermal behavior during the initial heating ramp
to the desired temperature. Interest in isothermal methods, however, has gradually waned because they are considered toilsome
[27]. Conversely, dynamic methods, which are performed under
non-isothermal conditions, have attracted much appeal given their
ability to investigate a range of temperatures expeditiously [27,28].
Non-isothermal analytical techniques use modern thermobalances
that subject samples to a programmed continuous temperature
rise, which ensures that no temperature regions are omitted, as
can occur during a sequence of discrete isothermal measurements.
Despite their touted convenience [29,30], non-isothermal techniques have received pointed criticism [31–35] and, sometimes,
outright rejection [36] because of their perceived inability to reliably assess kinetic parameters, besides their increased sensitivity
to experimental noise as compared to isothermal methods [37,38].
Benoit et al. [39] advised against the use of non-isothermal techniques for solid state decomposition processes where there is a
change in the reaction kinetics over the temperature range or
degree of conversion. Studies have shown that there are wide disparities among values obtained from dynamic techniques that use
only a single heating rate. A consensus emerged that the accuracy
of these methods could be improved using multiple sets of thermal data collected by performing experiments at multiple heating
rates [33,40]; it is a perspective shared by participants in a recent
kinetics project commissioned by ICTAC [41–45]. Paradoxically, the
inherent efficiency with which dynamic methods collect kinetic
data is partially negated in that reasonably resolved data typically
is obtained using low heating rates [46].
Thermogravimetric analysis (TGA) is the most commonly
applied thermoanalytical technique in solid-phase thermal degradation studies [47], and it has gained widespread currency in
thermal studies of biomass pyrolysis [48–54]. TGA measures the
decrease in substrate mass caused by the release of volatiles, or
devolatilization, during thermal decomposition [55]. In TGA, the
mass of a substrate being heated or cooled at a specific rate is
monitored as a function of temperature or time. Taking the first
derivative of such thermogravimetric curves (i.e., −dm/dt) curves,
known as derivative thermogravimetry (DTG), provides the maximum reaction rate [56]. The development of a system in 1899 by Sir
William Roberts-Austen [57] that uses thermocouples to measure
the temperature difference between a sample and an adjacent inert
reference material subjected to an identical temperature alteration
was the naissance of differential thermal analysis (DTA) [58]. By
4
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Table 1
Classification scheme of thermoanalytical techniques.
Property
Technique
Parameter measured
Abbreviation
Mass
Thermogravimetric analysis
Derivative thermogravimetry
Differential thermal analysis
Derivative differential thermal analysis
Differential scanning calorimetry
Thermomanometry
Thermodilatometry
Thermomechanical analysis
Thermoelectrical analysis
Thermomagnetic analysis
Thermoacoustic analysis
Thermoptical analysis
Sample mass
First derivative of mass
Temperature difference between sample and inert reference material
First derivative of DTA curve
Heat supplied to sample or reference
Pressure
Coefficient of linear or volumetric expansion
TGA
DTG
DTA
Temperature
Heat
Pressure
Dimensions
Mechanical properties
Electrical properties
Magnetic properties
Acoustic properties
Optical properties
Electrical resistance
Acoustic waves
plotting the time (t) versus temperature difference (T) a DTA
curve can be generated from which the reaction rate can be calculated in terms of the slope (dT/dt) and height (T) of the curve
at any temperature [59]. Another common method of thermal analysis is differential scanning calorimetry (DSC). In DSC, heat flux into
or out of a sample is compared against an inert reference material,
usually alumina, as the two specimens are simultaneously heated
or cooled at a constant rate. The integral (or area) of the DSC peak is
directly proportional to the heat of transition for a particular reaction and the change in heat capacity can readily be correlated to
the enthalpy change of the reaction. DTA is similar to DSC, except
that the conditions in DTA are adiabatic causing a temperature difference between the sample and the reference material. Table 1
provides a listing of thermoanalytical techniques classified according to the physical properties that are measured.
Thermal analysis provides an excellent tool that may provide
insight regarding the kinetic workings of heterogeneous reactions.
However, it cannot be overstressed that the kinetic data obtained
from a single thermoanalytical technique, in and of itself, does not
provide the necessary and sufficient evidence to draw mechanistic
conclusions about a solid state decomposition process [60]. The
kinetic behavior of a given heterogeneous reaction system may
change during the process and so it is possible that the complete
reaction mechanism cannot be represented suitably by a single specific kinetic model [61]. Various other analytical techniques (e.g.,
electrical, nuclear, optical, and X-ray) must be employed to detect
and analyze changes that occur in the chemical composition and/or
structure of the sample. One such specialized method, evolved gas
analysis (EGA), involves a qualitative and quantitative assessment
of the gases that are evolved during thermal analysis. EGA can
be performed using a variety of analytical tools, including Fourier
transform infrared spectroscopy (FTIR), gas chromatography (GC),
high performance liquid chromatography (HPLC), mass spectrometry (MS), and GC–MS. The use of these species-specific techniques
in consort with thermal analysis can help facilitate the elucidation
of an appropriate kinetic scheme and, hopefully, bring investigators
one step closer to understanding the actual reaction mechanism.
2.3. Arrhenius rate expression and the significance of the kinetic
parameters
Virtually every kinetic model proposed employs a rate law that
obeys the fundamental Arrhenius rate expression:
k(T ) = A exp
−E a
RT
(1)
where T is the absolute temperature in K, R is the universal gas
constant, k(T) is the temperature-dependent reaction rate constant, A is the frequency factor, or pre-exponential, and Ea is the
activation energy of the reaction. The main temperature dependence in the Arrhenius equation arises from the exponential term,
DSC
TMA
TEA
TAA
TOA
although the frequency factor, A, does exhibit a slight temperature
dependency [17,62]. For homogeneous reactions involving gases,
the physical significance of the Arrhenius parameters (i.e., Ea and
A) can be interpreted in terms of molecular collision theory. The
activation energy, Ea , can be regarded as the energy threshold that
must be overcome before molecules can get close enough to react
and form products. Only those molecules with adequate kinetic
energy to surmount this energy barrier will react. Alternatively,
transition state theory describes the activation energy as the difference between the average energy of molecules undergoing reaction
and average energy of all reactant molecules [63]. The frequency
factor provides a measure of the frequency at which all molecular
collisions occur regardless of their energy level [64]. The exponential term in Eq. (1) can be thought of as the fraction of collisions
having sufficient kinetic energy to induce a reaction [65]. Thus,
the rate constant, k(T), being the product of A and the exponential term, exp−Ea /RT , yields the frequency of successful collisions
[65].
Vociferous debate continues to swirl about the relevancy of
kinetic parameters obtained from solid state reactions. The crux
of the controversy stems from the indiscriminate adoption of
homogeneous reaction kinetic theory to describe heterogeneous
processes [66–68]. Indeed, it is plausible that much of the inconsistency arising in biomass kinetic data is ascribable to the use of
kinetic expressions that are merely adaptations of those used in
homogeneous reactions and that do not incorporate terms that
depend upon the solid state nature of biomass. Over thirty years
ago, Garn [69] contended that the discrepancies observed in calculated activation energies for solid phase decomposition are a
reminder that the concept of a symmetric distribution of energy
states as implied by the Arrhenius equation does not apply to solids.
The fact that the most commonly occurring and minimum possible energy state in solids is that of the perfect crystal obviates
the use of a statistical treatment for solids [70]. Garn advised [69]
that if the calculated “activation energy varies with experimental
conditions then it is necessarily true that: (1) there is no uniquely
describable activated state and consequently the Arrhenius equation has no application to solid reactions; or (2) the assumption
that the rate is a function only of temperature and the [mass] fraction remaining is incorrect; or (3) both”. Consequently, the physical
connotation of the Arrhenius parameters in heterogeneous kinetics
is opaque and “. . .they do not characterize the chemical reaction
itself, but only the whole complexity of processes occurring during the pyrolysis under the given experimental conditions” [71].
Hence, experimentally determined kinetic parameters from thermally activated, solid state transformations can only be expected
to provide a rough approximation for the overall rate of a complex process that typically entails numerous steps, each having
distinct activation energies [40,72]. Garn [66] also raised salient
concerns about other weaknesses associated with the transfer of
homogeneous kinetic principles to heterogeneous processes.
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Table 2
Unconventional phenomena represented by the Arrhenius rate law.
5
conditions by the following canonical equation:
Temperature-dependent phenomenon
(applicable temperature range)
Ea (kJ mol−1 )
Rate of counting
Rate of forgetfulness
Frequency of the heart beat of a terrapin
(18–34 ◦ C)
Creeping velocity of the millipede (Parajulus
pennsylvanicus) (6–30 ◦ C)
Creeping velocity of the ant (Liometopum
apiculatum) (16–38.5 ◦ C)
Frequency of flashing of fireflies
Rate of chirping of common tree crickets
(Oecanthus)
Velocity of amoeboid progression in human
neutrophilic leucocytes (27–40 ◦ C)
Creeping velocity of the spotted leopard slug
(Limax maximus) (11–28 ◦ C)
Rate of filament movements in the blue-green
algae (Oscillatoria) (6–36 ◦ C)
Human alpha brain-wave rhythm
100.4
100.4
76.6
51.2
51.0
51.0
51.0
45.2
44.8
38.7
29.3
Although alternative expressions (e.g., linear relationships
between ln k and T, and between ln k and ln T) do exist for describing
the influence of temperature on the rates of chemical reactions, Laidler [73] emphasized that none of these other relationships enjoys
the universal acceptance bestowed upon the Arrhenius equation
because of their “theoretical sterility”. The additional parameters
that are included in these surrogate rate expressions presumably would permit better fitting of experimental data, but there
is no theoretical rationale for their existence, thereby, depriving
them of any physico-chemical significance [62]. Were the thermal analysis community to approve an alternative expression for
the temperature dependence of reaction rates, it would necessitate the recalculation of all previous Ea and A values so that
kinetic parameters dating back to 1899 could be compared against
those generated by the new rate law [62]. An undertaking of this
magnitude would be incredibly laborious and seems improbable.
Moreover, rejection of the Arrhenius expression would, as Šesták
[74] said, “certainly deny the fifty [i.e., now eighty] years’ work
of famous scientists in the field of heterogeneous kinetics”. For all
the barbed accusations that have been hurled against the Arrhenius rate law, it remains the only such kinetic expression that can
satisfactorily account for the temperature-dependent behavior of
even the most unconventional processes, as shown in Table 2 and
noted originally in a series of review papers by Crozier et al. [75–77],
and subsequently expanded by Laidler [78] and then tabulated by
Brown [68]. Laidler’s purpose for revisiting these intriguing processes was to underscore that relatively complex reaction systems
can be represented by the Arrhenius law and also that above a certain energy threshold (i.e., about 21 kJ mol−1 ) many phenomena
are likely to proceed via chemical reactions rather than by physical processes. The prominent role of the Arrhenius expression in
heterogeneous reaction systems is undeniable and was acknowledged by Agrawal [28], who stated, “. . .it is perhaps the most
widely used equation and is satisfactory in explaining the temperature dependence of the rate constant in solid-state decomposition
kinetics”.
3. Biomass pyrolysis kinetics
3.1. Kinetic expressions for biomass thermal decomposition
The kinetics of biomass decomposition are routinely predicated
on a single reaction [79,80] and can be expressed under isothermal
d˛
= k(T )f (˛) = A exp
dt
−E a
RT
f (˛)
(2)
where t denotes time, ˛ signifies the degree of conversion, or extent
of reaction, d˛/dt is the rate of the isothermal process, and f(˛) is
a conversion function that represents the reaction model used and
depends on the controlling mechanism. The extent of reaction, ˛,
can be defined either as the mass fraction of biomass substrate that
has decomposed or as the mass fraction of volatiles evolved and
can be expressed as shown below:
˛=
w0 − w
v
=
w0 − wf
vf
(3)
where w is the mass of substrate present at any time t, w0 is the
initial substrate mass, wf is the final mass of solids (i.e., residue and
unreacted substrate) remaining after the reaction, v is the mass of
volatiles present at any time t, and vf is the total mass of volatiles
evolved during the reaction. The combination of A, Ea , and f(˛) is
often designated as the kinetic triplet, which is used to characterize
biomass pyrolysis reactions [81,82]. Non-isothermal rate expressions, which represent reaction rates as a function of temperature
at a linear heating rate, ˇ, can be expressed through an ostensibly
superficial transformation [81,83] of Eq. (2):
d˛
d˛ dt
=
dT
dt dT
(4)
where dt/dT describes the inverse of the heating rate, 1/ˇ, d˛/dt
represents the isothermal reaction rate, and d˛/dT denotes the nonisothermal reaction rate. An expression of the rate law for nonisothermal conditions can be obtained by substituting Eq. (2) into
Eq. (4):
d˛
k(T )
A
=
f (˛) = exp
dT
ˇ
ˇ
−E a
RT
f (˛)
(5)
The use of reaction-order models is ubiquitous in the thermal
analysis of biomass because of their simplicity and propinquity to
relations used in homogeneous kinetics [28,83]. In these orderbased models, the reaction rate is proportional to the fraction of
unreacted substrate raised to a specific exponent, known as the
reaction order:
d˛
= k(T )(1 − ˛)n
dT
(6)
where (1 − ˛) is the remaining fraction of volatile material in the
sample and n represents the reaction order. The devolatilization
dynamics of biomass pyrolysis are frequently expressed as a first
order decomposition process that results in the formation of discrete volatile fractions [49,84–91]:
dVi
= ki (T )(Vi∗ − Vi )
dt
(7)
where ki (T) is the rate constant for an evolved volatile fraction
i, Vi is the cumulative mass of released volatiles corresponding to fraction i through time t, and Vi * is the effective volatile
content for fraction i. In most devolatilization schemes, the
separate volatilized fractions are classified in terms of three principal biomass pseudo-components (i.e., hemicellulose, cellulose,
and lignin) and, sometimes, moisture [49,88,89,92,93]. The total
devolatilization rate for a particular system is given by linear summation of the individual volatilization rates for each fraction, which
are weighted according to the percentage of respective pseudocomponent initially present in the unreacted solid substrate. The
release of biomass volatiles has also been hypothesized to involve
several independent concurrent reactions that produce a set of
lumped volatile products [94,95]. This alternative kinetic representation uses Eq. (7) as a template but the rate of devolatilization is
6
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Table 3
Expressions for the most common reaction mechanisms in solid state reactions.
Reaction model
Reaction order
Zero order
First order
nth order
Nucleation
Power law
Exponential law
Avrami–Erofeev (AE)
Prout–Tompkins (PT)
Diffusional
1-D
2-D
3-D (Jander)
3-D (Ginstling–Brounshtein)
Contracting geometry
Contracting area
Contracting volume
a
f(˛) = (1/k)(d˛/dt)
g(˛) = kt
(1 − ˛)n
(1 − ˛)n
(1 − ˛)n
˛
−ln(1 − ˛)
(n − 1)−1 (1 − ˛)(1−n)
n(˛)(1−1/n) ; n = 2/3, 1, 2, 3, 4
ln ˛
n(1 − ˛) [−ln(1 − ˛)](1−1/n) ; n = 1, 2, 3, 4
˛(1 − ˛)
˛n ; n = 3/2, 1, 1/2, 1/3, 1/4
˛
[−ln(1 − ˛)]1/n ; n = 1, 2, 3, 4
ln[˛(1 − ˛)−1 ] + Ca
1/2˛
[−ln(1 − ˛)]−1
3/2(1 − ˛)2/3 [1 − (1 − ˛)1/3 ]−1
3/2[(1 − ˛)−1/3 − 1]−1
˛2
(1 − ˛)ln(1 − ˛) + ˛
[1 − (1 − ˛)1/3 ]2
1 − 2/3˛ − (1 − ˛)2/3
(1 − ˛)(1−1/n) ; n = 2
(1 − ˛)(1−1/n) ; n = 3
1 − (1 − ˛)1/n ; n = 2
1 − (1 − ˛)1/n ; n = 3
Integration constant.
measured with respect to individual reactions rather than volatile
fractions. Integration of the preceding kinetic equations is often
performed using a fourth order Runge–Kutta method [39,96,97]
and the method of least squares using nonlinear regression analysis
[39,98–100] is regularly employed to fit the experimental data and
evaluate the Arrhenius parameters as predicted by the kinetic models. Some of the more important rate equations used to describe
the kinetic behavior of solid state reactions are listed in Table 3,
or simply “The Table”. Other than for didactic purposes or reviews,
authors should assume that their audience is acquainted with the
relevant background information and refrain from the repetitive
inclusion of “The Table” each time a new thermal analysis paper
is published. Furthermore, the argument that reference texts containing a comprehensive listing of reaction models are not readily
available is no longer valid. Elsevier Science Publishers [101] has
recently republished Vol. 22 of the Comprehensive Chemical Kinetics series entitled: Reactions in the Solid State by C.H. Bamford and
C.F.H. Tipper, Eds. [18], which includes a complete set of solid state
reaction models. Another fine thermal analysis reference book containing “The Table” that is accessible at most academic libraries is
the Handbook of Thermal Analysis and Calorimetry, Vol. 1: Principles and Practice by M.E. Brown, Ed. (P.K. Gallagher, Series Ed.)
[13].
It should be noted that the application of first order reaction
models in biomass pyrolysis kinetics has become almost formulaic
and their indiscriminate acceptance has occurred without rigorous
verification or sufficient awareness of their fundamental limitations [82,102]. The imposition of an order-based model on a solid
state reaction system can cause a substantial divergence in the
Arrhenius parameters (i.e., A and Ea ) [82]. This discrepancy arises
when an inappropriate reaction order is affixed to the last term
in Eq. (6). The strongly correlated Arrhenius parameters in the
rate constant, k(T), are then forcibly adjusted to accommodate the
chosen reaction order. Accordingly, any reaction model, not only
order-based models, can suitably fit kinetic data because of the
corresponding “kinetic compensation effect” among the Arrhenius
parameters [103]. The manifestation of this compensation relationship is common to both isothermal and non-isothermal kinetic
models, yet the increasing popularity of non-isothermal single
heating rate techniques in preceding decades necessarily gave rise
to a surge of unreliable and erratic results [28,104,105]. Much suspicion was cast upon the validity of non-isothermal model-fitting
methods, although isothermal methods are just as culpable in that
they are also susceptible to a similar vacillation in the Arrhenius
parameters [106]. To quote Ninan [47], “As far as the values of
the kinetic parameters are concerned, there is no significant differ-
ence between isothermal and non-isothermal methods or between
mechanistic and non-mechanistic approaches, in the sense that
they show the same degree of fluctuation or trend, as the case may
be”.
Garn [66] underscored several critical assumptions included in
the generalized rate expression (Eq. (2)), which is often used to
describe solid state decomposition kinetics. A violation of any of
these assumptions in a particular system will invalidate the use of
the rate equation. The use of the mathematical terms, f(˛) and k(T),
explicitly affirms that the reaction rate is exclusively a function
of the degree of conversion, ˛, and the temperature, T. Changes in
other process parameters (e.g., heating rate, residence time, particle
size, sample quantity, reaction interface, atmosphere, and pressure) theoretically should have no effect on the reaction rate. If
changes in reaction rate are found to result from variation in these
other parameters, the conventional rate equation has failed. In
other words, the rate of reaction may be influenced by parameters
besides the concentration that are not incorporated in the generalized “reaction statement”. A logical explanation for this can be
deduced by recognizing that the rate constant for a given reaction
is clearly an intensive property [34], like temperature or density,
because it is “measured from changes in an extensive property
of the system such as mass, enthalpy, and volume” [17]. Hence,
the rate constant has important merit because it is specific to a
particular substance and process and it can potentially be used to
discriminate amongst various reaction systems.
3.2. Biomass pyrolysis kinetic models
A comprehensive review of the myriad models available for
analyzing the kinetics of biomass pyrolysis reactions is beyond
the scope of this communication. Instead pertinent kinetic models used in biomass pyrolysis studies will be presented along
with selected additional models that are noteworthy for their
innovative efforts to achieve improved predictive success by better reflecting the heterogeneous character of biomass thermal
decomposition. The numerous pyrolysis models can be divided
into three principal categories: single-step global reaction models, multiple-step models, and semi-global models [107–110]. The
processes comprising pyrolysis frequently are described as proceeding along (a) concurrent (i.e., competitive and independent
parallel) routes [6,53,91,107–110], (b) consecutive (or sequential)
routes [111–115], or (c) combinations thereof [116–121]. Single
reaction global schemes describe the overall rate of devolatilization
from the biomass substrate. Single-step global models have provided reasonable agreement with experimentally observed kinetic
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
behavior [84,122–124]. One frequently cited study [125] revealed
that the pyrolysis of many different cellulosic substrates can be
adequately described by an irreversible, single-step endothermic
reaction that follows a first order rate law with a global apparent
activation energy of ca. 238 kJ mol−1 . The usefulness of single-step
global models, however, is limited by the assumption of a fixed
mass ratio between pyrolysis products (i.e., volatiles and chars),
which prevents the forecasting of product yields based on process conditions [126]. Furthermore, in most pyrolysis systems the
kinetic pathways are simply too complex to yield a meaningful
global apparent activation energy [127].
Much related work has examined the use of semi-global models, all of which assume that biomass pyrolysis products can
be aggregated into three distinct fractions: volatiles, tars, and
char. Semi-global models are able to facilitate a simpler ‘lumped’
kinetic analysis [53,89,107,126,128,129]. This analysis is used
widely because its depiction of biomass devolatilization in terms
of three concurrent first order reactions is intuitive [90]. This
technique is a suitable tool for correlating and evaluating kinetic
data from different biomass types under similar reaction conditions, but it is ill-suited for comparisons of thermal decomposition
data obtained from dissimilar reaction conditions [84]. Semi-global
models also allow coupling of transport phenomena parameters
with the secondary devolatilization reactions. This procedure has
been demonstrated to correctly predict trends in product yield as
a function of volatiles residence time [130].
3.3. Multiple-step models
The inability to predict the kinetic behavior of biomass under
different process conditions has vexed researchers and encouraged the development of complex multiple-step models. A rigorous
kinetic treatment of pyrolysis data must account for the formation rates of all the individual product species [88,108], along
with any potential heat and mass transfer limitations. Alves and
Figueiredo [113] concluded that the pyrolysis of cellulose could
be successfully modeled using three consecutive first order reactions. The first reaction represents approximately 30% of the total
devolatilization, while the third reaction releases the remaining
70% of the volatile matter [131]. The second reaction released no
volatile matter and is theorized to involve rearrangement of the
solid. Alternative reaction schemes, while possible, were deemed
impractical because they would require either more than three
reactions or three reactions of order other than unity to describe
the complex devolatilization process. A study by Diebold [132]
provided an elegant seven-step global kinetic model for cellulose
pyrolysis that achieved accurate predictions using published rate
constants for both fast and slow pyrolysis. The model accounted for
interactions between heating rate, residence time, pressure, and
temperature. It was demonstrated by Vargas and Perlmutter [112]
that the reaction kinetics of coal subjected to non-isothermal pyrolysis can be understood to proceed via a series of ten consecutive
isothermal steps, each associated with the degradation of a specific
pseudo-component of the coal. Not to be outdone, Mangut et al.
[133] revealed that kinetic data obtained from the pyrolysis of food
industry wastes related to tomato juice production (i.e., peels and
seeds) could be satisfactorily modeled using twelve consecutive
pyrolytic reactions that were identified from DTG curves. Although
useful in some applications, multi-step reaction models are limited
by their incorporation of several interdependent serial reactions,
wherein subtle inaccuracies in the kinetic parameters obtained
for the first rate equation can be greatly magnified in successive
reactions [134]. Except for a few extremely simple cases, comprehensive kinetic approaches are intractable because of the sheer
number of reactions that would need to be considered. Furthermore, the identification of constituents in pyrogenic tar mixtures
7
remains incomplete and the intermediate pyrogenic species have
scarcely been characterized. Consequently, these ‘elegant’ models
can sometimes be of limited practical use.
3.4. Isoconversional techniques
Historically, model-fitting methods were thought to satisfactorily predict reaction kinetics in solid state processes. Arrhenius
parameters obtained from model-fitted isothermal data are often
nearly independent of the kinetic models employed [40]. Iterative
approaches to model-fitting empirical endpoints from isothermal
data may provide consistent values for the Arrhenius parameters,
but only a single global kinetic triplet is obtained for each set of
data. As stated previously, solid state processes, such as biomass
pyrolysis, frequently proceed via a complex suite of concurrent and
consecutive reactions. Each step likely has its own unique apparent
activation energy, and thus the use of an average, global apparent
activation energy to describe the kinetics of such processes could
be construed as an inadequate oversimplification at best [135] and,
more alarmingly, the DTG curves from these models may conceal
the true multistage character of pyrolytic reactions under a single peak [136]. Conversely, force fitting models to non-isothermal
data obtained from a single heating rate can generate very inconsistent Arrhenius parameters that display a strong dependence on
the selected kinetic model [40]. Non-isothermal methods that use
multiple heating rates can provide more reliable estimates of the
kinetic parameters as mentioned earlier, but various decomposition processes can exhibit different dependencies on heating rate,
which may lead to overlapping reactions in the DTG curves that are
difficult to separate [137].
The consternation in the scientific community [68,138] over
the wide variation in Arrhenius parameters for similar reaction
conditions and biomass species using different reaction models
served as a lightning rod that precipitated additional research and
development [29,40,139–143]. Innovative methods for determining Arrhenius parameters based on a single parameter began to
emerge in the 1960s. These so-called “model-free” methods are
founded on an isoconversional basis, wherein the degree of conversion, ˛, for a reaction is assumed to be constant and therefore
the reaction rate, k, depends exclusively on the reaction temperature, T. By allowing Ea to be calculated a priori, isoconversional
approaches eliminate the need to initially hypothesize a form and
rate order for the kinetic equation. Hence, isoconversional methods do not require previous knowledge of the reaction mechanism
for biomass thermal degradation. Another advantage of isoconversional approaches is that the systematic error resulting from the
kinetic analysis during the estimation of the Arrhenius parameters
is eliminated [41].
Isoconversional models can follow either a differential or an
integral approach to the treatment of TGA data. The Friedman
method [144] is a differential isoconversional technique that can
be expressed in general terms as written below:
d˛
=ˇ
dt
d˛ dT
= A exp
−E a
RT
f (˛)
(8)
Taking natural logarithms of each side from Eq. (8) yields:
ln
d˛ dt
d˛ = ln ˇ
dT
= ln[Af (˛)] −
Ea
RT
(9)
It is assumed that the conversion function f(˛) remains constant,
which implies that biomass degradation is independent of temperature and depends only on the rate of mass loss. A plot of ln[d˛/dt]
versus 1/T yields a straight line, the slope of which corresponds to
−Ea /R.
The Flynn–Wall–Ozawa (FWO) method [62,145–150] is an
integral isoconversional technique that assumes the apparent acti-
8
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
vation energy remains constant throughout the duration of the
reaction (i.e., from t = 0 to t˛ , where t˛ is the time at conversion
˛). Integrating Eq. (9) with respect to variables ˛ and T:
˛
g(˛) =
0
d˛
A
=
f (˛)
ˇ
T˛
exp
−E a
RT
0
dT
(10)
where T˛ is equal to the temperature at conversion ˛. If we define
x ≡ Ea /RT, Eq. (10) becomes:
g(˛) =
AEa
ˇR
∞
˛
AEa
exp−x
=
p(x)
ˇR
x2
(11)
where p(x) representing the rightmost integrand in Eq. (10) is
known as the temperature integral. The temperature integral does
not have an exact analytical solution in closed form [29] but can be
approximated via an empirical interpolation formula proposed by
Doyle [62,149,151,152]:
log p(x) ∼
= −2.315 − 0.4567x,
for 20 ≤ x ≤ 60
(12)
Using Doyle’s approximation for the temperature integral and taking logarithms of both sides of Eq. (11) one obtains:
log ˇ = log A
Ea
Rg(˛)
− 2.315 − 0.4567
Ea
RT
(13)
In the FWO method, plots of log ˇ versus 1/T for different heating
rates produce parallel lines for a fixed degree of conversion. The
slope (−0.4567Ea /R) of these lines is proportional to the apparent
activation energy. The value of log A is given by the intercept of this
line with the y-axis, log ˇ.
Another widely utilized integral isoconversional method
is known as the Kissinger–Akahira–Sunose (KAS) method
[56,104,105,153,154]. The KAS method employs another empirical
approximation derived by Doyle [62,149,151,152]:
exp−x
log p(x) ∼
=
x2
,
for 20 ≤ x ≤ 50
(14)
Substitution of Eq. (14) into Eq. (11) and taking the ln of both
sides leads to the expression for the KAS integral isoconversional
method:
ln
ˇ
2
Tm
Ea
=−
R
1 Tm
− ln
E ˛
a
AR
0
d∂
f (˛)
(15)
where Tm is the temperature at the maximum reaction rate. Assuming ˛ has a fixed value, Ea can be determined from the slope of the
straight line obtained by plotting ln(ˇ/Tm 2 ) versus 1/Tm .
The integral method based on the Coats and Redfern (CR) equation [155,156] is a popular non-isothermal model-fitting method
that requires an assumption be made regarding the value of the
reaction order for g(˛). The method approximates p(x) in Eq. (11)
using a Taylor series expansion to yield the following expression:
ln
−ln(1 − ˛) T2
= ln
AR ˇEa
1−
2RT
Ea
−
Ea
RT
(16)
g(˛) T2
= ln
AR ˇEa
−
Ea
RT
ln
(17)
A straight line can be obtained from single heating rate data by
plotting ln[g(˛)/T2 ] versus T−1 . From the slope of the line, −Ea /R,
and its intercept ln(AR/ˇEa ), Ea and A can be derived. The attractiveness of the CR method resides in its ability to directly furnish
A and Ea for single heating rate. The criticism of the CR approach
follows the same general arguments presented against all of the
model-fitting methods, namely, that the kinetic triplet resulting
from evaluation of a single DTG curve may be non-unique, or indistinguishable, because of the high degree of correlation between ␣
ˇ
T 2 (1 − 2RT /Ea )
=−
Ea
+ ln
RT
AR (18)
g(˛)Ea
Given a fixed degree of conversion, the left-hand term is plotted
versus T−1 for each heating rate, generating a set of straight lines,
each having slope −Ea /R. The frequency factor, A, is calculated by
inserting −Ea /R into the intercept. Because the left-hand side of Eq.
(18) is weakly dependent on Ea , an iterative process must be used
by assuming an initial value for Ea and then re-evaluating the lefthand side until the desired level of convergence [161]. It should be
noted as a point of clarity that there are other so-called “modified
Coats–Redfern” methods in the literature, but they cannot be considered isoconversional because they still require the selection of
a reaction order. These alternative “modified Coats–Redfern” formulations often involve a regression analysis of one or more of the
kinetic triplet parameters [162,163]. One such “modified” method
[163] reported errors for Ea estimates that are an order of magnitude lower than those obtained from isoconversional techniques.
3.5. Comparative evaluation of integral and differential
isoconversional techniques
The advantages of the integral isoconversional methods are
tempered by several weaknesses not present in the differential
methods [164], viz.,
(1) Picard iteration [165] of the temperature integral is needed.
(2) Integral methods are prone to error accretion during such successive approximations.
(3) The temperature integral requires boundary conditions which
are frequently ill-defined.
Flynn [62] remarked that use of “. . .the mathematically
intractable temperature integral has often become a necessary evil
in the analysis of thermal analysis kinetics”. To circumvent the
hazards posed by these oversimplified approximations, Vyazovkin
and Dollimore [166] introduced a non-linear isoconversional technique, known as the Vyazovkin (V) method, which uses a revised
expression for the temperature integral, p(x):
T˛
I(Ea , T˛ ) =
exp
0
−E a
RT
dT = p(x)
(19)
The V method evaluates Ea for a set of q experiments conducted
at different heating rates, ˇj and ˇk , where the subscripts j and k
denote the ordinal number of the experiment:
q
Eq. (16) can be simplified by recognizing that for customary values
of Ea (e.g., 80–260 kJ mol−1 ), the term 2RT/Ea 1:
ln
and d˛/dt (or dT/d˛) [28,157–160]. A multi-heating rate application
of the original Coats and Redfern equation, known as the modified
Coats–Redfern (CR*) method [41,161], has been advanced that provides an integral isoconversional technique equivalent to those of
FWO and KAS. The CR* method rearranges terms in Eq. (16) to yield:
q
ˇk I(Ea , T˛,j )
j=1 k =
/ j
ˇj I(Ea , T˛,k )
= (Ea )
(20)
where I(Ea ,T˛,j ) and I(Ea ,T˛,k ) represent the temperature integral
p(x) corresponding to the heating rates ˇj and ˇk , respectively.
The apparent activation energy is given by the value that minimizes . Values of I(Ea ,T˛ ) can be determined via either numerical
integration or the Senum–Yang [167] approximation:
p(x) =
exp−x
x
(x3 + 18x2 + 88x + 96)
4
(x + 20x3 + 120x2 + 240x + 120)
(21)
Unfortunately, the constraints imposed by the mathematical constructs used in the standard integral isoconversional methods
(CR, FWO, and KAS) prevent a straightforward determination of
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
the remaining kinetic parameters, A and f(˛) [40,105]. The frequency factor obtained from standard isoconversional techniques
is tainted by association with the reaction model that must be
assumed to permit its calculation [40]. Flynn [164] developed a
general differential isoconversional method that allows A and f(˛)
to be disconnected and evaluated independently. Another procedure to unambiguously evaluate A was proposed by Vyazovkin and
Lesnikovich [168], wherein a linear relation that exists between the
Arrhenius parameters is used to extract the frequency factor for a
given isoconversional value of Ea :
ln A = aEa + b
(22)
where a and b are correlation parameters that are evaluated using
linear regression. The use of this procedure, however, is not entirely
faultless because the linear correlation, known as the apparent
compensation effect, has been the recipient of rigorous criticism
as noted later in this paper.
All of the integral isoconversional methods (viz., CR, FWO,
KAS, and V) assume that the values of Ea and A remain constant
throughout the reaction until the desired level of conversion, ˛,
is reached, making these techniques somewhat analogous to the
inflexible global one-step models, which also assume an unchanging Ea for pyrolysis processes [105]. The supposition of constant
Ea and A values is only possible when the Arrhenius parameters
are independent of the extent of reaction [140]. When Ea depends
on ˛, however, it was found that the use of integral isoconversional methods can lead to systematic errors [139,140,169,170].
Li et al. [139,171] found that values of Ea are consistently overestimated using integral isoconversional methods versus those
evaluated using Friedman’s differential isoconversional method
because of error introduced by the truncation of the additional
higher-order terms in Doyle’s approximations, given by Eqs. (11)
and (13). Data provided by Budrugeac et al. [169] for the dehydration of calcium oxalate indicates that Ea values obtained from
integral methods can deviate by up to 21% from values determined
by differential methods. In response, Vyazovkin [103] provided
a modification for the V isoconversional method that accounts
for the variation in apparent activation energy with increasing ˛.
Instead of evaluating the temperature integral over the complete
boundary conditions (i.e., 0–t˛ ), the integration is now performed
numerically over small time increments using the trapezoidal rule,
which requires considerable more computational effort than the
Senum–Yang approximation [168]. In a rebuttal, Budrugeac and
Segal [172] remarked that the modification proposed by Vyazovkin
[103] using “low ranges of variables” is an artifact that in reality
conceals the true differential character of the method.
Differential isoconversional methods are not encumbered with
a temperature integral and thus kinetic parameters can be directly
calculated. Numerical differentiation of experimental data is highly
susceptive to data noise [43,173] and can result in significant scatter in the resulting derivative curves. Widespread use of differential
techniques has also been inhibited because of the daunting calculations involved [164]. The advent of powerful computational
tools [164,174–176] coupled with the development of sophisticated smoothing and fitting functions [137,173,177–180] has
helped to curtail some of these objections, although some resistance yet remains among those who insist that integral methods
are a “safer alternative” [43] because differential methods still “suffer from excessive random errors” [139], especially in the vicinity of
the reaction onset and endpoint, where d˛/dt is often small [170].
Nonetheless, Burnham and Dinh [105] recently indicated that if the
rate of data collection is sufficiently high then the raw data can be
smoothed appreciably such that the vulnerabilities of the Friedman method to experimental noise can be “effectively mitigated”.
An examination by Burnham et al. of the predictive performance
of several isoconversional and model-fitting techniques applied on
9
data sets from the ICTAC kinetics project and other lifetime projects
revealed that the Friedman differential method was the most reliable and accurate method in all cases.
There are also some disadvantages that are common to all
“model-free” techniques. The use of the descriptor, “model-free”, is
deceptive [181] because it insinuates that awareness of the kinetic
model and, in particular, the conversion function f(˛), is superfluous information not needed in the kinetic analysis. An accurate
description of kinetic behavior is not possible when members of the
kinetic triplet are interpreted independently of one another [182].
“Model-free” methods simply “postpone” the consideration of an
appropriate conversion function until an estimate of the kinetic
parameters (i.e., Ea and A) is calculated [181]. Furthermore, isoconversional methods are unsuitable for those reaction schemes
containing competing reactions, where the net rate of reaction
depends on changes in temperature, or concurrent reactions that
switch which reaction is rate-limiting over the experimental temperature range [105].
It has also been cautioned that the selection of kinetic expressions wherein “f(˛) is assumed to be a function of mass can be a
very poor choice” because these models presume that the activity of every reactant particle is identical regardless of its location
in the substrate matrix (i.e., in the bulk or on the surface) [17].
In heterogeneous reactions this is seldom the case because substrate reactivity can vary depending on the location of active surface
sites, the partial pressure of the surrounding atmosphere, and
physical changes in the specimen that are temperature-dependent
phenomena (e.g., sintering, melting, and vitrification) [17,70,138].
According to Flynn [17], it is possible in certain solid state reactions
that the “. . .crucial, rate-controlling event may be the occurrence of
the temperature-dependent physical transformation which is not
mass dependent”. Šesták and Berggren [15] succinctly conveyed
these concerns regarding proper selection of ˛ when he stated,
“[DTA] is still of questionable validity, because a representative
value which would unambiguously define the change in the system
from the initial or from the final state is not yet available. . .”.
3.6. Other kinetic models
Kinetic models other than traditional reaction order models
have been proposed that ostensibly afford improved predictions
for biomass pyrolysis data. For example, an interesting deactivation theory was proposed by Balci et al. [183] that is based on
kinetic models typically applied toward catalyst deactivation. In the
biomass deactivation model (DM), the first order rate constant was
assumed to vary with the degree of decomposition due to changes
that occur in the chemical composition and physical structure of the
substrates during the pyrolysis process. Individual biomass components degrade at different temperatures, demonstrating that the
composition of the reactive portion of the substrate is modified during the reaction. A combination of altered solid geometry, shrinking
volume, and changing pore structure during pyrolysis results in a
depletion of the active surface area. The deactivation of the solid
during pyrolysis by the aforementioned changes influences the
apparent rate constant as shown below:
E i
kapp = zk = z() Ai exp −
RT
(23)
where z is the activity of the solid substrate expressed as a function of a deactivation rate constant, , and kapp is the apparent rate
constant.
Reynolds et al. [161,184,185] developed a generalized
nucleation-growth model, which is essentially a modification
of the Prout–Tompkins rate equation [186], first used to describe
10
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
the thermal decomposition kinetics of potassium permanganate
[187]:
d˛
= kyn (1 − ry)s
dt
(24)
where y designates the remaining fraction of substrate, n is still the
reaction order, r is an initiation parameter frequently set to 0.99, s
is used as an adjustable nucleation parameter that can reduce Eq.
(24) to a first order reaction, and the quantity in parentheses (1 − ry)
replaces (1 − y) to prevent the initial rate from being zero [188]. This
model demonstrated a better fit with experimental data than conventional first order models, yielding a much tighter degradation
curve [184].
The distributed activation energy model (DAEM) has been
successfully applied to both plant [91,117,189–196] and fossil
[95,190,197–202] biomass pyrolysis. The DAEM assumes that several irreversible first order parallel reactions having unique kinetic
parameters take place concurrently [202]. A continuous distribution function, f(Ea ), is used to represent the activation energies
from the various reactions. The distribution function is approximated by a Gaussian distribution that yields a mean value and
standard deviation of Ea . Várhegyi et al. [189] have asserted that the
DAEM is the best method available for mathematically representing
the physical and chemical heterogeneity of substances. Miura and
Maki [203] proposed a revised distributed activation energy model
(DAEM) that provides a method for estimating the frequency factor
and f(Ea ) without requiring a priori assumptions of either kinetic
parameter. This method was used to successfully predict weight
loss curves from the pyrolysis of coal at different heating rates. Cai
and Liu [204] advocated the use of a Weibull distribution model
to fit non-isothermal kinetic data. Under this approach, the kinetic
degradation for each biomass component is represented by one or
more Weibull distribution functions. This procedure allows overlapping processes in the TGA curve to be deconvoluted. The use of
this model requires estimation of the scale and shape parameters
that are unique to the Weibull distribution function.
The cacophonous debate over the relative merits of isothermal,
non-isothermal, and isoconversional methods can sometimes overarch the common thread among all these methods: the use of a
kinetic model that has been preordained by the scientific community. A significant liability can be incurred by simply consulting the
“Table” for the “best model” and expecting that it indeed is the
correct model. Galwey and Brown [13] commented that “the formal models in the accepted set [i.e., the “Table”] are far too simple
to account for all the features of real processes”. Using a “generalized description” of the kinetics involved in solid state reaction
systems offers the freedom and flexibility to choose the most appropriate elements from the set of existing formal models in order to
best characterize the various aspects of the true process [13]. The
Šesták–Berggren (SB) equation [15], as shown below, was the first
such “generalized description”:
d˛
= k˛c (1 − ˛)d (−ln(1 − ˛))e
dt
(25)
where c, d, and e are adjustable exponent factors that can be used to
model the different aspects of solid state reactions. The SB approach
offers two distinct theoretical advantages [205]: (1) no implicit
assumptions are made concerning the mechanism governing the
solid state reaction and (2) no approximations or heavy-handed
mathematical intricacies are involved as the values of c, d, and e
can be calculated directly using a matrix system of linear equations.
Vyazovkin and Lesnikovich [206] acknowledged the importance of
the generalized description afforded by the SB equation, remarking that “. . .a comprehensive comparison of the [SB] approach
with other methods based on model discrimination has demonstrated its preferability”. Other functions (e.g., polynomials, splines,
fractals, etc.) can also be used to provide a generalized phenomenological description of the reaction, though incorporation of too
many adjustable parameters can be rather unwieldy and cause the
parameters to lose their physical connotation and become strictly
procedural factors [13,80].
4. Analysis of kinetic data obtained from various nutshells
The validity of kinetic parameters derived from thermogravimetric data has become a topic fraught with controversy.
The substantial variation in apparent activation energies (i.e.,
11.2–262 kJ mol−1 ) among different nutshells listed in Table 4
is representative of the differences found across the entire
biomass spectrum. Even narrowing the type of biomass to a
specific species does not necessarily correlate to a satisfactory
contraction in the range of Ea values, as demonstrated by the values of Ea for hazelnut shells (e.g., 40.3–144.9 kJ mol−1 ), almond
shells (e.g., 11.2–254.4 kJ mol−1 ), and cashew nut shells (e.g.,
130.2–293.5 kJ mol−1 ) in Table 4. Accordingly, Wilson et al. [207]
aptly note in their recent publication about the thermal characterization of tropical biomass feedstocks that the marked variability
observed in the kinetic parameters of cashew nut shells is simply
a consequence of the geographical origin and “specific nature” of
given biomass materials. Besides the lack of parity in the kinetic
results, few trends are evident from Table 4 regarding the heating rate, the sample mass, or the kinetic model used. However, a
comparative plot of Ea values for nutshells using various first order,
single-step kinetic models, as shown in Fig. 1, does reveal that use
of the DM model generally results in lower apparent activation
energies than those obtained using the corresponding standard
Arrhenius kinetic model (SM). Specifically the DM model yields
values of Ea that are approximately 56% lower than those of the
SM model, with respect to almond [183,208] and hazelnut shells
[183,209,210], and about 31% lower than those given by the first
order Friedman method in the case of peanut shells [52,183,211].
The Ea values (78.9–131.1 kJ mol−1 ) obtained by Bonelli et al. [211]
for hazelnut shells using the DM would appear to contradict the
previous findings, yet the Ea values reported by Demirbaş’s group
[209,210] for hazelnut shells may be uncharacteristically low as a
result of the probable heat and mass transfer limitations incurred
by the use of large sample sizes (250–1000 mg), which has been
observed to correspond with pronounced decreases in apparent
activation energy [212].
A conspicuous feature that is exposed by Table 4 concerns the
lower Ea values obtained under isothermal, or static, conditions
for both almond and coconut shells. Closer examination of the
isothermal experiment [208] that recorded an overall Ea value of
99.7 kJ mol−1 for almond shells reveals that the reaction model used
in the kinetic analysis was a first order, single-step SM. The Ea
value derived from this static experiment is 27% lower than the
average minimum Ea value computed for almond shells whose
non-isothermal, or dynamic, reactions were modeled using an nth
order, parallel reaction SM [213,214], but this difference decreases
to just 6% when the latter group is replaced with almond shells
whose dynamic reactions were modeled using a first order, parallel reaction SM [216], which compares well with the 7% difference
obtained between the static and dynamic almond shell pyrolysis
experiments that were both evaluated using a first order, singlestep SM [183,208]. In the case of coconut shells, there is a 67%
decrease in the Ea values calculated for a non-isothermal study and
those for an isothermal study. Both studies were modeled using
parallel reactions with the salient exception that the dynamic test
employed the CR method, while the static test used the standard
SM method. Although some of the differences within the activation
energies reported for both almond and coconut shells in Table 4
Table 4
Kinetic parameters for thermal decomposition of various nutshell types.
Heating profile, rate (◦ C min−1 )
Temp. range (◦ C)
Sample mass (mg)
Reaction scheme,
order and model
Almond shell
Dynamic, 5–100
RT–850
NAa
Almond shell
Dynamic, 5–100
RT–850
NAa
Almond shell
Dynamic, 5–25
100–550b
5
Almond shell
Dynamic, 2
100–700
3–4
Almond shell
Dynamic, 10
100–700
3–4
Almond shell
Dynamic, 25
100–700
3–4
Almond shell
Dynamic, 2–25
100–700
3–4
Almond shell
Dynamic, 2–25
100–700
3–4
Almond shell
Static, 1.2 × 106
RT–900b
0.7–1
Almond shell
Static, 1.2 × 106
RT–900b
0.7–1
Almond shell
Dynamic, 5–45
100–800
<2b
b
Single step
1st order DM
Single step
1st order SM
2 parallel reactions
nth order SM
2 parallel reactions
nth order SM
2 parallel reactions
nth order SM
2 parallel reactions
nth order SM
2 parallel reactions
nth order SM
3 parallel reactions
nth order SM
Serial dual step
1st order SM
Single step
1st order SM
2 parallel reactions
1st order SM
2 parallel reactions
1st order SM
2 parallel reactions
1st order SM
2 parallel reactions
1st order SM
2 parallel reactions
1st order SM
2 parallel reactions
1st order SM
Single step
1st order DM
2 parallel reactions
1st order CR
Single step
1st order CR
2 parallel reactions
1st order SM
2 parallel reactions
1st order CR
Almond shell
Dynamic, 5–45
100–800
<2
Almond shell
Dynamic, 5–45
100–800
<2b
Almond shell
Dynamic, 5–45
100–800
<2b
100–800
b
Almond shell
Dynamic, 5–45
<2
b
Almond shell
Dynamic, 5–45
100–800
<2
Brazil nut shell
Dynamic, 10–100
RT–900
10
Cashew shell
Dynamic, 5–50c
<15
Cashew shell
Dynamic, 10
RT–110
110–900
RT–1200
Coconut shell
Static, 13
250–750
1000
Coconut shell
Dynamic, 5–50c
RT–110
110–900
<15
a
NA
Ea (kJ mol−1 )
Equipment
Refs.
42.4
Netzch STA 429
[183]
92.9
Netzch STA 429
[183]
123.6–199.6
Perkin-Elmer TGA7
[213]
97.9–254.4
Perkin-Elmer TGA7
[214]
112.3–239.2
Perkin-Elmer TGA7
[214]
118.7–234.7
Perkin-Elmer TGA7
[214]
191.4–196.3
Perkin-Elmer TGA7
[214]
171.4–193.5
Perkin-Elmer TGA7
[214]
11.2–70.1
Pyroprobe 100
[215]
99.7
Pyroprobe 100
[208]
112.0–242.1
Mettler TG50
[216]
107.8–243.3
Mettler TG50
[216]
106.2–225.3
Mettler TG50
[216]
108.3–229.1
Mettler TG50
[216]
104.5–215.3
Mettler TG50
[216]
100.3–203.6
Mettler TG50
[216]
Netzch STA 409
[217]
130.2–174.4
Setaram 92
[110]
293.5
Netzch STA 409
PC Luxx
Tube furnace
[207]
Setaram 92
[110]
47.2–82.0
58.9–114.8
179.6–216.0
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Nutshell type
[218]
11
12
Table 4 (Continued)
Heating profile, rate (◦ C min−1 )
Temp. range (◦ C)
Sample mass (mg)
Reaction scheme,
order and model
Hazelnut shell
Dynamic, 20
RT–800
NAa
Hazelnut shell
Dynamic, 20
RT–800
NAa
Hazelnut shell
Dynamic, 15
RT–900
10
Hazelnut shell
Dynamic, 10
RT–500b
1000
Hazelnut shell
Dynamic, 120
150–625
250
Hazelnut shell
Dynamic, NAa
RT–475b
1000
Single step
1st order DM
Single step
1st order SM
Single step
1st order DM
Single step
1st order SM
Single step
1st order SM
Single step
1st order SM
Single step
1st order Friedman
Single step
1st order DM
Complex multi-step
nth order DAEM
Serial dual step
1st order CR
Serial dual step
1st order FWO
Serial dual step
3/2 order CR
Serial dual step
3/2 order FWO
Serial dual step
1st order SM
b
a
Peanut shell
Dynamic, 5–100
RT–400
NA
Peanut shell
Dynamic, 15
RT–900
10
Peanut shell
Dynamic, 10
RT–550
NAa
Pistachio shell
Dynamic, 5–20
RT–800
20
Pistachio shell
Dynamic, 5–20
RT–800
20
Pistachio shell
Dynamic, 5–20
RT–800
20
Pistachio shell
Dynamic, 5–20
RT–800
20
Walnut shell
Dynamic, 5–40
RT–550
2
a
b
c
NA, data not available.
Estimated or inferred value.
10 ◦ C min−1 to 110 ◦ C, isothermal hold 110 ◦ C for 10 min; non-isothermal to 900 ◦ C, isothermal hold 900 ◦ C for 10 min.
Ea (kJ mol−1 )
Equipment
Refs.
40.3
Netzch STA 429
[183]
92.4
Netzch STA 429
[183]
78.9–131.1
Netzch STA 409
[211]
77.6–123.3
Netzch 429/409
[209]
89.8–128.6
Netzch 429/409
[210]
97.1–144.9
Tube furnace
[209]
84.5
Seiko TG-DTA6200
[52]
44.3–71.5
Netzch STA 409
[211]
150.0–183.3
NAa
[219]
124–149
Shimadzu TGA-50
[8]
248–262
Shimadzu TGA-50
[8]
122–156
Shimadzu TGA-50
[8]
146–181
Shimadzu TGA-50
[8]
120.2–154.4
Perkin-Elmer Pyris 1
[220]
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Nutshell type
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
13
Fig. 1. Comparison of apparent activation energies for nutshells evaluated using various 1st order, single-step kinetic models, including the biomass deactivation model
(DM), the standard kinetic model (SM), and the Friedman model.
may be attributable to dissimilarities in the thermal characteristics of the experiments themselves (i.e., static versus dynamic), it
would appear from the preceding analysis that the nature of the
kinetic approach used to model the reactions also has a substantive
impact on the activation energy and should, therefore, not be discounted. This latter observation is further borne out if the results for
cashew nut shells in Table 4 are evaluated [110,207]. In both cases,
the experiments were conducted under non-isothermal conditions
and modeled using first order CR kinetics. The only major difference
is that one lab group used a parallel reaction scheme [110], whereas
the other scientific team used a single-step format [207]. Accordingly, the minimum Ea value obtained using the single-step method
is 56% lower than the Ea value realized using the parallel reaction
scheme.
The effect of heating rate on Ea for non-isothermal almond
shell pyrolysis [214,216] modeled using two concurrent reactions is
depicted in Fig. 2. The maximum Ea value for the first order reactions
declines 16% when the heating rate is increased from 5 ◦ C min−1 to
40 ◦ C min−1 , while the minimum Ea value for first order reactions
decreases 10% over the same heating rate increase. Interestingly,
the minimum Ea value for nth order reactions rises 21% when the
heating rate is increased from 2 ◦ C min−1 to 25 ◦ C min−1 . A histogram illustrating the effects of particle size on Ea is presented
in Fig. 3. A reduction in the particle size range of pistachio shells
[8] from 0.250–0.600 mm to 0.071–0.125 mm decreases the aver-
Fig. 3. Comparison of apparent activation energy values obtained for pistachio shells
for various particle sizes using two-step sequential CR and FWO models.
age value of Ea by 10% and 20% for the CR and the FWO models,
respectively. This result serves to reaffirm the theory that larger
particles require a higher level of energy to react because they are
more prone to transport limitations. Fig. 3 also depicts that the CR
model consistently returns higher Ea values than the FWO model.
Taken collectively, the data from Figs. 1–3 indicate that there is
a strong correlation between the kinetic model that is chosen to
evaluate Ea and the resulting value. Another probable source of
variance in the presented nutshell data might be a result of changes
in major reaction mechanisms occurring at different temperatures.
The differences in lignocellulosic composition of the various nutshell types, as shown in Table 5, are also a possible factor behind
the inconsistent Ea values. In the case of heterogeneous thermal
reactions, the measured kinetic data are “. . .primarily influenced
by the experimental conditions and not the reaction itself. Therefore, a change in experimental factors makes the interpretation of
the estimated parameters impossible” [221]. In light of this, the
unpredictability of the results provided in Table 4 illustrates the
frustrating inability to use kinetic parameters for anything other
than providing local comparisons of the thermal stability of identical processes.
5. Biomass thermal decomposition mechanisms
Fig. 2. Comparison of apparent activation energies for almond shells at different
heating rates using parallel reaction models of either 1st order or nth order.
In addition to the large assortment of kinetic models available
for biomass pyrolysis, the literature contains a diverse set of possible decomposition pathways. It is generally accepted that biomass
14
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Table 5
Lignocellulosic composition of various nutshell types (dry wt% basis).
Nutshell type
a
Almond shell [214]
Almond shella [222]
Almond shella [223]
Almond shellb [224]
Brazil nut shella [217]
Coconut shell [225]
Coconut shellb [224]
Hazelnut shella [209]
Hazelnut shella [223]
Macadamia nut shellb [224]
Peanut shell [226]
Peanut shell [52]
Pecan shellb [224]
Pistachio shell [227]
Walnut shella [223]
Walnut shellb [224]
a
b
c
Cellulose
Hemicelluloses
Lignin
31.1
37.4
50.7
24.7
48.5c
35.0
24.2
25.9
26.8
26.9
36.6
35.7
5.6
60.6
25.6
21.0
38.0
31.2
28.9
27.0
–
29.0
24.7
28.7
30.4
17.8
19.4
18.7
3.8
NA
22.1
18.8
27.7
27.5
20.4
27.2
59.4
28.0
34.9
44.4
42.9
40.1
33.4
30.2
70.0
20.8
52.3
32.7
Dry ash free basis.
Calculated using the following formulas: % cellulose = 0.9 (% glucose) and % hemicellulose = 0.9 (% galactose + % mannose) + 0.88 (% xylose + % arabinose).
Value reported is for holocellulose which is the term used to indicate the total fraction of plant material left after removal of lignin.
pyrolysis proceeds via the following primary transformations: initially free moisture in the solid evaporates, followed by degradation
of the more unstable polymers, and, finally, with increasing temperature the more refractory components begin to decompose and
volatiles are released from the substrate matrix [228,229]. Solid
char residue that is formed during the primary decomposition
phase, i.e., 200–400 ◦ C, slowly undergoes aromatization in a secondary pyrolysis stage that takes place at temperatures in excess of
400 ◦ C [229]. Apart from the broad scheme presented above, there
is little consensus on the mechanisms behind the pyrolysis process.
Perhaps this is in no small part because there has been “little real
progress towards understanding the chemistry of these solid state
reactions” [230]. Incidentally, it is appropriate to comment here
regarding the flagrant misuse of the term ‘mechanism’ in biomass
pyrolysis literature. Frequently, ‘mechanism’ is used interchangeably with “model” to denote the characterization of the kinetic
rate equation for a given decomposition reaction [230]. It would be
advisable to reserve the use of ‘mechanism’ for its traditional purpose of describing the detailed sequence of physicochemical steps
involved in the process of transforming reactants into products.
Cellulosic decomposition is believed to proceed primarily by
two separate routes that are dependent on the reaction temperature [9,231,232]. The first route predominates at lower
temperatures (<280 ◦ C) and involves reactions that lower the DP
via bond scission, dehydration, free radical formation, creation
of oxygenated moieties (e.g., carbonyls, carboxyls, and peroxides), evolution of CO and CO2 , and ultimately the production of
carbonaceous residues. At higher temperatures (280–500 ◦ C) cellulose degradation follows a different pathway. In this temperature
region, depolymerization reactions associated with the cleavage
of glycosidic bonds prevail and yield a tarry pyrolyzate containing levoglucosan, other anhydrosugars, oligosaccharides, and some
glucose decomposition products [9,233]. A possible third route
employing flash pyrolysis at even higher temperatures (>500 ◦ C)
could involve the direct conversion of cellulose to low molecular
weight gases and volatiles via fission, disproportionation, dehydration, and decarboxylation reactions [9]. The DP, crystallinity, and
crystallite orientation of cellulose fibers in lignocellulosic materials
have been proposed as fundamental factors that regulate thermal
decomposition behavior [234,235].
The seminal predictive mechanism for cellulose pyrolysis kinetics, which was developed during the mid 1960s to mid 1970s by
Broido and his colleagues [231,236–238], involved a competitive,
multi-step reaction sequence, as shown in Scheme 1. In Scheme 1,
a stable form of cellulose is converted to a more reactive cellulose
kv
Cellulose
ki
“Active” Cellulose
kcA
Volatile tars
CA +vols.
kcB
CB +vols.
kcC
CC +vols.
Scheme 1. Broido mechanism, where CA , CB , and CC denote successive fractions of
chars A, B, and C, respectively, that are produced along with accompanying volatiles
formation.
(i.e., labeled “active” cellulose) at elevated temperatures, with rate
constant ki . The “active” cellulose can then degrade thermally by
two parallel routes, forming either volatiles with no char, or proceeding via a sequence of serial reactions to form chars CA , CB , and
CC and accompanying volatiles.
In 1979, Shafizadeh [239] modified the Broido model slightly by
neglecting the secondary reactions in the char and gas product. This
proposed model, now known as the Broido–Shafizadeh (BS) model
(Scheme 2), has become widely cited in biomass pyrolysis and gasification literature [92,134,174,240–246]. Although the validity of
this model has also been frequently assailed [6,92,241,247–249],
there appears to be consensus that the main features of the BS
model are serviceable. Specifically, it is widely acknowledged that
pyrolysis consists of primary initiation and fragmentation reactions
followed by secondary cracking reactions of volatiles [250]. Conversely, the chief criticism regards the inclusion of the zero-order
initiation step at low temperatures (<300 ◦ C) to convert cellulose
from an “inactive” to an “active” stage. Once cellulose is converted
from an “inactive” to an “active” state, pyrolysis is then able to
proceed at higher temperatures. It is likely that this initiation step
was included because several cellulose pyrolysis studies produced
results suggesting the initial stage of pyrolysis did not follow a first
order reaction law. The initiation step is sometimes described as
a depolymerization process because the DP of the starting, native
cellulose typically has a value of around 2500, whereas the DP for
“active” cellulose is generally below 200 [251,252]. According to
the BS model the initiation step requires a high apparent activation energy (242.7 kJ mol−1 ), yet only a 3–6% mass loss is observed
during this period [251,252]. It has been shown that the rate of cel-
Scheme 2. Broido–Shafizadeh mechanism.
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
lulose pyrolysis can be influenced by several structural elements,
including the DP, crystallinity, orientation, and accessibility of the
sample [234,251,253].
The thermal decomposition behavior of plant biomass frequently is assumed to be approximated by the sum of the
contributions of the respective components [2,6,92,119,254–258].
Thermogravimetric (TG) curves for biomass pyrolysis data confirm
that the pyrolysis rate is related to the biomass composition. The
pyrolysis curves of biomass species closely trace the decomposition curves of their dominant lignocellulosic constituents; hence,
the curves of primarily cellulosic biomass share resemble those
of pure cellulose, while degradation curves for biomass with high
lignin contents are similar to those of lignin standards [118]. The
order of decomposition of the biomass components is a function
of their intrinsic reactivity [259]; hence, the typical sequence in
which biomass degrades is given here: extractives, hemicellulose,
cellulose, and finally, ash. Notably, lignin was excluded from the
preceding sequence because lignin begins to decompose beginning
at temperatures that are equivalent to those seen for hemicellulose
degradation and continues to degrade slowly over a very broad
temperature range [260]. Typically, the rate of biomass pyrolysis
is controlled by the rate of cellulose degradation which is subject
to autocatalytic effects [19].
The composition of lignin varies intrinsically according to its
source and the manner in which it is extracted [261]. The complex
hydrogen-bonding network present within lignin [262] serves as
a rigid structural lattice that is resistant to thermal decomposition
(i.e., tends to char more than less stable cellulose or hemicellulose) [263–265]. Although there typically is no discernible peak
assignable to lignin degradation because of its slow decomposition over a broad temperature span [241,257], the wide, oblique
tailing that follows the cellulose peak in DTG diagrams is suggestive of lignin degradation [49,266]. It has been noted that this broad
tailing baseline appears to be a prolongation of the first peak corresponding to hemicellulose degradation [214], suggesting that the
thermal decomposition of lignin may occur simultaneously with
that of hemicellulose. Some researchers have been able to overcome the challenges of delineating the boundaries of this poorly
defined lignin degradation zone, or fourth “lump”, by deconvoluting the TG curve through second-order differentiation techniques.
Using real-time molecular-beam, mass spectrometry (MS) Evans
and Milne [267] were able to monitor the chronological evolution
of primary pyrolysis oils from different biomass substrates under
both slow and rapid heating settings. Primary pyrolysis oils are
those that have not been subjected to temperatures (>600 ◦ C) and
residence times (>1 s) that would promote secondary gas-phase
cracking reactions. Mass spectra revealed that primary pyrolysis
oil composition was not significantly affected by changes in the
heating rate of the wood substrate. The mass spectra from sweet
gum revealed that products containing hardwood lignin monomers
were generated early and in high abundance. The earliest pyrolysis
product to form was coniferyl alcohol at a mass to charge (m/z) peak
of 180 amu. This was followed by a derivative of hemicellulose (3hydroxy-2-penteno-1,5-lactone) at m/z 114 amu. A species derived
from cellulose (CH3 O+ ) evolved next at m/z 43 amu and a ligninderived product (methylguaiacol) at m/z 138 amu eluted last [266].
Lignin peaks were observed to evolve sequentially over the duration of the pyrolysis suggesting that lignin decomposition coincides
not only with the degradation of hemicellulose, but also cellulose.
A separate study [268] has found substantial interactions between
cellulose and lignin during pyrolysis at high temperatures (800 ◦ C).
The presence of cellulose promoted the formation of guaiacol, 4methylguaiacol, and 4-vinylguaiacol but curtailed char production
from secondary cracking reactions. The presence of lignin was associated with increased production of levoglucosan, glycoaldehyde,
and hydroxyacetone from cellulose and reduced char formation.
15
These findings would appear to contradict the earlier postulate
[2,6,92,119,254–258] that suggests the pyrolysis of lignocellulosic
materials consists of three independent decomposition reactions,
each involving a major pseudo-component: cellulose, hemicellulose, and lignin.
The temperature regime giving the most rapid decomposition
rates is aptly designated the active pyrolysis zone, or sometimes,
primary pyrolysis region [269]. The active pyrolysis zone can vary
depending upon the heating rate applied in the thermal analysis and the type of biomass being investigated. Though there is
disagreement on the exact temperature boundaries of the active
pyrolysis zone, it is generally accepted to be in the range of
200–400 ◦ C for lignocellulosic biomass substrates [229]: 95% of the
weight loss from devolatilization occurs in this temperature band.
Lignocellulosic biomass is thought to be stable until 200 ◦ C, with
minor mass losses associated with the removal of moisture and the
hydrolysis of some extractives [54]. TGA data has revealed that the
degradation of the principal lignocellulosic components can be categorized into discrete temperature ranges [191,254]. This indicates
that a key step in the reaction mechanism of the primary biomass
components occurs at some critical transition temperature, Tc , during thermal decomposition.
6. Influence of experimental conditions on biomass
reaction kinetics
Seemingly slight differences in certain process variables along
with heat and mass transport limitations can have significant
impacts on the nature and rates of lignocellulosic decomposition reactions [259]. Experimentally derived kinetic parameters
are affected by reaction conditions, including temperature, heating rate, residence time (i.e., for solids and volatiles), particle
size, pressure, gaseous atmosphere, and the presence of inorganic
mineral content within the biomass material [85,229]. From the
observation that the amount of char produced in cellulose pyrolysis varies proportionally with sample size and reaction pressure,
it was inferred that the residence time of the volatiles in the
biomass matrix during pyrolysis is instrumental in determining
the extent of char formation [239,270]. Extended residence times
for the volatile components can promote secondary reactions (e.g.,
cracking, cross-linking, and repolymerization) that lead to more
char formation. Conversely, the yield of volatiles can be adversely
impacted if the residence time of various autocatalytic volatile
species in the biomass substrate is too brief. Lewellen et al. [270]
demonstrated that char formation can be nearly eliminated at very
short residence times (i.e., 0.2–30 s) given appropriate selection of
the operational temperature and heating rate. Cognizance of the
prominent role played by the residence time of volatiles within the
pyrolyzing biomass matrix foreshadowed the importance of diffusional constraints upon biomass kinetics because the residence
time of volatile vapors in the biomass matrix depends on the nature
of heat and mass transfer through the substrate.
6.1. Heat and mass transport models
Internal and external heat and mass transport limitations often
play a pivotal role in influencing biomass pyrolysis kinetics and
yields. Bamford et al. [271] developed the first kinetic model to
account for heat conduction and generation in pyrolytic reactions.
Kung [272] explored the dependence of weight loss rates on the
thermal conductivity of char. Through the use of dimensionless
groups, Pyle and Zaror [273] were able to validate whether pyrolysis reactions are controlled by kinetic processes or heat transfer (i.e.,
either external or internal). Chan et al. [130] extended the functionality of heat and mass transport models by considering a lumped
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J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
scheme and also by avoiding the necessity of having to assume final
char values. Alves and Figueiredo [274] provided a useful mathematical model for the pyrolysis of wet wood. These earlier models
provided satisfactory assessments of the heat and mass transfer
limitations in pyrolytic reactions and the hallmark common to all
was their pragmatic approach, which lends itself well for possible
implementation in an industrial environment. Since then, many
studies [275–289] have developed sophisticated kinetic models for
biomass pyrolysis that incorporate various elements of transport
phenomena. Generally these increasingly complex kinetics models are used to describe the pyrolysis of a single biomass particle
and are contingent upon several assumptions. Although some of
these transport models have been “validated” using simulated or
empirical data, it is unlikely that such complicated models will be
of practical use in industrial applications [290]. The environment in
actual pyrolytic systems is far from any normative standard used
in such models and the conditions “experienced” by one particle
may be wildly different than those “experienced” by an adjacent
particle, let alone the substrate bulk. Furthermore, in real thermal decomposition processes there are numerous factors that may
influence the rate of reaction that are often omitted from such models (i.e., lattice defects, impurities, melting, sintering, weak bonds,
mechanical strain, catalytic effects from metal reaction vessels,
and ambient or evolved gases that may interact with the reactant
or product) [13,291]. The validity of these models can also suffer from the erroneous assumption that the particles in the bulk
are entirely uniform and thus neglect the influence of particle-size
effects [13]. This is impracticable when dealing with lignocellulosic matter, whose constituent particles can have not only a range
of sizes and shapes but also different chemical compositions and
reactivities. A conclusion drawn by Garn [70] is apropos here, “Limiting the diffusion models to collections with uniform geometry and
size is not productive: it divorces the computation from reality.
Simple or uniform geometries are seldom encountered in practice, and should not be accepted even as approximations without
experimental evidence”.
6.2. Heating rate and particle size effects
The dependence of biomass pyrolysis kinetics on heating rate is
still unresolved, with some evidence supporting the notion that the
use of different heating rates during biomass pyrolysis has minimal
impact on the frequency factor [191], and other data indicating that
biomass conversion reactions are kinetically slower at higher heating rates [134,241,292]. Suuberg et al. [293] hypothesized that mass
transport limitations become increasingly influential as the heating rate increases during rapid cellulose pyrolysis. The evaporative
escape of tars from the substrate matrix via diffusive processes or
convective flow was proposed as the primary weight loss route.
This result has been corroborated by recent research at Philip
Morris that employed EGA-FTIR [233,294]. Milosavljevic and Suuberg [292] observed that a shift in the mechanism of cellulose
pyrolysis occurs at 327 ◦ C when heating rates above 10 ◦ C min−1
are used, such that a relatively low apparent activation energies
(140–155 kJ mol−1 ) are obtained above this temperature. Below
this temperature threshold at lower heating rates, Milosavljevic
et al. reported that the pyrolytic weight loss of cellulose was characterized by a high apparent activation energy (218 kJ mol−1 ).
It has been established that high heating rates significantly
lower char yields when compared with slower heating rates
[108,295]. A study involving rapeseed revealed that the total quantity of substrate that was decomposed decreased when the heating
rate was increased, but the loss was more pronounced when the
heating rate was changed from 25 to 50 ◦ C min−1 (4.8 wt%) than it
was changed from 50 to 100 ◦ C min−1 (1.9 wt%). It was speculated
that the increased heating rate allowed ample time for the comple-
tion of thermal degradation reactions. Grønli et al. [296] observed
that the apparent activation energy of cellulose (242 kJ mol−1 at
5 ◦ C min−1 ) decreased with increased heating rate (222 kJ mol−1 at
40 ◦ C min−1 ). It has been suggested that inter-particle diffusion limitations are accentuated at increased heating rates, thereby leading
to reduced kinetic rates [293]. Studies of cellulose pyrolyzed at
15 ◦ C min−1 and 60 ◦ C min−1 yielded an apparent activation energy
of 140 kJ mol−1 , a value which is similar to the latent heat of
vaporization of fresh cellulose tar (141 kJ mol−1 ) [293]. Pyrolysis of
mustard straw and stalk under a nitrogen atmosphere at different
heating rates gave further evidence that the heating rate can influence reaction kinetics [297]. The reaction order was observed to
be higher at lower heating rates, which may imply the occurrence
of complex, concurrent reactions. Nassar [298] noticed the existence of a transition temperature corresponding to 360 ◦ C, based
on changes measured in the apparent activation energy of sugarcane bagasse pyrolyzed in air. Bagasse in the slow decomposition
regime below this temperature had an Ea value of 139.7 kJ mol−1 ,
while in the exothermic zone above this temperature bagasse had
an Ea value of 76.6 kJ mol−1 .
In general, the solid-state kinetic theory involves the assumption that solid materials are at uniform temperatures during
pyrolytic decomposition. However, the poor thermal conductivity exhibited by lignocellulosic substances impedes heat transfer
within biomass particles and can result in a particle temperature gradient. As heating rates increase, the temperature gradient
within the biomass particle increases, elevating the minimum temperature by which the pyrolysis process may progress [52]. The
kinetic rate of biomass decomposition eventually surpasses the
associated heat transfer rate as the reaction temperature rises.
At some point the biomass degradation kinetics will be restricted
by heat transfer limitations and kinetic analysis then requires a
transport model for the system [299]. The regime in which this
crossover occurs (i.e., between kinetically driven rates and heat
transfer regulated rates) is dependent upon the biomass particle
dimension, making the use of relatively small particles absolutely
imperative for the validity of the aforesaid uniform biomass temperature assumption. It has been reported [299] that the thermal
decomposition of biomass materials with particle thicknesses up
to 0.2 mm may be kinetically evaluated up to about 450–500 ◦ C
without accounting for internal heat transport restrictions. Lower
temperature thresholds, however, apply if the rate of external heat
transfer to the particle surface is sufficiently slow. Coincidentally,
most of the biomass pyrolysis conversion is completed in this
temperature range, which implies that conclusions derived from
previous kinetic studies conducted at or below this temperature
zone are not affected by transport limitation inaccuracies. Detailed
mathematical kinetic models have been developed to describe
larger biomass particles up to 2 cm in dimension [279,300,301].
6.3. Significance of surrounding atmosphere
The ambient gas atmosphere in the reaction system can have
a substantial impact on the behavior of biomass thermal decomposition. It has long been known that the thermal degradation of
wood is greater in the presence of air than in a vacuum [302].
Thermal degradation in air has been shown to lower the active
pyrolysis temperature and boost the combustion of chars at higher
temperatures [4]. Roque-Diaz et al. [303] noticed that the thermal decomposition of sugarcane bagasse was more active in an
oxidative environment than in an inert atmosphere. In this study,
the activation energy of bagasse in air between 170 and 250 ◦ C
was 1429% higher than it was in helium for the corresponding
temperature region (see Tables 8 and 9). The greater production of char in the presence of air supports the observation of
Mamleev et al. [244] that oxygen interacts vigorously with the
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
products derived from the thermal depolymerization of cellulose.
Reduced tar production from biomass pyrolyzed in air can be
explained by returning to the reaction interface of the biomass
substrate. It is conceivable that the cellulose structure, which is
chemically resilient to the penetration of even the most aggressive
chemical agents (e.g., H2 SO4 ), is equally inaccessible for oxygen
diffusion; hence, only the surface of the cellulose is available for
oxidation.
6.4. Catalytic effect of inorganic material
The inorganic mineral matter present in biomass has previously
been found to catalytically promote char-forming secondary tarcracking reactions while concomitantly suppressing additional tar
formation [304]. Müller-Hagedorn et al. [305] found that alkaline
metal chlorides can substantially lower the pyrolysis temperature
of biomass. Anion type was also observed to affect the pyrolysis temperature, as given in order of decreasing influence by the
following list: chlorides > sulfates > bicarbonates. The presence of
even trace levels (e.g., 0.1 wt% NaCl) of mineral matter in biomass
can alter pyrolysis behavior appreciably [92,306]. The pyrolysis
rate, tar yield, and initial degradation temperature are all observed
to increase with decreasing mineral content [306]. For instance,
wood (e.g., 1 wt% [average] ash) undergoes more rapid thermal
degradation than bagasse (e.g., 4 wt% ash) because of the lower
mineral content in wood [307]. Broido [308] discovered that cellulose pyrolysis was affected by the addition of as little as 0.15 wt%
potassium carbonate. Tang [309] detected that the reaction rate
for wood pyrolysis jumped by two orders of magnitude when
2 wt% monobasic ammonium phosphate was added. Exceptions
to this rule include species that have high lignin contents coupled with high potassium levels (e.g., rice husks, ground nutshells,
and coir pith). Lignin is known to be intractable in pyrolytic
processes [309,310] and potassium strongly promotes char gasification [306]. Nassar [298] concluded that the presence of alkaline
salts in biomass (i.e., rice straw and bagasse), whether added
or innate, acts to lower the apparent activation energy of thermal reactions and promote the formation of char. Várhegyi et al.
[311] treated sugarcane bagasse samples with dilute inorganic
salt solutions (i.e., MgCl2 , NaCl, FeSO4 , and ZnCl2 ). Treated and
untreated samples were then thermally decomposed and the evolution of low molecular weight products was evaluated using MS.
The treated samples had higher char yields than the untreated
samples, except in the case of MgCl2 for which there was no significant difference. The increased char production was attributed
to the alteration of reaction pathways by the salts. The MS intensities of all the catalytically treated samples were lower than
those of the untreated samples, suggesting that the presence of
inorganic additives suppresses the secondary cracking of high
molecular weight primary products. It was speculated that inorganic salts cause the fibrous structure of the bagasse to expand,
thereby assisting the release of vapors from the solid matrix. Washing experimental samples with water before has been shown to
eliminate much of the mineral salt content present in the native
biomass [305]. Removal of the catalytically active mineral matter via washing has been linked with a corresponding increase in
the apparent activation energy of biomass. Teng and Wei [312]
compared the kinetic data from pyrolysis experiments that utilized both water-washed rice hulls (i.e., 80 ◦ C water for 2 h) and
unwashed rice hulls. The main lignocellulosic components in the
washed rice hulls displayed higher peak pyrolysis temperatures
and activation energies than the untreated rice hulls. Furthermore, the washed rice hulls also had higher volatile and lower
char yields, which were ascribed to the loss of hydrocarbon moieties capable of promoting cross-linking reactions that foster char
production.
17
7. Variations in kinetic data
7.1. Systematic errors
Systematic errors are presumed responsible for much of the
scatter present in published values of the kinetic triplet. The presence of unrecognized secondary reactions coupled with the highly
disparate chemical composition of biomass materials immediately
draws attention to mechanistic inadequacies, which are usually the
chief source of systematic errors [63]. Lack of a standard procedure
that establishes rigid criteria for evaluating the endpoint of pyrolysis reactions has introduced further discrepancy into the derived
kinetic parameters. Some laboratories take the final substrate mass,
wf , to be the remaining ash content after the entire reaction, while
other laboratories deem the final substrate mass to be the mass
remaining after the rapid pyrolysis zone. Inconsistencies in the
definition of wf have doubtlessly introduced further scatter in the
published kinetic data. There is also a fundamental flaw inherent to
the differential isoconversional methods that have been customarily used to evaluate kinetic data collected by non-isothermal TGA.
Temperature values for given degrees of conversion are necessarily obtained by nonlinear interpolation of the conversion data and
conversion rates must be extracted via numerical differentiation of
the experimental results. Both of these techniques are extremely
sensitive to experimental noise and slight systematic inaccuracies
in this data can be grossly amplified in the corresponding differential conversion rates [173]. One approach to solve the systematic
errors related to noise in the data is to apply generalized functions
that will provide a better fit to the experimental conversion data
than the traditional Arrhenius rate expression.
7.2. Temperature gradients
In thermal kinetic measurements, systematic errors may arise
not only from methodological errors or mechanistic inaccuracies
but also from fundamental instrumental shortcomings. Flynn [17]
commented that “temperature imprecision is probably the greatest
source of error in thermal analysis experiments”. It has been posited
that the reduction in apparent activation energy and frequency factor values that occurs during rapid pyrolysis may be the result of
unfulfilled heat requirements [313]. During the highly endothermic cellulosic devolatilization, the demand for heat by the chemical
reaction and the endothermic pyrolysis reaction overwhelms the
finite heat supply which results in a phenomenon wherein the process temperature remains almost constant throughout the reaction.
Consequently, thermal equilibrium between the biomass substrate
and the heating apparatus may not be realized at all experimental conditions, especially if heat transfer characteristics between
them are poor, in which case there will be a large temperature
gradient between the sample and the thermobalance. In turn, this
thermal lag can cause substantial errors if the researcher simply
assumes that the sample realized the same temperature as the
thermobalance furnace. Indeed, Sharp [27] remarked that “temperature gradients of 5 ◦ C are unavoidable, 10 ◦ C are common, and
20 ◦ C, or even more, not unknown”. Samples that have a variable
temperature distribution will not react uniformly and the kinetic
data generated from such processes “may not only be meaningless
but also can be misleading” [27].
7.3. Temperature lag
Because the size of the sample had long ago been implicated as
a crucial factor in determining the magnitude of the temperature
gradient, it was recommended that sample size be kept as small
as possible [212]. The use of small sample sizes in thermoanalytical studies, however, prevents the placement of thermocouples
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in direct contact with samples, effectively requiring thermocouple
tips to be positioned proximally to the sample in order to estimate
sample temperature [313]. This inability to accurately measure the
sample temperature results in conventional thermocouple thermal
lag, which is the difference between the true sample temperature and an externally measured sample temperature. Thermal lag
was identified by Antal et al. [125] as an insidious agent persistently lurking within thermogravimetric studies [86]. Antal et al.
[314] discovered as much as a 25 ◦ C temperature difference when
thermocouple position in the thermal analyzer was switched from
an upstream to a downstream position relative to the sample.
Variations in the temperature measurements among the different
thermobalances utilized by laboratory researchers were isolated in
a round-robin study as a likely source of the significant variation in
biomass kinetic data [296]. The threat of instrumental error arising
from thermal lag is so acute that the architect of the round-robin
study advised that the resulting paper [296] was the single “most
important paper ever written on thermogravimetry as applied to
biomass” and that it is due to these instrumental limitations that
researchers now “favor ‘model-free’ approaches” [315].
Although it is common for small samples to be employed in
TGA, their use can give rise to the aforementioned thermal lag
effect and its deleterious consequences. Milligram-size samples
are commonly used in thermogravimetry to combat the influence
of transport phenomena, yet experimental results have shown
that even very small samples (e.g., less than 1 mg) still experience diffusional effects [316]. Additionally, the surface to bulk
ratio increases with decreasing sample size so that the importance of surface reactions in small sample sizes is often magnified
at the expense of underlying rate-controlling processes. Thus, the
kinetic data obtained from thermal studies involving small sample sizes often provides an unsatisfactory correlation with large
industrial processes [316]. The needs of both the scientific and
industrial community would be better served if the thermogravimetric characterization of biomass substrates were performed
across a continuum of sample sizes, ranging from a single-crystal
layer to large gram-size samples.
7.4. Kinetic compensation effect
In biomass pyrolysis the apparent activation energy has frequently been observed to increase with the frequency factor. As
early as 1980, Chornet and Roy [317] commented that a kinetic
compensation effect (KCE) exists in the pyrolysis of various biomass
materials such that there is a definite linear correlation between
the variables ln A and Ea . According to the (KCE), any alteration in
experimental conditions that impels Ea to change will also prompt
a complementary compensating response in A. A group of reactions that demonstrates a linear fit of ln A and Ea values is known as
compensation set. It is claimed that reactions within a given compensation set exhibit unique properties, including shared chemical
characteristics and the existence of an isokinetic temperature, Ti ,
at which all reactions advance at the same rate, ki [318]. The linear
relation between ln A and Ea is derived from the Arrhenius equation
and is provided below:
ln A = ln kiso +
Ea
RTiso
(26)
Although several theories have been expounded that impart
either a mathematical or physicochemical explanation for the
appearance of such compensating behavior [319–323], the validity and physical relevance of the KCE are a source of contentious
debate amongst the scientific community [318,324]. Much of the
skepticism regarding the KCE has arisen because a satisfactory
mechanistic interpretation of such compensation behavior has not
yet been established [325,326]. Indeed, it has been asserted that the
presence of a KCE when studying “identical specimens under the
same conditions must be a false effect and either the result of scatter of the experimental data, misapplication of kinetics equations,
or errors in the experimental procedures” [17].
A possible explanation for the KCE arises from the inevitable
scatter of ln A and Ea /R values, which occurs when thermoanalytical
data is collected over narrow bands of rate and temperature [17].
Agrawal [28] concluded that the “compensation behavior for the
pyrolysis of cellulosic materials reported by Chornet and Roy [317]
is primarily due to inaccurate temperature measurement and large
temperature gradients within the sample”. Further experimental
work by Narayan and Antal [313] revealed that values of Ea and
log A monotonically decrease with increasing thermal lag in such a
fashion that the ratio Ea /log A remains nearly unchanged. Besides
the existence of experimental inaccuracies, computational errors
and inappropriate conversion function selection are also commonly
cited as important causal factors behind the KCE [327].
Garn [328] submitted another viable justification for the occurrence of the KCE in solid state reactions explaining that the KCE
is mathematically inevitable because of the reciprocal relationship between A and exp(−Ea /RT) in the Arrhenius expression. Any
change in one of these calculated quantities necessarily demands
a compensatory change in the other. Given that the temperature
range over which most reactions are studied is so narrow that T
may be considered essentially constant and that measured rate constants generally remain within two to three orders of magnitude in
contrast to calculated pre-exponential terms which vary by twenty
or more orders of magnitude, Garn contends that the ensuing linear relationship between ln A and Ea is but a foregone mathematical
conclusion.
Reports abound in thermal analysis literature regarding observations of an experimental KCE, whose existence is often
substantiated solely by correlating ln A with Ea . Unfortunately, the
veracity of an experimental KCE is rarely transparent from plots of
ln A versus Ea because, as Agrawal [329] remarked, “the occurrence
of a linear relation between ln A and Ea does not imply the occurrence of a true compensation effect”. Agrawal declared that the
thermal analysis community would be better served if the validity
of potential compensation effects were confirmed using Arrhenius plots of ln k versus the inverse temperature. Reaction systems
whose Arrhenius plots do not contain a single point of concurrence
are devoid of a KCE. A compensation set that behaves linearly in a
plot of ln A versus Ea but does not display a unique isokinetic point
in the Arrhenius plot may be described as having a pseudo KCE.
Although some researchers [330,331] questioned Agrawal’s procedures to distinguish between a true and a pseudo KCE, Agrawal
[332,333] rejoined that these criticisms were unfounded and the
Arrhenius plot has since become the “critical test” for validating
the KCE [318,324].
8. Sugarcane bagasse case study
8.1. Sugarcane bagasse – background and properties
Agricultural residues and food processing wastes from agroindustry represent an important source of biomass having
widespread availability. Sugarcane is an important agricultural
commodity that is cultivated in over 100 countries with an annual
worldwide production in 2008 of 1.74 billion metric tons [334].
It is grown commercially in a broad swath that extends roughly
from 13.5◦ latitude north of the Tropic of Cancer (i.e., Salobreña,
Spain) [335,336] to 8◦ latitude south of the Tropic of Capricorn
(Salto, Uruguay) [336]. Sugarcane is a perennial C4 grass whose
photosynthetic efficiency is virtually nonpareil in the plant kingdom [337]; only the giant sequoia tree (Sequoia gigantea) is capable
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
of producing more biomass [338]. Despite the current excitement surrounding the efficacy of microalgal carbon dioxide fixation
[339–345], sugarcane still appears superior to microalgae at converting incident solar radiation into carbohydrates (maximum
recorded solar energy capture efficiency of 5.0% for sugarcane
in Hawaii [346] and 5.1% for sugarcane in S. Africa [347] versus
4.9% for green algae in Thailand [348]) [346–351]. Interestingly,
the debate regarding whether microalgae or sugarcane is the better synthesizer of sunlight is not new and dates back at least
60 years, when Ledón and González [352] determined that sugarcane had a higher photosynthesis conversion efficiency (3.4%)
than the microalgae Chlorella pyrenoidsa. It is germane to point out
that microalgae grown outdoors under full sunlight experiences a
substantially lower rate of photosynthesis than microalgae that is
cultivated in a precisely controlled laboratory environment because
of the “light saturation effect”. Productivity of microalgae grown
under full sunlight is at least 75% lower than that of microalgae
grown under low level lighting [353]. Alexander [354] determined that the average annual energy output for a first-generation
energy cane grown in Puerto Rico was 1138 GJ ha−1 year−1 , while
Huber et al. [355] reported a maximum annual energy productivity of 1460 GJ ha−1 year−1 for sugarcane. These values are 23%
and 57% greater than the net annual energy yield for microalgae
(928 GJ ha−1 year−1 ), respectively, as calculated by Christi [356].
The predominant components in sugarcane are water, soluble
solids, of which sucrose is foremost, and lignocellulosic fiber, of
which cellulose is the main constituent. The composition of sugarcane is influenced by numerous environmental determinants
and cultural practices, including climatic factors, weather hazards, topography, soil type, sugarcane variety, planting practices,
drainage, irrigation, diseases, pests, fertilization, and harvesting
methods [336–359]. Contemporary harvesting of sugarcane is performed with mechanical combines that cut whole cane stalk into
sections called billets. The billeted sugarcane is then processed
in a sugar mill where it is macerated and shredded using swinghammer crushers. After this stage, the crushed cane is conveyed to
a train of multiple-roller mills to be pressed. During this step, imbibition water is introduced to the system so as to increase the juice
extraction efficiency at each successive mill. The shredded fibrous
residue that exits the last mill is called bagasse.
Given its provenance from sugarcane, it is natural that bagasse
also exhibits great compositional and morphological heterogene-
19
ity. On average, fresh bagasse consists of 44–56 wt% moisture,
43–52 wt% lignocellulosic fiber, and 2–6 wt% soluble solids, and
1–5 wt% inorganic matter [360–362]. The amount of ash in bagasse
is largely dependent on the amount of dirt brought in from the
fields with the sugarcane [307]. The stem structure of sugarcane
is akin to that of other monocotyledons (grasses) with the exception that the sugarcane stalk is not hollow as are most grass stems
[363]. Sugarcane bagasse contains four major structural components [361,362,364], viz.,
(1) Long, hard-walled cylindrical cells that compose the rind are
designated as the true fiber.
(2) Fibrous vascular bundles, also called sclerenchyma bundles,
comprised of large exterior xylem vessels and separate groupings of small phloem vessels and thick-walled, lignified
sclerenchyma cells, respectively, in the interior.
(3) Soft, thin-walled parenchyma cells from the inner stalk that are
known as pith.
(4) A dense, non-fibrous epidermis commonly referred to as wax.
Dry bagasse typically contains about 50 wt% true fiber, 15 wt%
fibrovascular bundles, 30 wt% pith, and 5 wt% wax [338,361,362].
The proportion of the major components in bagasse depends largely
on the aforementioned environmental factors that influence sugarcane, the variety of cane, its maturity at harvest, harvesting
practices, and the milling efficiency [361]. Table 6 provides a
compositional analysis of bagasse cultivated in various countries.
Multiple listings for a single country indicate that the analyzed
bagasse came from samples collected at different locations within
the country, in different years, or possibly both. An indication of the
compositional variation that arises because of varietal differences
in sugarcane is given in Table 7. The danger of falsely assuming
that bagasse samples collected from a sugar mill pile are uniformly
homogeneous is clearly illustrated in Table 7 by examining the
compositional differences that occur between “average” samples
1 and 2. The chemical composition of bagasse varies between 27
and 50% cellulose, 20 and 35% hemicellulose, 10 and 25% lignins,
and 1 and 6% ash on a dry weight basis. A nominal composition of
40% cellulose, 32% hemicellulose, 20% lignin, 6% extractives, and 2%
ash for dry bagasse is sometimes reported [365,366].
The calorific values of most biomass materials and fossil fuels
are commonly reported in terms of the gross calorific value (GCV)
Table 6
Composition of whole bagasse from various origins (dry wt% basis).
Origin
Cellulose
Hemicellulose
Lignin
Ash
Extractives
Australia [367]
China [368]
Egypt [369]
Guadeloupe [307]
Mauritius [361]
Mexico [361]
Mexico [361]
Mexico [370]
Philippines [364]
South Africa [371]
Hawaii [361]
Hawaii [372]
Louisiana [361]
Louisiana [373]
Louisiana [374]
Louisiana [375]
Puerto Rico [364]
41.3
43.6
41.8
41.7
26.6
34.9
37.6
40.0
34.9
38.5
38.1
36.5d
36.8
36.3
50.4
36.7f
30.1
30.3
33.5
27.5
28.0
29.7
31.8
31.1
32.0
31.8
31.4
23.7
25.0d
29.4
28.2
28.5
24.7f
29.6
10.0
18.1
17.9
21.8
14.3
22.3
19.4
20.0
22.3
22.2
20.5
25.5
21.3
20.2
14.9
24.5
18.1
6.1
2.3
2.0
3.5
2.4
2.3
3.2
2.0
2.3
3.1
2.4
3.7
2.9
2.3
2.0
4.4
3.9
12.3
0.8a
NAb
4.0
NAb
2.8c
2.2c
6.0
NAb
NAb
2.5c
1.8e
4.0c
12.8
4.2
NAb
NAb
a
b
c
d
e
f
Alcohol, toluene extractives; represents wax fraction.
NA, data not available.
Hot water extractives.
Calculated using the following formulas: % cellulose = 0.9 (% glucose) and % hemicellulose = 0.9 (% galactose + % mannose) + 0.88 (% xylose + % arabinose + % uronic acids).
Alcohol extractives.
An amount equivalent to the detected level of arabinose (2.4 wt%) was deducted from the total glucan content (39.1 wt%) and attributed to the hemicellulose complex.
20
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Table 7
Composition of whole bagasse from different sugarcane varieties (dry wt% basis).
Origin
Variety
Cellulose
Hemicellulose
Lignin
Ash
Extractives
Australia [376]
Australia [376]
Australia [376]
Australia [376]
Cuba [361]
Mauritius [361]
South Africa [361]
Florida [361]
Hawaii [361]
Hawaii [361]
Hawaiid [377]
Badilla
1900
Mixed sample 1b
Mixed sample 2b
Mecladas P. Noriega
M 134.32
PO3 2878
CL-41-233
44-3098
37-1933
H65-7052
28.2
30.6
32.5
28.0
46.6
40.6
45.3
30.6
38.7
38.3
36.2e
22.2
23.9
24.3
21.8
25.2
28.4
24.1
26.6
27.1
27.3
22.5e
24.4
24.4
21.7
21.7
20.7
19.6
22.1
18.2
21.6
19.4
24.2
4.1
2.6
2.5
2.5
2.6
6.3
1.6
1.0
4.6
1.3
4.0
3.0a
1.9a
3.2a
4.4a
4.1c
3.1c
4.7c
15.1c
2.6c
2.2c
4.4f
a
b
c
d
e
f
Alcohol, benzene extractives.
Samples were collected from a bagasse pile containing different varieties and thus represent an “average” variety.
Hot water extractives.
NIST reference material 8491.
Calculated using the following formulas: % cellulose = 0.9 (% glucose) and % hemicellulose = 0.9 (% galactose + % mannose) + 0.88 (% xylose + % arabinose + % uronic acids).
Alcohol extractives.
and the net calorific value (NCV). The GCV is the amount of heat
released from a specific quantity of fuel (initially at 20 ◦ C) after it is
combusted and the products cool back to 20 ◦ C. The latent heat of
vaporization of water is included in the GCV. The NCV is equal to the
GCV less the latent heat of the vapor, and it is often used to denote
the true calorific value of moist biomass. Hugot [378] reported the
average GCV of dry bagasse to be 19.25 MJ kg−1 and the average NCV
of dry bagasse to be 17.78 MJ kg−1 . Hugot also reported the average
GCV and average NCV of wet bagasse (i.e., 50 wt% moisture) to be
9.62 MJ kg−1 and 7.64 MJ kg−1 , respectively. Behne [379] analyzed
eleven varieties of dry, ash-free bagasse and found the average GCV
to be 19.52 MJ kg−1 . Nicolai [380] disclosed that the GCV of dry, ashfree bagasse obtained from sugarcane in six countries ranged from
19.13 to 23.97 MJ kg−1 with a mean value of 20.42 MJ kg−1 .
There are nearly 1200 sugar mills in 80 nations that process
almost 1.2 Gt of sugarcane annually [381]. About 280 kg of wet
bagasse (i.e., 50 wt% moisture) is generated per metric ton of milled
sugarcane. Up to 90% of this quantity is combusted in furnaces to
supply the heat and steam requirements for the sugar mill, while
the remainder is simply discarded by burning, composting, stockpiling, or landfilling it [382]. Bagasse is often intentionally burned at
low efficiencies to avoid the preceding disposal issues. The extravagant intake of raw bagasse as a principal fuel source at sugar
mills could be deemed “wasteful”, considering its low NCV [383].
Upgrades to aging sugar mill boiler units and ancillary infrastructure could decrease overall sugar mill energy demand to 50% of
the bagasse generated [384]. Naturally, the thermochemical conversion of sugarcane bagasse into a gaseous or liquid fuel would
enhance the overall energy value of this residue and solve a substantial biomass disposal dilemma.
8.2. Review of sugarcane bagasse pyrolysis studies
As expected, thermoanalytical investigations of sugarcane
bagasse pyrolysis have revealed that there are essentially three
distinct zones of degradation, corresponding with the main lignocellulosic fractions in bagasse (hemicellulose, cellulose, and lignin)
[366,385,386]. Although bagasse pyrolysis has been detected as low
as 150 ◦ C [386], it is generally agreed that active pyrolysis occurs
above 200 ◦ C [135,385,386] and below 450 ◦ C [387]. Bagasse pyrolysis experiences its maximum decomposition rate between 250
and 400 ◦ C [135,307,386–388]. These results are in good agreement with a Cuban study [389] on the kinetics of the thermal
decomposition of sugarcane bagasse, which indicated that volatile
organics were evolved beginning at 205 ◦ C, while the maximum
degradation rate of hemicellulose and cellulose occurred at 305
and 350 ◦ C, respectively. Antal’s group [366] pyrolyzed bagasse
and obtained two peaks for hemicellulose degradation: a small,
poorly defined peak at 240 ◦ C and a larger peak at 310 ◦ C; the
largest peak observed was at 370 ◦ C which was attributed to cellulose decomposition. Nassar [385] obtained a robust, bifurcated
exothermic peak between 280 and 520 ◦ C. An endothermic peak
attributed to the vaporization of volatile products interposed itself
in the exothermic peak at about 420 ◦ C. The first exothermic spike at
350 ◦ C was credited to oxidation of the products, while the second
exothermic spike at 460 ◦ C was reasoned to denote the oxidation of
char. Researchers have observed inflection points in the TG curves
for bagasse at 325–350 ◦ C indicating a transition in the pyrolysis
decomposition mechanism [303,385,390]. At temperatures above
325–350 ◦ C bagasse pyrolysis is primarily a result of lignin and
cellulose devolatilization, while below 325–350 ◦ C lignin and hemicellulose degradation control the rate of bagasse decomposition
[307,385].
Similar to most other biomass types, pyrolysis of sugarcane
bagasse under an oxidative environment influences the reaction
dynamics by lowering the pyrolytic reaction temperature and substantially increasing the rate of bagasse volatilization [307,385]. For
instance, it was found that 5 wt% of bagasse is vaporized at 262 ◦ C in
N2 , 240 ◦ C in dry air, and 228 ◦ C in O2 [307]. A recent investigation of
bagasse pyrolysis by Munir et al. [387] found that peak devolatilization under an oxidative (air) environment occurred between 304
and 312 ◦ C, while rate of weight loss under inert (N2 ) conditions
reached its apex between 346 and 355 ◦ C. The average devolatilization rate for oxidative degradation was calculated to be twice that
for devolatilization in an inert atmosphere. Besides lowering the
peak pyrolysis temperature and active pyrolysis zone, the presence
of oxygen was associated with an increase in overall apparent activation energy. It has also been observed that the elevated levels of
moisture present in raw bagasse can retard the onset of primary
pyrolysis by requiring additional time for drying, thereby affecting the overall pyrolysis rate and product yields [388,391]. The
apparent activation energies of bagasse are in the vicinity of those
reported for hardwoods [385], which is presumably because the
chemical constitutions of sugarcane bagasse (i.e., 32% hemicellulose, 40% cellulose, and 20% lignin) [365] and hardwoods (i.e., 35%
hemicellulose, 39% cellulose, and 19.5% lignin) [9] are similar.
8.3. Analysis of published kinetic data for sugarcane bagasse
pyrolysis
Extensive data on the thermal decomposition of sugarcane
bagasse under different reaction environments is provided in
Tables 8–10. Parenthetical number ranges following certain Ea
values demarcate the temperature regions in which the given
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
activation energy values are valid. Despite the good agreement
among intra-laboratory results, there is a frustrating lack of consistency when results are compared amongst groups. As illustrated
in Table 8, the sheer breadth of Ea values, irrespective of pseudocomponent fractions, obtained from slow bagasse pyrolysis under
an inert atmosphere (N2 , He, or Ar) is simply egregious (i.e.,
14 kJ mol−1 [assumed hemicellulose fraction] to 460.6 kJ mol−1
[assumed cellulose fraction]). A sizeable gulf in Ea values remains
even after the comparison is restricted to just hemicellulose
degradation (e.g., 14 kJ mol−1 [assumed hemicellulose fraction] to
250 kJ mol−1 [hemicellulose fraction]). A comparison of apparent
activation energy values for rapid pyrolysis under nitrogen provides more consistent results, as shown in Table 10, wherein a
16% difference was observed between two independent studies
[383,391] conducted in furnaces at a heating rate of 60,000 ◦ C min−1
and with a residence time of 30 s. The choice of kinetic model surfaced as a parameter that had a crucial impact on the evaluated
apparent activation energy. An average total Ea value was calculated for every pyrolytic process in Table 8 that incorporated a
sequential reaction model (N.B., all of the experiments employing
a sequential model used unwashed bagasse). The mean value of
Ea for the five sets of sequential processes is 72.3 kJ mol−1 , with a
standard deviation of 13.1 kJ mol−1 .
In Table 8, fourteen sets of kinetic data evaluated using a parallel reaction model are presented, of which three utilized washed
bagasse and the remainder used unwashed bagasse. It should be
noted that the four sets of data for the unwashed bagasse that
were obtained by Garcia-Perez et al. [382] at various heating rates
all have identical Ea values resulting from the use of a compensatory shift in the log A values and can, thus, be considered as a
single set of unique Ea values. The apparent activation energies
for each of the resulting eight unique sets of data for unwashed
bagasse pyrolysis were separated into three fractions according
to the respective contributions from each lignocellulosic component. An overall average Ea value was obtained by normalizing the
pseudo-component fractions according to a nominal average lignocellulosic composition of sugarcane bagasse [361] taken on a dry
ash- and extractive-free basis (i.e., 24% lignin, 32% hemicellulose,
and 44% cellulose). The mean value of Ea obtained for the eight
parallel processes was determined to be 159.6 kJ mol−1 , with a standard deviation of 40.5 kJ mol−1 . The 121% average increase in Ea that
occurs when the kinetic model is amended from a consecutive to
a concurrent reaction scheme is a stark reminder that inappropriate model selection can have dire implications on the validity of
the generated kinetic parameters. The four isoconversional techniques (Friedman, CR, FWO, and KAS) used by Yao et al. [245] to
analyze bagasse pyrolyzed under inert conditions (N2 ) had a mean
Ea value of 167.0 kJ mol−1 , which is only 5% higher than the mean
value for the concurrent model but also 131% higher than the mean
value for the consecutive model. Miranda et al. [370] evaluated
kinetic data from bagasse pyrolyzed under a nitrogen atmosphere
using the Friedman differential isoconversional method, along with
serial and parallel methods, and obtained an overall Ea value of
154.4 kJ mol−1 , which was calculated based on their reported composition of bagasse (i.e., 40 wt% cellulose, 32 wt% hemicellulose, and
20 wt% lignin). This value compares reasonably well with the Ea
value of 168.5 kJ mol−1 reported by Yao et al. using the Friedman
isoconversional method.
The impact of an oxidative environment versus that of an inert
atmosphere upon bagasse pyrolysis was investigated by several
research groups [303,387,392,393]. In each case, there was an
increase in apparent activation energy when the inert (N2 ) atmosphere was replaced with an oxidative environment. Excluding
the extraordinary 1429% increase in E given by Roque-Diaz et al.
[303], the average increase in Ea on the basis of five studies by
these four groups was 47% with a standard deviation of 17%. Nassar
21
[298,385,392] conducted his bagasse pyrolysis experiments under
two different types of inert atmosphere (N2 and He). The Ea values recorded for pyrolysis under nitrogen were 87.9 kJ mol−1 and
46.7 kJ mol−1 for the low and high temperature regions, respectively, while the corresponding Ea values obtained for pyrolysis
under helium were 118.1 kJ mol−1 and 69.1 kJ mol−1 , respectively.
These results suggest that the type of inert atmosphere also has
an impact on the apparent activation energy of sugarcane bagasse.
This is consistent with findings in literature that report a shift in the
DTA and DTG peaks toward higher temperatures as the molecular
weight of the inert gas increases [138,398].
The last set of kinetic data given for oxidative pyrolysis in
Table 9 was obtained from non-isothermal thermogravimetric
experiments run at different heating rates using unwashed bagasse
and then estimated as a function of temperature using the V isoconversional technique [135]. The first Ea value (76.1 kJ mol−1 )
reported occurs in the region of 2–5% bagasse conversion (i.e.,
T < 200 ◦ C) and corresponds with the dehydration of the bagasse
sample. The highest Ea value (333.3 kJ mol−1 ) is associated with
the primary pyrolytic combustion zone (i.e., 200 ◦ C ≤ T ≤ 350 ◦ C),
where there is 15–60% bagasse conversion. The final step involves
the secondary combustion of the initial pyrolysis products (i.e.,
400 ◦ C ≤ T ≤ 600 ◦ C); this stage attains 70–95% bagasse conversion
and has an Ea value of 220.1 kJ mol−1 . Interestingly, the aforementioned highest Ea value (333.3 kJ mol−1 ) that was obtained using
the V isoconversional approach in Table 9 is still 27.6% lower
than the maximum Ea value (460.6 kJ mol−1 ) [citation here] provided in Table 8 for milled bagasse pyrolyzed under nitrogen,
yet it is 35% greater than the next highest value (246.5 kJ mol−1
[cellulose fraction]) [97] given in Table 8 for unwashed bagasse
pyrolyzed in nitrogen, 47% greater than the value (226 kJ mol−1
[cellulose fraction]) [241] reported in Table 8 for unwashed bagasse
pyrolyzed in nitrogen that had previously been the highest and
most oft-cited for bagasse [97], and 56% greater than the next highest value (214 kJ mol−1 [likely hemicellulose fraction]) [303,396]
for unwashed bagasse pyrolyzed in an oxidative environment, as
shown in Table 9. It is also observed that inter-laboratory values
of Ea obtained via isoconversional techniques do not correlate well
with each other. The Ea value of 333.3 kJ mol−1 that was obtained
by Ramajo-Escalera et al. [135] (Table 9) for the bagasse conversion range of ˛ = 0.15–0.6 was compared against the global Ea value,
169.5 kJ mol−1 , recorded by Yao et al. [245] (Table 8) over the range
of ˛ = 0.1–0.6, using a similar integral isoconversional approach
(FWO). Although Ramajo-Escalera et al. performed the bagasse
pyrolysis under an oxidative (O2 ) environment and Yao et al. utilized an inert (N2 ) atmosphere, it is dubious that the 97% increase
in the value of Ea in the presence of oxygen can be justified on
the mere basis of converting from anoxic to oxidative conditions,
given that the average increase in Ea by switching to an oxidative
atmosphere is 39%, as mentioned earlier.
An estimation of a theoretical rate constant at 800 K using
the reported kinetic parameters for ultrafast bagasse pyrolysis
(Table 10) with a heated screen assembly at a heating rate of
up to 600,000 ◦ C min−1 (Ea = 59.5 kJ mol−1 , A = 1.10 × 104 s−1 ) [391]
and for a slow pyrolysis (Table 8) at 10 ◦ C min−1 (Ea = 215 kJ mol−1 ,
A = 2.51 × 1015 s−1 ) [125] returns values of 1.4 s−1 and 23 s−1 ,
respectively, which is a factor of almost 16. Although it could
ordinarily be surmised from the above result that rapid pyrolysis processes have much lower rate constants than slow pyrolysis
reactions, the capriciousness of the data indicates otherwise. The
above conjecture is proven to be incorrect when the theoretical
rate constant at 800 K calculated for ultrafast bagasse pyrolysis (Table 10) at heating rates between 60,000 and 600,000 ◦ C
min−1 (Ea = 54.0 kJ mol−1 , A = 3.31 × 103 s−1 ) [391] and that for a
moderately slow pyrolysis (Table 8) conducted at 50 ◦ C min−1
(Ea = 52 kJ mol−1 , A = 5.50 × 102 s−1 ) [386] are compared, providing
ˇ
(◦ C min−1 )
5
5
5d
10
Sample mass
(mg)
18
10
10
–
Particle size
(mm)
Temp. range
(◦ C)
Reaction
model
n
0.841–1.00
RT–800
Sequential
(dual-step)
1
Parallel
(3 reactions)
1
1
3
1
1
3
1
0.25–1.2
0.25–1.2
–
RT–900
RT–900
RT–1500
2
<0.2
RT–500
10/20f
5–7
<0.3
RT–105–950
10/20f
5–7
<0.3
RT–105–950
20d
50
50
2–15i
1–40k
10
10
10
10
8–10
10
0.25–1.0
0.25–1.0
0.037–0.044
0.037–0.044
0.595–0.841
≤0.450
RT–900
RT–900
25–450
Parallel
(3 reactions)
Single-step
Initial rate
(single-step)
Sequential
(triple-step)
Sequential
(triple-step)
Parallel
(3 reactions)
Parallel
(3 reactions)
Single-step
Ea
(kJ mol−1 )
Nitrogen atmosphere
87.9 (225–350)a
46.7 (380–560)b
Tucumán,
Argentina
[97]
Cahn TG-151
Tucumán,
Argentina
[97]
Tanzania
[207]
Hawaii
[393]
C Punjab,
Pakistan
S Punjab,
Pakistan
[387]
Tucumán,
Argentina
Tucumán,
Argentina
[394]
–
0.5
71 (214–424)
–
Shimadzu TGA-50
1
1
3
1
1
3
1
198.0 hemicellulose
246.5 cellulose
57.3 lignin
202.4 hemicellulose
253.5 cellulose
52.3 lignin
49g
15.67
18.00
2.58
15.43
18.09
2.28
2.75
Netzsch STA 409
2.74
Netzsch STA 409
–
–
Single–step
1
25–800
Model-freej
–
168.5 Friedman
169.5 FWO
168.7 CR*
161.1 KAS
250 hemicellulose
125 cellulose
60 lignin
93.2 (195–395)
Differentiall
Parallel/Serial
(3 reactions)
Single-step
1
0.450–1.00
RT–600
Parallel
(3 reactions)
1
20
4
0.450–1.00
RT–600
Parallel
(3 reactions)
1
40
4
0.450–1.00
RT–600
Parallel
(3 reactions)
1
60
4
0.450–1.00
RT–600
Parallel
(3 reactions)
1
18
0.841–1.00
RT–800
Sequential
(dual-step)
1
–
RT–800
Sequential
(multi-step)
0.1
1
0.4
1
Parallel
(3 reactions)
Cahn TG-151
58 (216–445)
25–900
RT–450n
[392]
0.5
4
–
Egypt
63 (220–260)
10
1–2
CST Stona Premco
Model 202 DTA
Model 1050 TGA
1
RT–800
10
4.60a,c
−0.22b,c
Netzsch STA 409
PC Luxx
Mettler-Toledo
TGA/SDTA 851e
Shimadzu TGA-50
0.064–0.076
–
Refs.
2.70c
4.3–7.5
10
Region
15.7
18.0
1.9
15.7
18.0
2.3
2.58
5–50m
5
Apparatus
194.0 hemicellulose
243.3 cellulose
53.6 lignin
200.0 hemicellulose
249.6 cellulose
58.2 lignin
460.6
52h
20–1000
log A
(s−1 )
1
235 hemicellulose
105 cellulose
26 lignin
235 hemicellulose
105 cellulose
26 lignin
235 hemicellulose
105 cellulose
26 lignin
235 hemicellulose
105 cellulose
26 lignin
Helium atmosphere
118.0 (RT–350)
69.0 (350–800)
21.0 (110–170)
14.0 (170–250)
64.0 (250–310)
188.0 (310–380)
Argon atmosphere
o
(1)
215p
5.64
17.71
7.43
−0.78
17.62
7.52
−0.42
17.48
7.58
−0.18
17.50
7.67
−0.08
–
–
15.4
Cahn TG-151
Cahn TG-151
[387]
[394]
Tucuman,
Argentina
Tucuman,
Argentina
[395]
TA Instrument
TGA Q50
Louisiana
[245]
TA Instrument
TG/DTG Q500
Tamaulipas,
Mexico
[370]
DuPont 951 TGA/
Dupont Series 99
Thermal Analyzer
Seiko SSC/5200
TG/DTA 220
Queensland,
Australia
[390]
Clewiston,
Florida
[382]
Seiko SSC/5200
TG/DTA 220
Clewiston,
Florida
[382]
Seiko SSC/5200
TG/DTA 220
Clewiston,
Florida
[382]
Seiko SSC/5200
TG/DTA 220
Clewiston,
Florida
[382]
CST Stona Premco
Model 202 DTA
Model 1050 TGA
DuPont 1090
Thermal Analyzer/
MOM OD-130
Egypt
[298]
Cuba
[303]
[396]
Perkin Elmer TGS-2
Hawaii
[241]
[395]
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
10e
20
22
Table 8
Kinetic parameters for slow pyrolysis of sugarcane bagasse under an inert atmosphere.
[366]
8.4. Suggestions for mitigating inconsistencies in kinetic triplet
data
Hawaii
Irrespective of the multiple causes, the incongruence among the
kinetic parameters clearly reflects the need for a more uniform
approach toward the kinetic analysis of biomass pyrolysis, especially one that minimizes the substantial impact that experimental
conditions can have upon the process chemistry, physical properties of the biomass substrate, and systematic experimental errors.
Várhegyi [80] has recently proffered a list of suggestions to circumvent the evaluative quandary posed by changing experimental
conditions, viz.,
r
q
o
p
n
l
m
k
i
j
h
f
g
e
c
d
Volatilization stage.
Decarbonization stage.
Calculated from available rate constant data.
Bagasse initially washed with 80 ◦ C water for 2 h.
Isothermal conditions (heating rate shown used to reach desired reaction temperatures).
10 ◦ C min−1 ramp from RT to 105 ◦ C followed by 10 min hold; 20 ◦ C min−1 ramp from 105 ◦ C to 950 ◦ C followed by 40 min hold.
Kinetic model uses a conventional Arrhenius rate expression.
Kinetics are modeled according to the DM.
Kinetic studies performed using six different heating rates: 2, 3.5, 5, 7.5, 10, and 15 ◦ C min−1 ; kinetic parameters represent the mean values for all heating rates.
Isoconversional kinetic analysis; all ˛ = 0.1–0.6.
Kinetic studies performed using five different heating rates: 1, 5, 10, 20, and 40 ◦ C min−1 ; kinetic parameters assumed to represent averages for all heating rates.
Process modeled using the Friedman method and two differential (serial and parallel) reaction schemes; roughly identical kinetic parameters obtained for each.
Kinetic studies performed using four different heating rates: 5, 10, 20, and 50 ◦ C min−1 ; kinetic parameters represent the optimum fit for all heating rates.
Estimated from DTG curve plots.
Independent parallel reactions, presumably all first order.
Values reported are for the cellulosic fraction of bagasse.
Bagasse subjected to thermal pretreatment at 260 ◦ C for 2 h.
IEA-NIST standard bagasse sourced from sugarcane hybrid HP65-7052 planted on the Island of Oahu, Hawaii.
a
b
(1)o
Parallel
(3 reactions)
RT–450n
1–2
80
–
RT–450n
1–2
10
–
RT–450n
1–2
20d
–
1–2
20
–
RT–450n
Parallel
(3 reactions)
Parallel
(3 reactions)
Parallel
(3 reactions)
Parallel
(3 reactions)
RT–450n
–
1–2
10q
23
values of 0.99 s−1 and 0.22 s−1 , respectively. Not only are the rate
constants much closer but this comparison would lead to the spurious conclusion that rate constants obtained from fast pyrolysis
are larger than those from slow pyrolysis; exactly contrary to the
earlier hypothesis.
Perkin Elmer TGS-2
[241]
[366]
Hawaii
Perkin Elmer TGS-2
187 hemi (200–260)
111 hemi (210–360)
213 cell (290–400)
148 hemi (200–260)
105 hemi (210–360)
195 cell (290–400)
(1)o
17
7.7
15.3
13
7.5
13.7
Hawaiir
Perkin Elmer TGS-2
233p
(1)o
16.6
[241]
Hawaii
Hawaiir
Perkin Elmer TGS-2
Perkin Elmer TGS-2
226p
(1)o
16.2
210p
(1)o
14.9
[241]
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
(1) The experiments can be evaluated simultaneously by the
method of least squares and using exactly the same kinetic
parameters [49,87,189,214,257].
(2) Additional terms can be included in the kinetic model (i.e., similar to the general description approach used in the SB model)
to describe the systematic experimental errors [51]. Again, the
inclusion of too many terms may lead to strong interdependencies among the kinetic parameters that can obscure their
physical significance and also complicate the numerical solution of the model.
(3) A few parameters can be allowed to “float”, while the remaining parameter(s) is/are held constant [249,312]. This technique
can help assess model validity over a specified range of experimental conditions.
(4) Each experiment can be evaluated individually so that comparisons can be made among the resulting kinetic parameters
[214,248,249,399]. This procedure requires a comprehensive
experimental design that will permit collection of sufficient
data to determine the unknown parameters.
Aiman and Stubington [390] emphasized that the derived
kinetic parameters are highly sensitive to the value of wf that is used
calculate the degree of conversion. Drummond and Drummond
[383] concluded that the use of different heating rates can affect the
kinetic parameters obtained for the pyrolysis of sugarcane bagasse.
These conclusions might now be amended to accurately reflect
the kinetic triplet’s dependence on differences in the chemical and
physical properties of the pyrolyzed bagasse (e.g., moisture, particle
size, sugarcane variety, and lignocellulosic composition), different
operating conditions (e.g., heating rate, temperature range, process
atmosphere, sample size, and isothermal or non-isothermal operational mode), experimental systematic errors (e.g., thermocouple
and reaction thermal lag), the kinetic model selected, the mathematical approximations employed in these models, and the criteria
used to evaluate the endpoint (i.e., wf ) of pyrolytic reactions.
8.5. Evaluation of kinetic compensation effect for sugarcane
bagasse data
A comprehensive survey of the published kinetic data for sugarcane bagasse pyrolysis would be incomplete without ascertaining
the existence of a KCE between the variables ln A and E. The
data used to construct the KCE plot in Fig. 4 was obtained from
Tables 8–10 using only those investigations whose activation energies and frequency factors were evaluated using first order models.
A few important caveats are specified forthwith regarding the
24
Table 9
Kinetic parameters for slow pyrolysis of sugarcane bagasse under an oxidative atmosphere.
ˇ
(◦ C min−1 )
18
5a
–
Particle size
(mm)
Temp. range
(◦ C)
Reaction
model
0.841–1.00
RT–800
Sequential
(dual-step)
0.250–0.420
RT–480b
b
c
–
0.250–0.420
RT–480
10
–
–
RT–800
10/20d
5–7
< 0.3
RT–105–950
10/20d
5–7
< 0.3
RT–105–950
10e
2
<0.200
RT–500
5–20
1–2
5
a
b
c
d
e
f
g
–
25–1000
Sequential
(multi-step)
Sequential
(multi-step)
Sequential
(multi-step)
Sequential
(triple-step)
Sequential
(triple-step)
Initial rate
(single-step)
Model-freeg
n
Ea
(kJ mol−1 )
log A
(s−1 )
Apparatus
Region
Refs.
139.7 (RT–360)
76.6 (360–800)
–
Egypt
[298]
1
53.6 (212–380)
2.90
CST Stona Premco
Model 202 DTA
Model 1050 TGA
Netzch 348472c
Egypt
[397]
1
38.5 (220–430)
1.54
Netzch 348472c
Egypt
[397]
0.84
0.36
0.90
1.00
0.62
0.5
34.0 (20–110)
46.5 (110–170)
214.0 (170–245)
74.8 (245–380)
33.2 (380–600)
75 (226–350)
–
DuPont 1090
Thermal Analyzer/
MOM OD-130
Cuba
[303]
[396]
–
Shimadzu TGA-50
[387]
0.5
116 (247–357)
–
Shimadzu TGA-50
C Punjab,
Pakistan
S Punjab,
Pakistan
2.95f
Mettler-Toledo
TGA/SDTA 851e
Mettler-Toledo
TGA/SDTA 851e
DSC 822e
Hawaii
[393]
Olimpia,
SP, Brazil
[135]
Air atmosphere
1
Oxygen atmosphere
1
78 (220–260)
–
76.1 (25–100)
333.3 (200–350)
220.1 (400–600)
Values reported are for bagasse holocellulose.
Estimated from DTG curve plots.
Values reported are for bagasse hemicellulose.
10 ◦ C min−1 ramp from RT to 105 ◦ C followed by 10 min hold; 20 ◦ C min−1 ramp from 105 ◦ C to 950 ◦ C followed by 40 min hold.
Isothermal conditions (heating rate to desired temperature).
Calculated from available rate constant data.
Isoconversional kinetic analysis; ˛ = 0.02–0.05, 0.15–0.60, 0.70–0.95, in order of increasing temperature ranges.
–
[387]
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
5
Sample mass
(mg)
Queensland, Australia
Queensland, Australia
Queensland, Australia
Queensland, Australia
Queensland, Australia
Pernambuco, Brazil
DC grid furnace
DC grid furnace
DC grid furnace
DC grid furnace
DC grid furnace
Wire mesh reactor
[391]
[391]
[391]
[391]
[391]
[383]
Region
4.04
3.74
4.78
3.52
4.42
6.33
1
1
1
1
1
1
300–1000
300–1000
300–1000
300–1000
300–1000
300–900
Nitrogen atmosphere
Single-step
Single-step
Single-step
Single-step
Single-step
Single-step
0.064–0.422
0.064–0.076
0.064–0.076
0.064–0.076
0.064–0.076
0.10–0.15
n
Temp. range (◦ C)
Particle size (mm)
Reaction model
59.5
60.3
77.9
54.0
66.1
92.6
treatment of the data. A single set of averaged ln A values was
used for the data supplied by Garcia-Perez et al. [382]; the datum
point from Wilson et al. [207] was rejected from the analysis
because of its anomalously high Ea value (460.6 kJ mol−1 ) at a
relatively low ln A value (5.94 s−1 ). The remarkably linear relationship between ln A and E in Fig. 4 (i.e., coefficient of determination
equal to 0.972) would seem to imply the existence of a KCE. However, the plot in Fig. 4 contains several important assumptions
regarding the data used therein. Namely, it is assumed that a
valid kinetic conversion function was chosen and that the data
is free of computational, experimental, and instrumental errors.
If none of these assumptions is violated, then the only possible conclusion that can be drawn from Fig. 4 is that there is an
apparent KCE.
However, an Arrrhenius plot, as shown in Fig. 5, is required to
establish whether the necessary criterion met by the data in Fig. 4
is indeed sufficient to confirm an actual KCE in the pyrolysis of
sugarcane bagasse. The Arrhenius plot in Fig. 5 consists of a subset of data from Fig. 4 because valid temperature ranges were not
available for all of the calculated activation energies. The lack of a
common isokinetic point in the Arrhenius plot indicates that the
linear relation between ln A and Ea in Fig. 4 is spurious and representative of a pseudo KCE. This reviewer does not find the preceding
result entirely unexpected given the tremendously diverse testing
conditions employed in the sugarcane pyrolysis reactions surveyed
in this paper.
Primary tar production kinetic parameters.
a
0–1
10
30
1
1
30
1.2–60 × 104
60,000
60,000
6.0–60 × 104
12,000a
60,000
20–35
20–35
20–35
20–35
20–35
7
9. Recommendations
Res time (s)
Sample mass (mg)
25
Fig. 4. Compensation plot for Arrhenius parameters obtained from sugarcane
bagasse pyrolysis data listed in Tables 7–9.
ˇ (◦ C min−1 )
Table 10
Kinetic parameters for rapid pyrolysis of sugarcane bagasse under an inert atmosphere.
Ea (kJ mol−1 )
log A (s−1 )
Apparatus
Refs.
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
The gross disparities evidenced in the kinetic data from the nutshells and sugarcane bagasse are representative of the ambiguous
kinetic results that have paralyzed the broader biomass pyrolysis
community. In the rush to identify the culprits behind this “shifty”
data, another skulking variable is frequently forgotten: the heterogeneity of the biomass itself. Such inconsistencies demonstrate
the need to reassess the fundamental principles and phenomena
underlying biomass thermal degradation. In particular, the identification and improved control of all possible experimental factors
(seen and unseen) that may regulate the behavior of solid state
reactions is imperative. Moreover, elucidation of reaction mechanisms for solid state thermal processes cannot occur unless thermal
analysis is used in tandem with an ancillary analytical tool that
can evaluate the chemical composition and structure of evolved
products, such as FTIR [12,233,400,401], GC [84,108,402,403], HPLC
26
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
Fig. 5. Arrhenius plot for a subset of data shown in Fig. 4 illustrating the absence of a true compensation effect for sugarcane bagasse pyrolysis. The labels for the individual
lines refer to the references cited in Tables 7–9. Lines from reference sources containing more than one data pair are labeled in order of appearance from Tables 7–9 (e.g.,
[399-2] refers to the second set of data from Ref. [399]). Lines from reference sources containing Arrhenius parameters for multiple reactions or lignocellulosic components
are also listed in order of appearance of the respective reactions or components (e.g., [366-2c] refers to the third component from the second set of data for Ref. [366]).
[12], MS [311,401,404,405], GC–MS [305], and scanning electron
microscopy (SEM) [53,211].
Extravagant mathematical manipulations of kinetic data will
do nothing to further the understanding of the fundamental
physicochemical mechanisms that govern the thermal decomposition of biomass. Elaborate models that integrate reaction kinetics
with transport phenomena are often developed in a theoretical vacuum that fails to properly account for the myriad factors
involved in actual pyrolysis reactions. Application of these intrinsically incomplete models to industrial processes is constrained
by idealized assumptions that are not valid under a bona fide
pyrolytic environment. Furthermore, the use of numerous input
variables that cannot be measured accurately presents an engineering nightmare. Antal and Várhegyi [241] commented that
the best approach to modeling the kinetic behavior of single,
macroscopic biomass particles may involve statistical methods
developed by Krieger-Brockett’s laboratory [406,407] that correlate
kinetic data from judiciously designed experiments using empirical
methods.
It has been suggested that the existing body of heterogeneous
kinetic data is so hopelessly flawed that much of it should simply
be relegated to a circular file [182]. The current authors strenuously oppose the notion that previously collected data should be
dismissed as rubbish. Although it is possible that the analytical
treatment of such data was unsound, the data itself should be preserved. Discarding old empirical data to make room in the “kinetics
cupboard” is not a viable solution, and it disregards the possibility of future advances in heterogeneous kinetics theory that may
afford the opportunity to accurately interpret the kinetic behavior
of re-examined data. Nevertheless, the current authors can appreciate the paucity of reliable kinetic data in the current literature;
it is true that kinetic parameters drawn from the raw data may
indeed be unsalvageable. Still, it would be premature to discard
these “flawed” kinetic triplets before agreement can be achieved
regarding which mathematical methods are truly inappropriate
and, ergo, which kinetic results are also incorrect.
Although integral isoconversional techniques (i.e., CR*, FWO,
KAS, and V) appear to provide reasonably consistent results for the
kinetic triplet in certain controlled situations, it remains unclear
whether these isoconversional methods can be used reliably to
compare kinetic data obtained from identical biomass species
tested under similar, yet not identical, conditions. Regrettably,
there appears to be a perception that the current concepts used
to describe biomass pyrolysis kinetics are satisfactory. Perhaps the
field of solid state kinetics has become somewhat jaded after all the
years of acrimonious and incisive debate regarding the “competition” between isothermal and non-isothermal kinetic techniques.
Nevertheless, there is also a growing undercurrent of exasperation
in the biofuels community regarding the failure of modern kinetic
theory to accurately predict the pyrolytic behavior of biomass.
A literature survey [38] of the apparent activation energies for
wood and cellulose pyrolysis reactions reveals an Ea range of
15–217 kJ mol−1 for wood and 109–251 kJ mol−1 for cellulose; a situation which is described as “very unsatisfactory” and that “needs
to be clarified”. This annoyance is further compounded by the
inability to use the resulting kinetic data for comparative evaluations between different biomass feedstocks under similar process
conditions or identical biomass species under different operating
conditions. Maciejewski and Reller [106] recognized that interest
in the course of solid state thermal decomposition processes is
spurred in part by the desire to obtain “. . .kinetic and mechanistic
data [that] could be of great help in accurate process control. . .” A
subsequent paper by Maciejewski [138], however, concludes that
if “. . .for whatever reason, the quantitative characterization of the
process is required, it is necessary to treat the kinetic parameters as mathematical numbers only, which describe the course of
the reaction under particular conditions, but which do not have
particular significance and are not intrinsic to the investigated
compound”. Obviously, this paradoxical disconnect between the
needs of industry and the exclusivity of the kinetic data obtained
from solid state reactions is problematic. Thermochemical biomass
conversion facilities often operate using variable feedstocks under
different operating conditions. It is naive to assume that such industrial systems can be optimized without the use of generalized
correlations to predict the kinetic behavior of different biomass
materials under various processing environments. Font et al. [408]
recognized the industrial importance of being able to compare
kinetic rate constants and devised a convenient, yet seldom used
J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33
[409], comparison factor to relate rate constants having similar
activation energy and reaction order.
Underlying principles in solid state reaction theory need to be
thoroughly re-evaluated and those that are unsound should be discarded. The venerability and prior adequacy of certain constructs,
including the Arrhenius rate law, should not be used as justification for their continued presence in kinetic expressions. At the same
time, it may be appropriate to revisit generalized kinetic equations
that permit additional process factors to be introduced into the theoretical model. In addition, the use of novel kinetic approaches that
fit data according to semi-empirical and logistic models may help
identify phenomenological regularities and patterns present in the
measurements [173,400,410].
10. Conclusion
The chaos in solid state reaction kinetics has spilled over into the
biomass pyrolysis community and continuation of the status quo
is utterly unacceptable. Ultimately, the thermal analysis community may have to further probe troublesome reaction systems on
an individual basis to develop rate equations specific to each one
[102]. It was the long-suffering work of Bodenstein on the gaseous
reaction between bromine and hydrogen that led to his discovery
of the unique rate equation for hydrogen bromide formation [411].
In conclusion, a few memorable quotations found in Churchill’s
engrossing book, The Interpretation and Use of Rate Data: The Rate
Concept [412] are befitting of the quandaries confronting the field of
solid state reaction kinetics: ‘It is a condition that confronts us – not
a theory’ President Grover Cleveland; ‘No satisfactory justification
has ever been given for connecting in any way the consequences of
mathematical reasoning with the physical world’ Bell; ‘Life is the
art of drawing sufficient conclusions from insufficient premises’
Samuel Butler; ‘Close to the western summit there is the dried and
frozen carcass of a leopard. No one has explained what the leopard was seeking at that altitude’ Ernest Hemingway in The Snows of
Kilimanjaro.
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