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). 1 Deceased. 0165-2370/$ – see front matter. © 2011 Published by Elsevier B.V. doi:10.1016/j.jaap.2011.01.004 2 3 3 3 4 5 5 6 7 7 8 9 10 13 15 15 16 2 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 . 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 , which ravage 550 million ha worldwide annually . 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 . 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 . 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 . 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 . 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 16 17 17 17 17 17 18 18 18 20 20 23 23 25 27 27 and chemical kinetics of heterogeneous processes can be affected by three key elements , 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 . 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 . The only extant review of sugarcane pyrolysis was published more than thirty years ago . 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 , and as early as 1780, Bryan Higgins had observed the effect of heating chalk and limestone at various temperatures . 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” . The ICTAC deﬁnition has been criticized  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” . 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 . 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  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.  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 . Thermogravimetric analysis (TGA) is the most commonly applied thermoanalytical technique in solid-phase thermal degradation studies , 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 . 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 . The development of a system in 1899 by Sir William Roberts-Austen  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) . 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 . 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 . 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 . 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 . The frequency factor provides a measure of the frequency at which all molecular collisions occur regardless of their energy level . The exponential term in Eq. (1) can be thought of as the fraction of collisions having sufﬁcient kinetic energy to induce a reaction . Thus, the rate constant, k(T), being the product of A and the exponential term, exp−Ea /RT , yields the frequency of successful collisions . 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  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 . Garn advised  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” . 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  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  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 . 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 . An undertaking of this magnitude would be incredibly laborious and seems improbable. Moreover, rejection of the Arrhenius expression would, as Šesták  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  and then tabulated by Brown . 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 , 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  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. , 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.) . 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 ) . 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 . 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 . To quote Ninan , “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  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 , like temperature or density, because it is “measured from changes in an extensive property of the system such as mass, enthalpy, and volume” . 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  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 . Furthermore, in most pyrolysis systems the kinetic pathways are simply too complex to yield a meaningful global apparent activation energy . 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 . 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 . 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 . 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  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 . 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  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  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.  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 . 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 . 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  and, more alarmingly, the DTG curves from these models may conceal the true multistage character of pyrolytic reactions under a single peak . 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 . 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 . 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 . Isoconversional models can follow either a differential or an integral approach to the treatment of TGA data. The Friedman method  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  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 . 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  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 , viz., (1) Picard iteration  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  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  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  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 . Flynn  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 , 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 . The supposition of constant Ea and A values is only possible when the Arrhenius parameters are independent of the extent of reaction . 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.  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  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 . In a rebuttal, Budrugeac and Segal  remarked that the modiﬁcation proposed by Vyazovkin  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 . 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”  because differential methods still “suffer from excessive random errors” , especially in the vicinity of the reaction onset and endpoint, where d˛/dt is often small . Nonetheless, Burnham and Dinh  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  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 . “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 . 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 . 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) . 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 , 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  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.  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 , 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 : 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 . This model demonstrated a better ﬁt with experimental data than conventional ﬁrst order models, yielding a much tighter degradation curve . 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 . 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.  have asserted that the DAEM is the best method available for mathematically representing the physical and chemical heterogeneity of substances. Miura and Maki  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  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  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 . The Šesták–Berggren (SB) equation , 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 : (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  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.  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.  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 . 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  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 , 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  92.9 Netzch STA 429  123.6–199.6 Perkin-Elmer TGA7  97.9–254.4 Perkin-Elmer TGA7  112.3–239.2 Perkin-Elmer TGA7  118.7–234.7 Perkin-Elmer TGA7  191.4–196.3 Perkin-Elmer TGA7  171.4–193.5 Perkin-Elmer TGA7  11.2–70.1 Pyroprobe 100  99.7 Pyroprobe 100  112.0–242.1 Mettler TG50  107.8–243.3 Mettler TG50  106.2–225.3 Mettler TG50  108.3–229.1 Mettler TG50  104.5–215.3 Mettler TG50  100.3–203.6 Mettler TG50  Netzch STA 409  130.2–174.4 Setaram 92  293.5 Netzch STA 409 PC Luxx Tube furnace  Setaram 92  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  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  92.4 Netzch STA 429  78.9–131.1 Netzch STA 409  77.6–123.3 Netzch 429/409  89.8–128.6 Netzch 429/409  97.1–144.9 Tube furnace  84.5 Seiko TG-DTA6200  44.3–71.5 Netzch STA 409  150.0–183.3 NAa  124–149 Shimadzu TGA-50  248–262 Shimadzu TGA-50  122–156 Shimadzu TGA-50  146–181 Shimadzu TGA-50  120.2–154.4 Perkin-Elmer Pyris 1  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 , whereas the other scientiﬁc team used a single-step format . 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  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” . 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  Almond shella  Almond shella  Almond shellb  Brazil nut shella  Coconut shell  Coconut shellb  Hazelnut shella  Hazelnut shella  Macadamia nut shellb  Peanut shell  Peanut shell  Pecan shellb  Pistachio shell  Walnut shella  Walnut shellb  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 . 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” . 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 . 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 . 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  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 . 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 . The order of decomposition of the biomass components is a function of their intrinsic reactivity ; 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 . Typically, the rate of biomass pyrolysis is controlled by the rate of cellulose degradation which is subject to autocatalytic effects . The composition of lignin varies intrinsically according to its source and the manner in which it is extracted . The complex hydrogen-bonding network present within lignin  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 , 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  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 . 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  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 . 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 : 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 . 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 . 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.  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.  developed the ﬁrst kinetic model to account for heat conduction and generation in pyrolytic reactions. Kung  explored the dependence of weight loss rates on the thermal conductivity of char. Through the use of dimensionless groups, Pyle and Zaror  were able to validate whether pyrolysis reactions are controlled by kinetic processes or heat transfer (i.e., either external or internal). Chan et al.  extended the functionality of heat and mass transport models by considering a lumped 16 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  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 . 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 . 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  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 , and other data indicating that biomass conversion reactions are kinetically slower at higher heating rates [134,241,292]. Suuberg et al.  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  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.  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 . 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 ) . 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 . The reaction order was observed to be higher at lower heating rates, which may imply the occurrence of complex, concurrent reactions. Nassar  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 . 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 . 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  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 . Thermal degradation in air has been shown to lower the active pyrolysis temperature and boost the combustion of chars at higher temperatures . Roque-Diaz et al.  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.  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 . Müller-Hagedorn et al.  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 . 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 . Broido  discovered that cellulose pyrolysis was affected by the addition of as little as 0.15 wt% potassium carbonate. Tang  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 . Nassar  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.  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 . 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  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 . 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 . 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  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 . 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  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” . 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 . The use of small sample sizes in thermoanalytical studies, however, prevents the placement of thermocouples 18 J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33 in direct contact with samples, effectively requiring thermocouple tips to be positioned proximally to the sample in order to estimate sample temperature . 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.  as an insidious agent persistently lurking within thermogravimetric studies . Antal et al.  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 . 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  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” . 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 . 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 . 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  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 . 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” . 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 . Agrawal  concluded that the “compensation behavior for the pyrolysis of cellulosic materials reported by Chornet and Roy  is primarily due to inaccurate temperature measurement and large temperature gradients within the sample”. Further experimental work by Narayan and Antal  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 . Garn  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  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 . 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) . Sugarcane is a perennial C4 grass whose photosynthetic efﬁciency is virtually nonpareil in the plant kingdom ; 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 . 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  and 5.1% for sugarcane in S. Africa  versus 4.9% for green algae in Thailand ) [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  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 . Alexander  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.  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 . 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 . 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 . 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 . 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  China  Egypt  Guadeloupe  Mauritius  Mexico  Mexico  Mexico  Philippines  South Africa  Hawaii  Hawaii  Louisiana  Louisiana  Louisiana  Louisiana  Puerto Rico  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  Australia  Australia  Australia  Cuba  Mauritius  South Africa  Florida  Hawaii  Hawaii  Hawaiid  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  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  analyzed eleven varieties of dry, ash-free bagasse and found the average GCV to be 19.52 MJ kg−1 . Nicolai  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 . 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 . 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 . Upgrades to aging sugar mill boiler units and ancillary infrastructure could decrease overall sugar mill energy demand to 50% of the bagasse generated . 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 , it is generally agreed that active pyrolysis occurs above 200 ◦ C [135,385,386] and below 450 ◦ C . 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  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  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  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 . A recent investigation of bagasse pyrolysis by Munir et al.  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 , which is presumably because the chemical constitutions of sugarcane bagasse (i.e., 32% hemicellulose, 40% cellulose, and 20% lignin)  and hardwoods (i.e., 35% hemicellulose, 39% cellulose, and 19.5% lignin)  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.  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  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.  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.  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. , 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 . 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])  given in Table 8 for unwashed bagasse pyrolyzed in nitrogen, 47% greater than the value (226 kJ mol−1 [cellulose fraction])  reported in Table 8 for unwashed bagasse pyrolyzed in nitrogen that had previously been the highest and most oft-cited for bagasse , 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.  (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.  (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 )  and for a slow pyrolysis (Table 8) at 10 ◦ C min−1 (Ea = 215 kJ mol−1 , A = 2.51 × 1015 s−1 )  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 )  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 )  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  Cahn TG-151 Tucumán, Argentina  Tanzania  Hawaii  C Punjab, Pakistan S Punjab, Pakistan  Tucumán, Argentina Tucumán, Argentina  – 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  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   Tucuman, Argentina Tucuman, Argentina  TA Instrument TGA Q50 Louisiana  TA Instrument TG/DTG Q500 Tamaulipas, Mexico  DuPont 951 TGA/ Dupont Series 99 Thermal Analyzer Seiko SSC/5200 TG/DTA 220 Queensland, Australia  Clewiston, Florida  Seiko SSC/5200 TG/DTA 220 Clewiston, Florida  Seiko SSC/5200 TG/DTA 220 Clewiston, Florida  Seiko SSC/5200 TG/DTA 220 Clewiston, Florida  CST Stona Premco Model 202 DTA Model 1050 TGA DuPont 1090 Thermal Analyzer/ MOM OD-130 Egypt  Cuba   Perkin Elmer TGS-2 Hawaii   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.  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  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   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  Hawaii Hawaiir Perkin Elmer TGS-2 Perkin Elmer TGS-2 226p (1)o 16.2 210p (1)o 14.9  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 . 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  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  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  1 53.6 (212–380) 2.90 CST Stona Premco Model 202 DTA Model 1050 TGA Netzch 348472c Egypt  1 38.5 (220–430) 1.54 Netzch 348472c Egypt  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   – Shimadzu TGA-50  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  Olimpia, SP, Brazil  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. –  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       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. ; the datum point from Wilson et al.  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. ). 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. ). , MS [311,401,404,405], GC–MS , 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  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 . 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  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  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 , 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.  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 , 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 . 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 . 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