Biomass Pyrolysis Kinetics- A Comparative Critical Review With Relevant Agricultural Residue Case Studies

 Journal of Analytical and Applied Pyrolysis Pyrolysis 91 (2011) (2011) 1–33 Contents lists available at ScienceDirect at  ScienceDirect

 Journal of Analytical and Applied Pyrolysis  j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / j a a p

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  Audubon Sugar Institute, Louisiana State University AgCenter, 3845 Hwy 75, St. Gabriel, LA 70776, USA b Laboratory for Ecological Chemistry, Comparative Biomedical Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA 70803, USA

a rt ic le

i nf 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 Biomas Biomasss pyroly pyrolysisis sisis a fundam fundament entalthermo althermoche chemic mical al conver conversio sion n proces processs that that is of both both indust industria riall andecological logical importance.From importance.From designing designing and operating operating industrialbiomass industrialbiomass conversion conversion systems systems to modeling 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, sample, and systematic systematic errors.An analysis analysis of thermal thermal decompositi decomposition on dataobtained from two agricultura agriculturall residues, nutshells and sugarcane bagasse, reveals the inherent difficulty and risks involved in modeling heterogeneous reaction systems. © 2011 Published by Elsevier B.V.

Contents

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4. 5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Fundamentals of thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1. Concise history of thermal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2. Experimental kinetic analysis techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3. Arrheni heniu us rate expression sion and the sig significance of the kinetic parameters. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 4 Biomass pyrolysis kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1. Kinetic expressions for biomass thermal decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2. Biomass pyrolysis kinetic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3. Multiple-step models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.4. Isoconversional techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.5. 3.5. Com Compara parati tive ve eva evalua luation tion of inte integgral ral and diff differ eren enti tial al isoco soconv nver ersi sion onaal tech techni niqu ques.. es.. .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. 8 3.6. Other kinetic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Analysis of kinetic data obtained from various nutshells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Biomass thermal decomposition mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Influence of experimental conditions on biomass reaction kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6.1. Heat and mass transport models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6.2. Heating rate and particle size effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

∗ 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 [email protected] @ars.usda.gov (J.E.  (J.E. White). 1 Deceased.

0165-2370/$ 0165-2370/$ – see front matter. © 2011 Published by Elsevier B.V. doi:10.1016/j.jaap.2011.01.004 doi:10.1016/j.jaap.2011.01.004

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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. Anal nalysis of published kinetic data for sugarcane bagasse pyroly olysis sis .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 8.4. Suggestions for mitigating inconsi nsistencies in kinetic triplet data .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 8.5. Evaluation of kinetic compensat sation effect for sugarcane bagasse sse data. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 9. Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Co Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introducti Introduction on

Increa Increased sed volati volatilit lityy in traditi traditiona onall fossil fossil fuel fuel market marketss has revive revived d interestintheproductionofalternativefuelsfrombiomass.Renewable energy derived from biomass reduces reliance on fossil fuels and it does not add new carbon dioxide to the atmosphere [1] [1].. Pyrolysis Pyrolysis is a fundamentalthermochemi fundamentalthermochemical calconver conversion sionproce process ss that can be used to transform biomass directly into gaseous and liquid fuels.Pyrol fuels.Pyrolysisis ysisis also also animportan animportantt stepin combus combustio tion n andgasificaandgasificationprocesses.Inthisregard,athoroughunderstandingofpyrolysis kineti kinetics cs is vital vital to the assess assessmen mentt of items items includ including ing the feasib feasibili ility, ty, design, and scaling of industrial biomass conversion applications [2,3].. An awaren [2,3] awareness ess of pyroly pyrolysis sis kineti kinetics cs can also also be useful useful in modmodeling the propagation of wildfires [4] wildfires  [4],, which ravage 550 million ha worldwide annually [5] annually  [5].. Vegetative biomass, also known as phytomass, is comprised primarily of cellulose, hemicellulose, and lignin along with lesser amount amountss of extract extractive ivess (e.g., (e.g., terpen terpenes, es, tannin tannins, s, fatty fatty acids, acids, oils, oils, and resins), moisture, and mineral matter [6] [6]..  Cellulose is the most abundant abundant organic compound compound in nature, comprising comprising up to 50 wt% of dry biomass  [7,8]  [7,8]..   It is a linear polysaccharide formed from repetitive -(1,4)-glycosidic linkage of  d  d-glucopyranose units. Cellulose lulose from different different biomass biomass types is chemically chemically indistinguis indistinguishable hable except for its degree of polymerization (DP), which can range from 500 to 10,000 depending depending on the type of biomass [9] biomass [9].. Strong hydrogen bonding between the straight chains imparts a crystalline structure to the cellulose, making it highly impervious to dissolution and hydrolysis using common chemical reagents [9,10]..  Unlike cellulose, the composition of hemicelluloses and [9,10] lignin is heterogeneous and can vary greatly even within a given biomass species. Hemicelluloses have an amorphous structure and displa displayy branch branching ing in their their polymer polymer chains chains.. Several Several sugar sugar monomers are contained in hemicellulose, including xylose, mannose, galactose, and arabinose. Lignin accounts for almost 30% of terrestrial organic carbon and provides the rigidity and structural framework for plants  [11]  [11]..  The lignin biopolymer consists of a complex network of cross-linked aromatic molecules, which serves to inhibit the absorption of water through cell walls. The structure and chemical composition of lignin are determined by the type and age of the plant from which the lignin is isolated [12]..  Studies addressing the transformation kinetics of biomass [12] must must accoun accountt for the intrin intrinsic sicall allyy hetero heterogene geneousnatureof ousnatureof the subsubstrate. 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. Pyroly Pyrolysis sis of solid solid state state materi materials als,, such such as biomas biomass, s, can be classi classi-fied as a heterogeneous chemical reaction. The reaction dynamics

16 17 17 17 17 17 18 18 18 20 20 23 23 25 27 27 27

and chemical kinetics of heterogeneous processes can be affected by three key elements [13] elements [13],, i.e., i.e., the breakage and redistribution of  chemical chemical bonds, changing reaction geometry, and the interfacial 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] spatially  [13–16].. Heterogeneous reactions usually involve a superposition of several elementary processes such as nucleation, nucleation, adsorption adsorption,, desorption, desorption, interfacial interfacialreacti reaction, on, and surface/bulk diffusion, each of which may become rate-limiting depending depending on the experimental experimental conditions. conditions. The initiation initiation step in solid state decomposition reactions frequently involves a “random walk” walk” of defect defectss andvacancie andvacanciess within within thecrystal thecrystal latticewhichgives latticewhichgives rise to nucleation growth  [17]  [17]..  Equally significant is the concept of a “reaction interface”, which is defined as the boundary surface face between between the reacta reactant nt and the produc product. t. This This repres representa entatio tion n has been been used used extens extensive ively ly to model model the kineti kinetics cs of solid solid state state reacti reactions ons [18].. [18] The only extant review of sugarcane sugarcane pyrolysis pyrolysis was published more than thirty years ago [19] ago  [19]..  Solid state kinetic theory was in a state of considerable disarray during this era and decomposition mechanisms for cellulose pyrolysis were in their formative stages. Understanding of the reaction dynamics involved in pyrolytic processes has evolved substantially since then, and the corresponding kinetic schemes have been refined to encompass the entire lignocellulosic substrate. In light of this, the original intent of this paper was to provide a succinct overview of modern biomass pyrolysis kinetics supported by an analytical survey of rate data obtained from a particular biomass species (i.e., sugarcane bagasse). However, ever, consid consideri ering ng the uncerta uncertainty inty and flux that that contin continue ue to envelo envelop p the field of thermal analysis, it was decided that an experimental case case study study isolat isolated ed from from a contex contextua tuall discour discourse se on the curren currentt state state of affairs in heterogeneous kinetics might only add to the existing turmoi turmoil.l. Theref Therefore ore,, the objecti objective ve of this this critica criticall review review is to not only only exposethenatureandoriginoftherampantinconsistenciesinpublished biomass kinetic data but also emphasize the urgent need to dispense with the “ . . .hundreds hundreds of cute and clever mathematical mathematical manipu manipulat lation ionss [that] [that] were were perfor performed med on variat variation ionss of three three (highl (highlyy stylized) stylized) equations” equations” [i.e., the degree of conversion conversion rate equation equation (Eq. (2) (Eq.  (2)), ), the  the Arrhenius expression (Eq.  (1)  (1)), ), and  and the temperature integral (Eq. (11) (Eq. (11))] )],, and instead focus on the reexamination of fundamenta damentall solid solid state state reacti reaction on kineti kineticc theory theory as it applie appliess to biomas biomasss pyrolysis.Afteraprécisofexperimentalkinetictechniquesandfundamental 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.

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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. Anal nalysis of published kinetic data for sugarcane bagasse pyroly olysis sis .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 8.4. Suggestions for mitigating inconsi nsistencies in kinetic triplet data .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 8.5. Evaluation of kinetic compensat sation effect for sugarcane bagasse sse data. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 9. Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. Co Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introducti Introduction on

Increa Increased sed volati volatilit lityy in traditi traditiona onall fossil fossil fuel fuel market marketss has revive revived d interestintheproductionofalternativefuelsfrombiomass.Renewable energy derived from biomass reduces reliance on fossil fuels and it does not add new carbon dioxide to the atmosphere [1] [1].. Pyrolysis Pyrolysis is a fundamentalthermochemi fundamentalthermochemical calconver conversion sionproce process ss that can be used to transform biomass directly into gaseous and liquid fuels.Pyrol fuels.Pyrolysisis ysisis also also animportan animportantt stepin combus combustio tion n andgasificaandgasificationprocesses.Inthisregard,athoroughunderstandingofpyrolysis kineti kinetics cs is vital vital to the assess assessmen mentt of items items includ including ing the feasib feasibili ility, ty, design, and scaling of industrial biomass conversion applications [2,3].. An awaren [2,3] awareness ess of pyroly pyrolysis sis kineti kinetics cs can also also be useful useful in modmodeling the propagation of wildfires [4] wildfires  [4],, which ravage 550 million ha worldwide annually [5] annually  [5].. Vegetative biomass, also known as phytomass, is comprised primarily of cellulose, hemicellulose, and lignin along with lesser amount amountss of extract extractive ivess (e.g., (e.g., terpen terpenes, es, tannin tannins, s, fatty fatty acids, acids, oils, oils, and resins), moisture, and mineral matter [6] [6]..  Cellulose is the most abundant abundant organic compound compound in nature, comprising comprising up to 50 wt% of dry biomass  [7,8]  [7,8]..   It is a linear polysaccharide formed from repetitive -(1,4)-glycosidic linkage of  d  d-glucopyranose units. Cellulose lulose from different different biomass biomass types is chemically chemically indistinguis indistinguishable hable except for its degree of polymerization (DP), which can range from 500 to 10,000 depending depending on the type of biomass [9] biomass [9].. Strong hydrogen bonding between the straight chains imparts a crystalline structure to the cellulose, making it highly impervious to dissolution and hydrolysis using common chemical reagents [9,10]..  Unlike cellulose, the composition of hemicelluloses and [9,10] lignin is heterogeneous and can vary greatly even within a given biomass species. Hemicelluloses have an amorphous structure and displa displayy branch branching ing in their their polymer polymer chains chains.. Several Several sugar sugar monomers are contained in hemicellulose, including xylose, mannose, galactose, and arabinose. Lignin accounts for almost 30% of terrestrial organic carbon and provides the rigidity and structural framework for plants  [11]  [11]..  The lignin biopolymer consists of a complex network of cross-linked aromatic molecules, which serves to inhibit the absorption of water through cell walls. The structure and chemical composition of lignin are determined by the type and age of the plant from which the lignin is isolated [12]..  Studies addressing the transformation kinetics of biomass [12] must must accoun accountt for the intrin intrinsic sicall allyy hetero heterogene geneousnatureof ousnatureof the subsubstrate. 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. Pyroly Pyrolysis sis of solid solid state state materi materials als,, such such as biomas biomass, s, can be classi classi-fied as a heterogeneous chemical reaction. The reaction dynamics

16 17 17 17 17 17 18 18 18 20 20 23 23 25 27 27 27

and chemical kinetics of heterogeneous processes can be affected by three key elements [13] elements [13],, i.e., i.e., the breakage and redistribution of  chemical chemical bonds, changing reaction geometry, and the interfacial 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] spatially  [13–16].. Heterogeneous reactions usually involve a superposition of several elementary processes such as nucleation, nucleation, adsorption adsorption,, desorption, desorption, interfacial interfacialreacti reaction, on, and surface/bulk diffusion, each of which may become rate-limiting depending depending on the experimental experimental conditions. conditions. The initiation initiation step in solid state decomposition reactions frequently involves a “random walk” walk” of defect defectss andvacancie andvacanciess within within thecrystal thecrystal latticewhichgives latticewhichgives rise to nucleation growth  [17]  [17]..  Equally significant is the concept of a “reaction interface”, which is defined as the boundary surface face between between the reacta reactant nt and the produc product. t. This This repres representa entatio tion n has been been used used extens extensive ively ly to model model the kineti kinetics cs of solid solid state state reacti reactions ons [18].. [18] The only extant review of sugarcane sugarcane pyrolysis pyrolysis was published more than thirty years ago [19] ago  [19]..  Solid state kinetic theory was in a state of considerable disarray during this era and decomposition mechanisms for cellulose pyrolysis were in their formative stages. Understanding of the reaction dynamics involved in pyrolytic processes has evolved substantially since then, and the corresponding kinetic schemes have been refined to encompass the entire lignocellulosic substrate. In light of this, the original intent of this paper was to provide a succinct overview of modern biomass pyrolysis kinetics supported by an analytical survey of rate data obtained from a particular biomass species (i.e., sugarcane bagasse). However, ever, consid consideri ering ng the uncerta uncertainty inty and flux that that contin continue ue to envelo envelop p the field of thermal analysis, it was decided that an experimental case case study study isolat isolated ed from from a contex contextua tuall discour discourse se on the curren currentt state state of affairs in heterogeneous kinetics might only add to the existing turmoi turmoil.l. Theref Therefore ore,, the objecti objective ve of this this critica criticall review review is to not only only exposethenatureandoriginoftherampantinconsistenciesinpublished biomass kinetic data but also emphasize the urgent need to dispense with the “ . . .hundreds hundreds of cute and clever mathematical mathematical manipu manipulat lation ionss [that] [that] were were perfor performed med on variat variation ionss of three three (highl (highlyy stylized) stylized) equations” equations” [i.e., the degree of conversion conversion rate equation equation (Eq. (2) (Eq.  (2)), ), the  the Arrhenius expression (Eq.  (1)  (1)), ), and  and the temperature integral (Eq. (11) (Eq. (11))] )],, and instead focus on the reexamination of fundamenta damentall solid solid state state reacti reaction on kineti kineticc theory theory as it applie appliess to biomas biomasss pyrolysis.Afteraprécisofexperimentalkinetictechniquesandfundamental 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

frequency factor (s−1 ) correlation parameters in the linear compensation effect relation constant of integration C  apparent activation energy (kJ mol −1 ) E a  f (˛) reac reacti tion on model model (fun (funct ctio ion n exp expre ress ssin ingg the the depe depenndence of the reaction rate on the conversion) integ integra rate ted d reac reacti tion on model model  g (˛) equivalent function function for p( x) I (E a ,T ˛ ) equivalent k reaction rate constant (s−1 ) k(T ) tempera temperatur ture-d e-depe ependen ndentt rate rate consta constant nt (s−1 ) reaction order n temp temper erat atur uree inte integr gral al  p( x) r  reaction initiation parameter R universal gas constant (8.3144 × 10−3 kJmol−1 K−1 ) time (s) t  absolute temperature (K) T  V i   cumulativemassofreleasedvolatilescorresponding to fraction  i through time  t  effe effecti ctive ve vola volati tile le cont conten entt for for frac fractio tion n  i V i * volatile mass at time  t  v w substrate mass at time  t   x equivalent to  E a /RT  unreacted fraction of substrate  y activity of solid  z   A a, b

Greek letters ˛ extent of reaction (degree of conversion) ˇ heating rate (◦ C s−1 )   minimization function   deactivation rate constant Superscripts adjustable reaction exponents in the SB equation c , d, e reaction order n q number of experiments s adjustable nucleation parameter used in the modi-

fied Prout–Tompkins model Subscripts

0 a  f 

   

iso i  j k m

 

initial apparent final isokinetic volatile fraction ordinal number of experiment ordinal number of experiment maximum

2. Fundamentals of thermal thermal analysis 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 contro controver versy. sy. Althou Although gh Le Chatel Chatelier ier is freque frequently ntly credit credited ed with with havhaving initiated thermal analysis in 1887 [20–23] 1887  [20–23],, Jakob J akob Rudberg had alreadyemployedacrudeformofthermalanalysisin1829toobtain rate data for various various metals and their alloys [22] alloys  [22],,  and as early as 1780, Bryan Higgins had observed the effect of heating chalk and limestone at various temperatures [24] temperatures  [24].. Likewise, dissent has pre-

3

vented vented the adopti adoption on of a mutuall mutuallyy accept acceptabl ablee definiti definition on forthermal forthermal analysis methods. Thermal analysis has been formally defined by theInternationalConfederationforThermalAnalysisandCalorimetry (ICTAC) as “a group of techniques in which a property of the sample is monitored against time or temperature while the temperatu perature re of the sample sample,, in a specifi specified ed atmosp atmospher here, e, is progra programme mmed” d” [25]..  The ICTAC definition has been criticized [26] [25] criticized  [26] f   f or or 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 definiti definition) on).. It has been been propos proposed ed that that the essenc essencee of therma thermall analyanalysiscanbesummarized“asthemeasurementofachangeinasample proper property, ty, which which is the result result of an impose imposed d tempera temperatur turee altera alteratio tion” n” [26].. [26]  2.2. Experimental kinetic analysis techniques

Kinetic data from solid state pyrolysis reactions has traditional tionally ly been obtain obtained ed using using discret discretee isother isothermal mal methods methods of  analysis. analysis. Isothermal kinetic data usually usually is acquired by performperforming several experiments under isothermal conditions at different temperature temperatures. s. Additionally,isotherma Additionally,isothermall experimentsstill experimentsstill possess possess an elementofnon-isothermalbehaviorduringtheinitialheatingramp to the desired temperature. Interest in isothermal methods, however, has gradually gradually waned because because they are considered considered toilsome [27]..  Conversely, dynamic methods, which are performed under [27] non-isother non-isothermal mal conditions, conditions, have attracted attracted much appeal appeal given their ability ability to investigate investigate a range of temperature temperaturess expeditiousl expeditiouslyy [27,28] [27,28].. Non-isother Non-isothermal mal analytical analytical techniques techniques use modernthermo modern thermobalanc balances es that subject samples to a programmed continuous temperature rise, which ensures that no temperature regions are omitted, as can occur occur during during a sequen sequence ce of discre discrete te isother isothermal mal measur measureme ements. nts. Despite their touted convenience   [29,30], [29,30],   non-isothermal techniques niques have received pointed pointed criticism criticism [31–35]  [31–35] a  and, nd, sometimes, outright rejection [36] rejection  [36] b  because ecause of their perceived inability to reliably assess kinetic parameters, besides their increased sensitivity to experi experimen mental tal noise noise as compar compared ed to isothe isotherma rmall methods methods [37,38] [37,38].. Benoit Benoit et al. [39] al. [39] a  advised dvised 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] rates [33,40];; it is a perspective shared by participants in a recent kinetics kinetics project project commissionedby commissionedby ICTAC[41–45] ICTAC [41–45].. Paradoxical Paradoxically, ly, the inherent efficiency with which dynamic methods collect kinetic data is partially negated in that reasonably resolved data typically is obtained using low heating rates [46] rates  [46].. Thermog Thermograv ravimet imetric ric analysi analysiss (TGA) (TGA) is the most most common commonly ly applied thermoanalytical technique in solid-phase thermal degradation studies   [47], [47],  and it has gained widespread currency in thermal thermal studies of biomass biomass pyrolysis pyrolysis [48–54]  [48–54]..  TGA measures the decrease in substrate mass caused by the release of volatiles, or devolatilization, during thermal decomposition  [55]  [55]..  In TGA, the mass of a substrate being heated or cooled at a specific rate is monitored as a function of temperature or time. Taking the first derivative of such thermogravimetric curves (i.e., −dm/dt ) curves, known as derivative thermogravimetry (DTG), provides the maximumreaction mumreaction rate rate [56] [56].. Thedevelopmentofasystemin1899bySir William Roberts-Austen [57] Roberts-Austen  [57] t  that hat uses thermocouples to measure the temper temperatu ature re differe difference nce betwee between n a sampleand sampleand an adjace adjacent nt inert inert reference reference material material subjected subjected to an identical identical temperature temperature alteration alteration was the naissance naissance of differential differential thermal analysis analysis (DTA) [58] (DTA)  [58]..  By

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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 theslope (dT /dt ) and height (T ) ofthe curve atanytemperature [59]. Anothercommon methodof thermal analysisis differential scanning calorimetry (DSC). In DSC, heat fluxinto or out of a sample is compared against an inert reference material, usually alumina, as the two specimens are simultaneously heated or cooled at a constant rate. The integral (or area) of the DSC peak is directly proportional to the heat of transition for a particular reaction and the change in heat capacity can readily be correlated to the enthalpy change of the reaction. DTA is similar to DSC, except that the conditions in DTA are adiabatic causing a temperature difference between the sample and the reference material.  Table 1 provides a listing of thermoanalytical techniques classified according to the physical properties that are measured. Thermal analysis provides an excellent tool that may provide insight regarding the kinetic workings of heterogeneous reactions. However, it cannot be overstressed that the kinetic data obtained from a single thermoanalytical technique, in and of itself, does not provide the necessary and sufficient evidence to draw mechanistic conclusions about a solid state decomposition process  [60]. The kinetic behavior of a given heterogeneous reaction system may change during the process and so it is possible that the complete reaction mechanismcannot be represented suitably by a singlespecific kinetic model [61]. Various other analytical techniques (e.g., electrical, nuclear, optical, and X-ray) must be employed to detect and analyzechanges 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 schemeand, hopefully,bringinvestigators 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  E a  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.,  E a  and  A) can be interpreted in terms of molecular collision theory. The activation energy,  E a , 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 energyof molecules undergoingreaction and average energy of all reactant molecules  [63]. The frequency factor provides a measure of the frequency at which all molecular collisions occur regardless of their energy level  [64]. The exponential term in Eq. (1) can be thought of as the fraction of collisions having sufficient kinetic energy to induce a reaction  [65]. Thus, the rate constant, k(T ), being the product of  A  and the exponential term, exp−E a /RT , yields the frequency of successful collisions [65]. Vociferous debate continues to swirl about the relevancy of  kinetic parameters obtained from solid state reactions. The crux of the controversy stems from the indiscriminate adoption of  homogeneous reaction kinetic theory to describe heterogeneous processes [66–68]. Indeed, it is plausible that much of the inconsistency arising in biomass kinetic data is ascribable to the use of  kinetic expressions that are merely adaptations of those used in homogeneous reactions and that do not incorporate terms that depend upon the solid state nature of biomass. Over thirty years ago, Garn [69] contended that the discrepancies observed in calculated activation energies for solid phase decomposition are a reminder that the concept of a symmetric distribution of energy statesasimpliedbytheArrheniusequationdoesnotapplytosolids. The fact that the most commonly occurring and minimum possible energy state in solids is that of the perfect crystal obviates the use of a statistical treatment for solids  [70]. Garn advised [69] that if the calculated “activation energy varies with experimental conditions then it is necessarily true that: (1) there is no uniquely describable activated state and consequently the Arrhenius equation has no application to solid reactions; or (2) the assumption that the rate is a function only of temperature and the [mass] fraction remainingis incorrect;or (3) both”.Consequently,the physical connotationof the Arrhenius parametersin heterogeneous kinetics is opaque and “ . . .they do not characterize the chemical reaction itself, but only the whole complexity of processes occurring during the pyrolysis under the given experimental conditions” [71]. Hence, experimentally determined kinetic parameters from thermally activated, solid state transformations can only be expected to provide a rough approximation for the overall rate of a complex process that typically entails numerous steps, each having distinct activation energies [40,72]. Garn [66] also raised salient concerns about other weaknesses associated with the transfer of  homogeneous kinetic principles to heterogeneous processes.

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conditions by the following canonical equation:

 Table 2

Unconventional phenomena represented by the Arrhenius rate law. Temperature-dependent phenomenon (applicable temperature range)

E a  (kJmol−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 betweenln k and T , andbetweenln k andln T )doexistfordescribing the influence of temperature on therates of chemical reactions, Laidler [73] emphasized that none of these other relationships enjoys the universal acceptance bestowed upon the Arrhenius equation because of their “theoretical sterility”. The additional parameters that are included in these surrogate rate expressions presumably would permit better fitting of experimental data, but there is no theoretical rationale for their existence, thereby, depriving them of any physico-chemical significance  [62]. Were the thermal analysis community to approve an alternative expression for the temperature dependence of reaction rates, it would necessitate the recalculation of all previous E a and A   values so that kinetic parameters dating back to 1899 could be compared against those generated by the new rate law [62]. An undertaking of this magnitude would be incredibly laborious and seems improbable. Moreover, rejection of the Arrhenius expression would, as  ˇ  Sesták [74] said, “certainly deny the fifty [i.e., now eighty] years’ work of famous scientists in the field of heterogeneous kinetics”. For all the barbed accusations that have been hurled against the Arrhenius rate law, it remains the only such kinetic expression that can satisfactorily account for the temperature-dependent behavior of  even the most unconventional processes, as shown in  Table 2 and notedoriginallyinaseriesofreviewpapersbyCrozieretal. [75–77], and subsequently expanded by Laidler [78] and then tabulated by Brown [68]. Laidler’s purpose for revisiting these intriguing processes was to underscore that relatively complex reaction systems can be represented by the Arrhenius law and also that above a certain energy threshold (i.e., about 21kJmol −1 ) many phenomena are likely to proceed via chemical reactions rather than by physical processes. The prominent role of the Arrhenius expression in heterogeneous reaction systems is undeniable and was acknowledged by Agrawal  [28], who stated, “. . .it is perhaps the most widely used equation and is satisfactory in explaining the temperature dependence of the rate constant in solid-state decomposition kinetics”. 3. Biomass pyrolysis kinetics  3.1. Kinetic expressions for biomass thermal decomposition

The kinetics of biomass decomposition are routinely predicated on a single reaction [79,80] and can be expressed under isothermal

−E a d˛  f (˛) = k(T ) f (˛) =  A exp (2) RT  dt  where t denotestime, ˛ signifies thedegreeof 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 w0 − w f 

=

v v f 

(3)

where  w  is the mass of substrate present at any time  t ,  w 0  is the initial substrate mass, w f  is the final mass of solids (i.e., residueand unreacted substrate) remaining after the reaction,  v  is the mass of  volatiles present at any time  t , and  v f  is the total mass of volatiles evolved during the reaction. The combination of  A ,  E a , 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  = (4) dT  dt  dT  where dt /dT  describes the inverse of the heating rate, 1/ ˇ, d˛/dt  representstheisothermalreactionrate,andd ˛/dT denotesthenonisothermal reaction rate. An expression of the rate law for nonisothermal conditions can be obtained by substituting Eq. (2) into Eq. (4): d˛ dT 

=

k(T )  A f (˛) = exp 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˛ n = k(T )(1 − ˛) (6) dT  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]: dV i ∗ = ki (T )(V  − V i ) (7) i dt  where ki (T ) is the rate constant for an evolved volatile fraction i, V i   is the cumulative mass of released volatiles corresponding to fraction i  through time t , and V i * 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 summationof theindividual volatilization rates foreach 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 alternativekinetic representation uses Eq. (7) as a template but the rate of devolatilization is

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 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

˛

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 ] + C a

1/2˛ [−ln(1 − ˛)]−1 3/2(1 − ˛)2/3 [1 − (1 − ˛)1/3 ]−1 3/2[(1 − ˛)−1/3 − 1]−1

(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

ln(1 − ˛) (n − 1)−1 (1 − ˛)(1−n) −

˛2

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] andthe method of least squares using nonlinearregression analysis [39,98–100] is regularly employed to fit the experimental data and evaluate theArrheniusparameters as predicted by thekinetic models. Some of the more important rate equations used to describe the kinetic behavior of solid state reactions are listed in  Table 3, or simply “The Table”. Other than for didactic purposes or reviews, authors should assume that their audience is acquainted with the relevant background information and refrain from the repetitive inclusion of “The Table” each time a new thermal analysis paper is published. Furthermore, the argument that reference texts containing a comprehensive listing of reaction models are not readily available is no longer valid. Elsevier Science Publishers  [101] has recently republished Vol. 22 of the Comprehensive Chemical Kinetics series entitled:  Reactions in the Solid State by C.H. Bamford and C.F.H. Tipper, Eds. [18], which includes a complete set of solid state reaction models. Anotherfine thermal analysis reference book containing “The Table” that is accessible at most academic libraries is the Handbook of Thermal Analysis and Calorimetry, Vol. 1:  Principles and Practice  by M.E. Brown, Ed. (P.K. Gallagher, Series Ed.) [13]. It should be noted that the application of first order reaction models in biomass pyrolysis kinetics has become almost formulaic and their indiscriminate acceptance has occurred without rigorous verification or sufficient awareness of their fundamental limitations [82,102]. The imposition of an order-based model on a solid state reaction system can cause a substantial divergence in the Arrhenius parameters (i.e.,  A  and  E a ) [82]. This discrepancy arises when an inappropriate reaction order is affixed to the last term in Eq. (6). The strongly correlated Arrhenius parameters in the rate constant, k(T ), are then forcibly adjusted to accommodate the chosen reaction order. Accordingly, any reaction model, not only order-based models, can suitably fit kinetic data because of the corresponding “kinetic compensation effect” among the Arrhenius parameters [103]. The manifestation of this compensation relationship is common to both isothermal and non-isothermal kinetic models, yet the increasing popularity of non-isothermal single heating rate techniques in preceding decades necessarily gave rise to a surge of unreliable and erratic results  [28,104,105]. Much suspicion was cast upon the validity of non-isothermal model-fitting methods, although isothermal methods are just as culpable in that they are also susceptible to a similar vacillation in the Arrhenius parameters [106]. To quote Ninan  [47], “As far as the values of  the kinetic parameters are concerned, there is no significant differ-

ence between isothermal and non-isothermal methods or between mechanistic and non-mechanistic approaches, in the sense that they show the same degree of fluctuation or trend, as the case may be”. Garn [66] underscored several critical assumptions included in the generalized rate expression (Eq. (2)), which is often used to describe solid state decomposition kinetics. A violation of any of  these assumptions in a particular system will invalidate the use of  the rate equation. The use of the mathematical terms, f (˛)and k(T ), explicitly affirms that the reaction rate is exclusively a function of the degree of conversion,  ˛, and the temperature,  T . Changes in otherprocessparameters(e.g.,heatingrate,residencetime,particle size, sample quantity, reaction interface, atmosphere, and pressure) theoretically should have no effect on the reaction rate. If  changes in reaction rate are found to result from variation in these other parameters, the conventional rate equation has failed. In other words, the rate of reaction may be influenced by parameters besides the concentration that are not incorporated in the generalized “reaction statement”. A logical explanation for this can be deduced by recognizing that the rate constant for a given reaction is clearly an intensive property  [34], like temperature or density, because it is “measured from changes in an extensive property of the system such as mass, enthalpy, and volume”  [17]. Hence, the rate constant has important merit because it is specific to a particular substance and process and it can potentially be used to discriminate amongst various reaction systems.  3.2. Biomass pyrolysis kinetic models

A comprehensive review of the myriad models available for analyzing the kinetics of biomass pyrolysis reactions is beyond the scope of this communication. Instead pertinent kinetic models used in biomass pyrolysis studies will be presented along with selected additional models that are noteworthy for their innovative efforts to achieve improved predictive success by better reflecting the heterogeneous character of biomass thermal decomposition. The numerous pyrolysis models can be divided into three principal categories: single-step global reaction models, multiple-step models, and semi-global models  [107–110]. The processes comprising pyrolysis frequently are described as proceeding along (a) concurrent (i.e., competitive and independent parallel) routes [6,53,91,107–110], (b) consecutive (or sequential) routes [111–115], or (c) combinations thereof   [116–121]. Single reaction global schemes describe the overall rateof devolatilization from the biomass substrate. Single-step global models have provided reasonable agreement with experimentally observed kinetic

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behavior [84,122–124]. One frequently cited study [125] revealed that the pyrolysis of many different cellulosic substrates can be adequately described by an irreversible, single-step endothermic reaction that follows a first order rate law with a global apparent activation energy of  ca. 238kJ mol−1 . The usefulness of single-step global models, however, is limited by the assumption of a fixed mass ratio between pyrolysis products (i.e., volatiles and chars), which prevents the forecasting of product yields based on process conditions [126]. Furthermore, in most pyrolysis systems the kinetic pathways are simply too complex to yield a meaningful global apparent activation energy [127]. Much related work has examined the use of semi-global models, all of which assume that biomass pyrolysis products can be aggregated into three distinct fractions: volatiles, tars, and char. Semi-global models are able to facilitate a simpler ‘lumped’ kinetic analysis   [53,89,107,126,128,129].   This analysis is used widely because its depiction of biomass devolatilization in terms of three concurrent first order reactions is intuitive   [90].   This technique is a suitable tool for correlating and evaluating kinetic data from different biomass types under similar reaction conditions, but it is ill-suited for comparisons of thermal decomposition data obtained from dissimilar reaction conditions [84]. Semi-global models also allow coupling of transport phenomena parameters with the secondary devolatilization reactions. This procedure has been demonstrated to correctly predict trends in product yield as a function of volatiles residence time [130].  3.3. Multiple-step models

The inability to predict the kinetic behavior of biomass under different process conditions has vexed researchers and encouraged the developmentof complex multiple-step models. A rigorous kinetic treatment of pyrolysis data must account for the formation rates of all the individual product species   [88,108],  along with any potential heat and mass transfer limitations. Alves and Figueiredo [113] concluded that the pyrolysis of cellulose could be successfully modeled using three consecutive first order reactions. The first reaction represents approximately 30% of the total devolatilization, while the third reaction releases the remaining 70% of the volatile matter [131]. The second reaction released no volatile matter and is theorized to involve rearrangement of the solid. Alternative reaction schemes, while possible, were deemed impractical because they would require either more than three reactions or three reactions of order other than unity to describe the complex devolatilization process. A study by Diebold  [132] provided an elegant seven-step global kinetic model for cellulose pyrolysis that achieved accurate predictions using published rate constants forboth fast and slow pyrolysis. The model accounted for interactions between heating rate, residence time, pressure, and temperature. It was demonstrated by Vargas and Perlmutter [112] that thereaction kinetics of coal subjected to non-isothermal pyrolysis can be understood to proceed via a series of ten consecutive isothermal steps, each associated withthe degradation of a specific pseudo-component of the coal. Not to be outdone, Mangut et al. [133] revealed that kinetic data obtained from the pyrolysis of food industry wastes related to tomato juice production (i.e., peels and seeds) could be satisfactorily modeled using twelve consecutive pyrolytic reactions that were identified from DTG curves. Although useful in some applications, multi-step reaction models are limited by their incorporation of several interdependent serial reactions, wherein subtle inaccuracies in the kinetic parameters obtained for the first rate equation can be greatly magnified in successive reactions [134]. Except for a few extremely simple cases, comprehensive kinetic approaches are intractable because of the sheer number of reactions that would need to be considered. Furthermore, the identification of constituents in pyrogenic tar mixtures

remains incomplete and the intermediate pyrogenic species have scarcely been characterized. Consequently, these ‘elegant’ models can sometimes be of limited practical use.  3.4. Isoconversional techniques

Historically, model-fitting methods were thought to satisfactorily predict reaction kinetics in solid state processes. Arrhenius parameters obtained from model-fitted isothermal data are often nearly independent of the kinetic models employed [40]. Iterative approaches to model-fitting empirical endpoints from isothermal data may provide consistent values for the Arrhenius parameters, but only a single global kinetic triplet is obtained for each set of  data. As stated previously, solid state processes, such as biomass pyrolysis, frequently proceed viaa complex suite of concurrent and consecutive reactions. Each step likely hasits ownunique apparent activation energy, and thus the use of an average, global apparent activation energy to describe the kinetics of such processes could be construed as an inadequate oversimplification at best [135] and, more alarmingly, the DTG curves from these models may conceal the true multistage character of pyrolytic reactions under a single peak [136]. Conversely, force fitting models to non-isothermal data obtained from a single heating rate can generate very inconsistent Arrhenius parameters that display a strong dependence on the selected kinetic model [40]. Non-isothermal methods that use multiple heating rates can provide more reliable estimates of the kinetic parameters as mentioned earlier, but various decomposition processes can exhibit different dependencies on heating rate, which may lead to overlapping reactions in the DTG curves thatare difficult to separate [137]. The consternation in the scientific community  [68,138] over the wide variation in Arrhenius parameters for similar reaction conditions and biomass species using different reaction models served as a lightning rod that precipitated additional research and development [29,40,139–143]. Innovative methods for determining Arrhenius parameters based on a single parameter began to emerge in the 1960s. These so-called “model-free” methods are founded on an isoconversional basis, wherein the degree of conversion,  ˛ , for a reaction is assumed to be constant and therefore the reaction rate,  k , depends exclusively on the reaction temperature, T. By allowing E a  to be calculated  a priori, isoconversional approaches eliminate the need to initially hypothesize a form and rate order for the kinetic equation. Hence, isoconversional methods do not require previous knowledge of the reaction mechanism for biomass thermal degradation. Another advantage of isoconversional approaches is that the systematic error resulting from the kinetic analysis during the estimation of the Arrhenius parameters is eliminated [41]. Isoconversional models can follow either a differential or an integral approach to the treatment of TGA data. The Friedman method [144] is a differential isoconversional technique that can be expressed in general terms as written below: d˛ dt 

=

ˇ

d  ˛ dT 

=  A

−E a

  exp ( ) RT 

(8)

 f  ˛

Taking natural logarithms of each side from Eq.  (8) yields:

     d d ln ln ˛

dt 

=

ˇ

˛

dT 

=

ln[ Af (˛)] −

E a 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 −E a /R. The Flynn–Wall–Ozawa (FWO) method   [62,145–150]   is an integral isoconversional technique that assumes the apparent acti-

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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˛  f (˛)

T ˛

    exp d

 A = ˇ 0

−E a

RT 

 

T 

(10)

where  T ˛  is equal to the temperature at conversion  ˛. If we define  x ≡ E a /RT , Eq. (10) becomes:  AE a  g (˛) = ˇR

∞

 

exp− x  x2

˛

=

 AE a  p ( x) ˇR

(11)

where p( x) representing the rightmost integrand in Eq.   (10) is known as the temperature integral. The temperature integral does not have an exact analytical solution in closed form [29] butcanbe approximated via an empirical interpolation formula proposed by Doyle [62,149,151,152]: log p( x) ∼ = −2.315 − 0.4567 x,   for20 ≤  x ≤ 60

(12)

Using Doyle’s approximation for the temperature integral and t aking logarithms of both sides of Eq.  (11) one obtains:



log ˇ = log  A

E a Rg (˛)



−

2.315 − 0.4567

 E a 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 (−0.4567E a /R) of these lines is proportional to the apparent activation energy. The value of log A is givenby 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) = ,   for20 ≤  x ≤ 50 (14) 2  x

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 T m

=−

E a R

˛

 1  ln     d  T m

−

E a  AR

∂  f  ˛ ( ) 0

 

(15)

where T m is thetemperature at themaximum reaction rate. Assuming ˛ has a fixed value,  E a  can be determined from the slope of the straight line obtained by plotting ln( ˇ/T m 2 ) versus 1/T m . 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:  AR 2RT  E a −ln(1 − ˛) = ln − ln 1−   (16) 2



T 

   ˇE a

E a



RT 

Eq. (16) can be simplified by recognizing that for customary values of  E a  (e.g., 80–260kJmol−1 ), the term 2RT /E a  1:  g (˛)  AR E a = ln − ln   (17) 2

    T 

ˇE a

RT 

A straight line can be obtained from single heating rate data by plotting ln[ g (˛)/T 2 ] versus  T −1 . From the slope of the line, −E a /R, and its intercept ln( AR/ˇE a ),  E a  and  A  can be derived. The attractiveness of the CR method resides in its ability to directly furnish  A  and  E a  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 

andd˛/dt (ordT /d˛) [28,157–160]. Amulti-heatingrateapplication 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  FWOandKAS.TheCR*methodrearrangestermsinEq. (16) toyield: ln



ˇ T 2 (1 − 2RT /E a )



=−

E a AR + ln RT   g (˛)E a





 

(18)

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  − E a /R. The frequency factor,  A , is calculated by inserting −E a /R into the intercept. Because the left-hand side of Eq. (18) is weakly dependent on  E a , an iterative process must be used by assuming an initial value for  E a and then re-evaluating the lefthand side until the desired level of convergence  [161]. It should be noted as a point of clarity that there are other so-called “modified Coats–Redfern” methods in the literature, but they cannot be considered isoconversional because they still require the selection of  a reaction order. These alternative “modified Coats–Redfern” formulations often involve a regression analysis of one or more of the kinetic triplet parameters [162,163]. One such “modified” method [163] reported errors for  E a  estimates that are an order of magnitude lower than those obtained from isoconversional techniques.  3.5. Comparative evaluation of integral and differential isoconversional techniques

The advantages of the integral isoconversional methods are tempered by several weaknesses not present in the differential methods [164], viz., (1) Picard iteration [165] of the temperature integral is needed. (2) Integral methods are prone to error accretion during such successive approximations. (3) The temperature integral requires boundary conditions which are frequently ill-defined. Flynn   [62]   remarked that use of “. . .the mathematically intractable temperature integral has often become a necessary evil in the analysis of thermal analysis kinetics”. To circumvent the hazards posed by these oversimplified approximations, Vyazovkin and Dollimore [166] introduced a non-linear isoconversional technique, known as the Vyazovkin (V) method, which uses a revised expression for the temperature integral,  p( x): T ˛

I (E a , T ˛ ) =

    exp −E a

RT 

0

dT  =  p( x)

(19)

The V method evaluates E a for a set of q experiments conducted at different heating rates,  ˇ j  and  ˇ k , where the subscripts  j  and  k denote the ordinal number of the experiment: q

q

 /  j  j=1 k =

ˇk I (E a , T ˛,j ) ˇ j I (E a , T ˛,k )

=

 (E a )

(20)

where I (E a ,T ˛, j ) and I (E a ,T ˛,k ) represent the temperature integral corresponding to the heating rates ˇ j and ˇk , respectively. The apparent activation energy is given by the value that minimizes  . Values of  I (E a ,T ˛ ) can be determined via either numerical integration or the Senum–Yang [167] approximation:

 p( x)

 p( x) =

 exp  − x

 x

( x3 + 18 x2 + 88 x + 96) ( x4 + 20 x3 + 120 x2 + 240 x + 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 

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the remaining kinetic parameters, A and f (˛) [40,105]. The frequency factor obtained from standard isoconversional techniques is tainted by association with the reaction model that must be assumed to permit its calculation  [40]. Flynn [164] developed a general differential isoconversional method that allows  A  and  f (˛) to be disconnected and evaluated independently. Another procedure to unambiguously evaluate A was proposed by Vyazovkin and Lesnikovich [168], wherein a linearrelationthat existsbetween the Arrhenius parameters is used to extract the frequency factor for a given isoconversional value of  E a : ln A = aE a + b

 

(22)

where  a and  b  are correlation parameters that are evaluated using linearregression.The useof this procedure,however,is notentirely 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  E a  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 E a  for pyrolysis processes  [105]. The supposition of constant E a  and  A  values is only possible when the Arrhenius parameters are independent of the extent of reaction [140]. When  E a  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] f ound that values of  E a   are consistently overestimated using integral isoconversional methods versus those evaluated using Friedman’s differential isoconversional method because of error introduced by the truncation of the additional higher-order terms in Doyle’s approximations, given by Eqs.  (11) and (13). Data provided by Budrugeac et al.  [169] f or the dehydration of calcium oxalate indicates that  E a  values obtained from integral methods can deviate by up to 21%from values determined by differential methods. In response, Vyazovkin  [103] provided a modification for the V isoconversional method that accounts for the variation in apparent activation energy with increasing  ˛ . Instead of evaluating the temperature integral over the complete boundary conditions (i.e., 0– t ˛ ), the integration is now performed numerically over small time increments using the trapezoidal rule, which requires considerable more computational effort than the Senum–Yang approximation  [168]. In a rebuttal, Budrugeac and Segal [172] remarked that the modification proposed by Vyazovkin [103] using “low ranges of variables” is an artifact that in reality conceals the true differential character of the method. Differential isoconversional methods are not encumbered with a temperature integral and thus kinetic parameters can be directly calculated.Numerical differentiation of experimentaldata is highly susceptive to data noise [43,173] and can result in significant scatterin theresultingderivative curves.Widespread useof differential techniques has also been inhibited because of the daunting calculations involved  [164]. The advent of powerful computational tools   [164,174–176]  coupled with the development of sophisticated smoothing and fitting functions   [137,173,177–180] has helped to curtail some of these objections, although some resistance yet remains among those who insist that integral methods area “saferalternative” [43] becausedifferential methodsstill “suffer from excessive random errors” [139], especiallyinthevicinityof  the reaction onset and endpoint, where d ˛/dt  is often small [170]. Nonetheless,Burnham and Dinh [105] recently indicated that if the rate of data collection is sufficiently high then the raw data can be smoothed appreciably such that the vulnerabilities of the Friedman method to experimental noise can be “effectively mitigated”. An examination by Burnham et al. of the predictive performance of several isoconversional and model-fitting techniques applied on

data sets from theICTAC kinetics project andother lifetime projects revealed that the Friedman differential method was the most reliable and accurate method in all cases. There are also some disadvantages that are common to all “model-free” techniques. The use of the descriptor, “model-free”, is deceptive [181] because it insinuates that awareness of the kinetic model and, in particular, the conversion function  f (˛), is superfluous information not needed in the kinetic analysis. An accurate descriptionofkineticbehaviorisnotpossiblewhenmembersofthe kinetic triplet are interpreted independently of one another  [182]. “Model-free” methods simply “postpone” the consideration of an appropriate conversion function until an estimate of the kinetic parameters (i.e., E a and A) is calculated  [181]. Furthermore, isoconversional methods are unsuitable for those reaction schemes containing competing reactions, where the net rate of reaction depends on changes in temperature, or concurrent reactions that switch which reaction is rate-limiting over the experimental temperature range [105]. It has also been cautioned that the selection of kinetic expressions wherein “ f (˛) is assumed to be a function of mass can be a very poor choice” because these models presume that the activity of every reactant particle is identical regardless of its location in the substrate matrix (i.e., in the bulk or on the surface)  [17]. In heterogeneous reactions this is seldom the case because substratereactivity canvarydepending onthe locationof activesurface sites, the partial pressure of the surrounding atmosphere, and physical changes in the specimen that are temperature-dependent phenomena (e.g., sintering, melting, and vitrification)  [17,70,138]. According to Flynn [17], it is possible in certain solid state reactions thatthe“. . .crucial, rate-controllingevent may be the occurrence of  the temperature-dependent physical transformation which is not ˇ  mass dependent”. Sesták and Berggren [15] succinctly conveyed these concerns regarding proper selection of  ˛  when he stated, “[DTA] is still of questionable validity, because a representative value which would unambiguously define thechangein the system from the initial or from the final state is not yet available . . .”.  3.6. Other kinetic models

Kinetic models other than traditional reaction order models have been proposed that ostensibly afford improved predictions for biomass pyrolysis data. For example, an interesting deactivation theory was proposed by Balci et al.  [183] that is based on kineticmodelstypicallyappliedtowardcatalystdeactivation.Inthe biomass deactivation model (DM), the first order rate constant was assumed to vary with the degree of decomposition due to changes that occurin thechemicalcompositionand physicalstructure ofthe substrates during the pyrolysis process. Individual biomass componentsdegrade at different temperatures, demonstrating that the compositionof thereactiveportion ofthe substrateis modified duringthe 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: kapp

E i RT 

  

( )  Ai exp

=  zk =  z   

−

 

(23)

where  z  is the activity of the solid substrate expressed as a function of a deactivation rate constant,  , and kapp is the apparent rate constant. Reynolds et al.   [161,184,185]   developed a generalized nucleation-growth model, which is essentially a modification of the Prout–Tompkins rate equation  [186], first used to describe

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J.E. White et al. / Journal of Analytical and Applied Pyrolysis 91 (2011) 1–33

the thermal decomposition kinetics of potassium permanganate [187]: d˛ dt 

=

kyn (1 − ry)s

(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) toafirstorderreaction,andthequantityinparentheses(1 − ry) replaces(1 − y)topreventtheinitialratefrombeingzero [188]. This model demonstrated a better fit with experimental data than conventional first order models, yielding a much tighter degradation curve [184]. The distributed activation energy model (DAEM) has been successfully applied to both plant   [91,117,189–196]  and fossil [95,190,197–202] biomass pyrolysis. The DAEM assumes that several irreversible first order parallel reactions having unique kinetic parameters take place concurrently  [202]. A continuous distribution function, f (E a ), 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 E a .Várhegyietal. [189] haveassertedthat the DAEMisthebestmethodavailableformathematicallyrepresenting the physical and chemical heterogeneity of substances. Miura and Maki [203] proposed a revised distributed activation energy model (DAEM) that provides a method for estimating the frequency factor and  f (E a ) without requiring  a priori  assumptions of either kinetic parameter. This method was used to successfully predict weight loss curves from the pyrolysis of coal at different heating rates. Cai and Liu [204] advocated the use of a Weibull distribution model to fit non-isothermal kinetic data. Under this approach, the kinetic degradation for each biomass component is represented by one or more Weibull distribution functions. This procedure allows overlapping processes in the TGA curve to be deconvoluted. The use of  this model requires estimation of the scale and shape parameters that are unique to the Weibull distribution function. The cacophonous debate over the relative merits of isothermal, non-isothermal,andisoconversionalmethodscansometimesoverarch the common thread among all these methods: the use of a kinetic model that has been preordained by the scientific community. A significant liability can be incurred by simply consulting the “Table” for the “best model” and expecting that it indeed is the correct model. Galwey and Brown [13] commented that “the formal models in the accepted set [i.e., the “Table”] are far too simple to account for all the features of real processes”. Using a “generalized description” of the kinetics involved in solid state reaction systemsoffers thefreedomand flexibility to choosethe most appropriate elements from the set of existing formal models in order to best characterize the various aspects of the true process [13]. The ˇ  Sesták–Berggren (SB) equation [15], as shown below, was the first such “generalized description”: d˛ dt 

=

k˛c (1 − ˛)d (−ln(1 − ˛))e

(25)

where c , d,and e areadjustable exponent factors that canbe used to model thedifferent aspects ofsolidstate reactions. TheSB approach offers two distinct theoretical advantages  [205]: (1) no implicit assumptions are made concerning the mechanism governing the solid state reaction and (2) no approximations or heavy-handed mathematical intricacies are involved as the values of  c ,  d , and  e canbe calculated directly using a matrix system of linearequations. Vyazovkin and Lesnikovich [206] acknowledged the importance of  the generalized description afforded by the SB equation, remarking that “. . .a comprehensive comparison of the [SB] approach with other methods based on model discrimination has demonstratedits preferability”.Otherfunctions (e.g.,polynomials, splines,

fractals,etc.) canalso 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., 11.2–262kJmol−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  E a  values, as demonstrated by the values of  E a   for hazelnut shells (e.g., 40.3–144.9kJmol −1 ), almond shells (e.g., 11.2–254.4 kJ mol−1 ), and cashew nut shells (e.g., 130.2–293.5kJmol −1 ) in Table 4. Accordingly, Wilson et al. [207] aptly note in their recent publication about the thermal characterization of tropical biomass feedstocks that the marked variability observed in the kinetic parameters of cashew nut shells is simply a consequence of the geographical origin and “specific nature” of  given biomass materials. Besides the lack of parity in the kinetic results, few trends are evident from  Table 4 regarding the heating rate, the sample mass, or the kinetic model used. However, a comparativeplot of E a values fornutshellsusing 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  E a  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 E a values (78.9–131.1 kJ mol−1 ) obtained by Bonelli et al. [211] for hazelnut shells using the DM would appear to contradict the previous findings, yet the  E a  values reported by Demirbas¸’s group [209,210] f or 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 (250–1000mg), which has been observed to correspond with pronounced decreases in apparent activation energy [212]. A conspicuous feature that is exposed by  Table 4 concerns the lower E a  values obtained under isothermal, or static, conditions for both almond and coconut shells. Closer examination of the isothermal experiment [208] that recorded an overall  E a  value of  99.7kJmol−1 foralmondshellsrevealsthatthereactionmodelused in the kinetic analysis was a first order, single-step SM. The E a value derived from this static experiment is 27% lower than the average minimum E a  value computed for almond shells whose non-isothermal, or dynamic, reactions were modeled using an  nth order, parallel reaction SM [213,214], but this difference decreases to just 6% when the latter group is replaced with almond shells whose dynamic reactions were modeled using a first order, parallel reaction SM [216], which compares well with the 7% difference obtained between the static and dynamic almond shell pyrolysis experiments that were both evaluated using a first order, singlestep SM [183,208]. In the case of coconut shells, there is a 67% decrease in the E a 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. Nutshell type

Heating profile, rate (◦ Cmin−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

100–550 b

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–900 b

0.7–1

Almond shell

Static, 1.2 × 106

RT–900 b

0.7–1

100–800