modeling the nonisothermal devolatilization kinetics of typical south african coals

Modeling the Nonisothermal Devolatilization Kinetics of TypicalSouth African CoalsBurgert B. Hattingh,* Raymond C. Everson, Hein W. J. P. Neomagus, John R. Bunt, Daniel van Niekerk,and Ben P. Ashton

Research Focus Area for Chemical Resource Beneficiation, North-West University, Potchefstroom Campus, Private Bag X6001,Potchefstroom, 2520 North West, South Africa

Energy Systems, School of Chemical and Minerals Engineering, North-West University, Potchefstroom Campus, Private Bag X6001,Potchefstroom, 2520 North West, South Africa

Sasol Technology (Pty) Ltd., Research & Development, Coal & Gas Processing Technology, Box 1, Sasolburg, 1947 Free State,South Africa

*S Supporting Information

ABSTRACT: Multicomponent model fitting was conducted in order to evaluate the devolatilization rate behavior of four typicalSouth African coals, with the aid of nonisothermal thermogravimetry. Rate evaluation was conducted at four different heatingrates (5, 10, 25, and 40 K/min) by heating the samples under an inert N2 atmosphere to 950 °C. Evaluation of the kineticparameters of each coal involved the numerical regression of nonisothermal rate data in MATLAB 7.1.1 according to apseudocomponent modeling philosophy. The number of pseudocomponents used ranged between three and eight, as largervalues induced the risk of over fitting. Quality of fit (QOF) was found to decrease with decreasing heating rate as a result ofimproved separation of the individual component reactions at the lower heating rates. All four coals showed the occurrence ofsimilar pseudocomponent reactions, although significant differences were observed in the fractional contributions of the differentpseudocomponents to the overall reaction rates. Modeling results indicated that the assumption of eight pseudocomponentsproduced the lowest QOF values and subsequently the best fit to the devolatilization profiles of each coal. For the vitrnite-richcoals (G#5 and TSH), no remarkable decrease in QOF could be observed after 6 pseudocomponent reactions, suggesting thateven 6 or 7 pseudocomponent reactions would have provided accurate experimental predictions. Activation energies determinedfrom the selected number of pseudocomponents (between 3 and 8) were found to range between 20 and 250 kJ/mol.

1. INTRODUCTION

Coal devolatilization plays an important role in not only themetallurgical industry for producing coke but also during coalgasification where it normally constitutes the initial step of theprocess.1,2 It is therefore important to evaluate the devolatiliza-tion behavior of a coal feedstock in order to assess and optimizethe production of valuable products such as char/coke, tar, andgas. Extensive research during the past few decades has advancedour knowledge of the kinetics and mechanisms of thedevolatilization process. Furthermore, it has also provided uswith valuable techniques for predicting, to a reasonable extent,the behavior of coals.3−5 Devolatilization modeling is quitestraightforward if the chemical reaction step is rate controllingand the fuels are of a simple characteristic nature. Kinetic modelsfor describing thermal decomposition range in different levels ofcomplexity from free radical mechanistic models for simplehydrocarbon species such as propane6 to more complex reactionschemes. The latter involves a number of individual reactions,incorporating extra transport steps such as in the case of naphthadevolatilization.7 The kinetic description of more complex poly-aromatic substances such as coal presents a challenging task, dueto a vast amount of reactions involved. Kinetic evaluation of thesesubstances is therefore normally conducted using pseudome-chanistic models, which attribute the overall measured reactionrate to the cumulative effect of a number of separate reactions.8,9

A large number of possible modeling strategies are currentlyavailable, of which the simplest are empirical in nature andemploy global kinetics.8−11 Available models can be divided intoeither general weight-loss models or structural models. Typicalweight-loss models include models employing a (1) single rate,(2) two rates, (3) multiple rates, and (4) distributed rates.12−21

Although simplistic in nature, the validity of a single reaction ratemechanism is quite limited. Kinetic parameters derived at a singleheating rate has been generally shown not to be appropriate toother heating rates.22

Currently, the Distributed Activation Energy Model (DAEM)(Anthony-Howard model) has been shown to be the most power-ful model for predicting devolatilization behavior.10,18,19,22−25 Thiscomplicated model was first proposed by Pitt26 and assumesthe devolatilization process to consist of an infinite series ofindependent parallel first-order reactions. Accordingly, coaldevolatilization can be explained by a distribution of activationenergies about some mean activation energy value (Ea,0). Thefunction within the model f(Ea) accounts for a distribution ofactivation energies and is assumed to be of Gaussian form. Asimplistic approach for solving the DAEM considers a common,

Received: October 25, 2013Revised: December 25, 2013Published: December 26, 2013

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© 2013 American Chemical Society 920 dx.doi.org/10.1021/ef402124f | Energy Fuels 2014, 28, 920−933

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constant frequency factor applicable for all activation energies(or reactions) in the distribution.27 This simplification has,however, been criticized by Alonso et al.28 who demonstratedthat the isokinetic effect, which involves the mutual relationshipbetween pre-exponential constant and activation energy, cannotbe neglected in the calculation procedure. Furthermore, thevalidity of using a constant pre-exponential factor becomesquestionable when the function f(Ea) spreads over a wide rangeof Ea values.

29 The use of continuous distribution curves (i.e.,Gaussian), for the description of overall activation energy by aconstant average activation energy and a standard deviation ofenergies (σ), has also raised concerns.29,30 From this perspective,the use of a Gaussian distribution does not necessarily guaranteethe correct prediction of the characteristic f(Ea) curve of thesubstance under investigation. Although a very powerful modelfor estimating devolatilization behavior, the DAEM requires anextensive numerical discretization procedure for solving therequired parameters.Recent advances in the understanding of the coal molecular

structure has led to the development of some structural/networkmodels of which the FG-DVC (Functional Group-Depolyme-rization Vaporization Cross-linking), the FLASHCHAIN,and the percolation lattice theory are the most commonlyknown.31−33 More comprehensive chemical models have alsobeen formulated for describing char and tar formation.31 Thesemodels address the influence of coal molecular structureon volatile evolution rate by assuming that aromatic groups arelinked by bridges and peripheral groups.34,35 However,evaluation of the kinetic parameters relevant to the differentbridge and peripheral functional groups requires extensiveknowledge of the coal molecular structure as determined usingadvanced characterization techniques such as NMR (NuclearMagnetic Resonance spectroscopy), etc. The choice of a suitablekinetic model should therefore bear relevance to the processunder investigation.The norm for kinetic studies is to conduct reactions under

isothermal conditions, especially for fast reactions such asdevolatilization at high temperatures. Time-resolved measure-ments of coal devolatilization are therefore very difficult andpresent uncertainty due to the fact that the devolatilizationprocess normally completes within a few seconds before theisothermal state is reached.9 Currently, nonisothermal techni-ques have proven to be more useful than isothermal techniquesfor deriving the kinetic triplets (activation energy, pre-exponential factor, and reaction order).9,28 In addition, theprocess of deconvolution of differential thermogravimetric(DTG) curves into pseudocomponent curves has been foundto be much easier for model- and less complex carbon-containingcompounds (such as biomass and oil shales) than coals.36−38

This challenge necessitates the need for further elaboration onthe behavior of typical DTG curves of coals, in order to formulateand evaluate an appropriate model.In general, a typical coal DTG curve is characterized by a mass

loss peak in the low temperature region with a maximum rateoccurring between 40 and 100 °C. This corresponds to the initialrelease of absorbed moisture. In some cases an adjacent peak tothe absorbed moisture peak is observed, which has beenattributed to either the release of crystal water associated withinherent minerals or chemically bonded moisture.28,39 The maindevolatilization zone (>300 °C) constitutes the release of tar,primary gases, secondary gases, and the subsequent formation ofchar.14,28 The extensive asymmetric nature of a typical DTGcurve of coal devolatilization therefore makes the use of a single

first-order reaction model impractical in determination of thekinetic parameters. In a response to this, authors such as Alonsoet al.28 formulated a lumped first-order model allowing for thefractional contribution (ξ) made by the different individual peaksor parallel first-order reactions.Extensive research has been conducted in an attempt to

understand the devolatilization kinetics of northern hemisphere(Carboniferous) coals, which are normally characterized by theirhigh proportions of vitrinite, large amounts of reactive inertinite,and very low ash contents.40−45 These coals have been shown tobe very different from South African coals, due to their dif-ferences in depositional environment.46−48 In contrast, Permianaged Gondwanaland coals are mainly rich in inertinite with a highabundance of minerals, while some coal deposits (Grootegelukand Venda-Pafuri districts) also display higher abundances ofvitrinite-rich coals. Although very limited, investigations such asthose conducted by Aboyade et al.49 have provided a means ofdescribing the devolatilization behavior of some South Africancoals. However, this work did not include the evaluation of anydecomposition reactions below 200 °C, therefore neglecting therelease of inherent moisture, crystal water, and amorphousphases from the coal particles.An investigation was therefore undertaken to gain a better

understanding of the kinetic behavior of four typical SouthAfrican coals (including for the release of moisture). Evaluationof the devolatilization behavior of the selected coals entailed thedetermination of the total mass loss behavior of the amount ofvolatile matter and not of individual species. Mass loss behaviorduring devolatilization was therefore described at the hand of thepseudocomponent modeling approach as proposed by Alonsoet al.28 Kinetic parameters derived using this approach can beultimately used in the evaluation of large particle devolatiliza-tion models (including for heat and mass transport effects) foreffectively describing commercial coal conversion processes.This paper therefore aims to provide a comprehensive kineticdescription of a variety of South African coal types, ranging fromdifferences in maceral composition to differences in swellingbehavior.

2. EXPERIMENTAL SECTION2.1. Coal Selection. Four coals were selected from South African

collieries: three noncaking coals originating respectively from theWitbank no.2 (INY), 4 (UMZ), and 5 (G#5) seams and one coking coal(TSH) originating from the Venda-Pafuri sector of the Soutpansbergcoalfields.50 The three noncoking coals were beneficiated samples fromthe respective mines, while coal TSH was density separated elsewhere.51

The choice of the four coals was based on their (1) similarity inbituminous rank, (2) varying vitrinite content, (3) relatively low ashcontent (<20 wt.% d.b.), and (4) their difference in seam origin. All fourcoals were characterized according to standard chemical and petro-graphic methods of which details are provided in Tables 1 and 2,respectively.51

2.2. Experimental Method. Devolatilization rate measurementswere performed on a Mettler-Toledo TGA/DSC 1 STARe small particle,thermogravimetric system. Mass loss measurements were performed atfour different heating rates, by heating the samples under nitrogen fromambient temperature to 950 °C as described in Table 3. The regionbetween the initial- and final temperature was chosen to be representativeof the range of expected coal devolatilization. Nitrogen was used as bothcarrier gas and purge gas and set to a total flow rate (combined flow rate ofcarrier/reactant gas and purge gas) of 1.5 L·min−1 to ensure an inertenvironment and to prevent the secondary cracking of volatiles. Samplemasses of approximately 20 mg, with a particle size distribution ofless than 200 μm, were used in order to reduce the occurrence ofpossible secondary gas−solid reactions as well as the effects of mass- and

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intraparticle heat transfer.37,49,57,58 The selection of these experimentalconditions were based on preliminary runs and ranges obtainedfrom investigations conducted on the devolatilization of a largenumber of different solid fuels including biomass and coal.28,37,49,57,59,60

2.3. Kinetic Modeling and Analysis. Kinetic modeling of coaldevolatilization was based on the rate equation for solid statedecomposition, which can be formulated as61−63

= − · −Xt

k E RT Xdd

exp( / ) (1 )a0 (1)

In eq 1 X represents the fractional conversion (-), k0 is the pre-exponentialconstant (s−1), Ea is the activation energy (kJ·mol

−1), R is the universal gasconstant, t is the time (s), and T is the temperature (K). The fractionalconversion, X, was derived with the aid of the following equation:37,49

=−−

Xm mm m

t0

0 f (2)

In eq 2 m0 represents the initial sample mass (mg), mt is the timeconstrained sample mass (mg), and mf is the final sample mass afterdevolatilization (mg). Devolatilization of the four coals was assumed tofollow a pseudocomponent decomposition mechanism, which could bedescribed by multiple independent parallel reactions corresponding tothe amount of pseudocomponents.28,49,62,64 In this respect the termpseudocomponent refers to a group of reactive species exhibiting similarreactivity.49,62 The formulation of an appropriate mathematical modeldescribing the evaporation rate of moisture is a tedious task, and modelssuch as the heat sink model, first-order evaporation rate model, andthe equilibrium model have generally been used.65 In a number ofinvestigations, the evaporation of moisture from the coal matrix isdescribed by an additional first-order reaction expression, due to itsintegratability into the overall kinetic scheme.59,65−67 Using thisassumption, eq 3 can be used for the entire devolatilization process:

∑ ξ= ·−

· −=

⎛⎝⎜

⎞⎠⎟

Xt

kE

RTX

dd

exp (1 )t

i

n

i ia i

i1

0,,

(3)

For nonisothermal TGA measurements the above equation can berearranged by substituting dtwith dT/β (with β the heating rate applied)and integrating as follows

∫ ∫∑ ξβ−

= ·−

·=

⎛⎝⎜

⎞⎠⎟

XX

k E

RTT

d(1 )

exp dX

t

t i

n

ii

T

T a i

0 1

0, ,t

0 (4)

where ξi is defined as the fractional contribution of pseudocomponenti (-), and β is the heating rate (K·s−1). It has been shown that thetemperature integral on the right-hand side has no exact analyticalsolution, but with the aid of integration by parts and substitution it canbe written into49,68

∫ ∫−· = ·

−−

−

=

∞⎛⎝⎜

⎞⎠⎟

⎡⎣⎢⎢

⎤⎦⎥⎥

E

RTT

E

R

y

y

y

yy

yE

RT

exp dexp( ) exp( )

d

with

T

T a i a i i

i y

i

i

ia i

, ,

,

0

(5)

For n amount pseudoreactions eq 6 can therefore be formulated afterintegration as

∫

∑ ξ

β

= ·

× − · ·−

−−

=

∞

⎪ ⎪

⎪ ⎪⎛

⎝⎜⎜

⎧⎨⎩

⎡⎣⎢⎢

⎤⎦⎥⎥⎫⎬⎭

⎞

⎠⎟⎟

X

k E

R

y

y

y

yy1 exp

exp( ) exp( )d

ti

n

i

i a i i

i y

i

i

1

0, ,

(6)

The evaluation of the kinetic parameters for each coal required thenumerical solution of eq 6 with application of the direct integral method.This was accomplished with an appropriate algorithm and the expintfunction in MATLAB 7.1.1. Optimization of the kinetic parameters wasperformed by multidimensional nonlinear regression. This involvedsearching for values of k0,i, Ea,i, and ξi that minimized the objectivefunction (OBF) as formulated in eq 7.

∑ ∑= −

= =

= =

⎡⎣⎢⎢⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥OBF

Xt

Xd

N N

dd

dt

with 4, 200

k

N

m

Nt

k m

t

calc k m

k m

1 1 exp , , , ,

2k m

(7)

In addition, eqs 6 and 7 were applied to the differential TG data (DTG),mainly due to the fact that small changes in the features and peaks of thecorresponding TGA curves are magnified when using DTG, which easesthe identification of kinetics.49,68−72 Initial estimates for the kineticparameters algorithm were scaled and based on ranges published in

Table 1. Maceral Composition of the Four Coals51

maceral composition(vol.%, m.m.f.b.)a

coalsamples

vitrinite %

inertinite %

liptinite %

vitrinite reflectanceb

mean Rr%

INY 37 60 3 0.81UMZ 25 72 3 0.81G#5 60 30 10 0.61TSH 69 30 1 1.23

aAnalyses conducted according to ISO 7404-3.52 bAnalyses conductedaccording to ISO 7404-5.53

Table 2. Chemical Properties of Raw Coal Samples51

elemental analysis (wt.%, d.a.f.)a proximate analysis (wt.%, d.b.)

coal samples FSI C H Ob N S atomic H/C ratio ash %c VM %d FC %e

INY 1.0 81.2 4.7 10.0 2.0 2.1 0.69 18.6 25.5 55.9UMZ 0.5 83.8 4.3 11.5 2.1 1.0 0.62 15.2 25.2 59.6G#5 0.5 79.2 5.5 12.1 2.3 0.9 0.83 13.5 34.1 52.4TSH 9.0 90.8 5.0 1.2 2.1 0.9 0.66 17.8 20.5 61.7

aAnalyses conducted according to ISO12902.54 bAnalyses conducted according to by difference. cAnalyses conducted according to SABS ISO1171.55 dAnalyses conducted according to SABS ISO 562.56 eAnalyses conducted according to by difference.

Table 3. Experimental Methodology

variable experimental range or composition

coal feed stocks INY, UMZ, G#5, and TSHcoal particle size <200 μmoven program Heat to 30 °C at 1 K/min and isothermal for 5 min. Heating

at specified heating rate to 950 °C and isothermal for 30min.heating rates 5, 10, 25, and 40 K/minoperatingpressure

atmospheric pressure (∼89 kPa)

gas medium used nitrogen, ultra high purity grade, ≥99.99%total gas flow rate 1.5 L/minsample mass ∼20 ± 2 mgrepeatabilitytests (repeats)

5 K/min (3), 10 K/min (2), 25 K/min (2) and 40 K/min (1)



literature.37,49,68 Furthermore, the validity of the predicted model valueson the quality of fit (QOF) of the experimental data was evaluated withthe aid of eq 8 for each heating rate as well as for the overall process:

∑= ×−

| |

==

QOFX t X t N

X t

N

(%) 100[(d /d ) (d /d ) ] /

max d /d

with 200

m

Nt m t calc m m

m

m

1

exp , ,2

exp ,

m

(8)

The basic structure of the MATLAB algorithm used for solvingthe necessary equations and evaluating the kinetic parameters issummarized in Figure 1. TGA results from multiple heating rates (4 inthis case) are provided as input to the algorithm in the form of tem-perature (K) and mass fraction loss. The MATLAB 7.1.1 algorithmconverts the input data to the rate of devolatilization (dXt/dt) (DTGcurve) as well as fractional conversion (Xt) for each heating rate.Hereafter, the subsequent converted data is filtered with the aid of theSavitzky-Golay filter (polynomial order of 4 and frame size of between9 and 21) in order to remove any systematic noise from the calculated

DTG curves. Savitzky-Golay parameters were chosen according to thesuggestions made by Caballero and Conesa.68 Evenly spacedexperimental DTG points were selected for each heating rate andused for parameter estimation. This simultaneous, multiple, nonlinearregression of different heating rate DTG data has been widely used andrecommended for assistance in the breakage of the kinetic compensationeffect.37,49,68,73 For this particular investigation the amount of variables(i.e., ξi, k0, and Ea) ranged from 9 for the 3 pseudocomponent models to24 for the 8 pseudocomponent parameter estimations.

The Levenberg−Marquardt optimization algorithm was chosen forregression of the kinetic parameters/variables from the DTG curve withthe aid of the lsqcurvef it function in the MATLAB 7.1.1 optimizationtoolbox.68 A “for loop” was included to generate a large number ofdifferent initial values from the user specified values, by incrementallyscaling the user specified values with the for-loop counter.68 Within the“for-loop”, curve fitting was done in two steps by gradually decreasingthe values of the solver tolerances (from 1 × 10−8 to 1 × 10−10 for theindependent variable tolerance, “TolX”) (constraint 1). The latter two

Figure 1. MATLAB algorithm used for solving kinetic parameters.



measures were included in the algorithm in order to increase theprobability of an adequate model fit (reduced under fitting or over fittingof certain zones of the TG profile) with the use of a variety of distributedinitial values. Initial values were specified for i-1 of the assumed pseudo-components, while the estimation of the fractional contribution of theith pseudocomponent was constrained to the following conservationstatement (constraint 2):

∑ξ ξ= −=

−

1ij

i

j1

1

(9)

Solved kinetic parameters obtained from the Levenberg−Marquardtroutine were stored in a solution matrix for optimization. From thismatrix the optimum kinetic parameters were selected via a two-step“for loop − if statement” selection procedure. Parameters of whichξn > 0 (constraint 3) and which yielded the lowest residual error sum ofsquares (constraint 4) were selected as the optimum values fordescribing the kinetic behavior. Finally, the optimum values were usedfor model estimations and compared to the experimental TG and DTGcurves. The number of pseudoreactions necessary to accurately describethe devolatilization behavior of each coal was based on the improvementin the QOF of not only the individual heating rate data but also that of

the overall process. The number of pseudocomponents used was limitedto eight, as larger values could induce the risk of over fitting the ex-perimental rate data.49,74 CPU time varied from less than 3 min for the 3pseudocomponent modeling evaluations to close to 2 h for the 8pseudocomponent modeling evaluations, depending on the coal samplestudied. (For further reference to the model algorithm, the reader isreferred to the Supporting Information.)

3. RESULTS AND DISCUSSION

3.1. Small Particle Devolatilization Behavior. A compar-ison between the normalized mass versus temperature (°C)curves of the 5 K/min and 40 K/min experiments is provided inFigure 2 for the four coals (similar trends were observed for theother two heating rates). For all four heating rates the TGAprofiles showed a monotonic weight decrease with increasingtemperature, while the first noticeable change in mass wasobserved at temperatures below 150 °C. The latter has beenattributed to the presumable loss of absorbed moisture andoccluded gas.14,28,43,75−77 For temperatures confined betweenapproximately 110 and 350 °C, only slight changes in the loss of

Figure 2.Normalized mass versus temperature (TGA) results from the devolatilization of the four coals at a.) 5 K/min and b.) 40 K/min, respectively.

Figure 3. DTG profile comparison for coal devolatilization at the four different heating rates.



mass were observed and have been found to correspond to theevolution of both colloidal bound water (110−200 °C) andsecondary pyrolytic water (200−350 °C) generated from thethermal decomposition of minerals, phenolic-, carboxyl-, andcarbonyl groups.43

Accompanying this is the decomposition of peripheral partsof the molecular phase, which comprises mainly of polycyclicaliphatic compounds, at temperatures below 350 °C.41 Above350 °C, the TGA profiles are characterized by a significantdecrease in initial coal mass, which involves the thermal de-composition of aromatic compounds of different chemicalstructures (normally in two main regimes), present in the coal,to form tars and gases.14,41,78−83 The largest amount of volatilematter (moisture and volatiles) was generated from coal G#5(∼34.1 wt.%, d.b.), followed by coals UMZ and INY (∼25.2 wt.%,d.b. and 25.5 wt.%, d.b., respectively), while coal TSH containedthe least amount of volatile matter (∼20.5 wt.%, d.b.). Goodagreement was therefore obtained between these results andthose established from proximate analyses (Table 2). In addition,reproducibility measurements, performed on all coals, werefound to be very satisfactory with experimental errors notexceeding more than 0.2%. Similar orders of magnitude forexperimental error were also found during trial runs conductedduring the development of the appropriate TGA heating methodas summarized in Table 3 (i.e., initial heating period andtemperature, heating rate selection, and reactant gas flow rate).For a more pronounced comparison between coals subjected

to devolatilization, numerous authors have proposed theadditional use of the time derivative of the TGA results insteadof only the TGA profile.68−71 The corresponding DTG curves,shown as a function of temperature, are provided in Figure 3. Inaddition, to aid in the qualitative description of the DTG results,some characteristic peaks have been derived from the respectivecurves and are annotated in Figure 3.From a qualitative point of view, the DTG profiles showed

striking differences for the different coals. DTG results of the fourcoals were characterized by two distinct peaks; one at a tem-perature lower than 200 °C (P1) (to a very low extent for coalTSH) and the other in the temperature range between 400 and500 °C (P2). These peaks were shown to be representative of theevolution of moisture and primary degradation, respectively. Attemperatures exceeding 500 °C, two additional peaks (P3 andP5) were evident for coal UMZ, while three points of localmaxima could be observed for coal INY (P3, P4, and P5). Incontrast, however, the DTG profiles of coals G#5 and TSHexhibited only an additional low intensity peak (P5) in the rangefrom 700 to 850 °C. It is evident from Figure 3 that a significantshift in the main devolatilization zone (P2) was observed for coalTSH in comparison to the other coals, which could possiblybe attributed to the extensive thermoplastic nature of this coal(as depicted by the high free swelling index (FSI) in Table 2).According to Cai et al.,41 the main reaction zone (primarydevolatilization) is dominated by depolymerization reactionsleading to the formation of tars and gases. Furthermore, thesedecomposition reactions are continuously in competition withrepolymerization or cross-linking reactions controlling theformation of char. In contrast, the subsequent shift in the mainreaction region of coal TSH could have been the result of aretarded effect on the depolymerization reaction mechanismdue to repolymerization (cross-linking) reactions controlling thedevolatilization rate mechanism of this coal after Metaplastformation. A closer examination of P5 in the DTG profilesrevealed that the occurrence of this peak was much more

prominent for the inertinite-rich coals (UMZ and INY) than forthe vitrinite-rich coals (G#5 and TSH), suggesting a substantialdifference in the reaction mechanism toward the end ofdevolatilization. According to Cai et al.,41 the diminishing pres-ence of the last stage of devolatilization could be ascribed to adepletion of aliphatic structures, oxygen-containing function-alities as well as other thermally unstable molecular function-alities. The sharp increase in the reaction rate of P5 for INY andUMZ could therefore be the result of some previously thermallystable bonds being broken to form secondary char in the highertemperature regime. A comparison of the effect of heating rate(see the Supporting Information for further reference) on coaldevolatilization revealed that the TGA profiles of each coalshifted to the right (although only slightly) with increasing heatingrate, thus providing evidence of the kinetic compensation effectnormally observed during variable heating rate TG measure-ments.49,68,75,77

Investigations involving the evaluation of devolatilizationkinetics of coals and/or biomasses have attributed this delay(thermal lag) in thermal decomposition of samples to differencesin heat transfer and kinetic rates.75,84,85 In general, the mass lossrate was found to be the highest for peaks P1, P2, and P3 of coalG#5, followed by coals INY and UMZ, while the lowest valueswere determined for coal TSH. At higher temperatures, mass lossrates were found to be the highest for the two inertinite-richcoals. The significant difference in mass loss reactivity (inparticular for the main devolatilization zone) between thedifferent coals can also be related to substantial differences in coalstructural properties. From this perspective, the highly reactivenature of coals G#5 and TSH can be attributed to the presence ofmore reactive material (vitrinite, and especially the substantialamount of liptinite present in coal G#5), while the slowerthermal decomposition rate of the inertinite-rich coals stronglyagrees with their exceptional high amount of inert material (inert

Table 4. Quality of Fit or Percentage Deviation for theSimulated Rate Curves

QOF (number of pseudocomponent reactions)a

coalsamples

heatingrate 3 4 5 6 7 8

INY 5 K/min 9.84 8.31 7.06 5.44 4.26 3.8410 K/min 7.02 5.54 4.81 3.45 2.52 2.3325 K/min 3.94 2.74 2.76 2.22 2.04 1.7440 K/min 3.40 2.46 2.13 1.71 1.45 1.25Overall 6.05 4.76 4.19 3.21 2.57 2.29

UMZ 5 K/min 14.10 10.50 8.90 6.58 5.65 4.8810 K/min 9.27 6.94 5.37 3.94 3.40 2.7525 K/min 4.81 3.20 2.46 2.25 2.16 1.8540 K/min 3.65 2.68 2.12 1.77 1.58 1.01Overall 7.97 5.82 4.72 3.63 3.20 2.62

G#5 5 K/min 8.48 6.67 4.97 4.68 4.01 3.4610 K/min 5.62 4.09 3.26 2.96 2.46 2.1125 K/min 3.10 2.12 1.92 1.67 1.54 1.5040 K/min 2.81 1.87 1.55 1.13 1.03 0.90Overall 5.00 3.68 2.93 2.61 2.26 1.99

TSH 5 K/min 7.41 6.13 4.94 4.33 4.07 4.1210 K/min 5.08 4.44 3.54 3.27 2.96 2.9325 K/min 2.91 2.25 1.95 1.90 1.63 1.4940 K/min 2.84 2.02 1.75 1.68 1.21 1.04Overall 4.56 3.71 3.05 2.80 2.47 2.40

aEstimated from the experimental data according to eq 8.



inertodetrinite contents ranged between 13 and 15 vol.%,m.m.f.b., while inert semifusinite contents were found to bebetween 22 and 27 vol.%, m.m.f.b.) when compared to the othertwo coals (inert inertodetrinite and inert semifusinite contents ofclose to 7 vol.%, m.m.f.b. and 10 vol.%, m.m.f.b. respectively).Rate profiles and systematic trends observed in this investigationshowed excellent agreement with findings made by Aboyade

et al.,37,49 Seo et al.,75,84 Wang et al.,77 and Zhang et al.45 duringnonisothermal devolatilization studies on coals and/or bio-masses.

3.2. Kinetic Modeling and Curve Fitting Results. Kineticmodeling was performed on all TGA data by applying thestrategy as outlined in the Experimental Section. Kinetic analysiswas performed by varying the number of pseudocomponents

Figure 4. Simulated reaction rate curves for coal UMZ based on the first order model of a.) 3, b.) 4, c.) 5, and d.) 8 pseudocomponents.

Figure 5. Simulated reaction rate curves for coal G#5 based on the first order model of a.) 3, b.) 4, c.) 5, and d.) 8 pseudocomponents.



between 3 and 8, with the number of pseudocomponentsrepresenting the number of independent parallel reactions.28,49 Amaximum number of 200 initial value subsets were provided asinput to the Levenberg−Marquardt algorithm, in order to solvethe required kinetic parameters. Table 4 summarizes the qualityof fit (QOF) values determined separately for each heating rate

during the kinetic analyses as well as the global QOF for all fourheating rates (5−40 K/min) combined. Graphical comparisonsbetween the experimental and modeled DTG curves for all fourcoals are provided in Figures 4, 5, 6, and 7, respectively. Modelvalidations, assuming only three, four, five, and eight pseudo-components, of the 25 K/min and the 40 K/min experiments

Figure 6. Simulated reaction rate curves for coal INY based on the first order model of a.) 3, b.) 4, c.) 5, and d.) 8 pseudocomponents.

Figure 7. Simulated reaction rate curves for coal TSH based on the first order model of a.) 3, b.) 4, c.) 5, and d.) 8 pseudocomponents.



have been included for illustrative purposes in Figures 4, 5, 6,and 7. Similar trends were observed for the other two heatingrates (refer to the Supporting Information).From Table 4 it is clear that the assumption of three pseudo-

components resulted in relatively poor global QOF values(4.56%−7.97%), while a further increase in the amount ofassumed pseudocomponents resulted in a remarkable enhance-ment of both the individual- and global QOF values (overallQOF values of 1.99%−2.62% for eight pseudocomponents).This is also evident in the graphical representations provided inFigures 4, 5, 6, and 7, which show better reproduction of therespective experimental DTG curves for increasing amounts ofassumed pseudocomponents. Simulation of higher values ofpseudocomponents (7 and 8) did, however, require longercomputational times and provided only minor improvements inthe quality of fit in some cases. Incidentally this does not restrictthe use of more pseudocomponents to obtain a more refineddescription of the devolatilization behavior of the different coals.For future investigations it is highly recommended that theoptimum amount of pseudocomponents, used for devolatiliza-tion modeling, be selected based on a minimum for the value ofthe fractional contribution of each pseudoreaction. A typicalmethodology used to eradicate the occurrence of spuriouspseudocomponents (that do not significantly contribute to theoverall TG profile) can be found in Caballero and Conesa.86 Inaddition, the aforementioned results showed good agreementwith findings made by Aboyade et al.49 An evaluation of the effectof experimental reproducibility on the QOF yielded very similarresults (less than a 0.5% difference) as to those summarized inTable 4. This therefore suggests that the experimentalreproducibility (repeatability experiments) had a negligible effecton the estimation of QOF values.Further examination of the modeling results provided in

Table 4 revealed that significantly better fit qualities (global andindividual) were obtained for the vitrinite-rich coals whencompared to the results obtained for the inertinite-rich coals.This can be attributed to the fact that the DTG curves of thevitrinite-rich coals are not characterized by the presence of wellresolved reaction peaks confined to temperature ranges exceed-ing ∼500 °C, which eased peak deconvolution. Although theassumption of 4 pseudoreactions produced relatively poorQOF values, the assumption was consistent with generallyaccepted decomposition mechanisms for coal as proposed byAlonso et al.,28 Serio et al.,14 and Van Heek and Hodek.87

Additionally, the description of inertinite-rich coal decom-position required further deconvolution of the secondarydevolatilization regime (above 500 °C) to obtain adequateimprovements in the fit quality, while the model predictionsfor the vitrinite-rich coals showed reasonable good fits foronly 4 pseudocomponents due to the less prominent nature ofsecondary reaction components when compared to theinertinite-rich coals.This postulation therefore suggests that secondary reactions

play a progressively larger role in the devolatilization mechanismof inertinite-rich coals compared to that of vitrinite-rich coalswhere devolatilization is concentrated largely in the primarydevolatilization regime as seen from the large contribution ofthe deconvoluted peak in the 350−550 °C temperature range.Furthermore, a decrease in heating rate resulted in thedeterioration of the subsequent QOF values as observed fromTable 4. For all four coals it was evident that QOF values for thelower heating rates (5 and 10 K/min) were substantially higherthan those estimated for 25 K/min and 40 K/min, which could

be ascribed to the simultaneous fitting of kinetic parameters tothe different heating rates. This is consistent with findings madeon the devolatilization of biomasses and/or coals by Aboyadeet al.49 and Branca et al.88 According to Branca et al.,88 thedisparity in the QOF values between different heating rates canbe explained by the fact that the complex structure of bothbiomasses and coal consist of more components that can bephysically envisaged by kinetic models. In other words, better fitqualities can be obtained by assuming a larger number ofpseudocomponents during multicomponent analysis, which hasbeen found to be particularly true for lower heating rates wherethe probability of better separation into individual componentreactions exists.37 Consequently, in order to achieve similar levelsof fit as higher heating rates, multicomponent kinetic analysis oflower heating rates necessitates the assumption of morepseudocomponents. For higher heating rates (in the range of100−1000 K/min) adequate model simulation/fitting toexperimental data might be possible using the kinetic parametersderived in this investigation. Caution should however be taken asexperimental results obtained from substantially higher heating

Table 5. Kinetic Parameters Determined for All Four CoalsAssuming 8 Pseudocomponent Reactions

8 reactionsa

inertinite-rich coals vitrinite-rich coals

kineticparameter coal INY coal UMZ coal G#5 coal TSH

Ea1 (kJ/mol) 24 ± 0.7 26 ± 0.8 26 ± 0.9 27 ± 1.0

k0,1 (s−1) (1.7 ± 0.5) ×

101(3.6 ± 0.1) ×101

(3.5 ± 0.1) ×101

(6.0 ± 0.2) ×10°

ξ1 (-) 0.05 ± 0.01 0.06 ± 0.01 0.07 ± 0.01 0.03 ± 0.01

Ea2 (kJ/mol) 82 ± 2.3 34 ± 1.1 54 ± 1.8 115 ± 4.5

k0,2 (s−1) (6.4 ± 0.2) ×

103(1.9 ± 0.1) ×100

(4.2 ± 0.1) ×102

(2.3 ± 0.1) ×107

ξ2 (-) 0.09 ± 0.01 0.05 ± 0.01 0.03 ± 0.01 0.04 ± 0.01

Ea3 (kJ/mol) 192 ± 5.3 176 ± 5.5 171 ± 5.6 170 ± 6.6

k0,3 (s−1) (5.6 ± 0.2) ×

1011(3.7 ± 0.1) ×1010

(2.2 ± 0.2) ×1010

(8.0 ± 0.3) ×1010

ξ3 (-) 0.23 ± 0.01 0.27 ± 0.01 0.42 ± 0.01 0.06 ± 0.01

Ea4 (kJ/mol) 194 ± 5.4 197 ± 6.2 190 ± 6.3 223 ± 8.7

k0,4 (s−1) (1.3 ± 0.1) ×

1011(1.7 ± 0.1) ×1011

(7.6 ± 0.3) ×1010

(1.5 ± 0.1) ×1013

ξ4 (-) 0.12 ± 0.01 0.13 ± 0.01 0.14 ± 0.01 0.37 ± 0.01

Ea5 (kJ/mol) 163 ± 4.5 187 ± 5.9 163.71 ± 5.39 236 ± 9.2

k0,5 (s−1) (1.5 ± 0.1) ×

108(5.9 ± 0.2) ×109

(2.0 ± 0.1) ×108

(2.2 ± 0.1) ×1013

ξ5 (-) 0.13 ± 0.01 0.10 ± 0.01 0.11 ± 0.01 0.17 ± 0.01

Ea6 (kJ/mol) 176 ± 4.9 178 ± 5.6 151 ± 5.0 184 ± 7.2

k0,6 (s−1) (1.5 ± 0.1) ×

108(3.0 ± 0.1) ×108

(4.3 ± 0.1) ×106

(1.6 ± 0.1) ×109

ξ6 (-) 0.12 ± 0.01 0.10 ± 0.01 0.11 ± 0.01 0.09 ± 0.01

Ea7 (kJ/mol) 182 ± 5.0 175 ± 5.5 175 ± 5.8 107 ± 4.2

k0,7 (s−1) (2.2 ± 0.1) ×

107(1.2 ± 0.1) ×107

(8.4 ± 0.3) ×106

(1.2 ± 0.1) ×103

ξ7 (-) 0.18 ± 0.01 0.21 ± 0.01 0.09 ± 0.01 0.17 ± 0.01

Ea8 (kJ/mol) 141 ± 3.9 138 ± 4.4 244 ± 8.0 181 ± 7.0

k0,8 (s−1) (1.7 ± 0.1) ×

104(2.1 ± 0.4) ×104

(1.6 ± 0.1) ×109

(1.3 ± 0.1) ×108

ξ8 (-) 0.07 ± 0.01 0.09 ± 0.01 0.03 ± 0.01 0.06 ± 0.01

OBFb 1.5 × 10‑6 1.4 × 10‑6 2.2 × 10‑6 4.4 × 10‑6

Overall QOFc 2.3 2.6 2.0 2.4aKinetic parameters evaluated by the Levenberg−Marquardt algorithmaccording to eq 6. bObjective function (OBF) evaluated according toeq 7. cGlobal/overall quality of fit evaluated according to eq 8.



rates (in the range of 100−1000 K/min) may suffer from manyexperimental errors due to mass- and heat transfer effects.89

An overview of kinetic parameters (ξi, Ea,i, and k0,i) derivedfrom multicomponent kinetic analysis of the different coals isprovided in Table 5 for coals INY, UMZ, G#5, and TSH,respectively. The table includes only the kinetic results for theassumption of 8 pseudocomponents as well as the respectivevalues obtained for OBF and QOF (values for the assumption of3, 4, 5, 6, and 7 pseudocomponents were also determined but arenot included).From the table it is evident that 6 pseudocomponent reactions

(reaction 1 for INY, reaction 2 for UMZ, reactions 2 and 8for G#5 and reactions 1 and 2 for TSH) might be classified asspurious reaction components due to their remarkable lowcontribution (≤0.05) to the overall TG profile of each coal. It is,however important to note that for pseudoreaction 1 of coal TSHand INY, inherent moisture values were found to be 0.7 wt.%,a.d.b. and 2.1 wt.%, a.d.b., respectively, from which it is expectedthat fractional contributions would be in the range of 0.05. Forthe third pseudocomponent reaction of coals UMZ, TSH, andG#5 the fractional contributions ranged between 0.03 and 0.05.The occurrence of these pseudocomponent peaks within thetemperature range between 300 and 400 °C has been previouslyobserved by Serio et al.14 and has been attributed to the simul-taneous vaporization and transport of so-called “guest-molecules”(molecular phase) within the coal matrix during devolatilization. Inaddition, the occurrence of a pseudocomponent peak in thepreviously mentioned temperature regime could also have been theresult of crystal water being released from inherent mineral forms(clays or aluminum silicates) during thermal decomposition.28

Similar to the other three coals, modeling results for coal TSHshowed the occurrence of a pseudocomponent (with a smallfractional contribution) in the temperature range exceeding 800 °C.From a mechanistic point of view, this can be explained by the finalrepolymerization and restructuring of the formed char, possiblyaccompanied by a very small release of H2 due to aromatic ringcondensation, depletion of aliphatic structures, and the decom-position of thermally unstable bonds.40

A comparison between the results presented in Tables 5revealed that activation energies typically ranged between 22 and

244 kJ/mol for the different coals, with the lowest activationenergies (22−29 kJ/mol) confined to the deconvoluted peak(for 4 pseudocomponents and higher), which has been pre-viously attributed to the formation of moisture and the evolutionof the so-called molecular phase.14,28,43,75−77 Although theassumption of describing water evolution as a first order chemicalreaction is questionable, the reported activation energies for mois-ture evaporation showed good agreement with results reported inthe literature (27.6 and 26.6 kJ/mol, respectively).67,90

Furthermore, from Table 5 it is evident that reportedactivation energies showed similar orders of magnitude for thedifferent coals and number of pseudocomponents, althoughsubstantial differences in fractional contributions were found.The apparent similarity observed in the order of magnitude ofactivation energies suggests in some cases that the possibilityexists that a set of intrinsic kinetic parameters (k0,i and Ea,i) can atleast be derived for a portion of the pseudocomponents andcould be of interest for future investigations emanating from thisinvestigation. Reaction processes requiring lower activationenergies showed higher fractional contributions to the overallrate of coals TSH and G#5 (0.37 and 0.42, respectively) com-pared to those of coals INY and UMZ (0.23 and 0.27,respectively). Researchers have often questioned the relativelylow orders of magnitude for reported activation energies of coaldevolatilization (lower than 209 kJ/mol) due to the fact thattypical energies for the cleavage of single carbon bonds normallyrange between 335 and 420 kJ/mol.5 Authors such as Yue5 haveattributed this discrepancy to the fact that activation energies forthe thermal decomposition/devolatilization of organic hetero-geneous material, such as coal, cannot be interpreted in terms ofspecific bond-breaking processes but should rather be seen as aunique set of kinetic parameters representative or descriptive of aset of reactive species exhibiting similar reactivity.49 This is inaccordance with findings by Anthony and Howard91 and Juntgenand Van Heek,92 which showed that both the computed activa-tion energy as well as the pre-exponential constant was sub-stantially smaller when a single first order expression is used todescribe a set of overlapping, parallel, independent first orderreactions. In addition, it has been proposed by Suuberg93 that thefactor largely responsible for the observation of low apparent

Table 6. Comparison of Evaluated Kinetic Parameters with Those Reported in the Literature

kinetic parameters

reference type of solid fuel model usedb Ea (kJ/mol) k0 (s‑1) n (-)

this investigation coal MPRM 24−244 1.9 × 100−2.2 × 1013 1.0Aboyade et al.49 coal and biomass MPRM 38−360 7.1 × 102−3.5 × 1017 1.0−6.0Ahmaruzzaman and Sharma40 vacuum residue, coal, plastics, Petrocrop MPRM 11−153 1.1 × 10°−6.5 × 107 0.0−4.0Biswas and Sharma95 oil, vacuum residue, HDPE MSRM 37−297 7.7 × 101−4.7 × 1021 0.0−4.0Biswas and Sharma96 oil ICM 100−244 N/A -Alonso et al.28 coal MPRM 27−224 1.0 × 10°−1.2 × 1016 1.0Cai et al.41 coal and plastic MPRM 36−559 1.6 × 103−1.0 × 1040 1.0Dhumal and Saha42 coal DAEM 120−295 1.0 × 105−5.7 × 1016 1.0Guruz et al.15 coal SRM 14−21 6.0 × 10°−5.1 × 105 2.1−30.6Lazaro et al.9 coal MPRM and DAEMa 189−264 N/A 1.0Sadhukhan et al.97 coal DAEM 194−206 5.1 × 1010−6.0 × 1011 1.0Sharma and Ghoshal98 coal, LDPE NOM 188−195 1.5 × 1013−2.6 × 1013 0.3−2.8Sutcu43 peat/coal MSRM 11−109 5.2 × 10−2−1.1 × 102 1.0Wiktorsson and Wanzl44 coal MPRMa 26−239 3.8 × 101−5.1 × 107 1.0−2.0Zhang et al.45 coal MPRM 155−245 3.8 × 106−3.9 × 107 N/AZhang et al.99 lignite DAEM 100−827 3.8 × 107−1.6 × 1028 1.0

aKinetic parameters evaluated based on gaseous and liquid components. bModel abbreviations - DAEM: distributed activation energy model,MPRM: multiple, parallel reaction model, MSRM: multiple stage reaction model, NOM: nth order model, and SRM: single reaction model.



activation energies could be attributed to the possible existenceof a set of concerted and/or radical reactions. From this perspec-tive, it has been established that activation energies may bereduced to as low as 21−42 kJ/mol when a radical reactionmechanism is adopted.5,94 Furthermore, it can be seen fromTable 5 that the derived kinetic parameters (Ea,i and k0,i) for allfour coals could be linearly correlated with the isokinetic effect,which suggests that high Ea,i values generally correspond to highk0,i values.

37,49 Although the kinetic compensation effect isintrinsic to the Arrhenius expression, large systematic errors inthe prediction of the kinetic parameters might have beenobtained if parameter regression was only performed on the TGresults from a single heating rate. The use of multidimensional(or multiple heating rate) regression has, however, ensured thatthe kinetic compensation effect is extensively minimized.68

Table 6 summarizes the ranges of kinetic parameter values asobtained from this investigation as well as those reported in theliterature for other studies involving the devolatilization of coals.From the table it is therefore evident that the kinetic parametersobtained from this investigation showed excellent agreementwith those established from other studies. A comparison betweenthe results obtained in this study and those obtained frominvestigations done by Alonso et al.28 revealed close resemblancein values obtained for Ea,i and k0,I, while notable differences couldbe observed in the fractional contributions to the overall DTGcurve for especially the inertinite-rich coals. From thisperspective the kinetic results for coals UMZ and INY revealeda significant fractional contribution (ξ7) to the occurrence ofa prominent peak in the temperature region between 700 and900 °C. The prominence of such a peak for northern hemispherecoals could, however, not be found in most of the DTG resultsas presented by Alonso et al.,28 which suggests a substantialdifference in the devolatilization reaction mechanism for SouthAfrican (Gondwanaland) coals. This could possibly be attributedto the fact that South African coals are characterized by sub-stantial amounts of inert material (inert inertodetrintites andinert semifusuinites) having a lower devolatilization rate andhigher thermal stability.41,100,101

4. CONCLUSIONAssessment of the kinetics of devolatilization involved theevaluation of small particle rate behavior (−200 μm) with the aidof nonisothermal thermogravimetry using four different heatingrates (5, 10, 25, and 40 K/min) and a final isothermal tem-perature of 950 °C. TG results obtained at the different heatingrates indicated that an increase in temperature led to a sub-sequent decrease in sample mass, while ultimate volatile yields at950 °Cwere found to decrease in the order G#5 > UMZ > INY >TSH. Further investigation of the respective TG results of eachcoal revealed the division of the overall TG profile into clearregions of mass loss i.e., the release of moisture, occluded gases,and secondary pyrolytic water at temperatures below 350 °C anda main devolatilization regime where the parent coal structuredecomposes to form tars, gases, and char at temperatures ex-ceeding 350 °C. From DTG results it was evident that all fourcoals exhibited a clear, primary peak of devolatilization confinedto the temperature range between 350 and 600 °C, while asubsequent shift in peak temperature occurred for the maximumevolution rate of the main peak of coal TSH.This subsequent shift in peak temperature for coal TSH could

be attributed to both its higher aromaticity (rank) as well asits extensive thermoplasticity, which could have resulted inrepolymerization reactions becoming more favorable in the first

stages of Metaplast formation. In addition, mass loss rate in themain region of devolatilization was found to be significantlylarger for coals G#5 and TSH in comparison to the other twocoals and could be related to the presence of more reactivematerial (vitrinite and especially the substantial amount ofliptinite present in coal G#5) within the organic structures ofcoals G#5 and TSH. Evaluation of the kinetic parametersdescribing the devolatilization behavior of each coal involved thesimultaneous, nonlinear regression of nonisothermal reactionrate data (DTG data) in MATLAB 7.1.1, according to thepseudocomponent reaction modeling approach. From themodeling results it was evident that an increase in the amountof pseudocomponents led to substantial decreases in the QOFparameter, with modeling predictions assuming a total of eightpseudocomponents providing the best description of the experi-mental DTG curves. Estimated activation energies were foundto range between 22 and 244 kJ/mol for the different coals,with the lowest activation energies (22−29 kJ/mol) confined tothe deconvoluted peak (for 4 pseudocomponents and higher)describing the release of moisture during devolatilization. Kineticresults for coals UMZ and INY revealed notable differences infractional contributions confined to the high temperature region(700 to 900 °C), which suggested a substantial difference in thedevolatilization reaction mechanism of inertinite-rich coals.

■ ASSOCIATED CONTENT*S Supporting InformationFigures S1−S.5, MATLAB 7.1.1 algorithm for deriving intrinsickinetic parameters, and references. This material is available freeof charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Phone: +27 82 767 9945. E-mail: [email protected] author address: Sasol Group Services (Pty) Ltd.,SHE PSS, Process Safety, Private Bag X1000, Secunda, 2302,South Africa.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors would like to acknowledge and thank the followingparties: Sasol for financial support, Anglo Coal and Exxaro forproviding the necessary coal samples, and Dr. Marion Carrier(University of Stellenbosch) for her valuable inputs regardingcoal devolatilization kinetics. The work presented in this paper isbased on the research supported by the South African ResearchChairs Initiative of the Department of Science and Technologyand National Research Foundation of South Africa (NRF). Anyopinion, finding or conclusion or recommendation expressed inthis material is that of the author(s), and the NRF does notaccept any liability in this regard.

■ NOMENCLATURE

Abbreviationsd.a.f. = dry, ash-free basisd.b. = dry basisFSI = free swelling indexm.m.f.b. = mineral matter free basisOBF = objective functionQOF = quality of fit



http://pubs.acs.org

mailto:[email protected]

Greek symbolsβ = heating rateσ = standard deviation of DAEM distributionξi = fractional contribution of component, i

Roman symbolsEa = activation energyEa,i = activation energy of component ik0 = pre-exponential constantk0,i = pre-exponential constant of the ith pseudocomponentm0 = initial sample massmf = final sample massmt = logged mass at a certain time tNk = number of heating ratesNm = number of DTG experimental pointsR = molar gas constantt = timeT = temperatureX = fractional conversionXi = fractional conversion of the ith pseudocomponentXt = overall fractional conversion of volatiles

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modeling the nonisothermal devolatilization kinetics of typical south african coals

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