Available online at www.sciencedirect.comProceedings

Proceedings of the Combustion Institute 34 (2013) 2461–2469

www.elsevier.com/locate/proci

of the

CombustionInstitute

Characterizing char particle fragmentationduring pulverized coal combustion

Matthew B. Tilghman ⇑, Reginald E. Mitchell

High Temperature Gasdynamics Laboratory, Mechanical Engineering Department, Stanford University, Stanford,

CA 94305, USA

Available online 12 August 2012

Abstract

A particle population balance model was developed to predict the oxidation characteristics of an ensem-ble of char particles exposed to an environment in which their overall burning rates are controlled by thecombined effects of oxygen diffusion through particle pores and chemical reactions (the zone II burningregime). The model allows for changes in particle size due to burning at the external surface, changes inparticle apparent density due to internal burning at pore walls, and changes in the sizes and apparent den-sities of particles due to percolation type fragmentation. In percolation type fragmentation, fragments ofall sizes less than that of the fragmenting particle are produced. The model follows the conversion of par-ticles burning in a gaseous environment of specified temperature and oxygen content. The extent of con-version and particle size, apparent density, and temperature distributions are predicted in time.

Experiments were performed in an entrained flow reactor to obtain the size and apparent density dataneeded to adjust model parameters. Pulverized Wyodak coal particles were injected into the reactor andchar samples were extracted at selected residence times. The particle size distributions and apparent den-sities were measured for each sample extracted. The intrinsic chemical reactivity of the char to oxygen wasalso measured in experiments performed in a thermogravimetric analyzer. Data were used to adjust ratecoefficients in a six-step reaction mechanism used to describe the oxidation process.

Calculations made allowing for fragmentation with variations in the apparent densities of fragmentsyield the type of size, apparent density, and temperature distributions observed experimentally. These dis-tributions broaden with increased char conversion in a manner that can only be predicted when fragmen-tation is accounted for with variations in fragment apparent density as well as size. The model also yieldsthe type of ash size distributions observed experimentally.� 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Fragmentation; Percolation; Coal; Solid; Particle

1. Motivation

The world’s energy demands are projected toincrease well into the 21st century and beyond.

1540-7489/$ - see front matter � 2012 The Combustion Instithttp://dx.doi.org/10.1016/j.proci.2012.07.065

⇑ Corresponding author.E-mail address: mtilghma@stanford.edu (M.B.

Tilghman).

As much of this forecasted rise will occur in devel-oping countries, use of cheap fossil fuels will con-tinue to grow despite environmental concerns.Since fossil fuel combustion, in particular coalcombustion, has a well-documented implicationon climate change and air quality, burning thefuel cleanly and efficiently remains a paramountgoal.

ute. Published by Elsevier Inc. All rights reserved.

Nomenclature

bi,j element i, j of the progeny matrix b,representing size distribution duringfragmentation

Ci,k fraction of particles in bin i, k thatburn out of size-class i due to externalburning

D diameter of particleDi,k fraction of particles in bin i, k that

burn out of density-class k due tointernal burning

DO oxygen bulk diffusion coefficient inparticle boundary layer

kd mass transfer coefficientkfrag fragmentation rate coefficientm particle massbM molecular massNdens number of density classes imple-

mented in modelNi,k number of particles which reside in

size–density bin i, kNsize number of size classes implemented in

modelNu Nusselt numberPi,j,k,m element i, j,k,m of the tensor P; repre-

sents the fraction of particles which[start in size class i, end in size classj, and start in density class k] thatends in density class m

Pg oxygen partial pressure in ambient gasPs oxygen partial pressure at the exterior

particle surfaceR universal gas constantRex external reactivity of the particle (g/

m2/s)Rin internal reactivity of the particle (g/

m2/s)q overall burning rate of the particle (g/

m2/s)Sg specific internal surface area (m2/g)Si,k fraction of particles in size–density

bin i, k which will fragment withintime step dt

Sh Sherwood numberTp particle temperatureTg ambient gas temperatureTw wall temperature to which particles

radiatex conversion fractionxi diameter of size-class i

Greek symbols

DH heat of reactionDqk apparent density difference between

density class k and k + 1Dxi diameter difference between size class i

and i + 1a size sensitivity parameter for

fragmentatione particle emissivityk thermal conductivity of gasc constant factor by which size interval

varies for each size bin, c = xi/xi+1

co change in volume upon reaction perunit oxygen consumed

g effectiveness factor which relatesinternal reactivity to maximum possi-ble internal reactivity

qc apparent density of the carbonaceousmaterial

qk density of density-class kw structural parameter used to fit inter-

nal surface area throughout thecourse of conversion

r piecewise standard deviation of theGaussian distribution used to predictfragment densities

rsb Stephan–Boltzmann constantx density sensitivity parameter for

fragmentationtO moles O2 reacted per mole carbon

reacted

2462 M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469

The efficient burning of any particular fossilfuel relies on accurate characterization of the fuelconversion process so that optimal reaction condi-tions can be identified. This requires the develop-ment of models that accurately predict fuelconversion rates for specified temperature, pres-sure, and gas composition. With porous solidfuels, the models must not only have parametersthat accurately describe the rates of chemicalreactions that consume the carbonaceous materialbut they must also have parameters that accu-rately describe the transport of reactive gasesthrough particle pores as well as parameters that

accurately describe the mode of burning, i.e.,how the size and apparent density of the particlevary with mass loss during the conversion process.Even with accurate chemistry, transport, andmode of conversion models, accurate predictionof mass loss during the combustion of solid fuelswill depend upon the extent of fragmentation dur-ing the conversion process. All coal particles frag-ment to some extent during coal combustion.Fragmentation reduces the particle size, and smallparticles are converted to gaseous species at fasterrates than large particles. Fragmentation occursduring coal devolatilization and during char

M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469 2463

oxidation, fragmentation during devolatilizationpotentially occurring to a greater extent. Despitethe known occurrence of fragmentation duringcombustion, most models of the coal combustionprocess do not include fragmentation duringeither devolatilization or char oxidation. In thispaper, focus is placed on the prediction of frag-mentation during char oxidation under conditionsthat exist in pulverized fuel combustors.

2. Theoretical approach

2.1. Particle population balance model

A model has been developed that is capable ofpredicting overall conversion rates of an ensembleof pulverized coal of biomass char particlesexposed to gaseous environments of specified tem-perature, pressure, and gas composition. The par-ticle population balance model employed buildson our earlier models [1,2] and includes trackingparticles in a size–density matrix, as shown inFig. 1. Each column i represents a certain sizeclass, and each row k represents a certain appar-ent density class. Large particles are representedby large values of i and high apparent density par-ticles are represented by large values of k. In thismodel, the smallest particles (i = 1) and the lowestapparent density particles (k = 1) represent ashparticles. The number of particles in each size–density bin i, k, henceforth referred to as Ni,k, istracked. With each differential time interval dt,the effects of burning and fragmentation maychange particle sizes and apparent densitiesenough to warrant bin change, changing Ni,k.While burning can only change a particle’s sizeclass or density class by one at a time, fragmenta-tion can produce particles that may instanta-neously populate any size–density bin below thatof the fragmenting particle.

The differential equation that governs the vari-ations in the number of particles in each size–density bin with time is given in the followingequation:dNi;k

dt¼�ðCi;kþDi;kþSi;kÞN i;kþCi�1;kN i�1;k

þDi;k�1N i;k�1þXi

j¼1

XNdens

m¼1

bi;jP i;j;k;mSj;mN j;m ð1Þ

Fig. 1. Visualization of the effects of burning andfragmentation.

For Nsize size classes and Ndens density classes,there are Nsize � Ndens similarly structured ODEsthat must be solved simultaneously to track theparticles in each size–density bin. The first termon the right hand side of Eq. (1) accounts for allparticles that leave bin i,k. The variable Ci,k repre-sents the fraction of particles in bin i, k that burnout of the bin per unit time because of a decreasein particle diameter due to external burning, thevariable Di,k represents the fraction of particlesthat will burn out of the bin per unit time becauseof a decrease in apparent density due to internalburning, and the variable Si,k represents the frac-tion of particles that will experience a fragmenta-tion event and leave the size–density bin.

The second and third terms on the right handside of Eq. (1) account for particles that will enterbin i, k due to diameter-related burning in theimmediately larger size class and density-relatedburning in the immediately higher density class.The final term on the right hand side of Eq. (1)accounts for the particles that enter bin i,k due tofragmentation events occurring in all bins, includ-ing itself. Particles can fragment into bin i,k fromany bin of an equal or larger size class. The bi,j areelements of the progeny matrix that describes thesize distribution of a group of fragmenting parti-cles. Element bi,j is the fraction of fragmenting par-ticles in size class i that fragment into size class j.The Pi,j,k,m are elements of the P tensor thatdescribes the density distribution of a group offragmenting particles. Element Pi,j,k,m is the frac-tion of the particles changing from size j to i thatare also changing from apparent density m to k.The fraction of particles in the size–density classj,m that will experience a fragmentation event dur-ing the time interval dt is given by Sj,m. Whensummed over j and m, the final term represents allparticles that enter bin i, k due to fragmentation.

2.2. Char particle burning

We use the same approach taken earlier [1–3]to derive an expression for the overall particleburning rate q per unit external surface area,and then relate the two burning variables Ci,k

and Di,k to q. By differentiating the equation relat-ing particle mass, apparent density and size(m = qpD3/6), the equations for the external andinternal burning rates per unit external surfacearea, Rex and Rin, respectively, can be defined asfollows:

Rex �1

pD2

dmdt

����ex

¼ qc

2

dDdt

and

Rin �1

pD2

dmdt

����in

¼ D6

dqc

dtð2Þ

In terms of the external and internal burningrates, the overall particle burning rate per unitexternal surface area can be expressed as

2464 M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469

q ¼ 1

pD2

dmdt¼ ðRex þ RinÞ ¼ ð1þ Rin=RexÞRex ð3Þ

Employing the concepts put forth by Thiele[4], the internal particle burning rate is related tothe maximum possible internal burning rate byan effectiveness factor g, such that Rin = g Rin,max.The maximum possible rate of internal burningcorresponds to the situation when the particletemperature and oxygen concentration are uni-form throughout the particle, and equal to thoseexisting at the outer surface of the particle. Thisimplies that the maximum possible internal burn-ing rate per unit internal surface is equal to theexternal burning rate per unit external area, andhence

Rin;max

ðp=6ÞD3qcSg¼ Rex

pD2ð4Þ

where Sg is the specific surface area of the carbo-naceous material. Combining the above equationsresults in the following expression for the overallparticle burning rate in terms of the effectivenessfactor and the burning rate at the external particlesurface, which depends on the temperature andoxygen concentration (or partial pressure) existingat the external surface of the particle

q ¼ 1þ gqcSgD6

� �Rex ð5Þ

The overall particle burning rate per unit exter-nal surface area can also be written in terms of theoxygen partial pressure in the ambient gas Pg andthe oxygen concentration at the external particlesurface Ps, as follows:

q ¼ kd Pc

ln1� cP s=P1� cP g=P

� �ð6aÞ

where

kd ¼bM CDOShbRT mDmO

ð6bÞ

This equation assumes spherical, isothermalparticles with no chemical reaction in the bound-ary layer surrounding the particle; account is alsomade for Stefan flow in the boundary layer.Assuming steady-state burning, the particle tem-perature is determined from the following energybalance equation:

qDH ¼ NukD

j1� j

ðT p � T gÞ þ �rðT 4p

� T 4wÞ where j

¼ ccp;gDmOqbM CkNuð7Þ

Account is made for energy losses via conduc-tion, convection, and radiation from the outersurface of the particle and energy generation dueto burning. Equations5, 6a, 6b, 7 permit the deter-

mination of the oxygen partial pressure at theexternal surface of the particle and the particletemperature, given the temperature and oxygenpartial pressure in the particle’s environment,and a path to determine the burning rate at theexternal particle surface, Rex, which depends uponthe rates of chemical reactions on the externalsurface.

We use the following six steps heterogeneousreaction mechanism developed in previous work[5] to describe the effects of chemical reaction:

2Cf þO2 ! CðOÞ þ CO ðR1aÞ2Cf þO2 ! C2ðO2Þ ðR1bÞ

Cb þ Cf þ CðOÞ þO2 ! CðOÞ þ CO2 þ Cf ðR2ÞCb þ Cf þ CðOÞ þO2 ! 2CðOÞ þ CO ðR3ÞCb þ CðOÞ ! Cf þ CO ðR4ÞCb þ C2ðO2Þ ! 2Cf þ CO2 ðR5Þ

In the above mechanism, Cf represents a free car-bon site available for adsorption, Cb represents anunderlying bulk carbon site, C(O) represents anoxygen atom adsorbed onto a carbon site, andC2(O2) represents two adjacent carbon sites, bothhaving adsorbed oxygen atoms. Using this reac-tion mechanism, intrinsic carbon reactivity tooxygen is given by Eq. (8), where RRi stands forthe rate of reaction i

Ri;C ¼ bM CðRR1a þ RR2 þ RR3 þ RR4 þ RR5Þ ð8ÞThe rate of each reaction is written in terms of

the concentrations of the species involved in thereaction and a reaction rate coefficient, which isexpressed in Arrhenius form. Reactions (R1–R3) are approximated as having a single activa-tion energy, whereas the desorption reactions(R4) and (R5) account for a distribution of acti-vation energies due to the range of carbon bind-ing energies present on a real coal char surface.The model does not take into account the impactof thermal annealing on char reactivity. Differen-tial equations based on the mechanism are solvedsimultaneously with the particle population bal-ance model equation to determine the concentra-tions of the adsorbed species on particle surfacesduring char conversion. The total number ofdifferential equations that are solved simulta-neously is 3 � Ndens � Nbin, tracking Ni,k, C(O)i,k,and C2(O2)i,k.

In environments containing small amounts ofCO (as in this study), the reaction mechanism pre-dicts a char conversion rate that is almost firstorder in the oxygen concentration. Accordingly,we use the concepts put forth by Thiele [4] todetermine the effectiveness factor from the Thielemodulus assuming first order kinetics.

The specific surface area of the carbonaceousparticle material, Sg, must also be trackedthroughout the course of burning. We use Eq.

M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469 2465

(9) to follow the specific surface area with charconversion; the structural parameter w is deter-mined by fitting surface areas measured duringthe course of oxidation, as described in previouswork [5]. This surface area model is consistentwith the one developed by Bhatia and Perlmutterto follow surface area during carbon conversion[7]

Sg ¼qc;0

qcSg;0ð1� xÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� w lnð1� xÞ

pð9Þ

The variables Ci,k and Di,k in Eq. (1) are calcu-lated via Eqs. (10) and (11). In these equations,Dxi and Dqk are the size-class and density-classspacing, respectively

Ci;k ¼1

Dxi

dDdt

� �i;k

wheredDdt¼ 2Rex

qcð10Þ

Di;k ¼ qc1

Dqk

dqc

dt

� �i;k

wheredDdt¼ 6Rin

D¼ gqcSgRex ð11Þ

2.3. Particle fragmentation

As shown previously [2,7], the type fragmenta-tion that occurs during char oxidation is percola-tion, in which the fragmenting particle producesfragments in all smaller size classes. The elementsof the progeny matrix for percolation are calcu-lated via Eq. (12), originally formulated byDunn-Rankin and Kerstein [7]. This form of theprogeny matrix is consistent with prior combus-tion models which attempt to account for percola-tive fragmentation during char combustion [2,7]

bi;j ¼c3ði�jÞ

Nsize�jþ1i P j

0 otherwise

(ð12Þ

The elements of the matrix S, which representsthe fraction of particles that experience a fragmen-tation event during the time span dt, are definedbelow:

Si;k ¼ kfragq0

qk

� �x

xai ð13Þ

This form of the matrix S builds on the formula-tion by Dunn-Rankin and Kerstein, which consid-ers a fragmentation rate to be power-lawdependent in size. In our expression, we considerit to be power-law dependent in both size and den-sity, since low density particles are assumed tofragment more readily than high density particles.The fragmentation rate coefficient kfrag increasesthe rate of fragmentation uniformly for all sizesand apparent densities. The apparent density sen-sitivity parameter, x, defines the dependency offragmentation rate on apparent density. The sizesensitivity parameter, a, defines the dependencyof fragmentation rate on particle size. Theseparameters are adjusted such that the model givesfragmentation rates that are consistent with exper-

imental observations for both size and apparentdensity variations during char conversion.

The tensor P is used to describe the variationin apparent density distribution as particles frag-ment. Each element Pi,j,k,m represents, of the par-ticles changing from size class i to j, the fractionwhich also change from density class k to m.The physical basis for the P tensor is that particlefragments do not necessarily embody the internalpore structure of the original fragmenting particle,meaning not all particles are expected to have thesame apparent density as the fragmenting particle.In our approach, the distribution of fragment den-sities is modeled as a Gaussian distribution cen-tered about the apparent density of thefragmenting particle. It is expected that most frag-ments will retain similar apparent densities to theparent particle, but that some particles will have ahigher or lower apparent density. This results invalues for the P tensor as follows:

P i;j;k;m ¼1ffiffiffiffiffiffiffiffiffiffi

2pr2p e�

ðqm�qk Þ2

2r2 ð14Þ

The variance r is treated as a function of i andj. If the parent and fragment sizes are vastly differ-ent, then the fragment is less likely to embody thesame internal pore structure as the parent particle.Thus it is more likely to have a different apparentdensity than the parent particle. The variance istreated as a piecewise factor with three differentvalues, as shown in Eq. (15). Each value isadjusted to provide good agreement betweenmodel predictions and experimental observations.

r ¼r1 if i� j < Nsize

5

r2 if N size5< i� j < Nsize

2

r3 if i� j > Nsize2

8><>: ð15Þ

3. Experimental methods

In our experimental approach, size-classifiedcoal particles were injected into our entrainedlaminar flow reactor and particles were extractedat selected residence times. A sample wasextracted just subsequent to coal devolatilization(at a residence time of 37 ms in the flow reactorenvironments employed), as evidenced by the dis-appearance of radiating volatile gases surround-ing particles. The extracted, partially reactedchar particles were examined to determine particlesize distributions, apparent densities, specific sur-face areas and extents of conversion. The tech-niques involved are described in previous work[1,2,5]. In this work, we also measured particle set-tling fractions (the mass fractions of a sample ofparticles that sank in water) by placing char parti-cles in a water column above filter paper andweighing the mass of particles that sank, as a

Table 1Kinetic parameters for the reactivity of Wyodak coal tooxygen.

Reaction Pre-exponentialA

ActivationEnergy E (kJ/mol)

Std Dev r(kJ/mol)

R1a 4.50 � 107 100 –R1b 1.95 � 103 55 –R2 1.18 � 109 120 –R3 3.74 � 1016 227 –R4 1.00 � 1013 320 36R5 1.00 � 1013 280 45

2466 M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469

qualitative indicator of the spread in apparentdensity of particles.

Wyodak coal, a subbituminous coal fromWyoming, was pulverized and screened to obtainparticles in the 75–106 lm size range for testing.Gas conditions in the entrained flow reactor wereset to yield a post-flame environment containing6% at nominally 1650 K. Values determined forSg,0 and W were 135 g/m2 and 3, respectively,values experimentally determined using CO2 asthe adsorption gas in BET surface areameasurements.

The kinetic parameters needed to describe therate coefficients of the reactions in the mechanismpresented above were determined under kineticallycontrolled conditions in oxidation experimentsperformed in our thermogravimetric analyzer.The Arrhenius parameters that best described themass loss data are listed in Table 1.

In the calculations discussed below, the mea-sured size distribution of particles extracted fromthe reactor just subsequent to devolatilization(i.e., at a particle residence time of 37 ms) was usedas the initial size distribution, and all particles wereassumed to have the same apparent density, takento be that measured for the ensemble of particlescollected at this residence time (qc,0 = 0.74 g/cm3). This gives the initial normalized number dis-tribution, Ni,k,0. Integration of Eq. (1) yields thenumbers of particles in each size–density bin afterburning for time t. Values of Ni,k at time t andNi,k,0 are used to evaluate m/m0 at this time. Atcomplete burnout, the calculations yield approxi-mations to the size distributions of the ashparticles.

Fig. 2. Observed and simulated mass loss rates (a) andapparent density (b) in 6% O2 environments.

4. Results and discussion

The mass loss and apparent density measure-ments indicate that in the environments estab-lished in the entrained flow reactor, charparticles burn in the zone II burning regime inwhich the overall particle burning rates are limitedby the combined effects of chemical reaction andpore diffusion – both internal and external burn-ing contribute to overall char conversion. These

measured values at the selected residence timesare shown in Figs. 1 and 2, along with the calcu-lated values. The calculated mass conversion pro-files do not match the observed conversionprofiles when it is assumed that there is no frag-mentation. Also with no fragmentation, the calcu-lated particle size distributions do not agree wellwith the measured particle size distributions, asseen in Fig. 3. The observed particle size distribu-tion shifts towards smaller sizes significantly fasterthan the calculated size distribution. This suggeststhe presence of fragmentation.

In the following discussion, we refer to sce-nario I fragmentation as fragmentation with allfragments having the same apparent density asthe fragmenting particle and scenario II fragmen-tation as fragmentation with variations in appar-ent densities of fragments. Assuming scenario Ifragmentation, values for kfrag, a, and x weredetermined that yielded calculated profiles thatadequately described the observed size distribu-tions on a volume fraction basis, as this is whatis measured by our Coulter Counter Multisizer,an electroresistive sizing device. The values deter-mined (kfrag = 0.025, a = 2, and x = 1), yield cal-culated size distributions that closely match themeasured size distributions, as shown in Fig. 4.The calculated size distributions are more accu-rate at early times than at late times. This is likelydue to the fact that in this model, the fragmenta-tion rate is assumed to be constant in timewhereas in actuality, the fragmentation rate mayvary as char conversion progresses. Scenario Ifragmentation yields calculated char conversion

Fig. 3. Observed and simulated volume-normalized sizedistributions without accounting for fragmentation.

Fig. 4. Observed and simulated volume-normalized sizedistributions with accounting for fragmentation.

Fig. 5. Observed settling fraction in water.

M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469 2467

profiles that agree with measured profiles moreclosely, as seen in Fig. 1. Such fragmentation alsoresults in an improved agreement between theobserved and calculated apparent density profiles,as noted in Fig. 2. However, calculations assum-ing scenario I fragmentation indicate that thereare no particles in apparent density bins higherthan those of the initial fragmenting particles.This is not in accord with the results of our parti-cle settling tests.

The particle settling tests were initiated todetermine if particles having higher apparent den-sities than the initial fragmenting particles couldbe produced during fragmentation. It wasobserved that with the char sample extracted fromthe entrained flow reactor just subsequent to dev-olatilization, relatively few of the partially reacted

char particles settled (sank) in water. However,with the partially reacted chars extracted fromthe reactor at longer residence times, several ofthe particles in the sample did sink to the bottomof the container. As residence time increased, themass fraction of particles that settled increased.The results are shown in Fig. 5. Due to insufficientwetting and the complex rheological effects thatwater can have on coal char particles, this does

Fig. 6. Simulated apparent, ash-free density distribu-tions.

2468 M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469

not necessarily imply that the particles that sankhave a higher density than water. However, wedo believe that it indicates that during char burn-out, particles are being created via fragmentationevents that have higher apparent densities thanthose formed just subsequent to devolatilization.Upon fragmentation, it is possible that pore wallstransition from being internal surfaces to externalsurfaces, rendering an increase in the apparentdensity of a particle after losing its fragments.With scenario I fragmentation, this observationcannot be predicted. However with scenario IIfragmentation, it can.

Calculations were made assuming scenario IIfragmentation with standard deviations of 0.05,0.08, and 0.12 g/cm3 for the piecewise formula inEq. (15). Shown in Fig. 6 are the mass fractionsof particles in each of the six apparent densityclasses used in the calculations at selected resi-dence times. With scenario I fragmentation, thereare no particles (mass fraction equal to zero) hav-ing apparent densities greater than the apparentdensity of the initial char. With scenario II frag-mentation, all of the apparent density bins are

populated with particles, even those apparent den-sity bins for qcqc,0 > 1. The predicted mass frac-tions of particles having qcqc,0 > 1 are alsosimilar to the observed mass fractions (Fig. 5) atcomparable residence times. Scenario II fragmen-tation does not significantly alter the particle sizedistributions calculated assuming scenario I frag-mentation. Char conversion profiles are also notsignificantly changed, although conversion tendsto be slightly slower when scenario II fragmenta-tion is assumed. In addition to predicting the pres-ence of high apparent density particles early inburnoff, assuming scenario II fragmentation alsoyields calculated apparent density profiles thatare in better agreement with the ones measuredat all residence times.

The overall char conversion rate is slightlyslower when scenario II fragmentation is assumedthan when scenario I fragmentation is assumed.This is a consequence of the high apparent densityfragments that are produced, which take longer toburnout than lower apparent density particles ofcomparable size. The effect is more pronouncedat early conversion times – with scenario II frag-mentation, the overall apparent density of charparticles decreases slower at early times than itdoes assuming scenario I fragmentation. As con-version progresses, the two fragmentation scenar-ios tend to mimic each other, a likely consequenceof particle apparent densities approaching thehigher apparent density of the ash with increasedburnoff.

5. Conclusions

As coal char particles burn in the type of envi-ronments established in pulverized coal-fired com-bustors, they fragment. To accurately predictoverall mass loss rates, char particle oxidationmodels must include the effects of fragmentation.Without fragmentation, at the rates that chemicalreactions occur, all particles less than about 20 lmwould be consumed early in burnoff, and the par-ticle size distribution would decrease withincreased char conversion, a scenario not experi-mentally observed.

Fragmentation with variations in the apparentdensities of the fragments yields calculated sizeand apparent density distributions that are inaccord with experimental observations. The frag-mentation model put forth in this paper is capableof accurately predicting the observed m/m0, sizeand apparent density distributions as well as theobservation that particles of higher densities thanthe apparent densities of the initial char particlesare created during both the early and late stagesof char conversion. Since small particles burn atfaster rates than large particles, these results sug-gest that deriving accurate kinetic parametersfrom char oxidation data obtained in experiments

M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469 2469

in which char particles burn in the zone II burningregime requires that fragmentation be accountedfor during the burning process. Allowing for sce-nario II fragmentation results in a broadening ofthe temperature distribution with conversion, asobserved experimentally, and a more accurateprediction of the size distribution of the ash parti-cles produced during burnout.

Acknowledgments

M.B.T. acknowledges Stanford’s TermanFamily Fellowship for support; the authors alsoacknowledge the support of the U.S.D.O.E., man-aged through N.E.T.L. (Stephen Seachman, Pro-ject Manager). The authors also thank studentsSam Garret and Ian Girard for help collectingsome of the experimental data.

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[4] E.W. Thiele, Ind. Eng. Chem. 31 (7) (1939) 916–920.[5] R.E. Mitchell, L. Ma, B. Kim, Combust. Flame 151

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