3137

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 3137–3144

THE IMPACT OF FRAGMENTATION ON CHAR CONVERSION DURINGPULVERIZED COAL COMBUSTION

REGINALD E. MITCHELL and A. E. JACOB AKANETUKHigh Temperature Gasdynamics Laboratory

Mechanical Engineering DepartmentStanford University

Stanford, CA 794305-3032, USA

Synthetic char particles with controlled macroporosity are used to study char fragmentation behaviorduring pulverized coal combustion. The chars are burned in an atmospheric laminar flow reactor thatpermits the control of gas temperature and composition. Char particles are extracted from the reactor atselected residence times and characterized for extent of mass loss and particle size distribution.

Chars of 23% and 36% porosity are subjected to environments containing 12 mol % O2 at nominally1500 K. Number distributions show a large increase in the numbers of small particles during devolatili-zation, the higher porosity char exhibiting the larger increase. Results show that char burn off increaseswith porosity at any given residence time, demonstrating an impact of fragmentation on char burn off.The data indicate that both particle diameter and apparent density decrease during burn off and supportpower-law relations between char particle mass, apparent density, and diameter.

A particle population balance model is developed and used to characterize the type of fragmentationthat occurs during char oxidation and to quantify the rates of fragmentation events. The model allows forattrition-type behavior (in which only fines are produced), breakage-type behavior (in which particles breakinto two or three smaller particles), and percolation-type behavior (in which particles fragment into adistribution of smaller-size particles).

Calculations using the model indicate that fragmentation during burn off is percolative in nature andchar burning rate parameters determined from mass loss, size, and temperature measurements are toohigh if account is not made for the effects of particle fragmentation. Calculations also suggest that frag-mentation during devolatilization is percolative in nature and the extent of fragmentation increases withcoal volatile yield. Fragmentation rates during devolatilization are estimated to be as high as five times thefragmentation rates during char oxidation.

Introduction

During pulverized coal combustion, a significantnumber of char particles is formed during devolatil-ization that have large voids within them. Thesemacrovoids allow oxygen to penetrate the particleduring char oxidation and consume the inner parti-cle material. As a consequence, particles may frag-ment as interior surfaces are consumed. Char frag-ments burn at rates governed by their individualsizes and not at rates controlled by the sizes of theirparent particles. Consequently, overall mass lossrates depend on the extent of fragmentation. Thispaper reports on work aimed at characterizing theimpact of fragmentation on carbon conversion dur-ing pulverized coal combustion.

Three types of fragmentation behavior are consid-ered: attrition, breakage, and percolation. During at-trition fragmentation, numerous small fragments areproduced while the overall sizes of parent particlesdiminish only slightly. During breakage fragmenta-tion, only a few fragments are produced and these

are relatively large, having sizes not much smallerthan their parent particles. Percolation fragmenta-tion refers to the transition from a connected solidnetwork to a completely fragmented state. Whereasattrition produces fine fragments and breakage pro-duces relatively large fragments, percolation frag-mentation produces fragments ranging in size fromthe diameters of the parent particles to those of thesmall fragments.

Experimental Approach

Synthetic chars with controlled pore structures areused in the study so that complications associatedwith the heterogeneity of real coal chars are elimi-nated. The chars are produced from the polymeri-zation of furfuryl alcohol with p-toluenesulfonic acid[1,2]. Carbon black particles added during the syn-thesis procedure form micropores by causing thecarbonized furfuryl alcohol matrix to crack aroundthe locations of the carbon black inclusions [3].

3138 COAL AND CHAR COMBUSTION

Fig. 1. Micrographs of synthetic chars having porositiesof 16% (top) and 55% (bottom). Particles are in the 90–106-lm size range.

Akan-Etuk and Niksa [4] found that the addition oflycopodium plant spores produces macropores of auniform size (;20 lm in diameter) when they va-porize during the thermal curing step of the synthe-sis procedure.

The chars produced are ground and size classified.True densities of the chars are determined using he-lium pynometry, and apparent densities are deter-mined using mercury intrusion porosimetry com-bined with a tap density procedure [5] for bulkdensity. Figure 1 shows synthetic char particles rep-resenting a range of porosities from 16% to 55%.Mercury porosimetry indicates that the largest intra-particle pores for the 16% porosity chars are ;0.05lm.

Chars are burned in an atmospheric, laminar flowreactor that permits the control of gas temperatureand oxygen content. The reactor is similar in designto that used by Mitchell et al. [5]. Particles are in-jected along the reactor centerline and extractedfrom the reactor at selected residence times using ahelium-quench solids sampling probe [5]. The re-acted chars are characterized for extents of burn off(determined from the measured weights of char fedand char extracted) and particle size distributions.Size distributions are measured with a Coulter Mul-tisizer, using 256 channels to classify approximately20,000 particles per measurement in the 6–168 lmsize range.

Theoretical Approach

The Particle Population Balance Model

A particle population balance model was devel-oped to describe changes in the particle size distri-bution with time as a result of char oxidation andfragmentation. The approach taken is similar to thatof Dunn-Rankin [6], who modified the model de-veloped by Austin et al. [7] for simulating the grind-ing of particles using a ball mill. A number of sizebins are used to describe the particle size distribu-tion. Bin i is characterized by its upper and lowercutoffs, xi and xi`1, respectively. Bin 1 contains thelargest-size particles in the distribution (diameters inthe range x1 to x2) and bin n, the smallest-size par-ticles (diameters in the range xn to 0). The upperand lower cutoffs of each size interval vary by a con-stant factor c, defined as

xic 4 (1)

xi`1

This treatment yields uniformly spaced size intervalsin the log domain and is effective in resolving sizedistributions in the small-size range in which particlenumber densities can be large.

The model is represented by a differential equa-tion of the following form for each bin i:

idNi4 1S N ` b S N 1 C N ` C Ni i o ij j j i i i11 i11dt j41

(2)

where Ni represents the number of particles withinbin i. Si and Ci are the fragmentation and burningrate constants, and bij are elements of the fragmen-tation progeny matrix, which specify the number offragments that enter bin i per particle that fragmentsin bin j.

Fragmentation rate parametersThe fragmentation rate constant gives the fraction

per unit time of particles of size xi that fragment andis expressed as

rS 4 kx (3)i i

where the frequency of fragmentation events isgiven by the fragmentation rate coefficient k, and therelative tendency for a particle of size xi to fragmentis given by the fragmentation sensitivity parameterr. Based on the investigations of Dunn-Rankin [6]and Austin et al. [7], r is set equal to 1.0.

The distribution of fragments is specified by theelements of the fragmentation progeny matrix, bij.Particles fragmenting in bin j can produce fragmentsonly in bin i where i $ j; therefore, bij 4 0 for i ,j. Conservation of volume requires that

CHAR FRAGMENTATION DURING PULVERIZED COAL COMBUSTION 3139

n3 3x 4 b x (4)j o ij i

i4j

where xj is the size of the fragmenting particle andxi are the sizes of the resultant fragments.

Attrition behavior is modeled by assuming thateach particle undergoing attrition in bin j loses asmall fraction f (taken as 0.1%) of its mass from itsperiphery during a single fragmentation event. Onelarge fragment is produced (the parent particle) thatremains in bin j (or possibly enters bin j ` 1 if theparticle had a diameter near the lower-size cutoff ofbin j), and numerous small fragments are producedthat fall into bins mj to n. The subscript j on mj in-dicates that the size of the largest attrited fragmentsdepends on the size of the attriting particle. For at-trition, elements of the progeny matrix are evaluatedas follows:

0 j ` 2 # i # m 1 1j

3fcm # i # njn 1 m ` 1j

3(1 1 f )c 1 1b 4 i 4 jij 3c 1 1

3fc5 i 4 j ` 13c 1 1

0 i 4 n or i , j

(5)In accord with experimental observations, we as-sume that attrited particles can be as large as 10%of the radius of a particle.

For breakage, only a few fragments are produced,and these have sizes close to those of the fragment-ing particles. For breakage in bin j, fragments mayfall into bins j to j ` 1. Presently, we assume break-age into fragments that fall into the next lower sizeclass from the fragmenting particle. For this situa-tion, the elements of the progeny matrix are givenby

0 i # j3b 4 c i 4 j ` 1 (6)ij 50 i . j ` 1

Results from the percolation model of char oxi-dation used by Kerstein and Edwards [8] indicatethat at high carbon conversions, the fragment num-ber distribution varies linearly with mass on a log–log plot. Their results indicate that a particle ulti-mately yields a family of fragments such that loga-rithmically spaced size bins each contain an equalmass fraction of the parent particle. Employing thisresult, the elements of the progeny matrix for per-colation are expressed as

3(i1j)ci $ j

n 1 j ` 1b 4 (7)ij 5 0 otherwise

Burning rate parametersThe burning rate constants describe the rates at

which particles in bin i are reduced in diameter as aresult of burning. Ci is expressed in terms of

, the rate of change in diameter of a burn-(dD/dt)xi`1

ing particle of size xi`1, the lower cutoff of bin i. Itcan be shown that

fraction of particles|dD/dt|in bin i at time t that xi`1C [ 4 (8)i burn out of the size x 1 xi i`11 2

bin per unit time

An expression for dD/dt in terms of the overallparticle burning rate is derived from the particle’srate of mass loss, expressed as

dm 24 1qpD (9)dt

where m is the mass of a particle of diameter D andq is the overall particle burning rate per unit externalsurface area. The particle mass, diameter, and ap-parent density are assumed to be related via the fol-lowing two relations [5,12]:

bam q m D4 4 (10a,b)1 2 1 2m q m D0 0 0 0

where a and b are the burning mode parameters.Justification for such power-law relations for carbonparticles has been given by Essenhigh [9]. For spher-ical particles, a and b satisfy the relation a ` 3b4 1.

Differentiating Eq. (10b) with respect to time andusing the result in Eq. (9) with the relation m0 4 p/6 (D0)3 q0 yields

(311/b)dD 6bq D4 1 (11)1 2dt q D0 0

Employing this result in Eq. (8) yields(311/b)6bq xi`1C 4 (12)i 1 2q (x 1 x ) x0 i i`1 i

The Char Combustion Model

The single-film model [10] of a burning carbonsphere is used to describe a burning particle. Allow-ance is made for CO and CO2 formation at the par-ticle surface, and account is made for Stefan flow.The particle burning rate per unit external surfacearea is given by the following implicit expression[5,11]:

1/2P cqq 4 k 1 1 (1 1 cP /P) exp (13)s g5 3 1 246c kd

where ks is the apparent chemical reaction rate co-efficient (ks 4 Aa exp(1Ea/RTp)), Pg is the oxygenpartial pressure in the ambient gas, and P is the total

3140 COAL AND CHAR COMBUSTION

Fig. 2. Cumulative number distributions for the (a) 23%and (b) 36% porosity chars.

pressure. The volume change upon reaction per unitof oxygen present at the surface is c and the masstransfer coefficient, kd, is given by

M D ShC oxk 4 (14)d DR8T mm o

Here, Mc is the molecular weight of carbon; Dox, theeffective diffusion coefficient of oxygen in the par-ticle’s boundary layer; Sh, the Sherwood number(taken as 2); R8, the gas constant; Tm, the mean tem-perature in the boundary layer; and mo, the stoichio-metric oxygen coefficient.

Particle temperatures during burn off are deter-mined from an energy balance, wherein the rates ofenergy generation due to char oxidation are bal-anced by the rates of energy loss by conduction, con-vection, and radiation. The key adjustable parame-ters in the particle population balance model are theArrhenius parameters for the apparent chemical re-action rate coefficient (Aa and Ea) and the fragmen-tation rate coefficient (k). These are adjusted to pro-vide time-resolved agreement between measuredand calculated extents of mass loss and particle num-ber distributions.

Results and Discussion

The extent of fragmentation associated with theparticle feeding and collection systems was assessed

in cold-flow experiments. Results indicated that thefeed system causes insignificant fragmentation andthat the collection system causes attrition-type frag-mentation with fragments as large as 10% of the ra-dius of the attriting particles. Calculations using thepopulation balance model with Aa set to zero (noburning) were used to determine that for chars withporosities in the range 16% to 60% passing throughthe sampling system, k 4 2.5 lm11 s11 [ kprobe.

Combustion tests were performed in 12 mol %oxygen at nominally 1500 K using chars of 23% and36% porosity with particles in the 76–125 lm sizerange. Partially reacted chars were extracted fromthe flow reactor at residence times of 28, 72, and117 ms. For the 23% porosity char, values for m/m0were determined to be 0.71, 0.21, and 0.19 at therespective residence times and for the 36% porositychar, 0.41, 0.20, and 0.21.

Figures 2a and 2b show the measured cumulativenumber distributions, each based on about 20,000particles. The distributions for the 23% porosity charshow increases in the number of particles having di-ameters less than about 20 lm up to the 72-ms res-idence time. Thereafter, particles with diameters inthe 5–20 lm size range are being consumed fasterthan they are being generated.

For the 36% porosity char, the distribution at 28ms shows a large increase in the number of particleshaving diameters less than about 40 lm. (A duplicatetest at this residence time yielded an almost identicaldistribution.) Particles at this residence time wereextracted just subsequent to devolatilization, as evi-denced by the disappearance of luminous cloudsthat surround particles during volatile release. De-volatilization tests performed in a thermogravimetricanalyzer indicate that the higher the weight fractionof lycopodium used in the synthesis procedure, thelower the volatile matter content of the syntheticchar. Thus, the 36% porosity char has a lower volatilematter content than the 23% porosity char, as wellas a more open internal structure. The data suggestthat these factors (volatile matter content and voidvolume) enhance particle fragmentation during heatup and devolatilization.

The distributions at 72 and 117 ms indicate a re-duced level of fragmentation in comparison with thatduring the first 28 ms in the flow reactor. Factorsthat govern fragmentation during heat up and de-volatilization differ from those that control fragmen-tation during char oxidation. It is not expected thatthe same fragmentation rate parameters apply in thetwo regimes.

Figures 3 and 4 show cumulative and differentialweight distributions for the 23% and 36% porositychars. The lines are curves drawn through the datato facilitate interpretation. The distributions show amonotonic reduction of particle size with time and,hence, with mass loss. Values of D/D0 determinedusing weight-averaged diameters for each size dis-

CHAR FRAGMENTATION DURING PULVERIZED COAL COMBUSTION 3141

Fig. 3. (a) Cumulative and (b) differential weight distri-butions for the 23% porosity char.

Fig. 5. Diameter and apparent density variations withburn off. The lines are calculated using Eq. (10b) and se-lected values of b.

Fig. 4. (a) Cumulative and (b) differential weight distri-butions for the 36% porosity char.

tribution are plotted against the measured m/m0 val-ues in Fig. 5. Values obtained with a 16% porositychar are also included in the plot. The lines in thefigure are calculations in accord with Eq. (10b) usingselected values for the particle burning mode param-eter b. For b 4 1/3, particles burn at constant den-sity; for b , 1/3, particles burn with decreases inboth size and apparent density. The data support avalue of b near 0.25. The corresponding value for ais 0.25, a value consistent with those determinedpreviously [5,12].

The population balance model was used to cal-culate the number distributions at residence timesof 72 and 117 ms using the distributions at 28 ms asstarting distributions. One hundred size bins wereused in the calculation with xi/xi`1 4 1.06 and xn 40.55 lm. The set of 100 differential equations wassolved using LSODE [13], an ordinary differentialequation solver. Ambient conditions were specified(Tgas 4 1500 K, Pg 4 0.12 atm); char combustionmodel parameters were taken from the literature[5,11]. The apparent activation energy was taken as26 kcal/mol, consistent with results of previous work[11] for chars containing 90% carbon. Adjustable pa-rameters included Aa and k. Sampling-induced at-trition-type fragmentation was accounted for by re-adjusting Aa to zero and k to kprobe at the end of thespecified residence time in the reactor and integrat-ing an additional 171 ms, the time it takes particlesto pass through the sampling system.

It was not possible to determine values of Aa andk that resulted in number size distributions that re-flected the measured trends when attrition- orbreakage-type fragmentation was assumed. Onlypercolation-type fragmentation yielded calculatedcumulative number distributions having the char-acteristic shapes of those observed.

Figure 6 shows calculated cumulative number dis-tributions for the 23% porosity char assuming nofragmentation. To get good agreement betweenmeasured and calculated cumulative and differential

3142 COAL AND CHAR COMBUSTION

Fig. 6. Calculated cumulative number distributions(broken lines) assuming diffusion-limited burning and nofragmentation. Calculated m/m0 values agree with the mea-surements at the various residence times. Solid linesthrough the data at 0 and 28 ms represent fits used asstarting distributions in the calculations.

Fig. 7. Calculated cumulative number distributions(broken lines) assuming Aa 4 200 gC/cm2 s atm0.5 and k4 0.05 lm11 s11. Calculated m/m0 values agree with themeasurements at the various residence times. Solid linesthrough the data at 0 and 28 ms represent fits used asstarting distributions in the calculations.

weight distributions, diffusion-limited burning hadto be assumed. The calculated number distributions,however, do not reflect the trends depicted in Fig.2. With diffusion-limited burning, small particles inthe feed char are completely burned before the 72-ms residence time in the reactor is reached. No in-creases in the numbers of small particles are pre-dicted at the high particle burning rates needed tomatch the weight-loss data.

Figure 7 shows the distributions calculated assum-ing percolation-type fragmentation with Aa 4 200gC/cm2 s atm0.5 and k 4 0.05 lm11 s11. With thisvalue of Aa, particles in the 30–80-lm size rangeburn at rates ranging from 78% to 94% of their dif-fusion-limited rates in 12 mol % oxygen at 1500 K.The distributions reflect the trends observed withthe data. For better agreement, it is necessary tomodel more accurately apparent density changes as-

sociated with fragmentation. When a particle frag-ments, its fragments do not have the same apparentdensities as those of the smaller classes of particlesinto which the fragments fall. In the present particlepopulation model, variations in apparent density foreach size class of particles are determined by inte-grating the differential equation obtained when Eq.(10a) is differentiated with respect to time and com-bined with Eq. (9). Such an approach assumes thatall particles in a given size class have the same ap-parent density, a reasonable assumption when thereis no fragmentation. Only by having density classesassociated with each size class can apparent densityeffects be modeled accurately when account is madefor char fragmentation.

Using the measured size distribution at t 4 0 msfor a starting distribution and the value determinedfor Aa, calculations indicate that fragmentation ratesof the 23% porosity char during the first 28 ms inthe flow reactor (i.e., during heat up and devolatili-zation) are about five times the fragmentation ratesduring the later stages of char oxidation. This esti-mate is based on the apparent density of the un-burned char and assumes very rapid devolatilizationrates and no swelling during devolatilization. Cal-culations also indicate that the frequency of frag-mentation events during heat up and devolatilizationis about three times higher with the 36% porositychar than with the 23% porosity char.

Conclusions

During pulverized coal combustion, particles frag-ment as they heat up and devolatilize and as theyundergo oxidation. Results show that char burn offincreases with porosity at any given residence timeand that number distributions exhibit greater num-bers of small particles with increases in porosity,demonstrating an impact of fragmentation on burnoff rates. The fragmentation behavior can be char-acterized as being percolative, where fragmentingparticles produce fragments of all sizes.

The data indicate that both particle diameter andapparent density decrease during char oxidation andsupport power-law relations between particle mass,diameter, and apparent density. Since overall parti-cle burning rates depend on particle size, it is ap-parent that accurate determination of mass loss ratesduring the char oxidation phase of coal combustionrequires that account be made for char particle frag-mentation. The neglect of fragmentation can resultin the determination of apparent chemical reactionrate coefficients that are too high.

A particle population model that accounts for charfragmentation and oxidation has been developed andshown to be able to predict qualitatively the evolu-tion of the number size distribution during burn off.The adjustment of model parameters to fit data

CHAR FRAGMENTATION DURING PULVERIZED COAL COMBUSTION 3143

indicates that char fragmentation is percolative innature and that fragmentation rates increase withchar porosity. The model also indicates that the rateof fragmentation during heat up and devolatilizationis about five times the rate of fragmentation duringchar oxidation. Before the effects of fragmentationon the extent of mass loss can be predicted withgreater accuracy, the model must be modified to al-low for variations in density for each size class ofparticles considered.

Acknowledgment

This work is supported by the U.S.D.O.E. through thePittsburgh Energy Technology Center.

REFERENCES

1. Senior, C. L., “Submicron Aerosol Formation duringCombustion Of Pulverized Coal,” Ph.D. Thesis, Cali-fornia Institute of Technology, 1984.

2. Senior, C. L. and Flagan, R. C., Twentieth Symposium(International) on Combustion, The Combustion In-stitute, Pittsburgh, 1984, pp. 921–929.

3. Levendis, Y. A. and Flagan, R. C., Carbon 27:265–283(1989).

4. Akan-Etuk, A. and Niksa, S., Energy Fuels 5:614–615(1991).

5. Mitchell, R. E., Hurt, R. H., Baxter, L. L., and Har-desty, D. R., “Compilation of Sandia Coal Char Com-bustion Data and Kinetic Analyses: Milestone Report,”Sandia National Laboratories, September 1991.

6. Dunn-Rankin, D., Combust. Sci. Technol. 58:297–314(1988).

7. Austin, L. G., Klimpel, R. R., and Luckie, P. T., ProcessEngineering of Size Reduction: Ball Milling, Society ofMining Engineers, New York, 1984.

8. Kerstein, A. R. and Edwards, B. F., Chem. Engineer.Sci. 42:1629–1634 (1987).

9. Essenhigh, R. H., Twenty-Second Symposium (Inter-national) on Combustion, The Combustion Institute,Pittsburgh, 1988, pp. 89–96.

10. Field, M. A., Gill, D. W., Morgan, B. B., and Hawk-sley, P. G. W., Combustion of Pulverized Coal,BCURA, Leatherhead, 1967, p. 186.

11. Hurt, R. H. and Mitchell, R. E., Twenty-Fourth Sym-posium (International) on Combustion, The Combus-tion Institute, Pittsburgh, 1992, pp. 1243–1250.

12. Smith, I. W., Combust. Flame 17:421–428 (1971).13. Radhakrishnan, K. and Hindmarsh, A. C., “Descrip-

tion and Use of LSODE, the Livermore Solver for Or-dinary Differential Equations,” Lawrence LivermoreNational Laboratories, UCRL-ID-113855, 1983.

COMMENTS

Jon Gibbins, Imperial College, UK. Fragmentation bypercolation certainly seems to be occurring in a real utilityplant since, for situations where good burn-out is occur-ring, roughly 50% of the unburnt C is below 38 lm andSEM examination confirms it has come from larger, porousstructures. If the particles have burnt enough to fragment,however, they will also have got hot enough for thermaldeactivation so (as usual in char burn-out) there is no singlemechanism that can be invoked to explain the observedresults! It also appears that, when poor burnout occurs, theabundance of the larger char particles, rather than thesmaller particles in the fly ash, increases, which perhapssuggests that fragmentation is not always a burnout-deter-mining process.

Author’s Reply. Yes, we agree with your conclusion thatfragmentation is not the only cause of unburned carbon inash. Indeed situations do exist where unburned carbon canbe due to other factors, among them differences in reac-tivity of coal components, thermal annealing, and ash in-hibition.

●

L. Douglas Smoot, Brigham Young University, USA.Your observation of a very large average number of frag-ments for each initial synthetic char particle seems to be

counter to various observations for coal chars which sug-gest up to a few to several fragments per initial particle.Does this suggest that the synthetic particles are not rep-resentative of coal in this regard?

Author’s Reply. The results of Sarofim et al. [1], Helbleet al. [2], and Helble and Sarofim [3] support that between3 and 5 ash particles above 10 lm in diameter and from200 to 500 ash particles with diameters in the range 1–10lm are produced from a single pulverized coal particle. Ifthere were no fragmentation, one would expect only oneash particle produced per coal particle. Thus, these resultssuggest a much larger number of fragments generated dur-ing combustion of pulverized coal than indicated in yourquestion. The number of fragments generated during com-bustion of our synthetic char are consistent with the largernumbers. Using the fragmentation rate coefficient deter-mined for the 23% porosity char, calculations indicate thatabout 11 fragments per particle were generated having di-ameters greater than 10 lm during the 28 to 117 ms char-oxidation period in the reactor. Hundreds of smaller frag-ments were generated over this same time period. Thus,with regards to its fragmentation behavior, we believe thatour synthetic char is representative of the char of a low-ash, low-volatile coal.

3144 COAL AND CHAR COMBUSTION

REFERENCES

1. Sarofim, A. F., Howard, J. B., and Padia, A. S., Com-bust. Sci. Technol. 16:187 (1977).

2. Helble, J. J., Neville, M., and Sarofim, A. F., Twenty-First Symposium (International) on Combustion, Com-bustion Institute, Pittsburgh, 1988, p. 411.

3. Helble, J. J. and Sarofim, A. F., Combust. Flame 76:183(1989).

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Robert Hurt, Brown University, USA. I agree with yourconclusion the fine fragments can undergo “extinction”, butwould like to comment on the implications of the “extinc-tion” for carbon burnout. According to our models of zoneII combustion it is possible under special conditions (lowgas temperature and high oxygen concentration) for frag-mentation and “extinction” to result in a decrease in overallburning rate, as suggested. At the high gas temperaturesand relatively low oxygen concentrations of interest to pul-verized-coal-fired boilers, however, the net effect of frag-mentation and “extinction” is an increase in overall burningrate due to increased external surface. Mathematically, asparticle diameter approaches zero, the particle tempera-ture must approach the local gas temperature (the “extin-guished” state), which, in this application, however, is stillhigh enough to produce rapid burnout of the fine frag-ment. Do your models predict the same trends—that frag-mentation favors burnout under pulverized coal combus-tion conditions?

Author’s Reply. In zone II, the shapes of resulting frag-

ments play a key role in determining whether fragmenta-tion increases or decreases burnout. If all particles andfragments are assumed to be spherical, then fragmentationenhances burnout, as predicted by our model. If all frag-ments were non-spherical, then fragmentation could de-crease burnout owing to the impact of surface-to-volumeratio on the relative rates of heat generation and loss, whichdetermine equilibrium particle temperatures. Because ofradiative losses to the cooler combustor walls, non-spher-ical fragments having characteristic sizes as large as 50 lmwould burn at temperatures from 50 to 100 K below thelocal gas temperature. Calculations using burning rate pa-rameters determined for a lv-bituminous coal [1] indicatethat a 50 lm diameter spherical particle would obtain atemperature of 1825 K in its fully-ignited state and requireabout 250 ms for 99% burnoff in 6% O2 at 1800 K. A 50lm fragment burning at a rate that limited its temperatureto 1750 K could require over 650 ms to reach this extentof burnoff in 6% O2 at 1800 K (estimated assuming a spher-ical particle with reduced reactivity to effect the lower tem-perature). Depending upon whether the fragment was gen-erated during the early stages of char oxidation or late,sufficient time may not be available in the reactor for itscomplete burnout and hence, portions of this 50 lm frag-ment could contribute to unburned carbon in the ash.

REFERENCE

1. R. H. Hurt and R. E. Mitchell, Twenty-Fourth Sympo-sium (International) on Combustion, The CombustionInstitute, Pittsburgh, 1992, p. 1243.