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Characterizing char particle fragmentation during pulverized coal combustion
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Proceedings of the
Combustion Institute
Proceedings of the Combustion Institute 34 (2013) 2461–2469
www.elsevier.com/locate/proci
Characterizing char particle fragmentation during 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 ensemble of char particles exposed to an environment in which their overall burning rates are controlled by the combined effects of oxygen diffusion through particle pores and chemical reactions (the zone II burning regime). The model allows for changes in particle size due to burning at the external surface, changes in particle apparent density due to internal burning at pore walls, and changes in the sizes and apparent densities of particles due to percolation type fragmentation. In percolation type fragmentation, fragments of all sizes less than that of the fragmenting particle are produced. The model follows the conversion of particles burning in a gaseous environment of specified temperature and oxygen content. The extent of conversion 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 data needed to adjust model parameters. Pulverized Wyodak coal particles were injected into the reactor and char samples were extracted at selected residence times. The particle size distributions and apparent densities were measured for each sample extracted. The intrinsic chemical reactivity of the char to oxygen was also measured in experiments performed in a thermogravimetric analyzer. Data were used to adjust rate coefficients in a six-step reaction mechanism used to describe the oxidation process. Calculations made allowing for fragmentation with variations in the apparent densities of fragments yield the type of size, apparent density, and temperature distributions observed experimentally. These distributions broaden with increased char conversion in a manner that can only be predicted when fragmentation is accounted for with variations in fragment apparent density as well as size. The model also yields the type of ash size distributions observed experimentally. Ó 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 to increase well into the 21st century and beyond. ⇑ Corresponding author.
E-mail address: Tilghman).
[email protected]
(M.B.
As much of this forecasted rise will occur in developing countries, use of cheap fossil fuels will continue to grow despite environmental concerns. Since fossil fuel combustion, in particular coal combustion, has a well-documented implication on climate change and air quality, burning the fuel cleanly and efficiently remains a paramount goal.
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.07.065
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Nomenclature bi,j Ci,k D Di,k DO kd kfrag m b M Ndens Ni,k Nsize Nu Pi,j,k,m
Pg Ps R Rex Rin q Sg Si,k
element i, j of the progeny matrix b, representing size distribution during fragmentation fraction of particles in bin i, k that burn out of size-class i due to external burning diameter of particle fraction of particles in bin i, k that burn out of density-class k due to internal burning oxygen bulk diffusion coefficient in particle boundary layer mass transfer coefficient fragmentation rate coefficient particle mass molecular mass number of density classes implemented in model number of particles which reside in size–density bin i, k number of size classes implemented in model Nusselt number element i, j, k, m of the tensor P; represents the fraction of particles which [start in size class i, end in size class j, and start in density class k] that ends in density class m oxygen partial pressure in ambient gas oxygen partial pressure at the exterior particle surface universal gas constant external reactivity of the particle (g/ m2/s) internal reactivity of the particle (g/ m2/s) overall burning rate of the particle (g/ m2/s) specific internal surface area (m2/g) fraction of particles in size–density bin i, k which will fragment within time step dt
The efficient burning of any particular fossil fuel relies on accurate characterization of the fuel conversion process so that optimal reaction conditions can be identified. This requires the development of models that accurately predict fuel conversion rates for specified temperature, pressure, and gas composition. With porous solid fuels, the models must not only have parameters that accurately describe the rates of chemical reactions that consume the carbonaceous material but they must also have parameters that accurately describe the transport of reactive gases through particle pores as well as parameters that
Sh Tp Tg Tw x xi
Sherwood number particle temperature ambient gas temperature wall temperature to which particles radiate conversion fraction diameter of size-class i
Greek symbols DH Dqk Dxi a e k c co g qc qk w r rsb x tO
heat of reaction apparent density difference between density class k and k + 1 diameter difference between size class i and i + 1 size sensitivity parameter for fragmentation particle emissivity thermal conductivity of gas constant factor by which size interval varies for each size bin, c = xi/xi+1 change in volume upon reaction per unit oxygen consumed effectiveness factor which relates internal reactivity to maximum possible internal reactivity apparent density of the carbonaceous material density of density-class k structural parameter used to fit internal surface area throughout the course of conversion piecewise standard deviation of the Gaussian distribution used to predict fragment densities Stephan–Boltzmann constant density sensitivity parameter for fragmentation moles O2 reacted per mole carbon reacted
accurately describe the mode of burning, i.e., how the size and apparent density of the particle vary with mass loss during the conversion process. Even with accurate chemistry, transport, and mode of conversion models, accurate prediction of mass loss during the combustion of solid fuels will depend upon the extent of fragmentation during the conversion process. All coal particles fragment to some extent during coal combustion. Fragmentation reduces the particle size, and small particles are converted to gaseous species at faster rates than large particles. Fragmentation occurs during coal devolatilization and during char
M.B. Tilghman, R.E. Mitchell / Proceedings of the Combustion Institute 34 (2013) 2461–2469
oxidation, fragmentation during devolatilization potentially occurring to a greater extent. Despite the known occurrence of fragmentation during combustion, most models of the coal combustion process do not include fragmentation during either devolatilization or char oxidation. In this paper, focus is placed on the prediction of fragmentation during char oxidation under conditions that exist in pulverized fuel combustors. 2. Theoretical approach 2.1. Particle population balance model A model has been developed that is capable of predicting overall conversion rates of an ensemble of pulverized coal of biomass char particles exposed to gaseous environments of specified temperature, pressure, and gas composition. The particle population balance model employed builds on our earlier models [1,2] and includes tracking particles in a size–density matrix, as shown in Fig. 1. Each column i represents a certain size class, and each row k represents a certain apparent density class. Large particles are represented by large values of i and high apparent density particles are represented by large values of k. In this model, the smallest particles (i = 1) and the lowest apparent density particles (k = 1) represent ash particles. The number of particles in each size– density bin i, k, henceforth referred to as Ni,k, is tracked. With each differential time interval dt, the effects of burning and fragmentation may change particle sizes and apparent densities enough to warrant bin change, changing Ni,k. While burning can only change a particle’s size class or density class by one at a time, fragmentation can produce particles that may instantaneously populate any size–density bin below that of the fragmenting particle. The differential equation that governs the variations in the number of particles in each size– density bin with time is given in the following equation: dN i;k ¼ ðC i;k þ Di;k þ S i;k ÞN i;k þ C i1;k N i1;k dt i N dens X X þ Di;k1 N i;k1 þ bi;j P i;j;k;m S j;m N j;m ð1Þ j¼1 m¼1
Fig. 1. Visualization of the effects of burning and fragmentation.
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For Nsize size classes and Ndens density classes, there are Nsize Ndens similarly structured ODEs that must be solved simultaneously to track the particles in each size–density bin. The first term on the right hand side of Eq. (1) accounts for all particles that leave bin i, k. The variable Ci,k represents the fraction of particles in bin i, k that burn out of the bin per unit time because of a decrease in particle diameter due to external burning, the variable Di,k represents the fraction of particles that will burn out of the bin per unit time because of a decrease in apparent density due to internal burning, and the variable Si,k represents the fraction of particles that will experience a fragmentation event and leave the size–density bin. The second and third terms on the right hand side of Eq. (1) account for particles that will enter bin i, k due to diameter-related burning in the immediately larger size class and density-related burning 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 to fragmentation events occurring in all bins, including itself. Particles can fragment into bin i, k from any bin of an equal or larger size class. The bi,j are elements of the progeny matrix that describes the size distribution of a group of fragmenting particles. Element bi,j is the fraction of fragmenting particles in size class i that fragment into size class j. The Pi,j,k,m are elements of the P tensor that describes the density distribution of a group of fragmenting particles. Element Pi,j,k,m is the fraction of the particles changing from size j to i that are also changing from apparent density m to k. The fraction of particles in the size–density class j, m that will experience a fragmentation event during the time interval dt is given by Sj,m. When summed over j and m, the final term represents all particles 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 particle burning 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 relating particle mass, apparent density and size (m = qpD3/6), the equations for the external and internal burning rates per unit external surface area, Rex and Rin, respectively, can be defined as follows: 1 dm q dD ¼ c Rex and 2 dt pD2 dt ex 1 dm D dqc ð2Þ ¼ Rin pD2 dt in 6 dt In terms of the external and internal burning rates, the overall particle burning rate per unit external surface area can be expressed as
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1 dm ¼ ðRex þ Rin Þ ¼ ð1 þ Rin =Rex ÞRex ð3Þ pD2 dt Employing the concepts put forth by Thiele [4], the internal particle burning rate is related to the maximum possible internal burning rate by an effectiveness factor g, such that Rin = g Rin,max. The maximum possible rate of internal burning corresponds to the situation when the particle temperature and oxygen concentration are uniform throughout the particle, and equal to those existing at the outer surface of the particle. This implies that the maximum possible internal burning rate per unit internal surface is equal to the external burning rate per unit external area, and hence q¼
Rin;max Rex ¼ 3 ðp=6ÞD qc S g pD2
ð4Þ
where Sg is the specific surface area of the carbonaceous material. Combining the above equations results in the following expression for the overall particle burning rate in terms of the effectiveness factor and the burning rate at the external particle surface, which depends on the temperature and oxygen concentration (or partial pressure) existing at the external surface of the particle gq S g D q¼ 1þ c Rex ð5Þ 6 The overall particle burning rate per unit external surface area can also be written in terms of the oxygen partial pressure in the ambient gas Pg and the oxygen concentration at the external particle surface Ps, as follows: kd P 1 cP s =P ln ð6aÞ q¼ c 1 cP g =P where kd ¼
b C DO Sh M b m DmO RT
ð6bÞ
This equation assumes spherical, isothermal particles with no chemical reaction in the boundary layer surrounding the particle; account is also made for Stefan flow in the boundary layer. Assuming steady-state burning, the particle temperature is determined from the following energy balance equation: qDH ¼
¼
Nuk j ðT p T g Þ þ rðT 4p D 1j T 4w Þ where j ccp;g DmO q b C kNu M
ð7Þ
Account is made for energy losses via conduction, convection, and radiation from the outer surface of the particle and energy generation due to burning. Equations5, 6a, 6b, 7 permit the deter-
mination of the oxygen partial pressure at the external surface of the particle and the particle temperature, given the temperature and oxygen partial pressure in the particle’s environment, and a path to determine the burning rate at the external particle surface, Rex, which depends upon the rates of chemical reactions on the external surface. We use the following six steps heterogeneous reaction mechanism developed in previous work [5] to describe the effects of chemical reaction: 2Cf þ O2 ! CðOÞ þ CO 2Cf þ O2 ! C2 ðO2 Þ
ðR1aÞ ðR1bÞ
Cb þ Cf þ CðOÞ þ O2 ! CðOÞ þ CO2 þ Cf Cb þ Cf þ CðOÞ þ O2 ! 2CðOÞ þ CO Cb þ CðOÞ ! Cf þ CO
ðR2Þ ðR3Þ ðR4Þ
Cb þ C2 ðO2 Þ ! 2Cf þ CO2
ðR5Þ
In the above mechanism, Cf represents a free carbon site available for adsorption, Cb represents an underlying bulk carbon site, C(O) represents an oxygen atom adsorbed onto a carbon site, and C2(O2) represents two adjacent carbon sites, both having adsorbed oxygen atoms. Using this reaction mechanism, intrinsic carbon reactivity to oxygen is given by Eq. (8), where RRi stands for the rate of reaction i b C ðRR1a þ RR2 þ RR3 þ RR4 þ RR5 Þ Ri;C ¼ M
ð8Þ
The rate of each reaction is written in terms of the concentrations of the species involved in the reaction and a reaction rate coefficient, which is expressed in Arrhenius form. Reactions (R1– R3) are approximated as having a single activation energy, whereas the desorption reactions (R4) and (R5) account for a distribution of activation energies due to the range of carbon binding energies present on a real coal char surface. The model does not take into account the impact of thermal annealing on char reactivity. Differential equations based on the mechanism are solved simultaneously with the particle population balance model equation to determine the concentrations of the adsorbed species on particle surfaces during char conversion. The total number of differential equations that are solved simultaneously is 3 Ndens Nbin, tracking Ni,k, C(O)i,k, and C2(O2)i,k. In environments containing small amounts of CO (as in this study), the reaction mechanism predicts a char conversion rate that is almost first order in the oxygen concentration. Accordingly, we use the concepts put forth by Thiele [4] to determine the effectiveness factor from the Thiele modulus assuming first order kinetics. The specific surface area of the carbonaceous particle material, Sg, must also be tracked throughout the course of burning. We use Eq.
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(9) to follow the specific surface area with char conversion; the structural parameter w is determined by fitting surface areas measured during the course of oxidation, as described in previous work [5]. This surface area model is consistent with the one developed by Bhatia and Perlmutter to follow surface area during carbon conversion [7] pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qc;0 Sg ¼ S g;0 ð1 xÞ 1 w lnð1 xÞ ð9Þ qc The variables Ci,k and Di,k in Eq. (1) are calculated via Eqs. (10) and (11). In these equations, Dxi and Dqk are the size-class and density-class spacing, respectively 1 dD dD 2Rex ¼ where Dxi dt i;k dt qc 1 dqc dD 6Rin ¼ qc where ¼ ¼ gqc S g Rex Dqk dt i;k dt D
C i;k ¼
ð10Þ
Di;k
ð11Þ
2.3. Particle fragmentation As shown previously [2,7], the type fragmentation that occurs during char oxidation is percolation, in which the fragmenting particle produces fragments in all smaller size classes. The elements of the progeny matrix for percolation are calculated via Eq. (12), originally formulated by Dunn-Rankin and Kerstein [7]. This form of the progeny matrix is consistent with prior combustion models which attempt to account for percolative fragmentation during char combustion [2,7] ( 3ðijÞ c iPj bi;j ¼ N size jþ1 ð12Þ 0 otherwise The elements of the matrix S, which represents the fraction of particles that experience a fragmentation event during the time span dt, are defined below: x q S i;k ¼ k frag 0 xai ð13Þ qk This form of the matrix S builds on the formulation by Dunn-Rankin and Kerstein, which considers a fragmentation rate to be power-law dependent in size. In our expression, we consider it to be power-law dependent in both size and density, since low density particles are assumed to fragment more readily than high density particles. The fragmentation rate coefficient kfrag increases the rate of fragmentation uniformly for all sizes and apparent densities. The apparent density sensitivity parameter, x, defines the dependency of fragmentation rate on apparent density. The size sensitivity parameter, a, defines the dependency of fragmentation rate on particle size. These parameters are adjusted such that the model gives fragmentation rates that are consistent with exper-
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imental observations for both size and apparent density variations during char conversion. The tensor P is used to describe the variation in apparent density distribution as particles fragment. Each element Pi,j,k,m represents, of the particles changing from size class i to j, the fraction which also change from density class k to m. The physical basis for the P tensor is that particle fragments do not necessarily embody the internal pore structure of the original fragmenting particle, meaning not all particles are expected to have the same apparent density as the fragmenting particle. In our approach, the distribution of fragment densities is modeled as a Gaussian distribution centered about the apparent density of the fragmenting particle. It is expected that most fragments will retain similar apparent densities to the parent particle, but that some particles will have a higher or lower apparent density. This results in values for the P tensor as follows: ðqm qk Þ2 1 P i;j;k;m ¼ pffiffiffiffiffiffiffiffiffiffi e 2r2 2pr2
ð14Þ
The variance r is treated as a function of i and j. If the parent and fragment sizes are vastly different, then the fragment is less likely to embody the same internal pore structure as the parent particle. Thus it is more likely to have a different apparent density than the parent particle. The variance is treated as a piecewise factor with three different values, as shown in Eq. (15). Each value is adjusted to provide good agreement between model predictions and experimental observations. 8 N size > < r1 if i j < 5 r ¼ r2 if N 5size < i j < N 2size ð15Þ > : N size r3 if i j > 2
3. Experimental methods In our experimental approach, size-classified coal particles were injected into our entrained laminar flow reactor and particles were extracted at selected residence times. A sample was extracted just subsequent to coal devolatilization (at a residence time of 37 ms in the flow reactor environments employed), as evidenced by the disappearance of radiating volatile gases surrounding particles. The extracted, partially reacted char particles were examined to determine particle size distributions, apparent densities, specific surface areas and extents of conversion. The techniques involved are described in previous work [1,2,5]. In this work, we also measured particle settling fractions (the mass fractions of a sample of particles that sank in water) by placing char particles in a water column above filter paper and weighing the mass of particles that sank, as a
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Table 1 Kinetic parameters for the reactivity of Wyodak coal to oxygen. Reaction
Preexponential A
Activation Energy E (kJ/ mol)
Std Dev r (kJ/mol)
R1a R1b R2 R3 R4 R5
4.50 107 1.95 103 1.18 109 3.74 1016 1.00 1013 1.00 1013
100 55 120 227 320 280
– – – – 36 45
qualitative indicator of the spread in apparent density of particles. Wyodak coal, a subbituminous coal from Wyoming, was pulverized and screened to obtain particles in the 75–106 lm size range for testing. Gas conditions in the entrained flow reactor were set to yield a post-flame environment containing 6% at nominally 1650 K. Values determined for Sg,0 and W were 135 g/m2 and 3, respectively, values experimentally determined using CO2 as the adsorption gas in BET surface area measurements. The kinetic parameters needed to describe the rate coefficients of the reactions in the mechanism presented above were determined under kinetically controlled conditions in oxidation experiments performed in our thermogravimetric analyzer. The Arrhenius parameters that best described the mass loss data are listed in Table 1. In the calculations discussed below, the measured size distribution of particles extracted from the reactor just subsequent to devolatilization (i.e., at a particle residence time of 37 ms) was used as the initial size distribution, and all particles were assumed to have the same apparent density, taken to be that measured for the ensemble of particles collected at this residence time (qc,0 = 0.74 g/ cm3). This gives the initial normalized number distribution, Ni,k,0. Integration of Eq. (1) yields the numbers of particles in each size–density bin after burning for time t. Values of Ni,k at time t and Ni,k,0 are used to evaluate m/m0 at this time. At complete burnout, the calculations yield approximations to the size distributions of the ash particles.
measured values at the selected residence times are shown in Figs. 1 and 2, along with the calculated values. The calculated mass conversion profiles do not match the observed conversion profiles when it is assumed that there is no fragmentation. Also with no fragmentation, the calculated particle size distributions do not agree well with the measured particle size distributions, as seen in Fig. 3. The observed particle size distribution shifts towards smaller sizes significantly faster than the calculated size distribution. This suggests the presence of fragmentation. In the following discussion, we refer to scenario I fragmentation as fragmentation with all fragments having the same apparent density as the fragmenting particle and scenario II fragmentation as fragmentation with variations in apparent densities of fragments. Assuming scenario I fragmentation, values for kfrag, a, and x were determined that yielded calculated profiles that adequately described the observed size distributions on a volume fraction basis, as this is what is measured by our Coulter Counter Multisizer, an electroresistive sizing device. The values determined (kfrag = 0.025, a = 2, and x = 1), yield calculated size distributions that closely match the measured size distributions, as shown in Fig. 4. The calculated size distributions are more accurate at early times than at late times. This is likely due to the fact that in this model, the fragmentation rate is assumed to be constant in time whereas in actuality, the fragmentation rate may vary as char conversion progresses. Scenario I fragmentation yields calculated char conversion
4. Results and discussion The mass loss and apparent density measurements indicate that in the environments established in the entrained flow reactor, char particles burn in the zone II burning regime in which the overall particle burning rates are limited by the combined effects of chemical reaction and pore diffusion – both internal and external burning contribute to overall char conversion. These
Fig. 2. Observed and simulated mass loss rates (a) and apparent density (b) in 6% O2 environments.
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Fig. 4. Observed and simulated volume-normalized size distributions with accounting for fragmentation.
Fig. 3. Observed and simulated volume-normalized size distributions without accounting for fragmentation.
profiles that agree with measured profiles more closely, as seen in Fig. 1. Such fragmentation also results in an improved agreement between the observed and calculated apparent density profiles, as noted in Fig. 2. However, calculations assuming scenario I fragmentation indicate that there are no particles in apparent density bins higher than those of the initial fragmenting particles. This is not in accord with the results of our particle settling tests. The particle settling tests were initiated to determine if particles having higher apparent densities than the initial fragmenting particles could be produced during fragmentation. It was observed that with the char sample extracted from the entrained flow reactor just subsequent to devolatilization, relatively few of the partially reacted
Fig. 5. Observed settling fraction in water.
char particles settled (sank) in water. However, with the partially reacted chars extracted from the reactor at longer residence times, several of the particles in the sample did sink to the bottom of the container. As residence time increased, the mass fraction of particles that settled increased. The results are shown in Fig. 5. Due to insufficient wetting and the complex rheological effects that water can have on coal char particles, this does
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populated with particles, even those apparent density bins for qcqc,0 > 1. The predicted mass fractions of particles having qcqc,0 > 1 are also similar to the observed mass fractions (Fig. 5) at comparable residence times. Scenario II fragmentation does not significantly alter the particle size distributions calculated assuming scenario I fragmentation. Char conversion profiles are also not significantly changed, although conversion tends to be slightly slower when scenario II fragmentation is assumed. In addition to predicting the presence of high apparent density particles early in burnoff, assuming scenario II fragmentation also yields calculated apparent density profiles that are in better agreement with the ones measured at all residence times. The overall char conversion rate is slightly slower when scenario II fragmentation is assumed than when scenario I fragmentation is assumed. This is a consequence of the high apparent density fragments that are produced, which take longer to burnout than lower apparent density particles of comparable size. The effect is more pronounced at early conversion times – with scenario II fragmentation, the overall apparent density of char particles decreases slower at early times than it does assuming scenario I fragmentation. As conversion progresses, the two fragmentation scenarios tend to mimic each other, a likely consequence of particle apparent densities approaching the higher apparent density of the ash with increased burnoff. Fig. 6. Simulated apparent, ash-free density distributions.
not necessarily imply that the particles that sank have a higher density than water. However, we do believe that it indicates that during char burnout, particles are being created via fragmentation events that have higher apparent densities than those formed just subsequent to devolatilization. Upon fragmentation, it is possible that pore walls transition from being internal surfaces to external surfaces, rendering an increase in the apparent density of a particle after losing its fragments. With scenario I fragmentation, this observation cannot be predicted. However with scenario II fragmentation, it can. Calculations were made assuming scenario II fragmentation with standard deviations of 0.05, 0.08, and 0.12 g/cm3 for the piecewise formula in Eq. (15). Shown in Fig. 6 are the mass fractions of particles in each of the six apparent density classes used in the calculations at selected residence times. With scenario I fragmentation, there are no particles (mass fraction equal to zero) having apparent densities greater than the apparent density of the initial char. With scenario II fragmentation, all of the apparent density bins are
5. Conclusions As coal char particles burn in the type of environments established in pulverized coal-fired combustors, they fragment. To accurately predict overall mass loss rates, char particle oxidation models must include the effects of fragmentation. Without fragmentation, at the rates that chemical reactions occur, all particles less than about 20 lm would be consumed early in burnoff, and the particle size distribution would decrease with increased char conversion, a scenario not experimentally observed. Fragmentation with variations in the apparent densities of the fragments yields calculated size and apparent density distributions that are in accord with experimental observations. The fragmentation model put forth in this paper is capable of accurately predicting the observed m/m0, size and apparent density distributions as well as the observation that particles of higher densities than the apparent densities of the initial char particles are created during both the early and late stages of char conversion. Since small particles burn at faster rates than large particles, these results suggest that deriving accurate kinetic parameters from char oxidation data obtained in experiments
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in which char particles burn in the zone II burning regime requires that fragmentation be accounted for during the burning process. Allowing for scenario II fragmentation results in a broadening of the temperature distribution with conversion, as observed experimentally, and a more accurate prediction of the size distribution of the ash particles produced during burnout.
Acknowledgments M.B.T. acknowledges Stanford’s Terman Family Fellowship for support; the authors also acknowledge the support of the U.S.D.O.E., managed through N.E.T.L. (Stephen Seachman, Project Manager). The authors also thank students Sam Garret and Ian Girard for help collecting some of the experimental data.
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References [1] R.E. Mitchell, Proc. Combust. Inst. 28 (2000) 2261– 2270. [2] R.E. Mitchell, A.E. Akanetuk, Proc. Combust. Inst. 26 (1996) 3137–3144. [3] R.H. Essenhigh, Combust. Flame 99 (2) (1994) 269– 279. [4] E.W. Thiele, Ind. Eng. Chem. 31 (7) (1939) 916–920. [5] R.E. Mitchell, L. Ma, B. Kim, Combust. Flame 151 (3) (2007) 426–436. [7] S.K. Bhatia, D.D. Perlmutter, AIChE J. 26 (3) (1980) 379–386. [9] D. Dunn-Rankin, A.R. Kerstein, Combust. Flame 69 (2) (1987) 193–209.
Proceedings of the
Combustion Institute
Proceedings of the Combustion Institute 34 (2013) 2461–2469
www.elsevier.com/locate/proci
Characterizing char particle fragmentation during 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 ensemble of char particles exposed to an environment in which their overall burning rates are controlled by the combined effects of oxygen diffusion through particle pores and chemical reactions (the zone II burning regime). The model allows for changes in particle size due to burning at the external surface, changes in particle apparent density due to internal burning at pore walls, and changes in the sizes and apparent densities of particles due to percolation type fragmentation. In percolation type fragmentation, fragments of all sizes less than that of the fragmenting particle are produced. The model follows the conversion of particles burning in a gaseous environment of specified temperature and oxygen content. The extent of conversion 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 data needed to adjust model parameters. Pulverized Wyodak coal particles were injected into the reactor and char samples were extracted at selected residence times. The particle size distributions and apparent densities were measured for each sample extracted. The intrinsic chemical reactivity of the char to oxygen was also measured in experiments performed in a thermogravimetric analyzer. Data were used to adjust rate coefficients in a six-step reaction mechanism used to describe the oxidation process. Calculations made allowing for fragmentation with variations in the apparent densities of fragments yield the type of size, apparent density, and temperature distributions observed experimentally. These distributions broaden with increased char conversion in a manner that can only be predicted when fragmentation is accounted for with variations in fragment apparent density as well as size. The model also yields the type of ash size distributions observed experimentally. Ó 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 to increase well into the 21st century and beyond. ⇑ Corresponding author.
E-mail address: Tilghman).
[email protected]
(M.B.
As much of this forecasted rise will occur in developing countries, use of cheap fossil fuels will continue to grow despite environmental concerns. Since fossil fuel combustion, in particular coal combustion, has a well-documented implication on climate change and air quality, burning the fuel cleanly and efficiently remains a paramount goal.
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.07.065
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Nomenclature bi,j Ci,k D Di,k DO kd kfrag m b M Ndens Ni,k Nsize Nu Pi,j,k,m
Pg Ps R Rex Rin q Sg Si,k
element i, j of the progeny matrix b, representing size distribution during fragmentation fraction of particles in bin i, k that burn out of size-class i due to external burning diameter of particle fraction of particles in bin i, k that burn out of density-class k due to internal burning oxygen bulk diffusion coefficient in particle boundary layer mass transfer coefficient fragmentation rate coefficient particle mass molecular mass number of density classes implemented in model number of particles which reside in size–density bin i, k number of size classes implemented in model Nusselt number element i, j, k, m of the tensor P; represents the fraction of particles which [start in size class i, end in size class j, and start in density class k] that ends in density class m oxygen partial pressure in ambient gas oxygen partial pressure at the exterior particle surface universal gas constant external reactivity of the particle (g/ m2/s) internal reactivity of the particle (g/ m2/s) overall burning rate of the particle (g/ m2/s) specific internal surface area (m2/g) fraction of particles in size–density bin i, k which will fragment within time step dt
The efficient burning of any particular fossil fuel relies on accurate characterization of the fuel conversion process so that optimal reaction conditions can be identified. This requires the development of models that accurately predict fuel conversion rates for specified temperature, pressure, and gas composition. With porous solid fuels, the models must not only have parameters that accurately describe the rates of chemical reactions that consume the carbonaceous material but they must also have parameters that accurately describe the transport of reactive gases through particle pores as well as parameters that
Sh Tp Tg Tw x xi
Sherwood number particle temperature ambient gas temperature wall temperature to which particles radiate conversion fraction diameter of size-class i
Greek symbols DH Dqk Dxi a e k c co g qc qk w r rsb x tO
heat of reaction apparent density difference between density class k and k + 1 diameter difference between size class i and i + 1 size sensitivity parameter for fragmentation particle emissivity thermal conductivity of gas constant factor by which size interval varies for each size bin, c = xi/xi+1 change in volume upon reaction per unit oxygen consumed effectiveness factor which relates internal reactivity to maximum possible internal reactivity apparent density of the carbonaceous material density of density-class k structural parameter used to fit internal surface area throughout the course of conversion piecewise standard deviation of the Gaussian distribution used to predict fragment densities Stephan–Boltzmann constant density sensitivity parameter for fragmentation moles O2 reacted per mole carbon reacted
accurately describe the mode of burning, i.e., how the size and apparent density of the particle vary with mass loss during the conversion process. Even with accurate chemistry, transport, and mode of conversion models, accurate prediction of mass loss during the combustion of solid fuels will depend upon the extent of fragmentation during the conversion process. All coal particles fragment to some extent during coal combustion. Fragmentation reduces the particle size, and small particles are converted to gaseous species at faster rates than large particles. Fragmentation occurs during coal devolatilization and during char
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oxidation, fragmentation during devolatilization potentially occurring to a greater extent. Despite the known occurrence of fragmentation during combustion, most models of the coal combustion process do not include fragmentation during either devolatilization or char oxidation. In this paper, focus is placed on the prediction of fragmentation during char oxidation under conditions that exist in pulverized fuel combustors. 2. Theoretical approach 2.1. Particle population balance model A model has been developed that is capable of predicting overall conversion rates of an ensemble of pulverized coal of biomass char particles exposed to gaseous environments of specified temperature, pressure, and gas composition. The particle population balance model employed builds on our earlier models [1,2] and includes tracking particles in a size–density matrix, as shown in Fig. 1. Each column i represents a certain size class, and each row k represents a certain apparent density class. Large particles are represented by large values of i and high apparent density particles are represented by large values of k. In this model, the smallest particles (i = 1) and the lowest apparent density particles (k = 1) represent ash particles. The number of particles in each size– density bin i, k, henceforth referred to as Ni,k, is tracked. With each differential time interval dt, the effects of burning and fragmentation may change particle sizes and apparent densities enough to warrant bin change, changing Ni,k. While burning can only change a particle’s size class or density class by one at a time, fragmentation can produce particles that may instantaneously populate any size–density bin below that of the fragmenting particle. The differential equation that governs the variations in the number of particles in each size– density bin with time is given in the following equation: dN i;k ¼ ðC i;k þ Di;k þ S i;k ÞN i;k þ C i1;k N i1;k dt i N dens X X þ Di;k1 N i;k1 þ bi;j P i;j;k;m S j;m N j;m ð1Þ j¼1 m¼1
Fig. 1. Visualization of the effects of burning and fragmentation.
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For Nsize size classes and Ndens density classes, there are Nsize Ndens similarly structured ODEs that must be solved simultaneously to track the particles in each size–density bin. The first term on the right hand side of Eq. (1) accounts for all particles that leave bin i, k. The variable Ci,k represents the fraction of particles in bin i, k that burn out of the bin per unit time because of a decrease in particle diameter due to external burning, the variable Di,k represents the fraction of particles that will burn out of the bin per unit time because of a decrease in apparent density due to internal burning, and the variable Si,k represents the fraction of particles that will experience a fragmentation event and leave the size–density bin. The second and third terms on the right hand side of Eq. (1) account for particles that will enter bin i, k due to diameter-related burning in the immediately larger size class and density-related burning 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 to fragmentation events occurring in all bins, including itself. Particles can fragment into bin i, k from any bin of an equal or larger size class. The bi,j are elements of the progeny matrix that describes the size distribution of a group of fragmenting particles. Element bi,j is the fraction of fragmenting particles in size class i that fragment into size class j. The Pi,j,k,m are elements of the P tensor that describes the density distribution of a group of fragmenting particles. Element Pi,j,k,m is the fraction of the particles changing from size j to i that are also changing from apparent density m to k. The fraction of particles in the size–density class j, m that will experience a fragmentation event during the time interval dt is given by Sj,m. When summed over j and m, the final term represents all particles 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 particle burning 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 relating particle mass, apparent density and size (m = qpD3/6), the equations for the external and internal burning rates per unit external surface area, Rex and Rin, respectively, can be defined as follows: 1 dm q dD ¼ c Rex and 2 dt pD2 dt ex 1 dm D dqc ð2Þ ¼ Rin pD2 dt in 6 dt In terms of the external and internal burning rates, the overall particle burning rate per unit external surface area can be expressed as
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1 dm ¼ ðRex þ Rin Þ ¼ ð1 þ Rin =Rex ÞRex ð3Þ pD2 dt Employing the concepts put forth by Thiele [4], the internal particle burning rate is related to the maximum possible internal burning rate by an effectiveness factor g, such that Rin = g Rin,max. The maximum possible rate of internal burning corresponds to the situation when the particle temperature and oxygen concentration are uniform throughout the particle, and equal to those existing at the outer surface of the particle. This implies that the maximum possible internal burning rate per unit internal surface is equal to the external burning rate per unit external area, and hence q¼
Rin;max Rex ¼ 3 ðp=6ÞD qc S g pD2
ð4Þ
where Sg is the specific surface area of the carbonaceous material. Combining the above equations results in the following expression for the overall particle burning rate in terms of the effectiveness factor and the burning rate at the external particle surface, which depends on the temperature and oxygen concentration (or partial pressure) existing at the external surface of the particle gq S g D q¼ 1þ c Rex ð5Þ 6 The overall particle burning rate per unit external surface area can also be written in terms of the oxygen partial pressure in the ambient gas Pg and the oxygen concentration at the external particle surface Ps, as follows: kd P 1 cP s =P ln ð6aÞ q¼ c 1 cP g =P where kd ¼
b C DO Sh M b m DmO RT
ð6bÞ
This equation assumes spherical, isothermal particles with no chemical reaction in the boundary layer surrounding the particle; account is also made for Stefan flow in the boundary layer. Assuming steady-state burning, the particle temperature is determined from the following energy balance equation: qDH ¼
¼
Nuk j ðT p T g Þ þ rðT 4p D 1j T 4w Þ where j ccp;g DmO q b C kNu M
ð7Þ
Account is made for energy losses via conduction, convection, and radiation from the outer surface of the particle and energy generation due to burning. Equations5, 6a, 6b, 7 permit the deter-
mination of the oxygen partial pressure at the external surface of the particle and the particle temperature, given the temperature and oxygen partial pressure in the particle’s environment, and a path to determine the burning rate at the external particle surface, Rex, which depends upon the rates of chemical reactions on the external surface. We use the following six steps heterogeneous reaction mechanism developed in previous work [5] to describe the effects of chemical reaction: 2Cf þ O2 ! CðOÞ þ CO 2Cf þ O2 ! C2 ðO2 Þ
ðR1aÞ ðR1bÞ
Cb þ Cf þ CðOÞ þ O2 ! CðOÞ þ CO2 þ Cf Cb þ Cf þ CðOÞ þ O2 ! 2CðOÞ þ CO Cb þ CðOÞ ! Cf þ CO
ðR2Þ ðR3Þ ðR4Þ
Cb þ C2 ðO2 Þ ! 2Cf þ CO2
ðR5Þ
In the above mechanism, Cf represents a free carbon site available for adsorption, Cb represents an underlying bulk carbon site, C(O) represents an oxygen atom adsorbed onto a carbon site, and C2(O2) represents two adjacent carbon sites, both having adsorbed oxygen atoms. Using this reaction mechanism, intrinsic carbon reactivity to oxygen is given by Eq. (8), where RRi stands for the rate of reaction i b C ðRR1a þ RR2 þ RR3 þ RR4 þ RR5 Þ Ri;C ¼ M
ð8Þ
The rate of each reaction is written in terms of the concentrations of the species involved in the reaction and a reaction rate coefficient, which is expressed in Arrhenius form. Reactions (R1– R3) are approximated as having a single activation energy, whereas the desorption reactions (R4) and (R5) account for a distribution of activation energies due to the range of carbon binding energies present on a real coal char surface. The model does not take into account the impact of thermal annealing on char reactivity. Differential equations based on the mechanism are solved simultaneously with the particle population balance model equation to determine the concentrations of the adsorbed species on particle surfaces during char conversion. The total number of differential equations that are solved simultaneously is 3 Ndens Nbin, tracking Ni,k, C(O)i,k, and C2(O2)i,k. In environments containing small amounts of CO (as in this study), the reaction mechanism predicts a char conversion rate that is almost first order in the oxygen concentration. Accordingly, we use the concepts put forth by Thiele [4] to determine the effectiveness factor from the Thiele modulus assuming first order kinetics. The specific surface area of the carbonaceous particle material, Sg, must also be tracked throughout the course of burning. We use Eq.
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(9) to follow the specific surface area with char conversion; the structural parameter w is determined by fitting surface areas measured during the course of oxidation, as described in previous work [5]. This surface area model is consistent with the one developed by Bhatia and Perlmutter to follow surface area during carbon conversion [7] pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qc;0 Sg ¼ S g;0 ð1 xÞ 1 w lnð1 xÞ ð9Þ qc The variables Ci,k and Di,k in Eq. (1) are calculated via Eqs. (10) and (11). In these equations, Dxi and Dqk are the size-class and density-class spacing, respectively 1 dD dD 2Rex ¼ where Dxi dt i;k dt qc 1 dqc dD 6Rin ¼ qc where ¼ ¼ gqc S g Rex Dqk dt i;k dt D
C i;k ¼
ð10Þ
Di;k
ð11Þ
2.3. Particle fragmentation As shown previously [2,7], the type fragmentation that occurs during char oxidation is percolation, in which the fragmenting particle produces fragments in all smaller size classes. The elements of the progeny matrix for percolation are calculated via Eq. (12), originally formulated by Dunn-Rankin and Kerstein [7]. This form of the progeny matrix is consistent with prior combustion models which attempt to account for percolative fragmentation during char combustion [2,7] ( 3ðijÞ c iPj bi;j ¼ N size jþ1 ð12Þ 0 otherwise The elements of the matrix S, which represents the fraction of particles that experience a fragmentation event during the time span dt, are defined below: x q S i;k ¼ k frag 0 xai ð13Þ qk This form of the matrix S builds on the formulation by Dunn-Rankin and Kerstein, which considers a fragmentation rate to be power-law dependent in size. In our expression, we consider it to be power-law dependent in both size and density, since low density particles are assumed to fragment more readily than high density particles. The fragmentation rate coefficient kfrag increases the rate of fragmentation uniformly for all sizes and apparent densities. The apparent density sensitivity parameter, x, defines the dependency of fragmentation rate on apparent density. The size sensitivity parameter, a, defines the dependency of fragmentation rate on particle size. These parameters are adjusted such that the model gives fragmentation rates that are consistent with exper-
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imental observations for both size and apparent density variations during char conversion. The tensor P is used to describe the variation in apparent density distribution as particles fragment. Each element Pi,j,k,m represents, of the particles changing from size class i to j, the fraction which also change from density class k to m. The physical basis for the P tensor is that particle fragments do not necessarily embody the internal pore structure of the original fragmenting particle, meaning not all particles are expected to have the same apparent density as the fragmenting particle. In our approach, the distribution of fragment densities is modeled as a Gaussian distribution centered about the apparent density of the fragmenting particle. It is expected that most fragments will retain similar apparent densities to the parent particle, but that some particles will have a higher or lower apparent density. This results in values for the P tensor as follows: ðqm qk Þ2 1 P i;j;k;m ¼ pffiffiffiffiffiffiffiffiffiffi e 2r2 2pr2
ð14Þ
The variance r is treated as a function of i and j. If the parent and fragment sizes are vastly different, then the fragment is less likely to embody the same internal pore structure as the parent particle. Thus it is more likely to have a different apparent density than the parent particle. The variance is treated as a piecewise factor with three different values, as shown in Eq. (15). Each value is adjusted to provide good agreement between model predictions and experimental observations. 8 N size > < r1 if i j < 5 r ¼ r2 if N 5size < i j < N 2size ð15Þ > : N size r3 if i j > 2
3. Experimental methods In our experimental approach, size-classified coal particles were injected into our entrained laminar flow reactor and particles were extracted at selected residence times. A sample was extracted just subsequent to coal devolatilization (at a residence time of 37 ms in the flow reactor environments employed), as evidenced by the disappearance of radiating volatile gases surrounding particles. The extracted, partially reacted char particles were examined to determine particle size distributions, apparent densities, specific surface areas and extents of conversion. The techniques involved are described in previous work [1,2,5]. In this work, we also measured particle settling fractions (the mass fractions of a sample of particles that sank in water) by placing char particles in a water column above filter paper and weighing the mass of particles that sank, as a
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Table 1 Kinetic parameters for the reactivity of Wyodak coal to oxygen. Reaction
Preexponential A
Activation Energy E (kJ/ mol)
Std Dev r (kJ/mol)
R1a R1b R2 R3 R4 R5
4.50 107 1.95 103 1.18 109 3.74 1016 1.00 1013 1.00 1013
100 55 120 227 320 280
– – – – 36 45
qualitative indicator of the spread in apparent density of particles. Wyodak coal, a subbituminous coal from Wyoming, was pulverized and screened to obtain particles in the 75–106 lm size range for testing. Gas conditions in the entrained flow reactor were set to yield a post-flame environment containing 6% at nominally 1650 K. Values determined for Sg,0 and W were 135 g/m2 and 3, respectively, values experimentally determined using CO2 as the adsorption gas in BET surface area measurements. The kinetic parameters needed to describe the rate coefficients of the reactions in the mechanism presented above were determined under kinetically controlled conditions in oxidation experiments performed in our thermogravimetric analyzer. The Arrhenius parameters that best described the mass loss data are listed in Table 1. In the calculations discussed below, the measured size distribution of particles extracted from the reactor just subsequent to devolatilization (i.e., at a particle residence time of 37 ms) was used as the initial size distribution, and all particles were assumed to have the same apparent density, taken to be that measured for the ensemble of particles collected at this residence time (qc,0 = 0.74 g/ cm3). This gives the initial normalized number distribution, Ni,k,0. Integration of Eq. (1) yields the numbers of particles in each size–density bin after burning for time t. Values of Ni,k at time t and Ni,k,0 are used to evaluate m/m0 at this time. At complete burnout, the calculations yield approximations to the size distributions of the ash particles.
measured values at the selected residence times are shown in Figs. 1 and 2, along with the calculated values. The calculated mass conversion profiles do not match the observed conversion profiles when it is assumed that there is no fragmentation. Also with no fragmentation, the calculated particle size distributions do not agree well with the measured particle size distributions, as seen in Fig. 3. The observed particle size distribution shifts towards smaller sizes significantly faster than the calculated size distribution. This suggests the presence of fragmentation. In the following discussion, we refer to scenario I fragmentation as fragmentation with all fragments having the same apparent density as the fragmenting particle and scenario II fragmentation as fragmentation with variations in apparent densities of fragments. Assuming scenario I fragmentation, values for kfrag, a, and x were determined that yielded calculated profiles that adequately described the observed size distributions on a volume fraction basis, as this is what is measured by our Coulter Counter Multisizer, an electroresistive sizing device. The values determined (kfrag = 0.025, a = 2, and x = 1), yield calculated size distributions that closely match the measured size distributions, as shown in Fig. 4. The calculated size distributions are more accurate at early times than at late times. This is likely due to the fact that in this model, the fragmentation rate is assumed to be constant in time whereas in actuality, the fragmentation rate may vary as char conversion progresses. Scenario I fragmentation yields calculated char conversion
4. Results and discussion The mass loss and apparent density measurements indicate that in the environments established in the entrained flow reactor, char particles burn in the zone II burning regime in which the overall particle burning rates are limited by the combined effects of chemical reaction and pore diffusion – both internal and external burning contribute to overall char conversion. These
Fig. 2. Observed and simulated mass loss rates (a) and apparent density (b) in 6% O2 environments.
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Fig. 4. Observed and simulated volume-normalized size distributions with accounting for fragmentation.
Fig. 3. Observed and simulated volume-normalized size distributions without accounting for fragmentation.
profiles that agree with measured profiles more closely, as seen in Fig. 1. Such fragmentation also results in an improved agreement between the observed and calculated apparent density profiles, as noted in Fig. 2. However, calculations assuming scenario I fragmentation indicate that there are no particles in apparent density bins higher than those of the initial fragmenting particles. This is not in accord with the results of our particle settling tests. The particle settling tests were initiated to determine if particles having higher apparent densities than the initial fragmenting particles could be produced during fragmentation. It was observed that with the char sample extracted from the entrained flow reactor just subsequent to devolatilization, relatively few of the partially reacted
Fig. 5. Observed settling fraction in water.
char particles settled (sank) in water. However, with the partially reacted chars extracted from the reactor at longer residence times, several of the particles in the sample did sink to the bottom of the container. As residence time increased, the mass fraction of particles that settled increased. The results are shown in Fig. 5. Due to insufficient wetting and the complex rheological effects that water can have on coal char particles, this does
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populated with particles, even those apparent density bins for qcqc,0 > 1. The predicted mass fractions of particles having qcqc,0 > 1 are also similar to the observed mass fractions (Fig. 5) at comparable residence times. Scenario II fragmentation does not significantly alter the particle size distributions calculated assuming scenario I fragmentation. Char conversion profiles are also not significantly changed, although conversion tends to be slightly slower when scenario II fragmentation is assumed. In addition to predicting the presence of high apparent density particles early in burnoff, assuming scenario II fragmentation also yields calculated apparent density profiles that are in better agreement with the ones measured at all residence times. The overall char conversion rate is slightly slower when scenario II fragmentation is assumed than when scenario I fragmentation is assumed. This is a consequence of the high apparent density fragments that are produced, which take longer to burnout than lower apparent density particles of comparable size. The effect is more pronounced at early conversion times – with scenario II fragmentation, the overall apparent density of char particles decreases slower at early times than it does assuming scenario I fragmentation. As conversion progresses, the two fragmentation scenarios tend to mimic each other, a likely consequence of particle apparent densities approaching the higher apparent density of the ash with increased burnoff. Fig. 6. Simulated apparent, ash-free density distributions.
not necessarily imply that the particles that sank have a higher density than water. However, we do believe that it indicates that during char burnout, particles are being created via fragmentation events that have higher apparent densities than those formed just subsequent to devolatilization. Upon fragmentation, it is possible that pore walls transition from being internal surfaces to external surfaces, rendering an increase in the apparent density of a particle after losing its fragments. With scenario I fragmentation, this observation cannot be predicted. However with scenario II fragmentation, it can. Calculations were made assuming scenario II fragmentation with standard deviations of 0.05, 0.08, and 0.12 g/cm3 for the piecewise formula in Eq. (15). Shown in Fig. 6 are the mass fractions of particles in each of the six apparent density classes used in the calculations at selected residence times. With scenario I fragmentation, there are no particles (mass fraction equal to zero) having apparent densities greater than the apparent density of the initial char. With scenario II fragmentation, all of the apparent density bins are
5. Conclusions As coal char particles burn in the type of environments established in pulverized coal-fired combustors, they fragment. To accurately predict overall mass loss rates, char particle oxidation models must include the effects of fragmentation. Without fragmentation, at the rates that chemical reactions occur, all particles less than about 20 lm would be consumed early in burnoff, and the particle size distribution would decrease with increased char conversion, a scenario not experimentally observed. Fragmentation with variations in the apparent densities of the fragments yields calculated size and apparent density distributions that are in accord with experimental observations. The fragmentation model put forth in this paper is capable of accurately predicting the observed m/m0, size and apparent density distributions as well as the observation that particles of higher densities than the apparent densities of the initial char particles are created during both the early and late stages of char conversion. Since small particles burn at faster rates than large particles, these results suggest that deriving accurate kinetic parameters from char oxidation data obtained in experiments
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in which char particles burn in the zone II burning regime requires that fragmentation be accounted for during the burning process. Allowing for scenario II fragmentation results in a broadening of the temperature distribution with conversion, as observed experimentally, and a more accurate prediction of the size distribution of the ash particles produced during burnout.
Acknowledgments M.B.T. acknowledges Stanford’s Terman Family Fellowship for support; the authors also acknowledge the support of the U.S.D.O.E., managed through N.E.T.L. (Stephen Seachman, Project Manager). The authors also thank students Sam Garret and Ian Girard for help collecting some of the experimental data.
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References [1] R.E. Mitchell, Proc. Combust. Inst. 28 (2000) 2261– 2270. [2] R.E. Mitchell, A.E. Akanetuk, Proc. Combust. Inst. 26 (1996) 3137–3144. [3] R.H. Essenhigh, Combust. Flame 99 (2) (1994) 269– 279. [4] E.W. Thiele, Ind. Eng. Chem. 31 (7) (1939) 916–920. [5] R.E. Mitchell, L. Ma, B. Kim, Combust. Flame 151 (3) (2007) 426–436. [7] S.K. Bhatia, D.D. Perlmutter, AIChE J. 26 (3) (1980) 379–386. [9] D. Dunn-Rankin, A.R. Kerstein, Combust. Flame 69 (2) (1987) 193–209.