Energy & Fuels 1993,7, 721-133
72 1
Reactivity Distributions and Extinction Phenomena in Coal Char Combustion Robert H. Hurt Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550 Received April 8,1993. Revised Manuscript Received September 4, 199P
Based on in situ optical measurements and off-line analyses for four coals, the basic features of single-particlepulverized coalchar combustion have been elucidated as a function of carbon conversion. Two regimes can be clearly defined: one at low carbon conversion, where the reacting particle populations have properties that are nearly time invariant and a second regime at higher carbon conversion where the distribution properties change dramatically. At low carbon conversion, there is a broad distribution of single-particle combustion rates, reflecting the heterogeneity in the parent fuel. Particle-to-particle reactivity differences are shown to be the primary cause of the broad temperature distribution for Pocahontas coal char. At high carbon conversion, carbon-rich particles can be distinguished statistically from inorganic-richparticles by in situ measurement of their spectral emissive factors a t 800 nm. In each case where char carbon conversion proceeds past 50-60%, many particles are observed to undergo large temperature decreases resulting from a loss of reactivity, referred to as near-extinction events. Near-extinction is generally observed to occur before large changes are observed in the particle optical properties, suggesting that deactivation occurs when the particles are still carbon-rich. Plots of particle temperature vs emissive factor conveniently illustrate and summarize the process of char particle combustion to high conversion. These plots reveal two distinct stages in the combustion lifetime of a char particle: (1)a rapid combustion stage at low carbon conversion, followed by (2) a deactivation and near-extinction at roughly constant optical properties, initiating a final burnout stage that occurs slowly and at low temperatures. The two-stage nature of the char combustion process significantly lengthens the time required to achieve high carbon conversion, and the existence of two stages cannot be predicted by conversion-independent kinetic models. More realistic char oxidation models are needed that account for fuel heterogeneity and conversion-dependence effects.
Introduction The levels of unburned carbon in fly ash from commercial pulverized coal combustion processes is a topic of renewed interest.lt2 In particular, an increasing reliance on combustion modifications for NO, control have brought about increasing concerns about high unburned carbon levels. These in turn can lead to boiler operational problems, efficiency losses, and lost opportunities for fly ash reutilization. Char oxidation is the slowest step in pulverized coal combustion, and thus has an important effect on unburned carbon levels for a given furnace and set of operating conditions. High-temperature char combustion has most often been described by global kinetic laws that lump the effecta of surface chemical kinetics and pore diffusion, and express the temperature and pressure dependence of the combustion rate in convenient but arbitrary mathematical forms.3 While the global kinetic approach has been successfully applied to laboratory combustion datak7 in the early and
intermediate stages of combustion, its ability to predict the extent of carbon burnout to 99% and beyond in commercial scaleboilers is questionable for severalreasons. First, global kinetic treatments ignore changes that occur within the carbonaceous solid char as a consequence of oxidation, heat treatment, or mineral matter interactions during c o m b u ~ t i o n .Also ~ ~ ~ignored is the physical and chemical heterogeneity inherent in the parent fuel, which gives rise to a wide variety of combustion rates and burnout times for individual p a r t i ~ 1 e s . l These ~ ~ ~ effects are expected to be very significant in determining the extent of carbon burnout in the industrially relevant range of 95-99.9 5%. Indeed, the residual carbon carried over with the fly ash, representing on the order of 1%of the parent
(6) Smith, I. W.; Tyler, R. J. Fuel 1972,51, 313. (7)Hurt, R. H.; Mitchell, R. E. Unified High-Temperature Char Combustion Kinetics for a Suite of Coals of Various Rank. 24th International Symposium on Combustion; The Combustion Institute Pittsburgh, PA, 1992. (8) Hecker,W.C.;McDonald,K. M.;Reade, W.;Swensen,M.R.;Cope, R. F. Effects of Burnout on Char Oxidation Kinetics: 24th International Symposium on Combustion;The Combustion Institute: Pittsburgh, PA, 1992. (9) Suuberg, E. M. In Fundamental Issues in Control of Carbon Abstract published in Aduance ACS Abstracts, October 15, 1993. Gasification Reactiuity;Lahaye and Ehrburger, Eds.;Kluwer Academic (1) W&h,P.M.;Xie,Jianyang;Douglas,R.E.;Battista,J.J.;Zawadzki, Publishers: The Netherlands, 1991. E. A. EPRI Heat-Rate ImprovementConference,sponsoredby the Electric (10)Nandi, B. N.; Brown, T. D.; Lee, G. K. Fuel 1977,56, 126. Power Research Institute, November 17-19 1992. (11) Hurt, R. H.; Mitchell, R. E. On the Combustion Kinetics of (2) Chen,J.Y.;Mann,A.P.;Kent,J.H.24thInternatiorurlSymposium Heterogeneous Char Particle Populations 24thZntemtionul Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1992. on Combustion; T h e Combustion Institute: Pittsburgh, PA, 1992. (3)Eeeenhigh, R. H. In Chemistry of Coal Utilization, Second (12) Sahu, R.; Northrup, P. S.;Flagan, R. C.; Gavalas, G. R. Combust. Supplementary Volume; Elliott, M. A., Ed., John Wiley and Sons: New Sci. Technol. 1988,60, 215. York, 1981; Chapter 19, pp 1153-1312. (13) Wall, T. F.;Tate, A. G.; Bailey, J. G.; Jenness, L. G.;Mitchell, R. (4) Field, M. A. Combust. Flame 1970, 14, 237. E.; Hurt, H. H. 24th Znternhtional Symposium on Combustion; The (5) Smith, I. W. Combust. Flame 1971, 17, 303. Combustion Institute: Pittsburgh, PA, 1992.
oaa1-0~2419312~o1-0~2i~o4.0~1o 0 1993 American Chemical Society
722 Energy &Fuels, Vol. 7, No. 6, 1993
Hurt
Table I. Coals Investigated
seamname Pittsburgh
state PSOC PA
No. 8 Illinois No. 6 IL BeulahZap Pocahontas
rank
ASTM initial volatile particle dia matter range,fim (d&%
1451D hva bituminous
106-125
39.9
1493D hvb bituminous
106-125 106-125 106-125
46.6 17.0
ND 1507D lignite WV 1508D lv bituminous
44.7
No. 3
fuel, can vary dramatically in its properties and reactivity from those of the bulk fuel.14 The present paper examines the basic features of singleparticle pulverized coal combustion, drawing from experiments performed on particles of diameter 50-200 pm, oxygen concentrations from 6 to 12 vol %, and gas temperatures from 1500to 1700K. This study focuses on two aspects that are important for total carbon burnout: (1) the reactivity distributions early in the combustion process that reflect heterogeneity in the parent fuel and (2) extinction phenomena that occur at high carbon conversions. Combustion behavior at high conversion will be shown here to deviate dramatically from that predicted by global kinetic laws.
Experimental Section Char oxidation kinetics were recently reported for the ten United States coals of various rank and geographic rig in.^ The present paper examines the single-particle combustion behavior of four of these coals, listed in Table I, in more detail. Coal samples were obtained from the Pennsylvania State Sample Bank, pulverized, and sieved under nitrogen to obtain a narrow size fraction for study, 106-125 pm in particle diameter. The size classified samples were stored under argon prior to initiation of combustion studies. The coal combustion experiments were conducted in Sandia’s Coal Combustion Laboratory, which houses a bench-scale,laminar-flow reactor, in which the stoichiometry of a H2/CH$Oz/N2 flame is tailored to produce postflame gases simulating those found in the upper furnace region of a pulverized coal fired boiler. A dilute stream of 106-125 pm diameter coal particles is injected along the centerline of the laminar-flow reactor, and the kinetics of the char combustion stage (subsequent to devolatilization) are investigated in gas environments containing 6 and 12 mol 5% oxygen over the range of gas temperatures 1500 K < Tg< 1700 K. The reactor is equipped with an optical pyrometer that allows in situ measurements of the sizes, temperatures, velocities, and spectral emissive factors of individual, reacting char particles at various residence times in the combustor. [The spectral emissive factor for an irregularly-shaped, emitting particle, with a diameter along the flow axis of d,, is defined as the average spectral radiance (W/(cm2-st.pm))of the particle at a given wavelength (here 800 nm) divided by the spectral radiance of a spherical black body of diameter Cl,. The spectral emissive factor is, in essence, the particle spectral emissivity, multiplied by a shape factor, Al(?rd,2/4),where A is the projected area of the particle as viewed from the optical axis. Here (14) Hurt, R. H.; Davis, K. A.; Yang,N. Y. C.; Headley, T. H.; Gibbins, J. Combustion Reactivity and Physicochemical Properties of Residual Carbon from Pulverized Coal Fired Boilers. Proceedings of the 7th
International Conference on Coal Science, Banff,Alberta, Sept. 1993.
we will often abbreviate the “particle spectral emissive factor at 800 nm” (which is measured optically) as the “emissive factor”, and the “total, wavelength-integrated emissivity” (which is used in heat-transfer calculations) as the “emissivity”.] Particle temperatures are calculated from Planck’slaw using optical signal intensities in spectral bands centered at 500 and 800 nm with bandwidths of 50 and 90 nm, respectively. The reactor is also equipped with an isokinetic solids-sampling probe that permits the extraction of partially reacted chars for off-line physical and chemical analyses. The overall extent of conversion is determined from the chemical analysis of bulk extracted samples, using a combination of Alz03, Si02, TiO2, and total ash as tracers. The reactor, optical technique, and inorganic tracer technique are described in detail elsewhere.15 Partially reacted char samples were also examined through a long focal-length microscope (Model K2 from Infinity Photo-Optical), operating at a nominal magnification of 100X. The samples were examined on a diffuse, white background mounted perpendicular to the microscope axis, and the aperture was adjusted to achieve a depth-of-field adequate to bring groups of particles into simultaneous focus. Illumination was provided by a halogen lamp with two fiber-optic outputs equipped with spot lenses. Photographs were obtained through the microscope side port with a 35 mm camera (Nikon Model F3) and enlarged to 8 X 10 or 11 X 14 formats.
Results The experimental results are presented in Figures 1-8. At each location in the flow reactor, the optical technique records a distribution of particle sizes and a broad distribution of particle temperatures. Char particle sizes differ from the initial coal particle size due to both swelling during devolatilization and surface carbon consumption. Figures 1-4 present in situ optical measurements of particle temperatures and emissive factors at 800 nm, em, during char oxidation for four parent coals: Pocahontas No. 3, Illinois No. 6, Pittsburgh No. 8, and Beulah lignite. Also shown on two plots are theoretically derived ash particle bands, discussed later in the report. These temperature/emissive factor plots exhibit a number of interesting features and will be shown to play a useful role in the analysis of carbon burnout phenomena. A number of auxiliary experiments were performed to aid in the interpretation of the combustion data in Figures 1-4. To investigate the origin of the observed particle temperature distributions,in situ measurements of particle diameter and temperature were made for char from the Pocahontas coal in both an oxidizingand an inert (oxygenfree) environment. The results are presented in Figure 5. The char was first prepared by injecting raw Pocahontas coal in 6 mol % oxygen and collecting the sample at 47 ms residence time, after the extinction of the visible volatile flame and the onset of char oxidation. This char was then reinjected into two environments and optical data collected at 95 ms residence time. Additional optical measurements were made on a synthetic carbon material that is more homogeneous than (15) Mitchell, R. E.; Hurt, R. H.; Barter, L. L.; Hardesty, D. R. “Compilation of Sandia Coal Char Combustion Data and Kinetic Analyses: Milestone Report”, Sandia Technical Report SAND92-8208, June 1992.
Energy & Fuels, Vol. 7,No. 6, 1993 123
Extinction Phenomena in Coal Char Combustion .
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12% oxygen, 25 % 28% char conversions: 8% Figure 1. Optical measurements of particle temperature and emissive factor during combustion of Pocahontaa No. 3 coal char in 6 and 12 mol 5% oxygen. Initial coal particle size 106-125 Fm. Conversions are average values from analysis of bulk extracted samples and are on an char, rather than coal, basis.
coal char. Single particle temperatures were measured for 308 Spherocarb particles (100/120 mesh) after 95 ms residence time in the inert environment (1605 K gas temperature). This temperature distribution had a standard deviation of 15 K. Auxiliary experiments were also performed to develop a method for distinguishing inorganic-rich (ash-rich)from carbon-rich particles, based on the in situ optical measurements. Figures 6 and 7 present optical measurements made on anumber of fly ash samples from different origins. Finally, numerous partially reacted char samples were examined through the long-focal-length microscope, and photomicrographs of typical particle groups are reproduced in Figures 8 and 9. The most important features of this data set are highlighted in the following sections. Particle Temperature Distributions at Low Carbon Conversion. In this section we focus on Figures 1 and 2-a subset of the combustion data for which char carbon conversions are less than 50% . Consider Figure 1,which presents the complete set of single-particle temperatures and emissive factors measured during combustion of Pocahontas No. 3 coal char. These temperature distributions have three notable features. First, the higher rates
of reaction and heat release in the 12 mol % oxygen environment give rise to particle temperature distributions with a higher mean value and somewhat higher standard deviation. Second, early in the combustion process (at 72 ms residence time), a small group of particles are observed a t significantly lower temperatures than the population at large, but disappear before the next measurement position at 95 ms residence time. These particles are most likely in the fiial phases of the initial temperature transient that occurs upon injection of room temperature particles into the hot postflame gases. Third, aside from the few low-temperature particles a t the earliest residence time, the temperature distributions do not undergo significant change in shape or breadth with increasing residence time-only the absolute temperatures shiftto lower values in response to the decreasing local gas temperature. Similar behavior is observed in Figure 2 for the more reactive, lower-rank Illinois No. 6 high-volatilebituminous coal, but only in 6% oxygen. Similar behavior has also been observed in this laboratory for the unreactive, highrank, Lower Kittanning low-volatile bituminous coal in both 6 and 12 mol % oxygen.16 In each of these cases, where the overall carbon conversions are less than 50%,
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724 Energy & Fuels, Vol. 7,No. 6,1993 2100
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12% oxygen, 62% 69% char conversions: 29% Figure 2. Optical measurementa of particle temperature and emissive factor during combustion of Illinois No. 6 COL char in 6 and 12 mol % oxygen. Initial coal particle size 106-125 pm. Conversions are average values from analysis of bulk extracted samples and are on an char, rather than coal, basis.
the breadth and shape of the particle temperature distributions do not change significantly with increasing residence time. The high rank Pocahontas No. 3 coal char, in particular, provides a convenient model system for investigating the statistical variations in single-particle combustion at low carbon conversion and at pseudo steady state, Le., under conditions for which conversion-dependent or timedependent effectsare minimized. The data for Pocahontas coal char are analyzed quantitatively in a later section. Particle Temperature Distributions at High Carbon Conversion. This section considers the particle temperature distributions in Figures 2-4, where the combination of parent coal type and oxygen level leads to char carbon conversions in excess of 50 5%. In contrast to the pseudo-steady-state distributions observed at low carbon conversion, the temperature distributions in Figures 2-4 evolve significantly in time. In particular, at char carbon conversions above about 60% the particle temperature distributions begin to increase in breadth and to change in shape. In Figure 2 for example, which presents
data for combustion of Illinois No. 6 coal char in 12% oxygen, we see that the particle population bifurcates at 117 ms residence time, producing a group of particles with low temperatures at or near the local gas temperature. The overall char carbon conversion here is 69%. Similar, though less pronounced, behavior is observed for Pittsburgh No. 8 char in 12 % oxygen as seen in Figure 3. For the very reactive Beulah lignite in Figure 4,the temperature distribution becomes extremely broad at 117 ms residence time in 12 mol % oxygen (95% char carbon conversion) resulting in a large number of particles with low temperatures. For Beulah lignite we also begin to see a distinct group of particles lying in a recognizable band at low values of the emissive factor. For each of the coals in Table I that reaches an advanced stage of conversion in the residence time available in the CCL laminar flow reactor, the particle temperature distributions broaden significantly. The appearance of low-temperature particles at long residence times is clearly related to the extent of carbon
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conversion, as pointed out by Mitchell.16 Mitchell attributes the effect to the presence of highly oxidized, highash-content particles in these highly reacted samples. In a later section of this present work, we examine the phenomonon in more detail, and discuss its implications for combustion kinetics and the char burnout process. Particle Temperature Distributions in Inert Environments. Figure 5 compares particle temperature distributions for Pocahontas No. 3 coal char in an inert (0% oxygen, 1605 K) and an oxidizing (6 vol % 02,1555 K)environment. The reacting particle population in 6 % oxygen (open symbols) has a standard deviation, UT,, of 87K (or avariance, u ~ pof~7510 , K2),while the nonreacting population has a standard deviation of 21 K (or a variance, ulp2, of 441 K2). The temperature distribution of the synthetic carbon Spherocarb, measured in 0% oxygen a t a gas temperature of 1605 K, had a standard deviation of (16)Mitchell, R.E.23rd International Symposium on Combustion; The Combustion Institute: Pittsburgh, PA, 1990; pp 1297-1304.
15 K (or a variance, u n 2 ,of 225 K2), based on 308 singleparticle measurements. Temperature Distributions of Carbon-Free Ash Particles. In this section we consider the data in Figures 6 and 7, with the ultimate goal of developing a technique for the in situ discrimination of carbon-richfrom inorganicrich particles present at high conversion. Figure 6 presents particle temperature and emissive factor measurements for three samples of Illinois No. 6 coal with very different combustion histories. Figure 6a presents data for a predominantly carbon-rich laboratory-generated sample at 62% carbon conversion taken from Figure 2. The samples in Figure 6b is a 100-190 pm size fraction of a high-density extract from fly ash from a commercial boiler burning Illinois No. 6 coal. The sample and the fluidized bed density segregation technique are described elsewhere.14 This sample is a good source of large (- 100pm) ash particles but also contains 6 wt % residual carbon. The data fall into two groups: a dense collection of points
726 Energy &Fuels, Vol. 7, No. 6,1993
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in a curved band in the left portion of the diagram, and a scattering of points to the right over a wide temperature range, but at generally higher emissive factors. Figure 6c shows optical data taken on the same sample after pretreatment of the high density extract by slow heating in air to 700 "C followed by a 2-h hold time. This procedure removes the residual carbon and results in the disappearance of the second group of particles at high emissive factor. We can clearly associate the ash particles with the points clustered in the curved band in the left portion of the figure, and the carbon-containing particles with the scattered points at higher emissive factors. Also shown on Figure 6c is the range of expected ash particle temperatures calculated from an expected range ash total ash emissivities (0.1-0.5) and an expected range of ash particle densities (0.5-2.5g/cm3). The higher temperatures observed for many ash particles is an experimental artifact, as will be explained in a later section. Figure 7 shows the results of similar experiments performed on samples prepared by ashing size-fractionated samples of the four raw coals used in the char combustion experiments of Figures 1-4. In each of the four cases, the optical signature of the pure fly ash samples is similar to that seen in Figure 6c. Optical Microscopy. Microscopic examination of partially reacted chars at char carbon conversionslessthan 30 % reveals a predominance of black, carbon-rich particles with few or no distinct ash particles or mixed ash/carbon particle types. In contrast, Figure 8 shows a variety of particle morphologies in highlyreacted Beulah lignite char. A number of different particle types are represented, including black, carbon-rich particles: highly reflective, inorganic-rich particles; and various mixed types containing significant quantities of inorganic material and carbon visible within a single particle. The black material in Figure 8 is primarily due to elemental carbon or to various iron-bearingphases. For any given single particle, color and morphology alone are not sufficient to identify the presence of elemental carbon, and work is underway applying laser spark spectroscopy to relate the images to
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Figure 6. Optical measurements for several Illinois No. 6 char samples of varying combustion histories. Gas environment: 12 mol % oxygen,Tg= 1555K. Samplesare (a)laboratory-generated char at 62% conversion from Figure 2; (b) high density extract from fluid-bedseparation of fly ash collected from a commercial boiler; (c) same sampleas in (b),but after pretreatment by ashing in air at 700 O C for 2 h to remove residual carbon. composition on a single particle basis. Nevertheless, elemental carbon is clearly the most abundant black component in the residues of high-temperature combustion studied here, as can be seen by comparison of these samples with essentially carbon-free samples that have undergone an additional postoxidation in air at lo00 "C for several hours. The mixed particle types include those in which avisible ash layer surroundsa carbon-rich core and several asymmetric particles with segregated carbon-richand ashrich zones in different regions of the particle. Many of the highly reflectiveparticles contain dark inclusionswhich are removed by subsequent air oxidation at lo00 "C for 2 h. Many of the fine dark inclusions can be removed by ultrasonic treatment and are likely distinct fine carbon particles deposited on the inorganic-rich particles upon sampling. In contrast, the Pittsburgh No. 8 char, which reaches 59% conversion at 117 ma in 12 mol % oxygen, does not contain inorganic-richor mixed particle types at the longest residence time investigated. The photomicrograph in Figure 9 reveals the predominance of black, carbon-rich particles, and the corresponding optical data contains few, if any, particles with emissive factors below 0.3. Note at 117 ms (59% conversion) the early signs of the rapidly
Energy &Fuels, Vol. 7, No. 6, 1993 727
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Extinction Phenomena in Coal Char Combustion
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barriers, etc. These factors contributing to e, are not dealt with individually in this analysis. 2 2000 The first four factors listed above are believed to be minor contributors to the breadth of the temperature distributions for the Pocahontas coal char for the reasons listed below; more detailed arguments can be found elsewhere.” The standard deviation due to temperature 1400 measurement errors, e,, is estimated to be of order 20 K I or less, based on measurements made on the more 0.0 0.5 1.0 1 0.0 0.5 1.0 homogeneous synthetic carbon material Spherocarb, entrained in high-temperature inert (oxygen-free) environments. The term e, is small because of the absence of distinct ash particles in the Pocahontas char at low carbon conversions as indicated by the high emissive factors and confirmed by optical microscopy. The parameter e, is neglected based on the observed dependence of UT on oxygen concentration.17 The shape factor, e,, in intended to account for the effects of gross particle shape on mass and energy transport to and from the reacting particle. 0.0 0.5 1.0 1.5 0.0 0.5 1.0 Particles of high aspect ratio will have a characteristic Emissive factor Emissive factor dimension for heat and mass transport that approximates Figure 7. Optical measurements of particle temperature and the smallest dimension of the particle. Other aspects of emissive factor for various fly ash samples. Gas environment: particle morphology, such as the presence of large cavities 12 mol % ’ oxygen, Tg= 1555 K. Samples prepared from raw or protuberances, cenosphere structure, and surface struccoals by ashing in air at 700 O C for 2 h. ture (roughness) will affect global reactivity and are decreasing particle temperatures that are characteristic therefore implicitly included in the reactivity factor, e,. of the high conversion regime. Defined in this way, the parameter e, is related to and is of the same order as ed, which is shown to be small in the treatment below. Waters et al.lSand Choi and Gavalaslg Discussion have treated the effect of nonsphericity on the measureOrigin of the Particle Temperature Distributions ment of particle diameter and on particle combustion at Low Carbon Conversion. This section is devoted to behavior in some detail. characterizing the particle-to-particleheterogeneity in the Having excluded a number of possible influencingfactors parent fuel. Heterogeneity plays an important role in coal from the general case, a simplified expression for the combustion rates and carbon b u r n ~ u t , ’ ~and ’ ~ this exercise particle temperature is now: is an important prelude to developing single-particle-based kinetic models. A convenient model system for investiT, = T, + ed + e, + e, gating fuel heterogeneity is the Pochoatas No. 3 coal char, For the sake of this analysis, we assume that these which exhibits particle temperature distributions that are statistical e variables are normally distributed with a mean very nearly stationary at low carbon conversions, as value of zero and variances a?. The summation, T,,is a discussed in the results section. linear combination of Gaussian variables and is therefore The particle temperature distributions in Figures 1and itself Gaussian with a mean value of Tmand a variance of 5 are, in general, the product of a number of factors, including errors in temperature measurement, and variQTp2 = up2 + u,2 (3) ations in particle size, physical properties, and reactivity. The following analysis determines the relative contribuAfter estimating the individual contributions to the total tions of these factors to the observed distributions of variance due to diameter (Ud’) and physical properties particle temperature. In the most general case, a measured (up2), the remaining variance will be used to infer the particle temperature can be expressed as the following contribution of particle-to-particle variation in reactivity sum: by difference according to eq 3. Variationsin Particle Size, ea. A portion of the total T, = T, + temperature variation is due to the presence of particles where T, is the temperature of the particle with average of various size in the sample. The contribution of particle properties and ei are statistical variables that represent size variation to the total temperature variance can be the deviation from T m of a single particle due to i different assessed directly from the optical data in Figure 5. Here factors. These factors can be classified as follows, in we see single-particle measurements of temperatures and approximate order of increasing importance: errors in diameter along with linear regressions of the data in the temperature measurement, e,; the presence of (carbonform T = ad, + b. The total sum of squared residuals, free) ash particles, e,; variations in CO/COz product ratio, SST = Tp- Tm12can be divided into the regression sum e,; variations in particle shape, e,; variations in particle (17) Hurt, R. H.; Hardesty, D. R. In Coal Combustion Sciencediameter, ed; variations in thermodynamic and transport Quarterly ~ogre8aReport;Hardeaty, D. R., Ed.; SandiaTechnicalReport, properties, e,; and variations in global reactivity, e,. Note September 1992. that the term represents variations in global reactivity, (18) Waters, B. J., Mitchell, R. E., Squires, R. G., and Laurendeau, N. M. 22nd Symp. (Znt.)on Combustion,The Combustion Institute, 1986 which itself comprises a large number of effects, such as pp. 11-27.- variation in internal surface, active site concentration, (19) Choi, M. K.; Gavalas, G. A Theoretical Study of Combustion of Nonspherical Particles submitted to Combust. Sci. Technol. particle pore structure, the presence of inorganic diffusion
-
-
1
+
Cei
f[
Hurt
728 Energy & Fuels, Vol. 7,No. 6, 1993
Figure 8. Particle morphologies observed in highly-reacted Beulah lignite char. Coal particles initially 106-125 pm, reacted in 12 mol % oxygen for 117 ms. Nominal magnification 1OOX. 2 1 00
1721
2000
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,
,
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Partlcle emlrrlve factor
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1
0.5
1.0
1.5
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Particle emlrrlve factor
t
Figure 9. Optical measurements of particle temperature and emissive factor during combustionof Pittsburgh No. 8 coal char in 12 mol % oxygen. Initial coal particle size 106-125 pm. Carbon conversions are 33% at 72 ms and 57% at 117 ms (volatile free basis). Bottom: Photograph of particle types observed in sample extracted at 117 ms residence time, taken through long focallength microscope; nominal magnification 1 0 0 ~
of squares, SSR = c[Td - Tm12 plus the error sum of squares, SSE = c[Tp - TdI2, where Tp is the measured single-particle temperature, T m is the overall mean temperature, Td is the temperature predicted by the regression for particle diameter d, and c denotes the sum over all particles.
The fraction of the total variation in Tpthat is due to the dp/Tprelationship is SSR/SST = r2,the correlation coefficient of the regression. The coefficient r2 is 0.262 for the data in 0% oxygen and 0.0215for the data in 6 mol % oxygen. For the data in 6 mol % oxygen, the variance in ed = r2uTP2= 0.0215 X 7510 = 161 K2. Variations in Thermodynamic and Transport Properties, e,. The temperature attained by a char particle burning at a given rate is influenced by its emissivity, c, and, in nonisothermal cases, by the product pCp, which affects the particle thermal inertia. The particle-toparticle variation in these properties is difficult to measure directly but can be estimated from the breadth of the temperature distribution observed in the inert, oxygenfree environment in Figure 5. The portion of the temperature variance not due to the effect of particle size is (1 - r2)u2= (1 - 0.262).(459) = 339 K2, or u = 18 K. The range of variation of emissivity and density required to explain the remaining standard deviation of 18 K was estimated to be 0.96 > c > 0.65,or 1.6 > p > 0.12. Using these ranges of emissivity and density, a range of particle temperatures was calculated for combustionof Pocahontas No. 3 char in the 6mole- % oxygen environment, assuming a uniform reactivity. The physical property variations alone resulted in a temperature variance of 195 K2 (for density variations) or 780 K2 (for emissivity variations). Both values are much less than the total temperature variance of 7510 K2, indicating that physical properties alone cannot account for the broad distribution of particle temperatures. Variations in Global Reactivity, +. Here we infer the contribution of particle-to-particle variation in reactivity by rearrangement of eq 3:
The final results of the analysis of variance are summarized in Figure 10. Of the total temperature variance of 7510
Energy & Fuels, Vol. 7, No. 6, 1993 729
Extinction Phenomena in Coal Char Combustion
5
I
7000
L
'ii
[
-
""I"
6000
Ngg 5000 . as! v v 4000 c *=
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variation in physical properties variation in size
estlmate 1
estimate 2
"
Spherocarb, 0% oxygen
PSOC-l508D, 0% oxygen
PSOC-l508D, 6% oxygen
Figure 10. Variances of particle temperature distributions in inert and combustion environments and their individual components for Pocahontas No. 3 coal char.
K2 (u = 87 K) for combustionof Pocahontas coal, reactivity variations are responsible for at least 6573 K2 (a = 81 K), or 87 % . Reactivity variations are therefore the primary cause of the broad distribution of temperatures observed at low-to-intermediate carbon conversions for the Pocahontas coal char. Distribution of Single-ParticleCombustionRates. Based on the discussion above, let us assume that all of the temperature variations are due to variations in reactivity and let us compute single-particleburning rate distributions from the data in Figure 1. Using a previously determined empirical relation for the CO/CO2 product ratio,' we calculate a mean combustion rate of 2.8 X 103 g of carbon/(cm2.s)and a standard deviation of 1.3-10" in 6%, and a mean of 5.6010~g of carbon/(cm2-s)and a standard deviation of 2.3-1c3 in 12% oxygen, both at 95 ms residence time. For these standard deviations, and assuming a normal distribution, burning rates vary by about a factor of 3 among the 68% ofthe particles within 1standard deviation of the mean reactivity. Further, 16% of the particles have burning rates less than half of the mean burning rate, and 7% have burning rates less than one-fourth of the mean, underscoring the importance of heterogeneity in this process. Based on this detailed analysis for one coal char, we can reexamine the data in Figures 1-4, interpreting the temperature distributions primarily in terms of particle reactivity distributions. This will be useful in the second half of this paper, which considers extinction and final burnout-out phenomena at higher carbon conversion. In Situ Optical Discrimination of Inorganic-Rich andCarbon-RichParticles. In this section,we consider the data in Figures 2-4, where char carbon conversions often exceed 50%. These data will be used to identify and discuss an important new mechanism influencing carbon burnout: the phenomenon of char deactivation and near-extinction at high burnout. The distinctive feature of the high-conversion region (greater than 50-70% on a volatile-matter free basis) is the presence of particles with temperatures at or near the gas temperature. These may be either low-reactivity carbon-containingparticles or completely reacted particles consisting entirely of inorganic material. If the particles contain significantresidual carbon,their low temperatures cannot be accounted for by conventional, conversionindependent global kinetic models. Global kinetic models describe char combustion through a set of reactivity parameters that are assumed to be valid throughout conversion, resulting in high combustion rates and high
particle temperatures up to the point of complete burnout. It will therefore be important to develop a technique for the in situ discrimination of carbon-rich particles from inorganic-rich particles present in the highly reacted samples. The Ash Particle Band on TemperaturelEmissive Factor Plots. Both the size-fractionated boiler fly ash sample in Figure 6b and the four ash samples prepared directlyfrom the raw coals in Figure 7 show a similar optical signature, one that is very different from the carbon-rich char samples that predominate in Figures 1-4. For each ash sample, the data points fall in a curved band with the largest cluster of points at emissive factors less than 0.3. Also shown on Figure 7b is the range of predicted ash particle temperatures calculated assuming a wide range of possible values for ash particle density and total emissivity. The apparent high temperatures lying outside these limits in Figure 7b are experimental artifacts that result from the low spectral radiance of the inorganic-rich particles, as explained in the next paragraphs. The high temperatures are the result of errors that occur when the two-wavelength temperature measurement technique is applied to low-temperature, low-emissivefactor ash particles. The errors arise because the Sandia optical sizing/pyrometer is configured and optimized for measurement of the temperature of carbonaceousparticles at combustion temperatures, and not for low-temperature, low-emissive-factor ash particles. Nevertheless, we need to understand how the optical sizing pyrometer responds to particles of pure inorganic matter in order to interpret data at very high carbon conversions. The combination of low temperature and low emissive factor gives rise to very low radiation intensities and detector signal levels for many ash particles, especially at the shorter of the two pyrometer wavelengths, 500 nm. The behavior seen in Figures 6b and 7 can be numerically simulated by .(a) assuming a true ash particle temperature of 1535 K for 100 pm particles; (b) considering a range of values of the true ash particle emissive factor; measured at 800 nm, €800, and; (c) postulating random error in the signal level at 500 nm due to low signal levels. Even though the true particle temperature is constant at 1535K, the random error results in a range of apparent intensities, (I/Ibblb)500, defined as the measured radiation intensity at 500 nm divided by the intensity of a black body at the true particle temperature, Tp'For each combination of true emissive factor, em, and (I/Ibb&OO, Planck's radiation law is used to compute an apparent particle temperature. The apparent emissive factor at 800 nm, eappm, measured by the sizing pyrometer is then given by (5) where c1 and c2 are the Plank radiation law constants, h is 800 nm, Tp is the true ash particle temperature (1535 K) and Tapp the apparent temperature determined by twocolor pyrometry. Because the apparent temperature differs from the true temperature, the apparent emissive factor measured by the sizing pyrometer will differ from the true emissive factor according to eq 5. This calculation results in the set of curvesseen in Figure 11,where apparent particle temperature is plotted versus the apparent emissivefactor. Figure 11can be understood as follows. As measurements are made on ash particles of lower and lower true emissive factors, the 500-nm
Hurt
730 Energy & Fuels, Vol. 7, No.6,1993
s 2 2 2
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1800
. 1700
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I
0.1
0.2
0.3
0.4
0.5
0.6
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Apprront omiaalvo frotor
Figure 11. Optical measurements of apparent particle temperature and emissive factor for Illinois No. 6 fly ash with 0% residual carbon (from Figure 6). Gas environment 12 mol % oxygen, TI= 1555 K. Curves are theoretical results for various values of true particle emissive factor at 800nm, and various signal levels at the detector receiving 500 nm wavelength light (I/Ibb&ob
detector signal drops until it is of the same order of magnitude as the background noise level. In this signal range, low values that do not rise above a acceptance threshold for signal-to-noise ratio are discarded by a software routine. Only high values of the W n m signal (caused by noise peaks or reflection of flame radiation into the detector) are accepted, and these give rise to erroneously high temperatures. The error in the W n m detector signal thus produces a serious bias toward higher particle temperatures. This,in turn, produces an error in the measured emissive factor (at 800 nm), which is calculated from the measured temperature and diameter by eQ 5. Classificationby Particle Type Based on Emissive Factor. Returning to Figure 7, we see that most fly ash particles have emissive factors less than 0.3, while a small number have emissive factors from 0.3 to 1.2. These particles are believed to be primarily iron-bearinginorganic phases, which typically absorb in the visible and near infrared, or may contain small amounts of residual carbon that survive the ashing procedure. Out of a total of 886 fly ash particles in Figures 6b and 7,only 18(2%) have emissive factors greater than0.5 and only 34 (4%) have emissive factors greater than 0.3. In contrast,the char samples at low carbon conversion (Figure 1 and the 6% data in Figure 2) rarely exhibit emissive factors less than 0.3. These samples contain almost exclusivelycarbon-rich particles, as confirmed by optical microscopy on extracted samples. A useful statistical criterion can therefore be proposed for distinguishing carbon-rich particles from inorganic-rich (nearly carbonfree) particles based on the emissive factor. For the set of four coals examined here, an emissive factor of 0.3 can be used as a threshold value for distinguishing carbonrich and inorganic-rich particles with an error rate, or frequency of incorrect assignment, less than 4%.
Usingthiscriterion,letusretumtothephotomicrograph of highly-reactedBeulah lignite in Figure 8. The particles can be classified into three groups: black, carbon-rich particles; highly-reflective, inorganic-rich particles; and
1 2 4 0.0
I 0.5
1
1
1.O
1.5
1 2.0
I 2.5
Particle emissive factor
Figure 12. Rangegoftempe~~eandemiseivefactorforvarious particle types found in highly-reacted lignite (95% carbon conversion,volatile-freebaais). Parent materiak Beulah lignite, initial size 106-125 pm. Points are measured temperatures and emissive factors for single-particlesburning in 12 mol % oxygen at a gas temperatureof 1532 K. Shaded area indicatesprobable location of mixed particle types.
various mixed types containing significant quantities of visible carbon and ash within a single particle. In Figure 12,selected images of highly-reacted Beulah lignite particles representing each of the three classes (carbos-rich,inorganic-rich,and mixed) are superimposed on the optical data at 117 ms residence time. This f i i e integrates all of the available information on the highly reacted Beulah lignite sample and attempts to assign the various particle classes with the appropriate regions of the two-dimensional parameter space defined by particle temperature and emissive factor. T w o of the three particle classes, carbon-rich and inorganic-rich, can be accurately assigned based on the emissive factor criterion, with a frequency of incorrect assignment of about 4 % The dark, solid, nearly-vertical line in Figure 12 represents the dividing line between these two particle classes. No such criterion exists for distinguishing the mixed particle type class, due to the d W i d t y of isolating macroscopic samples of these intermediate particle types. Based on the microscope images, however, we expect the mixed particles to have intermediate emissive factors and, based on their advanced stage of oxidation, low particle temperatures. [The optical configuration used to generate the images is designed to facilitate comparison with the optical in situ measurements of the emissive factor. The opaque, diffuse, high-reflectivity substrate efficiently back-scatters incident light. The light incident on a given particle, 4,is either scattered, Ia, transmitted, It (e.g., by glassy fly ash particles),or absorbed, la.The image plane illumination that gives rise to the brightness of a given particle on the developed film consists of light scattered by the particle, Ia, and a significant fraction of the light transmitted through the particle, It,that is scattered by the reflective background. The differencesin particle image brightness are therefore primarily due to differences in absorptioe
.
Energy & Fuels, Vol. 7, No. 6,1993 731
Extinction Phenomena in Coal Char Combustion 10"
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Figure 13. Illustration of extinction phenomenonfor combustion reactions with high activation energy. Dashed lines: characteristic curves for a gas temperatures of 1645 and 1532 K during combustionin 12mol % oxygen. Solid lines: Example Arrhenius kinetic law k, = 55oooO e-@J/RTP.Triangles are points of intersection, representing allowed particle temperatures. properties among the various particle types. The absorptivity of a particle is, by Kirchoft's law, equal to the particle spectral emissivity at the same wavelength. If the particles are approximately gray throughout the visible and near infrared, the image brightness observed in photographs such as Figures 8 and 9 will be closely related to the emissive factor at 800 nm, and the images can be qualitatively related to the in situ optical data.] We can therefore identify a region in temperature/emissive factor space that is the probable location of most of the mixed particle types (see Figure 12). It is clear from this analysis that many of the lowtemperature particles observed at long residence times (high carbon conversions) are low reactivity particles that still contain significant amounts of residual carbon and whose final burnout is occurring at low temperatures and slow rates. The presence of carbon-containing particles at low temperatures is also clearly indicated in the long residence time data and photomicrographs for Pittsburgh No. 8 and Illinois No. 6 coal char (see Figure 2,3, and 9). In Figure 9 in particular, the 59% conversion data show the very beginning of the deactivation process leading to low particle temperatures for Pittsburgh No. 8 coal char. The optical data at this point show few, if any, particles with low emissive factors at 800 nm, and the corresponding photomicrograph shows a predominance of carbon-rich particles, with few if any distinct ash particles or mixed ash/carbon particle types. This data suggest that many of the low temperature particles are still carbon-rich. These incompletely reacted particles have undergone "nearextinction"-a phenomenon that will be defined and discussed in the next section. Extinction and Near-Extinction Phenomena. To understand extinction and near extinction phenomena, consider the characteristic curves in Figure 13 for combustion in 12 mol % oxygen at two different gas temperatures. The characteristic curves11 represent the gas-toparticle transport relations that determine particle temperature, Tp,for a given rate coefficient,k,. Also shown is an example Arrhenius-form kinetic expression, k, = 5.5 X 105e(401RTp). Allowed particle temperatures are the intersections of the kinetic expression and the transport relation (characteristic curve), as discussed in detail
I
I
50
60
I
I
I
70
80
90
1 05i T, (K)
Figure 14. Illustration of near-extinction phenomenon for particles with activation energies typical of zone I1 char combustion for several preexponential factors. Dashed curve: characteristic curve for combustion in 12 mol % oxygen, at a gas temperature of 1532 K. Solid lines: Arrhenius kinetic laws with a common and typical activation energyof 20k d m o l and several A values, 4,20,and 100 g of carbon/cm2s atmo". Triangles are points of intersection,representing allowedparticle temperatures.
elsewhere." This example kinetic expression has an activation energy significantly higher than that typically observed for zone I1 char combustion and intersects one of the characteristic curves at three points. The upper point represents a fully ignited state, the lower point an extinguished state, both of which are stable to small perturbation. The central point is an unstable state, in which small perturbations in temperature cause thermal imbalances that lead to rapid, large temperature changes and equilibration at one of the two stable states. Consider a fully ignited particle undergoing combustion at the conditions associated with the left-hand curve in Figure 13. As the kinetic law and characteristic curve are nearly parallel in the central section, small changes reductions in gas temperature (or particle reactivity) can eliminate the upper point of intersection and lead to an abrupt temperature drop to the lower point of intersection and thus to extinction of the reaction. This effect is seen in the right-hand characteristic curve as gas temperature is lowered to 1532 K. For activation energies more typical of zone I1 char combustion, such abrupt extinction events do not occur under these conditions. Small changes in gas temperature or particle reactivity can, however, bring about relatively large temperature changes under certain conditions, producing extinction-like events. This is illustrated in Figure 15 where the characteristic curve is plotted along with three different Arrhenius-form kinetic laws, representing varying reactivities. The three laws have a common and typical activation energy of 20 kcal/mo17but varying values of the preexponential factor, A, 4,20, and 100 g of carbon/(cm2.s.atm0.S). Under these more realistic conditions, the slopes of the characteristic curves are always greater than the slope of the kinetic law, making multiple steady-states an impossibility. There is always a unique particle temperature for each set of conditions, and that temperature falls gradually and continuously as the gas temperature or particle reactivity is reduced. There are conditions, however, where small changes in gas temperature or particle reactivity lead to large changes in particle temperature and burning rate. These conditions occur when the kinetic law crosses the characteristic curve in a region of low slope.
Hurt
732 Energy & Fuels, Vol. 7,No.6,1993
2000
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deactivationan near-extinction
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global kinetic prediction
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1.5
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Figure 15. Depiction of char particle combustion histories as trajectories in temperature/emissive factor space, illustrating deactivation and near extinction at high carbon conversion.
Consider a particle whose reactivity changes continuously from high to low during the course of combustion as depicted by the three kinetic expressions in Figure 14. As reactivity initially decreases(from high to intermediate, A = 100 to 20 g of carbon/(cm2-~*atm~.~)), only a modest temperature decrease of 55 K occurs, whereas a further reactivity decrease (from intermediate to low, A = 20 to 4 g of carbon/(cm2*s.atm0.5)) causes a large decrease in temperature of 345 K. Such large and abrupt (but continuous) changes in temperature will be referred to as near-extinction events, to distinguish them from the discontinuous true extinction events depicted in Figure 13. In conclusion,the combustion conditions in the CCL laminar flow reactor do not allow true extinction events as reactivity decreases, but can and do give rise to nearextinction events as the char particle reactivity decreases in the high burnoff regime. The Char Burnout Process. Based on a detailed analysis of four coals in this study, as well as data on six additional the process of carbon burnout is summarized in Figure 15. In this figure, char particle combustion lifetimes are conveniently depicted as trajectories on a plot of particle temperature vs emissive factor. Two distinct stages are revealed in the char combustion process: (1)a rapid, high-temperature combustion stage at low carbon conversion, followed by (2) a deactivation and near-extinction at roughly constant optical properties, initiating a final burnout stage that occurs slowly and at low temperatures,changingthe optical properties of the particle to those characteristicof ash. As we have shown, the near-extinction events are the result of a decreasedparticle reactivityat high carbon conversion. Another factor which may effect particle temperatures and burning rates in the latter phases of combustion is fragmentation, which is not dealt with directly in this paper. Based on the data for Illinois No. 6 in Figure 2 and for Pittsburgh No. 8 char in Figures 3 and 9, near-extinction occurs before large changes are observed in the particle optical properties. Indeed both the photomicrographand data in Figure 9 suggest that the extinction events begin to occur when the particles are still carbon-rich, before the appearance of distinct ash particles or mixed particle types. This suggests that the initial deactivation cannot be explained by the presence of an ash film diffusion barrier, or ash encapsulation, although these effects may, indeed, be important at yet higher conversions. Efforts are currently underway in this laboratory to relate the
deactivation phenomenon to changes in the chemical, physical, and crystallographic properties of the samples. The two-stage nature of the char combustion process significantly lengthens the time required to achieve high carbon conversion, and the existence of the two stages cannot be predicted by conversion-independent kinetie models, including the global kinetic models traditionally used in the numerical simulation of coal combustion processes.2 In fact, conversion-independentglobal kinetic models generallypredict particle temperatures to increase monotonically during combustion in isothermal environments, due to the decreasing particle size, up to the point of complete burnout, at which time the carbon-free ash particle extinguishes. An example of this behavior is also illustrated on Figure 15. More realistic, conversiondependent kinetic models are clearly needed. For the coals and conditions studied, the rapid combustion phase consumes 50-70% of the char carbon (on a volatile-free basis), the remainder being consumed during, or in the transition to, the low temperature, final burnout phase. Recent work in this laboratory suggests that this high temperature rapid combustion phase can account for only a small fraction of the totaltime required to reach carbon conversions in excess of 99 %
.
Conclusions Based on in situ optical measurements and off-line analysesfor four coals, the basic features of single-particle combustion have been elucidated as a function of carbon conversion. Two regimes can be clearly defined: one at low carbon conversion, where the reacting particle populations have properties that are nearly time invariant and a second regime at higher carbon conversion where the distribution properties change dramatically. At low carbon conversion, there is a broad distribution of singleparticle combustion rates, reflecting the heterogeneity in the parent fuel. Particle-to-particle reactivity differences are shown to be the primary cause of the broad temperature distribution for Pocahontas coal char. A t high carbon conversion, carbon-rich particles can be distinguishedstatisticallyfrom inorganic-richparticles by in situ measurement of their spectral emissive factors at 800 nm. Highly reacted samples are seen to consist of black, carbon-rich particles, reflective inorganic-rich particles, and various intermediate or mixed particle types, containing significant amounts of visible carbon and inorganic matter. In each case where char carbon conversion proceedspast 50-60%, many particlesare observed to undergo large temperaturedecreases, referred to as nearextinction events. Plots of particle temperature vs emissive factor conveniently illustrate and summarize the process of char particle combustionto high conversion. These plots reveal two distinct stages in the combustion lifetime of a char particle: (1) a rapid combustion stage at low carbon conversion, followed by (2) a deactivation and nearextinctiona t roughly constantoptical properties,initiating a final burnout stage that occurs slowly and at low temperatures. The near-extinction events are the result of a decreased global particle reactivity at high carbon conversion. Near-extinctionis observedto occur before large changes are observed in the particle optical properties, indicating that deactivationoccurs when the particles are stillcarbonrich. This suggests that the initial deactivation cannot be
Energy & Fuels, Vol. 7, No. 6,1993 733
Extinction Phenomena in Coal Char Combustion explained by the presence of an ash film diffusion barrier, or ash encapsulation, although these effects may, indeed, be important at yet higher conversions. Efforts are currently underway in this laboratory to relate the global particle deactivation to changes in the fundamental chemical, physical, and crystallographic properties of the samples. The two-stage nature of the char combustion process significantly lengthens the time required to achieve high carbon conversion, and the existence of two stages cannot be predicted by conversion-independent kinetic models, including the global kinetic models traditionally used in the numerical simulation of coal combustion processes. More realistic char oxidation models are needed that account for fuel heterogeneity and conversion-dependent effects.
Nomenclature A
global preexponential factor, g of carbon cm-2s-l atm” Planck radiation law constants specific heat, J/g of C particle diameter, pm statistical variables representing particle temperature variation due to: measurement error, presence of ash particles, variation in CO/COz ratio, shape, size, thermodynamic and transport properties, and reactivity global activation energy, kcal mol-’ normalized signal intensity recorded by the detector receiving 500 nm light emitted by the burning particles global chemical reaction rate coefficient, g of carbon cm-2 s-l atm”
n pox 9
R SST SSR SSE
TaPP T. T;, T ~Td,
X
global reaction order oxygen partial pressure in the bulk gas, atm overall particle burning rate per unit external surface area, g of carbon s-1 gas constant, kcal mol-’ K-l total s u m of squares regression sum of squares error s u m of squares apparent ash particle temperature by two-color pyrometry gas temperature, K particle temperature, mean particle temperature, K, particle temperature predicted by a linear regression of the data, for particle diameter, d char carbon conversion(volatilematter free basis)
Greek Symbols total (wavelength-integrated)particle emissivity (relevant to heat transfer) particle spectral emissive factor at 800 nm, or emissive factor apparent particle spectral emissive factor at 800 nm, or apparent emissive factor radiation wavelength, nm particle density, g/cm3 standard deviation of variables i
Acknowledgment. This work is supported by the US. Department of Energy’s Pittsburgh Energy Technology Center as part of the Advanced Research and Technology Development (AR&TD) Program. The technical support of James Ross and C. Scott Kelley is gratefully acknowledged.
