Percolative Fragmentation of Char Particles during Gasification

Energy & Fuels 2000, 14, 297-307

297

Percolative Fragmentation of Char Particles during Gasification Bo Feng and Suresh K. Bhatia* Department of Chemical Engineering, The University of Queensland, Qld 4072, Australia Received May 19, 1999

Percolative fragmentation was confirmed to occur during gasification of three microporous coal chars. Indirect evidence obtained by the variation of electrical resistivity (ER) with conversion was supported by direct observation of numerous fragments during gasification. The resistivity increases slowly at low conversions and then sharply after a certain conversion value, which is a typical percolation phenomenon suggesting the occurrence of internal fragmentation at high conversion. Two percolation models are applied to interpret the experimental data and determine the percolation threshold. A percolation threshold of 0.02-0.07 was found, corresponding to a critical conversion of 92-96% for fragmentation. The electrical resistivity variation at high conversions is found to be very sensitive to diffusional effects during gasification. Partially burnt samples with a narrow initial particle size range were also observed microscopically, and found to yield a large number of small fragments even when the particles showed no disintegration and chemical control prevailed. It is proposed that this is due to the separation of isolated clusters from the particle surface. The particle size distribution of the fragments was essentially independent of the reaction conditions and the char type, and supported the prediction by percolation theory that the number fraction distribution varies linearly with mass in a log-log plot. The results imply that perimeter fragmentation would occur in practical combustion systems in which the reactions are strongly diffusion affected.

Introduction Fragmentation of coal particles during combustion is believed to be responsible for decreased burnout time, enhanced production of fly ash in fluidized beds, as well as increased fineness of fly ash and increased emission of submicrometer unburnt carbon in pulverized coal combustion systems. Fragments can be formed by three mechanisms mechanistically:1,2 breakage of particles due to the internal force, for example the high internal pressure during devolatilization;3,4 attrition of particles1,2,5; and percolation, i.e., the loss of connectivity among the phases within the particle.6 The ash in the particle is also expected to influence the fragmentation.7,8 The potential importance of the percolative fragmentation in pulverized coal combustion has been realized * Author to whom correspondence should be addressed. Phone: 61 7 3365 4263. Fax: 61 7 3365 4199. E-mail: [email protected]. (1) Mitchell, R. E. A.; Jacob, A. E. 26th Symp. (Int.) on Combust.; The Combustion Institute, 1996. (2) Dunn-Rankin, D.; Kerstein, A. R. Combust. Flame 1987, 69, 193209. (3) Sundback, C. A.; Beer, J. M.; Sarofim. A. F. 20th Symp. (Int.) on Combust.; The Combustion Institute, 1984. (4) Srinivasachar, S.; Kang, S. W.; Timothy, L. D.; Froelich, D.; Sarofim, A. F.; Beer, J. M. Proceedings of the 8th International Coal Slurry Fuel Preparation and Utilization Symposium, Orlando, FL, 1986. (5) Salatino, P.; Miccio, F.; Massimilla, L. Combust. Flame 1993, 95, 342-350. (6) Kerstein, A. R.; Niksa, S. 20th Symp. (Int.) on Combust.; The Combustion Institute, 1984. (7) Helble, J.; Neville, M.; Sarofim, A. F. 21st Symp. (Int.) on Combust.; The Combustion Institute, 1988. (8) Baxter, L. L.; Mitchell, R. E. Combust. Flame 1992, 88, 1-14.

and has stimulated much theoretical work.5,6,9-18 Many of the results have been reviewed by Sahimi and coworkers.16,17 The percolation models can be classified into hybrid continuum models11,12 and network models9,18 and, although the ideas are somewhat different, all the models incorporate a critical porosity φf, at which the fragmentation occurs. The precise value of φf depends on the microscopic details of the solid matrix and its chemical composition. Kerstein and Niksa6 predicted the critical porosity for various pore shapes and network structure, and found a value varying between 0.2 and 0.9. Gavalas19 used a critical value of porosity of 0.8 in his char combustion model at which pore mouth coalescence occurs, which has been supported by Kerstein and Niksa.6 Indeed the percolation model predicts the importance of percolative fragmentation in pulverized coal combustion. Mitchell1 recently developed a particle population balance model for the fragmentation, taking the above three mechanisms into account. He showed that frag(9) Kerstein, A. R.; Edwards, B. F. Chem. Eng. Sci. 1987, 42, 16291634. (10) Sahimi, M.; Tsotsis, H. T. Chem. Eng. Sci. 1988, 43, 113-121. (11) Reyes, S.; Jensen, K. F. Chem. Eng. Sci. 1986, 41, 333-343. (12) Reyes, S.; Jensen, K. F. Chem. Eng. Sci. 1986, 41, 345-354. (13) Marban, G.; Pis, J.; Fuertes, A. Powder Technol. 1996, 89, 7178. (14) Marban, G.; Fuertes, A. Chem. Eng. Sci. 1997, 52, 1-11. (15) Fuertes, A.; Marban, G.; Muniz, J. Carbon 1996, 34, 223-230. (16) Sahimi, M.; Gavalas, G. R.; Tsotsis, T. Chem. Eng. Sci. 1990, 45, 1443-1502. (17) Sahimi, M. Applications of percolation theory; Taylor & Francis Ltd.: Philadelphia, 1994. (18) Sahimi, M. Phys. Rev. 1991, 43, 5367-5376. (19) Gavalas, G. R. Combust. Sci. Technol. 1981, 24, 197-209.

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mentation during burnoff is percolative in nature and char burning rate parameters determined from mass loss, size, and temperature measurements are too high if the effects of particle fragmentation are not considered. In other work Marban and co-workers14,15 studied the effect of fragmentation on the combustion behavior of carbon fiber and coal char, and concluded that the development of texture properties during gasification (porosity, pore volume, pore size distribution, and surface area) is strongly dependent on the reaction regime and percolation phenomena. The fragmentation could contribute to the particle size reduction exclusively in some cases. Under diffusional control, a decrease or an increase in the overall reactivity occurs, depending on whether the fragments could be burnt or not. The shape of the fragments could also play a key role in determining whether fragmentation increases or decreases burnout.1 If all particles and fragments are assumed to be spherical, then fragmentation enhances burnout. Otherwise fragmentation could decrease burnout owing to the impact of surface-to-volume ratio on the relative rates of heat generation and loss, which determine equilibrium particle temperature. While there is an abundance of theoretical work on percolative fragmentation as discussed above, experimental literature on the subject is scanty. One of the pioneering works is that of Kerstein and Niksa6 who measured the critical porosity for fragmentation of round disks upon oxidation, as evidenced from their mechanical failure. They found that the critical porosity was in the range of 0.28 to 0.83, depending on material properties in a complex way. However, subsequent work by Hurt and Davis20 and Weiss et al.21 did not indicate significant occurrence of percolative fragmentation. Hurt and Davis investigated the combustion of a single coal particle in the range of 50-300 µm in a flamesupported flow reactor using a captive particle imaging technique. Rare percolative fragmentation was found in the late stages of combustion, under conditions simulating pulverized coal combustion. Weiss et al.21 studied single-particle oxidation in an electrodynamic balance laser heated from below, as well as a thermogravimetric analyzer. No evidence of fragmentation was shown even at conversion as high as 95%. It also appears that various experiments for the number of fragments from a single particle yield contrasting results. The reported number varies from 3 to 47,22,23 to several tens of thousands.24,25 Baxter26 found that the extent of fragmentation is strongly dependent on size and coal rank. Bituminous coal may form over 100 fragments per char particle at large initial particle size (above 80 µm), and less than 10 at small initial char particle size (below 20 µm). Lignites fragment less extensively, with the number of fragments per original char particle being less than 5 at all particle sizes. (20) Hurt, R.; Davis, K. Combust. Flame 1999, 116, 662-670. (21) Weiss, Y.; Benari, Y.; Kantorovich, I. I.; Bar-Ziv, E.; Krammer, G.; Modestino, A.; Sarofim, A. F. 25th Symp. (Int.) on Combust.; The Combustion Institute, 1994. (22) Sarofim, A. F.; Howard, J. B.; Padia, A. S. Combust. Sci. Technol. 1977, 16, 187-193. (23) Helble, J. J.; Sarofim, A. F. Combust. Flame 1989, 76, 183196. (24) Quann, R. J.; Sarofim, A. F. Fuel 1986, 65, 40-49. (25) Quann, R. J.; Sarofim. A. F. 19th Symp. (Int.) on Combust.; The Combustion Institute, 1982. (26) Baxter, L. L. Combust. Flame 1992, 90, 174-184.

Feng and Bhatia

It is clear from the above discussion that there remain several issues in percolative fragmentation that still need clarification. The present paper demonstrates the occurrence of percolative fragmentation in two ways: measurement of the variation of electrical resistivity (ER) of coal chars during gasification, and direct observation of fragments during gasification. Since the electrical resistivity depends on the internal connectivity, a sharp increase in electrical resistivity at high conversion is indicative of internal fragmentation. In the work reported here, the variation of the ER value with carbon conversion was measured for three chars under chemically controlled and moderately diffusion-controlled conditions. The partially burnt particles were also observed microscopically to visualize any possible fragments, and the particle size distribution of the char as well as fragments was obtained. The number of fragments from a single particle was estimated statistically from the particle size distribution. Mathematical Modeling of Resistivity Variation with Conversion The electrical resistivity of carbonaceous materials has received much attention.27-43 The conducting phase in such materials is principally the nanoscale crystallites, comprising the turbostratic structure of chars and carbons, while unorganized carbon is essentially nonconducting. This view is supported by observations29,31 showing extremely high resistivities (of the order of 1012 Ω cm) for raw coal, as compared to annealed chars which have resistivities in the range of 0.01 to 10 Ω cm. The electrical resistivity is structure sensitive and its magnitude depends on the crystal orientation, due to structural anisotropy of turbostratic carbon crystallites. However, in a particle comprised of agglomerates of randomly oriented crystals, the resistivity would be expected to depend strongly on the internal connectivity of the agglomerates, i.e., on the inter-crystalline contacts. The latter is in turn a strong function of the volume fraction of the crystallites. The resistivity would (27) Aharoni, S. M. J. Appl. Phys. 1972, 43, 2463-2465. (28) Deraman, M. J. Phys. D 1994, 27, 1060-1062. (29) Emmerich, F. G.; De Sousa, J. C.; Torriani, I. L.; Luengo, C. A. Carbon 1987, 25, 417-424. (30) Ewen, P. J. S.; Robertson, J. M. J. Phys. D: Appl. Phys. 1981, 14, 2253-2268. (31) Freitas, J. C. C.; Cunha, A. G.; Emmerich, F. G. Fuel 1997, 76, 229-232. (32) Kavan, L.; Dousek, F. P.; Micka, K. J. Phys. Chem. 1990, 94, 5127-5134. (33) Kimura, S.; Yasuda, E.; Tanabe, Y. Yogyo Kyokai Shi 1985, 93, 89-95. (34) Kumar, M.; Gupta, R. Transactions of the Indian Institute of Metals 1994, 47, 103-109. (35) Kumar, M.; Gupta, R. Energy Source 1998, 20, 575-589. (36) Kupperman, D. S.; Chau, C. K.; Weinstock, H. Carbon 1973, 11, 171-175. (37) Langer, L.; Bayot, V.; Issi, J. P.; Stockman, L.; Van Flaesendonck, C.; Bruynseraede, Y.; Heremans, J. P.; Olk, C. H. Physics and Chemistry of Fullerenes and Derivatives. Proceedings of the International Winterschool on Electronic Properties of Novel Materials. World Scientific: Singapore, 1995. (38) Malliaris, A.; Turner, D. T. J. Appl. Phys. 1971, 42, 614-618. (39) Mrozowski, S. Third Conference on Carbon; Pergamon Press: New York, 1959. (40) Mutso, R.; Dubroff, W. Fuel 1982, 61, 305-306. (41) Pedraza, D. F.; Klemens, P. G. Carbon 1993, 31, 951-956. (42) Radeke, K. H.; Backhaus, K. O.; Swiatkowski, A. Carbon 1990, 28, 122-123. (43) Pike, G. E.; Seager, C. H. Phys. Rev. B 1974, 10, 1421-1434.

Percolative Fragmentation of Char Particles

Energy & Fuels, Vol. 14, No. 2, 2000 299

also be expected to display percolation behavior, increasing to very large values at small crystallite fractions approaching a threshold value.17 A well-known expression for the dependence of resistivity on volume fraction of the conducting phase in a random composite is that of Pike,43

F ∝ (V - Vc)-µ

(1)

where V and Vc are the volume fraction and the critical volume fraction of the conducting phase, respectively, and µ is the critical exponent. The constants Vc and µ depend on the packing structure and dimension of the system. Typically, Vc varies between 0.2 and 0.5, and µ between 2.5 and 3.5, depending on the percolative system.17,44 While there is limited work on the electrical resistivity of coal char, the results do indicate the relevance of eq 1 to this system. It may be anticipated that increased ordering and crystallinity due to heat treatment will reduce electrical resistivity of chars, and this feature has been exploited by Emmerich29 and Freitas et al.31 The former, in studies of increase of crystallinity of babassu nut char with heat treantment, found good fit of eq 1 with a critical volume fraction of 0.32. This value is in the expected range for typical 3D sytems. The approach was subsequently also supported by Deraman28 in studies of electrical resistivity of a carbon prepared from oil palm bunches. Support for the dependence of electrical resistivity on crystallite content is also available from correlations of ER with reactivity,40 since the latter is also believed to be influenced by the crystallinity of the carbon. Nevertheless, while the crystallite content may be the key variable influencing ER variation in a given carbon, the difference between carbons from different sources may also be partly attributable to other variables such as the oxygen content.42 As the inter-crystalline contacts are broken, and internal connectivity is lost, at the critical volume fraction of crystallites (the percolation threshold) it may be expected that fragmentation also occurs. No study has hitherto attempted to correlate particle fragmentation and the sharp resistivity increase at the percolation as the solid fraction reduces with gasification. This is investigated here, with the help of the percolation theory model in eq 1 and its modification. The model is used under the assumption that the char particles are comprised of aggregates of grains which are themselves comprised of an agglomerate of crystallites and mineral matter. We define the volume fraction of the intergranular space (the particle macroporosity) as a, and the grain microporosity (the volume fraction of micropores in a grain) as i. The latter represents the intercrystalline space in a grain. Two percolation-theorybased models are utilized here as follows, both considering the grains as the effective conducting phase. Percolation Model 1. The equation for this model is essentially the same as eq 1 except here we use the fraction of filled sites, p as the variable, i.e.,

F ∝ (p - pc)-µ

(2)

For simplicity and convenience, eq 2 is rewritten as,

F′ )

(

p - pc p0 - pc

)

-µ

(3)

where F′ is the relative resistivity, referenced to the initial resistivity of the fresh char, and p0 is the initial volume fraction of the conducting phase in char. Equation 3 is fitted to the experimental data using a leastsquares method and the values of pc and µ are obtained. The fraction of the filled site, p, follows:

p ) V/fm

(4)

where V is the volume fraction of the solid phase in a grain, and fm is the packing crystallite fraction. Thus, fm corresponds to the possible maximum volume fraction of crystallites in the packing. To complete the model, we need to correlate the volume fraction V to the conversion. This volume fraction corresponds to the crystallite fraction in the grains, and is obtained as

V ) 1 - ) (1 - 0 - vash)(1 - x)

(5)

where 0 is the initial grain microporosity, x is the conversion, and vash is the volume fraction of ash in the grains. Percolation Model 2. This model follows that of Ewen and Robertson,30 and utilizes the fraction of filled sites in the region spanned by the network, p′, rather than the fraction p for the system as a whole. Thus,

F ∝ (p′-pc)-µ

(6)

Similarly,

F′ )

( ) p′-pc p′0-pc

-µ

(7)

where30

p′ ) (pn + pnc )1/n

(8)

The parameter n is an indicator of the system compactness, relating to how well the conducting particles fill the random “lattice” over which they are distributed. The lattice is characterized by fm, the ideal packing fraction for the conducting phases. The greater the value of n, the closer the two models. As n approaches infinity, the models merge. Model 2 is based on the assumption that in the new percolative system any isolated clusters formed join with the rest of the system. In this case p′, the fraction of filled sites in the region occupied by the crystallites, can never be less than pc since by definition the structure must consist of isolated clusters when p′ < pc. This may be partially true for a char undergoing gasification, following the recent proposal of Bhatia45 who rationalized observed46 particle shrinkage during chemically controlled gasification as being due to the van der Waals forces. When a crystallite plane is gasified away, the (44) Stauffer, D. Phys. Rep. 1979, 54, 1-74. (45) Bhatia, S. K. AIChE J. 1998, 44, 2478-2493. (46) Hurt, R. H.; Dudek, D. R.; Longwell, J. P.; Sarofim, A. F. Carbon 1988, 26, 433-449.

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Table 1. Structural Parameters for Chars Prepared with 120 min Heating Time parameter

Bolga

Bayswater

MO12

ash content (dry, %) helium density (g/cm3) bulk density (g/cm3) micropore volume (cm3/g) macroporosity microporosity in grain total porosity CO2 surface area (m2/g)

8.00 1.99 0.520 0.073 0.701 0.127 0.739 176

7.15 2.01 0.800 0.082 0.535 0.142 0.601 206

12.64 2.01 0.488 0.063 0.726 0.113 0.757 151

space between the neighboring planes above and below closes, and the system shrinks. Shrinkage could also occur when the unorganized carbon in char is gasified and the crystallites come closer. Therefore the fraction of conducting phase based on the shrunk system will be higher than that based on the initial system. Another complication is that an isolated cluster may not move to the infinite cluster, but detach from the system to become a fragment if it is at the surface. This is discussed in another section. Experimental Section Char Characterization and Gasification. Three Australian coals with different porosity, Bolga, Bayswater, and MO12, were selected for the experiments. The chars were made by heating the raw coal in a Lindberg horizonal tube furnace at 1173 K in a nitrogen stream for up to 120 min. The heating rate prior to attaining the pyrolyzing temperature was estimated to be several hundreds of degrees per second. The resulting char was then ground and sieved. The chars were analyzed for initial pore structure and the ash content, and the results are shown in Table 1. The surface area and micropore volume were obtained by CO2 adsorption using a Micromeritics analyzer (ASAP2010). The porosities (total porosity t, microporosity µ, macroporosity a, and grain porosity i) were calculated by the following equations:

t ) 1 -

Fp Ft Figure 1. Effect of particle size on conversion time behavior for chars prepared with 120 min heating time. (a) Temperature ) 723 K, O2 ) 21%; (b) temperature ) 773 K, O2 ) 21%.

µ ) Fpνµ a ) t - µ i )

µ 1 - a

(9)

where vµ is the micropore volume determined by CO2 adorption, and Fp, Ft are the particle and true densities, respectively. The former was obtained as the envelope density using a Micromeritics Poresizer 9320 mercury porosimeter, while the latter was determined by helium pycnometry utilizing a Micromeritics AccuPyn 1330. The chars were gasified in a quartz boat in the tube furnace under air. The partially burnt particles were cooled in a desiccator, and then subject to the measurement of electrical resistance or particle size distribution. Preliminary runs were carried out to identify chemically controlled conditions. It was found that at a temperature of 723 K the reaction is chemically controlled while at 773 K some diffusion effect appears. Figure 1 depicts the effect of particle size on conversion time behavior, illustrating the absence of diffusional effects at 723 K and their significance at 773 K. Subsequently, five temperatures (673, 723, 773, 823, and 873 K) were chosen. Higher temperatures were not appropriate as the reaction is very fast at temperatures beyond 873 K. Various oxygen concentrations (from 4% to 100%) and various particle sizes were utilized in the

experiments. It may be noted that in particle size distribution experiments, narrow particle size ranges (90-106 µm, 180212 µm) were used. Electrical Resistivity Measurement. Electrical resistance was measured for all the chars during gasification using an ohmmeter (Hioki 3220 m HiTester, range 20 m to 20 K, accuracy 0.2%). The apparatus for determining the resistance of the powdered chars is essentially the same as that of Brodd and Kosawa,47 which consists of a hollow cylinder constructed with a nonconducting material. Two copper pistons in the both ends of the cell are used to press the samples in the cell and to connect to the ohmmeter. The cell has an inner diameter of 5 mm and a length of 23 mm, holding roughly 500 mg of char particles. A fresh char has a typical resistance of 3 ohm, and this value increases with burnoff. The reproducibility is within 10%. Espinola et al.48 have suggested that the approach can be improved by drilling two holes on the cylinder and measured the resistance between the two fixed points instead of the two pistons. The method was also used in the present study, (47) Brodd, L. R.; Kosawa, A. In Techniques of Electrochemistry; Yeager, E., Salkind, A. J., Eds.; Wiley-Interscience: New York, 1978; p 222. (48) Espinola, A.; Miguel, P. M.; Salles, M. R.; Pinto, A. R. Carbon 1986, 24, 337-341.



Figure 2. Effect of particle size on initial electrical resistivity of fresh chars. however no significant improvement in accuracy was found. One of the key variables affecting the electrical resistivity of powder beds is the applied pressure (P). According to Mrozowski,39 depending on the type of deformation, the resistivity varies as P-1/3 (elastic deformation) or P-1/2 (yielding deformation). Espinola et al.48 have experimentally studied the effect of pressure on resistivity, and although it is readily determined that their data do not yield the dependencies predicted by Mrozowski, the effect of pressure is very significant. Therefore in our experiments a constant pressure was applied by supporting a steel cylinder having a mass of 5 kg on the upper piston. Particle Size Measurement. Optical microscopy and image analyses were used for the particle size measurement. For this the particles were spread on a slide and observed under the microscope. The particle size was calculated from the area occupied by the particle measured in pixels, and images of the particles were saved. The particle size here refers to the equivalent spherical diameter. The width, breadth, and length could be obtained for any chosen particle.

Results and Discussion Effect of Particle Size on Resistivity of Fresh Chars. Initially, the effect of particle size was studied for fresh chars to determine if this influences the value of the electrical resistivity. Figure 2 presents the results for fresh Bolga, Bayswater, and MO12 chars prepared with 120 min heating time. The resistivities for the three chars are similar, being around 0.5 Ω cm, typical value of carbon. The resistivity declines slightly with the decrease of the particle size, within 15%. However, the particle size may influence the packing fraction φ. In the present paper, we use the same particle-size range for all the chars and based on the above results we expect a variation of less than 10% due to the shrinkage-related45,46 packing effect at high conversion. Because of the fixed bed and particle sizes, the ratio of resistance at any conversion to its initial value is taken as relative resistivity. Variation of Resistivity with Conversion. When the chars were oxidized to various conversions, in the chemically controlled regime (T ) 673 K or T ) 723 K), the electrical resistivity at first increased slowly. At

Figure 3. Variation of relative resistivity with conversion for three chars during gasification in chemical regime. Xc1: crtitical conversion by model 1; Xc2: critical conversion by model 2. (a) Bolga char; (b) Bayswater char; (c) MO12 char. Initial particle size: 45-90 µm in all cases.

conversions higher than a critical value, typically about 80-90%, however, the resistivity increased drastically, suggestive of percolation behavior. Figure 3 depicts these results for the different chars, showing them to be independent of temperature as well as oxygen

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Table 2. Percolation Model Parameters char Bolga MO12 Bayswater

model

f mp c

µ

n

xc

c

model 1 model 2

0.034 0.065

3.480 3.270

1.990

0.959 0.922

0.964 0.932

model 1 model 2

0.0 0.067

3.341 5.110

0.344

0.999 0.918

0.999 0.928

model 1 model 2

0.0 0.070

3.347 5.172

0.344

0.999 0.915

0.999 0.927

concentration, as it is to be expected under chemical control. Also shown in Figure 3 are the fits of the two percolation theory models discussed earlier (cf. eqs 3-8). Both models can fit the data almost equally well, while giving only slightly different values for the parameters. The parameters for the three chars for each model are listed in Table 2. The percolation thresholds predicted by model 1 are slightly lower than those by model 2. For MO12 and Bayswater fmpc is very close to zero with model 1. Model 2 gives similar threshold values for the three chars, which are around 0.06. This is somewhat lower than the expected value of 0.15 (the critical volume fraction) by percolation theory for disordered 3D systems,30 but support the results of Ehrburger-Dolle et al.49 who measured the resistivity of various carbon blacks. The values of µ are consistent with a highly branching structure for the crystallite organization, such as a Bethe lattice for which µ ) 3.17 Also shown in Figure 3 are the critical conversions from the models. For Bolga char, Model 1 predicts a critical conversion of 96% while model 2 gives 93%. Such high critical conversions are consistent with recent studies20,21 showing no evidence of percolative fragmentation at porosities as high as 95%. The values of n for the chars are rather small, consistent with predictions45 of shrinkage of chars during gasification in the chemical regime due to effects of van der Waals forces. The above results, showing the large increase in resistivity at conversion slightly less than unity, are indicative of internal fragmentation and loss of intercrystalline contacts at the percolation threshold. Correlation between Reactivity and Electrical Resistivity. No apparent correlation between the reactivity and the electrical resistivity was found, as shown in Figure 4. Here the reactivity is defined as the local specific reaction rate, and the electrical resistivity used is also the instantaneous local value. Data at various conversions is shown in the figure. Thus the reactivity does not vary with the resistivity, implying that the reactivity is not related to the internal connectivity though it does depend on the internal pore structure. In Mutso and Dubroff’s work,40 a correlation was found between the initial electrical resistivity and the average reactivity, which was defined as the percentage reacted in a certain time period (2 h). However, that correlation cannot be verified in the present study because the three chars showed similar values in initial electrical resistivity and average reactivity. Perimeter Fragmentation. The effects of reaction temperature, oxygen concentration, particle size and char preparation conditions on the electrical resistivity were also studied. Figure 5 (a) shows a comparison of

the ER of three chars at 673 and 823 K. At 673 K the gasification is chemically controlled, while at 823 K some diffusion appears, except for the Bayswater char which is still largely chemically controlled. The three chars show similar behavior of ER with conversion and the three curves are close to each other. However higher temperature magnifies the differences, especially for Bolga and MO12 chars. This is apparently due to the diffusional effects at higher temperature (823 K), which result in a conversion profile within the particle with a higher conversion near the surface. When the surface conversion reaches the critical conversion, the local conversion inside the particle is actually lower leading to a sub-critical overall value. Consequently fragmentation occurs peripherally at 823 K. It is expected that the amount of fragments increases with the increase of temperature, as predicted by Salatino et al.,50 which however is not verified in the present study. It appears that the fragmentation of Bayswater is not as severe as the other two chars at 823 K. Since Bayswater char is more microporous, it suggests that microporosity tends to slower fragmentation. Figure 5a is re-plotted as Figure 5b, which shows the dependence of relative resistivity on volume fraction of conducting phase in char on a log-log plot. The resistivities for the three chars at 673 K lie around a straight line, while the results at 823 K are far from each other. Also shown in Figure 5b is a dashed straight line which represents a complete perimeter fragmentation, or gas diffusioncontrolled gasification. In that case the particle fragments from the beginning of the reaction, and the particle size reduces while conversion increases mainly by fragmentation. Consequently, the electrical resistivity will be expected to remain constant during gasification. Marban and Fuertes14,15 have pointed out the possibility of such kind of perimeter fragmentation at high temperatures. Figure 6 shows the effect of particle size, temperature, and oxygen concentration on ER variation during Bolga char gasification. It can be seen from Figure 6a that ER

(49) Ehrburger-Dolle, F.; Lahaye, J.; Misono, S. Carbon 1994, 32, 1363-1368.

(50) Salatino, P.; Miccio, F.; Massimilla, L. Combust. Flame 1993, 95, 342-350.

Figure 4. Correlation between reactivity and resistivity during gasification. Initial particle size: 45-90 µm.



Figure 5. Relative resistivity variation for three coal chars during gasification in air at 673 and 823 K, using an initial particle size range of 45-90 µm. (a) Variation of relative resistivity with conversion; (b) variation of relative resistivity with volume fraction of conducting phase.

is independent of particle size at 673 K, while at 823 K the ER is mildly sensitive to the particle size, consistent with the appearance of diffusional effects. This result is supported in Figure 6b in which the ER behavior with the volume fraction of conducting phase at temperatures up to 748 K is similar, while perimeter fragmentation is becoming more and more active as temperature increases. At low temperature (673 K), oxygen concentration has no effect on ER variation. However, at higher temperature (823 K) the ER variation is sensitive to the oxygen concentration. This is suggestive of nonlinear dependence of intrinsic reactivity on oxygen concentration, for with a linear rate law there is no change in relative resistances of diffusion and reaction and the ER variation would be expected to be independent of conversion even in the presence of diffusional effects. It is clear from the above results that the ER value is sensitive to diffusional effects, indicating that the internal structural change and fragmentation are also sensitive to diffusional effects. A conclusion which

Figure 6. Relative resistivity vs volume fraction of conducting phase for Bolga char during gasification. (a) Effect of particle size at 21% O2; (b) Effect of gasification temperature for particles of initial size 45-90 µm; (c) Effect of oxygen concentration for particles of initial size 45-90 µm.

may be deduced directly is that perimeter fragmentation may be rather severe in practical gasification systems, in which the reaction temperature is much higher. The internal structure clearly influences the electrical resistivity, as shown in Figure 7. When Bolga char is

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Feng and Bhatia

Figure 7. Effect of heat treatment time on relative resistivity of Bolga char during gasification in air at 823 K. The char was heat treated in N2 at 1173 K for various times as indicated in the legend. Initial particle size: 0-212 µm.

heat treated for various times (10, 30, and 120 min) at 1173 K, the 120 min-treated char displays lower resistivity and more severe perimeter fragmentation tendency. Since the char particles were gasified at 823 K temperature in oxygen, a mild diffusional effect on ER is anticipated during gasification. The decrease in ER value with annealing time, for a given volume fraction of conducting phase, suggests increase in diffusional resistance. This is most likely due to the structural modification and decrease in particle porosity with annealing. The surface areas for the three heating times of 10, 30, and 120 min are 223.5, 205.0, and 176.0 m2/ gm, and the micropore volumes are 0.088, 0.082, and 0.073 cm3/gm, respectively. However, it may be expected that in CO2 or steam gasification the structural change due to heat annealing may influence the gasification behavior significantly because of the much higher gasification temperature. Observation of Fragments. Microscopic observations of particles confirmed perimeter fragmentation. Figure 8 shows the images of the MO12 char during gasification at 723 K. The particles are “clear” at low conversions. There are no fine particles at all at 0%, 16%, and 39% conversion. However at 55% conversion, there are a few fine particles appearing, which obviously come from breakage of larger particles. The number of the fragments increases steadily as conversion increases from 62% to 86%, and at 86% conversion, there are so many fine fragments that they appear to aggregate in large clusters. A similar phenomenon was found for the other chars in various conditions. Since the particles were burnt statically there is no attrition or breakage due to collision. The fine particles can come only from percolative fragmentation, supporting the previous findings by the ER method. The fact that they appear at conversions somewhat lower than the percolation threshold could suggest the existence of gradients in the particle, or possibly fragmentation near the surface during handling. The former is unlikely at 723 K, under which condition chemical control occurs.

Figure 8. Optical microscope images (20×) of MO12 particles during oxidation at 723 K. Initial particle size: 90-106 µm.

Nevertheless the observation of the appearance of fragments at about the same conversion at different temperatures within the chemical regime, and the increase of the number of fragments at higher conversions, imply that the percolative fragmentation is occurring. At the very least they indicate that the surface layers in particles are more fragile at higher conversion. If indeed the fragments result from handling only, then certainly surface fragmentation will occur significantly in practical systems in which condition the diffusional resistance is significant. Figure 9 shows images of the same char at 873 K at various conversions. In this case the fragments are observed at a conversion as low as 27%. This is almost certainly due to the fragmentation of the outer surface where the local conversion is significantly higher due to the existence of diffusional effects. The sensitivity of fragmentation to reaction temperature is consistent with the previous ER experiments, which implies that


Figure 9. Optical microscope images (20×) of MO12 particles during oxidation at 873 K. Initial particle size: 180-212 µm.

Figure 10. Temperature dependence of the conversion at which fragments start to appear.

perimeter fragmentation is active in the diffusioncontrolled regime. The temperature variation of the conversion at which the fragments start to appear is shown in Figure 10, displaying a steady decrease in this conversion with increase in reaction temperature. This result is consistent with the well-established diffusion-


reaction modeling which indicates that the diffusional resistance increases with increase in temperature. In the present case therefore, at higher temperatures, perimeter fragmentation appears at lower conversion because the surface conversion is then higher at a given total conversion. Criticality at the surface, or fragility and surface fragmentation then occurs earlier. The relatively flat shape of the curve at low temperatures (850 K), suggesting that at very high temperatures surface fragmentation will appear very early, at conversions approaching zero. This is completely consistent with the occurrence of total diffusional control under such circumstances, and in this case surface fragmentation and the shrinkage of an external surface of critical local conversion may be expected to govern the rate. This behavior has also been theoretically predicted recently.14,15 Particle Size Distribution of Fragments. The particle size distributions of the chars gasified at various temperatures to different conversions were also obtained. A clear bimodal distribution was found. The shrinkage of the parent particles was verified for all the chars. The particle distributions of the fragments at various conditions are presented in Figure 11. An average particle size for the fragments, 1.6 µm was found, although particles size smaller than 0.4 µm could not be visualized. A rather striking observation is that the particle distribution seems to be independent of experimental conditions, the conversion level, and even the char type. This feature would appear consistent with our conclusion that the fragmentation is due to the surface having reached a critical conversion. In this situation, the external particle surface forms a moving boundary of constant conversion equal to the critical value, and releases fragments of identical distribution as it shrinks. Although these fragments accumulate, they are also reacting away under chemical control, and a steady-state size distribution may be anticipated. Fragmentation, including the size distribution of fragments, has been modeled using percolation theory by many researchers as discussed in the Introduction section. For example, Sahimi18 found that the number of fragments of size s at time t, ns(t), obeys a dynamic scaling ns(t) ∝ tws-τf(s/tz), where w, τ, and z are dynamic exponents. Kerstein and Edwards9 indicate that at high carbon conversions, the fragment number distribution varies linearly with mass on a log-log plot. Figure 11b shows such a log-log plot in apparent agreement. Some deviation is found at low and high particle size, possibly due to the increasing measurement error in this region, or due to the effect of gasification of the fragments. Thus, the steady-state distribution may not conform exactly to the distribution of fragments as formed. This may also explain the fact that the slope of Figure 11b differs from that obtained by Holve.51 The fragments produced can be very irregular in shape, as shown in Figure 12. Many needle-shape particles were observed under microscope. These fragments are also very small, normally 1-2 µm. These small fragments are not easily observed in a moving system such as that of Hurt and Davis,20 or Weiss et (51) Holve, D. J. Combust. Sci. Technol. 1986, 44, 269-288.

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Figure 12. Fragments as observed under microscope at various magnifications.

Figure 11. Number distribution of fragments from partial gasification at various conditions, as determined by optical microscopy. (a) Number distribution versus particle size; (b) number distribution versus particle mass (replaced by cube of diameter).

al.21 It is even more difficult when a single particle is used as in these studies. The number of fragments at high conversions could be one or more orders of magnitude greater than the number of the parent particles. A ratio of 20 was found for Bolga char when burnt at 673 K to 68% conversion. Discussion. Discrepancy exists between the direct observation and the ER method in that the ER method predicts a higher critical conversion, which could also be due to the inappropriate assumption that before the threshold there are no isolated clusters detached from the whole particle. If we define XI(p) as the fraction of isolated sites, where p is the possibility that the sites are occupied, we have17 XI(p) ) p - XA(p), where XA(p) is the fraction of occupied sites belonging to the infinite cluster. Sahimi17 has shown the variation of XI(p) with p on a simple cubic lattice, using the method proposed by Stauffer44 for the calculation of XA(p). The value of XI(p) is zero initially (when p ) 1) and stays at zero as

p decreases until a value of p of 0.6. It then keeps increasing as p decreases, and reaches the maximum when pc is attained. During gasification p keeps decreasing and when it decreases to a certain value, some occupied sites are isolated from the infinite cluster, part of which probably detaches from the particle. However, the particle still maintains integrity because there is an infinite cluster inside the particle. It does not collapse until pc is attained. Therefore, the observation of the fragments at low conversion may come from the isolated clusters, which however do not influence the ER value significantly. Only when pc is approached, the ER value as well as the number of fragments increases sharply. The observation of fragments before the percolation threshold in the chemically controlled regime, suggests the necessity of considering isolated clusters in the formation of fragments at the surface. These surface clusters can easily separate from the parent cluster, and form the fragments observed. Therefore, it is not actually the lattice threshold, pc, that controls the appearance of surface fragments, but the critical volume fraction at which the isolated clusters start to appear, pf. The value of pf for a simple cubic lattice is 0.6,17 corresponding to a critical conversion of 27% for Bolga char in the present study. Depending on the coordination number of the percolative system, pf varies between 0.2 and 0.7.52 A value of 0.37 of pf, which is in the range for a practical system, can satisfactorily explain the observation of fragments at a conversion of 55% for Bolga char. Two questions need to be answered to develop a complete fragmentation model for carbon gasification. The first one relates to how important the isolated cluster-related fragmentation is in the chemical regime. It is naturally expected that the fraction of isolated clusters XI approaches pc as p approaches pc, and obviously XI equals pc when p equals pc. What we are concerned about is the fraction of isolated clusters on the surface, which form the fragments observed, and is a part of XI. This fraction can be obtained both experi-


mentally and theoretically. It is not determined in the present study because of the difficulty of separating the fine fragments from the parent particles without breaking the particles further. However, it is easy to obtain the value by percolation modeling using the Monte Carlo technique.52 Then it is feasible to estimate the relative importance of isolated cluster-related fragmentation to the fragmentation at the threshold. If we consider an extreme condition at which all the isolated clusters are located on the surface, then it is expected that the fragmentation before the threshold will be as important as that at the threshold. Another extreme condition is implicitly assumed in the existing simulation work discussed in the Introduction section, at which the isolated clusters do not separate at all. Thus, only the fragmentation at the threshold is concerned. It is likely from the present study that the practical circumstance is between the two extreme conditions, and the fragments from isolated clusters on the surface cannot be simply neglected. It should be pointed out here, however, that shrinkage due to the detachment of the isolated clusters does not contribute to the reduction of the particle size significantly, because the mass fraction of the fragments is negligible in the regime of chemical control. Another problem that needs to be explored is how fragmentation takes place under diffusional control. The experimental evidence from the present study shows that diffusional conditions favor perimeter fragmentation. Sahimi18 also showed that fragmentation under diffusion control differs from that under chemical control. More and finer fragments are formed when diffusional effects are more severe.18 The isolated clusters, which are formed on the surface first, soon detach from the particle. This implies that fragmentation phenomenon under diffusion control might be close to that at the first extreme condition, because the isolated clusters are mostly located near the surface. Under severe diffusional control, fragmentation occurs completely on the surface and contributes to the particle size reduction exclusively.14 This is another difference between the internal fragmentation and perimeter (52) Stauffer, D.; Aharony, A. Introduction to percolation theory, 2nd ed.; Taylor & Francis: London, 1992.


fragmentation. In conclusion, the isolated clusters may have to be considered in the modeling of fragmentation, in addition to the percolation threshold. Further experimental and theoretical efforts are needed to answer the two questions arising from the present study. Conclusions Our experimental and modeling studies have demonstrated that percolative fragmentation during char combustion can be effectively studied by measurements of the variation of char electrical resistivity with conversion. Further insight is obtained by combining these measurements with direct microscopic observations. The following specific conclusions can be drawn from the current study: 1. The electrical resistivity increases slowly at low conversions and then rapidly after a certain conversion, indicative of internal fragmentation. The percolation threshold is between 0.0 and 0.07 in terms of volume fraction of conducting phase, corresponding to a critical conversion of 90-99% or a critical porosity of 91-99%. 2. The electrical resistivity variation at high conversions is very sensitive to diffusional effects. The perimeter fragmentation becomes more and more important as particle size, gasification temperature, and oxygen concentration increase. 3. A large number of fragments appear during gasification in the chemical control regime, and this increases as gasification progresses. The conversion at which fragments start to appear decreases strongly with increasing reaction temperature. A portion of the fragments is very irregular, and more than 20 fine particles could be produced from a single parent particle at high conversions. 4. The particle size distribution of the fragments is independent of the reaction conditions and the char type. The measurement of the number distribution supports the prediction by percolation theory that the number distribution varies linearly with mass in a loglog plot. Acknowledgment. This research has been supported by the Australian Research Council. EF990090X

Percolative Fragmentation of Char Particles during Gasification

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