Variation of the pore structure of coal chars during gasification

Variation of the pore structure of coal chars during gasification

Carbon 41 (2003) 507–523 Variation of the pore structure of coal chars during gasification Bo Feng, Suresh K. Bhatia* Department of Chemical Engineer...

1MB Sizes 5 Downloads 203 Views

Carbon 41 (2003) 507–523

Variation of the pore structure of coal chars during gasification Bo Feng, Suresh K. Bhatia* Department of Chemical Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia Received 16 March 2002; received in revised form 10 October 2002; accepted 11 October 2002

Abstract The variation of the pore structure of several coal chars during gasification in air and carbon dioxide was studied by argon ˚ do adsorption at 87 K and CO 2 adsorption at 273 K. It is found that the surface area and volume of the small pores (,10 A) ˚ 20–50 A, ˚ not change with carbon conversion when the coal char is gasified in air, while those of the larger pores (10–20 A, ˚ increase with increase of carbon conversion. However in CO 2 gasification, all the pores in different size ranges 50–2500 A) increase in surface area and volume with increase of carbon conversion. Simultaneously, the reaction rate normalized by the ˚ for air gasification is constant over a wide range of conversion (.20%), while for CO 2 surface area of the pores .10 A gasification similar results are obtained using the total surface area. However, in the early stages of gasification (,20%) the normalized reaction rate is much higher than that in the later stage of gasification, due to existence of more inaccessible pores in the beginning of gasification. The inaccessibility of the micropores to adsorption at low and ambient temperatures is confirmed by the measurement of the helium density of the coal chars. The random pore model can fit the experimental data well and the fitted structural parameters match those obtained by physical gas adsorption for coal chars without closed pores.  2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Coal, char; B. Gasification; C. Modeling; D. Porosity, Surface areas

1. Introduction The gasification rate of coal char / carbon in oxygen, carbon dioxide and steam is well known to be governed by its structure. The reaction gas penetrates the particle and attacks the carbon atoms and the product gas then diffuses out through the solid structure. Therefore study of the internal structure of carbon is important in understanding the gasification process. The development of the pore structure of carbon during gasification has been extensively studied experimentally as well as theoretically [1–11], and various pore structure models have been reviewed in detail by Bhatia and Gupta [12]. The pore structure models generally assume that the gasification reaction occurs on the surface of the micropores, which form the main part of the surface area of char. The intrinsic reactivity is thus obtainable from the reaction rate per unit surface area of the micropores. There has been some additional work reporting the success of the normalization of reaction rate by the total surface area *Corresponding author. Tel.: 161-7-3365-4263; fax: 161-73365-4199. E-mail address: [email protected] (S.K. Bhatia).

(TSA) [13–16], suggesting the ratio of the reacting surface area and the TSA is constant during gasification. In contrast there have been numerous reports that the total surface area does not normalize the reaction rate successfully (e.g. [17,18]). Other work suggests that micropores might not be fully utilized during gasification [3,19–22]. The gasification reaction is considered to occur on the active surface area (ASA) which is part of the total surface area, or essentially on the reactive surface area (RSA) which in turn is part of the ASA. Normalization of the reaction rate by the ASA [14,17,19,23–32] and by the RSA [33–37] are reported to be more successful than by the TSA. Nevertheless the ratio of ASA:TSA has been found to be constant in a wide range of carbon conversion for some coals [14,16], rationalizing the utilization of the above pore structure models [34], though this may not hold in general. The active surface area is generally obtained from oxygen chemisorption experiments at low temperature, assuming that the ASA is located primarily in prismatic zig-zag [38] and arm chair [39] surfaces, where a carbon atom occupies on average about 0.083 nm 2 and that most of the oxygen atoms are bonded to only one carbon atom in these surfaces [18,23]. However, low temperature

0008-6223 / 02 / $ – see front matter  2002 Elsevier Science Ltd. All rights reserved. PII: S0008-6223( 02 )00357-3

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

508

chemisorption may underestimate the RSA because some sites where the activation energy required for oxygen dissociative chemisorption is very high are not covered [18]. On the other hand, compared with the determination of the ASA, that of the TSA by physical gas adsorption is well established and results are reproducible. Because the ratio of ASA:TSA is often constant over a wide range of conversion [14,16], the TSA can be (more) conveniently used to normalize the reaction rate and obtain the activation energy of the gasification reaction. The purpose of the present work is to clarify whether the TSA can be used to normalize the reaction rate in air gasification and CO 2 gasification. The variation of the pore structure of several coal chars during gasification was studied in this work. The raw coals were heat treated at various temperatures to study the effect of heat treatment on structural evolution. One coal was also demineralized to study the effect of mineral matter in coal, and one coal char was gasified in both air and CO 2 to study the effect of gasifying agent. The pore structure was characterized by argon adsorption and CO 2 adsorption isotherms using the density functional theory method.

2. Experimental

2.1. Char generation Three Australian coals (a semianthracite, Yarrabee, and two bituminous coals, Bolga and Bayswater) were used in this study, and their properties are shown in Table 1. The raw coal was dried and sieved to a particle size range of 90–180 mm and then subjected to heat treatment at various temperatures. The Yarrabee raw coal was also demineralized and the ash free coal heat treated. The demineralization procedure has been described in detail elsewhere [40]. The four coals, three raw coals and the demineralized Yarrabee coal, were heat treated under N 2 in a tube furnace at 1173, 1323 and 1423 K. The coal was inserted into the tube furnace after the temperature was stablized and held

Table 1 Properties of the raw coals studied Properties

Yarrabee

Bolga

Bayswater

Moisture (%) Ash (%) Volatile matter (%) Fixed carbon (%) Carbon, daf a (%) Hydrogen, daf (%) Nitrogen, daf (%) Oxygen, daf (%) Sulfur, daf (%)

3.0 10.0 9.5 77.5 92.77 3.54 1.83 0.64 1.22

3.4 6.4 34.6 55.6 79.06 5.11 1.78 13.58 0.47

3.3 15.3 28.1 56.6 82.50 5.10 1.80 10.20 0.40

a

Dry and ash free basis.

for 2 h under N 2 . The generated char sample was removed from the furnace and cooled in N 2 , and then sieved to 90–180 mm before being subjected to gasification. In total eight coal chars were generated and were named as follows: rawy900, rawy1050, rawy1150 (raw Yarrabee coal heat treated at 1173, 1323 and 1423 K for 2 h), HFy1050 (demineralized Yarrabee coal heat treated at 1323 K for 2 h), Bolga900, Bolga1050 (raw Bolga coal heat treated at 1173 and 1323 K for 2 h), Bayswater900, Bayswater1050 (raw Bayswater coal heat treated at 1173 and 1323 K for 2 h).

2.2. Gasification in air and carbon dioxide All the eight coal chars were oxidized in air in the tube furnace at 653 K for various times to generate char samples at various conversion levels. The temperature of 653 K was selected to ensure that the reaction was not affected significantly by intraparticle diffusion. The latter was confirmed by preliminary runs showing that for particle size ,200 mm the conversion–time curve of Yarrabee900 at 673 K in air was independent of particle size. Based on rate constants from conversion–time fits to be discussed the Thiele modulus was estimated to be less than 0.5 even in air gasification, assuming a conservative value of 1.0310 28 m 2 / s for the effective intraparticle diffusivity, further confirming the absence of intraparticle diffusion resistance. The reaction rate was estimated from the measured conversion–time data by curve-fitting the data followed by differentiation. The rawy1150 coal char was also gasified in carbon dioxide in the tube furnace at 1073 K for various times to generate chars with different conversion levels. Preliminary experiments were also carried out to ensure that the effect of particle size on the reaction rate is negligible.

2.3. Pore structure and helium density Argon adsorption at liquid argon temperature (87 K) and CO 2 adsorption at ice temperature (273 K) were carried out on a Micromeritics micropore analyser (ASAP2010). The isotherms were analyzed using the Micromeritics density functional theory (DFT) software package DFT PLUS. The pore size distribution was obtained in the size range of ˚ for argon adsorption and in the range of 4–10 A ˚ 4–2500 A for carbon dioxide adsorption. The helium density was measured for some samples using a Micromeritics AccuPyn 1330 helium pycnometer. Each sample was degassed at 300 8C for at least 12 h before gas adsorption and the helium density measurement. There are two widely used classical methods to determine the pore surface area of carbon by physical gas adsorption. One is the Brunauer–Emmett–Teller (BET) theory [41], most commonly employed with the nitrogen isotherm at 77 K. The other is the Dubinin–Radushkevich (DR) equation [42], often used with the CO 2 adsorption

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

509

isotherm at 273 K. However, apart from the theoretical drawbacks of applying the classical models to micropores of molecular dimensions, both adsorptives have limitations in determining the porosity of the microporous carbons. Nitrogen at 77 K is known to be subject to very slow diffusion in small pores [43], while at 273 K CO 2 cannot fill larger micropores and also may have additional interactions with carbon [44]. After comparing the results of nitrogen, argon and CO 2 adsorption, Suuberg and coworkers [21,22] concluded that CO 2 adsorption has no advantage over nitrogen adsorption, but the generality of this is not clear as it may be unique to their system. Webb and Orr [44] suggested that argon at liquid argon temperature (87 K) is preferable to nitrogen or argon at liquid nitrogen temperature (77 K) as a probe molecule in studies of microporosity of carbon, because argon is inert and its molecule is spherical, monatomic and nonpolar. The latter properties permit it to access small micropores more readily and also make the isotherm analysis more convenient. The DFT has the advantage of determining the pore size distribution over a wide range of pore size (micropore and mesopore), in addition to giving the pore surface area and volume. It is a molecular level statistical thermodynamic theory that relates the adsorption isotherm to the microscopic properties of the system: the fluid–fluid and fluid–solid interaction energy parameters, the pore size, the pore geometry, and the temperature. The Barrett–Joyner– Halenda (BJH) theory can be also used to obtain the pore size distribution but it is known to have accumulated errors in the micropore volume [44]. Therefore the density functional theory using the argon adsorption isotherm at 87 K appears to provide more complete and reliable results of the pore structure of carbon so far, though it has hitherto been scarcely used to investigate structural evolution with gasification. Nevertheless, it too loses accuracy below ˚ (for N 2 or argon) because of the inherent about 4–5 A mean-field treatment.

3. Results

˚ and (b) Fig. 1. Variation of (a) pore surface area (pores,2500 A), ˚ with carbon conversion, for Yarpore volume (pores,2500 A) rabee coal chars gasified in air at 653 K, determined from argon adsorption isotherms obtained at 87 K.

3.1. Variation of pore structure during gasification in air The variation of the total surface area and pore volume of the Yarrabee coal chars with carbon conversion is shown in Fig. 1, determined using the density functional theory from argon adsorption isotherms at 87 K. The curves for the coal chars heat treated at different temperatures and for the ash free coal char are very similar. The surface area and the pore volume initially increase rapidly and subsequently slowly with carbon conversion. In this and all subsequent figures surface areas and pore volumes are estimated per unit mass of residual carbon at any conversion level. The distribution of the pore surface area and pore volume of the rawy1150 coal char after partial gasification

in air is shown in Fig. 2. There are three peaks visible on ˚ the distribution curve in the pore size ranges of ,10 A, ˚ and 20–50 A, ˚ respectively. It appears that the 10–20 A ˚ do not surface area and pore volume in pores below 10 A change significantly with conversion, while those in the other two ranges increase with conversion. This can be seen clearly in Figs. 3 and 4, in which the pore surface area and pore volume in different ranges are depicted separately. Indeed for all of the four Yarrabee coal chars, ˚ do the surface area and volume of the small pores (,10 A) not change significantly or decrease slightly with increase of carbon conversion after an initial rapid rise. This rapid initial rise in surface area and volume is attributed to the

510

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

Yarrabee coal chars with increase of carbon conversion was also obtained from the CO 2 adsorption isotherms (see Fig. 5). Both of them do not change significantly with carbon conversion after the initial rise, consistent with the argon adsorption results in Figs. 3 and 4. It is noticed that the values of the surface area and volume obtained from CO 2 adsorption data are slightly lower than those obtained from argon adsorption isotherms in the same pore size ˚ This is in part likely to be related to the range (0–10 A). DFT being less accurate for polyatomic molecules such as CO 2 . It suggests that argon is a better adsorptive than CO 2 for the purpose of determining the micropore structure of carbon, if the DFT is used. Another advantage of using argon is that the pore size distribution obtained from the argon adsorption isotherms covers a wider range (up to ˚ 4000 A). Fig. 6 shows the variation of the pore surface area and volume of the Bolga and Bayswater coal chars with carbon conversion, determined from CO 2 adsorption isotherms at 273 K using density functional theory. The surface area and volume first increase with increase of carbon conversion, and decrease at higher conversions. It is also observed that there is an apparent difference between the coal chars heat treated at different temperatures. This is different from what was found for the Yarrabee coal chars, where there is no large difference between the coal chars heat treated at different temperatures, suggesting that the development of the pore structure is different for different coals.

3.2. Variation of pore structure during CO2 gasification

Fig. 2. (a) Pore surface area and (b) pore volume distribution of yarrabee1150 coal chars gasified to various conversions in air at 653 K, determined from argon adsorption isotherms obtained at 87 K. Symbols represent data at different carbon conversions: d 4.5%; s 15.4%; . 40.4%; \ 57.0%; j 57.3%; h 71.3%; ♦ 83.1%; 앳 94.8%. Both distributions are for unit mass of remaining carbon.

reopening of the micropores closed during heat treatment, which will be discussed later. However the surface area ˚ increase and volume of the larger pores (10–2500 A) significantly with the increase of carbon conversion. This suggests that the gasification reaction occurs predominant˚ Also the development of ly in the larger pores (.10 A). the pore structure is almost the same for the coal chars heat treated at different temperatures and for the ash free coal char. The variation of the surface area and volume of the

The rawy1150 coal char was also gasified in carbon dioxide at 1073 K and the variation of the surface area and volume with carbon conversion is shown in Fig. 7, determined from the argon adsorption isotherms at 87 K using density functional theory. Both the surface area and pore volume increase strongly with carbon conversion throughout the course of the gasification, showing the difference in pore development compared with air oxidation (Fig. 1) in which the increase occurs more strongly in the initial stages. Fig. 8 shows the surface area and volume of pores in various sizes changing with carbon conversion. Both the surface area and volume of pores in each size range increase with increase of carbon conversion significantly, again different from the results for air gasification (Figs. 3 and 4). This seems to suggest that all the pores participate in the gasification reaction in carbon dioxide. The surface area and volume in the pores smaller than ˚ determined from the CO 2 adsorption isotherms at 10 A, 273 K using the DFT, are displayed in Fig. 9, also show an increase with increase of carbon conversion.

3.3. Normalization of reaction rate ˚ do not change The observation that micropores ,10 A

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

511

˚ (b) 10–20 A, ˚ (c) 20–50 A, ˚ (d) 50–2500 A, ˚ Fig. 3. Variation of surface area with conversion, within various pore size ranges, (a) 0–10 A, for Yarrabee coal chars gasified in air at 653 K, determined from argon adsorption isotherms obtained at 87 K.

in volume and surface area after a certain conversion suggests that the rate depends on the surface area of pores ˚ rather than the total surface area. Thus the relation .10 A dx ] 5 k s Sg (1 2 x) dt

(1)

may be expected to yield a conversion-independent value of the intrinsic reactivity k s if the instantaneous specific ˚ rather than surface area Sg is taken as that for pores .10 A the total value. Here x is the carbon conversion of the char on an ash-free basis. The variation with conversion of the intrinsic reactivity in air based on surface area of pores ˚ is shown in Fig. 10. It is evident that the surface .10 A ˚ is a good normalization parameter for area of pores .10 A air gasification and yields a constant normalized rate after an initial decrease. The reaction rate normalized by the ˚ decreases quickly at low surface area of pores .10 A

conversions and remain essentially constant afterwards. Normalization of the reaction rate by the total surface area is not very successful and leads to an increase of the normalized rate with carbon conversion. The intrinsic reaction rate, i.e. the reaction rate normal˚ at the late ized by the surface area of the pores .10 A stage of gasification, is related to the initial fraction of the organized carbon, as shown in Fig. 11. The fraction of organized carbon has been obtained by fitting the X-ray diffraction patterns using an existing theory, and is discussed in detail elsewhere [40]. It appears that the intrinsic rate decreases with increase of fraction of organized carbon, as expected. The ash free coal char, HFy1050, has a lower intrinsic reaction rate, probably due to the lack of substances catalyzing the gasification reaction. The surface area determined by CO 2 adsorption was also used to normalize the reaction rate in air. The

512

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

˚ (b) 10–20 A, ˚ (c) 20–50 A, ˚ (d) 50–2500 A, ˚ Fig. 4. Variation of pore volume with conversion, within various pore size ranges, (a) 0–10 A, for Yarrabee coal chars gasified in air at 653 K, determined from argon adsorption isotherms obtained at 87 K.

normalized reaction rate increases with increase of conversion for all the coal chars, demonstrating that it is not a good normalizing parameter either. The reaction rate of rawy1150 in CO 2 gasification was also normalized using the total surface areas determined by argon adsorption and CO 2 adsorption, as shown in Fig. 12. The normalized reaction rate decreases quickly at low conversions and slowly at higher conversions, similar to that in air gasification.

x 5 1 2 exp f 2st 1 ct 2 / 4dg

(2)

was used to fit the conversion versus time curve, and the value of the structural parameter, c was obtained. Here t 5 k s0 t /(1 2 e0 ). Fig. 13 shows the fittings for char gasification in air and in carbon dioxide. The random pore model could fit the experimental data well for both the gasification of the coal chars in air and for the gasification of rawy1150 in CO 2 . The variation of surface area with carbon conversion can be also described by the random pore model as follows

3.4. Relationship between reaction rate and pore structure

]]]] Sv 5 Sv0 (1 2 x)œ1 2 c ln (1 2 x)

The random pore model [2,3] was used to study the development of pore structure and the variation of reaction rate. The model equation

in which the surface area, Sv , and the initial surface area, Sv 0 , are expressed as surface area unit particle volume. Since the surface area is measured in the unit of surface

(3)

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

˚ and (b) Fig. 5. Variation of (a) pore surface area (pores,10 A), ˚ with conversion for Yarrabee coal pore volume (pores,10 A) chars gasified in air at 653 K, determined from carbon dioxide adsorption isotherms obtained at 273 K. All pore volumes are estimated per unit mass of carbon remaining.

area per unit mass of remaining carbon, the above equation is rewritten as ]]]] Sg 5 Sg0œ1 2 c ln (1 2 x)

(4)

in which the unit of Sg and Sg 0 is surface area per unit mass of carbon remaining, using the following relations: Sv 5 Sg rb , Sv 0 5 S g0 rb0 , rb 5 (1 2 e )rt , rb0 5 (1 2 e0 )rt , e 5 e0 1 (1 2 e0 )x, where rb and rt are the bulk density and true density of carbon, respectively, and e is the porosity at any time. The variables rb 0 and e0 represent initial values of rb and e, respectively.

513

˚ and (b) Fig. 6. Variation of (a) pore surface area (pores,10 A), ˚ with conversion for Bolga and pore volume (pores,10 A) Bayswater coal chars gasified in air at 653 K, determined from carbon dioxide adsorption isotherms obtained at 273 K.

Eq. (4) indicates that the plot of S 2g against 2ln (12x) should be linear. Fig. 14 shows such a plot for the Yarrabee coal chars gasified in air using the total surface area from the argon adsorption isotherms and the surface ˚ It appears that the surface area of area of pores .10 A. ˚ gives more satisfactory results. However, for pores .10 A CO 2 gasification of rawy1150, the results using the surface area determined from the CO 2 adsorption isotherms show better linearity than those using the argon surface area, as shown in Fig. 15. The structural parameter, c, obtained by fitting the experimental conversion–time data for air gasification and CO 2 gasification, is shown in Tables 2 and 3, respectively.

514

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

˚ and (b) Fig. 7. Variation of (a) pore surface area (pores,2500 A), ˚ with conversion for rawy1150 coal pore volume (pores,2500 A) chars gasified in carbon dioxide at 1073 K, determined from argon adsorption isotherms obtained at 87 K.

Fig. 8. Variation of (a) pore surface area, and (b) pore volume with conversion, within various pore size ranges, for rawy1150 coal chars gasified in carbon dioxide at 1073 K, determined from argon adsorption isotherms obtained at 87 K.

This parameter is also determined from the physical 2 adsorption data as c 5 4p Lg /( rt S g0 ) [4], where Lg and Sg 0 are the pore length (meter per unit mass of carbon) and the initial pore surface area (meter square per unit mass of carbon), respectively, and rt is the true density of carbon, assumed to be 2.2 g / cm 3 . The pore length and surface area in different pore size ranges are calculated from the pore size distribution obtained from the argon adsorption isotherms using the DFT, as are also the structural parameters in different pore size ranges. In performing the calculations it was recognized that while the random pore model is

derived assuming cylindrical pores, the DFT characterization uses a slit pore model. To convert the slit width into an equivalent cylindrical pore radius we chose the pore radius as the value that yields the same surface area per unit pore volume. This provides the radius as being equal to slit width, since for a cylinder of r radius the surface area to volume ratio52 /r, while for an infinite slit of width H it is 2 /H. Theoretically, the value of c corresponds to that estimated from the initial value of the structural parameters. However, because of the abnormally large increase in

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

515

Fig. 10. Variation of reaction rate per unit surface area of pores ˚ (10 A,pores,2500 ˚ ˚ with carbon conversion for .10 A A), gasification in air at 653 K. Surface area is determined from the argon adsorption isotherms at 87 K.

the experimental value of c in the pore size range of ˚ matches the fitted c for most of the coal chars. 10–2500 A Interestingly the experimental value of c from the CO 2 adsorption isotherm is also in proximity of the fitted c

˚ and (b) Fig. 9. Variation of (a) pore surface area (pores,10 A), ˚ for rawy1150 coal chars gasified in pore volume (pores,10 A) carbon dioxide at 1073 K, determined from carbon dioxide adsorption isotherms obtained at 273 K.

surface area in the initial stages of gasification, attributed to apparently closed pores becoming accessible to the adsorption, we also determined the value of c at a low conversion, in the range of 15–25%, at which point the area no longer increased rapidly with conversion. The results are listed in Tables 2 and 3. For air gasification the experimentally determined (based on conversion–time data) structural parameter of the fresh coal char is much larger than the fitted value, probably due to many apparently closed pores in the fresh char. Indeed the structural parameters of the partially gasified chars (at low conversion of 15–25%) yield c values closer to the fitted c, and

Fig. 11. Variation of the intrinsic reaction rate (rate per unit ˚ with the initial fraction of organized surface area of pores .10 A) carbon in different Yarrabee coal chars for gasification in air at 653 K.

516

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

Fig. 12. Variation of the specific reaction rate of the rawy1150 coal chars with carbon conversion for gasification in carbon dioxide at 1073 K, normalized by the total surface area (pores, ˚ obtained from the argon adsorption isotherm at 87 K (m), 2500 A) ˚ (pores,10 A), ˚ and by the area of the pores smaller than 10 A determined from the CO 2 adsorption isotherm at 273 K (d).

though this is probably just a coincidence. However, for CO 2 gasification the experimental value of c fails to match the fitted value of c for all the partially gasified coal chars. This is probably due to the incomplete opening of the closed micropores to adsorption gas through the course of gasification, which will be discussed in detail later.

3.5. Inaccessibility of pores to physical gas adsorption As shown in Section 3.1, the surface area in the small ˚ increases quickly with the micropore size range (,10 A) progress of gasification in air at the early stage of gasification and remains almost unchanged afterwards. This behavior is attributed to the opening of the apparently closed small micropores to adsorption gas. While the surface area initially increases dramatically with conversion, this is not the case with the reaction rate. As a result an initial decrease in apparent reactivity is observed, as seen in Fig. 10. As discussed in Section 4 this is attributed here to nonparticipation of the small micropores in reaction, consistent with the observation of Aarna and Suuberg [21]. The closure of the micropores during heat treatment has been reported previously at temperatures above 800 8C [45,46]. Here the helium density of partially gasified coal chars has been measured in an effort to estimate the volume of closed pores. Helium is known to be able to penetrate into smaller pores compared with argon and CO 2 . Therefore if there are any pores that are not accessible to helium, they will also be inaccessible to argon and CO 2 adsorption. The specific volume of the

Fig. 13. Experimental and fitted random pore model (RPM) variation of carbon conversion with reaction time, for gasification (a) in air at 653 K, and (b) in carbon dioxide at 1073 K.

closed pores, vc , is calculated from the helium density following

ec 1 1 vc 5 ] 5 ] 2 ] rHe rHe r¯ s

(5)

where ec is the volume fraction of the closed pores in the apparent solid envelope, rHe is the measured helium density and r¯ s is the average density of the particle with all the pores accessible. The latter can be obtained by

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

517

which leads to inaccessibility of these pores to helium gas adsorption. It is clear that the volume of the closed pores increases with the increase of heat treatment temperature and time, as expected. It also shows that the volume of the closed pores increases slowly after some time of heat treatment. The pore structure of the coal chars heat treated at 1150 8C for various times (from 2 min to 12 h) was also examined. The total surface area and volume of all the chars are very small, less than 4 m 2 / g. The surface area ˚ decreased while and volume of the micropores (,20 A) those of the mesopores increased slightly with increase of heat treatment time. Together with the above results of the helium density experiments, showing an increase in closed pore volume with heat treatment, these findings suggest that the closed pores are predominantly the small micro˚ radius). pores (,10 A The helium density of partially gasified coal chars as well as the volume of closed pores at various conversions are also determined and shown in Fig. 17. The helium density increases from around 2.0 to 2.75 g / cm 3 which is the density of ash. The volume of closed pores decreases with increase of carbon conversion and approaches zero quickly, clearly indicating opening of the closed pores to gas adsorption gradually during gasification. This is probably due to the preferential gasification of the functional groups and heavy molecules that block the mouth of the micropores [45]. These molecules are disorganized and should react fast, consistent with our observation of initial higher reactivity.

4. Discussion

4.1. Effect of pore shape on pore structure development Fig. 14. Variation of the square of (a) the total surface area ˚ and (b) the surface area of pores larger than 10 (pores,2500 A), ˚ (10 A,pores,2500 ˚ ˚ with carbon conversion for gasification A A) in air at 653 K, determined from argon adsorption isotherms at 87 K.

12f fa 1 ] 5 ]]a 1 ] r¯ s rc ra

(6)

in which fa is the mass fraction of ash, while rc and ra are the density of carbon and ash, respectively. The value of rc was taken to be that of graphite (2.2 g / cm 3 ), while ra was determined from the ash of the coal char (2.75 g / cm 3 ). The variation of the helium density and the calculated volume of the closed pores with heat treatment time at various heat treatment temperatures are shown in Fig. 16 for the Yarrabee coal. The helium density decreases with the severity of heat treatment conditions, which can probably only be explained as the closure of micropores

One of the findings discussed above is the difference between measured and fitted values of the structural parameter c. While this may occur due to a variety of factors, one concern overlooked in the literature is that of pore shape. While the random pore model assumes cylindrical pores, the characterization often assumes slit shaped pores. Although both are clearly idealistic, and the real pore shape is more likely irregular and complex, it can be shown that for an enclosed pore space (as opposed to that of an infinite slit) the variation of surface area follows Eq. (3), albeit with a modified value of c. To investigate the effect of pore shape we assume the pores comprise an enclosed space in which the surface area is proportional to the measure of pore size, H, and the volume is proportional to H 2 . Consequently the nonoverlapping pore volume, VE , and the nonoverlapping pore surface area, SE , per unit volume can be written as `

E

VE 5 c 1 H 2 L(H )dH 0

(7)

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

518

˚ determined from the argon adsorption Fig. 15. Variation of the square of the specific surface area of all the pores (pores,2500 A), ˚ (pores,10 A), ˚ determined from the CO 2 adsorption isotherm at 273 K (d), isotherms at 87 K (m), and that of the pores smaller than 10 A with carbon conversion for gasification in carbon dioxide at 1073 K. `

`

E

SE 5 c 2 HL(H )dH

E

dVE 2c 1 dH ] 5 2c 1 ] HL(H )dH 5 ]kSE dt dt c2

(8)

0

(9)

0

`

where c 1 and c 2 are constants depending on pore shape, and L(H ) is the pore axis length distribution. The rate of change of VE and SE are then obtained as

E

dSE dH ] 5 c 2 ] L(H )dH 5 c 2 kLT dt dt

(10)

0

Table 2 Structural properties of coal chars partially gasified in air Properties

Rawy900 fresh

Rawy1050 fresh

Rawy1150 fresh

Rawy900 x514.9 %

Rawy1050 x524.5 %

Rawy1150 x515.4 %

HFy1050 x518.97 %

˚ Surface area (pores,2500 A) by argon adsorption (m 2 / g) ˚ Pore length (pores,2500 A) by argon adsorption (m / g) ˚ Surface area (pores,10 A) by argon adsorption (m 2 / g) ˚ Pore length (pores,10 A) by argon adsorption (m / g) ˚ ˚ Surface area (10 A,pores,2500 A) by argon adsorption (m 2 / g) ˚ ˚ Pore length (10 A,pores,2500 A) by argon adsorption (m / g) ˚ Surface area (pore,10 A) by CO 2 adsorption (m 2 / g) ˚ Pore length (pores,10 A) by CO 2 adsorption (m / g) ˚ c (pores,2500 A) argon adsorption ˚ c (pores,10 A) argon adsorption ˚ ˚ c (10 A,pores,2500 A) argon adsorption ˚ c (pores,10 A) CO 2 adsorption c, fitted

N /A

5.92

1.82

404

466

472

686

N /A

4.50310 8

7.71310 7

9.73310 10

1.08310 11

1.08310 11

1.51310 11

N /A

¯0

¯0

335

360

381

504

N /A

¯0

¯0

8.95310

N /A

5.92

1.82

68

N /A

4.50310

2.48

1.56

0.39

234

328

269

409

5.97310 8

2.33310 8

8.46310 7

6.45310 10

9.19310 10

7.39310 10

1.12310 11

N /A

73.45

132.74

3.41

2.84

2.77

1.83

N /A





10.01

4.24

3.84

2.95

N /A

73.45

132.74

9.45

6.01

7.11

3.39

599

547

3210

6.72

4.86

5.79

3.81

6.43

6.39

6.62

6.43

6.39

6.62

3.61

8

7.71310

7

7.83310

9

9.65310

10

105 9

1.17310

9.77310

10

91 10

1.04310

1.31310

11

180 10

1.94310

10

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

519

Table 3 Structural properties of coal chars partially gasified in carbon dioxide Properties

rawy1150 x50 %

rawy1150 x54.36 %

rawy1150 x55.64 %

rawy1150 x58.58 %

rawy1150 x524.13 %

rawy1150 x539.44 %

rawy1150 x574.75 %

˚ Surface area (pores,2500 A) by argon adsorption (m 2 /g) ˚ Pore length (pores,2500 A) by argon adsorption (m/g) ˚ Surface area (pores,10 A) by argon adsorption (m 2 /g) ˚ Pore length (pores,10 A) by argon adsorption (m/g) ˚ ˚ Surface area (10 A,pores,2500 A) by argon adsorption (m 2 /g) ˚ ˚ Pore length (10 A,pores,2500 A) by argon adsorption (m/g) ˚ Surface area (pore,10 A) by CO 2 adsorption (m 2 /g) ˚ Pore length (pores,10 A) by CO 2 adsorption (m/g) ˚ c (pores,2500 A) argon adsorption ˚ c (pores,10 A) argon adsorption ˚ ˚ c (10 A,pores,2500 A) argon adsorption ˚ c (pores,10 A) CO 2 adsorption c, fitted

2.3

2.8

4.5

6.2

31

225

217

9.64310

7

1.15310

8

2.01310

3.05310

8

3.27310

¯0.0

¯0.0

¯0.0

¯0.0

3.9

¯0.0

¯0.0

¯0.0

¯0.0

6.64310

2.3

2.8

4.5

6.2

27

9.64310

7

1.15310

8

2.01310

8

3.05310

8

9

4.95310

10

176 8

4.39310

9

5.56310

10

103 10

49

2.60310

3.71310

2.62310

10

114 10

1.09310

10

0.5

7.7

8.3

12.8

66

147

176

1.06310 9

1.84310 10

2.01310 10

3.09310 10

1.69310 11

3.88310 11

4.63310 11

106.19 –

85.32 –

106

56.86 –

45.21 –

19.19

5.56

4.48

251.58

8.10

14.03

85.3

56.9

45.2

19.9

13.00

4.77

2570.59

178.99

168.61

108.65

22.09

10.26

8.59

2.97

2.97

2.97

2.97

2.97

2.97

2.97

in which k is the linear rate of reaction, and LT the total pore length per unit volume. The above equations readily combine to yield the integrated form c 22 LT S 2E 2 S 2E0 5 ]](VE 2VE0 ) c1

(11)

where following the random pore model [2]e 5 1 2 e 2VE , and the overlapped surface area Sv 5 SE (1 2 e ), which are valid for arbitrary pore shape. These relations combine with Eq. (11) to yield S ]]]] ]v 5 (1 2 x)œ1 2 c ln (1 2 x) S0

have c 1 5c 2 5n. Therefore, c 5 nLT (1 2 e0 )2 /S 02 . These results indicate that the structural parameter is slightly sensitive to pore shape, and thus the development of the pore structure [Eq. (12)] is affected by pore shape to some extent through the value of c. Further the ratio of volume to surface area for slit pores, H / 2, is similar to that for cylindrical pores, r / 2, when r 5 H. Consequently the pore radius for cylindrical pores is considered to be equivalent to the pore width for slit pores in the view of pore development.

4.2. Difference between coals (12)

in which the structural parameter is c 5 c 22 LT /c 1 S 2E0 , and we have used the relation x 5 (1 2 e ) /(1 2 e0 ). Eq. (12) is exactly the same in form as Eq. (2) which is obtained by assuming cylindrical pores. However the structural parameter, c, now depends on the pore geometry according to

c 5 c 22 LT (1 2 e 02 ) /c 1 S 02

8

(13)

For cylindrical pores, we have c 1 5 p and c 2 52p, giving rise to c 5 4p LT (1 2 e0 )2 /S 02 . For square pores, we have c 1 51 and c 2 54, leading to c 5 16LT (1 2 e0 )2 /S 02 . For semi-infinite slit-like pores, e.g. pores with H 3nH shape in which n is a number much larger than unity, we

It is found that the development of the pore structure during gasification is similar for heat treated Yarrabee coal chars at different temperatures (Figs. 1, 3–5). This supports the results of Suuberg et al. [47] who found that the pore structure of coal chars become the same after a certain conversion. However, it is also observed that the pore development is different for the Bolga coal chars after heat treatment at two temperatures, and the same is found for the Bayswater coal chars. The coal char heat treated at higher temperature shows less pore surface area (Fig. 6). This suggests that the effect of heat treatment temperature is important for some coals but not important for the others. No larger difference in the pore development was observed between the raw Yarrabee coal char and the demineralized coal char. This is in disagreement with the

520

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

Fig. 16. Variation of (a) the helium density of Yarrabee coal chars, and (b) the volume of closed pores in the coal chars, with heat treatment time at various heat treatment temperatures.

results of Suuberg [22] who found little mesoporosity development in the demineralized Wyodak subbituminous coal char. Again this disagreement might be due to the coal type, since Yarrabee is a semi-anthracite. It is known that anthracite is more resistant to heat treatment than the other coals and has less content of mineral matter.

4.3. Inaccessibility of reactive surface area The normalized reaction rate decreases quickly at the early stage of air gasification and remains constant afterwards, consistent with the results of Adschiri and Furusawa [15] and De Koranyi [48], although they used the total surface area for normalization. Based on the XRD patterns which suggest that a considerable amount of

Fig. 17. Variation of (a) the helium density of Yarrabee coal chars, and (b) the volume of closed pores in the coal chars, with carbon conversion for gasification in air at 653 K.

disorganized carbon exists [49], we attribute the initial high reactivity to the functional groups, large molecules and disorganized carbon that are initially present in the char [45]. This disorganized matter is highly reactive and is consumed rapidly at the initial stages, leaving behind the less reactive crystallitic matter, and in the process exposing the micropores and increasing the accessible surface area. Therefore the normalized reaction rate at the early stage of gasification is larger than that at the later stage. It is also interesting to notice that this behavior of the normalized reaction rate resembles in shape the variation of the ratio of ASA:TSA with conversion reported in the literature [16,29]. The ASA:TSA ratio decreases quickly

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

until 20% conversion before it becomes almost constant. While other explanations, such as those related to chemisorption dynamics are possible, this is viewed here as being related to the early consumption of the defective or disorganized carbon sites (which are part of the active surface area), and the replacement of these by the inactive micropores. The ASA:TSA ratio is high initially because the micropores (which are seen to be inactive) are not accessible to physical adsorption while the blocking sites are accessible to reactant gases at reaction temperature while also being active. With the progress of gasification when the micropores are gradually opened to physical gas adsorption, this ratio becomes smaller, and remains almost constant when all the pores are open. The fact that the ˚ do not appear to participate in the micropores ,10 A oxidation reaction suggests that their surfaces comprise basal plane sites at the top or bottom of crystallites. Such basal planes are known to have much lower reactivity than edge sites and are essentially unreactive.

4.4. Difference between air gasification and CO2 gasification Although the normalization of the gasification rate in air using the total surface area was not successful, the random pore model still fit the experimental data well. This suggests that the validity of the random pore model should not be judged by the success of the normalization of the total surface area. The model can be validated by comparing the fitted structural parameter with the measured one, however cares should be taken to make sure that all the pores are open. As shown in Table 2 for air gasification, the fitted structural parameter matches the measured one of the partially gasified char without closed pores. Unfortunately the fitted structural parameter does not match the measured c for any char when gasified in carbon dioxide (Table 3). This is probably due to the closed pores still not being fully opened to adsorption throughout CO 2 gasification because carbon dioxide is known to be less reactive than oxygen in removing the heavy molecules and functional groups. This hypothesis may also explain the observation of the gradual increase of the surface area and volume of the small micropores during CO 2 gasification, as opposed to the rapid initial increase during air gasification. However this has to be supported by further experiments of gasifying the char without closed pores. This appears to be also supported by the studies of the crystallite structure of the same coal chars during gasification. The variation of the crystallite size with carbon conversion is almost the same for air gasification and for CO 2 gasification [49], despite the differences in pore structure variation. If the gasification process is completely different for air gasification and CO 2 gasification, a difference in the development of the crystallite structure is also expected. These results are discussed in more detail in another communication [49].

521

Salatino et al. [50] discussed about the difference between oxygen gasification and CO 2 gasification. Oxygen in the chemisorbed state is considered to be able to migrate along micropores until it reaches an active site where it reacts. Therefore the pathway chemisorption within micropores→migration of activated oxygen→reaction at reactive sites (either catalyzed or uncatalyzed) plays an important role in gasification with oxygen while it does not (or it does to a lesser extent) in gasification with CO 2 (as well as with steam, see Yang and Wong [51]). Another explanation provided by Ballal and Zygourakis [52] for a bituminous coal is the different degree of penetration of micropores by the two reactants which resulted in different patterns of pore growth and overlapping as carbon burn-off increased. Our results suggest that the different degree of opening of the closed micropores may be another explanation, as discussed above. This can be clarified by studying the development of the pore structure of carbons without closed pores. The effect of chemisorption dynamics on rate is unlikely to be important in this study. As shown in our recent work [53], chemisorption dynamics has negligible influence in CO 2 gasification under typical conditions of gasification, while it is generally important in oxygen gasification when the temperature is low and the oxygen pressure is high. The condition used in this work, 653 K, 0.21 bar O 2 , is near the boundary of the region in which the chemisorption dynamics is not important (T .720 K at 0.21 bar O 2 ).

4.5. Air gasification process It is interesting to observe that air gasification occurs ˚ resulting in the preservation of the outside of pores ,10 A pore volume and surface area in this pore range. It is also noticed that the peaks on the pore size distribution curves are located at the same pore sizes, for various coal chars gasified to different conversion levels (e.g. Fig. 2). For Yarrabee coal chars heat treated at various temperatures, ˚ are the same three peaks at around 6, 13 and 30 A identified in the pore size distribution curve in the pore ˚ For Bolga and Bayswater coal chars size range ,50 A. gasified to various conversion levels, two peaks of 5.5 and ˚ are found in the micropore range ,20 A. ˚ These 8.5 A observations have some implications on the air gasification process. That micropores are probably not fully utilized has been discussed by some investigators [3,19–21]. Hurt et al. [20] found that the rate of CO 2 gasification is insensitive to large changes in total surface area occurring during heat treatment or reaction. This behavior is attributed to an enhancement of the active site concentration on large pore surfaces. The active sites could represent crystallite edges or sites in contact with catalytically active inorganic impurities, which may lie preferentially outside of the small pores. This is consistent with our findings here that

522

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523

the small micropores do not change in pore volume and surface area, or in pore size. ˚ may represent regions Small micropores (at 6 A) between basal planes of two crystallites in Yarrabee coal char, rather than the spaces between two basal planes ˚ Their within a crystallite (as the distance is around 3.4 A). apparent initial closure or blockage may be due to functional groups or molecules comprising disorganized matter, that crosslink the crystallites. On the other hand, larger ˚ should represent spaces between edge micropores (at 13 A) sites of two crystallites as these pores participate in reaction. During gasification these pores do not appear to enlarge, suggesting that formation of mesopores from enlargement of micropores is unlikely to happen. This also implies that the carbon crystallite structure is shrinking during gasification while retaining the same distance between crystallites, probably at the minimum energy state. Mesopores may represent some spaces between grains. Similarly the mean size of mesopores does not change during gasification as grains shrink as well. At the ˚ beginning of air gasification, some micropores (at 13 A) are not accessible to gasification, therefore the normalized reaction rate is higher than the intrinsic reaction rate.

5. Conclusions The variation of the pore structure of several coal chars with carbon conversion in air and in CO 2 is studied and the following conclusions can be made: 1. The development of the pore structure in air gasification is different from that in CO 2 gasification. In air gasification the surface area and volume of the small ˚ does not change significantly with micropores (,10 A) carbon conversion after a certain conversion, while in CO 2 gasification the surface area and volume of the small micropores increase dramatically with the progress of gasification. The surface area and volume of the pores in other pore size ranges increase with the increase of carbon conversion in both air gasification and CO 2 gasification. This difference might be due to the different rate of reopening of the apparently closed or blocked pores between air gasification and CO 2 gasification, because carbon dioxide is known to be less reactive than oxygen in removing the heavy molecules and functional groups. 2. The closure of pores occurs during heat treatment and the volume of closed pores is a function of heat treatment time and temperature. The pore closure or blocking may be due to the presence of large molecules or groups, comprising disorganized carbon, crosslinking crystallites. The volume of closed pores increases with increase of heat treatment temperature and time. The closed pores are reopened quickly in air gasification before 20% conversion.

3. The gasification rate in air can be normalized by the ˚ and the normalized surface area of the pores .10 A, rate can be related to the initial fraction of organized carbon in char. The random pore model is shown to be able to fit the experimental data well and the fitted structural parameters match those obtained from argon ˚ for the adsorption data in the pore size range of .10 A partially gasified coal chars without closed pores. 4. The size of various pores does not change with conversion, suggesting shrinkage occurs maintaining the same distance between crystallites as they react, possibly due to Van der Waals forces.

Acknowledgements The financial support of the Australian Research Council (ARC) under the Large Research Grant Scheme is gratefully acknowledged.

References [1] Hashimoto K, Miura K, Yoshikawa F, Imai I. Ind Eng Chem Process Des Dev 1979;18(1):72–80. [2] Bhatia SK, Perlmutter DD. AIChE J 1980;26(3):379–85. [3] Gavalas GR. AIChE J 1980;26(4):577–84. [4] Su JL, Perlmutter DD. AIChE J 1985;31(6):973–81. [5] Reyes S, Iglesia E, Jensen KF. Solid State Ionics 1989;32:833–42. [6] Ballal G, Zygourakis K. Ind Eng Chem Res 1987;26:911– 21. [7] Sotirchos SV, Crowley JA. Ind Eng Chem Res 1987;26:1766–73. [8] Sahimi M, Tsotsis TT. Chem Eng Sci 1988;43(1):113–21. [9] Tseng HP, Edgar TF. Fuel 1989;68:114–20. [10] Chi WK, Perlmutter DD. AIChE J 1989;35(11):1791–802. [11] Sahimi M, Gavalas GR, Tsotsis TT. Chem Eng Sci 1990;45:1443–502. [12] Bhatia SK, Gupta JS. Rev Chem Eng 1994;8(3–4):177–258. [13] Adschiri T, Zhu ZB, Furusawa T. In: Int. Conf. Coal Sci. Maastricht (The Netherlands), 1987. [14] Alvarez T, Fuertes AB, Pis JJ, Ehrburger P. Fuel 1995;74(5):729–35. [15] Adschiri T, Furusawa T. Fuel 1986;65(7):927–31. [16] McEnaney B. In: Lahaye J, Ehrburger P, editors, Fundamental issues in control of carbon gasification reactivity, Kluwer, 1991, pp. 175–204. [17] Ehrburger P, Louys F, Lahaye J. Carbon 1989;27(3):389–93. [18] Walker Jr. PL. Carbon 1990;28(2 / 3):261–78. [19] Radovic LR, Walker Jr. PL, Jenkins RG. Fuel 1983;62(7):849–56. [20] Hurt RH, Sarofim AF, Longwell JP. Fuel 1991;70(9):1079– 82. [21] Aarna I, Suuberg EM. In: 27th Symp (Intl) on Combust: The Combustion Institute, 1998. [22] Suuberg EM. In: Abstracts of papers of the american chemical society, 1999, p. 217.

B. Feng, S.K. Bhatia / Carbon 41 (2003) 507–523 [23] Laine NR, Vastola FJ, Walker Jr. PL. J Phys Chem 1963;67(10):2030–4. [24] Huttinger KJ, Fritz OW. Carbon 1991;29(8):1113–8. [25] Huttinger KJ, Nill JS. Carbon 1990;28(4):457–65. [26] Khan MR. Fuel 1987;66(12):1626–34. [27] Walker Jr. PL, Taylor RL, Ranish JM. Carbon 1991;29(3):411–21. [28] Garcia X, Radovic LR. Fuel 1986;65(2):292–4. [29] Causton P, McEnaney B. Fuel 1985;64(10):1447–52. [30] Cypres R, Planchon D, Braekman-Danheux C. Fuel 1985;64(10):1375–8. [31] Marsh H, Diez MA, Kuo K. In: Lahaye J, Ehrburger P, editors, Fundamental issues in control of carbon gasification reactivity, Kluwer, 1991, pp. 205–20. [32] Lahaye J, Dentzer J, Soulard P, Ehrburger P. In: Lahaye J, Ehrburger P, editors, Fundamental issues in control of carbon gasification reactivity, Kluwer, 1991, pp. 143–62. [33] Fritz OW, Huttinger KJ. Carbon 1993;31(6):923–30. [34] Lizzio AA, Jiang H, Radovic LR. Carbon 1990;28(1):7–19. [35] Radovic LR, Jiang H, Lizzio AA. Energy Fuels 1991;5:68– 74. [36] Radovic LR, Lizzio AA, Jiang H. In: Lahaye J, Ehrburger P, editors, Fundamental issues in control of carbon gasification reactivity, Kluwer, 1991. [37] Adschiri T, Nozaki T, Furusawa T, Zhu ZB. AIChE J 1991;37(6):897–904.

[38] [39] [40] [41] [42] [43]

[44] [45] [46] [47] [48] [49] [50] [51] [52] [53]

523

Nandi SP, Walker Jr. PL. Fuel 1975;54:169–72. Thomas JM. Angew Chem Int Ed Engl 1988;27:1673–6. Feng B, Bhatia SK, Barry JC. Carbon 2002;40(4):481–96. Brunauer S, Emmett P, Teller E. J Am Chem Soc 1938;60:309–15. Dubinin M, Radushkevich L. Proc Acad Sci USSR 1947;55:331–5. Mahajan OP, Walker Jr. PL. In: Karr C, editor, Analytical methods for coal and coal products, New York: Academic, 1978. Webb PA, Orr C. Analytical methods in fine particle technology. Micromeritics Instrument, 1997. Buiel ER, George AE, Dahn JR. Carbon 1999;37:1399–407. Blazewicz S, Swiatkowski A, Trznadel BJ. Carbon 1999;37:693–700. Suuberg EM, Wojtowicz M, Calo JM. Carbon 1989;27:431– 40. De Koranyi A. Carbon 1989;27(1):55–61. Feng B, Bhatia SK, Barry JC, Energy and Fuels 2002, in preparation. Salatino P, Senneca O, Masi S. Carbon 1998;36(4):443–52. Yang RT, Wong C. J Catal 1983;82:245–55. Ballal G, Zygourakis K. Ind Eng Chem Res 1987;26:1787– 93. Feng B, Bhatia SK. Chem Eng Sci 2002;57(15):2907–20.