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The intrinsic reactivity of carbons to oxygen
The intrinsic reactivity of carbons to oxygen* Ian W. Smith CSIRO Division of Process Technology, New South Wales, Australia 2113 (Received 20 July 1977)
Minerals Research Labora tories, P. 0. Box 136, North
Ryde,
The intrinsic reactivities, that is the reaction rates per unit area of pore surface in the absence of any mass transfer restrictions, for combustion of a wide range of carbons have been calculated from published data. The intrinsic reactivities, corrected to a common oxygen pressure of 101 kPa, were ascertained over the temperature range 580 to 2200 K. The reactivities of ‘non-porous’ carbons (diamond, soot, vitreous carbon and pyrolytic graphite) between 770 and 4000 K were also considered. Porous carbons of various origins show intrinsic reactivities that differ by up to 4 orders of magnitude at a given temperature. However, after high-temperature heat treatment, certain carbons of different origin (e.g. sugar and wood charcoals, nuclear and spectroscopic graphites) show closely similar reactivities when reacted with purified oxygen. The reactivities of the ‘non-porous’ carbons show a temperature dependence similar to the average temperature dependence of the porous carbons, but their reactivity expressed per unit external surface area is generally higher than the median intrinsic value of the porous materials.
Specimens of carbon produced from different original materials, or in different ways from the same material, are found to burn at very different rates under otherwise similar conditions. The speed at which an individual carbon particle of given size or mass burns depends in part on the rate of oxygen transfer from the bulk gas to the particle, and in part on the particle’s reactivity. This reactivity depends on the extent and accessibility to oxygen of the pores within the particle, and on the velocity of chemical reaction between oxygen and the pore surface. The latter factor, when properly defined, may be termed the intrinsic reactivity of the carbon. Intrinsic reactivity is defined as the reaction rate per unit area of pore surface in the absence of any mass-transfer restrictions. The purpose of this paper is to derive from published data, including data from the Minerals Research Laboratories, the intrinsic reactivities of as large a variety of carbons as possible, with the object of comparing one with another. In order to make this comparison, the observed kinetics were corrected for system effects, e.g. for the extent to which external mass transfer affected burning rates, and then the parallel processes of pore diffusion and reaction on the pore wall were separated. For some of the carbons it has also been possible to derive the value of the ‘true’ activation energy and reaction order. The original data treated here represent only a small part of the large amount of information to hand on the carbon-oxygen reaction. Only those experiments could be considered where sufficient information is available on mass-transfer effects, pore structure, the difference between particle and reactor temperatures, and so on. Nevertheless it was possible to obtain results for some 32 porous, and 17 ‘non-porous’ carbons. * Complete text of paper presented in brief to ‘Conference on Fundamentals of Carbon-Gas Reactions’, sponsored by the University of Newcastle, the Institute of Fuel (Australian Membership) and the Combustion Institute (Australia). Conference held at CSIRO Minerals Research Laboratories, May 1976
METHOD OF CALCULATING
1NTRlNSIC REACTIVITY
The means of calculating intrinsic reactivity has been given in detail elsewhere ‘p2. The desired qu antity is the intrinsic rate coefficient for carbon oxidation, Ri, expressed in relation to unit area of pore surface, and to unit concentration of oxygen raised to the power m where m is the true order of reaction. The relation between Ri and p, the observed rate of carbon burning per unit area of external surface of the particle, is P = Wr~A&C,”
[ 1 - d&Kg)1
m (k/m2s)
(1)
y, CT,and A, are, respectively, the characteristic size, density and specific (total) surface area of the particle. C’ is the concentration of oxygen in the bulk gas and Rd is the coefficient for mass transfer of oxygen to the particle. The term within square brackets allows a correction for the extent to which the oxygen concentration at the outer surface of the particle (C,) differs from Cg owing to external mass-transfer limitations. n is the effectiveness factor, the ratio of the actual rate per particle to the rate attainable (all else being equal) if no pore diffusion resistance existed. 7) is a function of the Thiele modulu?, $J, which is defined as: 9 = (7/2j (Ago~R~Csm-1/D,)o~5
(2)
D, is the effective diffusion
coefficient for oxygen diffusion through the pores which depends on the properties of the diffusing gas and on the nature of the pore structure. It is convenient to introduce an alternative relation (derivable analytically) which is: 77@2(m+ I)/2 = y&r
+ 1)/W&)
(3)
Thus vti2(rn + 1)/2 can be calculated from the experimentally determined quantities on the right-hand side of equa-
0016-2361/78/5707-040!3$02.00 0 1978 IPC Blrsiness Press
FUEL, 1978, Vol 57, July
409
The intrinsic reactivity of carbons to oxygen: I. W. Smith Table 1 Data on porous carbons
Reference
Carbon
Temperature
Oxygen pressure
type
(K)
(kPa)
(mm)
1227-2196
15-20
1.3 x 10-s to 7x 104 0.15 1.2 x 10-t 4 x 10-s 1.5 x 10-s 0.21 7 x 10-s 1.2 x 10-Z 2.1 x 10-l 7 x 10-s 1.3 x 10-s 6x10-3to 1.2 x 10-s 0.12 7 x 10-6 0.12 9.2 x 10-s 21 21 1.15 6.7 x 10-a
5 Petroleum
(a) 6 I 2
coke
Brown-coal
7 5
char
Lignite char
676-752 773 634-l 788
51 21 1 O-20
573-673 1293-2304
10-61 15-20
773 1389-2157
21 1 O-20
Anthracite 8 I 1
Semi-anthracite Bituminous-coal char Metallurgical coke soot Pitch coke Pitch resin
5. 9 6 10 6 11 12 13 14 I 15
Nuclear graphite Cracker carbon funcatalysed) Cracker carbon (catalysed)
15 (a)16 fb)l6 17 18 19 19 20 21 22 (a) 20 14 20 23 23
I
AGKSP
graphite
I AUF SPI SPI (boron doped) SPI Spectroscopic graphite Graphon Purified carbons Sterling FT Graphite NC Graphite AFC4
845-l
665
20
Particle size’, 7
773 1315-1650 773 673-798 708-758 848-898 893 723-873
21 21 1 O-20 17 21 21
623-723
21
6.7 x 1O-a
905-995
4.6-9 10 10 10 13 13 21 101 7.1-27 3.0-22 33 21 33 21 21
1.5 1.5 2.4 0.23 0.4 0.4 1.7 x 10-s 1.6 2.5 1.7 x 10-s -
980-1015 877-976 699-851 898 898 834-869 694-803 793-923 773-873 773 893 873 928 892
21 4-12
0.30 1.19
Pore surface,
Activation
A!7 ilO3 ms/kg)
energy, E (kJ/mol)
0.56-l
.4
Order, m Experimental
113
Assumed 1 -
to
2.0 0.85 337-l 346
to
550 242-433
151
150 20-400
100 167
-
to
1
0.5 -
134
-
1 0.5 -
146481
155 -
0.6 -
138
0
0.5 -
-
-
0.5 1
-
-
112 -
163 -
1
50-370 0.2 0.2 0.44 2000
163 188 -
-
159
0.6 0.65 -
2000
159
-
0.5
0.28 0.3 1 1 0.6 0.6 0.5 0.6 1 0.7 0.54 -
-
0.5
0.5 -
0.5 0.5
0.9 1.0 0.16 0.88 3.7 2.7 2.35 0.86 2.5 80 110 -
265 243 163 155 222 222-193 289 175 209 205 247-281 230
11.9 0.8 0.86
-
0.5 0.5 0.5 0.5
-
l 7 = particle volume/particle external area (Aris, Ft. C/rem. Engng Sci. 1957,6, 262) (a) Tyler (personal communication, 1974); (b) Wouterlood (personal communication, 1969)
tion (3), and 1) can then be found for the graphical relations between Q and QY#J~(~+ 1)/2 given by Mehta and Aris4. The then-known value of n can be used in equation (1) and the appropriate value of Ri calculated. It is not always necessary to carry out the correction procedures set out above. Under conditions where the chemical reaction is sufficiently slow it is often found by measurement, or calculation, or both, that the external transport of oxygen is sufficiently rapid for external mass transfer to offer negligible resistance to reaction, i.e. C, -+ Cg. Likewise, pore diffusion can be sufficiently rapid for 77+ 1. In this case Ri is calculated directly from equation (1). Q was found to be indistinguishable from unity for about half the data given here, especially for measurements below about 1000 K. As will be seen below, this circumstance allows some check on the validity of determining Ri when pore diffusion has a notable influence on the observed rate. RESULTS AND DISCUSSION Reactivity of porous carbons Ri was calculated for the porous carbons listed in
410
FUEL, 1978, Vol 57, July
Table 1 under the conditions summarized in columns 2-5. As the original data had been determined over a range of oxygen concentrations, and as various values of reaction order have been reported, a further step is necessary to enable the reactivities to be compared on a common basis. The means of making the comparison was by calculating pi, the oxidation rate to be found if the pore surface of each carbon were exposed to an oxygen concentration C,, corresponding to a partial pressure of 10 1 kPa. Each value of pi was calculated by means of the relation: pi = Rico”
(kg/m2
S)
As far as possible the values of m used were derived from experimental measurements. However, in certain cases (specified in Table I), it was necessary to assume values of m, as experimental information was lacking. In order to minimize errors due to uncertainties about the order, the present study is restricted to experiments carried out at oxygen pressures of 1 to 101 kPa. The selection of appropriate values of m, and errors in calculating pi, are discussed below. Values of pi are shown as a function of temperature m
The intrinsic reactivity of carbons to oxygen: 1. W. Smith T
Arrhenius form in Figure 1. The line, resulting from a least squares regression taken over all the data, is given by:
i°C)
pi = 3050 exp [-I 79.4/(RT)j
B
6
4
10 lo’,/
figure of 101
I Intrinsic kPa KEY
Ref.
TO
reactivity
SYMBOLS
i
IN
16
18
K-‘)
of various
carbons
at oxygen
FIGURES
1
AND
pressure
2
Material
No. 5 fa 1 b 2 7 5 8 1 5.9 6 10 6
Petroleum
coke
Brown -coal char Lignite char Anthracite Semi-anthracite Bituminous-coal char Metallurgical coke soot Pitch coke Pitch resin
11 12 13 14 15 15 16. la I 16, lb) 17 18 19 20 19 21 22 la
II
12 T
Nuclear
graphite
Cracker Cracker
carbon carbon
AGKSP
graphite
AGKSP AUF
graphite
( uncataiysed ) I catalysed I
SPI SPI Spectroscopic
1
graphite
Graphon
20 14 20 23 23
Purified Sterlino Acheson Acheson
carbons FT NC AFC 4
( personal communication, 1971) [ personal communication,
(a)
Tyler
(b]
Wooterlood
1969)
(kg/m2
S)
(5)
where R(k.T/mol K) is the gas constant and T is the temperature of the carbon. The data in Figure 1 show a strong dependence on temperature, corresponding to the average activation energy of 179.4 kJ/mol shown above, but data from individual carbons yield values from 126 up to 290 kJ/mol. The higher values, as will be seen below, are characteristic of the combustion of carbons which themselves, as well as the surrounding oxidizing gas, contain low levels of impurities. Values from 247 to 281 kJ/mol were found by Lang, Magnier and MayI for the combustion of nine very pure carbons; Thomas and Glenda Hughesz4 obtained values of 260 and 276 kJ/mol for purified Ticonderoga graphite; and Tyler, Wouterlood and Mulcah~‘~, values of 247 to 285 kJ/ mol for spectroscopic graphite. Fimre 1 shows that large differences in reactivity still remain between different carbons after the effects associated with different pore sizes and areas of pore surface are eliminated. The intrinsic reactivity of petroleum coke, for example, is about four orders of magnitude higher than that of graphon and two orders of magnitude higher than that of nuclear graphite at 775 K. It is a striking fact that the intrinsic reactivity of petroleum coke, higher than all but two of the carbons shown in Figure 1, is much higher than that of brown-coal char and lignite char. At 1250 K the reactivity of petroleum coke is 1000 times higher than brown coal, and at 700 K higher by a factor of ten. These observations relate to measurements made in this laboratory where brown-coal chars and petroleum coke particles were burned in entrainment2T5, and samples from the same sources were burned in a fixed-bed reactor by Tyler (personal communication) and Smith and Tyler2. Similar results were found by G&in and co-workers using fixed-bed reactors, for petroleum coke6 and lignite char7 from other sources. The range of intrinsic reactivities found presumably reflects the effects of the atomic structure of the carbons, as well as different levels of catalytic and inhibiting impurities in the solid and gaseous reactants. Mulcahy and Smith2’ have reviewed the roles of inorganic materials and water vapour as catalytic or inhibiting agents. At low levels of concentration (of the order of 10 ppm) impurities can have a notable influence on the rate, especially at temperatures below 1000 K, but the effect reaches saturation at impurity levels of about 1000 ppm. Most of the carbons listed in Table I were derived from fossil fuels with little or no purification and could, therefore, be expected to show some effect of catalysis (or inhibition). However Figure I does contain a set of data derived from experiments with highly purified carbons and oxygen, where a wide spread of reactivities is not found. These data, determined by Tyler (personal communication) and Wouterlood (personal communication) of the Minerals Research Laboratories, and by groups in three other laboratories14~‘6~19*20 are shown in Figure 2. Of particular note are the results of Lang, Magnier and May14 who measured the intrinsic reactivities of some fifteen carbons, ranging from nuclear and spectroscopic graphites to sugar and wood charcoals, after these materials had been heated to at least 2973 K, and after several of the carbons had been exposed to chlorine
FUEL, 1978, Vol 57, July
411
The intrinsic reactivity of carbons to oxygen: I. W. Smith
at high temperatures. After this treatment all the carbons showed similar intrinsic reactivities when oxidized in air at 893 K: the highest and lowest values (shown in Figures I and 2) differed only by a factor of about 3. The preliminary heat treatment to which these and the other carbons included in Figure 2 were subjected would reduce the impurity levels substantially. However, it would also cause re-arrangement of the carbon atoms to a more uniform structure. The average temperature dependence of the data in Figure 2 corresponds to an activation energy of about 250 kJ/mol.
lie mainly above this line, but show a similar temperature dependence at medium and low temperatures. Two sets of high-temperature data 29,sashow the negative temperature coefficient often found for gas reactions of carbon at high temperatures. EXAMINATION
OF ASSUMPTIONS
In order to calculate pi and pa, it has been necessary at times to make assumptions concerning the value of the reaction order (m), and also, for some of the cases, to correct
The reactivity of ‘non-porous’ carbons T 1°C)
The behaviour of carbon with little or no internal surface is now considered. Figure 3 is an Arrhenius plot of the reactivity of the various ‘non-porous’ carbons listed in Table 2. The reactivity &), corrected as previously to 101 kPa oxygen pressure, in this case is expressed per unit external surface area. Also shown in Figure 3 is the regression line from Figure I (equation (5)). The data points of Figure 3
4000 2500
1600
1000
600
I
I
loo
’
‘\
’
0
)
-179.4
*
10-l
RT
5
10-Z
lo-’ v) NE
E = 250 kJ/mol
1o-4
y” 10-5 G 10-s
10-l
10-s
1o-9
lo’/
Figure
2
Oxidation pressure of 101 kPa
Table 2
Data on ‘non-porous’
e
Dlomond
III1 late 1
26
q
Dlomond
I100
21
+
Dlamood
dust
29
0
29
d
29
v
30
.
31
0
31
b
32 33
A v
34
.
32
@
31
II
10
x
35
8)
36
8
0
face
1
grophlte
Pyralytlc
Pyrolyl~c
grophlte,
basal
pione
grophlte.
edge
lace
Pyrolytic
graphite
Vitreous
carbon
2
4
6 104/T
Figure 3 Oxidation sure of 101 kPa
m
&\Q
Pyrolytic
1K”J
rate of highly purified carbons at oxygen (symbolsas in Figure 1)
8
10
12
14
(K-‘1
rate of ‘non-porous’
carbons at oxygen pres-
carbons
Reference
Material
35 35 36 37 14 14 38 39 39 40 41 42 40 39 25 35 15
Diamond (111 face) Diamond (100 face) Diamond dust Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Vitreous carbon soot soot soot
412
7
26
Temperature (K)
877-980
basal edge edge edge
FUEL, 1978, Vol 57, July
plane face face face
877-l 026 723-873 1042-I 104 1333-2000 1473-2674 887-l 273 887-l 273 952-l 064 985-l 235 882-l 214 971-1075 985-l 235 873-l 036 1315-1650 1190 1515-3850
Oxygen fkPa) 101 101 l-39 21 20-33 21 21 21 21 21 21 2.6 21 21 4-12 12-21 5-50
pressure
Activation energy, E (kJ/mol)
Order, m
230 230 167 180 -
Assumed
0 -
-
1 -
155 180 180 113-201 =I47 197 109-142 234 163 -
Experimental
0.5 -
0.6 1 =l =I
1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 -
-
The intrinsic reactivity of carbons to oxygen: I. W. Smith for the effect of pore diffusion using a simplified model of the pore structure. The important consequences of these matters are now considered. Reaction order The reactivitics were calculated for a common oxygen pressure, as noted, using measured or assumed values of m. The data in Tables 1 and 2 show that there is no common order of reaction, even at a specified level of temperature and pressure. This observation, taken together with the wide range of absolute reactivities and activation energies already noted. underlines the lack of mechanistic understanding of the kinetics of carbon oxidation already emphasized, for example, by Essenhigh and co-workers37t3a. It is even doubtful if the concept of ‘order’ has much more than experimcrttal validity. Careful measurements of order during the reaction between purified graphite and oxygen at about 1000 K I6 showed m changing from 0.2 to 0.34 as the oxygen pressure fell from 33 to 2 kPa. The combustion of soot at about 2500 K was found to have an order of 0.8 at 5 kPa 02. reducing to close to zero at 1010 kPa %. Crystals of purified natural graphite were reacted with oxygen at pressures below 13 kPa and at about 1100 K and the value of m was found to be about 0.2 24. The reaction of graphon with oxygen at about 800 K and a pea of 2.7 kPa showed a value of m of about 0.5 39. An order of unity was found for pulverized-coal chars burned with 5 to 10 kPa of oxygen over 1200 to 2000 K40,41. This brief summary of facts concerning m shows that there is, as yet. no general way of determining reaction order in the absence of experimental measurements. Therefore, in order to calculate pi and pa for the conditions shown in Tables I and 2 whcrc no measured values of m were available, the order was taken as unity above 1000 K, and 0.5 below this temperature. This gives moderately good approximations to the bulk of the measured values in the respective temperature ranges. If the data of Gutrin er al’ for lignite char burning at 10 kPa oxygen were corrected to 101 kPa, assuming an order of 0.5 when the true value was zero, the result of this correction would be too high by a factor of 3.2. If the oxidation of petroleum coke’ were in fact zero order, rather than unity as assumed, the relevant data shown in Figure I would bc too high by a factor of 6.7. These errors, which arc extreme estimates, do not substantially affect the previous arguments. Pore structure model The calculation of the intrinsic reactivity rcquircs a knowledge of the pore structure, including the properties necessary to determine the effective pore diffusion coefficient II,. For the present study D, was calculated using the simple pore structure mode142 that assumes a uni-modal distribution of pores which can be adequately represented by a mean pore size calculated from pore volume and area measurements, with only a simple allowance for the tortuous nature of the pores. In fact pore geometries arc complex, often having poly-modal size-distributions. Many carbons contain large pore systems, through which gas passes by bulk diffusion into finer pores in which transport is by Knudsen diffusion. It is difficult to find adequate information to estimate the magnitude of the effect of the simplifying assumptions noted above, but where such information is available the result is encouraging. Smith and Tyler’ calculated the intrinsic reactivity of semi-anthracite from the same data
firstly using a single mean pore size corresponding to a unimodal model of the port structure, and then two mean pore sizes to characterize a bi-modal model. In the latter case the larger pores (down to 0.02 pm in size) were regarded as ‘transport’ pores through which the oxygen diffused to enter the micro-pore system (below 0.02 pm in size) where reaction took place. Them arc no significant differences in the reactivities calculated on the two diffcrent bases. The reactivities of petroleum cokesv6 and brown-coal char’ are shown in Figure J : the burning rates of both materials were measured in an entrainment reactor above 900 K. and in a fixed bed reactor below 750 K. In both cases strong port diffusion restriction existed above 900 K and hcrc the reactivities were calculated usirrg the procedures noted above. However, rt was found by calculation and cxpcrimcnt that no significant diffusion restriction was prcscnt below 750 K, and thcrcforc no assumptions concerning the pore structure were needed for rhc calculation of R;. The continuity in the Arrhcnius plots of the reactivitics for both materials is good evidence that the unimodal assumption does not introduce serious error. It is relevant to note that Goard and MulcahyJ3. in calculating the oxidation rate of graphite under strong pore diffusion restriction. found that the use of a single mean pore size @iVC a value of p only 30% higher than the value calculated allowing separately for reaction in each of the pores of all sizes present . CONCLUSION After the rate-r-estricting effects of mass transfer and porediffusion have been allowed for, carbons of various origins still show a wide range of reactivities towards oxygen. Values of the intrinsic reaction rate (kg carbon removed per second per square metre of total surface area at an oxygen pressure of 101 kPa) for different types of carbon, at a given temperature and otherwise constant conditions, can differ by up to four orders of magnitude. Wide ranges of true activation energies (126 to 290 k.I/mol) and true reaction orders (zero to one) are also found. Carbons which are ‘non-porous’, i.e. have little or no internal pore structure, show rcactivities per unit external area that are generally higher than the intrinsic rcactivitics (as defined above) of the porous carbons. Both groups of carbons, however, show similar average tcmpcrature dependences. ACKNOWLEDGEMENTS H. J. Wouterlood kindly made available reactivity data on AGKSP graphite. R. J. Tyler supplied data on the reactivity of petroleum coke and AGKSP graphite, and also provided the structural data by which intrinsic reactivities were calculated from the observed kinetics reported in references 5 and 9. M. F. R. Mulcahy contributed much valuable discussion.
LIST OF SYMBOLS A,
Specific surface area of particle Gas concentration, bulk gas Common gas concentration Gas concentration, outer surface of particle
FUEL, 1978, Vol 57, July
413
The intrinsic reactivity of carbons to oxygen: I. W. Smith
4 E Rd Ri R T m Y 77 P Pa Pi oa 4
Effective pore diffusion coefficient (mz/s) Activation energy (kJ/mol) (kg/m2 s kPa) Rate coefficient for mass transfer Intrinsic reactivity coefficient (kg/m2 s(kPa)m) Gas constant (kJ/mol K) Particle temperature (K) True order of reaction Particle size (m) Effectiveness factor Observed reaction rate (kg/m2 s) &grni s; Rate per unit external area Intrinsic rate Particle density (kg/E3 ,” Thiele modulus
17
Gulbransen, E. A., Andrew, K. F. and Brassart, F. A. J. elec-
18
Gulbransen, E. A. and Andrew, K. F. Znd. Engng Chem. 1952,44,1034 Allardice, D. J. and Walker, P. L. Carbon 1970, 8,315 Magne, P. and Duval, X. Bull. Sot. Chim. France 1971, 1585 Effron, E. and Hoelscher, H. E. A. I. Ch. E. J. 1964, 10 (3), 388 Rossberg, M. and Wicke, E. Chemie-Zngr-Tech. 1956, 28,
trochem. Sot. 1962, 110,476
19 20 21 22
181
23 24
209
25 26 21
Smith, I. W. and Tyler, R. J. Fuel 1972,51,312 Smith, I. W. and Tyler, R. J. Combust. Sci. & Technol. 1974, 9, 81
Thiele, Mehta. Smith; GrilIet, I 8 9
10 11 12
France 1967,2423 Gulrln, H., Siemieniewska, T., Grillet, Y. and Fraqois, M. Carbon 1970,8,127 Jozefczak-Ihler, M. and Guerin, H. Bull. Sot. Chim. France 1966, 2018 Sergeant, G. D. and Smith, I. W. Fuel 1973,52,52 Lee, K. B., Thring, M. W. and Beer, J. M. Cornbust. & Flame 1962,6,137 DoIlimore, D. and Turner, A. Trans. Farad. Sot. 1970,66, 2655
31 32 33 34
15 16
Tyler, R. J., Wouterlood, H. J. and Mulcahy, M. F. R.
2, 391 Carbon 1976,14,
271
FUEL, 1978, Vol 57, July
(4), 121
Levy, M. and Wong, P. J. eiectrochem. Sot. 1964,3 (2), 1088 Wails, J. R. and Strickland-Constable, R. F. Carbon 1963, 1, 333 Horton, W. S. Proc. 5th Conf on Carbon, Pergamon Press, New York, 1963, Vol. 2, p 233 Lewis, J. C. 2nd Industrial Carbon & Graphite Con&, Society of Chemical Industry, 1965, p 258 Tominaga, Y. and Nagaoki, T. Symposium on Carbon, Tokyo, Carbon Society of Japan, 1964, p VIII4-l-VIII44 Horton, W. S. J. Res. Nat. Bur. Standards 1910, 74A, 325 Rodriguez-Reinoso, F., Thrower, P. A. and Walker, P. L. Carbon 1974, 12,63
35
Fenimore, C. P. and Jones, G. W. J. phys. Chem. 1967,71,
36
Park, C. and Appleton, J. P. Cornbust. & Flame 1913, 20, 369 Gray, D., Cogoli, J. G. and Essenhigh, R. H. Adv. in Chem. Series, No 131, Coal Gasification 1914, p 12, Am. Chem. Sot., Washington, D. C. Essenhigh, R. H., 16th Symp. (Znt.) on Combustion, Combustion Institute, Pittsburgh, 1977, p 353 Tucker, B. G. and Mulcahy, M. F. R. Tmns. Farad. Sot. No. 553, 1969,65 (l), 274 Field, M. A. Combust. & Flame 1969, 13, 231 Field, M. A. Combust. & Flame 1970, 14, 231 Wheeler, A. Adv. in Catal. 1951, 3, 249 Goard, P. R. C. and Mulcahy, M. F. R. Carbon 1967,5, 137
593
31
Hawtin, P., Gibson, J. A., Murdoch, R. and Lewis, J. B. Lewis, J. B., Dix, J. and Murdoch, R. Carbon 19653,321 Lang, F. M., Magnier, P. and May, S. Z’roc. 5th Confi on Carbon. Pereamon Press. New York. 1962. Vol. 1. D 171 Weisz, P. B.&d Goodwin, R. B. J. Catal. 1966,6; 227; 1963,
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28 29 30
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13 14
Mulcahy, M. F. R. and Smith, I. W. Rev. Pure & Appl. Chem. 1969,19,81 Evans, T.-and Phaal, C. Proc. 5th Con& on Carbon, Pergamon Press, New York, 1962, Vol. 1, p 147 Tekunova, T. V. and Tesner, P. A. Khimiya Tverdogo Top Ziva 1974,8
REFERENCES :
Hoynant, G. Zng-Doct. Thesis, 1959, University of Nancy, France Thomas, J. M. and Glenda Hughes, E. E. Carbon 1963, 1,
38 39
!
t 42 43
Minerals Research Labora tories, P. 0. Box 136, North
Ryde,
The intrinsic reactivities, that is the reaction rates per unit area of pore surface in the absence of any mass transfer restrictions, for combustion of a wide range of carbons have been calculated from published data. The intrinsic reactivities, corrected to a common oxygen pressure of 101 kPa, were ascertained over the temperature range 580 to 2200 K. The reactivities of ‘non-porous’ carbons (diamond, soot, vitreous carbon and pyrolytic graphite) between 770 and 4000 K were also considered. Porous carbons of various origins show intrinsic reactivities that differ by up to 4 orders of magnitude at a given temperature. However, after high-temperature heat treatment, certain carbons of different origin (e.g. sugar and wood charcoals, nuclear and spectroscopic graphites) show closely similar reactivities when reacted with purified oxygen. The reactivities of the ‘non-porous’ carbons show a temperature dependence similar to the average temperature dependence of the porous carbons, but their reactivity expressed per unit external surface area is generally higher than the median intrinsic value of the porous materials.
Specimens of carbon produced from different original materials, or in different ways from the same material, are found to burn at very different rates under otherwise similar conditions. The speed at which an individual carbon particle of given size or mass burns depends in part on the rate of oxygen transfer from the bulk gas to the particle, and in part on the particle’s reactivity. This reactivity depends on the extent and accessibility to oxygen of the pores within the particle, and on the velocity of chemical reaction between oxygen and the pore surface. The latter factor, when properly defined, may be termed the intrinsic reactivity of the carbon. Intrinsic reactivity is defined as the reaction rate per unit area of pore surface in the absence of any mass-transfer restrictions. The purpose of this paper is to derive from published data, including data from the Minerals Research Laboratories, the intrinsic reactivities of as large a variety of carbons as possible, with the object of comparing one with another. In order to make this comparison, the observed kinetics were corrected for system effects, e.g. for the extent to which external mass transfer affected burning rates, and then the parallel processes of pore diffusion and reaction on the pore wall were separated. For some of the carbons it has also been possible to derive the value of the ‘true’ activation energy and reaction order. The original data treated here represent only a small part of the large amount of information to hand on the carbon-oxygen reaction. Only those experiments could be considered where sufficient information is available on mass-transfer effects, pore structure, the difference between particle and reactor temperatures, and so on. Nevertheless it was possible to obtain results for some 32 porous, and 17 ‘non-porous’ carbons. * Complete text of paper presented in brief to ‘Conference on Fundamentals of Carbon-Gas Reactions’, sponsored by the University of Newcastle, the Institute of Fuel (Australian Membership) and the Combustion Institute (Australia). Conference held at CSIRO Minerals Research Laboratories, May 1976
METHOD OF CALCULATING
1NTRlNSIC REACTIVITY
The means of calculating intrinsic reactivity has been given in detail elsewhere ‘p2. The desired qu antity is the intrinsic rate coefficient for carbon oxidation, Ri, expressed in relation to unit area of pore surface, and to unit concentration of oxygen raised to the power m where m is the true order of reaction. The relation between Ri and p, the observed rate of carbon burning per unit area of external surface of the particle, is P = Wr~A&C,”
[ 1 - d&Kg)1
m (k/m2s)
(1)
y, CT,and A, are, respectively, the characteristic size, density and specific (total) surface area of the particle. C’ is the concentration of oxygen in the bulk gas and Rd is the coefficient for mass transfer of oxygen to the particle. The term within square brackets allows a correction for the extent to which the oxygen concentration at the outer surface of the particle (C,) differs from Cg owing to external mass-transfer limitations. n is the effectiveness factor, the ratio of the actual rate per particle to the rate attainable (all else being equal) if no pore diffusion resistance existed. 7) is a function of the Thiele modulu?, $J, which is defined as: 9 = (7/2j (Ago~R~Csm-1/D,)o~5
(2)
D, is the effective diffusion
coefficient for oxygen diffusion through the pores which depends on the properties of the diffusing gas and on the nature of the pore structure. It is convenient to introduce an alternative relation (derivable analytically) which is: 77@2(m+ I)/2 = y&r
+ 1)/W&)
(3)
Thus vti2(rn + 1)/2 can be calculated from the experimentally determined quantities on the right-hand side of equa-
0016-2361/78/5707-040!3$02.00 0 1978 IPC Blrsiness Press
FUEL, 1978, Vol 57, July
409
The intrinsic reactivity of carbons to oxygen: I. W. Smith Table 1 Data on porous carbons
Reference
Carbon
Temperature
Oxygen pressure
type
(K)
(kPa)
(mm)
1227-2196
15-20
1.3 x 10-s to 7x 104 0.15 1.2 x 10-t 4 x 10-s 1.5 x 10-s 0.21 7 x 10-s 1.2 x 10-Z 2.1 x 10-l 7 x 10-s 1.3 x 10-s 6x10-3to 1.2 x 10-s 0.12 7 x 10-6 0.12 9.2 x 10-s 21 21 1.15 6.7 x 10-a
5 Petroleum
(a) 6 I 2
coke
Brown-coal
7 5
char
Lignite char
676-752 773 634-l 788
51 21 1 O-20
573-673 1293-2304
10-61 15-20
773 1389-2157
21 1 O-20
Anthracite 8 I 1
Semi-anthracite Bituminous-coal char Metallurgical coke soot Pitch coke Pitch resin
5. 9 6 10 6 11 12 13 14 I 15
Nuclear graphite Cracker carbon funcatalysed) Cracker carbon (catalysed)
15 (a)16 fb)l6 17 18 19 19 20 21 22 (a) 20 14 20 23 23
I
AGKSP
graphite
I AUF SPI SPI (boron doped) SPI Spectroscopic graphite Graphon Purified carbons Sterling FT Graphite NC Graphite AFC4
845-l
665
20
Particle size’, 7
773 1315-1650 773 673-798 708-758 848-898 893 723-873
21 21 1 O-20 17 21 21
623-723
21
6.7 x 1O-a
905-995
4.6-9 10 10 10 13 13 21 101 7.1-27 3.0-22 33 21 33 21 21
1.5 1.5 2.4 0.23 0.4 0.4 1.7 x 10-s 1.6 2.5 1.7 x 10-s -
980-1015 877-976 699-851 898 898 834-869 694-803 793-923 773-873 773 893 873 928 892
21 4-12
0.30 1.19
Pore surface,
Activation
A!7 ilO3 ms/kg)
energy, E (kJ/mol)
0.56-l
.4
Order, m Experimental
113
Assumed 1 -
to
2.0 0.85 337-l 346
to
550 242-433
151
150 20-400
100 167
-
to
1
0.5 -
134
-
1 0.5 -
146481
155 -
0.6 -
138
0
0.5 -
-
-
0.5 1
-
-
112 -
163 -
1
50-370 0.2 0.2 0.44 2000
163 188 -
-
159
0.6 0.65 -
2000
159
-
0.5
0.28 0.3 1 1 0.6 0.6 0.5 0.6 1 0.7 0.54 -
-
0.5
0.5 -
0.5 0.5
0.9 1.0 0.16 0.88 3.7 2.7 2.35 0.86 2.5 80 110 -
265 243 163 155 222 222-193 289 175 209 205 247-281 230
11.9 0.8 0.86
-
0.5 0.5 0.5 0.5
-
l 7 = particle volume/particle external area (Aris, Ft. C/rem. Engng Sci. 1957,6, 262) (a) Tyler (personal communication, 1974); (b) Wouterlood (personal communication, 1969)
tion (3), and 1) can then be found for the graphical relations between Q and QY#J~(~+ 1)/2 given by Mehta and Aris4. The then-known value of n can be used in equation (1) and the appropriate value of Ri calculated. It is not always necessary to carry out the correction procedures set out above. Under conditions where the chemical reaction is sufficiently slow it is often found by measurement, or calculation, or both, that the external transport of oxygen is sufficiently rapid for external mass transfer to offer negligible resistance to reaction, i.e. C, -+ Cg. Likewise, pore diffusion can be sufficiently rapid for 77+ 1. In this case Ri is calculated directly from equation (1). Q was found to be indistinguishable from unity for about half the data given here, especially for measurements below about 1000 K. As will be seen below, this circumstance allows some check on the validity of determining Ri when pore diffusion has a notable influence on the observed rate. RESULTS AND DISCUSSION Reactivity of porous carbons Ri was calculated for the porous carbons listed in
410
FUEL, 1978, Vol 57, July
Table 1 under the conditions summarized in columns 2-5. As the original data had been determined over a range of oxygen concentrations, and as various values of reaction order have been reported, a further step is necessary to enable the reactivities to be compared on a common basis. The means of making the comparison was by calculating pi, the oxidation rate to be found if the pore surface of each carbon were exposed to an oxygen concentration C,, corresponding to a partial pressure of 10 1 kPa. Each value of pi was calculated by means of the relation: pi = Rico”
(kg/m2
S)
As far as possible the values of m used were derived from experimental measurements. However, in certain cases (specified in Table I), it was necessary to assume values of m, as experimental information was lacking. In order to minimize errors due to uncertainties about the order, the present study is restricted to experiments carried out at oxygen pressures of 1 to 101 kPa. The selection of appropriate values of m, and errors in calculating pi, are discussed below. Values of pi are shown as a function of temperature m
The intrinsic reactivity of carbons to oxygen: 1. W. Smith T
Arrhenius form in Figure 1. The line, resulting from a least squares regression taken over all the data, is given by:
i°C)
pi = 3050 exp [-I 79.4/(RT)j
B
6
4
10 lo’,/
figure of 101
I Intrinsic kPa KEY
Ref.
TO
reactivity
SYMBOLS
i
IN
16
18
K-‘)
of various
carbons
at oxygen
FIGURES
1
AND
pressure
2
Material
No. 5 fa 1 b 2 7 5 8 1 5.9 6 10 6
Petroleum
coke
Brown -coal char Lignite char Anthracite Semi-anthracite Bituminous-coal char Metallurgical coke soot Pitch coke Pitch resin
11 12 13 14 15 15 16. la I 16, lb) 17 18 19 20 19 21 22 la
II
12 T
Nuclear
graphite
Cracker Cracker
carbon carbon
AGKSP
graphite
AGKSP AUF
graphite
( uncataiysed ) I catalysed I
SPI SPI Spectroscopic
1
graphite
Graphon
20 14 20 23 23
Purified Sterlino Acheson Acheson
carbons FT NC AFC 4
( personal communication, 1971) [ personal communication,
(a)
Tyler
(b]
Wooterlood
1969)
(kg/m2
S)
(5)
where R(k.T/mol K) is the gas constant and T is the temperature of the carbon. The data in Figure 1 show a strong dependence on temperature, corresponding to the average activation energy of 179.4 kJ/mol shown above, but data from individual carbons yield values from 126 up to 290 kJ/mol. The higher values, as will be seen below, are characteristic of the combustion of carbons which themselves, as well as the surrounding oxidizing gas, contain low levels of impurities. Values from 247 to 281 kJ/mol were found by Lang, Magnier and MayI for the combustion of nine very pure carbons; Thomas and Glenda Hughesz4 obtained values of 260 and 276 kJ/mol for purified Ticonderoga graphite; and Tyler, Wouterlood and Mulcah~‘~, values of 247 to 285 kJ/ mol for spectroscopic graphite. Fimre 1 shows that large differences in reactivity still remain between different carbons after the effects associated with different pore sizes and areas of pore surface are eliminated. The intrinsic reactivity of petroleum coke, for example, is about four orders of magnitude higher than that of graphon and two orders of magnitude higher than that of nuclear graphite at 775 K. It is a striking fact that the intrinsic reactivity of petroleum coke, higher than all but two of the carbons shown in Figure 1, is much higher than that of brown-coal char and lignite char. At 1250 K the reactivity of petroleum coke is 1000 times higher than brown coal, and at 700 K higher by a factor of ten. These observations relate to measurements made in this laboratory where brown-coal chars and petroleum coke particles were burned in entrainment2T5, and samples from the same sources were burned in a fixed-bed reactor by Tyler (personal communication) and Smith and Tyler2. Similar results were found by G&in and co-workers using fixed-bed reactors, for petroleum coke6 and lignite char7 from other sources. The range of intrinsic reactivities found presumably reflects the effects of the atomic structure of the carbons, as well as different levels of catalytic and inhibiting impurities in the solid and gaseous reactants. Mulcahy and Smith2’ have reviewed the roles of inorganic materials and water vapour as catalytic or inhibiting agents. At low levels of concentration (of the order of 10 ppm) impurities can have a notable influence on the rate, especially at temperatures below 1000 K, but the effect reaches saturation at impurity levels of about 1000 ppm. Most of the carbons listed in Table I were derived from fossil fuels with little or no purification and could, therefore, be expected to show some effect of catalysis (or inhibition). However Figure I does contain a set of data derived from experiments with highly purified carbons and oxygen, where a wide spread of reactivities is not found. These data, determined by Tyler (personal communication) and Wouterlood (personal communication) of the Minerals Research Laboratories, and by groups in three other laboratories14~‘6~19*20 are shown in Figure 2. Of particular note are the results of Lang, Magnier and May14 who measured the intrinsic reactivities of some fifteen carbons, ranging from nuclear and spectroscopic graphites to sugar and wood charcoals, after these materials had been heated to at least 2973 K, and after several of the carbons had been exposed to chlorine
FUEL, 1978, Vol 57, July
411
The intrinsic reactivity of carbons to oxygen: I. W. Smith
at high temperatures. After this treatment all the carbons showed similar intrinsic reactivities when oxidized in air at 893 K: the highest and lowest values (shown in Figures I and 2) differed only by a factor of about 3. The preliminary heat treatment to which these and the other carbons included in Figure 2 were subjected would reduce the impurity levels substantially. However, it would also cause re-arrangement of the carbon atoms to a more uniform structure. The average temperature dependence of the data in Figure 2 corresponds to an activation energy of about 250 kJ/mol.
lie mainly above this line, but show a similar temperature dependence at medium and low temperatures. Two sets of high-temperature data 29,sashow the negative temperature coefficient often found for gas reactions of carbon at high temperatures. EXAMINATION
OF ASSUMPTIONS
In order to calculate pi and pa, it has been necessary at times to make assumptions concerning the value of the reaction order (m), and also, for some of the cases, to correct
The reactivity of ‘non-porous’ carbons T 1°C)
The behaviour of carbon with little or no internal surface is now considered. Figure 3 is an Arrhenius plot of the reactivity of the various ‘non-porous’ carbons listed in Table 2. The reactivity &), corrected as previously to 101 kPa oxygen pressure, in this case is expressed per unit external surface area. Also shown in Figure 3 is the regression line from Figure I (equation (5)). The data points of Figure 3
4000 2500
1600
1000
600
I
I
loo
’
‘\
’
0
)
-179.4
*
10-l
RT
5
10-Z
lo-’ v) NE
E = 250 kJ/mol
1o-4
y” 10-5 G 10-s
10-l
10-s
1o-9
lo’/
Figure
2
Oxidation pressure of 101 kPa
Table 2
Data on ‘non-porous’
e
Dlomond
III1 late 1
26
q
Dlomond
I100
21
+
Dlamood
dust
29
0
29
d
29
v
30
.
31
0
31
b
32 33
A v
34
.
32
@
31
II
10
x
35
8)
36
8
0
face
1
grophlte
Pyralytlc
Pyrolyl~c
grophlte,
basal
pione
grophlte.
edge
lace
Pyrolytic
graphite
Vitreous
carbon
2
4
6 104/T
Figure 3 Oxidation sure of 101 kPa
m
&\Q
Pyrolytic
1K”J
rate of highly purified carbons at oxygen (symbolsas in Figure 1)
8
10
12
14
(K-‘1
rate of ‘non-porous’
carbons at oxygen pres-
carbons
Reference
Material
35 35 36 37 14 14 38 39 39 40 41 42 40 39 25 35 15
Diamond (111 face) Diamond (100 face) Diamond dust Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Pyrolytic graphite Vitreous carbon soot soot soot
412
7
26
Temperature (K)
877-980
basal edge edge edge
FUEL, 1978, Vol 57, July
plane face face face
877-l 026 723-873 1042-I 104 1333-2000 1473-2674 887-l 273 887-l 273 952-l 064 985-l 235 882-l 214 971-1075 985-l 235 873-l 036 1315-1650 1190 1515-3850
Oxygen fkPa) 101 101 l-39 21 20-33 21 21 21 21 21 21 2.6 21 21 4-12 12-21 5-50
pressure
Activation energy, E (kJ/mol)
Order, m
230 230 167 180 -
Assumed
0 -
-
1 -
155 180 180 113-201 =I47 197 109-142 234 163 -
Experimental
0.5 -
0.6 1 =l =I
1 1 1 0.5 0.5 0.5 0.5 0.5 0.5 -
-
The intrinsic reactivity of carbons to oxygen: I. W. Smith for the effect of pore diffusion using a simplified model of the pore structure. The important consequences of these matters are now considered. Reaction order The reactivitics were calculated for a common oxygen pressure, as noted, using measured or assumed values of m. The data in Tables 1 and 2 show that there is no common order of reaction, even at a specified level of temperature and pressure. This observation, taken together with the wide range of absolute reactivities and activation energies already noted. underlines the lack of mechanistic understanding of the kinetics of carbon oxidation already emphasized, for example, by Essenhigh and co-workers37t3a. It is even doubtful if the concept of ‘order’ has much more than experimcrttal validity. Careful measurements of order during the reaction between purified graphite and oxygen at about 1000 K I6 showed m changing from 0.2 to 0.34 as the oxygen pressure fell from 33 to 2 kPa. The combustion of soot at about 2500 K was found to have an order of 0.8 at 5 kPa 02. reducing to close to zero at 1010 kPa %. Crystals of purified natural graphite were reacted with oxygen at pressures below 13 kPa and at about 1100 K and the value of m was found to be about 0.2 24. The reaction of graphon with oxygen at about 800 K and a pea of 2.7 kPa showed a value of m of about 0.5 39. An order of unity was found for pulverized-coal chars burned with 5 to 10 kPa of oxygen over 1200 to 2000 K40,41. This brief summary of facts concerning m shows that there is, as yet. no general way of determining reaction order in the absence of experimental measurements. Therefore, in order to calculate pi and pa for the conditions shown in Tables I and 2 whcrc no measured values of m were available, the order was taken as unity above 1000 K, and 0.5 below this temperature. This gives moderately good approximations to the bulk of the measured values in the respective temperature ranges. If the data of Gutrin er al’ for lignite char burning at 10 kPa oxygen were corrected to 101 kPa, assuming an order of 0.5 when the true value was zero, the result of this correction would be too high by a factor of 3.2. If the oxidation of petroleum coke’ were in fact zero order, rather than unity as assumed, the relevant data shown in Figure I would bc too high by a factor of 6.7. These errors, which arc extreme estimates, do not substantially affect the previous arguments. Pore structure model The calculation of the intrinsic reactivity rcquircs a knowledge of the pore structure, including the properties necessary to determine the effective pore diffusion coefficient II,. For the present study D, was calculated using the simple pore structure mode142 that assumes a uni-modal distribution of pores which can be adequately represented by a mean pore size calculated from pore volume and area measurements, with only a simple allowance for the tortuous nature of the pores. In fact pore geometries arc complex, often having poly-modal size-distributions. Many carbons contain large pore systems, through which gas passes by bulk diffusion into finer pores in which transport is by Knudsen diffusion. It is difficult to find adequate information to estimate the magnitude of the effect of the simplifying assumptions noted above, but where such information is available the result is encouraging. Smith and Tyler’ calculated the intrinsic reactivity of semi-anthracite from the same data
firstly using a single mean pore size corresponding to a unimodal model of the port structure, and then two mean pore sizes to characterize a bi-modal model. In the latter case the larger pores (down to 0.02 pm in size) were regarded as ‘transport’ pores through which the oxygen diffused to enter the micro-pore system (below 0.02 pm in size) where reaction took place. Them arc no significant differences in the reactivities calculated on the two diffcrent bases. The reactivities of petroleum cokesv6 and brown-coal char’ are shown in Figure J : the burning rates of both materials were measured in an entrainment reactor above 900 K. and in a fixed bed reactor below 750 K. In both cases strong port diffusion restriction existed above 900 K and hcrc the reactivities were calculated usirrg the procedures noted above. However, rt was found by calculation and cxpcrimcnt that no significant diffusion restriction was prcscnt below 750 K, and thcrcforc no assumptions concerning the pore structure were needed for rhc calculation of R;. The continuity in the Arrhcnius plots of the reactivitics for both materials is good evidence that the unimodal assumption does not introduce serious error. It is relevant to note that Goard and MulcahyJ3. in calculating the oxidation rate of graphite under strong pore diffusion restriction. found that the use of a single mean pore size @iVC a value of p only 30% higher than the value calculated allowing separately for reaction in each of the pores of all sizes present . CONCLUSION After the rate-r-estricting effects of mass transfer and porediffusion have been allowed for, carbons of various origins still show a wide range of reactivities towards oxygen. Values of the intrinsic reaction rate (kg carbon removed per second per square metre of total surface area at an oxygen pressure of 101 kPa) for different types of carbon, at a given temperature and otherwise constant conditions, can differ by up to four orders of magnitude. Wide ranges of true activation energies (126 to 290 k.I/mol) and true reaction orders (zero to one) are also found. Carbons which are ‘non-porous’, i.e. have little or no internal pore structure, show rcactivities per unit external area that are generally higher than the intrinsic rcactivitics (as defined above) of the porous carbons. Both groups of carbons, however, show similar average tcmpcrature dependences. ACKNOWLEDGEMENTS H. J. Wouterlood kindly made available reactivity data on AGKSP graphite. R. J. Tyler supplied data on the reactivity of petroleum coke and AGKSP graphite, and also provided the structural data by which intrinsic reactivities were calculated from the observed kinetics reported in references 5 and 9. M. F. R. Mulcahy contributed much valuable discussion.
LIST OF SYMBOLS A,
Specific surface area of particle Gas concentration, bulk gas Common gas concentration Gas concentration, outer surface of particle
FUEL, 1978, Vol 57, July
413
The intrinsic reactivity of carbons to oxygen: I. W. Smith
4 E Rd Ri R T m Y 77 P Pa Pi oa 4
Effective pore diffusion coefficient (mz/s) Activation energy (kJ/mol) (kg/m2 s kPa) Rate coefficient for mass transfer Intrinsic reactivity coefficient (kg/m2 s(kPa)m) Gas constant (kJ/mol K) Particle temperature (K) True order of reaction Particle size (m) Effectiveness factor Observed reaction rate (kg/m2 s) &grni s; Rate per unit external area Intrinsic rate Particle density (kg/E3 ,” Thiele modulus
17
Gulbransen, E. A., Andrew, K. F. and Brassart, F. A. J. elec-
18
Gulbransen, E. A. and Andrew, K. F. Znd. Engng Chem. 1952,44,1034 Allardice, D. J. and Walker, P. L. Carbon 1970, 8,315 Magne, P. and Duval, X. Bull. Sot. Chim. France 1971, 1585 Effron, E. and Hoelscher, H. E. A. I. Ch. E. J. 1964, 10 (3), 388 Rossberg, M. and Wicke, E. Chemie-Zngr-Tech. 1956, 28,
trochem. Sot. 1962, 110,476
19 20 21 22
181
23 24
209
25 26 21
Smith, I. W. and Tyler, R. J. Fuel 1972,51,312 Smith, I. W. and Tyler, R. J. Combust. Sci. & Technol. 1974, 9, 81
Thiele, Mehta. Smith; GrilIet, I 8 9
10 11 12
France 1967,2423 Gulrln, H., Siemieniewska, T., Grillet, Y. and Fraqois, M. Carbon 1970,8,127 Jozefczak-Ihler, M. and Guerin, H. Bull. Sot. Chim. France 1966, 2018 Sergeant, G. D. and Smith, I. W. Fuel 1973,52,52 Lee, K. B., Thring, M. W. and Beer, J. M. Cornbust. & Flame 1962,6,137 DoIlimore, D. and Turner, A. Trans. Farad. Sot. 1970,66, 2655
31 32 33 34
15 16
Tyler, R. J., Wouterlood, H. J. and Mulcahy, M. F. R.
2, 391 Carbon 1976,14,
271
FUEL, 1978, Vol 57, July
(4), 121
Levy, M. and Wong, P. J. eiectrochem. Sot. 1964,3 (2), 1088 Wails, J. R. and Strickland-Constable, R. F. Carbon 1963, 1, 333 Horton, W. S. Proc. 5th Conf on Carbon, Pergamon Press, New York, 1963, Vol. 2, p 233 Lewis, J. C. 2nd Industrial Carbon & Graphite Con&, Society of Chemical Industry, 1965, p 258 Tominaga, Y. and Nagaoki, T. Symposium on Carbon, Tokyo, Carbon Society of Japan, 1964, p VIII4-l-VIII44 Horton, W. S. J. Res. Nat. Bur. Standards 1910, 74A, 325 Rodriguez-Reinoso, F., Thrower, P. A. and Walker, P. L. Carbon 1974, 12,63
35
Fenimore, C. P. and Jones, G. W. J. phys. Chem. 1967,71,
36
Park, C. and Appleton, J. P. Cornbust. & Flame 1913, 20, 369 Gray, D., Cogoli, J. G. and Essenhigh, R. H. Adv. in Chem. Series, No 131, Coal Gasification 1914, p 12, Am. Chem. Sot., Washington, D. C. Essenhigh, R. H., 16th Symp. (Znt.) on Combustion, Combustion Institute, Pittsburgh, 1977, p 353 Tucker, B. G. and Mulcahy, M. F. R. Tmns. Farad. Sot. No. 553, 1969,65 (l), 274 Field, M. A. Combust. & Flame 1969, 13, 231 Field, M. A. Combust. & Flame 1970, 14, 231 Wheeler, A. Adv. in Catal. 1951, 3, 249 Goard, P. R. C. and Mulcahy, M. F. R. Carbon 1967,5, 137
593
31
Hawtin, P., Gibson, J. A., Murdoch, R. and Lewis, J. B. Lewis, J. B., Dix, J. and Murdoch, R. Carbon 19653,321 Lang, F. M., Magnier, P. and May, S. Z’roc. 5th Confi on Carbon. Pereamon Press. New York. 1962. Vol. 1. D 171 Weisz, P. B.&d Goodwin, R. B. J. Catal. 1966,6; 227; 1963,
414
28 29 30
E. W.Znd. Engng Chem. 1939,31,916 B. N. and Aris. R. Chem. Emma Sci. 1971.26.1699 ’ I. W. Cornbust: & Flame 1971,~17,303 Y., Rebaudieres, P. and Gudrin, H. Bull. Sot. Chim.
Carbon 1964, 2, 299
13 14
Mulcahy, M. F. R. and Smith, I. W. Rev. Pure & Appl. Chem. 1969,19,81 Evans, T.-and Phaal, C. Proc. 5th Con& on Carbon, Pergamon Press, New York, 1962, Vol. 1, p 147 Tekunova, T. V. and Tesner, P. A. Khimiya Tverdogo Top Ziva 1974,8
REFERENCES :
Hoynant, G. Zng-Doct. Thesis, 1959, University of Nancy, France Thomas, J. M. and Glenda Hughes, E. E. Carbon 1963, 1,
38 39
!
t 42 43