Kinetic study of pulverized coal combustion at high pressure using a shock tube

Kinetic Study of Pulverized Coal Combustion at High Pressure Using a Shock Tube V. E. BANIN,* F. A. C. M. COMMISSARIS, J. H. J. MOORS, and A. VEEFKIND Faculty of Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Combustion of pulverized coal and char particles has been studied in shock tube experiments. The gas temperature was varied between 1200-1800 K and the gas pressure was about 8 bar. Experiments involved different relative fractions of nitrogen and oxygen in the gas mixture, with particles of char and two different types of coal. In all cases, 95% of the particles had a diameter smaller than 6 p.m. It has been found that coal particles combustion occurs in the reaction-controlled regime and the true reaction order is close to 0 under high oxygen partial pressure. The influence of the internal surface on combustion is found to be negligible in the case of coal and to be comparable with the influence of the external surface in the case of char. The comparison of the energy release and the burn-out shows the influence of homogeneous reactions on the combustion process. Copyright © 1997 by The Combustion Institute

INTRODUCTION Investigations to determine the combustion and gasification characteristics of pulverized coals and chars with the aid of shock tube experiments is in progress in the Eindhoven laboratory [1-4]. Shock tubes were used to investigate the ignition behavior of coal particles [5-7] and for coal and char combustion experiments [5, 8-10]. The main advantages of the shock tubes are the short time for the creation of hot gas conditions (about 100 /~s) and the high pressure operational range. It is generally assumed that under high temperatures and moderate pressures the conditions of zone II apply [11-13]. The measured reaction order is in this case close to 0.5, which means that the real reaction order is close to zero. So far this fact is based on mostly indirect evidence because most of the experiments deal with combustion under conditions in which internal or external diffusion plays a key role or the oxygen pressure is insufficient to enter the desorption-controlled regime with a reaction order equal to zero. This paper presents results of shock tube measurements and analysis of the combustion rates for two types of bitumi-

* Corresponding author.

nous coal and char, with a mean diameter (determined as in [2]) close to 5 ~m. ARRANGEMENT AND CONDITIONS OF THE EXPERIMENTS The full details of the experimental installation and techniques can be found in [2]. The experiments were carried out behind the reflected shock in a 13 m long shock tube of 0.224 m diameter. Postreflected shock conditions, such as the gas density and temperature, were calculated from the measured incident shock velocity and the gas conditions prior to the incident shock. Coal particles were introduced into the system prior to the incident shock. The gas temperature was varied between 1200 and 1800 K and the gas pressure was about 8 bar. The partial oxygen pressure in the mixture with nitrogen was varied from 0 to 8 bar. Two types of bituminous coal were employed (see Table 1): from mine Paryz, Poland, with 41.40% of volatile matter, and from mine Illawara, Australia, with 30.36% of volatile matter. The coal specimens were prepared at the European Center for Coal Specimens (SBN). The char was made from Illawara coal, prepared in a drop tube reactor at KEMA, The Netherlands, in a nitrogen atmosphere at about 1300 K. The particle temperature Te and size measurements were based on IR two wavelength pyrometry. The wavelengths were 1.36 and 2.2

COMBUSTION AND FLAME 108:1-8 (1997) Copyright © 1997 by The Combustion Institute Published by Elsevier Science Inc.

0010-2180/97/$17.00 PII S0010-2180(96)00019-3

2

V . E . BANIN ET AL. TABLE 1 Analysis of Coal Samples Used in Experiments Coal Sample 217AU24, Illawara, Australia Proximate Analysis (% weight)

Ash (dry) 4.42 C

Ultimate analysis (dry) (% weight)

Vol. Fix-C Calc. (dry) (dry) (MJ/kg) (dry) 30.36 65.22 34.49 H

76.60 4.18

N

S

1 . 3 6 0.30

CI

O-dif

0.04

3.10

Coal Sample 236PO42, Paryz, Poland Proximate Analysis (% weight)

Ash (dry) 3.50 C

Ultimate analysis (dry) (% weight)

Vol. Fix-C Calc. (dry) (dry) (MJ/kg)(dry) 41.40 55.10 32.94 H

7.70 5.66

N

S

1 . 8 6 0.96

CI

O-dif

0.05

10.30

/.tm. The intensity of the particle continuum emission can be written for two different wavelengths 1 and 2 similar to Wien's formula as

I1, 2 = A l , 2 e l , 2 exp

AI,2Tp

AA],2,

(1)

where A], 2 is the pre-exponential factor, el, 2 is the particle emissivity, A1,2 is the pyrometrical wavelength, C is the second constant in Wien's law, and A A1,2 is the spectral width of the filters. The coal particles were considered to emit as a grey body, with e~ = ~2. A detailed analysis of the pyrometrical measurements of particle clouds is given in [2]. Calibration of the pyrometrical system with a ribbon lamp removes an uncertainty in the determination of Al, 2 and AA1,2. From the ratio of the intensities, derived from Eq. 1 at the two wavelengths, a particle temperature can be calculated. The band lamp temperature was calibrated to an accuracy of + 10 K. For an optically thin cloud the pre-exponential factor A1, z is proportional to the effective radiative surface (ERS), which is the number of particles multiplied by the radiating surface of a single particle (n • Sp), seen from the measuring system. It is not possible to determine the absolute value of Am,2 from Eq. 1, but it is possible to measure its relative change in time,

which corresponds to the temporal change of the effective radiative surface. The number of particles remains constant during the experiment. Thus the ERS signal is proportional to the surface of a single particle. Figure 1 presents the results of two coal experiments with nitrogen and with a nitrogen-oxygen mixture, performed at comparable gas temperatures (within 50 K). Both the effective radiation surface and the particle temperature curves are presented as functions of time. The steep rise of the temperature in both figures corresponds to the arrival of the reflected shock and hence to the starting point at which the stable hot gas conditions are set. In the nitrogen experiment, the particle temperature stays close to the temperature of the gas, while in the experiment with the nitrogen-oxygen mixture it exceeds the gas temperature, obviously due to the heat release during combustion. The temporal change of the effective radiation surface (ERS) also reveals a quite different behaviour. In the nitrogen experiment, the value of the effective radiation surface remains almost constant, while for the oxygen-nitrogen mixture it decreases significantly. In the nitrogen experiment the single particle surface does not change because no combustion occurs. In addition to IR pyrometry, emission spectroscopy and an extinction technique with a HeNe laser were used. Reaction rates of the coal particle combustion were measured in two different ways: direct measurements of change in particle size (burn-out method) and measurements of en-

2400t

~

../'.

."

02-N2[

ooo

~1600

O 0

N2f 1

~

2

3

4

5

t~ Ills

Fig. 1. Particle temperature and ERS time dependence for experiments with N2 and N2-O 2 mixture.

HIGH PRESSURE COAL COMBUSTION ergy release due to combustion (energy balance method). Both methods are based on two wavelength infrared pyrometry. Using the assumption of combustion at the surface of a perfect sphere, the equation for the particle combustion rate can be written as Rp. m

da dt lap'

(2)

where a is the particle radius (initially ~ 2.5 /zm), pp is the particle density ( ~ 1200 kg/m3), and Rp, m is the measured reaction rate (kg/m 2 s). When thermal equilibrium between the particle and the gas is established, the timedependent particle temperature graph becomes fiat and the first derivative of the particle temperature with respect to time becomes zero. From the energy balance equation [2] one can find K

Rp, m = aHc (Tp - T~),

(3)

where K is thermal conductivity, H c is the energy release per kilogram of coal, Tp is the particle temperature, and T~ is the gas temperature. Radiative cooling is considered to be small in comparison with heat conduction. A simple evaluation performed in [2] shows that if the particle temperature is 2500 K and the gas temperature is 1500 K, then for a particle with a radius of about 3 /xm, cooling due to radiation is about 2 M W / m 2, while cooling due to the heat conduction is about 30 M W / m 2. It is very important to use a correct value of the mean particle radius a because different parts of the particle size distribution can have different influences on the measurements. The choice of the averaging procedure depends on the type of measurements. For the pyrometry measurements the intensity signal is proportional to the particle surface or to the square of the particle size. Furthermore, due to the characteristics of the two wavelength pyrometry, particles of higher temperature will have a greater influence on the temperature and effective radiation surface measurements. Analysis of the influence of the different parts of the particle distribution gives a value for the mean

3 particle size close to 5 /xm, which is somewhat different from the mean square size [2]. The value for H c was taken as 10 M J / k g [14], which corresponds to the surface combustion of C with 0 2 to give CO. The values for the heat conductivity were taken from [15]. The temperature for the value of the heat conductivity is the average of particle and gas temperatures. EXPERIMENTAL RESULTS Dependence of the Combustion Rate on Temperature The experiments determined the particle temperature dependence on the reaction rate for the particles of two different kinds of coal and char in pure oxygen. The results of both energy balance and burn-out methods are presented in Arrhenius plots in Fig. 2a for the Polish coal, in Fig. 2b for the Illawara coal, and in Fig. 2c for the char. The data lie in a straight line, which suggests that an Arrhenius type of reaction rate expression is valid. In both cases though, there is a difference in the reaction rate between that measured from burn-out and that measured from the energy balance. This difference is greatest for the Polish coal. A possible reason for this difference is discussed later. Dependence of the Combustion Rate on the Partial Oxygen Pressure Both the burn-out and energy balance methods were used to determine the dependence of the combustion reaction rate on the partial oxygen pressure. In order not to introduce additional difficulties into the calculation of reaction rates, the experiments were performed such that the particle temperatures in different experiments were as close to each other as possible. Nevertheless, there is some particle temperature variation between different experiments. To present the reaction rate behaviour more clearly, the value of the reaction rate, measured by both burn-out and energy balance method, has been extrapolated on the Arrhenius plots (see Figs. 2a-c) to the same particle temperature of about 1800 K.

4

V. E. BANIN ET AL. 10o

100 ..............................

2 ff

,.,,,,...,,,

........

,,,,,.,,

.......

.,,.

diffusion limit

¢

u"

to

diffusion limit

r.

0.4 0.30

0.40

0.50

0.00

o.2o2

0.70

1

tO

partial pressure of 02, bar

1000/Tp, I/K to0

100

~tiffusion

limit

..................

1o

diffusi

limi

balance~

~"~ergy 1

burnout 0.2 0.40

0.50

0.80

0.70

o.~:,

0.80

.......

;

100

~oo I .................................. burnout

.

.

.

.

.

.

.

10

. . . . . . . . . . . . . .

diffusion limit e energy balance

-

E corrected for internal combustion 0

.

partial pressure of 02, bar

lOoOfrp, IlK

"1~ ..~ lo ~

.

~ * "~,30

*

i

r

I i 0.40

~

-''"'-~._- - % . . " -~'"~,~..~ i

I it 0.50

i

i

[

lO00fI'p, IlK

Figure 3a presents the reaction rate behaviour for Polish coal at this temperature (1800 K) as a function of the partial pressure of oxygen. With the burn-out method, there is a slight decrease in reaction rate with decrease in oxygen concentration. A stronger decrease appears with the energy balance method. For partial oxygen pressures higher than 1 bar, both methods show almost no dependence of reaction rate on oxygen concentration. Figure 3b and c show a similar behaviour for Illawara coal and for char, respectively. The nature of this behavior will be discussed later.

J

i

i

r r I

" " ~ urn~ut i

,i

i

i

i

I partial pressure of 02 , bar

I -,'"~-._ , I , 0.80 0,70

Fig. 2. Arrhenius plot of the diffusion limit and measured combustion rates based on burn-out and energy balance methods for (a) Polish and (b) Illawara coals and (c) char (a = 2.5/~m)

. . ~.~::..;r-.- ..... 0.

A i

i

I0

Fig. 3. Comparison of experimentally measured combustion reaction rates at ]800 K for (a) Polish coal, (b) Illawara coal, and (e) Illawara char with calculated diffusion limit (a = 2.5 /zm) in experiments with O 2 + N 2 mixture

DISCUSSION OF EXPERIMENTAL RESULTS It is useful to analyse the experimental results using the "zone theory" presented in [13]. Zone III in this case corresponds to combustion limited by diffusion, zone II corresponds to combustion with partial penetration of oxygen in the particle body, and zone I corresponds to combustion with complete penetration of oxygen in the particle body.

H I G H PRESSURE COAL COMBUSTION Diffusion Limit

It is very important to ascertain whether the combustion rate is limited by the chemical reaction at the particle surface (or close vicinity to it) or by the diffusion of oxygen toward the reacting particle. The maximum oxygen flux (h m) ( k g / m 2 s) is calculated from the following equation (see [13] and [16]):

hm = 0 " 7 5 0 °

P ] ~ T0]

a '

5 sion limit for the experiments with coal and lie under the curve for the experiments with char. This shows that in this regime the combustion rate is substantially limited by diffusion. For the experiments with a partial pressure of oxygen higher than 1 bar the reaction rate is chemically limited. Thus the conditions of zone III diffusion-controlled combustion [13, 16] were fulfilled only in the coal experiments with a partial oxygen pressure below 1 bar.

(4)

where Tm is the mean temperature in the boundary layer around the particle, Po2 is the oxygen density far from the particle, P is the total gas pressure, and D is the diffusion coefficient. The subscript 0 denotes a value at the reference conditions, namely, P0 = 1 bar and TO = 1500 K. For these conditions D O = 3.1 × 10 -4 m2/s. The chemical reaction at the particle surface is considered to be combustion of C with 0 2 to CO. Figure 2a-c compares the experimental results with the calculated diffusion limit as a function of temperature. The oxygen pressure in these experiments was maintained almost constant at about 8 bar, the gas temperature varied between 1200 and 1800 K, while the particle temperature changed from 1600 to 2600 K. A mean value of the diffusion coefficient was calculated for each experiment on the basis of an average temperature, between that at the particle surface and that far from the particle. As can be seen from Fig. 2a and b, all experimental data lay well below the diffusion limit, implying the measured combustion rates with pure oxygen were determined by chemical reaction at the surface (or in close vicinity to it). In the experiments with oxygen-nitrogen mixtures the particle and gas temperatures did not alter much when the partial oxygen pressure was changed from 0.3 to 10 bar. Figure 3a-c compares the experimental data with the calculated diffusion limit curve as a function of partial oxygen pressure. No experimental point appears above the diffusion limit, as was to be expected. For partial oxygen pressures lower than 1 bar, all experimental points, measured by both methods, lie on the curve of the diffu-

Chemical Control of Combustion

Evaluations similar to those performed in [11] and [17] were made to define the combustion regime more precisely. Some preliminary qualitative conclusions already can be made from analyses of the experimental data. Within zone II, a particle burns in a shrinking mode that reveals the apparent reaction order n, which is related to the true reaction order m by n = (m + 1)/2. As was shown in [2], particles actually combust with a decrease in particle size. Experiments in nitrogen [2] have shown that neither significant swelling or noncombustion shrinking occurs. Thus the change in particle radius is due to combustion only. With the first condition for combustion within zone II fulfilled, it is still difficult to imagine that this zone applies to the experiments. Figure 3a and b shows that the measured order n of the reaction is close to zero for partial pressures of oxygen higher than 1 bar. The corresponding value for the true reaction order m would be - 1 , which is hardly possible for coal combustion kinetics. Combustion in zone I, on the other hand, can reveal the true order of reaction equal to the apparent one, but it occurs in the nonshrinking regime, which is not the case in the present experiments. This leaves the possibility of "rough sphere" combustion, which occurs with a decrease in particle size and reveals the true order of reaction. The effective depth of oxygen penetration in this case is small. Reaction in the pores is comparable with the reaction at the external surface or can even be neglected completely, so that it can be considered to take place only at the external particle surface. The calculations of the penetration depth or the effectivity GTe) are performed directly in [11],

6

V . E . BANIN ET AL.

[18], and [19] using the generalised Thiele modulus ~b [20, 21]. The general Weisz-Prater criterion for strong pore diffusion limitations is formulated in [21] and can be written

r(Cs)

fo C'Der(C)

dC ] - 1 / 2

>> 1,

(5)

tiveness tie ~ 1/~b [21]. This means that the penetration depth (le) is about 1% of the particle radius. An expression for the measured reaction rate (Re, m) with the influence of both the external (Sex) and internal (S i) surface can be written

(s,)

= L-- W where L is the characteristic size, r(C) is the volumetric reaction rate per kilogram of coal, C is the oxygen concentration per unit volume of coal, Dp is the Knudsen diffusion coefficient, and the subscript s denotes conditions at the surface. This equation can be rewritten for a cylindrical pore with diameter re and length a in terms of the surface reaction rate (R e) and oxygen density ( p ) as

~

a~ Mo2

qb = R p , s

2Mc

1 DpfoPSRp dp

(7)

Re, m = Rp, s 1 + --ff~xTle

with Ps

te

re 2Mo

'Te --- a =

Redp

De T -ff o

(o,

(8)

Rp,s

(6)

where Mo2 and M c are molecular weights of oxygen and carbon, respectively. At high oxygen pressures the experiment shows low dependence of the measured reaction rate on oxygen pressure. This implies that the real reaction rate is limited by chemical desorption rather than by adsorption of oxygen at the particle surface; see [22]. The value of ~b is evaluated below, assuming that R e does not depend on oxygen concentration. For a pore radius equal to about 1-2 nm and Knudsen diffusion coefficient equal to 8 × 10 -7 m2/s [18], ~b lies between 85 and 120 for the conditions of the experiment. A mean pore radius has been evaluated as in [11] using data from [22] for bituminous coals. If ~b >> 1, the effec-

If m ~ 0, r/e ~ pl/2 and if m ~ 1, r/e ~ p0. This implies that if the measured reaction order n is 0, then the real reaction order m = 0 and (Si/Sex)rle << 1. this is the case for the experiments with coal, where the reaction order is 0 within experimental error (see Fig. 3a and b). The value of Si/Sex must be less than 120, which is possible for bituminous coal. Thus the experiments with coal produce real values for the combustion rate at high pressures and can be written in Arrhenius form

Rp =Appm exp ---Te '

(9)

where Ap is the pre-exponential factor, E is the activation energy, Tp is the particle temperature, and m = 0 for the coal experiments. Values of Ap and E are given in Table 2.

TABLE 2

Characteristics Calculated from Experimental Data a Characteristics

Burn-out Ap (kg/m 2 s)

Burn-out Ep (K)

Energy Balance Ap (kg/m 2 s)

Illawara Polish Char Char corrected

2550 + 690 50 -I- 7 40 + 10 65 + 25

12,600 -I- 550 7,075 + 315 6,140 -1- 450 8,860 + 740

290 + 70 690 -1- 170 240 + 70 --

Energy Balance Ep (K) 8,230 + 520 10,140 -I- 560 8,690 + 630 --

aOxygen pressure 8 bar and reaction order equal to 0. Burn-out and energy balance methods were used. The energy produced in combustion was taken equal to 10 MJ/kg.

HIGH PRESSURE COAL COMBUSTION In the experiments with char (see Fig. 3c) the measured reaction order at high pressures is about 0.3. This is possible if the second term in Eq. 6 is of order unity. The best fit for this gives (Si/S~x) ~ = 0.8. This can be explained by the fact that the pores of the char particles are much more developed compared with the pores of coal particles. The Arrhenius dependence in Fig. 2c is given for experiments with about 10 bar oxygen pressure. Because the reaction order in this case is close to zero, the expression for the measured reaction rate can be deduced from Eqs. 7-9:

¢, expt

E

),

rp 2M c _ a2Mo21-)p " The factor X can be found by fitting the dependence of the reaction rate in Fig. 3c, under constant temperature and with changing oxygen density at high oxygen pressure. This yields a value of 1.1. The best fit of the Arrhenius curve to the measured reaction rate with the burn-out method in Fig. 2c, with the known value of X, and using Eq. 10 produces the corrected values of Ap and E; see Fig. 2c and Table 2. It is interesting to note here that from Eqs. 7 and 8 for 77 ~ l/~b, if the measured reaction order at high pressure is zero, and thus the reaction rate is real, the measured reaction rates at lower pressures also are real. This is because the effectiveness factor "0, or penetration depth lp, can never become higher with a lower oxygen concentration. Influence of Homogeneous Combustion Volatile matter produced during devolatilisation, as well as carbon monoxide produced during surface combustion, can burn in the gas

7 phase and change the energy balance significantly. The difference between combustion rate measurements with the burn-out and energy balance method presented in Fig. 2a, b, and c can be explained by the influence of homogeneous combustion. Furthermore, the difference is greater for the experiments with coal of higher volatile content. Combustion of volatiles can occur near the particle surface or in the gas volume far from it. The change of particle size during combustion shows that there is enough oxygen at the particle surface for a volatile flame to be attached to the particle. Another experimental fact supports this point. The emission spectroscopy measurements (see [2]) showed no sign of volatile matter in the gas volume, which implies that the volatiles burn close to the surface. The fact that not only CO but also CO 2 is present in the gas volume suggests some combustion of CO and volatile matter, assuming that CO2 is not formed heterogeneously. CONCLUSIONS It has been found that for small coal particles heterogeneous combustion occurs in the regime of "rough sphere" kinetics for a partial oxygen pressure higher than 1 bar. The true reaction order measured under these conditions is very close to 0. The influence of the internal surface on combustion is negligible in the case of coal and comparable with the influence of the external surface in the case of char. When the partial oxygen pressure is lower than 1 bar, the combustion is limited by diffusion. A good agreement between the evaluated diffusion limit and the experimentally measured combustion rate confirms the validity of the methods used. A strong influence on the coal particle energy balance of homogeneous combustion in a thin layer close to the particle surface is demonstrated. In the case of Polish coal, in the heat balance, a heat of combustion value that is higher than the value corresponding to heterogeneous combustion with carbon monoxide production should be used. This is not the case with Illawara coal, which has a lower volatile content, or with char.

8 The experiments show that a shock tube technique can be used to characterise coal combustion as well as for basic studies of pulverized coal combustion.

These investigations in the programme of the Foundation for Fundamental Research on Matter (FOM) have been supported by the Netherlands Technology Foundation (STW). The authors would like to thank Herman Koolmees, Ad Holten, and Ad van Iersel for their technical support. REFERENCES 1. Banin, V. E., Veefldnd, A., Ivanov, V. A., and Bityurin, V. A., Proceedings of the Seventh International Conference on Coal Science, CANMET, Canada, 1993, pp. 31-34. 2. Banin, V. E. Shock Tube Research on Kinetics of Pulverized Coal Particles Combustion and Ignition, Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 1994. 3. Commissaris, F. A. C. M., Banin, V. E., and Veefkind, A., Proceedings of the Eighth International Conference on Coal Science, Elsevier, Amsterdam, 1995, pp. 519-522. 4. Banin, V. E., Commissaris, F. A. C. M., and Veefkind, A., Proceedings of the Eighth International Conference on Coal Science, Elsevier, Amsterdam, 1995, pp. 591-594. 5. Seeker, W. R., Wegener, D. C., Lcster, T. W., and Merklin, J. F. Proceedings of the Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1978, pp. 155-166. 6. Nettleton, M. A , and Stifling, R., Proc. Roy. Soc. London Ser. A 300:62-77 (1967). 7. Boiko, V. M. et al., Fizika Gorenia i Vzriva 27(2):101-111 (1991)(in Russian).

V . E . BANIN ET AL. 8. Nettleton, M. A., and Stifling, R., Combust. Flame 22:407-414 (1974). 9. Park, C., and Appleton, J. P., Combust. Flame 20:369-379 (1973). 10. Brandt, O., and Roth, P., Combust. Flame 77:69-78 (1989). 11. Mulcahy, M. F. R., and Smith, I. W., Rev. PureAppl. Chem. 19:81-108 (1969). 12. Walker, P. L., Jr., Rusinko, F., Jr., and Austin, L. G., in Advances in Cata(vsis, Vol. XI (D. D. Eley et al. Eds.), Academic Press, New York, •969. 13. Smith, I. W., Proceedings of the Ninteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 1045-1065. 14. Kapteijn, F., and Moulijn, J. A., in Carbon and Coal Gasification (J. L. Figueiredo and J. A. Moulijn, Eds.), NATO ASI Series E, Nijhoff, Dordrecht, 1986, p. 105. 15. Weast, R. S. (Ed.), Handbook of Chemistry and Physics, 56th ed. CRC Press, Cleveland, OH, 1975-1976. 16. Prado, G., Froelich, D., and Lahaye, J., in Fundamentals of the Physical-Chemistry of Pulverized Coal Combustion J. Lahaye and G. Prado, Eds.), NATO ASI Series E, Nijhoff, Dordrecht, 1987, p. 137. 17. Seeker, W. R., The Kinetics of Ignition and Particle Burnout of Coal Dust Suspensions under Rapid Heating Conditions, Ph.D. Thesis, Kansas State University, 1979. 18. Wheeler, A., in Advances in Catalysis and Related Subjects, Vol. III (W. G. Frankeburg et al., Eds.), Academic Press, New York, 1951. 19. Frank-Kamenetskii, D. A., Diffusion and Heat Transfer in Chemical Kinetics, Plenum, New York, 1969. 20. Mehta, B. N., and Aris, R., Chem. Eng. Sci. 26:1699-1712 (1971). 21. Froment, G. F., and Bischoff, K. B., Chemical Reactor Ana(ysis and Design, 2rid ed., Wiley, New York, 1990. 22. Essenhigh, R. H., in Chemistry of Coal Utilisation, 2nd Suppl., (M. A. Elliot, Ed.), Wiley, New York, 1981. Received 24 January 1995; revised 29 January 1996