A single particle model for the evolution and combustion of coal volatiles

A single particle model for the evolution combustion of coal volatiles Pradeep

and

K. Agarwal

Department of Chemical Engineering, The University Adelaide, SA 5001, Australia (Received 13 November 1984; revised 25 September

of Adelaide,

GPO Box 498,

1985)

A single particle model is proposed for the evolution and combustion ofcoal volatiles. The analysis is divided into preignition and postignition stages. The rate limiting steps for devolatilisation are assumed to be heat transfer (both to and through the coal particle) as well as chemical reaction (overall decomposition represented by the distributed activation energy kinetics). Approximate expressions are proposed for the estimation of volatile burnout times. The model results are compared with the experimental data reported for single coal particles in stagnant as well as convective oxidizing environments. The application of the model to fluidized beds is discussed. Model predictions are also compared with the volatile burnout times in fluidized beds.

(Keywords: coal; particle size; combustion)

bed combustion has received wide research attention in view of its potential as an economic and environmentally acceptable technology for burning lowgrade coals’ ‘. The importance of considering devolatilization in the overall modelling of fluidised bed combustion is now recognized’!-lo. Little has, however, been reported on the detailed process of evolution and combustion of coal volatiles, and the impact of these phenomena on the subsequent combustion of residual char” -’ 3 and the inadequacy of the existing models for devolatilization in fluidised bed combustors has been pointed out14. In this paper, a simple single particle model is proposed. The evolution of the coal volatiles is modelled using the coupled heat transfer (both to and through the coal particle) and chemical reaction (represented by the distributed activation energy model) limited formulation presented earlier’. The combustion of volatiles is modelled using a modified Schwab-Zeldovich approach. The effect of the heat transmitted from the volatiles flame to the coal particle and the consequent increase in the rate of devolatilization is considered. The approach is also applied to the large particle model for evolution of volatiles” to obtain analytical expressions. Simplified approximate expressions are also proposed. The model predictions compare well with the experimental volatile burn-out times reported in the literature for single isolated coal particles in stagnant as well as convective oxidizing conditions. Application of the model to fluidized beds is discussed. Volatile burn-out times in fluidized beds are also compared with model predictions. Fluidised

BACKGROUND Experimental studies on the devolatilization of coal in combusting systems suggest that the devolatilization time, z,, in most cases measured as the time between the 0016-2361/86/060803-08$3.00 0 1986 Butterworth & Co. (Publishers)

Ltd

ignition and extinction of volatiles, has been correlated an expression of the form: T,,=k,

d”

by (1)

where k, and n are constants and d is the coal particle diameter. However, there does not appear to be a theoretical explanation for the values of k, obtained experimentally’ 5. Nor have the variations (or the lack of variation) with the type of coal and the operating conditions been understood. The results of previous investigations’5-24 have recently been discussed by La Nauze25. The disparity between the assumptions for volatile release in the overall modelling of fluidized bed combustors has been pointed out’- l”,14. The volatile evolution sub-model has been either ignored or treated as a non-rate process based on the relative time scales for devolatilization, particle mixing and char burn-out6326,27. Borghi et al.’ recognising the importance of treating volatile release as a rate process, considered heat transfer to the coal particle and the isothermal kinetics of coal decomposition28,29 as the possible rate limiting steps. The inadequacy of the isothermal particle assumption has formulation of been pointed out 9*10and the mathematical the diffusion flame has also been questioned14. THE MODEL Since coal is a partially pyrolysing substance, the detailed modelling of single particle volatile combustion would require the consideration of several phenomena including pyrolysis, ignition of coal, combustion of volatiles and the effect of combustion of volatiles on the subsequent devolatilization. To make the analysis tractable, several simplifying assumptions have to be made. In the following, the analysis is presented in two stages separated by ignition.

FUEL, 1986, Vol 65, June

803

A single particle

model for the evolution

and combustion

Stage 1 In this stage, prior

to ignition, the cold coal particle introduced into the hot bed/gas would heat up to the point where the volatiles would start evolving from the surface of the particle. This stage corresponds to pyrolysis prior to ignition. As the details have already been in presented 9,10, the relevant equations are summarized Table 1 and only an outline is presented here. The volumetric average fractional amount of volatiles retained within the spherical particle of radius R, is given by: RO

Xavg= L Xr’dr K3 s

(2)

0

In model I calculations, X is represented by the nonisothermal distributed activation energy formulation of profile is Anthony et al. 28*29. The particle temperature calculated from the analytical solution30*31 of the unsteady state heat conduction equation with a convective boundary and uniform initial temperature conditions. Xavg was determined by numerical integration using Gaussian quadrature (of order 12) at each of three nested levels3’ to obtain the devolatilization characteristics of the coal particle. In Model II calculations, for the specific case of large particles (> 1 mm), heat transfer was assumed to be the mechanism with chemical reaction rate limiting controlling only the residual amount of volatiles”. Using this approach it was possible to obtain analytical expressions for the volumetric average devolatilization. The relevant equations are summarized in Table 1.

Stage

II It has been suggested 32 that for particle sizes greater than 65~~ homogenous ignition is expected to take place as the surface flux of the volatiles would be large enough to prevent the oxygen from reaching the coal surface. Thomas et al. j3 have, however, pointed out that the ignition phase would depend on the reactivity of the coal. Table 1

Model equations

of coal volatiles:

For brown coal, they have shown that heterogeneous ignition could take place for particle sizes as large as 1 mm. For the sake of simplicity, it is assumed that spontaneous ignition of volatiles would take place in the gas phase once 25% of the initial volatiles content is pyrolyzed. A more detailed analysis would require the incorporation of an appropriate criterion such as those reported previously35,36. Once a diffusion flame is formed within the boundary layer of the coal particle, the flame would increase the rate of devolatilization depending on its temperature. This in turn would increase the flux of volatiles from the coal particle pushing the flame further away from the particle. The flux, if large enough, may prevent oxygen from entering the boundary layer around the coal particle. If the Damkiihler number (defined in general as the ratio of the characteristic flow time to the characteristic reaction time) gets below a critical value, the volatiles flame may be extinguished. As the characteristic flow time would be minimum outside the boundary layer, the possibility of extinction increases when the volatiles flux prevents the oxygen from entering the boundary layer. Within a fluidized bed, the possibility of such extinction increases even further because of the thermal as well as free radical quenching provided by the bed particles3’. This extinction would then result in the lowering of the volatiles flux and the re-establishment of the flame. Within a fluidized bed, volatile combustion is then expected to predominantly occur when the coal particle is in the bubble phase and be negligible when it is in the emulsion phase. This ignition extinction process could be repeated several times depending on the combustor operating conditions before a stable phase of volatile combustion. Finally the volatiles would be depleted from within the coal particle, the flame would decrease in intensity, move closer to the particle surface and collapse permitting oxygen to attack the residual char. The complete mechanism could thus involve a complex sequence of linked events in which the flame radius (as well as the flame temperature) would change with time) The complexity of the problem would be compounded by the effect of time dependent release of different gaseous and tarry species from within the coal particle.

for stage I calculations9S’0 Model II”

Model I9

1.0 x=(T,-TMT,-T,) 0.0

Point devolatilization expression

Temperature

profile where &‘s are the roots of the transcedental

Solution

804

P. K. Agarwal

Numerical

FUEL, 1986, Vol 65, June

solution

required

equation

pcos D=(

1- Bi,) sin p

T< T, Tl rc T< T, n

Tz

A single particle model for the evolution In this analysis, it is assumed that the flame is spherical and the combustion of volatiles is rapid (flame sheet approximation). In view of the complexity of the movement of the flame front with the associated changes in flame temperature, it is assumed that on a timeaveraged basis, the flame temperature may be represented by T, and the flame radius is (R,+6/2) where 6 is the thickness of the boundary layer. Prior to ignition, assuming that the thermal and momentum boundary layer thicknesses are equal and that the temperature profile in the boundary layer is linear, it may be shown that: 6, zz 2R, k$Bid k, z 6

(34

The apparent similarity between the gas phase combustion of coal volatiles and the problem of fuel droplet combustion has been pointed out”. The solution of the liquid fuel dropletjx combustion may be adapted to the present problem keeping in mind that heat transmitted back raises the temperature of the whole solid with time and it is this changing temperature profile which results in the thermal breakup of bonds in the chemical structure (complete devolatilization” corresponds to the centre of the particle reaching the temperature T2) of the coal. The flame temperature F may then be estimated as:

(3b) With the assumptions of T,and the flame radius (R, + d/2), the devolatilization in the presence of the volatile flame may be characterized. Defining P = t - ti,, the temperature profile is estimated from the analytical solution of the heat spherical conduction equation in one-dimensional coordinates with a convective boundary and the following initial condition: T(r,t’=O)=

T,-

Ai

f

sinUWR,)

i=l sin Ai 3

2(T,

-

‘)

8, _

(44

UQ/RJ pi -PI sin

pi

‘OS

pi

cos

pi

e_(pf~t,g/R~ >

WI Following the analysis technique solution may be derived as:

outlined

by Jakob31, the

(54

and combustion

average devolatilization expressions presented earlier. For the more general model (Model I), numerical integration is required. For the large particle model (Model II), analytical expressions may be obtained:

where: NJ’ = Nje-L

RESULTS

1 .o-

-\

fl cos fi=(l

-Sir)

sin b

equation:

Y x”

.-.-.-. \

\.

\ \ \ I I IC

0.6-

(5b) and /?J’s are the roots of the following

R02

AND DISCUSSION

0.8-

flj cos bj

p2x t’

The effect of gas temperature, T, and the type of coal (reflected in the choice of kinetic parameters for the overall decomposition of coal) are examined parametrically in Figure 1. The standard parameters chosen are Y,,=O.lS, I/*=0.36, k,= 1.67x 1013s-1, c(= 0.1 mm’/s, Bi,= 1, R, = 2.0 mm. For curves A and B, E,=250kJmol-’ and a=40kJmoll’ but the gas temperatures are 1200 and 800 K respectively. As may be seen, a lower bed temperature results in a substantially longer preignition period. The values of zV, measured as the time between flame ignition (Xavg~0.95) and extinction (Xavg ~0.05) are not very different (within a factor of 2) for the comparatively large change in gas temperature. For curve C, the gas temperature is 1200 K but the mean of the activation energy distribution E,= 200 kJ mol- ‘. As may be seen, the length of the preignition period depends on E, (and hence on the type of coal), however the value of r, is fairly independent. It then appears that the preignition period would depend on gas temperature as well as the type of coal; however T” depends more on the gas temperature than on coal type for coals with similar physical properties. Results for z, for swelling coals, if compared with results for non-swelling coals (without proper correction), would appear to show a strong coal type dependence; however for coals with similar swelling characteristics, results should be similar. Consequently, it is felt that results on swelling properties and pyrolysis studies should also be reported with combustion results to obtain a more complete understanding.

where:

fij -sin

of coal volatiles: P. K. Agarwal

0.4

\

I \ \

-

\

\

\

\

(5c)

By the assumption that the flame radius is (R,+6/2), it may be shown that the effective Biot number for conduction of heat from the flame to the coal particle is given by Bi,=2Bi,. The particle temperature profile given by Equations 5a-5c may now be used in conjuction with the volumetric

0.2-

\

0

I 4

i.B

8

‘\

12

16

I 20

I 24

,

‘\.,

28

32

t(s) Figure 1 Effect ofcoal type and bed temperature on the time dependent devolatilization structure: (A: T, = 1200 K, E, =250 kJmol~ ‘; B: T,=800 K, E,=250kJmol-‘; C: T,=1200 K, E,=2OOkJmol~‘)

FUEL, 1986, Vol 65, June

805

A single particle model for the evolution Applicution to single isolated

and combustion

of coal volatiles: P. K. Agarwal

particles

/ I

Numerical calculations using Model II suggest that for d > 0.5 mm, it is possible to approximate the volatile burnout time for the model calculations by the expression

/

I / I

where (p-

T-T2 T-

Nu, = 2.0 + 0.6 Re,“’

Py113

is similar to the devolatilization T,. filfis the first ” estimated

from (8)

Equation (8) suggests that for lower Reynolds number (corresponding to devolatilization under stagnant oxidizing conditions l5 - ’ 9, the devolatilization time would be proportional to d2 because the Nusselt number would be approximately 2 for all particle diameters. Considering the experimental conditions of Essenthe flame temperature was estimated from high”, Equation (3b). The values of AH (10 3OOcal g -‘) and f(0.3) appear to be reasonably applicable for a large range of hydrocarbons3s; the value of C, was assumed as constant =0.3 calg-’ K (this assumption may be relaxed; however it would be more significant to remove the unity Lewis number assumption3’). Considering that radiative heating was employed (leading to T,z T,), T, may be on the estimated as ~2100 K. The data39 reported pyrolysis behaviour of different coals suggests that T2 may vary from 900-1200 K. From Nu,=2, Plr may be estimated as z 1 using Figure 5 of Agarwal et al.“. With the thermal diffusivity 8*40 chosen as 0.1 mm’s_I, it may be shown that Equation (7a) reduces to: 1.2)d2

(9)

Equation (9) is in good agreement with the data and the correlation of Essenhigh l5 . This equation also suggests that the effect of coal type on z, is not very strong for particle sizes >0.5 mm. It may be noted that the actual values fork, obtained by Essenhigh’ ’ varied between 0.44 and 1.3 1. However, the incorporation of a swelling factor resulted in the influence of coal type becoming negligible. The model predictions are in agreement with this experimental observation. In Figure 2, the reported experimental data1’-19 are compared with the model predictions in terms of the upper and lower limits constructed assuming that the flame temperature may vary from 2000-3000 K. More detailed comparison is not possible as swelling properties and oxygen concentrations employed do not appear to have been reported’ ‘. For larger Reynolds numbers, the value of Nusselt number (and consequently Biot number as well as plr) is expected to be larger according to Equation 8. Consequently the value for the coefficient ofd2 is expected to drop as noted by Carabogdan’7-19. Additionally, since Re, depends on the particle diameter, it is expected that the d2 relationship would not be valid. To demonstrate this aspect the experimental conditions of

808

/ I

T,

It may be noted that the above expression expression proposed earlier’0*32 for under inert conditions with T,replaced by root of Equation (5~). The heat transfer Biot number may be the single sphere correlation:

z,=(l.l-

IO-

Vb)

1

o
FUEL, 1986, Vol65,

June

2 l-

0.1-l-’

’ ’ ’

0.1

”

1 d (mm)

I

111111,

IO

1

Figure 2 Comparison between experimental and predicted volatile burn-out times for a single isolated coal particle in stagnant oxidizing conditions: __. .-, Ivanova and Babii16 (k, = 0.45, n = 2); p, Essenhigh” (k,=0.9, n =2); hatched area, data of Essenhigh15 and Carabogdan’7-‘9;---, upper and lower limits from Equation 7 with Nupr2

Ragland and Weiss” were simulated. The values of T, were calculated from Equation 3b as discussed earlier. Upper and lower limits were constructed, using Equations 7 and 8, for the calculated values of T, 4 and fill from the actual particle diameter and flow conditions. The predicted values of 2, for the average value of &Jare also shown. The results along with the experimental data of Ragland and Weiss” are presented in Figure 3. Both 7,’ as well as z, are plotted against particle diameter. Once again, the model predictions appear to be in agreement with the data. The correlation of Essenhigh15, obtained for stagnant oxidizing conditions, would increasingly overpredict the dependence of devolatilization time on particle size and should be used with caution for convective oxidizing conditions. Application

to jluidized

beds

An accurate estimate of the devolatilization time in fluidized beds requires the knowledge of the relative amounts of time spent by the coal particle in the bubble phase (where volatile combustion takes place) and in the emulsion phase (where the volatile flame is expected to be extinguished, however pyrolysis would still be taking place). Consequently it is assumed that: z”=P

h,+q

T”,

( 10)

where zVgis the devolatilization time if the coal particle was completely in the bubble phase (corresponding to single isolated particle as discussed earlier) and z,, is the

A single particle model for the evolution and combustion of coal volatiles: P. K. Agarwal bed fluidized at a higher gas velocity - the bubble sizes would be larger, the value of p higher and the volatiles could combust around the coal particles. Volatiles evolved in the emulsion phase would combust in the bubbles, the splash region as well as in the freeboard. This picture appears to be consistent with other visual observations23. Moreover, a high resolution slow motion video analysis43 has confirmed that ignition and burning of volatile matter occurred preferentially in bubbles. Flames attached to the coal particles were observed to extinguish when the particles entered the bubble cloud regions and no evidence was found for volatile matter in the emulsion phase. Several incombustion vestigators ’ 2,44 have observed that coal particles tend to float to the top of the bed during the volatile combustion phase. This is expected, given that over-bed feeding of coal was employed coupled with the facts that bubble sizes are largest at the top of the bed (hence increased likelihood of volatile combustion) and that individual tagged particles near the surface of fluidized beds have been observed to remain there for some time before dipping into the beda%

1 0

I 2

I 4

I

I

I

I

6

8

IO

12

d (mm) Figure 3 Comparison between experimental and predicted volatile bum-out times for a single isolated coal particle in convective oxidizing conditions: hatched area, Essenhigh’s correlation”; ~-upper and lower limits from Equations 7 and 8;--, Ragland and Weiss” (k,= 1.5, Ragland and WeissZO (time between flame ignition n= 1.5)t,‘; -p--, and extinctionh,; ---, calculations based on the average value of d

devolatilization time if the coal particle was completely in the emulsion phase (corresponding to pyrolysis as represented by Stage I equations); p and 4 are relative phase residence time probabilities such that p+q= 1. Obviously, p and q depend on the relative magnitudes of the coal and bed particle sizes as well as the superficial gas velocity. If the bubble size at any specified height within the fluidized bed is less than the size of the coal particle, then the particle would be expected to remain predominantly in the emulsion phase. Also since the bubble sizes increase with bed height and excess gas velocity41*42, the combustion of volatiles around the coal particle is expected to become more likely as the particle moves towards the top of the bed. Thus for the experimental conditions of Yates et al.“, employing a large coal particle constrained by a wire to remain within a bed fluidized at a low gas velocity, the bubble sizes would be small, the particle would remain predominantly in the emulsion phase (lower values of p) and the volatiles evolved would detach as bubbles. On the other hand, for the experimental conditions of Pillai2’ involving comparatively smaller, unconstrained coal particles in a

The contribution of the pyrolysis like conditions in the emulsion phase during devolatilization under combustion conditions would explain the strong dependence on bed temperature obtained in the experimental results of Pillaii3. In Figures 4 ax:, the experimental results are compared with model predictions (with Model I) using Equation (10) for three types of non-swelling or moderately swelling coals (swelling numbers 0 and 1). The results are seen to be in good agreement with the data. The type of coal (evidenced by the comparison between the activation mean energies for overall pyrolytic decomposition of the coals in Table 2) exerts a strong influence only for smaller particle sizes (< 1 mm). For larger coal particle sizes, the devolatilization time would be fairly independent of the type of coal. The coal type dependence observed by Pillail is then attributed more to the swelling of the coal particles. It may be noted that the values of k, obtained previously” are the highest for strongly swelling coals; also coals with similar swelling numbers have similar values of k, and n. This appears to be in agreement with the results of the parametric analysis discussed earlier. Figure 4 ax, however, confirm the strong bed temperature dependence obtained by Pillai’ j. The values of p and q have been used as adjustable parameters here. However, a preliminary justification is available from the experimental results of Mickley et aL4’ who observed that the fraction of the heater surface bathed by the bubble phase, at higher excess gas velocities’3 was about 0.5. More rigorous methods to determine these parameters from fluidized bed conditions are presently under consideration. More detailed validation of the model, in terms of time dependent release of volatiles under combustion conditions, is presently not possible due to lack of relevant data. The time dependent weight loss for Montana lignite in a fluidized bed has been reported4s and the experimental data was compared with the model of Borghi et al.’ (which includes volatile release as a rate process as well as subsequent combustion of char). However, the first set of data points appears to be taken after the volatile release is complete. The volatile release submodel’ based on an isothermal coal particle assumption, is compared with the predictions of the

FUEL,

1986,

Vol 65, June

807

A single particle model for the evolution and combustion of coal volatiles: P. K. Agarwal present model (Model I) for a 3 mm Montana lignite particle in 8% oxygen environment at two different temperatures in Figure 5. The distributed activation energy model kinetic parameters used, for the overall decomposition of Montana lignite28*29 (volatile matterz37%, k,= 1.67x 1013s-1, E,=236kJmol-‘, (T= 46 kJmo1 - ‘), are the same as used by Borghi et d7 but the thermal diffusivity value used by the latter is almost an order of magnitude greater than the value8q40 a = 0.1 mm’s_ i employed in the present calculations. The value of p has been chosen as 1 to stimulate overbed feeding of coal. The total devolatilization time appears to be of the same order of magnitude; however the time dependent release structure is seen to be quite different. An important difference between the isothermal and non-isothermal particle models arises in the estimation of

;; ,’

25-

Table 2 Kinetic parameters, thermophysical properties and operating: conditions for comparison of predictions from Model I with experimental datai in Figures 4ax 0

2

4

6

d (mm)

8

Kinetic

parameters

Coal type Texas lignite Rexco Nostell

40) 0

for overall E,(kJmol-‘)* 250 200 250

decomposition: o(kJmol-I)* 40 40 40

Thermophysical properties Coal type Texas lignite Rexco Nostell

30-

a(mm2/s)* 0.1 0.1 0.1

Us’) 1.67 x lOi 1.67 x IO’a 1.67 x lOi Swelling

C&alg -iK)* number

&g/cm?* 1.3 1.3 1.3

0.3 0.3 0.3

0 0 1

Fluidized bed conditions Supercial fluidizing velocities Bed temperature Bed particle size Oxygen concentration Hydrodynamic lo-

parameters*

21.2mss’ 1048 and 1283°K 620pm rr 13% for Equation p=q=os

10

* In the absence of reported data, reasonable parameter values are chosen to keep the number of adjustable values at a minimum. Minor variations could be expected but not enough to invalidate the

b

,

0

I

2

I d(mm)

I

4

I

6

18 t(s)

Figure 5 Comparison between time dependent devolatilization predicted by the isothermal particle model of Borghi et al.’ (---1023 K, ----, 1323 K) and Model I (----, 1023 K, p, 1323 K) for 8% oxygen concentration, 3 mm Montana lignite particle, Bi, = 1, kinetic parameters for Montana lignite: k, = 1.67 x lo-‘a s-i; E, =236 kJ/mol; 8=46 kJmol-i

1c- , 0

808

I

2

I

d(mm)

FUEL, 1986, Vol 65, June

1

4

I

,

Figure 4 Comparison between experimentalla and predicted volatile burn-out times using Model I and Equation 10: 0, 1048°K; l ,1283”K. (a) Rexco, (b) Texas lignite and (c) Nostell

A single particle

model for the evolution

the maximum temperature during devolatilization of the coal particle. The maximum temperature during devolatilization according to Borghi’s’ model would be approximately T,; the present model suggests that the surface temperatures may be substantially higher. These higher temperatures are expected to have an important influence on the subsequent combustion of char. Additionally the temperatures may be higher than the ash-softening temperature which could lead to the formation of ash shells around the coal particles possibly prior to the char combustion stage. This has been observed experimentally for Mississippi lignite49. CONCLUSIONS

8 9 10 11 12 13 14 15 16 17 18 19 20 21

Parametric studies suggest that for isolated particles, vo!atile burn-out time depends more on bed temperature (consequently on the flame temperature) than on types of coal with similar physical properties. However, the determination of the devolatilization structure including the pre-ignition period would depend on the type of coal. Consequently, it is recommended that results on swelling properties and pyrolysis studies should also be reported along with combustion results to facilitate a more complete understanding. The proposed model predicts volatile burn-out times for single isolated coal particles in stagnant as well as convective oxidizing environments. The d2 law for volatile burn-out times is expected to be applicable only for isolated particles in stagnant oxidizing environments. For convective oxidizing environments, the exponent of d is expected to be lower. For fluidized beds the combustion of volatiles is assumed to take place when the coal particle is in the bubble phase. In the emulsion phase, devolatilization is assumed to take place under pyrolysis like conditions. This appears to be consistent with reported visual observations. Moreover, with the introduction of phase residence time factors, the model predictions are in good agreement with experimental data for devolatilization times reported in the literature. The non-isothermal coal particle model predicts higher surface temperatures which would have an influence in the subsequent combustion of char. The higher temperatures may exceed the ash-softening temperature leading to the formation of ash shells and incomplete combustion.

22 23 24 25 26

ACKNOWLEDGEMENTS

46 47

The author wishes to thank Ms. Lyn Earnshaw Tonkin for typing the manuscript.

27 28 29

30 31 32 33 34 35 36 37

38 39 40 41 42 43 44

45

and Julie 48 49

and combustion

of coal volatiles:

P. K. Agarwal

La Nauze, R. D. Fuel 1982,61, 771 Agarwal, P. K., Genetti, W. E. and Lee, Y. Y. Fuel 1984,63, 1157 Agarwal, P. K., Genetti, W. E. and Lee, Y. Y. Fuel 1984,63, 1748 Pyle, D. L., Fluidized Combustion Models (Rapporteur’s Report) Inst. of Fuel Symp. Ser. 1975, 2(l), 6 Atimtay, A. ‘Fluidization’, (Eds. Grace, J. R. and Matsen, J. M.), 1980, 159 Pillai, K. K. J. Inst. Energy 1981, 54, 142 Stubington, J. F. J. Inst. Energy 1980, 53, 191 Essenhigh, R. H. J. Eng. Pow;; 1963,85, 183 Ivanova. I. P. and Babii. V. L. Teoloeneraerika 1966. 13(4). 54 Stambuleanu, A., ‘Flame Comb&ion Processes in In&try’, Abacuss Press, Kent, 1976 Carabogdan, I. St. cert. merg. electr. Bucaresti, 1965, lS(2) Carabogdan, I. St. cert. energ. electr. Bucaresti, 1967, 1 Ragland, K. W. and Weiss, C. A. Energy 1979, 4, 341 Yates, J. G., Macgillivray, M. and Cheesman, D. J. Chem. Eng. Sci. 1980, 35, 2361 Yates, J. G., personal communication, 1983 Pillai, K. K. j. Inst. Energy 1982, 55, 132 Jung. K. and Stanmore. B. R. Fuel 1980. 59. 74 La Gauze, R. D. Chem.‘Eng. Res. Des. J&x&y 1985,63, 3 Becker, H. A., Beer, J. M. and Gibbs, B. M. Institute ofFuel Symp. Ser. 1: Fluidized Combustion 1975 Gibbs, B. M. Institute of Fuel Symp. Ser. 1: Fluidized Combustion 1975 Anthony, D. B. and Howard, J. B. A. I. Ch. E. J. 1976,4, 625 Anthony, D. B., Howard, J. B., Hottel, H. C. and Meissner, H. P., Fifteenth Symp. (I&.) Combustion, Combustion Institute, Pittsburgh, 1975, 103 Kutateladze, S. S. ‘Fundamentals of Heat Transfer’, Academic Press, New York, 1963 Jakob, M. ‘Heat Transfer’, John Wiley and Sons, New York, 1959 Agarwal, P. K., Ph. D. Dissertion, University of Mississippi, 1984 Howard, J. B. Essenhigh, R. H., Eleventh Symp. (Intl.) Combustion, Combustion Institute, Pittsburgh, 1967, 399 Thomas, G. R., Harris, J. J. and Evans, D. G. Combust. FIumr 1968, 12, 391 Annamalai, K. and Durbetaki, P. Cornbust. Flame 1977,29, 193 Karcz, H., Kordylewski, W., Rybak, W. and Zembrzuski, M. Arch. Cornbust. 1983, 3(4), 247 Dennis, J. S., Hayhurst, A. N. and Mackley, I. G., Nineteenth Symp (Intl. ) Combustion, Combustion Institute, Pittsburgh, 1982, 1205 Kanury, A. M., ‘Introduction to Combustion Phenomena’, Gordon and Breach Publishers, New York, 1975 Wen, C. Y. and Dutta, S. in ‘Coal Conversion Technology’(Ed. C. Y. Wen and E. Stanley Lee), Addison-Wesley, 1979, 57 Badzioch, S.. Gregory, D. R. and Field, M. A. Fuel 1964,43,267 Agarwal, P. K. Chem. Eng. Res. Des. 1985,63, 323 Darton, R. C., La Nauze, R. D., Davidson, J. F. and Harrison, D. Truns. I. Chem. E. 1977, 55, 274 Cowley, L. T. and Roberts, P. Proc. Fluid. Combustion Con& Capetown 198 1, 2(5.3), 443 Yates, J. G. and Walker, P. R. ‘Fluidization’, (Eds. Davidson, J. F. and Keairns, D. L.), Cambridge University Press, Cambridge, 1978 Kunii, D. and Levenspiel, O., ‘Fluidization Engineering’, Wiley, New York, 1968 Kondukov, N. B. et al. Intern. Chem. Eng. 1964, 4, 43 Mickley, H. S., Fairbanks, D. F. and Hawthorn, R. D. Chem. Eng. Progr. Symp. Series 1961, 57(32), 3 1 Andrei, M. A., Sarofim, A. F. and Beer, J. M., paper presented A. I. Ch. E. 86th Annual Meeting, Houston, April 1979 Genetti, W. E., personal communication, 1984

REFERENCES Selle, S. J., Honea, F. I. and Sondreal, E. A. ‘New Fuels and Advances in Combustion Technology’, Institute of Gas and Technology, Chicago, 1979 Yaverbaum, L. H., ‘Fluidized Bed Combustion of Coal and Waste Materials’, Noyes Data Corporation, 1977 Avedesian, M. M. and Davidson, J. F. Trans. 1. Chem. E. 1973,51, 121 Ross, I. B. and Davidson, J. F. Trans. I. Chem. E. 1979,57,215 Chakraborty, R. K. and Howard, J. R. J. Inst. Fuel 1978,51,220 Park, D., Lenenspiel, 0. and Fitzgerald, T. J. A. I. Ch. E. Symp. Ser. 1981, 77, 116 Borghi, G., Sarofim, A. F. and Beer, J. M., paper presented A. I. Ch. E. 70th Annual Meeting, New York, November 1977

NOMENCLATURE Ai(i=l Bi, Bi, Bif

to E’)

coefficients heat transfer Biot number based on particle radius heat transfer Biot number based on particle diameter Biot number corresponding to the flame radius specific heat of the coal specific heat of the gas

FUEL, 1986, Vol 65, June

809

A single particle model for the evolution and combustion of coal volatiles: P. K. Agarwal d E

particle diameter, (mm) activation energy, (kJmol_‘) mean of the activation energy E, distribution, (kJmol_‘) stoichiometric coefficient (g fuelg -’ 0,) f heat of combustion of volatiles AH constant, (s/mm”) k,, thermal conductivity of the gas k, thermal conductivity of the coal k preexponential factor, (s-l) ko constant m constant n N,(j=l to c0) coefficients N,’ (i = 1 to W) coefficient Nusselt number N% probability of the coal particle being in P the bubble phase Prandtl number Pr probability of the coal particle being in 4 the emulsion phase Universal Gas Constant (kJmol_’ K.) R radius of the particle, (mm) RO Reynolds number based on coal particle Re, diameter radial position within particle (mm) radial position corresponding to f-1 temperature ( Tl, (mm) radial position corresponding to r2 temperature T2, (mm) swelling factor time, (s) t t’ = t - ti,, time in the post-ignition stage, t’ (s) ignition delay (s) t temperature, (K) ;_ environment/bed temperature, (K) T,

810

FUEL, 1986, Vol 65, June

T

V*

X X a”&?

YO,

original temperature of the cold coal particle, (K) temperature at which devolatilization commences, (K) temperature at which devolatilization is complete, (K) flame temperature, (K) initial volatile content of the coal, (gg-’ dry coal) fractional amount of volatiles retained volumetric average fraction of volatiles retained oxygen mass fraction in the environment

Greek Symbols a

z,’

thermal diffusivity of coal, (mm2s- ‘) roots momentum boundary layer thickness, (mm) thermal boundary layer thickness, (mm) density of gas, (gcmm3) density of coal, (gem - 3, standard deviation of the activation energy distribution, (kJmo1 - ‘) devolatilization time measured as the time between flame ignition and extinction, (s) devolatilization time measured as the total lapse time to flame extinction, (s) devolatilization time if the coal particle was to remain in the emulsion phase, (s) devolatilization time if the coal particle was to remain in the bubble phase, (s) parameter defined in Equation 7b