Combustion of pulverized coal using waste carbon dioxide and oxygen

Combustion of pulverized coal using waste carbon dioxide and oxygen

COMBUSTION A N D F L A M E 72: 301-310 (1988) 301 Combustion of Pulverized Coal Using Waste Carbon Dioxide and Oxygen C. S. WANG, G. F. BERRY, K. C...

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COMBUSTION A N D F L A M E 72: 301-310 (1988)

301

Combustion of Pulverized Coal Using Waste Carbon Dioxide and Oxygen C. S. WANG, G. F. BERRY, K. C. CHANG, AND A. M. WOLSKY Energy and Environmental Systems Division, Argonne National Laboratory, Argonne, Illinois 60439

Combustion of pulverized coal in CO2/O 2 as well as in air atmospheres is studied. Predictions using a onedimensional computer code were compared with actual experimental data from tests conducted by Battelle Columbus Laboratories. The comparison of predicted and measured data for all test cases show that the observed trends of distributions of temperature and of species concentrations are generally predictable. The study confirms that the combustion of pulverized coal can be completed in a CO2/O 2 atmosphere over a range of CO2-to-O2 mole ratios between 2.23 and 3.65.

I. INTRODUCTION Flooding with CO2, one of the most attractive enhanced oil recovery (EOR) technologies, is currently proposed to increase the production of crude oil but may in the future be constrained by the limited supplies of sufficiently pure and economical CO2. A concept for the combustion of pulverized coal in pure oxygen instead of air is proposed as an economical means of producing high-purity CO2 from utility power plants [1]. In the process being investigated, a portion of the resultant CO2-rich flue gas is recycled to the combustor to avoid too high a flame temperature using pure O2. Small amounts of SOx and NOx formed in the pulverized coal combustion would not have a detrimental effect on the use of CO2 for EOR technique. The process would thus eliminate the need for flue gas pollution control and appear to be economically competitive with other methods of producing high-purity CO2. Indeed, DOW has recently withdrawn its amine process from the market. This concept of CO2 recovery is being investigated by Argonne National Laboratory (ANL), with support from the U.S. Department of Energy. The experimental part of the study of pulverized coal combustion in various atmosCopyright © 1988 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017

pheres was performed by Battelle Columbus Laboratories (BCL) under contract to ANL [2]. This paper presents the results of the modeling part of this study. The purposes of the present modeling study are (1) to assess the feasibility of burning pulverized coal in CO2/O2 atmospheres under the conditions prescribed in the experimental studies conducted by BCL, (2) to compare the combustion performance of the test combustor burning pulverized coal in a CO2/O2 atmosphere to that burning in air, and (3) to provide a means of interpreting the experimental results. Several models have been developed for study of the combustion process of pulverized coal, and reviewed by Smoot et al. [3]. Among them, the one-dimensional coal combustion or gasification (1-DICOG) computer code developed by the Combustion Laboratory of Brigham Young University was selected for the theoretical combustor modeling study [4, 5]. The focus of the present work is not an evaluation of 1-DICOG which has been previously published and reviewed. The 1DICOG computer code was selected because of simplicity and the ability to investigate economically numerous experimental parameters, thereby facilitating the preparation of a test matrix. This

0010-2180/88/$03.50

302

C . S . WANG ET AL.

model describes the" response of a coal-particle system to its thermal, chemical, and physical environments. Moisture vaporization, coal reaction, gas-particle interchange, radiation, and gasphase combustion are considered.

The volatile components react further in the gas phase. Char reacts heterogeneously with oxidizer (CO2, 02, H20) at the particle surface by the following three reactions [9, 10]:

2. THEORETICAL MODEL

i C+~O 2 kco,

k = T j ( - 1.68× 10-2+ 1.32× 10-5 Tj) re~s,

The system under consideration is a pulverized coal combustion in a horizontal, cylindrical combustor. The schematic of a test combustor is shown in Fig. 1. A coal particle is assumed to be composed of specified amounts of raw coal, char, ash, and moisture. The raw coal, or that portion of the coal free of dry ash, undergoes devolatilization to volatile components and char. The two-competing-reaction model of coal devolatilization can give a reasonably good fit to the experimental data for application to high intensity combustion like the present study case [6]. Thus, the two-competing-reaction model, reported by Ubhayakar et al. [7], was used for the simulation of the process of coal devolatilization. They suggested that pyrolysis could be modeled with the following pair of parallel, first-order irreversible reactions: raw coal ~-k0.39 (volatiles)+0.61 (char),

A H ° = - 9.210 × 106 J/kg; C + CO2 ~ 2 C O , k = 4 . 4 T j e x p ( - 19476/~) m/s, AH* = + 1.439 x 107 J/kg; C+H20

E

~'~et

L

(5)

where Tj is the coal particle temperature (K) for jth size. The second char-oxidation reaction [Eq. (4)] plays a crucial role in CO2/O2 atmospheres, particularly at relatively high mole ratios. The gasphase combustion of the resultant combustible species constitutes, then, the second step of the char-combustion process. Thermal radiation in coal combustion systems has a significant effect on heat transfer. In the present calculations, a transparent gas phase and

(2)

where k2 = 1.46 x 1013 e x p ( - 3 0 2 0 0 / T j ) s -J.

I

~ 2 C O + H2,

A H ° = + 1.096 X 107 J/kg;

where kl = 3.7 x 105 e x p ( - 8 8 9 0 / T j ) s 1; k2

(4)

k = 1.33 Tj exp( - 17665/Tj) m/s,

(1)

raw coal --* 0.8 (volatiles)+ 0.2 (char),

(3)

1.829m 1.372m 0.864m "C

"E

I

I

Ports

1F I

J

Exit1---,~ To Stack

2.134m

Fig. 1. Schematic view of test combustor showing the positions of ports C, E, F.

COAL COMBUSTION IN CO: AND

nonscattering gray particles are assumed. Therefore, the only radiative energy transfer is between the particles within the combustion system and between the particle cloud and the walls. The zone method is used for the numerical solutions. The equations required to solve these radiative interchange within a one-dimensional, particle-laden combustion system by the zone method are summarized by Smith and Smooth [5]. Due to the one-dimensional assumption, the entrainment of the secondary air into the primary jet and the recirculation of the downstream fluids back to the upstream were required as inputs. By observing the measured mean axial velocities near the front end of the combustor at the centerline and wall regions, an amount of 10% of the total flow rates was selected as a recirculation value for the present study. The secondary air addition rate was assumed to be a function of the growth area angle. The growth area angle is an angle between the centerline of the combustor and the outer edge of the expanding inlet stream. The criterion used in this study for proper specification of the growth area angle was that the inlet stream (See Fig. 2) should fully expand into the combustion chamber to match the experimental condition in which Primary 0.01905 rn

~

Secondary One of Two Secondary Mixing and Recirculation Regions

2.134 m

0.6096 m

303

0 2

j

Fig. 2. Schematic view of mixing process in test combustor.

recirculation was no longer observed. A growth area angle of 13" was selected and used for the present analysis of all four test cases. The one-dimensional coal combustion or gasification (1-DICOG) computer code developed by the Combustion Laboratory of Brigham Young University was used for the present test data analyses. The major assumptions of 1-DICOG [4] are 1. negligible molecular and thermal diffusions in both radial and axial directions, i.e., a onedimensional first-order formulation; 2. gas phase in local equilibrium; 3. spherical particles of uniform local particle temperature; 4. coal reactions taking place by competing processes of devolatilization, gaseous homogeneous reactions, and heterogeneous char oxidation; 5. multiple particle sizes (disperse phases); and 6. nonequilibrium velocities between gas an particles. 3. D E S C R I P T I O N OF BCL'S COAL COMBUSTION TESTS

3.1. Combustor Geometry and Operating Conditions The experiments in which pulverized coal was burned in air as well as in COJO2 atmospheres were conducted at BCL by use of a subscale combustor which was operated to simulate, approximately, important combustion conditions such as flame temperature, combustor outlet temperatures, and residence times. The test combustor is a horizontal refractory lined, and cylindrical furnace without swirl flow, shown in Figs. 1 and 2, which is capable of burning pulverized coal at rates from 3.2 × l 0 -3 k g / s to 8 . 2 X 10 -3 k g / s (about 1/ 5000 that of a large utility boiler furnace). The test combustor was operated with a once-through gas supply of either air or a CO2/O2 mixture to avoid the experimental difficulties of cooling and recycling stack gas. Although the inlet conditions of this experimental combustor do not completely simulate the industrial boilers, the purpose of the present work is only to study the combustion characteristics inside the combustor.

304 3.2. Selection of Test Cases

A matrix of four tests were selected to accomplish the purposes of this study. Test 1 is the combustion of pulverized coal in an air atmosphere at conditions representative of those used in large utility boiler furnaces. Test 1 would provide a baseline with which to compare results of the following tests where pulverized coal would be burned in a CO/O2 atmosphere. Tests 2, 3, and 4 are the combustion of pulverized coal in COJO2 atmospheres at mole ratios of 3.65, 2.42, and 2.23, respectively. Test 2 would examine combustion performance produced by the direct substitution of CO2 for N2 in air (about the same mole ratio) as the oxidant diluent. It would be expected that the flame temperature in Test 2 would be cooler than the coal-air combustion for the reason of the greater heat capacity of CO2 reducing flame temperature. Tests 3 and 4 were designed to obtain approximately the same theoretical adiabatic flame temperature as that for the coal-air combustion. Table 1 summarizes input data used in predicting results of the four test cases with 1-DICOG computer code.

C . S . WANG ET AL. the furnace based on a mole fraction basis has been established [8]. The mean gas temperature is solved from an integration relationship among the enthalpy of the mixture, average velocity, and average mole fraction of the gaseous species. The calculated mean values of temperature and species concentrations from 2-D measurements have been plotted in Figs. 4-7 as measured quantities. 4. RESULTS A N D D I S C U S S I O N Four experimental tests which were conducted at Battelle Columbus Division were modeled. Test 1 is the combustion of pulverized coal in an air atmosphere; Test 2, 3, and 4 are the combustion of pulverized coal in composite CO2/O2 atmospheres at mole ratios of 3.65, 2.42, and 2.23, respectively. Calculations were performed using 1-DICOG computer code for the test combustor shown in Figs. 1 and 2 based on the coal compositions and the input data listed in Tables 1 and 2, respectively. Three measured discrete coal particle sizes (20, 40, and 60 /~m), were used in the TABLE 1

Coal Properties and Particle Size Distribution

3.3. Coal Properties

The Wage coal from Colorado was used for study mainly for the reason that an important geographical area of application for the proposed CO2 recovery process would be the U.S. Southwest. Results of the proximate and ultimate analyses of coal composition are summarized in Table 1. One important consideration in obtaining accurate predictions for pulverized coal combustion is a reasonable particle-size distribution. Three discrete sizes (see Table 1) were used in the study to simulate the measured size distribution of coal particles. These three coal particle sizes were measured at ANL's Chemical Division. 3.4. Presentation of Measured Data

In order to compare the 2-D measured values of velocity, species concentration, and temperature with 1-D predictions, a calculation method that averages the measured quantities radially across

Parameter

% of Total Weight

Proximateanalysis Moisture Volatile materials Fixed carbon

3.37 40.70 50.19 5.74

Ash

5.94 5.02 73.92

Ash Ultimateanalysis H c N

S O

HHV (kJ/kg)

1.77

0.43 12.92 29,015

Particle diameter s

20 #,m

40 #m 60/~m

13.13 48.01 38.86

As measured in the Chemistry Division of Argonne National Laboratory.

305

C O A L C O M B U S T I O N IN CO2 A N D 02 TABLE 2

Input Information for Modeling Study Operating Condition CO2/O2 mole ratio Primary gas flow rate u (kg/s × 10 -3) Secondary gas flow rate b (kg/s x 10 -3) Coal flow rate c (kg/s × 10 -3) Combustor wall temperature (K)

Test 1

Test 2

Test 3

Test 4

6.748 39.73 4.002 1600

3.65 9.785 58.63 4.000 1470

2.42 9.370 40.30 4.237 1510

2.23 10.13 37.50 4.118 1530

o Temperature of primary gas: 298.2K. b Temperature of secondary gas: 394.3K. " Temperature of coal: 298.2K.

4.1. Coal Burnout

calculations. Since a limited amount of information on recirculation flow in one-dimensional modeling applications has been found in the literature, recirculation flow rates were selected as 10% of the total inlet gas flow rate (primary and secondary) based on the observation of axial velocity measurements near the front end of the test combustor. This value is consistent with those used by other researchers. Both the measured and calculated results of Test 4 are very similar to that of Test 3. For clarity, the results presented in Figs. 3-7 will not include Test 4.

0.9

Figure 3 shows the predicted axial profiles of the mass fractions of coal components for Tests 1-3. For coal combustion in an air atmosphere (Test 1), pulverized coal is heated by radiation from the combustor wall and the downstream flame, and by the recirculation of hot gases. Rapid devolatilization is predicted to begin at about 0.4 m from the combustor inlet and to be complete at about 0.6 m. As the coal devolatilizes, it liberates gaseous and liquid volatile materials and forms char. The mass fraction of char rises to a peak at the point of

".~

\ 0803.~

- -

o.6 . . . . . . . ............

Total Raw Coal Char Water

ii ~ ~,"

,

o.s-

13

0.4-

:l '\/,

03o._

j

0.1 1,2,3 o

I

o

, o2

._..-" . , 0.4

tl

/

~,~ --

,

,

,, \

ii

\-.,

o6

o.e

,

,

~

1.2

Axial Distance (m)

Fig. 3. Comparison of calculated axial distributions of component mass fractions for coal combustion in various atmospheres (Tests 1-3).

306

C . S . WANG ET AL. 2400 2200 20003

1

1800 1600 ¢'

1400 -

'~

1200-

~-

1000 -

I--

800 600 Predicted

400 ....

200 -

012

0!4

0!6

i

018

i

,

12

114

Measured

i

18

l!S

i

2

2!2

Axial Distance (m) Fig. 4. Comparison of calculated and measured axial temperature distributions for coal combustion in various atmospheres (Tests 1 - 3 ) .

complete devolatilization. The char reacts heterogeneously with gaseous oxidizers (such as 02, CO2, and H20) and then produces the combustible products. These combustible products and volatile materials further react with the oxidizer. For Test 1, the predicted complete coal burnout occurs at an axial distance of 0.81 m. For coal combustion in CO2/O2 atmospheres (Test 2--4), the combustion processes (such as coal devolatilization, char oxidation, and coal burnout)

are similar to that in air atmosphere. The axial distances required for complete coal burnout (or the flame lengths) in the four tests are listed in Table 3. Based on Battelle's measured unburned carbon content in ash samples [2] and based on all carbon equally distributed among all fly ash (captured and noncaptured), the measured carbon conversion efficiencies at ports C, E, and F are listed in Table 4. In order to compare the calculated and measured values of coal burnout (or

303 03

25-

~

Predicted

----

Measured

2

J3t

~" "o

- -

20-

1

o~

o E,E

15-

10-

0

('~

3

~ .....

5-

~_ .......

-~ . . . . . . .

.~ - y _ , . .

1 0

012

014

016

01.0

2 i

112

114

110

118

~'

212

Axial D i s t a n c e (rn)

Fig. 5. Comparison of calculated and measured axial distributions of 02 concentration for c o a l combustion in various atmospheres (Tests 1 - 3 ) .

COAL COMBUSTION IN CO2 AND 02

307

100 "

2.-

_ _ ~ - - ~

----. . . . . .

~"

. . . . . .

~

........

~.t . . . .

Lv . . . .

80-

,.¢1 Z"

'1o o~

60-

-

Predicted

-

0

....

Measured

¢-. .0

40-

et-

20-

O

1

o

o12 oi,

f

~

i

i

i

0.6

0.8

1

.......

~

....

[

112

""9

i

1.4

116

11.0

2

21.2

Axial Distance (m) Fig. 6. Comparison of calculated and measured axial distributions of CO2 concentration for coal combustion in various atmospheres (Tests 1-3).

efficiencies are 96, 95, 97, and 96% for Tests 1, 2, 3, and 4, respectively. Good agreement has been obtained from these comparisons. Figure 8 also indicates that both measured and calculated combustion efficiencies of Test 2 have the same trends of delaying their complete combustion until further downstream locations with respect to those of Test 1, 3, and 4. Our study reveals that the higher the ratio of CO2 to O2 in a coal combustion atmosphere, the longer the distance needed for

combustion) efficiency, the measured carbon conversion efficiencies listed in Table 4 have been plotted in Fig. 8. The predicted combustion efficiencies for all four test cases are also shown in this figure. The predicted 100% coal combustion efficiencies occur at locations 0.81, 1.15, 0.72, and 0.69 m (same values as the calculated flame lengths listed in Table 3) from the combustor inlet for Tests 1, 2, 3, and 4, respectively. At these same locations, the measured coal combustion 1.5-

•--

?,

3 &

- -

Predicted

1

....

Measured

(~

1.2-

t~ ~t t~

am

I I

"10

~t

t I

0.9-

3

o

E c O

0.6-

e(D O (.~

0.3-

01.2

i

0,4

0.6

i

I

i

i

i

i

i

0.8

1

1.2

1.4

1.6

1.8

2

v 2.2

(m) Fig. 7. Comparison of calculated and measured axial distributions of CO concentration for coal combustion in various atmospheres (Tests 1-3). Axial Distance

308

C. S. WANG ET AL. TABLE 3

TABLE 4

Calculated Burnout Distance

Measured Carbon Conversion Efficiency (%)

Flame length (m) Mole ratio of C02/02 Stoichiometric ratio

Test 1

Test2

Test3

Test4

Port

Test 1

Test 2

Test 3

Test 4

0.81

1.16 3.65 1.18

0.72 2.42 I. 18

0.69 2.23 1.18

C E F

96.6 99.4 99.7

90.7 96.2 99.3

97.8 99.1 99.9

97.3 99.5 99.9

--

I. 19

complete coal burnout. Test 3 shows the closest resemblance to Test 1.

be confirmed from Fig. 8 which shows that the combustion efficiencies of Tests 1, 3, and 4 reaches a high value (e.g., 98%) at upstream location (about 1 m from combustor inlet); while that of Test 2 reaches its high value at downstream location (98% at x = 1.6 m). Figure 4 also summarizes the predicted and measured temperature distributions in three test atmospheres. From this figure, it is concluded that Tests 1 (air) and 3 (CO2/O2 at 2.42 mole ratio) have very similar temperature distributions, whereas both measured and predicted results of Test 2 show that the temperature peaks shift to the right and the coal burns at a relatively lower flame temperature relative to Tests 1 and 3. The thermal radiation enhancement by CO2 in Test 2 may reduce the flame temperature and need longer residence time (or flame length) for char pyrolysis (see Fig. 3). The discrepancy between the measured and pre-

4.2. Temperature Distribution Figure 4 compares the temperature distributions predicted by 1-DICOG with those measured by Battelle. The comparison between the measured and predicted temperature profiles shown in this figure illustrates that the coal particles in Test 2 burned more moderately than predicted in the model; the increase of measured mean temperature profile indicates that combustion still continued to occur in the aft region of Battelle's combustor for Test 2 (CO2/O2 = 3.65 mole ratio). The nearly fiat measured mean temperature profiles in the other three tests, however, indicates that not much heat was released in the downstream region of the combustor. The above reasoning can 100 - 98



o~

96

o to :I= UJ

=_o

Measured

....

94 -

i:

Predicted o

Test 1



A

Test 2



D

Test 3

4.

O

Test 4

!

i!/

92-

~= E O

90-

o

ip , H ii

88-

86

f~]

0.0

012

014

0.6

i i J , View Port ' #C I

I

0.8

110

View Port #F

View Port #E

11.2

a

I

1.4

1.6

1.8

2.0

Axial D i s t a n c e (m)

Fig. 8. Comparison of measured and predicted combustion efficiencies for all four test cases.

COAL COMBUSTION IN CO2 AND 0 2 dicted gas temperatures at downstream location may be due to the assumptions of specified wall temperatures and recirculation flow rates required for model calculations. As predicted by 1-DICOG, the combustion is a strong function of wall temperature profile, chemical kinetics and coal/ gas mixing. The discrepancy may also be due to the inadequate measurements in velocities as indicated in Refs. [2] and [8]. These inadequate velocity measurements affected the reduction of 2D measured temperature data to 1-D representation for comparison with the computer code predictions.

4.3. Species Concentration Distribution Similar observations can also be drawn from the studies of axial distributions of the CO2 and 02 concentrations (Figs. 5 and 6). The nearly fiat profiles in the downstream region of the combustor for all four tests illustrate that only minor combustion reactions occurred in this region. In Test 2, the measured 02 concentration (see Fig. 5) decreases while the measured CO2 concentration (see Fig. 6) increases along the axial distance from the mid section to the end of the combustor. These results show that the combustion rate was still significant in the downstream region of the combustor. In other words, the combustion intensity was more evenly distributed along the combustor for Test 2 than was the case for the other three tests. Predicted and measured CO concentrations for Tests 1-3 are displayed in Fig. 7, and the comparisons show that the theoretically predicted CO species appeared in regions upstream of those where the large quantity of CO species is found in experimental observations. These deviations between predictions and the measurements may stem from two of the assumptions adopted in the 1DICOG model: that gaseous species are well mixed (i.e., with negligible molecular and thermal diffusions in the radial direction) and in the state of local equilibrium at any axial position. These two assumptions lead to the results that the CO species in theoretical predictions is formed in the upstream regions of the combustor and then converted quickly to the final product (CO2) via further

309 oxidation with 02. As shown in Fig. 7, the CO concentrations measured in Tests I and 2 are much higher than the ones predicted; this is to be expected according to the assumption that gaseous species are well mixed, a condition that does not occur in a real pulverized-coal flame. The same conclusion also applies to the comparisons for Tests 3 (see Fig. 7) and 4, however; in those cases, no data are presented for the upstream regions of the combustor in Battelle's experimental results, and peak predictions therefore cannot be correlated with experimental results. Most of the CO observed in the coal combustion processes is formed by the char oxidation mechanism. Temperature and oxidizer concentrations (such as 02, CO2, and H20) are two important factors that determine local CO production. Both the higher predicted and measured CO concentrations profiles of Tests 3 and 4, relative to those of Test 1, are attributable to the effect of higher CO2 concentration in combustion atmospheres. The lower predicted and measured CO concentration profiles of Test 2, relative to those of Tests 3 and 4, are attributed to the much lower combustor temperature (even though Test 2 was performed in an atmosphere with a higher CO2/O2 ratio). These discrepancies between the predicted and measured CO results do not strongly influence the overall results or the temperature profiles since the CO concentrations formed in the pulverized-coal combustion process are very small compared to the CO2 and 02 concentrations. 5. CONCLUSIONS Four test cases of pulverized-coal combustion has been examined using the 1-DICOG computer code and compared with corresponding experimental results measured by Battelle. Both predicted and measured results indicate that pulverized coal can be burned in an atmosphere of CO2 and 02 over a range of CO2-to-O2 mole ratios of 2.23-3.65. Moreover, the combustion performance of the coal combustion in a CO2/O2 atmosphere with a 2.42 mole ratio (Test 3) is relatively close that that of a coal combustion in air (Test 1). The coal combustion in a CO2/O2 atmosphere with a 2.23 mole ratio (Test 4) performed at the highest

310 combustion intensity for both predicted and measured results, and this test had a slightly higher intensity than Test 3. Both predictions and experiments indicate that the coal combustion in a CO2/ 02 atmosphere with a 3.65 mole ratio (Test 2) has a lower combustion rate than that of the coal-air combustion, and consequently a longer distance is needed to complete the combustion process. The simple one-dimensional predictions of the 1-DICOG computer code have provided useful insights (gained from confirming experimental data) for studying the combustion processes of pulverized coal in various atmospheres. There is a discrepancy between the measured and predicted gas temperature profile, which may be due to inadequate assumptions required for this aspect of the model and due to inadequate velocity measurements. Comparisons between predictions with measurements of coal burnout (combustion efficiency) and species concentrations for the four test cases studied show that observed trends are predictable despite the differences between CO2 and N2 concentrations in combustion products gas. This encouraged us to pursue a full-scale industrial boiler test and use a more sophisticated multidimensional computer code for analyses of our new approach to CO2 recovery. The good agreement between the predictions and measurements suggests that 1-DICOG may be a useful tool for pretest analysis, thus producing more information which can be useful in preparing the test matrix.

This work is one o f several that present results obtained by an Argonne National Laboratory program, System Analysis for Waste Carbon Dioxide Utilization, and supported by

C . S . WANG ET AL.

the U.S. Department o f Energy, Washington, D.C., under Contract No. W-31-109-ENG-38.

NOMENCLATURE HHV k T 0 AH*

higher heating value (J/kg) reaction rate constant temperature (K) growth area angle (degree) heat of reaction (J/kg)

Subscripts j

jth particle size

REFERENCES 1. Abraham, B. M., Oil and Gas J. 80(11):68-75 (1982). 2. Weller, A. E. et al., prepared by Battelle Columbus Division, Argonne National Laboratory, Report ANL/ CNSV-TM-168, Argonne, IL, Oct. 1985. 3. Smoot, L. D., Hedman, P. O., and Smith P. J., Progress in Energy and Combustion Science 10:359-441 (1984). 4. Smith, P. J., and Smooth, L. D., Electric Power Research Institute Report EPRI CS-2490-CCM, Vol. 2, July 1982. 5. Smith, P. J., and Smoot, L. D., Combustion Science and Technology 23:17-31 (1980). 6. Jamaluddin, A. S., Truelove, J. S., Well, T. F., Combust. Flame 62:85-89 (1985). 7. Ubhayakar, S. K., Stickler, D. B., Von Rosenberg, C. W., Jr., and Gannon, R. E., 16th Syrup. (International) on Combustion, The Combustion Institute, Pittsburgh, 1976 pp. 427-436. 8. Berry, G. F., Wang, C. S., Chang, K. C., Wolsky, A. M., and Choi, U. S., Argonne National Laboratory Report, ANL/CNSV-57, Argonne, IL, Oct. 1986. 9. Field, M. A., Combust. Flame 13 (1969). 10. Mayers, A. M., Am. Chem. Soc. J. 56 (1934). Received 6 January 1986; revised 5 October 1987