Model predictions of the extent of heterogeneous coal combustion during rapid evolution of volatiles

Model predictions of the extent of heterogeneous coal combustion during rapid evolution of volatiles

0360.5442/92 $5.00 + 0.00 Copyright 0 1992 Pergamon Press Ltd Energy Vol. 17, No. 7, pp. 669478, 1992 Printed in Great Britain. All rights reserved ...

861KB Sizes 0 Downloads 47 Views

0360.5442/92 $5.00 + 0.00 Copyright 0 1992 Pergamon Press Ltd

Energy Vol. 17, No. 7, pp. 669478, 1992 Printed in Great Britain. All rights reserved


SANJAY AGRAWALt and K. C. MJDKJFF Department of Mechanical Engineering, The University of Alabama Tuscaloosa, Alabama 35487-0276, USA (Received

3 June



for publication

18 March


Abstract - Two relatively simple, single-particle coal combustion models are developed and used to predict the extent of heterogeneous combustion during rapid devolatilixation. The lirst model uses the flame sheet approximation while the second employs &rite gas-phase reaction rates. Both models predict that small particles (< 10 w diameter) burn heterogeneously and large particles (> 100 w diameter) burn homogeneously, but heterogeneous mass loss is severely underestimated by the simpler flame-sheet model in comparison to the more realistic link-ratechemistry model for intermediate sized particles typical of a utility grind. Small particle size, high oxygen concentration and low devolatilization rate, in that or&r of importance, yield more extensive heterogeneous combustion, while temperature, volatiles composition, gas-phase kinetics, and surface reaction rates have negligible impact.

INTRODUCTION The Faraday mechanism, which simplifies coal particle burning to the three sequential steps of (i) particle heatup and devolatilization, (ii) homogeneous ignition and burning of volatiles throughout the period of rapid volatiles evolution, and (iii) heterogeneous char burnout, has been the dominant paradigm of coal particle combustion for many decades. 1 However, for sufficiently large oxidizer concentration or small particle size, the volatiles flux is apparently insufficient to shield the particle surface from oxidation, and the heterogeneous regime overlaps the regime of homogeneous volatiles burning. The amount of fixed carbon combustion and the rate of heterogeneous versus homogeneous removal of volatile matter in coal dust flames can be estimated experimentally from proximate analyses of solids samples removed after various flame residence times. Such a method of cakulating the extent of heterogeneous mass loss was developed in a seminal study by Howard and Essenhigh 2~ in the mid-1960s. Their results appear to demonstrate significant heterogeneous combustion during rapid devolatilization, particularly for particles smaller than 65 cun diameter. The results of more recent experimental and analytical studies also show that heterogeneous ignition and/or combustion can occur for sufficiently small particles.4-9 Saito et al lo recently reported measurements of significant heterogeneous combustion for particles much larger than 65 ~.un that were burned in 21 percent oxygen. Jn the intervening years since their study, some investigators 11.12of pulverized-coal devolatilization have inferred that the results of Howard and Essenhigh may be due not to heterogeneous combustion but simply to evolution of volatiles in excess of that predicted by the ASTM proximate analysis test. In fact, the existence of extensive heterogeneous combustion during rapid devolatilization remains somewhat conttoversial. and the Faraday mechanism continues to enjoy widespread application in coal combustion modeling and analysis. 13-16 Whether coal volatile matter is consumed heterogeneously or homogeneously is critical in several processes, e.g., the formation of pollutant species, l7 the interpretation of radiative emission measurements during multiple-wavelength infrared pyrometry l8 and the modeling of coal t Resent Addtws: Department of Mechanical Engineering, Michigan State University, East Lansing. MI 48824; author to whom amspondence should be addressed. 669



combustion. In order to investigate the extent of heterogeneous combustion during rapid volatiles evolution, a pair of relatively simple, single-particle combustion models are developed here. The models are used to estimate the influence of various physical parameters on heterogeneous combustion. Comparison of these models to experimental results with some success is reported by Agrawal.l9 It should be pointed out that the applicability of these single-particle models is limited in situations where particle cloud combustion effects are important The use of more sophisticated models along the lines of Annamalai and Bamalingam u, is warranted for the case of high particle concentrations where cloud effects are predominant MODEL DEVELOPMENT Steady-state, isothermal, single particle combustion models are developed to predict the gas-phase species mass fraction profiles, the surface mass flux due to heterogeneous combustion, and that due to homogeneous devolatilization. Gas species considered are 0 2, CO, CO 2, H20, volatile species CH, 0,, and inert, diluent species N. Additional assumptions are that all gases are ideal and have the same diffusivity, that mean molecular weight, density and pressure of the gas are constant, that particles are spherical and that only processes varying in the mdial direction are important and that mass lost heterogeneously has the elemental composition of the solid phase. Two models are developed, a thin flame sheet model that assumes infinitely fast gas-phase chemistry, and a finiterate gas-phase chemistry model. Flame Sheet Model- The flame-sheet model assumes inllnitely rapid gas-phase kinetics and follows the work of Libby and Blake,” but it is extended to account for thezresence of H and 0 in the to CO2 and H@ in an fuel. Volatiles evolved from the particle are oxidized completely in&&&mally-thin flame sheet, The flame stands at the location where fuel and oxidizer meet in stoichiometric proportions, which can be at the particle surface for a sufficiently weak volatiles flux. Formed CO2 diffuses away from the flame sheet and reacts with the coal surface to form Hz0 and CO. The CO formed at the particle surface reacts with O2 at the flame sheet to form co2. It is desired to determine radial gas-phase species mass traction profiles (Yi), but is simpler to solve the equations of element (Yi), rather than species, conservation because they contain no non-linear source terms. For element i ,


mt rp -


d 2d% --g , i=1,2,3.

= pD;i;r


Elements are numbered as: 0 + F1, C + F2, H + F3, and N + r’,; and species as: 0, -, Y1, CO2 + Y2, CO + Y3, H&l + yS, and CH 0, + Y5. Using the boundary conditions Yi=Yb at the particle surface (k=l) and E=Yim in the f& stream (k+=), the solution of Eq. (1) is r‘






, i=1,2,3 ,


where 5 is the dimensionless radial coordinate r/r,, K the dimensionless mass loss due to heterogeneous combustion mprp/pD , and V the dimensionless volatiles mass loss, V=m,,r,lpD . The total mass flux away Tom the particle surface is m,, which is the sum of the surface flux of mass removed heterogeneously mp and the volatiles mass flux m,. Conditions in the free stream are assumed to be known, thus the surface boundary conditions must be determined in order to obtain the gas-phase element mass fractions. A steady mass-balance is applied at the particle surface. The diffusive flux is given by Fick’s law as pD (dYil&)p. The transfer of element i to the surface from the solid phase is %f i+wFi, where fi and Fi are the solid-phase and vojatiles element i mass fractions, respectively. The total convected flux of element i is (mp+m,,)Yip. In dimensionless terms, element i is conserved at the surface if 21 1 d5

= (K +V)E-Fi V-fi K s


coal combustion during rapid devolatilization


Differentiating Eq. (2), the surface condition at \=l is

w+wK.l-~p) )

& dS -










Substituting Eq. (4) into Eq. (3) and solving for &,, the surface element mass fractions are determined as



+ ViK+Fi

-(~+y)y’ i-



Heterogeneous mass loss has generally been modeled as consisting only of carbon removal. 22 This assumption is valid during the char combustion regime, but during rapid devolatilization coal contains significant oxygen and hydrogen as well as carbon. It is assumed that heterogeneously removed mass has the composition CHb 0,. where b and c are specified, e.g., by ultimate analysis of partially burned solids. The solid fuel of the above composition reacts heterogeneously with 02 and CO2 to form CO and HzO. Reaction of Hz0 with the surface is neglected due to low water vapor concentration, but should be included, e.g., for models of coal slurry combustion. Reaction rates for carbon oxidation, R 1, and carboncarbon dioxide reaction, Rz, are assumed to be adequate to describe the reactions of O2 and CO2 with the surface because of the relatively low H and 0 mass fractions of the coal. Considering these two heterogeneous reactions, and defining Ki=Rj r,lpD , the surface flux of heterogeneously removed mass is given by the dimensionless relationship K = K,Y1,+KzY2,


Coal devolatilization is described by a first-order Arrhenius rate constant, k=kge-E’RT,where ku is the preexponential factor in s-l. In terms of k and coal density pc, the dimensionless volatiles loss parameter is V=p, rtkl3pD. The values of K and V are specilied, thus Eq. (2) can be solved for the radial mass fraction profiles of elements C, H and 0, with the surface element mass fractions given by Eq. (5). The fraction of the inert component is determined by closure. Other than the inert diluent fraction, the species whose mass fraction profiles are to be determined are 0s. CO, CO2, Hz0 and the volatiles “species”, MY Oz. Apparently five independent equations are required to determine these species mass fracttons, but the flame sheet approximation results in no more than four species being present at any location in the gas phase. Two cases of interest are Case (i) The flame is collapsed to the particle surface. The three gas-phase species, CO2, Hz0 and 0s. are determined by the atom balance equations. Case (ii) The flame stands in the gas and divides it into two regions; outside the flame sheet the conditions of Case. (i) apply, and inside it there can be no oxidizer, thus the four species present are C02, H20, CO and CH, 0,. Inside the the flame sheet a relation in addition to the three atom balances is required to obtain the four species mass fractions. Because gas diffusivities are equal and gas-phase reactions occur only at the flame sheet, the solutions YJ and Y5 satisfy the same conservation equation with identical conditions at the flame (Yi=O)and with a constant ratio at the surface (Y+IYs,= constant). Therefore, Ys/Y5 is constant between the surface and the flame. For this case CO is formed at the surface and there is no O2 at the surface. Because two moles of CO are formed by the heterogeneous removal of a mole of carbon from the surface, the mass flux of CO is 56m,,f,/12. The mass flux of volatiles is simply m,. Thus, YJIYsinside the flame is given by its value at the surface, which, in dimensionless form, is y3


-- 56m,f c





Finite-Rate Gas-Phase-Chemistry Model Gas-phase reaction rates am assumed to be finite. The isothermal, steady-state species conservation equations are #i d 2dYi L mf, - dr = pD;~;r dr+~r2riti”’

, i=l-5



where liti’”is the rate of creation of species i in reaction 1, and there are L total reactions in which species i is created. The free stream conditions of Eq. (8) are known. The surface condition is determined by the balance between the rate of creation of species i at the surface and its diffusion and convection away from the surface. Again, the heterogeneous processes considered are the reaction of O2 and CO2 with the coal particle surface, and the gas-phase reactions considered are the oxidation of volatiles (CH 0,) and CO. These mass balances result in the following surface condition for species i=l --J

$$nijRjYj =m,Yi-pD c








Here, M, is the molecular mass of the assumed coal molecule, CH, 0,. Mi is the molecular mass of species i , and nij is the moles of species i created in reaction J’. A volatiles balance yields the surface condition m,, =m,YS-pD



[ dr



rp ’

Equations (8) are solved to determine the species mass traction profiles, and then the heterogeneous mass loss is obtained from Eq. (6). RESULTS AND DISCUSSION The two models were used to determine species mass fraction profiles and the fraction of the total mass flux resulting from heterogeneous combustion, which is HML=m,l(m,+m,,) in dimensional form or HML=KI(K +V) in dimensionless form. A parametric study was performed to determine the effect of particle size, temperature, devolatilization rates, gas-phase reaction rates, and free stream oxygen concentration on HML. The solution procedure, flame conditions studied, and results of the parametric study are presented. Finally, a discussion of the validity of the isothermal assumption is presented. Modeling and Parametric Study Results Using the flame sheet model requires only the solution of the set of algebraic equations for the flame location in question. The reaction rate for carbon oxidation, R Ir suggested by Field et al, 23and the carbon-carbon dioxide reaction rates, R2, suggested by Dobnera and by Mon and Amundson,z are used for surface reactions. The first-order devolatilization rate constants used are experimental values of Badzioch and Hawksley, l1 Goldberg and Essenhigh, 26Kobayashi et al,” and Midkiff et al. s The finite-rate chemistry model is solved numerically using a finite-difference approach. Rather than implicitly solving the non-linear steady species conservation equations pq. (S)], an explicit formulation of the full transient equations, JYi



ar+mtrp2r =pDsr



-+~r2~i”’ ar


, i=l-5



is solved by marching through time until the steady-state solution is obtained. The surface conditions are given by Eqs. (9) and (10). Trial and error indicates that assuming that the known free stream conditions apply at 5=20 in most cases yields results essentially the same as those for much


coal combustion during rapid devolatilization


larger 5. The coal devolatilization and surface reaction rates used are identical to those used for the flame sheer model. Gas-phase rates for the oxidation of CO and volatiles (as approximated by CzH4 oxidation) suggested by Westbrook and Dryera are used. The two models were used to estimate the effect of the pammeters on the magnitude of HML by 5rst obtaining solutions for standard conditions and then varying one parameter at a time to determine its influence. The standard conditions are a temperature (solid and gas phase) of T=T,=1900 K , free rate measured coal, particle using the flame sheet model at the standard conditions for particle diameters of 20 and 50 m are shown Figs. and respectively, (the largest diameter for which flame is attached these conditions, thus 5ame is located particle [Fig. &4.5) for the 50 tun diameter particle lFig. l(b)]. One-fourth loss is due to heterogeneous processes for the 20 CM particle, while surface oxidation is virmally negligible for the larger particle. thus the surface volatiles flux, increase with size, it is difficult With the surface volatiles Aux resulting from latilization, given particle size fracof the total mass 511xresulting from HML, the total mass given by m,=mJ( l-HML ). The total surface flux these conditions lm2s for the 20 and 50 trm diameter particles, respectively.

k=103Oexp(-4740/T,) s-l,


Fig. 1. Species mass fraction profiles predicted by the Aame sheet model for (A) 20 jrm and (B) 50, and by the finite-rate chemisny model for (C)20 w and (D) 50 trm diameter particles at a surface temperature of 1900 K.




Figures l(c) and (d) show species profiles for 20 and 50 AIMdiameter particles at the same set of stat&d conditions, but using the finite-rate gas-phase chemistry modeL As did the flame sheet model, the finite-rate model predicts decreakg HML with increasing particle sire, but HML is substantiaUy Larger for the physically more realis& finite-rate model, particularly for the larger particle. The region of intense chemical activity is much closer to the surface for the case of the finite-rate model, as evidenced by the shapes of the species profiles. Volatiles are completely oxidized within 3 particle radii for both particle sixes. The model pmdictions of Musarra et al= show a considerably broader reaction xone than was obtained in this study using the finite-rate model. The total surface fluxes predicted by the finite-rate model are 1.1 and 1.3 kg /m’s for the smaller and Largerparticles, respectively. Comparing these results to those obtained for the flame sheet model, the finite-rate model predicts instantaneous rates of combustion that are 2.4 and 1.4 times more .mpid for the 20 and 50 pm diameter particles, respectively. Table 1 summarixes effects of particle size, temperature, free stream oxygen concentration, and devoiatilixation rate on HiUL. The dcvolafilizationrate wed, designated “MAP”, is that of Ref. 7. Patti& diameters were varied from 4 to 100 w. The finite-rate and flame sheet models yield similar results in the extremes of the particle sixe range, with virtually complete heterogeneous combustion for vety small particles, and negligible heterogeneous combustion for very large particles. Widely divergent values of HhfL are predicted for the intermediate particle sixes by the two models. This is a crucial difference because mass mean diameters for typical pulverixed utility coaislieinrangeof20-4Otuu.

Table 1. Resultsof the parametricstudy.



-02 hu

FiniteRate F&h FiniteRMC Ftitc Rate

4 10


Ftitc Rate

50 100

FlBmuhee8 Flamuhcct l+muhca

4 10 20


50 100


Fire Rate Ftirc Rue Finite Rare Ftite Rate Finite Rate Flamerhea Flamahect Fimeshee Flamesheet Flamerhea Finite Rate Ftile Rate Finite Rate Flamerhea Flamesheet Flamesheet Finite Rate Fiitc Rate Finite Rate Flamesheet Flamesheet Flameshea

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20






1900 1900 1900

02 0.2 0.2








1900 1900 1900 1900 1900 1900 1400 1700 2100 2500 3Oal 1400 1700 2100 2500 3000 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900

0.2 0.2 0.2


30 4 93 75









0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.05 0.1 0.5 0.05 0.1 0.5 0.2 0.2 0.2 0.2 0.2 0.2





69.3 68.9 68.4 67.8 15 27 16 13 27 37 53 84 0.7 1.2 67 10 1.7 71 0.07 0.01 25

Heterogeneous coal combustion during rapid devolatilization


Figure 2 shows that the flame sheet model drastically tmdaestimates the extent of heterogeneous combustion in the important particle size range of 20 - 60 lrm diameter. It should be noted that the predictions of HML by this linite-rate gas-phase chemistry model are probably low because it is assumed that the volatiles flux is uniformly distributed over a spherical particle surface. In reality, coal particles are decidedly non-spherical, and devoiatilixation has been observed to occur in strong jets. 2%~~Both of these factors could elevate oxidizer levels in some areas near the surface and result in more extensive surface burning.





Fig. 2. The effect of particle sixe on the extent of heterogeneous mass loss for a surface tempernmreof 19OOK. Temperature was varied from 1400 to 3tXlOK with negligible effect on HML for the finiterate model and modcrate effect on HML for the flame sheet model. The gas reaction rates depend strongly on temperature for the finite-rate model, but are independent of temperature for the flame sheet model (infinitely-fast gas kinetics). Free stream oxygen was varied loom 5% to 50% by mass, and higher oxygen concentrations clearly increase HML for both models. This effect is more dramatic for the flame sheet model because it predicts either no oxygen, or, for the flame collapsed to the surface, much lower oxygen concentrations at the surface. Thus, heterogeneous removal depends more on the slow CO2 reduction reaction for the flame sheet model. In the study of &volatilization-rate effects (Table I), we compare results for the base case rate constant (Ref. 8) with results for constants from Ref. 11 (designated as B&II), Ref. 26 (designated as G&E) and from Ref. 27 (designated as KHS). Because the magnitude of the flux of volatiles depends directly on the devolatilixation rate, HML is strongly affected by the rate constant At the temperature used, the G&E rate constant predicts the most rapid volatiles evolution, thus surface oxygen concentration and HML a~ minimkd. Use of the KHS rate constant yields the lowest devolatilixation rate and the largest HML. Thevariation for these two extreme cases is large, with Hh4L=71% using the KHS rate constant and HML=2% using the G&E rate for the 20 ~PPZdiameter particle and the linite-rate model. The base case rate constant of MAP yields predictions of HML similar tothose resulting from the KHS constant It is interesting to note that using the G&E constant in the finite-rate model for a 20 pm diameter particle yields a total surface flux of m,=16 kg/&. This corresponds to a gas velocity on the order of 90 m/s, which seems quite large. Nevertheless, it is clear that devolatik&on kinetics are crucial in determining the magnitude of HML, and, ashasbeen noted often before. the ability to accurately estimate volatiles evolution rates is critical to the success of any coal combustion model.

EGY 17:7-D



The effect .of gas-phase reaction rates on the fini~rate model was studied using various multiples of the standard case rate, in effecf varying the preexponemkl factor. The results are shown in Pig. 3 for a 50 w particle. The rate multiplier was varied from 1V’ to lo’, and Pig. 3 shows percent HML as a function of the base 10 logarithm of the rate multiplier. HML decreases within creasing gas-phase reactionrates until, at very large rates, the prediction of the finite-rate chemistry model approaches that of the flame sheet model (in which intinitely fast gas-phase rates are assumed). Only for extremely rapid gas-phase rates do the finite-rate and the tlame sheet models predict similar magnitudes of heterogeneous mass loss.

s a 20 k 2

E 10 2 0 -1



Pig. 3. The effect of gas-phase reauion rates on the extent of heterogeneous mass loss for a 50 w diameter particle at a surface temperature of 1900 K Evaluation of the Isothermal Aur.noximatkn Constant temperature conditions throughout the gas and solid phase have been assumed in the models discussed here. The assumption of isothermal conditions eliminates the need to solve the energy equation. Although the aim of this study is to determine species rather than tempemture profiles, the gas-phase temperature distribution does affect the species concentrations. In both the flamesheet and the finiterate chemistry models, species concentrations depend on density and diffusivity, which are functions of temperature. Gas-phase reaction rates used in the llnite-rate chemistry model are also strongly dependent on temperature. To estimate the error in predicted HiUL resulting from the isothermal assumption, the energy equation was solved for a small set of cases in conjunction witlt the finite-rate chemistry model. Particle temperature and free stream temperature were specifled in these calculations, and the energy and species conservation equations were solved simultaneously. The governing steady-state energy equation for the gas-phase is 2fl mrpz=


d 2fl rr’r+Crqis

L I=1






T is the gas temperature, Kt the gas thermal conductivity, ii the volumetric heat release rate for reaction of species i , and AH the enthalpy of combustion. The enthalpies of combustion for reactions of volatiles (assumed to be C#,J and CO are 47.567 and 9.924 MJlkg , respectively. The


coal combustion

during rapid devolatilization


thermal conductivity and specific heat are assumed to be those of air. The solution to the combined energy and species equations was obtained by explicitly solving the transient forms of the equations until the steady-state solution was obtained, using the previously obtained isothermal solutions as the initial conditions. The gas-phase energy and species conservation equations were solved simultaneously for a specified particle temperature of 1900 K, specified gas temperatures of 1500,170O and 1900 K, a particle diameter of 20 pm. a volatiles flux containing 2 moles of hydrogen per mole of carbon, and a free stream oxygen mass fraction of 20%. The results of these calculations show that the temperature profiles vary considerably, but the predicted extent of heterogeneous mass loss is within 1% of HML=69% for all three free stream temperatures. This minimal effect of freestream temperature can be explained by the relative insensitivity of HML to gas-phase reaction rates, as shown, e.g., in Figure 3. Recall that the most important parameters, particle size, devolatilization rate and free stream oxidizer concentration, as well as surface reaction rates, do not depend on gas temperature once the particle temperature is specifted. From the results of this limited number of computations for a non-isothermal model, it appears that the isothermal model yields reasonable predictions of the extent of heterogeneous mass loss for the conditions of this study.

CONCLUSIONS Two single-particle coal combustion models have been developed and used to predict the extent of heterogeneous combustion during the rapid devolatilixation regime. Both models predict that small particles (< 10 pm diameter) burn heterogeneously and large particles (> 100 w diameter) burn homogeneously, but HML is severely underestimated by the IIame-sheet model in comparison to the more realistic finite-rate chemistry model for intermediate particle sizes, which comprise the bulk of a typical pulverized coal. A parameter sensitivity analysis reveals that particle size, free stream oxygen concentration and devolatilization rate, in that order, are the important determinants of the extent of heterogeneous combustion. It was demonstrated that, for the conditions of the study, the assumption of isothermal conditions results in little error in the predicted extent of heterogeneous mass loss. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

R. H. Essenhigh, Sixteenth Symposium(inti.) on Combustion,pp, 353-374, The Combustion Institute, Pittsburgh (1977). J. B. Howard and R. H. Essenhigh, Ind. Eng. Chem., Proc. Des. Dev. 6, 74 (1967). J. B. Howard and R. H. Essenhigh, Eleventh Symposium(Intl.) on Combustion,pp. 399-408, The Combustion Institute, Pittsburgh (1967). K. Annamalai and P. Durbetaki. Combust. Flume 29, 193 (1977). W. R. Seeker, D. C. Wegener, T. W. Lester and J. F. Merklin, Seventeenth Symposium(Id.) on Combustion,pp. 155-168,The Combustion Institute, Pittsburgh (1979). E. M. Suuberg, W. A. Peters and J. B. Howard, Seventeenth Symposium(Id.) on Combustion, pp. 117-130, The Combustion Institute, Pittsburgh (1979) K. Okazaki, H. Shishido, T. Nishikawa and K. Ohtake, Twentieth Symposium (Id.) on Combustion,pp. 1381-1389,The Combustion Institute, Pittsburgh (1985). K. C. Midkiff, R. A. Altenkirch and R. E. Peck, Combust. Flame 64,253 (1986). K. C. Midkiff, PhD Dissertation, Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky (1986). M. Saito, M. Sadakata and T. Sakai, Combust. Sci. Technol. 51, 109 (1987). S. Badzioch and P. G. Hawksley, Id. Eng. Chem., Proc. Des. Dev. 9, 521 (1970). G. M. Kimber and M. D. Gray, Combust. Flume 11,360 (1967). L. D. Smoot, M. D. Horton and G. Williams, Sixteenth Symposium (Intl.) on Combustion, pp, 375-388, The Combustion Institute, Pittsburgh (1977). M. Hertzberg, K. L. Cashdollar and C. P. Iazzara, Eighteenth Symposiumtfntl.) on Combustion. DD. 717-730. The Combustion Institute. Pittsbureh (1981).


15. 16. 17. 18.

19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.


P. J. Smith, T. H. Fletcher and L. D. Smoot, Eighteenth Symposium (Id.) on Combustion, pp. 11851202, The Combustion Institute, Pittsburgh (1981). M. Hertzberg, K. L. Cashdollar, D. L. Ng and R. S. Conti, Nineteenth Symposium Untl.) on Combustion, pp. 1169-1180,The Combustion Institute, Pittsburgh (1982). K. C. Midkiff and R. A. Altenkirch, Fuel 67,459 (1988). D. W. Mackowslci,R. A. Ahenkirch, R. E. Peck and T. W. Tong, Combust. Sci. Technol. 31, 139 (1983). S. Agrawal, MS Thesis, Department of Mechanical Engineering, University of Alabama, Tuscaloosa, Alabama (1988). K. Annamalai and S. C. Ramalingam, Comhst. Flume 70, 307 (1987). P. A. Libby and T. R. Blake, Cornbust. Flame 36, 139-169 (1979). S. P. Musarra, T. H. Fletcher, S. Niksa, and H. A. Dwyer, Combust. Sci. Technol. 45,289 (1986). M. A. Field, D. W. Gill, B. B. Morgan, and P. G. W. Hawksley, The Combustion of Pulverized Coaj, The British Coal Research Assoc., Leatherhead, England (1967). S. Dobner, “Modelling of Entrained Bed Gasification”, EPRI Memo, London (1976). E. Mon and N. R. Amundson, Ind. Eng. Chem., Fund. 17,313 (1978). P. M. Goldberg and R. H. Essenhigh, Seventeenth Symposium (Intl.) on Combustion, pp. 145-154, The Combustion Institute, Pittsburgh (1979). H. Kobayashi, J. B. Howard, and A. F. Sarofim, Sixteenth Symposium (Intl.) on Combustion, pp. 411425, The Combustion Institute, Pittsburgh (1976). C. K. Westbrook, F. L. Dryer, Combust. Sci. Technol. 27, 3 1 (1981). W. J. McLean, D. R. Hardesty, and J. H. Pohl, Eighteenth Symposium (Intl.) on Combustion, pp. 1239-1248,The Combustion Institute, Pittsburgh (1981). W. R. Seeker, G. S. Samuelson, M. P. Heap and J. D. TroIinger, Eighteenth Symposium (Intl.) on Combustion, pp. 1213-1226,The Combustion Institute, Pittsburgh (1981).