Conversion Efficiency of Gasifier

8/4/2019 Conversion Efficiency of Gasifier

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ERWORTHE I N EMANN

0016-2361(95)00051-S

Fuel Vol. 74 No. 10, pp. 1452-1460, 1995Copyright 0 1995 Elsevier Science LtdPrinted in Great Britain. All rights reserved0016-2361/95/%10.00 0.00

Modelling of an entrained flow coal gasifier1. Development of the model and general predictions

Despina Vam vuka, Edward T. Woodburn and Peter R. SeniorDepartment of Chemical Engineering, University of Manchester Institute of Science andTechnology, Manchester M60 100, UK(Received 7 October 1992; revised 19 October 1994)

A one-dimensional, steady-state mod el for an entrained flow coal gasifier is develo ped, incorporatingthermo gravim etric analysis data on a bituminous coal. The mod el is based on mass and energy balances,heteroge neous reaction rates and hom ogeneo us gas-ph ase equilibria:The resulting set of non-linear mixedordinary differential-implicit algebraic equations was solved by a mod ified Euler meth od in conjunctionwith a non-linear algebraic equation solver. Tem perature, reaction rate and composition profiles in atubular gasifier were predicted at 0.1 and 2 MP a operating pressures, at constant feed rates. Realisticconversions of carbon could not be predicte d if the devolatilization reaction and the heteroge neous surfacereactions between the coal and oxygen and steam were assumed to proceed sequentially. The model showedthat as the combustion was much faster than the gasification, temperature maxima for both the particles andthe gas occurre d at the point of final consumption of oxygen. T he gasification proc eeded only in the absenceof oxygen.(Keywords: coal; gasikation; entrained flow; modebg)

Entraine d flow gasifiers are of interest both in theproduction of synthesis gas, from which chemicals andliquid fuels can be obtained, and as a possible route ingenerating electric power from low-grade coal. This isprimarily due to the fact that because they operate at hightemperatures with small coal particles they can achievehigh rates of gasification, producing a relatively clean gas.The use of syngas for the generation of electric powerprovides an alternative to natural gas in combined-cyclepowe r generation. The high efficiencies of combined-cyclesystems result in lower rates of CO 2 emissions per kW h. Itis also possible to envisage the complete remova l of sulfurand particulates by wet scrubbing of the crude gasifier gas.For th is to be feasible, an efficient heat-recovery systemfor gas treatme nt is required. The presence of particulatesin the crude gas causes difficulties with the heat exchangesystem, a nd one of the objects of the present simula tion isto evaluate the likely amoun t and size of the unconvertedcarbon in the crude ga s.A mathematical model of the gasifier is a first step in theevaluation of operability studies which are necessary toassess the economic potential of dem ineralized coal finesas a feedstock for synthesis gas to be used in a combined-cycle power generation schem e. Field et al. havesummarized work in this area up to 1967. The modelsthey reviewed w ere plug-flow in nature. The complexity ofcoupling the fluid dynamics with the local reactionprocesses in such systems has necessarily requiredsignificant simplifying assumptions.Ubhayakar et aL2 and Smooth and Smith3 allowed foraxial mixing in their one-directional flow models.Ubhayakar et al. neglected the surface reactions, because

of the rapid heating, while allowing for the gas-phasereactions of the volatiles, includin g the rmal cracking .Smoot and Sm iths model offers a method for evaluatingvarious kinetic schemes, and provides estimates of modelparameters and therefore forms a basis for multidimen-sional solutions of coal reaction processes. How ever, it isstill of restricted generality.Wen and Chaung4 adopted a cells-in-series approach todescribe the mixing in a Texaco pilot plant downflowentrainm ent gasifier. Each cell wa s treated as a perfectlystirred-tank reactor for the gas, while the solid phase wasin plug flow throughout the whole reactor volume. Thevelocity of the solid particles wa s mode lled by a Stokesslaw approximation. The gasifier was fed with coalliquefaction residues and coal-wa ter slurries. Govindand Shah have refined the above model by includingmom entum balances. In both investigations, parametricstudies were conducted to provide a better understandingof the sensitivity of reactor performance to variousoperating conditions. Experim ental data for differenttypes of coal are still needed to verify and refine theproposed models.The models developed by Sprouse6 and Goyal andGidaspow dealt with hydrogasification rather thancom bustion, in a different type of reactor system. Theformer employed emp irical correlations, wh ich proved tobe inapplicable to subbituminous coals, while the latter,although more general an d complete, seems difficult touse because of its complexity.All previous models have been based on data derivedfrom flow experiments under rapid heating conditions,and have been mainly concerned with the gasification of

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Mod elling of an entrained flow co al gasifier: D. Va mvuka et al.

To ,Tw5 _ +Jst Ts, _I . ws L + dL TS L + dL. . a. w.* ,I ,. , II I

%,L TgL . ., ; , FgI.L + dL TgL + dLm w* I ?? , I

Figure 1 Schematic diagram of concurrent entrained flow coal gasifier

large samples. It was the purpose of this study to developa model w hich could predict the essential features ofgasifier behaviour as a function of steam: coal andoxygen:coal ratios and operating pressure, in terms ofparameters obtained from thermogravimetric analysis.As these measurements are relatively easy to obtain,they offer potentially a convenient mea ns of allow ing forthe effects of variations in coal quality on gasifierperformance.GENERAL DESCRIPTION AND ASSUMPTIONSThe entrained flow gasifier used for mod elling isschematically shown in F i g u r e I , as a horizontal reactorwith concurrent flow of solid and gaseous streams.The model assumes that the gas phase is perfectly mixedradially and that the solid particles are distributeduniformly in the radial direction. There a re differences intemperature between the solid particles and the surround-ing bulk gas, and in addition the composition of the gas at

Table 1 Major reactions assumed to take place in the gasitier

the solid surface differs from the bulk gas composition.How ever, the dispersion of coal in gas is considered tomove in plug flow axially through the reactor.Pulverized coal and a hot gas stream of steam a ndoxygen, at an adjusted ratio, are mixed at the reactorentrance and travel concurrently through the reactor. T heassum ption of plug flow for the dispersion requires thatthe solid particles move with the gas stream at the bulk gasvelocity. This is considered reasonab le in view of the smallsize of the particles (initially 41 pm ), w hich decreasesduring transit because of combustion and gasification.Vam vuka examined the postulate that the devolatili-zation of coal wa s followed by heterogeneou s surfacecombustion and gasification reactions with the resultingchar. It was found that coal conversion of only N 20%could be achieved within acceptable residence times.From the computations it was apparent that the reactionshell of the combustion of the volatiles was indistinguish-able from the particle surface. The rate of evolution of thevolatiles as determined by thermogravimetric analysis was

Stage Reactions kCoal combustion C,H~O,A+ (z+f-z)02 + (f- l)oC0,+2(1 - ~ ) u C O + ~H ,O + a s h 1Coal gasification C,H,O,A + (o - r)H,O + c&O + 2

c,H~O,A + (2o - y)H*O + d Z 0 2 + (>2a + 2 - Y H2 + ash 3C,HBO,A + aCOz -+ 2aC0 + oHsO + 4C,H@O,A+ (Zo-f+y)H, 5

Gas-phase combustion CHr + 202 = COz + 2H20 6co+;o,=co* 7H2 + $0, = Hz0 8

Water-gas shift H,O+CO=H1+CO1 9a For 1OOgof coal: cr = 6.007 ; p = 4.923; y = 0.735, assuming volatile matter a mixture of CH4 , CO and HzO (g) in proportions 2 : 1 1

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Modeling of an entrained flow coal gasifier: D. Vamvuka et al.

slow relative to the inw ard oxygen diffusion, so thatreaction took plac e on the coal surface.Consequ ently the coal wa s considered to react directlywith oxygen and steam at its surface, and its compositionchang ed according to the reaction stoichiometry. Table 2represents the minimum set of reactions chosen torepresent the essential fea tures of the gasification process.The surface reactions were assumed to be irreversible,and to proceed in parallel at the high temperaturesprevailing in the reactor. Similar assumptions have beenemployed by Wen and Chaung4 and Lupa and Kliesch.The coal particles were allowed to shrink, but the residualash wa s not conside red to be a barrier to diffusion, as inthe shrinking core model. Gas-phase combustions areknown to be very fast under gasifier conditions29319an dwere therefore assumed to be at equilibrium at the localtemperature and gas composition. The water-gas shiftreaction, which proved to dominate the bulk gas, was alsoconsidered to be at equilibrium41519.

The gasification proceeded autothermally, with heatbeing generated by the combustion, but not adiabatically,since heat w as lost through the gasifier walls.Molecular transport processes transferred mass acrossa stagnant boundary layer surrounding each particle tothe bulk gas. Heat was similarly transferred by conduc-tion, but radiation effects were also included . U nder thehigh local temperature and concentration gradients, theseprocesses were reasonably rapid. A s the turbulentprocesses in these boundary layers are not understood,they were not included in the model. It is possible that infuture the model w ill be further refined to allow for theseeffects. Axial variations in composition and temperaturewere determine d by the bulk flow rate of the dispersionfollowing the radial interchange of heat and mass betweenthe particle and the surrounding gas.The basic assumptions used in the model developmentare summarized below:(a) the bulk flow was a steady-state, one-dimensionalplug flow in the axial direction and well-mixed radially;(b) the mom entum balance was neglected;(c) all gases obeyed the ideal gas law and binary diffusion-coefficient pairs were considered equal;(d) owin g to the sma ll particle size of the coal concernedand the high temperatures in the gasifier, internal masstransport effects were ignored, and ash did not remain onthe reacting coal particle surface;(e) the temperature of the solid was assumed uniformthroughout the particle (as shown by Vamv uka*).

MATHEMATICAL FORMULATIONOn the basis of the above assumptions, a series ofequation s governing the gasification of coal wa s for-mulated, as follows.M a s s b a l a n c e s

These were set up for each component, in an element ofreactor volume AP (Figure 1) and were expressed as afunction of conversion or reaction extent and feed flowrate. Thus the mass balance equations for the solidcomponent and any lth gaseous component involved inthe solid-gas reactions could be described in terms ofreactor length as follows (see Nomenclature for meaningof symbols):


Solid component:-= -N,A&T,,L)KdL k= lws Wdl - xs)

Gaseous component:2 = &f 2 U,kYk(Ts, )

k=l

F;r = &IO + 5 Vlktkk=l

The molal flow rate of each gaseous component in thefinal gas could be determined similarly to Equation (4), byusing the reaction stoichiometry and extent:$1 = &IO + 5 vlk tk

k=l(5)

The concentrations of the product gases were alsorelated to the gas-phase reaction equilibrium constants, atthe operating temperature.Reac t io n ra te expres s ions

The rate of diffusion of each gase ous reactant I to thesolid surface w as related to the chem ical reac tion rate atthe surface. Hence the overall rate of each heterogeneousprocess was controlled by gas-phase diffusion a ndchem ical kinetics, accordin g to the general expression:

The surface reaction rate, which was proportional tothe partial pressure of the gaseou s reac tant I and theexternal surface are a of the coal, was described byQ(Tsr L) = %/JTs)(0/,)47&, k = 1, . . . 75 (7)

The reaction order in the above equation was assumed asfollows:n= 1 fork= 1,2,4n=2fork=3,5

The first-order assumption was in agreement withprevious findings of Vam vuka and Dobner, while thesecond-order assumption was in line with the datareported by von Fredersdorff and Elliott.The consumption of solid material by each coal-gasreaction could be evaluated by eliminating the molefraction at the surface, yls, betwee n E quation s (6) and (7).The overall reaction rate of coal was a summ ation ofthe individua l reaction rates:r,(Ts,L)=&k(Ts>L)dt (8)

k= lFrom this, the coal conversion could be estimated and theresulting particle radius yPs computed.H eat ba lances

The heat balance equations of the solid and gas phaseswere based on the following considerations.


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Modeling of an entrained flow coal gasifier: D. Vamvuka et al.

The change in energy between the streams entering andleaving an element of reactor volume was due to thetemperature change and composition change associatedwith the reactions. The rate of energy transfer betwe enphases in the differential volume was assumed to take placeby conduction (by approximating the Nusselt number to 2for a non-turbu lent system) and radiation. The energy lostfrom the gas to the reactor wa ll occurred by radiation andconvection between the gas and reactor wall.The differential energy balance s written in terms ofreactor length were formulated as shown below:Solid phase

(9)Gas phase:

+ N,A 2 (Tg - T,) + cpcr(T; - T:)17rr;,+ C~O( i - Ti)rDi + h,( Tg - Tw)rDi (10)

METHOD OF SOLUTION AND DATA REQUIREDThe solutions to the formulations described above weresough t in the form of profiles of coal conversion, gascomposition and solid and gas temperatures with respectto axial position in the gasifier. The initial conditionswere:

at L = 0,


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Modelling of an entrained flow coal gasifier: 0. Vamvuka et al.

Set initial conditions

Choose first increment of reactor length

Estimate change in composition, solid ond gas temperatures,within this increment, from material and energy balances

Apply Eulers algorithm to estimatecomposition and temperature of solid and gos phases

at the end of the increment

I Set initial conditionsfor the next reactor

. increment ond goto further calculation4

Calculate(i) Reaction extents

(ii) Final composition of gas(iii) Reaction rotes

($ Coo! conversionResrdence time

(vi) Solid ond gos propertiesat the end of the increment

4

Use modified Eulersmethod to find o

better opproximationto the solution

/ succesive reaction rote values

Figure 2 Comp uter flow diagram for the model

Briefly, the solution procedure wa s as follows:(1) From the initial conditions (Equation 1 ), thecomposition and molar flow rates of the inlet gaseswere known. Using these as bulk gas compositions,the initial reaction rates of reactions l-5 could becalculated.(2) For the chosen slice length, first estima tes of the gascomposition and solid and gas temperatures leavingthe slice were obtained from the mass and energybalance equation s (l), (3) and (9), (10) respectively.(3) From the first estimate of values of the variables instep (2), the extents of the solid-ga s reactions were

(4)

computed first, from Equation (4), by using a least-squares method13. These were then used a s initialestimates to calculate the extents of the gas-phaseequilibria. This implicit solution was obtainedusing a modified P owell hybrid m ethod14. Usingthese data, the composition and temperature of thegas leaving the slice were used to calculate thereaction rates at this position in the reactor.Stage s (2) and (3) were repeated for conditionsaveraging those entering and leaving the slice. Thusmore precise values for the comp osition andtemperatures were obtained and a third estimateof the reaction rates was obtained. Whe n successive



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Modelling of an entrained flow coal gasifier: D. Vamvuka et al.

Table 4 Operating conditions of the gasifierCoal feed rate (g s-)Steam/coal ratio (g g-l)Oxygen/coal ratio (gg-)Feed gas temperature (C)Gasifier pressure (MPa)Gasifier internal diameter (cm)Gasifier external diameter (cm)Emissivity of wall material

50.00.20.8630.00.1-2.0150.0153.00.78

a -

c60 0 IA I I I I0 0 . 1 0 1 0 0 200 300 LOO 5ooReactor length km)

Figure 3 Temperature and coal conversion profiles along the reactor at2 MPa

calculated rates agreed within a tolerance, theprocedure wa s repeated over the next slice, untilthe required total gasifier length was reached.The above procedure is shown graphically in the logicflow diagram of the computer program in Figure 2.The model could predict the performance of the gasifierin terms of coal conversion, product gas comp osition andtemp erature profiles, as a function of steam : coal andoxygen : coal ratios and the particle size of the coal feed. Itcould also predict the effect of operating pressure onperformance.Gas-phase properties such as diffusivity, thermalconductivity, heat capacity and heat of reaction wereevaluated as described in Perrys handbook15. Theequilibrium-constant equations used for the gas-phasereactions are shown in Table 2. The heat transfercoefficient for natural convection to air wa s estimate d

according to the expression recommended by Eberle et al.as quoted by Mc Adam s16. Fluid properties weredetermined at a temperature half way between the walltemperature (approximated to the arithmetic m ean of thegas temperature in each reactor slice) and the atmospherictemperature.The solid-phase properties and parameter values usedin the simula tion, together with source references, aresummarized in Table 3. The coal combustion kineticparameters were taken from thermogravimetric analysisdata for Whitw ick bituminous coa18. Ow ing to the lack ofexperimental data, gasification kinetic parameters forchar were selected from the literature to calculate thosefor coal, by analogy with the coal char combustion data.

MODEL PREDICTIONSSome of the model predictions, including temperature,reaction rate and concentration profiles along the reactor,for the conditions indicated in Table 4, are presented hereto illustrate the degree of consistency with previous data.Acceptable consistency would m ake the use of t.g.a. datain this type of a comp utation a valid method of predictingthe performance of various c oals. A more detaileddiscussion of individual parameters is envisaged in asubsequent paper.Figure 3 show s the tempe rature profiles for solid andgas obtained at a pressure of 2 MP a. The most interestingfeature is an extremely sharp maxim um in the tempera-ture profile of the solids, which seems to have adiscontinuity in the first derivative. The gas tempe raturemaximu m is less sharp a nd is significantly smaller. Themaxim a occur at an extremely short distance, N 0.6 mm ,from the reactor entrance. These peaks are associatedwith the point at which the oxygen is wholly consum ed.Only when the oxygen concentration falls to zero dohydrogen and carbon monoxide appear in the bulk gas.This suggests that the gas-phase equilibria (reactions 6, 7,8) are driven to the right in the presence of even sma llamounts of oxygen and also that the gasification reactions(2,3,4) are much slower than the combustion reaction (1).The temperature peak can be used to define the end of thecom bustion period, only after whic h do the gasificationreactions becom e effective. As long as oxygen exists in thebulk ga s there is a significant tempe rature differencebetween the coal particles and the bulk gas, since thesimultaneous burning of solid carbon and combustiblevolatiles generate heat in the solid phase . After oxygen isdepleted, the difference be tween the solid and gastemperatures drops rapidly and becomes negligible at10 cm.The change in gas composition over the reactor lengthat 2M Pa is illustrated in Figure 4. The behaviourobserved near the inlet is the result of the com petitionbetween the combustion and gasification reactions, therates of which are very sensitive to the temperaturevariations produced. During the initial combustion, if thegasification rea ctions occur, any meth ane, hydroge n orcarbon monoxide produced is immediately consumed inthe gas phase. Consequently, in the initial oxidationperiod the concentrations of steam and carbon dioxidealso increase, showing maxima just after the oxygendisappears. Subsequently, formation of carbon monoxideand hydrogen is predicted and the concen trations of bothincrease m onotonically with gasifier length, from 0 to 42

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-I0

Re a c t o r l e n g t h (cm1Figure 4 Composition profiles of solid and gas phases along the reactorat 2 MPa

and 35% respectively. Similarly the concentration s ofsteam an d carbon dioxide dec rease tow ards the exit of thereactor, from 25 to 5% an d from 30 to 18% respectively.At this point it is of interest to note that the

Table 5 Composition and calorific value of product gas using the model

- 20

603,0 1 0 0 20 0 30 0 LOO 5oo

I - 20aoo-,,I6006 I I I I0 1 0 0 200 300 LOO 5000

Re a c t o r l e n q t h ( c m1

p-

- 60XS 2/ -60 0a\ $\ N - Ts .z

-r-- -- -LO 2---- -- 3S

Figure 5 Temperature and coal conversion profiles along the reactor at0.1 MPa

Operating pressure (MPa)0.12.0

Composition (dry basis) (mol%) Calorific value (MJ mm3 )co 2 co HZ (334 At operating pressure At s.t.p.18.97 49.19 31.83 0.01 2.26 8.3118.91 43.82 36.62 0.65 62.48 8.95

homogeneous oxidation in the absence of oxygen was ofzero extent and could be ignored in the computations. Thegas-phase com positions had to be consistent with thewater-gas shift equilibrium. The very small quantity ofmethane reported in Figure 4 shows that the kinetics ofthe hydrogasification of coal could also be ignored underthese conditions.Figures 5 and 6 show the performance at 0.1 MP a.Although atmospheric pressure performance is quantita-

tively similar in showing tem perature maxima for thesolids and gas and no production of hydrogen and carbonmonoxide in the presence of oxygen, these maxima takemuch longer to develop and are less sharp than thosepredicted for operation at 2 MP a. T his indicates a muchlower oxidation rate at atmospheric pressure, which isconsistent with the low conversion.

Finally, Table 5 shows the calorific value of thegas mad e. T he calorific value referred to the volumeat the operating pressure is much higher at 20MPa,which is obviously advantageous in reducing trans-mission costs, but when the value is corrected tostanda rd conditions there is only a slight gain byoperating at high pressure. However, the increasedhydrogen and methane concentrations at highpressure obviously reduce the CO2 emission perkWh for power generation at constant conversionefficiency.CONCLUSIONS

1. The model predicts a combustion zone and subse-quently a gasification zone. The boundary between



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Modeling of an entrained flow coal gasifier: 0. Vam vuk a et al.

8 0 10 0

- 8 0

- LO

8 D0 Y

/CoHz

Coal

- 60

- LO

/ -20/ /HtOv co 2

OO/ I I I I10 0 20 0 300 LOO 500

Reactor length lcmlFigure 6 Composition profiles of solid and gas phases along the reactorat 0.1 MPa

2.

3.

4.5.

6.

the two zones is distinct, with its location dependenton the gasifier pressure.Peak solid and gas temperatures occur near theboundary between the combustion and gasificationzones. At high pressure the maximu m, particularlyfor the solid temp erature, is very sharp, b ut at loweroperating pressure the maxima take longer todevelop and are smoother.In the absence of oxygen, during the gasificationperiod, the bulk gas composition is determined bythe water-gas shift equilibrium.Coa l conversion is not sensitive to the pyrolysis rate.Coal conversion is sensitive to operating pressure,with 2M Pa giving acceptably low amounts ofunconverted carbon.The model predictions are consistent with operatingpractice, which suggests that thermogravimetricdata are acceptab le for characterizing coals asfeedstocks for entrained flow gasifiers.

ACKNOWLEDGEMENTSThe authors would like to thank Dr D. J. Pickett forproviding the equilibrium data an d Mr S. Grace for helpin the drawing of the graphs.

REFERENCES1 Field, M. A., Gill, D. W., Morgan, B. B. and Haw ksley, P. G. W.Combustion of Pulverised Coal, BCUR A, Leatherhead, 196 72 Ubhayak ar, S. K., Stickler, D. B. and Gannon, R. E. Fuel 1977,56. 281

3

456789

1011

121314

151617

Smoot, L. D. and Smith, P. J. In Pulverized-Coal Combustionand Gasification (Eds L. D. Smoot and D. J. Pratt), P lenumPress, New York, 1979 , Ch. 1 3Wen, C. Y. and Chaung, T. Z. Ind. Eng. Chem. Process Des. Dev.1979,18,684Govind, R. and Shah, J. AZChE J. 1984,30, 79Sprouse, K. M. AZChE J. 1980, 26, 964Goyal, A. and Gidaspow, D. Ind. Eng. Chem. Process Des. Dev.1982, 21, 611Vam vuka, D. Ph. D Thesis, Department of Chemical Engineer-ing, UMIS T, Manchester, 198 8Lupa, A. J. and Kliesch, H. C. Report EP RI-AF-117 9, Vol. 1,EPRI, Palo Alto, CA, 1979Dobner, S. Modelling of Entrained Bed Gasification: the Issues,EPRI, Palo Alto, CA, 1976Von Fredersdorff, C. G. and Elliott, M. A. In Chemistry of CoalUtilization, Supplem entary Volume (Ed. H. H. Lowry), Wiley,New York, 1963, Ch. 20Dorn, W. S. and McCracken, D. D. Numerical M ethods withFortran IV Case Studies, Wiley, New York, 197 2Lawson, C. L. and Hanson , R. J. Solving Least Squares Prob-lems, Prentice-Hall, Englewood Cliffs, NJ, 1 974Powell, M. J. D. Numerical Methods for Nonlinear AlgebraicEquations (E d. P. Rabinowitz), Gordon and Breach, London,1970Perry, R. H. and Green, W. D. Perrys Chemical EngineersHandbook, 6th Edn, McGraw-Hill, New York, 1984McAdam s, W. H. Heat Transmission, 2 nd Edn, McGraw-H ill,London, 1951Ergun, S. In Coal Conversion Technology (Eds C. Y. Wen andE. S. Lee), Addison-Wesley, USA, 1979 , Ch. 1

NOMENCLATUREa

h,

AH-x,LnNNPPrTPI;rRtTW S

XY:

amount of gaseous reactant required to react withunit mass of coal (mol gg )cross-sectional area of the gasifier (cm*)specific heat capacity of gas (Jmol- K-l)specific heat cap acity of solid (J gg K-l)diam eter of coal particle (p m)diffusion coefficient of gas (cm* s-)external diame ter of gasifier (cm)internal diam eter of gasifier (cm)flow rate of gas (mol s-)flow rate of gaseo us compon ent involved in thesolid-ga s reactions (mol s-l)overall heat transfer coefficient for energy lossthrough the gasifier wall to the ambient(cal s-l cm-2 K-l)heat of reaction (cal g-l; cal mall cmp3)surface reaction rate coefficient of solid-ga sreaction (g s-l cmm 2atm-)gasifier length (cm)reaction ordernum ber of coal particles per second (s-l)number of coal particles per unit volume (m-3)partial pressure of gaseous component (MPa )total gasifier pressure (atm)rate of solid-gas reaction (g s-l)radius of coal particle (cm)overall solid-ga s reaction rate (g s-l)universal gas constant (kJ mol-1 K-i)universal gas constant (cm3 atm mall K-l)residence time (s)temperature (K)flow rate of solid (g s-l)fractional conversionmole fraction of gaseous componentemissivitytherma l condu ctivity (cal s-l cm- K-)

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% stoichiome tric coefficient for the Ith gaseou s k kth reactioncomponent in the kth solid-gas reaction 1 Ith gaseous component< extent of reaction (mol s-l) m mixture of gasP density (g cme3) 0 initial condition(T Stefan-Boltzmann constant (cal s-l cmP2 KP4) p particleSubscripts S condition at the coal particle surface; solid-ph asea ambient atmosphere W wall of gasifierg gas-phase

1460 Fuel 1995 V olume 74 Number 10

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Conversion Efficiency of Gasifier